Calculating. Without calculating.

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Engineers have designed a metamaterial device that can solve integral equations. The device works by encoding parameters into the properties of an incoming electromagnetic wave; once inside, the device’s unique structure manipulates the wave in such a way that it exits encoded with the solution to a pre-set integral equation for that arbitrary input. (1)

Calculating. Based on rules.

Rules imposed by humans.

Humans thinking.

Thinking based on logic.

Logic based on axioms.

Axioms based on nothing.

Calculating.

So irrational.

So wise…

Religion as the single foundation of Science

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MCDSARE: 2020

International Multidisciplinary Scientific Conference on the Dialogue between Sciences & Arts, Religion & Education

Religion as the single foundation of Science

Author: Ph.D. Spyridon I. Kakos

Abstract: For centuries, science was considered as something radically different from religion. Yet, the foundations of true science are deeply religious in nature. This paper seeks to show how religion is the only foundation needed for the formulation of scientific theories, since it provides the core principles on which the building of exact sciences is based upon. Our need to understand the cosmos and our faith in us being able to do so, are the main prerequisites for conducting science; prerequisites that are derived from our belief in us being the sons of God and, thus, being able to read His mind. From its birth on 7 March 1277 up to today, science seems to be the only logical attitude of religious people towards the unknown cosmos.

Keywords: science; science philosophy; foundations of science; religion; axioms; scientific principles

Published at: Academia (here), PhilPapers (here)

> Related YouTube video can be found here

1. INTRODUCTION

People see science as something different and many times at war with religion. Thus, many would be surprised to know that the foundations of science lie in religion per se. If someone wants to do science then he must first believe in some of the basic principles of religion. This is not a figure of speech, a metaphor or a symbolical aphorism, but a very practical truth. Only religion can offer the justification to do science. The religiousness of so many great scientists is not a random phenomenon that can be attributed to the norm of society back at the time, but a logical consequence of what religion teaches for humans and their relation to God and the cosmos. Once one understands the needs of the scientific method, it is evident that the very first steps of the scientific inquiry could never be taken inside a sterile atheistic (or even agnostic) environment, but only inside the womb of deep religious belief in God.

2. PURPOSE OF THE STUDY

The purpose of this study is to investigate the core foundations of science and its relationships with the relevant foundations of religion. The goal is to show that religion is not only compatible with science, but it is actually a fundamental prerequisite for science. Without religion, man would not be able to even start his exploration of the cosmos in a systematic way as per the scientific method. Science is not just another way of exploring the cosmos, but a logical consequence of religion when it comes to analyzing and understanding the universe.

3. RESEARCH METHODS

The problem under analysis was examined with the help of two tools: Philosophy and History of science. The latter was the tool that provided evidence for the way science has been evolving throughout centuries of human endeavour. This provided helpful insights of how scientific theories are formulated and how scientists think in order to create new scientific models for explaining the cosmos. The former was used to show why the philosophy of religion is the basic principle on which scientific research is based upon. By using specific logical arguments, it was shown that the basic principles of science are the basic beliefs of Christianity regarding the relationship between humans and God.

4. FINDINGS

The findings of the research clearly show that the principles used by exact science today are based on two basic Christian principles. The belief in the existence of God and the belief that we are part of Him (or that we can be part of Him). An analysis of how scientific theories are formed makes it obvious that these beliefs are the basic pre-requisites for conducting science and precede all other axiomatic assumptions needed for the formulation of any scientific theory.

4.1 How science builds scientific theories

Science builds theories to formulate models, which in turn explain (and predict) how the cosmos works. What we call “scientific method” uses various tools to build and verify or falsify hypotheses (e.g. statistical analysis) so as to create those models that explain the cosmos (Hanne Andersen, Brian Hepburn, 2015). These models do not exist in the void but are always part of general theories, which offer an overall understanding of how the cosmos operates. Scientists build these theories based on axioms or principles via the application of specific methods (e.g. logical induction). These principles are essentially the starting points on which the theory is based upon; there can be no theory without such principles, for even the simplest of theories must start from somewhere.

A note regarding nomenclature is of importance here. The term ‘axiom’ is mainly used in mathematics and geometry. The axioms of geometry are a good example (H. G. Forder, 1929). The infamous fifth axiom of Euclid is being taught around the world as the leading example of how axioms are used to build theories. Based on that and four more axioms, Euclid built his geometry, which dominated the world of mathematics for almost two thousand years up until very recently. When the time came to choose another axiom, different types of geometries emerged. All other sectors of science also have their own foundations, which are usually not called ‘axioms’ but ‘principles’. The principle of the conservation of energy is a good such example. This principle is usually referred to as a ‘law’, which can be confusing. What is significant here is to know that in both physics and geometry, theories are based on specific foundation building blocks.

These building blocks are not proven propositions (in the absolute philosophical meaning of the term), but propositions which are accepted as correct based on intuition and strong indications. An axiom or an accepted principle is by definition something not proved. This does not mean however that there are not arguments in favor of accepting them. As it is logical to infer that you can only draw one parallel line from another line, it is also logical to say that energy is conserved in a system – even though we have not examined all the physical systems in the universe. This conclusion is based on evidence currently available, but these evidence are in any case circumstantial when compared to the vastness of space and all the possible systems that can exist in the cosmos. At the end, the conservation of energy is accepted on terms of faith that all the other systems we have not yet examined will continue to work like the systems we have. For the time being, the belief in that principle (or ‘law’) is an axiom that we have to adhere to, if we want to move to the next step of building the theory, while keeping in mind that in the next day some new evidence or logical arguments could prove that principle wrong.

Taking the above for grated, a serious implication becomes evident: It is easy to change theories. In case we change axioms/ principles, then the theories change as well. Examining some indicative – but highly representative – examples of theories will make that point more clear.

4.1.1 From gravitational field to curved spacetime

The planetary movements had for a long time been the subject of discussion among philosophers and scientists alike. Gravitation is one of the most significant phenomena that attracted the attention of humankind for ages. The two most influential theories for gravitation currently are, namely, Isaac Newton’s Theory of Gravitation and Albert Einstein’s General Theory of Relativity, which includes an alternative explanation of the gravitation phenomena (Tomas Kala, 2019). These theories offer the context to explain and understand why things appear to attract things and why planets move the way they do in the vast space. Both theories are essentially consisting of a set of assumptions that formulate the foundations of a self-consistent explanation for the celestial phenomena we observe.

What is self-evident here is that no matter how we change the explanation, the observed phenomena[1] stay the same. No matter what the theory is, apples keep on falling down on the ground. What changes is the explanation of the why (or how) this happens.

Newtonian mechanics explain the planetary movements on the basis of the existence of a gravitational field, which exerts power over all bodies placed inside it. To formulate that theory, one has to begin with properly defining the notions used, e.g. with the definition of the mass (Rasmus Grønfeldt Winther, 2015), of time and of space. Then we need to accept that this field would exert a force instantly to every body of mass placed inside that field. The existence of that instant force was a point that finally led to the replacement of the gravitational field with the idea of curved spacetime. The Theory of Relativity stated that there was no way a signal or a force could be transferred ‘instantly’, given that the speed of light posed a limit to that interaction (Pierre Fleury, 2018). Therefore, curved spacetime came into play. This curved spacetime in the eyes of Einstein was what caused planets to move. As already mentioned, the phenomena stayed the same. Yet, the theory explaining them was utterly different from the previous one: In the new theory of relativity there is no field whatsoever, no instantaneous force, no absolute space and time. Just curved spacetime within the context of relativity.

In other words, the explanation (theory) is not only dictated by the evidence on which it is based upon; we already saw how the same evidence could provide support to different (and even conflicting) explanations. This is not limited to one area but it is an inherent part of the nature of science per se. In future it might well be that the Theory of Relativity will be replaced by another theory (and indeed, since this is the way science works, we can safely predict that this will happen) that will have an entirely different notion as the basis of gravity. In all cases, what all those contradicting theories have in common is that they explain the same phenomena. And the latter gives to outside observers the illusion that the theories are similar – if not in their calculations[2] at least in their essence, something that is fundamentally wrong as portrayed above.

4.1.2 Quantum mechanics and possible interpretations

Staying in the realm of physics, we can find numerous other examples of how contradicting theories can be built based on the same observations but on different assumptions. Modern particle physics is a good example. The Standard Model shows how basic assumptions are turned into the main founding blocks for theories and how these theories can change in an instant if these assumptions are assumed wrong.

The currently accepted Standard Model of the cosmos is based on the idea of point particles. A point particle is a geometric concept with discrete feature, and its typical representatives are point mass and point charge. Quantum theory – yet another pillar of modern physics – builds on that concept further on and uses the idea of wave particles as its core assumption. Wave particles are figment with both wave and particle features (Z. C. Liang, 2019) and within quantum theory they behave in many unintuitive ways.

To deal with the weird implications of observed quantum phenomena, scientists came up with many interpretations of quantum mechanics (Peter J. Lewis, 2020) (Graham P. Collins, 2007), but not one of them has gained the level of confidence that humanity once had placed on the axioms of Euclid. It is noteworthy to mention that these interpretations are incompatible with one another or even contradicting one another (Graham P. Collins, 2007). From the classical Copenhagen interpretation to the Many-Worlds interpretation, there are multiple ways to explain the observed quantum phenomena. Besides the abovementioned different interpretations of quantum physics, it is also important to know that there are other theories that propose a completely new way of looking into things altogether. So for example in the case of particles, there is a theory which claims that particles are in fact not at all what the Standard Model says they are, but instead one-dimensional objects called ‘strings’ (“String theory”, 2020).

As in the case of gravity, we see the same pattern emerging: One set of universally observed phenomena, but multiple different theories attempting to explain them. A disturbing truth is coming into light as one examines more and more such examples. A truth that destroys the ideal picture we have in mind regarding the relationship between science and reality, by showing how assumptions dictate the theories regardless of the facts and evidence[3] at hand. The facts anyway have to be respected, since they are the starting point of everything. But the theories change when the assumptions change. Based on the same facts and evidence there can be more than one theories that fit the data. Theories that are built upon different assumptions, which are then in turn questioned by other (newer) theories. The multiplicity of theories and interpretations mentioned in this chapter is not a temporary flaw in our understanding of the cosmos that we will someday resolve, but an inherent limitation of the way science works. As long as you have to start your analysis from assumptions, your theories will always be subject to debate by someone else who uses different assumptions than you.

As I will show below however, there are some assumptions that are more fundamental than others. These are the assumptions which form the basis of science itself and the realm from which they emerge is anything but scientific.

4.2 Principles of science’s principles

Having established that there are many principles (axioms) that are used to build scientific theories, the next step is to try to explore whether there are any assumptions that transcend all scientific theories, in the sense that they are more global and universal than others. What is of interest here are the basic principles that make the other principles (and thus science) even possible. If one could envisage a hierarchy of principles, then the principles presented in this section are the ‘principles of principles’ of modern science. Without those, there would be no way to even formulate other principles or axioms, in order to start building new theories. Knowing these assumptions is of high importance, since they are connected to the very essence of science per se. Exploring them will lead to a greater and deeper understanding of science.

4.2.1 The comprehensibility of the cosmos

When people speak about science, they usually omit the most obvious of principles on which science is based upon: The (seemingly unfounded) belief that the cosmos is comprehensible. People use to quote Einstein on saying that the most incomprehensible thing about our cosmos is its comprehensibility (James B. Hartle, 2016). However the actual expression used by Einstein was much more ‘religious’ in nature. Einstein actually wrote in a U.S. science journal in 1936 that “The eternal mystery of the world is its comprehensibility… The fact that it is comprehensible is a miracle”. (Andrew Robinson, 2016) This comprehensibility or – to be exact – our faith in it, lies in the foundations of science in all its aspects, common to both the Scientific Revolution and the Enlightenment (Steve Fuller, 2008, p. 5). The assumption that the world is (rationally) intelligible transcends all scientific enterprise (Alan Thomas, 2018) and without that assumption (call it an ‘axiom’ or a ‘principle’ and the essence will not change) there is no point in even starting to analyse the cosmos with scientific tools. If one could state which is the most fundamental assumption used by all science sectors and all scientists regardless of their field of expertise, this would be it.

It is so fundamental that one does not even think of it. But it is there. Buried under every scientific endeavour. Almost tautological in nature[4], it transcends all efforts of the human intellect to make sense of the cosmos and to comprehend its workings. And this is logical in every sense. One does not start walking unless he believes he will reach his destination. One does not start analysing gravity or the physics of particles unless he firmly believes that his efforts will result in something. Such a fundamental principle does not require more analysis or elaboration for it is self-explanatory. Yet, it is still not sufficient to explain science. For the scientist to get out of bed and start experimenting, something more is needed.

4.2.2 Our ability to comprehend the cosmos

The acceptance (by faith) of the comprehensibility of the cosmos may provide a potential goal, but this is not sufficient by itself to make someone start building science. For even if something is possible, this does not mean that it will happen as well. One also needs to believe that he is capable of reaching that something as well. It is not enough that the cosmos is comprehensible. In order to embark on a journey to understand it and explain it, we need to believe that we are able to attain the comprehension the cosmos offers. In other words, if we are to start building theories to explain the universe, we need to believe that we are capable of building those theories – they will not be built by themselves.

Again, this assumption is so self-evident and tautological in nature that it sounds almost paradoxical to speak about it. But if we are to break down the required assumptions for doing science, this belief into our ability to make science is necessary. The possibility of science happening is not enough. We must have – or at least believe that we have – the capability of developing that science. This faith is instilled in everything science tries to achieve today; evident in the efforts of scientists to understand the universe, present in the efforts of researchers to understand the human brain, obvious in our efforts to explain the very existence of the cosmos. We are making science because we believe we can make science.

This second assumptions completes the list of fundamental assumptions needed to start conducting science. After taking these two assumptions for granted, the road is open for analysing specific phenomena, formulating scientific models to explain them and trying to reach a theoretical understanding of their nature. This paper will focus on those two basic assumptions – although it is needless to say that the epistemology of all other principles used by science in its various fields is a topic of immense importance.

The next element to examine is how we came to believe into the above assumptions. What drove us into accepting them and, thus, allowing us to start being scientists in the first place? The results of this analysis will show that the cause of our belief into these assumptions is unscientific and at the same time hugely religious in nature, at least as per the modern way of defining science.

4.3 Reading the mind of God

The quest to find out how humans started believing (or accepting) the two principles described above as the pillars of science, leads to religion. Because it is religion that offers us faith in the importance of man. Without believing in our importance, it would be laughable to even consider the possibility that we have the ability to create theories, let alone comprehend the cosmos. The belief that we can comprehend the universe is based on two major Christian assertions: The belief that we are made in the image of God (Matt Stefon, Geoffrey Wainwright, Carter H. Lindberg, William Richey Hogg, Henry Chadwick, …, Linwood Fredericksen, 2020) and essentially part of Him (Mark Shuttleworth, 2020) (Lossky, Vladimir, 2002) (Athanasius of Alexandria, 2011) [5] and the belief that, consequently, we can comprehend how His mind works.

This was the main idea behind every scientist’s mind up until very recently in human history. As Newton said, “This Being governs all things, not as the soul of the world, but as Lord over all: And on account of his dominion he is wont to be called Lord God παντοκράτωρ or Universal Ruler” (Newton, 1729).

It is not just that if we exclude God from the definition of science then, in one swoop, we exclude the greatest natural philosophers of the so-called scientific revolution – Kepler, Copernicus, Galileo, Boyle, and Newton to name just a few (Helen De Cruz, 2017). Faith in God was important not only due to social or personal reasons. It was of paramount importance for the actual scientific work of these men as well. So deeply rooted is that belief that even so-called agnostic or atheistic scientists cannot escape referring to the same faith when making science. For example, one of the most famous pages of the well-known book “A Brief History of Time” by Stephen Hawking is that in which the writer speaks of an imminent ‘theory of everything’ and claims that such a theory would allow us to know “the mind of God” (Stephen W. Hawking, 1988). For Hawking, an agnostic, the phrase is supposedly little more than a metaphor (at least for his atheist readers), but yet again it is also true that γλώσσα λανθάνουσα τα αληθή λέγει[6]. And surely no one else can interpret what he meant but himself, who for a long time disliked the label “atheist” (Karl Giberson, Mariano Artigas, 2007)[7], even though at the end he started to identify as such.

Hawking aside, one can trace the importance of believing that we can read the mind of God in the thought of all prominent scientists especially in the early era of modern scientific endeavour. To the eighteenth-century mind, the whole world seemed to be evidence of God’s special provisions. God had provided the Earth with an atmosphere with the intention of allowing men and animals to breathe. He had created humans with complicated organs whose purposes were evident, but whose workings were obscure. Kant quite understandably wanted to save God the trouble of making special provisions for each plant and animal, and argued for the possibility of an overriding system of physical law that could result in the world of living organisms that we know, without the need of innumerable particular divine interventions (Roger Caldwell, 1995).

The overall point is that, despite the details, in all cases of scientific thought the idea of a God penetrates everything – either consciously or unconsciously, but always essentially. Overall, humans believe that they can understand the cosmos only because they believe in the idea of them being created as creatures in imago dei. Thus, nature is intelligible for them (Steve Fuller, 2008, p. 5). The cosmos is not considered as something foreign but as a place on which we can exert our mind to make sense of. And even though we were temporarily cast out of heaven, we are still His sons. And as the sons of God, we can understand Him, so that we can eventually reach Him again.

Going back into the first years of modern science is important can help us understand and appreciate the nature of the issues we are dealing with here. The birth of science in the womb of religion was a very important milestone in human intellectual history that we often and easily (perhaps also knowingly) tend to ignore.

4.3.1 The birth of a new child

If we are to understand the true nature of science, we must go far beyond Newton and Leibnitz (who also had God as a cornerstone of his science, refer to Brandon C. Look, 2013), to the beginning of science as we know it today. From ancient Greece up to the time before Thomas Aquinas, science and religion were not separated. At some point though, something happened which separated the two realms of knowledge and gave birth to what we know today as modern science. Understanding how this happened is important to gain an understanding of the character of this new child of human intellect.

There is a lot of discussion on how modern science was born. For many, the birth date is 7 March 1277, when Bishop Tempier condemned a great number of “errors” from teachers. The condemnation sought to stop the Master of Arts teachers from interpreting the works of Aristotle in ways that were contrary to the beliefs of the Church (Condemnations of 1277, 2020). Among the theses condemned were sixteen of Aquina’s theses (J.J. Chambliss, 2013). There is much debate on the significance of this event (Hans Thijssen, 2018). For many, this denoted the separation of theology from natural sciences, where the latter where deemed incompatible with the wisdom of the scriptures. Others claim that this event freed up Christianity from the dogmatic Aristotelian view of the cosmos. Other believe that Thomism allowed the two schools or realism and idealism to agree to disagree to the extent that in the graduate curriculum of the university, natural philosophy could be taught apart from theology. This separation of secular or natural philosophy from theology opened the way for the development of the empirical sciences. The disparities between these two separate ways of knowing were resolved, not by compartmentalizing them into separate domains, but by proving the domains to be philosophically complementary, creating a holistic framework in which we could reconcile apparent conflicts between theology (religion) and natural philosophy (science) (Kondrick LC, 2008). Others believe that Tempier’s condemnation was a symptom of the existence of rationalist currents at the University of Paris, in the sense of the emergence of philosophy as an autonomous discipline vis-à-vis divine revelation, has been further developed by scholars such as Alain de Libera, Kurt Flasch, and Luca Bianchi (Hans Thijssen, 2018).

The details of what really happened are mute. What is certain is that science was born; science that we use today as a separate domain of thought, different than that of religion. Before a point in time, religion and science were not separated, but from that point onwards science as we know it today started following its own separate path. Going forward some centuries, the next important milestone in the life of modern science is the time when it reached adulthood. And even if the exact date of birth of science is a matter of debate, most would agree that the date when science reached adulthood can be placed with the era of the Galileo trial and its implications on how science stood up against its own parent. Again, the details are insignificant in the face of the actual facts[8]. What is important is that from a point onwards the child became a parent, after killing its own father. And from Galileo’s time onwards, science dictated terms in its relationship with religion.

This philosophical separation resulted in the scientists forgetting what was the real reason they do science. They still kept looking for answers, but without religion they had forgotten why they even do it. And in order to compensate for this lost knowledge, they needed to add the foundations to their structure as assumptions. The child was orphan now. And to explain its existence, it needed to invent its parents. The only problem is that when you decide the destination on your own, it is easy to change destination at your own free will. When there is no compass, the final destination is never certain.

4.3.2 Killing our Father (From Understanding to just Knowing)

As a spoiled child, modern science tries hard to get free of the “bondage” of its true father. In its effort to do so, it has created a fantasy of a cosmos that is intelligible (if it was not, there would be no science) but with no reason at all. In its effort to do so, it has created a cosmos where humans are able to understand the cosmos (if they could not, there would be no reason to strive for science), but again for no apparent explanation for that wonder.

The phrase of Einstein about a “miracle” starts now to reveal its true meaning. With religion around, trying to find answers for how the cosmos works did not require any special explanation. It was simply part of the knowledge we were destined to acquire as children of God and as parts of the cosmos itself. But in an era without religion, in an era were God is dead (only because we killed Him as Nietzsche said), the mere action of doing science is absurd. Why search for answers in a cosmos ruled by randomness? Why do science if there is no reason to believe that you can understand the cosmos? In an era without religion, we desperately need the assumptions described in the sections above, while in the years when science was not separated from religion, there was no need for such assumptions since they were embedded in the way humans thought in the first place. Not as assumptions or principles but as facts of life; facts based on the faith on something bigger than life itself as Rilke used to say. And as weird as it may sound, today, in an era when we do not believe in miracles, we do science only because of them.

The ripples of the religion and science separation do not stop at why we do science. The removal of God’s Logos from scientific effort made also science void of any true meaning. That is the reason why science gradually turned from philosophy to a simple data gathering exercise. As Levy Bruhl correctly pointed out, science turned from understanding to just knowing (Wilbur M. Urban, 1924). And the story of science turned from a tragedy into a farce. Because knowing is nothing more than an illusion; with different assumptions we can easily ‘know’ completely different things than the ones we currently do. In a science based on nothing more than miracles, there is nothing to stop us from believing in some other kind of miracles and, thus, changing course to another direction altogether. In the post-modern era when people constantly doubt about everything, there is nothing to stop science from doubting its own existence. Funnily enough, this was not even possible when religion was the dominant way of thinking in Europe.

千里之行,始於足下 (A journey of a thousand miles begins with a single step)

~ Lao Tzu, Tao Te Ching

4.4 Why do we do science?

We have almost reached the end of the road. Having established why the cosmos is intelligible and why we can grasp that intelligibility, we are yet one small step away from fully explaining the existence of science. Because even after taking all of the above for granted, the question still remains. Why do we do science anyway? Even if the world is intelligible and even if we can understand it, why do we choose to do so? A question so simple and yet – as every simple question – hard to answer. Knowing why this happens provides an additional insight on the relation between religion and science, at an even more essential level than the one mentioned already.

We can only reach that level if we see beyond the details of epistemology, details that do nothing but obscure the real question we should try to answer. Behind the surface of trying to comprehend a cosmos and of believing that we can achieve that comprehension, there lies something more fundamental: A basic need for knowledge per se. Science is accepted and used on the very practical basis of fulfilling that basic need to understand and know. Our belief that the cosmos can be understood and our belief that we can achieve that knowledge, only come as a consequence of our most basic initial need for knowledge as such. A need that existed long before we had the tools to attain it

In other words, if our belief that we can answer our questions for the cosmos is the basis of us using science, us having those questions is the reason we begun the journey of science in the first place. Our fundamental need to know, is translated in religion as our need to reach theosis. This was a need that existed for Christians aeons before science came into the scene as an independent realm of human intellect and translated this need for theosis in the need to acquire knowledge. This more fundamental element missing to answer why we do science has been lying in the foundations of religion for millennia now: It is our need to reach God.

And the only reason humans dare to start this journey is because they believe they occupy a privileged position in the cosmos, something evident in the creation accounts of religion. In Christianity, Judaism, and some strands of Islam, humans are created in the image of God. There are at least three different ways in which this image-bearing is understood. According to the functionalist account, humans are in the image of God by virtue of things they do, such as having dominion over nature. The structuralist account emphasizes characteristics that humans uniquely possess, such as reason. The relational interpretation sees the image as a special relationship between God and humanity (Helen De Cruz, 2017). In any of those cases, the result is essentially the same: this special relationship between man and God is what drives the former to start a journey towards the latter. And the first step is the most important part of any journey.

It is weird that so many articles on the matter fail to see and examine the obvious question lingering in science from the beginning: even if we are able to understand the universe, even if the universe is comprehensible and able to be understood, why would someone start the journey towards that understanding? Mere curiosity is one way to explain this; however, this would reduce thousands of years of philosophy to a mere caprice. And would make the non-development of science as logical as the current path we have chosen. But could we ever imagine a world without science? In a world full of God, there is only one destination we could choose. And that is towards achieving a union with Him. That is the only meaning one can ever find in science and the only goal science can ever strive for; for if we are to accept that the cosmos is void of anything meaningful then there is no reason to disembark on any journey even though we know we can.

“If we do discover a theory of everything… it would be the ultimate triumph of human reason, for then we would truly know the mind of God”

~ Stephen Hawking, Brief history of Time

5. CONCLUSION

When Jesus Christ came back to Earth after His resurrection, He visited his students for the last time. What did He offer as this last appearance? Did He offer any great philosophical quote for us to remember Him by? Did He provide any deep spiritual piece of wisdom for us to ponder upon? Perhaps He gave us a hint on how to understand and decipher the secrets of the cosmos? No. He just asked them “Are you catching any fish?”. And the students answered “No”. And He helped them. And then He prepared food for them. “Come and have breakfast” He told them (John: 21). And they came.

This very simple story reveals the common ground not only between religion and science but between all types of human endeavour in general. We have specific needs and these basic needs are those which govern our lives from the moment we started walking on this Earth. Our need is to eat. And grow. Our need is to know. And become part of God. It is just that we are progressing too fast to realize that we might be wandering off course, our arrogance making it impossible to know that we are astray. We will eat the apple. Not yet though.

Heisenberg was famous to note that “The first gulp from the glass of natural sciences will turn you into an atheist, but at the bottom of the glass God is waiting for you”. Newton had certainly reached that point when he wrote about gravity that “Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left open to the consideration of my readers” (Andrew Janiak, 2006). In his theory, as in every other scientific theory, something is ever-present beyond the words written on paper. Something beyond the plain numbers and scientific models. Something that could explain the existence of science per se – and why we would even start drinking from the glass of science to begin with.

Science is not a way towards God nor a path away from Him. It is God himself speaking to us. Look at the most basic assumptions of every theory, any scientific paper. And beyond the words of children who have been lost for a long time, you will recognize their agony that one day they will return home. For unlike religion that has God as its ultimate goal, science has God as its sole starting point. And when we reach the bottom of the glass, He will lovingly remind us the obvious. “You wouldn’t be searching for Me if you hadn’t already found Me”…

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[1] It is important to keep on using the proper nomenclature: Phenomena instead of ‘facts’. The former is what we observe. The latter refer to an ideal form of objective reality many philosopher – and even scientists – deny its existence.

[2] In any case, the calculations of any theory can be improved to fit better with the data, regardless of the theoretical background explaining the phenomena. It is just that when a new theory comes along, the old theories are rarely (if ever) updated accordingly and, thus, appear outdated. This could be misleading and has nothing to do with their actual fitness for purpose. The equations of Newton do not have any inherent inability to provide proper results due to insufficient theoretical reasoning; they can just as easily be fitted to the new observations and be adjusted to fit with the new data we have (regarding the speed of light etc). However scientists are reluctant to perform such work and rightfully so, for practical reasons. If everyone in the scientific community is doing research on the latest theory available, why spend time to update the ‘old’ one? The hasty world of research today does not allow space for such work.

[3] By ‘facts’ and ‘evidence’ we refer to anything we perceive with our senses. This may well be completely invalid or insufficient to describe reality, but that is a philosophical question that is currently unanswered and beyond the scope of this paper.

[4] Tautology could be the only valid form of knowledge, which needs no assumptions to be considered true. However, the analysis of this very important topic is beyond the scope of this paper.

[5] “I said, You are gods, and all of you are children of the Most High” (Psalm 82:6) In the Orthodox Church, the concept of humans being god is neither new nor startling. It even has a name: theosis. Theosis is the understanding that human beings can have real union with God, and so become like God to such a degree that we participate in the divine nature. Also referred to as deification, divinization, or illumination, it is a concept derived from the New Testament regarding the goal of our relationship with the Triune God. [AA16] As Athanasius of Alexandria wrote, “He was incarnate that we might be made god” (Αὐτὸς γὰρ ἐνηνθρώπησεν, ἵνα ἡμεῖς θεοποιηθῶμεν). (“Athanasius of Alexandria”, 2011)

[6] Logos which refers to something by mistake, speaks the truth.

[7] To provide the full picture, it must be noted that this changed during the latest stages of his life though, where he declared that there is little or no possibility of God into our universe (Brandon Specktor, 2018).

[8] For Galileo one can find a detailed account on how he was scientifically and philosophically wrong in defending his views the way he did, in the article “From Galileo to Hubble: Copernican principle as a philosophical dogma defining modern astronomy”, International Journal of Theology, Philosophy and Science 2 (3), 13-37 (S. Kakos, 2018).

How do we know the stars are suns? (On the limits of astronomy)

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Abstract: The Sun being another star is common knowledge. However, as it happens with all things that are considered obvious, few can actually name exactly who and how the Sun was considered as just another star. It seems that besides evidence from stellar spectroscopy and the measurement of astronomical distances, philosophical principles also played a major role in the building of this knowledge. From the De l’infinito universon e mondi (On the Infinite Universe and Worlds) of Bruno in 1584 up to the Principia Philosophiae of Rene Descartes in 1644, people had started adhering to the idea of the Sun being nothing more than a common star. This idea – also enhanced by the ideas of Copernicus – was later on verified by spectral data and since the era of the Jesuit priest and astronomer Angelo Secchi it is considered an established fact nowadays. However the current huge gaps of our understanding on the nature of the universe call for being much more careful when calling any such knowledge a ‘fact’. More humility is highly advised, especially in a sector of knowledge where we have recently realized we can only account for only the ~5% of it. At the end, acknowledging our limitations is far more important than projecting our beliefs…

[Greek abstract can be found at the end of the article]

1. A question posed…

Once upon a time I had a discussion with friends on cosmology. There, among other things, the question of what are the stars came up. And it was very interesting for me to acknowledge that the answer to this seemingly simple question is not so simple after all…

So what are the stars?

How do we know our Sun is a star?

Who discovered that the stars are “Suns”?

To answer this we must first travel many centuries back and delve into philosophy and the history of science. There, we will find long forgotten assumptions that still dictate how we think about the cosmos.

At the end, you need not worry about the stars not being stars.

They could be, or they could be not – at the end it matters not.

What matters is the human tendency of clinging to dogmas for thousands of years without a single hint of remorse. And this is something we should certainly look into and fix if we are – ever – to unlock the mysteries of the cosmos around us…

2. Searching for an answer…

The first thing to do when you have a question is to search for an answer. But the answer to the question “How do we know the Sun is like the stars?” is not easy to find.

The questions seems to most people so obvious (and perhaps stupid) that they do not even care of explaining why we consider the Sun a star (or vice versa). When this is asked they most usually answer with a simple “Yes they are the same, end of story” attitude that leaves little room of questions, unless of course you want to be ridiculed online that you are unaware of basic astronomy that even kids in the kindergarden know.

Let us look together some of the answers found online for the matter…

2.1 Answers that are not clear answers…

Below I document what various resource in the Internet have to say on the nature of the Sun and the stars. They show clearly the main problem: When something is considered obvious, little effort is put into explaining it. And it is in these ‘obvious’ things that the problems usually arise…

Let us see some excerpts from these resources below…

Who determined that the sun was a star, like the stars in the nighttime sky? Answer: No single astronomer had this realization. Prominent thinkers considered the possibility since classical antiquity; they had creative rhetorical argument on their side, but no proof. By the late 19th century, we knew what stars were, and we knew the distances from the earth to a few stars and to the sun; with that data, astronomers determined that these bodies released energy in roughly comparable amounts. Then spectroscopic examination revealed that the chemical elements in the solar atmosphere were just like those found in common yellow-colored stars spread across the sky. (David H. DeVorkin, senior curator, National Air and Space Museum) [3]

In other words: That the Sun is a star and vice-versa we know because we… know.

Q: im having a hard time believing that the stars are really suns. So from a stars distance, does our sun look like a tiny little star? – Christine (age 16)
A: Yes. [4]

In other words: Don’t ask. The stars are suns. And it is a sin to question that.

Given that the only observational information we have on stars is the light we receive, you might think there isn’t much we can learn about them. But by comparing positions, brightness, and spectra over time, and comparing these with observations of our own star, the Sun, we can actually create accurate models that explain and predict stellar characteristics and behavior. [1]

In other words: We use the comparison between the Sun and the stars to draw conclusions. But what about the Sun being a star? Is that something we consider valid because of some specific reason? Again, this “knowledge” is implied but not specifically mentioned (let alone proved).

As astronomers gaze into the depths of space, they do so with unease: They don’t know precisely what the universe is made of. It’s not just the true nature of dark matter that eludes them; so does the essence of the stars that speckle the sky and populate the many galaxies throughout the cosmos. Surprisingly, no one knows the stars’ exact chemical composition: how many carbon, nitrogen and oxygen atoms they have relative to hydrogen, the most common element. These numbers are crucial, because they affect how stars live and die, what types of planets form and even how readily life might arise on other worlds. [5]

In other words: We do not know many things about stars or the universe. (keep that in the back of your head, we will use it again)

William Herschel was the first astronomer to attempt to determine the distribution of stars in the sky. During the 1780s, he established a series of gauges in 600 directions and counted the stars observed along each line of sight. From this he deduced that the number of stars steadily increased toward one side of the sky, in the direction of the Milky Way core. His son John Herschel repeated this study in the southern hemisphere and found a corresponding increase in the same direction.[30] In addition to his other accomplishments, William Herschel is also noted for his discovery that some stars do not merely lie along the same line of sight, but are also physical companions that form binary star systems. [6]

In other words: Here is the first specific mention of something concrete. Someone did measure something regarding the stars and drew a specific conclusion. Of course the only thing he was based upon was what he saw: the light of the stars. (keep that also in mind)

The science of stellar spectroscopy was pioneered by Joseph von Fraunhofer and Angelo Secchi. By comparing the spectra of stars such as Sirius to the Sun, they found differences in the strength and number of their absorption lines—the dark lines in stellar spectra caused by the atmosphere’s absorption of specific frequencies. In 1865, Secchi began classifying stars into spectral types.[31] However, the modern version of the stellar classification scheme was developed by Annie J. Cannon during the 1900s. [6]

In other words: Here we have another specific example of concrete science. We measure something and compare the data we have for the Sun and other stars (given that the other stars are suns of course). Spectroscopy is a big leap towards understanding the stars and their nature, since it can provide many data for the properties of these celestial objects. It is only a pitty that this is all we have, along with distance measurements. What else could we have anyway? We have never gone to the stars, we have only approached somehow our own star.

Various Quora questions (Q) and answers (A) can also be found below:

Q: Are the stars we see in the sky actually Suns from other solar systems? – A: Yes – our Sun is just another “star” and those stars are really “suns”. Same exact thing. [7]

Q: Are the night sky stars all suns? A: Yes, almost all of what we see with our eyes in the night sky as ‘stars’, are actual stars (or suns, as it was stated in the question, presumably to avoid using the word ‘stars’ twice, with different meanings). [8]

In other words: Yes, the stars are like the sun. And it is obvious.

The Sun is the dominant object in the solar system by mass and total energy content. The irradiance of the Sun drives climate on the planets and is the primary source of energy for the biosphere of the earth. The Sun is a Rosetta Stone for the study of astrophysical processes at resolutions that cannot be easily attained for other stars. The results of these solar studies can be applied toward an understanding of other stars, including the properties of their atmospheres and interior structures. In the realm of physics the Sun plays a unique role. The element helium—the second most abundant element in the universe after hydrogen—was discovered in the solar spectrum. The Sun serves as among the test beds for Einstein’s theory of General Relativity. The nature of subatomic particles called neutrinos—the byproducts of nuclear reactions in the hot and dense core of the Sun and sun-like stars—was elucidated as a result of solar investigations. The Sun serves as a laboratory for the study of plasma physics, i.e., the study of the interactions between ionized gas and magnetic fields. [9]

In other words: The Sun is used as a reference to induce assumptions regarding the other stars. So the assumption that the Sun is like the other stars is even more important that we might have thought: The stars are used to draw conclusions for our Sun and the Sun is used to study better the other stars.

ELI5:How do we know that stars are suns? Answer 1: Through spectroscopy, we can determine the composition of stars through their emissions. The experiment you’re looking for is performing this spectroscopy on the sun, and on stars, and discovering that they have similar characteristics. Answer 2: I think to short answer is parallax and spectral analysis. Parallax is a small shift in relative position when the point of view changes. This can tell us the distance. Spectral analysis is a way of determining elemental make up because different sets of wavelengths of light are caused by different elements. [10]

In other words: Again the importance of spectroscopy is emphasized in determining the nature of the Sun and the stars. Indeed this is an excellent tool in analysing the temperature, the composition even the rotation of the celestial objects. Is it a perfect tool? Of course not. What tool is perfect? But it is a very scientific and credible tool in giving us insight in these fascinating objects that linger in the night sky…

So is this the answer we were looking for?

Is spectroscopy the answer to why we consider the Sun another star?

It seems so, yes.

Even though most resources do not mention it clearly, it is evident that similarities of the spectra of the Sun and the stars have made scientists figure out that they must be similar objects. However this answer should not satisfy the researcher here.

Is such a similarity enough?

Looking more into the subject we will discover that there are additional elements needed in order to accept that the sun and the stars are one and the same thing…

3. Regarding spectral analysis

A small parenthesis regarding the spectral analysis based on which we deduce the similarity between the Sun and the stars is needed here.

Electromagnetic radiation with the shortest wavelengths, no longer than 0.01 nanometer, is categorized as gamma rays. Electromagnetic radiation with wavelengths between 0.01 nanometer and 20 nanometers is referred to as X-rays. Radiation intermediate between X-rays and visible light is ultraviolet (meaning higher energy than violet). Electromagnetic radiation with wavelengths between roughly 400 and 700 nm is called visible light because these are the waves that human vision can perceive. Between visible light and radio waves are the wavelengths of infrared or heat radiation. After infrared comes the familiar microwave, used in short-wave communication and microwave ovens. All electromagnetic waves longer than microwaves are called radio waves, but this is so broad a category that we generally divide it into several subsections. [43]

Looking into the light coming to us from the sky, we can deduce many information. Essentially by using the emission or absorption spectra we can conclude things regarding the composition of the stars or the atmosphere of planets, their temperature, density, mass, radius, distance, luminosity, and relative motion [35] [40].

In 1860 Gustav Kirchhoff proposed the idea of a black body, a material that emits electromagnetic radiation at all wavelengths. In 1894 Wilhelm Wien derived an expression relating the temperature (T) of a black body to its peak emission wavelength (λmax). [35]

This equation is called Wien’s Law. By measuring the peak wavelength of a star, the surface temperature can be determined. For example, if the peak wavelength of a star is 502 nm the corresponding temperature will be 5778 kelvins. [35] An object at a higher temperature emits more power at all wavelengths than does a cooler one. In a hot gas, for example, the atoms have more collisions and give off more energy. In the real world of stars, this means that hotter stars give off more energy at every wavelength than do cooler stars [43].

Figure: Radiation Laws Illustrated. This graph shows in arbitrary units how many photons are given off at each wavelength for objects at four different temperatures. The wavelengths corresponding to visible light are shown by the colored bands. Note that at hotter temperatures, more energy (in the form of photons) is emitted at all wavelengths. The higher the temperature, the shorter the wavelength at which the peak amount of energy is radiated (this is known as Wien’s law). [43]

Also the higher the temperature, the shorter the wavelength at which the maximum power is emitted [43] (see figure above).

So that could be a way to distinguish between planets and stars.

The study of many thousands of stellar spectra in the late Nineteenth Century led to the development of our modern classification system for stars [37].

However note that there are also hot planets at the size of Jupiter that have a temperature between an Earth-sized planet and a star. These planets reside in an intermediate section and called for corrections in the models used to analyze spectra [36].

Also note that there are other objects rthat are not exactly stars and which give out similar (but different) spectra, like the quasars or some types of exotic stars [37].

Credit: 2dF Quasar Survey Characteristic QSO spectrum showing distinct, strong, redshifted emission lines of a quasar. [37]

Credit: The Sloan Digital Sky Survey Exotic star spectra example [37]

These are examples that simply make the problem of accepting the similarity of the Sun with the other stars also more of a definition (and, thus, philosophical) one. What is the cut-off point beyond which we decide that a celestial object is ‘different’ than another?

It seems that searching into the philosophy behind modern cosmology we can find out more factors that weighted in the acceptance of the ‘stars-sun analogy’.

4. Assumptions in modern astronomy

Two basic assumptions of today’s cosmology are the homogeneity and isotropy [25] of the universe, something also known as the Cosmological Principle [24] [26] [27].

Also related to that principle is the Copernican principle, a principle on which many articles have been written in Harmonia Philosophica. You can see the “Earth at the center of the universe?” article for more on that.

Essentially the Copernican principle postulates that humans are not in any way in a priviledged position in the cosmos. As already said this is connected with the notion of isotropy in the cosmos (the Cosmological principle) in various ways: If we are in a non-priviledged position then we are not seeing anything ‘different’ in any direction and, vice-versa, if we do not look anything ‘different in any direction we are not in a priviledged position.

I will not argue here for or against these principles (you can read the above-mentioned article or the paper “Philosophical dogmatism inhibiting the anti-Copernican interpretation of the Michelson Morley experiment” if you want such an analysis). The main thing to remember is that they are… principles! In other words axioms accepted as true based on some evidence and… faith.

So to summarize…

  • The universe is the same everywhere
  • We are insignificant

Let us now start a journey in the history behind the acceptance of the Sun as being an ordinary star to see how philosophy had also a thing or two to say regarding what we believe about our star…

5. The role of philosophy in accepting that the Sun is a star

In everything, our philosophy plays a very important and crucial role in what we say, decide and believe. Astronomy and cosmology is not an exception.

The above-mentioned assumptions guided astronomers throughout the recent centuries in deriving conclusions for the stars, as much as observational data did.

To acknowledge this is important not only because it allows us a better understanding of the way science works, but also because it may help us avoid prejudiced thinking in the future.

5.1 A world of ‘worlds’: The philosophers speak of the Sun as a ‘star’

What is a world according to modern throught?

As a result of shifting views of the universe the very idea of “world” (in Latin, Mundi) was changing. In the Aristotelian cosmos, the world was effectively synonymous with the Earth. The sphere of the world and the terrestrial realm were one in the same [29].

In part, what we think to-day when we think of a ‘word’ is based on the ideas of the Dominican Friar Giordano Bruno (an Italian philosopher who lived from 1548 to 1600) who published De l’infinito universon e mondi (On the Infinite Universe and Worlds), in 1584. As part of a suite of mystical, magical and heretical ideas and in part, spurred on by Copernicus’s ideas, he suggested that Earth was one of many inhabited worlds in an infinite universe and that the stars were suns, which had their own worlds [29].

Giordano Bruno decided that if the Earth is a planet just like the others, then it does not make sense to divide the Universe into a sphere of fixed stars and a solar system. He said that the Sun is a star (i.e. not anything special), that the Universe is infinitely large, and that there are many worlds. He was condemned by both the Roman Catholic and Reformed Churches for this as well as other things and was burnt alive in Rome in 1600 for heresy [2]. As he wrote at the time: “The composition of our own star and world is the same as that of as many other stars and worlds as we can see” [13].

In other words, it seemed reasonable to him that the Sun was merely another star, and he subsequently made a distinction between “suns” which generate their own light and heat; and the “earths” and moons which revolve and are nourished and powered by them. One esteemed modern astrophysicist, Steven Soter, has even suggested that Bruno was the first person in history to truly grasp the concept that “stars are other suns with their own planets” [13].

Once Earth became one planet among many orbiting the sun, those planets became Earth like worlds. This new understanding of worlds is reflected in the title of The Discovery of a World in the Moon from the 1630’s [29]. But as it took a long time for the Copernican model of the cosmos to win out over competing models, it took a considerable bit of time for ideas similar to Bruno’s to come to fruition. [29]

The overlapping circles in Tycho Brahe’s geocentric model of the cosmos created a significant problem for the Aristotelian notions of the heavenly spheres. If Brahe was right and the orbits of the planets crossed each other each other then they couldn’t be a set of solid. Rene Descartes offered a solution to this problem in his 1644 Principia Philosophiae. In Descartes system, like Aristotle’s, the universe was full of matter, there was no such thing as empty space. To explain motion Descartes introduced the concept of vortices. The system consisted of different kinds of mater or elements rubbing up against each other. His model included three different kinds of elements: luminous, transparent, and opaque. Luminous was the smallest and was what the stars were made of. Earth and the planets were made up of the denser opaque. The space between the planets and the stars was made up of transparent He stated that Lumnious would settle at the center of these vortices and the transparent and opaque elements would keep shifting around each other. This shifting created the movement of objects in the heavens. [30]

The increasing acceptance of Descartes theory of vortices in the later half of the 17th century brought with it the idea that the stars were like our sun and had their own planets orbiting around them. Bernard le Bovier de Fontenelle’s popular 1686 book Entretriens sur la pluralite des mondes (Conversations on the plurality of worlds) broadly disseminated this notion, in a range of editions and translations. (You can read a full-digitized copy External of an 1803 English translation of Conversations on the Plurality of Worlds online from the Library of Congress collections) [29].

The book Conversations on the Plurality of Worlds presents fictional discussions between a philosopher and his hostess, a marquise. As the two characters walk the grounds of her garden at night they discuss the stars above them. Their conversations touch on the features of the Copernican system, potential encounters with extraterrestrial life and the idea of the universe as a boundless expanse. As the book was translated into a variety of languages and republished in new editions for hundreds of years, it presented both this cosmology and the idea of life on other worlds to a range of audiences [29].

Changing ideas about the structure of the universe are also well illustrated in diagrams from William Derham’s 1715 book Astro-TheologyDerham, an English natural philosopher, astronomer and clergymen wrote a series of works exploring connections between natural history and theology. From his perspective, the shift to thinking about the plurality of worlds was significant enough that it should be set alongside the Copernican Revolution as one of the three major shifts in thinking about the nature of the universe [29].

The above history provides a good description on how philosophy and most importantly our idea of us being insignificant (part of a larger universe where everything is the same everywhere – a.k.a. Cosmological principle) like postulated by the Copernical principle dictated our journey towards understanding the cosmos.

The next steps came from ‘science’, in the modern sense of the word…

5.2 The advent of spectroscopy: The scientists speak of the Sun as a ‘star’

In 1666, Isaac Newton showed that a prism separated white light into a spectrum of its constituent parts, rather than creating the rainbow colors that are seen. In 1802, William Wollaston then constructed a spectrometer which showed the Sun’s spectrum on a screen, but noted that there were dark bands of missing colors [13].

In 1814, Joseph von Fraunhofer invented the spectroscope and mapped 574 of these lines, after which a number of scientists helped advance the study of spectroscopy, including Gustav Kirchhoff and Robert Bunsen who in 1857 were able to establish a connection between chemical elements and their own individual spectral patterns. [13]

Further study revealed that each element absorbs light of a particular color, thus leaving a specific “signature” line. And after spectroscopes were coupled to telescopes, scientist were able to identify additional chemical elements, and work our the chemical composition of the stars, as well as distinguish between nebulae and galaxies in the night sky. [13]

During this period, an Italian Jesuit priest and astronomer, Angelo Secchi (1818-1878), became a pioneer in the study of stellar spectroscopy, and through analysis of some 4,000 stellar spectrograms discovered that the stars came in a limited variety of types distinguishable by their unique spectral patterns. He subsequently devised the first stellar classification system, and is recognized as being one of the first scientists to definitively state that the Sun is a star [13].

So there you go.

What philosophers postulated centuries ago, was now verified by scientists. Strange how we always verify things we already know, is it not?

But again, could we even know what we do not?

Note: Search Harmonia Philosophica for more on the limits of knowledge, the limits of science and the limits of sensing the cosmos.

Instead of Conclusion: Things we do not know…

But what do we know exactly?

In astronomy the things we do not know are much more than the things we do. Cosmology is full of mysteries that are bravely admitted by astronomers are big gaps in our understanding of the cosmos.

Examples of things that we do not know include:

  • How does universe’s inflation work [32].
  • How singularities form and what they actually are [32].
  • How galaxies or stars formed [32].
  • Ultra-energetic cosmic rays [33].
  • Dark matter/ Dark energy [33] [34].
  • The Pioneer anomaly [33].
  • The Wow signal [33].
  • Details about massive stars: How far away they are, how they form, what is their maximum mass etc. [31]
  • Missing baryons [34].
  • How do stars explode [34].
  • Why is the sun’s corona so hot? [34]

All in all, even the example of dark matter and dark energy that account for more than ~95% of the cosmos [45] is enough for someone to understand that our knowledge is too much limited for us to draw safe conclusions about the cosmos around us.

So what is the Sun?

What are the stars?

Sure, stellar spectroscopy gives us many indications of the answer. But this is the only thing it provides: indications. We cannot know know unless we see. There are many other objects in the sky with similar yet different spectra, like quasars for example.

What is more one of the basic elements used for the classification and study of stars – distance – is measured by methods that have limitations (look at the Appendix I – Stellar parallax for more on that).

Put these notes together along with our knowledge gaps mentioned above, and you will see that our understanding of the Sun as a star (or the stars as Suns) is so safe as the understanding of a Neanderthal gazing the Sun millions of years ago.

Surely the stars may be sun and they most probably are. But our current knowledge of that is based as much in philosophy as it is based on scientific evidence from spectroscopy.

It is important to not only understand but also acknowledge that. Because through that acknowledgement we will understand not the stars but our own self here on Earth better.

At the end it is not about what is or what is not.

It is not about the Sun is a star or not.

All that matters is that we can think in the dark.

Without anything. Within everything.

Admiring the cosmos without need to categorize.

Because, as Shestov once said, when we try to categorize and understand things we just break them down into pieces that fit into the little boxes we have in our mind. (Shestov also wrote many interesting notes regarding astronomy and astrology, search Harmonia Philosophica for them)

Petty human.

Do you think you understand the stars?

Look again.

There is nothing new to see.

(Are you afraid?)

Except what you already have…

References

[1] How we Know what we know about Stars?, web lecture by Dr. Christe Ann McMenomy

[2] Who discovered that the Sun was a star?, Stanford Solar Center

[3] Who Determined That the Sun Was a Star, Smisthonian Magazine

[4] Q & A: What Are Stars?, University of Illinois, Department of Physics

[5] Astronomers still don’t know exactly what the sun is made of, PBS News

[6] Star, Wikipedia article

[7] Are the stars we see in the sky actually Suns from other solar systems?, Quora question

[8] Are the night sky stars all suns?, Quora question

[9] Sun as a star, Dr. Mark Giampapa, National Solar Observatory

[10] ELI5:How do we know that stars are suns?, reddit

[11] Parallax and Distance measurement, Las Cumbres Observatory

[12] Parallax and distance measurement limitations, NRAO

[13] Who Discovered the Sun is a Star?, Astronomy Trek

[14] Estimating distances from parallaxes, Coryn A.L. Bailer-Jones, Max Planck Institute for Astronomy, Heidelberg

[15] The problem with stellar distances, Astronomy Trek

[16] Negative parallax, Physics Stack Exchange

[17] What is the proper interpretation of a negative parallax, Astronomy stack exchange

[18] Gaia Data Release 2: Using Gaia parallaxes, Luri et al, 2018, Astronomy & Astrophysics manuscript no. 32964_Arxiv

[19] What’s with negative parallaxes?, Anthony G.A. Brown

[20] About negative parallax, Celestia forums

[21] On a reason for the appearance of negative parallaxes in the determination of the distances of stars, Lee, O. J., Annals of the Dearborn Observatory, vol. 4, pp.1-4

[22] Stellar parallax, Wikipedia article

[23] What is parallax? Space.com article

[24] Astronomy without a telescope – Assumptions, Universe today

[25] K. Migkas, G. Schellenberger, T. H. Reiprich, F. Pacaud, M. E. Ramos-Ceja, L. Lovisari. Probing cosmic isotropy with a new X-ray galaxy cluster sample through the LX–T scaling relation. Astronomy & Astrophysics, 2020; 636: A15 DOI: 10.1051/0004-6361/201936602

[26] Doubts about basic assumption for the universe, ScienceDaily

[27] Cosmological assumptions

[28] Negative parallax, article

[29] Stars as Suns & The Plurality of Worlds, Library of Congress

[30] Physical Astronomy for the Mechanistic Universe, Library of Congress

[31] 10 things we don’t know about massive stars, Astronomy.com

[32] What astronomers don’t know, IRC article

[33] 13 things that do not make sense, New Scientist article

[34] 8 Modern Astronomy Mysteries Scientists Still Can’t Explain, Space.com article

[35] Astronomical spectroscopy, Wikipedia article

[36] Modelling the spectra of planets, brown dwarfs and stars using VSTAR, Jeremy Bailey, Lucyna Kedziora-Chudczer, Monthly Notices of the Royal Astronomical Society, Volume 419, Issue 3, January 2012, Pages 1913–1929, https://doi.org/10.1111/j.1365-2966.2011.19845.x

[37] Types of Astronomical Spectra, Australia Telescope National Facility

[38] Using Light to Study Planets, JPL, NASA

[39] Spectroscopy of planetary atmospheres in our Galaxy, Tinetti, G., Encrenaz, T. & Coustenis, A., Astron Astrophys Rev 21, 63 (2013). https://doi.org/10.1007/s00159-013-0063-6

[40] Using Spectra to Measure Stellar Radius, Composition, and Motion, lumen astronomy article

[41] Spectroscopy of exoplanets, Michael Richmond

[42] Solar system analogs for extrasolar planet observations, Washington university

[43] The Electromagnetic Spectrum, lumen astronomy article

[44] Spectra of Stars, Sloan Digital Sky Survey

[45] Dark matter, CERN

Ελληνική Σύνοψις (Greek abstract): Το ότι ο Ήλιος είναι ένα απλό αστέρι είναι κοινή γνώση. Ωστόσο, όπως συμβαίνει με όλα τα πράγματα που θεωρούνται προφανή, λίγοι μπορούν στην πραγματικότητα να ονομάσουν ακριβώς ποιος το διατύπωσε πρώτος και πως και γιατί ο Ήλιος θεωρήθηκε αστέρι. Φαίνεται ότι εκτός από στοιχεία από την αστρική φασματοσκοπία και τη μέτρηση αστρονομικών αποστάσεων, ορισμένες φιλοσοφικές αρχές έπαιξαν επίσης σημαντικό ρόλο στην οικοδόμηση αυτής της γνώσης. Από το De l’infinito universon e mondi (On the Infinite Universe and Worlds) του Μπρούνο το 1584 έως το Principia Philosophiae of Rene Descartes το 1644, οι άνθρωποι είχαν αρχίσει να συνηθίζουν στην ιδέα ότι ο Ήλιος δεν είναι τίποτα περισσότερο από ένα κοινό αστέρι. Αυτή η ιδέα – ενισχυμένη και από τις ιδέες του Κοπέρνικου – επαληθεύτηκε αργότερα με τα φασματικά δεδομένα και από την εποχή του Ιησουίτη ιερέα και αστρονόμου Angelo Secchi θεωρείται ως καθιερωμένο γεγονός στις μέρες μας. Ωστόσο, τα σημερινά τεράστια κενά στην κατανόησή μας σχετικά με τη φύση του σύμπαντος απαιτούν να είμαστε πολύ πιο προσεκτικοί όταν αποκαλούμε τέτοια γνώση ως «γεγονός». Συνιστάται περισσότερη ταπεινοφροσύνη, ειδικά σε έναν τομέα της γνώσης όπου έχουμε πρόσφατα συνειδητοποιήσει ότι μπορούμε να μιλήσουμε μόνο το ~ 5% αυτής. Εν τέλει, το να αναγνωρίζουμε τα όρια μας είναι πολύ σημαντικότερο από το να προβάλλουμε τα πιστεύω μας…

APPENDIX I – Stellar parallax

Stellar parallax is the apparent shift of position of any nearby star (or other object) against the background of distant objects. Created by the different orbital positions of Earth, the extremely small observed shift is largest at time intervals of about six months, when Earth arrives at opposite sides of the Sun in its orbit, giving a baseline distance of about two astronomical units between observations. The parallax itself is considered to be half of this maximum, about equivalent to the observational shift that would occur due to the different positions of Earth and the Sun, a baseline of one astronomical unit (AU) [22].

The first known astronomical measurement using parallax is thought to have occurred in 189 B.C., when a Greek astronomer, Hipparchus, used observations of a solar eclipse from two different locations to measure the distance to the moon [23].

Limitations of Distance Measurement Using Stellar Parallax

Parallax angles of less than 0.01 arcsec are very difficult to measure from Earth because of the effects of the Earth’s atmosphere. This limits Earth based telescopes to measuring the distances to stars about 1/0.01 or 100 parsecs away. Space based telescopes can get accuracy to 0.001, which has increased the number of stars whose distance could be measured with this method. However, most stars even in our own galaxy are much further away than 1000 parsecs, since the Milky Way is about 30,000 parsecs across. The next section describes how astronomers measure distances to more distant objects. [11]

Although it is correct to take account of the relative motion of the solar system and the star being measured, in fact the trigonometric parallax method is limited to measurements of relatively nearby stars, so this relative motion is rather small. [12]

Astrometric surveys such as Gaia and LSST will measure parallaxes for hundreds of millions of stars. Yet they will not measure a single distance. Rather, a distance must be estimated from a parallax. In this didactic article, I show that doing this is not trivial once the fractional parallax error is larger than about 20%, which will be the case for about 80% of stars in the Gaia catalogue. Estimating distances is an inference problem in which the use of prior assumptions is unavoidable. I investigate the properties and
performance of various priors and examine their implications. A supposed uninformative uniform prior in distance is shown to give very poor distance estimates (large bias and variance). Any prior with a sharp cut-off at some distance has similar problems. The choice of prior depends on the information one has available – and is willing to use – concerning, for example, the survey and the Galaxy. I demonstrate that a simple prior which decreases asymptotically to zero at infinite distance has good performance, accommodates non-positive parallaxes, and does not require a bias correction. [14]

Calculating the distance to the object is easy since the parallax calculations are based on simple trigonometry, although the triangles found in parallax measurements have no relation to those found in “normal” trigonometry. In the picture at the top of the page, the distance that the star appears to have moved when viewed from different perspectives represents its distance. However, even at a relatively close distance, such as that of Proxima Centauri, which is only 4.2 light years away, this angle is extremely small. In fact, Proxima Centauri has a parallax angle of only 0.7687 ± 0.0003 seconds of arc, which roughly equates to an angle that subtends an object 2 cm across, but seen from a distance of 5.3 km away. As distances to objects increase, parallax angles get progressively smaller, until they become so small that they are impossible to measure, even with the most sophisticated equipment available today, and it is at this point that discrepancies in the distance/luminosity stats for objects arise.

The problem of negative parallax

The parallaxes of distant stars should be zero (or at least indistinguishable from zero). If the parallaxes have an uncertainty (which they do), then half of the parallaxes of distant stars will be negative. I think this is all that you are finding in the case of absolute Hipparcos parallaxes. The quote you give from the 1943 paper is talking about relative parallaxes. When you determine relative parallax you find the apparent movement in the sky with respect to a bunch of comparision stars in the same region. You make the assumption that most of these stars are very far away and have zero parallax. If a large fraction of the stars in fact have a positive and large parallax (because you are looking towards a nearby cluster), then the relative parallaxes of the genuinely distant stars in the cluster can end up negative on average. [16]

How should we handle negative parallax?

For closely aligned sources (separated by 0.2–0.3 arcsec), which are only occasionally resolved in the Gaia observations, confusion in the observation-to-source matching can lead to spurious parallax values which are either very large or have a negative value very far away from zero in terms of the formal parallax uncertainty quoted in the catalogue. These sources tend to be faint and located in crowded regions and are also associated with unreliable (large) proper motions (Gaia Collaboration et al. 2018b). Guidance on how to clean samples from spurious parallax values is provided in Lindegren et al. (2018). [17]

The systematic errors in the parallaxes are estimated to be below the 0.1 mas level (Lindegren et al. 2018) but the following systematics remain. There is an overall parallax zeropoint which, from an examination of QSO parallaxes, is estimated to be around −0.03 mas (in the sense of the Gaia DR2 parallaxes being too small). The estimated parallax zeropoint depends on the sample of sources examined (Arenou et al. 2018) and the value above should not be used to ’correct’ the catalogue parallax values. [17]

It depends how negative the parallax is and what your “prior” knowledge is of the distance to the star is. As another answer suggests, there are some spurious large negative (and positive) parallaxes for faint, crowded sources. If possible, these should be removed. If this is not the case, and the parallax is negative, but close to zero within its uncertainty, then it is telling you that you have a lower limit to the distance of the object (i.e. measurement uncertainties have led to a small negative parallax). Crudely speaking, you could add a couple of error bars to the parallax and treat that as a 95% upper limit (remember the 0.1 mas possible systematic error too). Under no circumstances should you “use them as is”, since there is no physical basis for a negative parallax or negative distance. [17]

Although should not use the negative parallaxes, you should not ignore them either. If you are looking at populations of objects, removing those with negative parallaxes will lead to significant bias in your results, as Luri et al. 2018 [18] has shown. [17]

Negative parallaxes can be interpreted as the observer (in this case Gaia satellite) going the “wrong way around the sun” as mentioned in this Jupyter Notebook by Anthony Brown. [17]

Any astrometric catalogue that lists parallaxes will contain negative parallaxes, which at first sight appear physically implausible, yet they are an entirely valid measurement of the true positive parallax in the presence of (large) noise. This notebook discusses how negative parallaxes may arise even for “perfect” measurements (suffering only from random Gaussian noise, without any systematic errors). [19]

The reason a parallax can turn up negative is simple. Errors can cause a star position to off by any direction. During the six months we measure the parallax, we expect the star’s position to shift from A to B. In this case, the true parallax was about the same size as a typical error, but the first error pushed the position reading to roughly where B is, and the second error pushed the star to roughly where A is. So the star appears to move from B to A instead of A to B: the parallax is the wrong way round. We can’t know what the error was, so we can’t subtract those. [20]

Other papers also emphasize that negative parallaxes are simply errors [21].

At the end, everything could be just a problem with the assumptions on which stars are “background stars”: Stellar parallax is the apparent motion of stars relative to other stars, which also have parallaxes. We do not know beforehand which stars are closer than the others, and these have to be inferred using statistical analysis from the entire data. The parallaxes of distant stars should be practically zero. And because they have a statistical uncertainty, then half of these near-zero parallaxes will be negative. [28]

Of course again this places the negative parallax in the category of an ‘error’, thus dismissing it altogether. It is like saying ‘If you have a negative parallax, then your measurement is wrong’.

All in all, the phenomenon deserves more attention and perhaps the advances in astronomy will soon provide a more definite answer on the problem of astronomical distance measurements.

APPENDIX II – Astronomical spectroscopy

Astronomical spectroscopy is the study of astronomy using the techniques of spectroscopy to measure the spectrum of electromagnetic radiation, including visible light and radio, which radiates from stars and other celestial objects. A stellar spectrum can reveal many properties of stars, such as their chemical composition, temperature, density, mass, distance, luminosity, radius and relative motion using Doppler shift measurements. Spectroscopy is also used to study the physical properties of many other types of celestial objects such as planetsnebulaegalaxies, and active galactic nuclei. [35] [40]

Electromagnetic radiation with the shortest wavelengths, no longer than 0.01 nanometer, is categorized as gamma rays. Electromagnetic radiation with wavelengths between 0.01 nanometer and 20 nanometers is referred to as X-rays. Radiation intermediate between X-rays and visible light is ultraviolet (meaning higher energy than violet). Electromagnetic radiation with wavelengths between roughly 400 and 700 nm is called visible light because these are the waves that human vision can perceive. Between visible light and radio waves are the wavelengths of infrared or heat radiation. After infrared comes the familiar microwave, used in short-wave communication and microwave ovens. All electromagnetic waves longer than microwaves are called radio waves, but this is so broad a category that we generally divide it into several subsections. [43]

Different celestial objects produce different types of spectra. The spectrum of an object is one means of identifying what type of object it is. How different spectra arise is shown in the schematic diagram below. [37]

Credit: Adapted from a diagram by James B. Kaler, in “Stars and their Spectra,” Cambridge University Press, 1989.: How continuous, emission and absorption spectra can be produced from same source. [37]

Continuum spectrum: In this diagram, a dense hot object such as the core of a star acts like a black body radiator. If we were able to view the light from this source directly without any intervening matter then the resultant spectrum would appear to be a continuum as shown bottom left in the figure above. [37] [38]

Absorption spectrum: Most stars are surrounded by outer layers of gas that are less dense than the core. The photons emitted from the core cover all frequencies (and energies). Photons of specific frequency can be absorbed by electrons in the diffuse outer layer of gas, causing the electron to change energy levels. Eventually the electron will de-excite and jump down to a lower energy level, emitting a new photon of specific frequency. The direction of this re-emission however is random so the chances of it travelling in the same path as the original incident photon is very small. The net effect of this is that the intensity of light at the wavelength of that photon will be less in the direction of an observer. This means that the resultant spectrum will show dark absorption lines or a decrease in intensity as shown in the dips in the absorption spectrum top right in the diagram above. Stellar spectra typically look like this. [37]

Emission spectrum: A third possibility occurs if an observer is not looking directly at a hot black body source but instead at a diffuse cloud of gas that is not a black body. If this cloud can be excited by a nearby source of energy such as hot, young stars or an active galactic nucleus then the electrons in atoms of the gas cloud can get excited. When they de-excite they emit photons of specific frequency and wavelength. As these photons can re emitted in any direction an external observer will detect light at these wavelengths. The spectrum formed is an emission or bright line spectrum, as shown by the middle spectrum in the figure above. [37]

Newton used a prism to split white light into a spectrum of color, and Fraunhofer’s high-quality prisms allowed scientists to see dark lines of an unknown origin. In the 1850s, Gustav Kirchhoff and Robert Bunsen described the phenomena behind these dark lines. Hot solid objects produce light with a continuous spectrum, hot gases emit light at specific wavelengths, and hot solid objects surrounded by cooler gases show a near-continuous spectrum with dark lines corresponding to the emission lines of the gases. By comparing the absorption lines of the Sun with emission spectra of known gases, the chemical composition of stars can be determined. [35]

An ideal thermal spectrum is shown on the left below. A spectrum of an actual star is shown on the right.

Stellar specturm example [44]

In addition to the continuous spectrum, a star’s spectrum includes a number of dark lines (absorption lines). Absorption lines are produced by atoms whose electrons absorb light at a specific wavelength, causing the electrons to move from a lower energy level to a higher one. This process removes some of the continuum being produced by the star and results in dark features in the spectrum [44].

In 1860 Gustav Kirchhoff proposed the idea of a black body, a material that emits electromagnetic radiation at all wavelengths. In 1894 Wilhelm Wien derived an expression relating the temperature (T) of a black body to its peak emission wavelength (λmax). [35]

This equation is called Wien’s Law. By measuring the peak wavelength of a star, the surface temperature can be determined. For example, if the peak wavelength of a star is 502 nm the corresponding temperature will be 5778 kelvins. [35] An object at a higher temperature emits more power at all wavelengths than does a cooler one. In a hot gas, for example, the atoms have more collisions and give off more energy. In the real world of stars, this means that hotter stars give off more energy at every wavelength than do cooler stars [43].

Figure: Radiation Laws Illustrated. This graph shows in arbitrary units how many photons are given off at each wavelength for objects at four different temperatures. The wavelengths corresponding to visible light are shown by the colored bands. Note that at hotter temperatures, more energy (in the form of photons) is emitted at all wavelengths. The higher the temperature, the shorter the wavelength at which the peak amount of energy is radiated (this is known as Wien’s law). [43]

By measuring the peak wavelength of a star, the surface temperature can be determined. For example, if the peak wavelength of a star is 502 nm the corresponding temperature will be 5778 kelvins. [35]

The spectra of galaxies look similar to stellar spectra, as they consist of the combined light of billions of stars. [35]

The reflected light of a planet contains absorption bands due to minerals in the rocks present for rocky bodies, or due to the elements and molecules present in the atmosphere. To date over 3,500 exoplanets have been discovered. These include so-called Hot Jupiters, as well as Earth-like planets. Using spectroscopy, compounds such as alkali metals, water vapor, carbon monoxide, carbon dioxide, and methane have all been discovered. [35]

Until recently, the modelling of the atmospheres of stars (e.g. Gray 2005) and that of the atmospheres of the Earth and other Solar system planets (e.g. Liou 2002) have developed largely independently. Models of stars applied to high-temperature objects with effective temperatures Teff > 3000K, with opacity dominated by the line and continuum absorption of atoms and atomic ions, whereas planetary atmosphere models applied to cool objects Teff∼ 100–300K, where the important processes were molecular absorption and scattering from molecules and cloud particles. [36]

This situation changed with the discovery in the mid-1990s of the first unambiguous brown dwarf, Gl 229B. (Nakajima et al. 1995Oppenheimer et al. 1995) and the first hot Jupiter planets beginning with 51 Peg b (Mayor & Queloz 1995Marcy et al. 1997). Many more such objects have now been discovered and reveal that planets and brown dwarfs populate an intermediate range of temperatures not explored previously. This has led to the requirement to develop new methods to model these atmospheres that cover the effective temperature range from below 1000K to more than 2000K. [36]

Spectroscopy is also used nowadays to detect exoplanets around distant stars [41] [42]. For example Transit spectroscopy is the ideal technique to probe temperate planets around M-dwarfs [38].

Related Google searches

Philosophical dogmatism inhibiting the anti-Copernican interpretation of the Michelson Morley experiment

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Photo by Spiros Kakos from Pexels

Author: Spyridon Kakos, phD, National Technical University of Athens

Goal of the paper

The goal of this paper is to investigate scientific assumptions and dogmas related to the mainstream interpretation of the Michelson Morley experiment. The current interpretation denies the possibility of a motionless Earth or the existence of ether, in the context of relativity that cannot accept the abovementioned notions without collapsing. Yet, even though in the most recent years mainstream science postulates that there is no absolute time or motion, the debate is far than settled. One would be surprised to find out that the main assumptions that support the relativistic view are not science-related but have deep philosophical roots related to specific dogmatic beliefs prevailing in the scientific world from the time of Copernicus. At the end, the need for some people to deny the existence of absolute rest and time is nothing more than a need to deny the importance of human existence in the vast space of the cosmos. This need, deeply rooted in our science via cosmology’s principles, seems to drive all scientific efforts to investigate observed phenomena, from the nature of light’s speed in relation to the way Earth moves, only because we are afraid to ask the most obvious of questions: Does it?

Related articles

Overview

From the beginning of time, humans believed they were the center of the universe. Such important beings could be nowhere else than at the very epicenter of existence, with all the other things revolving around them. Was this an arrogant position? Only time will tell. What is certain is that as some people were so certain of their significance, aeons later some other people became too confident in their unimportance. In such a context, the Earth quickly lost its privileged position at the center of the universe and along with this, the ideas of absolute motion and time became unbearable for the modern intellect, which saw nothing but relativeness in everything. After years of accepting the ideas of relativity at face value without doubting them, scientists are now mature enough to start questioning everything as any true scientist would do, including their own basic assumptions. And one would be surprised to see that the basic assumptions of today’s science in physics (and cosmology alike) are based on philosophically dogmatic beliefs that humans are nothing more than insignificant specks of dust. These specks cannot be in any privileged position in the cosmos, nor can their frames of reference. These specks cannot be living on a planet that is not moving while everything else is. There can be no hint of our importance whatsoever. Hence, the Copernican principle that has poisoned scientific thinking for aeons now. When one analyzes the evidence provided by science to support the idea of relativity though, he would see that the same evidence can more easily and simply fit into a model where the Earth stands still. Yet, scientists preferred to revamp all physics by introducing the totally unintuitive ides of relativity – including the absolute limit of the speed of light – than even admitting the possibility of humans having any notion of central position in the cosmos. True scientists though should examine all possible explanations, including those that do not fit their beliefs. To the dismay of so many modern scientists who blindly believe the validity of the theory of relativity at face value, the movement towards a true and honest post-modern science where all assumptions are questioned, necessarily passes through a place where the Earth we live in stands still. Non-relativistic explanations of the Michelson Morley experiment, related to a motionless Earth or to ether, are viable alternatives that deserve their place in modern scientific thought.

Method of research

The problem of trying to understand the philosophical assumptions behind the relativistic and non-relativistic interpretations of the Michelson Morley experiment will be analyzed with the help of three tools: Science, science history and philosophy. Science history will first provide the context of the theories and will give an explanation on how theories related to ether were discarded vis-à-vis the theory of relativity. The reasons for which specific assumptions were used instead of others will be analyzed and explained with the help of philosophy. Last but not least, science itself will help to explain – in simple terms – why and how the data many people see as proof for the theory of relativity can also be portrayed as evidence for theories which are supported by the exact opposite assumptions that theory uses.

1. The Michelson-Morley problem

The details of the nature of ether were for years a matter of research. Scientists tried to understand the properties ether must have to allow the propagation of waves or the effect ether had on objects travelling in it.

A very famous experiment took place in 1887 to investigate the speed of light in ether – the Michelson-Morley experiment (referred to as the “M-M experiment” from here on). The results of that experiment are widely known. Essentially the researchers tried to detect variations in the speed of light depending on the way Earth was moving towards or away from the Sun.

And they failed to do so.

The results were amazing and hard to manage. Based on the science of the time, these results indicated that the Earth was motionless, since no variation was detected in the speed of light. But this option could not be easily accepted, as we will see later on.

But before we can speak of this, a short description of the context is needed.

1.1 On the nature of Ether

One of the main questions of science is about the nature of space and time. Long before Einstein, great philosophers and scientists alike tried to answer this question with little or more success.

Despite the different opinions posed, what all scientists and philosophers agree on is that there must be ‘something’ that penetrates all existence. From Descartes to Kant and from Maxwell and Newton to Lorentz and Einstein, all people debating the subject inherently accept that space cannot be empty as in ‘nothing is there’.

Regardless of differences between theories, its role is important in numerous ways. If not filled with particles coming in and out of existence (quantum fluctuations) or with a field impacting everything inside it (gravity), space is filled with the potential of a field (e.g. curvature of spacetime) or it serves as the context of things we measure, providing the substrate of our observations.

Only to remind us what Parmenides said from the beginning…

Nothing cannot exist!

Nothing does not make sense.

Accepting the existence of ‘nothing’ in space led to a series of paradoxes that science could not accept. Thus, scientists of the time accepted what seemed logical: that things travel into a medium. That included matter as well as waves. That was the basic premise of science long before Einstein. And to answer this, scientists thought of the most obvious answer: a medium (tautology was always the best way to progress in science).

They named this medium “ether” (or aether, derived from the Greek word αιθέρας). And for years that followed, they accepted its existence as a fact. Everything that was travelling, from the planets to the light of the stars, was travelling inside ether.

But if ether is there and everything moves inside it, what is its nature?

There are many potential answers, everyone different than the other.

One of the attempts to dwell on the intricate details of ether was the event that initiated an avalanche of changes in modern physics.

1.2 Michelson & Morley measure the speed of light

At some point in time, Michelson and Morley tried to measure the speed of light in ether in the infamous homonymous Michelson-Morley experiment. Since scientists believed that the light traveled in ether and since Earth was moving in relation to ether, everyone believed that a measurable variance of light’s speed would be detected as our planet moved towards or away from the Sun.

Yes, the experiment did not detect any variance whatsoever. Michelson and Morley failed to measure any difference in that speed depending on how Earth is moving in space in relation to the Sun.

Because of that, Relativity was born to explain things: The speed of light is constant! And many paradoxes where created by that. And many more paradoxes where introduced to support and explain those paradoxes. And science, as Wittgenstein once said, took people to sleep…

But one day they will wake up they will see that a much simpler explanation is possible, as illustrated from the purposefully simplistic depiction of the problem above.

As I was already mentioned…

“Michelson and Morley failed to measure any difference in that speed depending on how Earth is moving in space in relation to the Sun”

Can you detect the problem?

If you read Aristotle, you would.

You see Aristotle was very intuitive in saying that the answers we seek are sometimes hidden in the questions we ask. Because depending on our beliefs, we formulate these questions by already accepting things that are not proved, things that we then take for granted without even noticing. Look carefully at the sentence above. Surely the experiment failed to measure any variation of the speed of light in relation to the moving Earth.

But…

Who said that the Earth is indeed “moving” in the first place?

Remember, a true scientist is never afraid to ask stupid and obvious questions. It is in these simple questions that the most obscure monsters of the intellect are hiding in plain sight…

Let us explore the monster while it is still breathing.

1.3 Possible interpretations

The Michelson Morley experiment results posed a serious problem to physicists of the day. The way the problem was solved however reflected specific philosophical beliefs and not based on purely scientific criteria. These beliefs we ought to acknowledge, since only by knowing the underlying assumptions of a theory can you truly judge it properly.

But else can we explain the negative result of the experiment?

Let us list the main three solutions here:

  1. Motionless Earth solution: There was no variance detected in the speed of light while Earth was moving, because the Earth is not moving.
  2. Ether-based solutions: The Earth is moving in ether and dragging it as it moves. That is why no variance in the speed of light in relation to ether was not detected. Or, in another alternative proposed by Lorentz, the ether exists and the M-M negative result is explained by the fact that the length contraction caused by the movement also applies to the measuring devices.
  3. The relativity solution: The Earth moves but there is no ether. The speed of light is absolute!

Out of these three options, all equally valid (at least based on the evidence available – we will see later on how this does not play a major role in the argument made by this paper), Einstein and mainstream science chose the third one.

1.4 Criteria to select the best solution

Is the option selected by Einstein (and later on by mainstream science) a correct solution?

Well, in science that question does not make much sense.

Every theory that adheres to the available data must be accepted at least as scientifically valid. And if all these three options are capable of generating theories which do that, then as far as science is concerned, they are all acceptable.

Yet, there are additional criteria that can help us analyze whether the option we have opted for is the optimal one. A list of such criteria includes:

  • The simplicity criterion: Is the option selected the most simple one? Does it require the less assumptions possible than the alternatives?
  • The practicality criterion: How much rework of all existing theories does the new theory require? Do we need to rewrite everything or small adjustments will just do the trick?
  • The philosophical dogma criterion: Does the theory adhere to my philosophical dogmas? If all are equivalent, why not select the one that

The first criterion is related to the common intuition we all have that the simplest of the solutions must be the one closest to the truth. Leaving aside the fact that philosophy does not even agree whether ‘truth’ per se exists, it is a type of common sense criterion. Not purely scientific in nature, but yet again, perhaps because of that the most scientific of them all.

The other two criteria are not scientific.

Guess which criteria were used to select the three option.

2. Earth standing still as a solution

The motionless Earth solution/ interpretation of the M-M experiment results is by far the most elegant one. After all, when you fail to detect any effect of the motion of something, the first thing that should come to the rational mind is to question the initial assumption that this something is indeed moving. The simplicity criterion is surely favoring this option.

Regarding the other two criteria mentioned in Chapter 1.4, we must note that by accepting that solution, we would nevertheless have to discard the Copernican Principle. On the other hand, it is equally (or even more) important to note that all our physics regarding movement, electromagnetism and waves would remain intact. Transformations with regards to coordinate systems which move in relation to each other would still work in the intuitive way they were working. Philosophically speaking, the option is the most philosophically-neutral one: There are no hidden philosophical dogmas guiding our selection.

As Lincoln Barnett said: The Michelson-Morley experiment confronted scientists with an embarrassing alternative. On the one hand they could scrap the ether theory which had explained so many things about electricity, magnetism, and light. Or if they insisted on retaining the ether they had to abandon the still more venerable Copernican theory that the earth is in motion. To many physicists it seemed almost easier to believe that the earth stood still than that waves – light waves, electromagnetic waves – could exist without a medium to sustain them. It was a serious dilemma and one that split scientific thought for a quarter century [1, p. 3]. In a book endorsed by Einstein, theoretical physicist James Coleman admitted: “The easiest explanation was that the earth was fixed in the ether and that everything else in the universe moved with respect to the earth and the ether….Such an idea was not considered seriously, since it would mean in effect that our earth occupied the omnipotent position in the universe, with all the other heavenly bodies paying homage by moving around it” [1, p. 3]

Do all the above ring a bell? They certainly do. Hubble was following the same line of thinking when selecting his cosmological model. Again, the infamous Copernican Principle came forward and forced science to choose one path instead of the other.

As explained already in the relative paper I published for Hubble and the Copernican Principle [2], the fact that Earth rotates around the Sun is not a fact at all. It is now known that a physicist can easily choose any point as the center of the system he examines, without that having any effect on the validity of the physical description of that system. The selection of the heliocentric over the geocentric system was made upon the philosophical dogma that we are insignificant; that is the main premise of the Copernican Principle. Not something ‘proved’ (anyway such a thing does not exist in the context of science), but a purely dogmatic stance dictated by religious (or rather, anti-religious) beliefs. Even though the available data showed that the Earth is at the center of the universe (literally) [3], Hubble chose to ignore them and opt for another option to explain the phenomena observed. Based on the Copernican Principle which holds that we cannot have a privileged position in the universe (Why? Just because! No, there is no justification for this principle that we use as an axiom), Hubble chose one cosmological model over the other.

In the same way and on the same grounds, the first solution to the M-M problem was discarded. The same line of thinking was followed by Einstein as well, when selecting the solution to the problem posed by the M-M experiment. The easiest potential solution was discarded from the beginning, simply because the Copernican Principle said so. Regarding physics, scientists made their selection loud and clear once more based on the principle that there can be no privileged position, that there can be no possibility of Earth standing still. Or for anything else actually, like ether (for that we will talk later on). All motion must be relative, there can be nothing at absolute rest.

As Ronald W. Clark describes it, the renouncing of the whole Copernican theory was “unthinkable”.[1]. In the same way Hubble thought it was unthinkable to accept the Earth at the center of the cosmos, Einstein thought it was unacceptable to speak about an immobile Earth. The common denominator for both being one: The Copernican Principle. We can have an in-depth analysis of why that principle is so pervasive and persuasive. Yet, this is not the scope of this paper. The goal of this paper is to show that the mainstream way of thinking is based on legs of clay. And that if we select different assumptions (simply by… choosing them), then we result in a whole different cosmos.

Of course, by rejecting the motionless Earth solution, a price had to be paid. And that was the total revamp of physics that resulted after the acceptance of the theory of relativity on the premise of the absolute light speed. (Remember, we always speak about the acceptance of the initial unproven premises here, not about the inherent internal consistency of the theory, which is taken for granted) And yet, scientists were accepting this cost in order to keep their precious unprivileged position in the cosmos.

The rest, as they say, is history.

What is our duty though, is to acknowledge that history.

And to be ready to change it.

To recognize the abovementioned process and to always remember that there are more than one ways to interpret the same evidence. That is and that has been the process followed by the scientific method. Theories formulated based on data and then new theories formulated to explain the same data[1] in a different way. In a cynical turn of events, the moment we accepted that everything is moving, was the moment science stopped in its tracks.

Note that the actual solution to the problem is not important here. What is important is to understand that the Earth standing still is one viable solution to the problem at hand. And that the alternative solutions to the M-M experiment were not only discarded without providing justification whatsoever, but they were deliberately buried under the veil of the history of science as irrelevant.

We must always keep in mind that it is very dangerous though to believe in facts. True scientists need to keep an open find for all possibilities.

3. Ether-based potential solutions

As already mentioned, the immobile Earth is not the only way to interpret the M-M experiment. There exist also other two alternatives based on ether:

  • The Earth moves and drags the ether along as it moves through space. That is why we cannot detect any change in the speed of light in ether as Earth moves.
  • The ether exists and the M-M negative result is explained by the fact that the length contraction caused by the movement also applies to the measuring devices.

For the relativistic solution (i.e. the Earth moves but there is no ether – the speed of light is an absolute number not related to the movement of the frames of reference) we will speak in the next chapter.

The ether-based solutions, were (and still are) equally acceptable solutions like any of the other two. And to be honest, even if they were not, adding more elements that would make them be compatible with the data would do the trick; this is what scientists have been doing with the relativity theory anyway (see below). The ether option was discarded based not on scientific criteria but based on philosophical grounds similar to the ones that led to the discarding of the motionless Earth option.

In a cosmos where motion is relative, ether could not stay as-is. Accepting its existence would imply the possibility of absolute rest. Even though ether dragged along Earth was moving, the ether per se would refer to something standing still in absolute terms. And the existence of absolute rest was incompatible with the (special) theory of relativity.

Einstein explained by means of his famous K and K’ models what led him, initially, to dispense with ether: “… if K be a system of coordinates relative to which the Lorentzian ether is at rest, the Maxwell-Lorentz equations are valid primarily with reference to K. But by the special theory of relativity the same equations without any change of meaning also hold in relation to any new system of coordinates K’ which is moving in uniform translation relative to K. Now comes the anxious question: Why must I in the theory distinguish the K system above all K’ systems, which are physically equivalent to it in all respects, by assuming that the ether is at rest relative to the K system? For the theoretician such an asymmetry in the theoretical structure, with no corresponding asymmetry in the system of experience, is intolerable. If we assume the ether to be at rest relative to K, but in motion relative to K’, the physical equivalence of K and K’ seems to me from the logical standpoint, not indeed downright incorrect, but nevertheless unacceptable.” [1, p. 635 – 648]

Again, the grand old debate of whether a ‘privileged’ position exists. Again the same grandiose expressions of ‘intolerable’ positions, erringly similar to the expressions used afterwards by Hubble. The aeons old debate of whether we are important or not, coming back at a different form, yet all the same whatsoever. Surely, the privileged position of the Earth is not at stake here, yet the existence of any privileged position is. You see the Copernican principle is nothing else than a special case of more general principles, namely the Cosmological and the Mediocrity principles.

The mediocrity principle is the philosophical notion that “if an item is drawn at random from one of several sets or categories, it’s likelier to come from the most numerous categories, than from any one of the less numerous ones”. The principle has been taken to suggest that there is nothing very unusual about the evolution of the Solar System, Earth’s history, the evolution of biological complexity, human evolution, or any one nation. It is a philosophical statement about the place of humanity. The idea is to assume mediocrity, rather than starting with the assumption that a phenomenon is special, privileged, exceptional, or even superior than others [16]. The Cosmological Principle on the other hand supports the idea that “on a large scale the universe is pretty much the same everywhere” [17]. Both of these principles essentially say the same thing as the Copernican principle but on a different level. Overall, all three state that there can be nothing ‘special’ about anything in the cosmos. There can be no God, sorry I mean there can be no ether standing still, no Earth standing still, no nothing in a more superior position than anything else [18].

If we are to judge the selection of the dragged-ether solution by our criteria laid down in Chapter 1.4, we would say that it seems like a viable yet not optimal option. Surely it is not as simple as the motionless Earth option, since it introduces the ether dragging phenomenon as well. Regarding the practicality aspect, the same as in the previous solution apply: we would keep the physics we have and we would have to revamp the cosmology. Last but not least, regarding the philosophical criterion, there are not many hidden assumptions here, except obviously from the fact the ether’s existence is assumed.

4. The relativity solution

The relativity solution was the solution finally selected and it is easy to find many books regarding the subject [4] that analyze it in great extent. The detailed analysis of this option is not in scope for this paper. The goal is mainly to show that alternative solutions to the M-M results exist.

A short description of how the relativity solution would stand up to the criteria we mentioned in Chapter 1.4 is crucial though into our analysis.

Regarding the simplicity criterion, the relativity fails big time. In order to explain the results of Michelson and Morley, it introduces an unintuitive absolute limit in the speed of light and then, based on that and other premises it creates a chaotic complex of paradoxes that still baffle physicists around the world[2]. Paradoxes that are still confused as ‘reality’ in the context of the general tendency of people to forget that science deals with theories and not with what is real [5]. Length contraction, time dilation, curvature of space-time are some of the components that are now necessary to explain the cosmos around us. Things which would be completely useless have we opted for the simplest of the solutions. But it seems we are too unimportant for that option.

Regarding the practicality criterion, again this option seems to not have a high score. Choosing to accept the relativity premises, science needs to revamp all the physics related to light and movement. Of course, cosmology would stay unaffected on the other hand. Accepting that two twins on a relative motion to each other age differently (check the “Against the realistic interpretation of the Theory of Relativity” paper [5] on an explanation on how the twins paradox is misinterpreted as ‘real’) at least makes us keep the most precious position of being nothing in the cosmos.

Last and most importantly, the relativity solution fails the philosophical criterion in an astounding scale. In order to accept that option we adhere to specific philosophical dogmas relating to our importance in the world. Such opinions are widely known to be related to anti-religious materialistic philosophies that have been in fashion for the last centuries. Humans who take a stand against religion tend to adhere to such philosophies with zeal. And although we cannot say anything regarding the actual connection of these philosophies with the people who made this specific choice and still support it, we cannot but admire the almost obvious connection of the Copernican Principle and all Copernican Principle-compatible premises with such ways of thinking. The selection of the relativity option is not a casual selection of one option over the other. Opting for that solution is full of philosophical dogmas charged with aeons of tension; hence the unusually and unscientifically super-charged language (‘intolerable’) used by scientists supporting this option over the others.

How astonishing beings humans are.

Capable for the most astounding of feats.

And for the most amazing of mistakes.

Einstein could not accept what would kill his theory.

And thus, as simple as that, ether died.

And thus, ‘space-time’ was born.

Along with complexities, paradoxes and unintuitive science based on contracting lengths, slowing clocks and twins who seem to age differently based on relative motions that we cannot define properly. All because we could not accept the much simpler solution of an immobile Earth.

But was this really the end of ether?

A more detailed look implies no.

4.1 Ether with a new name

Even though many people today believe that Einstein discarded ether altogether, Einstein actually replaced ether with something else that essentially had similar properties: “something” that penetrates all the cosmos, being the context for all the phenomena we observe. It must be evident by now that the change was not much of a change to speak of.

Essentially, Hermann Minkowski’s idea of four-dimensional spacetime is the conceptual substitute for the ether. [6] The metric tensor of Einstein [7] is essentially replaced ether that penetrates all space and provides the background substrate for gravity to manifest itself. Like ether provided the substrate for science back in the days of Lorenz.

Philipp Lenard, one of Einstein’s most vocal opponents at the time, in a 1917 speech titled “Relativity Principle, Ether, Gravitation” remarked that Einstein merely renamed ether as “space,” and concluded that General Relativity theory could not exist without ether. As Einstein himself describes it: “No space and no portion of space [can be conceived of] without gravitational potentials; for these give it its metrical properties without which it is not thinkable at all….According to the general theory of relativity, space without ether is unthinkable; for in such space, not only would there be no propagation of light, but also no possibility of existence for standards of space and time (measuring rods and clocks), nor therefore any space-time intervals in the physical sense.” [1, p. 635 – 648]

And now we do not have ether. But the metrical tensor field and space-time. An ether nonetheless, but without its most important characteristic: absolute rest. [1, p. 635 – 648]

4.2 Einstein on Ether

The best place to begin in discovering what constitutes that ether for relativity (or ‘space’ as we now know it) is to investigate the way Albert Einstein himself is theorizing on the subject.

In 1916, Einstein wrote: “in 1905 I was of the opinion that it was no longer allowed to speak about the ether in physics. This opinion, however, was too radical, as we will see later when we discuss the general theory of relativity. It does remain allowed, as always, to introduce a medium filling all space and to assume that the electromagnetic fields (and matter as well) are its states…once again “empty” space appears as endowed with physical properties, i.e., no longer as physically empty, as seemed to be the case according to special relativity. One can thus say that the ether is resurrected in the general theory of relativity… Since in the new theory, metric facts can no longer be separated from “true” physical facts, the concepts of “space” and “ether” merge together. It would have been more correct if I had limited myself, in my earlier publications, to emphasizing only the non-existence of an ether velocity, instead of arguing the total non-existence of the ether, for I can see that with the word ether we say nothing else than that space has to be viewed as a carrier of physical qualities” [1, p. 635 – 648].

What Einstein says here is the essence of his stance towards ether. Initially, the ether could not exist because if it did, it would imply that absolute rest is possible, thus nullifying the validity of the theory of relativity per se. But at the advent of the general theory of relativity, ether was needed to provide the substrate that would essentially explain the existence of gravity and action at a distance: the curvature of ‘something’ (now known as ‘space-time’) was required to explain the movement of planets on the sky.

In simple words, Einstein did not renounce ether. He renounced ether with physical properties as accepted by others at the time with the only goal not to leave an opening for the possibility of absolute rest. He did however use the notion of ether (albeit with a new name to avoid any misunderstandings or unwanted connotations) with specific physical qualities to support his action-at-a-distance explanation.

The ether of General Relativity only had to incorporate gravity, thus Einstein had to develop another type of ether in order to unify gravity with electromagnetism, which led to embellishing Riemann’s geometry with what was known as “tele-parallelism” and six more tensor fields in addition to the ten already being used by General Relativity. [1, p. 635 – 648].

4.3 Evidence for Ether

Even though the null result of the Michelson Morley interferometer experiment in 1887 has been widely regarded as proof that the ether does not exist, there are still evidence proposed by science that ether might actually do.

Poincaré continued to insist upon the existence of ether for three main reasons: (1) stellar aberration (check related studies of the Arago and Airy experiments); (2) “action-at-a-distance” whereby gravity and electromagnetism could be transmitted over vast distances; (3) rotational motions (of which we saw an example in Sagnac’s 1913 experiment). Although Einstein felt that he had answered the phenomenon of stellar aberration (but in reality he had not), he did not have a quick answer for rotation and action-at-a-distance. [1, p. 635 – 648].

To-day, ether keeps on coming back with various shapes and forms. Many scientists call for the need of ‘something’ that would act as an absolute frame of reference for our view of the cosmos [8] [9]. This was something already tackled in my previous papers [5]. When the theory of relativity speaks for ‘speed’ what speed does it refer to anyway? The hypothesis provided by ether gives a solution to that simple yet complex problem. There must be something relative to which we measure things, otherwise there is no meaning whatsoever in talking about speeds in the first place.

A number of experiments have detected anisotropy in the speed of light by exploiting the effect known as Fresnel Dragging to reveal the different travel times by light in each direction between two points [10].

Astrophysicist Toivo Jaakkola claims that “The ether hypothesis was thought to be buried by the Michelson-Morley experiment, but today it is more alive than ever, in the form of the CBR [Cosmic Background Radiation]” [1, p. 635 – 648].

That evidence call for a need to re-evaluate the premises we have placed our faith upon. And perhaps be ready to choose a different path than the current one.

4.4 Ether-based theories equivalence

One very important thing to understand when discussing alternative solutions to the M-M problem, is the equivalence of the possible solutions. There is no privileged solution based on the data available. The ether-based theories trying to explain the M-M experiment (e.g. the one postulated by Lorentz), are essentially identical with the theory of relativity proposed by Einstein. There is no way to distinguish one from the other based on the evidence available, which all fit both. (Note that in the theory that Lorentz postulated, the M-M experiment was explained by the length contraction also affecting the measuring devices, thus leading to a null result.)

Some believe that the difference between the two theories is mainly related to the way they formulate their assumptions. Both try to explain the cosmos and they are simply doing so in a different way.

Equivalence of Lorenz and Einstein’s theories [11]

Differences between the different theories obviously do exist. Choosing one over the other is at the end a matter of choice, if such a choice is valid when one of the them (the Lorentzian one) uses clearly less assumptions than the other (refer to the analysis made above based on the Chapter 1.4 criteria). Despite those differences though, they are both at the end empirically equivalent [11].

Special relativity and Lorentz’s theory are completely identical in both sense as physical theories and as theories of physical space-time. All statements of special relativity about those features of reality that correspond to the traditional meaning of terms ‘space’ and ‘time’ are identical with the statements of Lorentz’s theory. On the other hand, all statements of Lorentz’s theory about those features of reality that are called ‘space’ and ‘time’ by special relativity are identical with the statements of special relativity. The only difference between the two theories is terminological [12].

Of course there are points where there are differences. The theories themselves are too broad to even be possible for someone to claim complete equivalence in every single aspect. For example, there are scientists who claim that the Lorentz theory can explain more phenomena than the theory of relativity. For example, Lorentz invariant cosmology holds promise of being able to account for the ratio of gravitational mass of galaxies to their baryonic masses (though this requires a tedious computation yet to be accomplished); i.e., it conceivably could account for the existence of so-called “dark matter”. General relativity does not [13]. On the other hand, other writers explain the the Lorentz theory needs more assumptions that Einstein’s [14].

Again, the details of this debate are mute.

What is important is the possibility of alternative explanations [15].

And that they are largely compatible with the data.

True science is not about selecting a path.

It is about acknowledging the existence of other paths as well.

Conclusion

What is obvious is most of the times the hardest thing to grasp. For aeons now, humans thought of themselves as the center of everything. Did they hold that belief because they made an in-depth analysis of all possible explanations of the cosmos and after careful consideration they came up to this justified example? No. They did so because – out of their instinct – this sounded logical and true. It felt true. And perhaps especially for those reasons, this view was more scientific than it could ever be. Now we look at the Sun revolving around Earth at the sky. And we admire how Earth rotates around the Sun instead. We see evidence for us not moving. And yet we formulate theories on the premise that we do. We are so much convinced of our insignificance that any other solution is simply “intolerable”.  Instead of scientists we have become cowards. Look at our selves again we must. And honestly ask: Why can’t we catch that light?

BIBLIOGRAPHICAL REFERENCES

  1. Robert A. Sungenis, Robert J. Bennett, Ph.D., Galileo Was Wrong, The Church Was Right – The Evidence from Modern Science, Catholic Apologetics International Publishing, Inc., 2017.
  2. Spyridon Kakos, (2018), From Galileo to Hubble: Copernican principle as a philosophical dogma defining modern astronomy, International Journal of Theology, Philosophy and Science.
  3. Spyridon Kakos, 2010, “Earth at the center of the universe?”, Harmonia Philosophica.
  4. Philip Harris, Special Relativity, University of Sussex, retrieved from here on 2019-06-03.
  5. Spyridon Kakos, (2020), Against the realistic interpretation of the Theory of Relativity, Harmonia Philosophica.
  6. Scott Walter. Ether and electrons in relativity theory (1900-1911). Jaume Navarro. Ether and Modernity: The Recalcitrance of an Epistemic Object in the Early Twentieth Century, Oxford University Press, 2018, 9780198797258. ffhal-01879022f
  7. Metric tensor, Wikipedia article, retrieved from here on 2020-08-11.
  8. G. Builder, (1957), Ether and Relativity, Australian Journal of Physics, vol. 11, p.279, retrieved from here on 2020-08-11.
  9. Roger Ellman, The Einstein – Lorentz Dispute Revisited, retrieved from here on 2020-08-11.
  10. Declan Traill, (2019), Proof that the Ether exists and that the speed of light is anisotropic.
  11. László E. Szabó, Lorentzian theories vs. Einsteinian special relativity – a logico-empiricist reconstruction, Vienna Circle and Hungary – Veröffentlichungen des Instituts Wiener Kreis. Berlin and New York: Springer, retrieved from here on 2020-08-11.
  12. László E. Szabó, Lorentz’s theory and special relativity are completely identical, retrieved from here on 2020-08-11.
  13. Wasley S. Krogdahl, Α Critique of General Relativity, retrieved from here on 2020-08-11.
  14. Michael Heinrich Paul Janssen, (1995), A comparison between Lorentz’s ether theory and special relativity in the light of the experiments of Trouton and Noble, retrieved from here on 2020-08-11.
  15. Szabó L.E. (2011) Lorentzian Theories vs. Einsteinian Special Relativity — A Logico-empiricist Reconstruction. In: Máté A., Rédei M., Stadler F. (eds) Der Wiener Kreis in Ungarn/ The Vienna Circle in Hungary, Veröffentlichungen des Instituts Wiener Kreis, vol 16. Springer, Vienna, retrieved from here on 2020-08-11.
  16. Mediocrity principle, Wikipedia article, retrieved from here on 2018-09-05.
  17. Cosmological principle, Wikipedia article, retrieved from here on 2018-09-20.
  18. Spyridon Kakos, (2018), From Galileo to Hubble: The Copernican principle as a philosophical dogma defining modern astronomy, International Journal of Theology, Philosophy and Science.

[1] Surely this usually – but not always – happens with the advent of new data. However, the new theories do interpret the ‘old’ (existing) data as well. In that sense, the initial data are then seen in a completely different context of the new theory.

[2] For an analysis of how the Theory of Relativity should not be interpreted literally, check the related article “Against the realistic interpretation of the Theory of Relativity” by Spyridon Kakos here.

APPENDIX – Re-tweeting the Article

After I have posted the article some people decided to re-tweet it. To my astonishment, as shown below, these tweets of my article were tagged as “Media with sensitive content”, whatever that means.

The re-tweeted article marked as “sensitive” and, thus, hidden from general view!

Of course when you decided to click on the item and expand it (despite the… warning) you could still view the article. This is at least weird. I have been publishing articles for years now and I do not recall something like that again. Unless the tagging was about the picture of the article, which I doubt since it was a simple photo I myself have taken from cape Sounio.

You expand the “sensitive article” and then you can view it… At least for now…

It seems that the Copernican Principle is so powerful that not even Tweeter can freely allow publication of anti-Copernican articles without some warning ?!

If that happens with a simple article, just imagine the difficulty of publishing a paper on the matter, especially in one of the prestigious journals. Unfortunately we live in an era where censorship still exists, but only with a different name.

We now know it as… “facts”.

On the untrustworthiness of axiomatic-founded science

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Photo by Spiros Kakos from Pexels

On the untrustworthiness of axiomatic-founded science

Spyridon Kakos1, Athens, Greece, July 2020

1 phD, National Technical University of Athens

Table of Contents

Abstract

The idea of science being the best – or the only – way to reach the truth about our cosmos has been a major belief of modern civilization. Yet, science has grown tall on fragile legs of clay. Every scientific theory uses axioms and assumptions that by definition cannot be proved. This poses a serious limitation to the use of science as a tool to find the truth. The only way to search for the latter is to redefine the former to its original glory. In the days well before Galileo and Newton, science and religion were not separated. They worked together to discover the truth and while the latter had God as its final destination, the former had God as its starting point. Science is based on the irrational (unproven) belief that the world is intelligible along many other assumptions. This poses a serious limitation to science that can only be overcome if we accept the irrationality of the cosmos. The motto “Credo quia absurdum” holds more truth than one can ever realize at first glance. There is nothing logical in logic, whereas there is deep wisdom in the irrational. For while the former tries to build castles on moving sand, the latter digs deep inside the depths of existence itself in order to build on the most concrete foundations that there can be: the cosmos itself. The only way forward is backwards. Backwards to a time when religion led the quest for knowledge by accepting what we cannot know, rather than trying to comprehend what we do not. Science was anyway based on that in the first place.

Tags: science; science philosophy; irrational; axioms, foundations

Περίληψις (Summary in Greek)

Η ιδέα ότι η επιστήμη είναι η καλύτερη ή η μόνη οδός για να φτάσουμε στην αλήθεια για τον κόσμο μας, είναι μια βασική πίστη του μοντέρνου πολιτισμού. Και όμως, η επιστήμη έχει μεγαλώσει πολύ στηριζόμενη όμως σε πήλινα εύθραυστα πόδια. Κάθε επιστημονική θεωρία χρησιμοποιεί αξιώματα και παραδοχές οι οποίες εξ’ ορισμού δεν αποδεικνύονται. Αυτό θέτει σοβαρούς περιορισμούς στο τι μπορεί να κάνει η επιστήμη αναφορικά με την αναζήτηση της αλήθειας. Ο μόνος τρόπος να βρούμε την τελευταία είναι να αναθεωρήσουμε την πρώτη στην πρότερη της δόξα. Στις ημέρες πολύ πριν το Γαλιλαίο και τον Νεύτωνα, η επιστήμη και η θρησκεία δεν ήταν διαχωρισμένες. Εργαζόντουσαν μαζί για να ανακαλύψουν την αλήθεια και ενώ η δεύτερη είχε το Θεό ως τον τελικό προορισμό της, η πρώτη Τον είχε ως αφετηρία. Η επιστήμη βασίζεται στην (παράλογη) πίστη ότι ο κόσμος είναι  κατανοήσιμος, μεταξύ άλλων παραδοχών. Αυτό θέτει ένα σοβαρό περιορισμό στην επιστήμη που μπορεί να ξεπεραστεί μόνο εάν αποδεχτούμε τον παράλογο του Κόσμου. Η φράση “Credo quia absurdum” κρατά περισσότερη αλήθεια από ό, τι μπορεί κανείς να συνειδητοποιήσει ποτέ με την πρώτη ματιά. Δεν υπάρχει τίποτα λογικό στη λογική, ενώ υπάρχει βαθιά σοφία στο παράλογο. Γιατί ενώ η πρώτη προσπαθεί να χτίσει κάστρα σε κινούμενη άμμο, το δεύτερο σκάβει βαθιά μέσα στα βάθη της ίδιας της ύπαρξης, προκειμένου να στηριχτεί στα πιο στέρεα θεμέλια που μπορεί να υπάρχουν: τον ίδιο τον Κόσμο. Ο μόνος δρόμος προς τα εμπρός είναι προς τα πίσω. Πίσω σε μια εποχή που η θρησκεία οδήγησε την αναζήτηση της γνώσης αποδεχόμενη αυτό που δεν μπορούμε να ξέρουμε, αντί να προσπαθούμε να κατανοήσουμε αυτό που δεν γνωρίζουμε. Η επιστήμη ούτως ή άλλως βασιζόταν σε αυτό εξ’ αρχής.

1. INTRODUCTION

Science today is thought to be the cornerstone of human civilization. People trust science to find solutions to their problems, to search for explanations on how the cosmos is working, even to reach the ultimate goal that was the holy grail of human philosophy for thousands of years: Truth. However, science is inherently limited and cannot play such a central role in the search for answers. This paper will present arguments to justify this proposition and will also try to explain that the untrustworthiness of science can only be supplemented by religion in its most pure form. As Einstein once postulated, “Science without religion is lame, religion without science is blind”. The pages that follow will try to extrapolate on that line of thought and delve into the depths of the foundations of science, which surprisingly contain more religiosity than one would expect.

2. PURPOSE OF THE STUDY

The purpose of this study is to show that the foundations of modern science are not capable to support a method of thinking which can positively answer any of the great metaphysical questions of humanity; questions related to the “why” and not the “how” which is usually the subject of modern natural sciences. In order for us to reach an understanding of the cosmos, we need something beyond an axiomatic-based science. This paper will show how and why such a way of thinking can only be found within the realm of religion.

3. RESEARCH METHODS

The topic under analysis was examined with the help of three tools: Scientific analysis, Philosophy and History. The latter was the tool that provided evidence for how science has progressed into what it is today. That analysis provided insights on what are the main limitations of science due to the axioms it is using. These axioms were further analyzed to show what Gödel has showed many years ago: That an axiomatic-based theory can never be proved consistent or full. The analysis was performed based on the basic premise that “If something needs an assumption to be held as true, then it cannot be considered as true per se” (this should not be considered an assumption but rather a tautology: what is not proved to be true cannot be considered true). Finally yet most importantly, the research tried to find the prerequisites for a method of thinking that could overcome those obstacles and regain the trustworthiness of humanity to science as a way to reach the truth. The path revealed is described at the last chapters of the current thesis.

4. FINDINGS

The present research analyzes the foundations of science and shows that they are unreliable markers for the quest for truth. This is done by examining not only one of the major exact sciences of today (physics) but also the major tool utilized by all exact sciences to elaborate on the workings of the cosmos (logic). The results of the exercise portray a picture that is widely different than the one promoted by mainstream science today: The holy grail of modern science (the “truth”) cannot be found unless we stop searching for it…

In summary, the scientific method [1] tries to examine which assumptions best fit the observed phenomena[1] and then formulate the best scientific model that could explain those phenomena in a self-consistent way. The method (e.g. logical deduction) or the tools (e.g. statistical analysis) used to perform the modeling of the cosmos are not of importance here. What is important is that for the scientific models to exist, there need to exist some assumptions which scientists take for granted. Nothing can be built based on nothing (except ‘Nothing’ of course, but Parmenides would have objections on whether this exists).

What will be shown is that these foundations of science (assumptions, a.k.a. axioms or principles) do not have any inherent truthfulness or validity. And if the foundations are not to be trusted to lead us to the truth, then neither science as we know it today can be trusted as well for that task.

4.1 Axioms: From Euclid to quantum physics

The Elements of Euclid constituted the first time a sector of mathematics[2] was founded on axioms. Euclid made a great work in formulating a specific set of principles on which his theory was based upon and this way of thinking dominated the western scientific thought for millennia. Even today, every scientific field from mathematics to physics and chemistry is based upon specific axioms and scientists struggle to create (or discover – depending on the philosophical theoresis you adhere to) new theorems based on those axioms.

Terminology note No. 1: Axioms are also known as ‘principles’ in other fields of science besides mathematics. It is important to note that the name really makes no difference. What is important is that we speak about unproven assumptions that we take for granted when developing a theory.

It is important to note that ‘unproven’ does not mean that there is no evidence whatsoever for the axioms or principles used. It simply means that these axioms are not proved with the certainty one would want to declare them ‘true’ in the philosophical sense of the word, meaning valid in every possible case. Nobody starts pulling axioms out of thin air because he just thought about them; usually there is a long process of thought involving both observation and induction reasoning to derive a specific axiom. (Later on, we will see how indeed this could be futile anyway, but for now let’s assume that this process is of great significance) So for example, physics contains the principle of conservation of energy, which may be proven in specific cases but which has certainly not been proven for every possible case. This is clearly self-evident, since only a specific set of observations has been conducted so far. Drawing a general universal principle based on such a limited set of information (limited in relation to what we will discover one million years from now and surely limited in relation to the extent of the cosmos) is inductive in nature and can in no case substantiate the principle as a ‘fact’ beyond any doubt.

In other words, the fact that axioms are based on scientific observations does not mean that they are proved, as a theorem is proved in geometry for example. It is true that most axioms or principles are evidence-based, but this means nothing to a scientist – proof of something entails a long and painful process that would make certain that something holds true in every possible scenario. Even though the conservation of energy is something that seems to be true based on what we have seen so far in the physical systems we have examined, we cannot possibly be absolutely (100%) certain that this principle is true in the whole universe or at every possible circumstance. Our “facts” are based – at best – on circumstantial evidence; examining all the possible physical systems in the whole universe is something we will never accomplish anyway. Hence, the conservation of energy is a ‘principle’ and not a ‘fact’.

Terminology note No. 2: Principles of physics (and other areas of science) are many times called ‘laws’. This can be really confusing to the uneducated reader, since the word ‘law’ implies something that has been proven to exist in the whole cosmos (universal laws). One should always keep in mind that regardless of the name used, we are still speaking about unproven assumptions that we take for granted when developing a theory.

Nevertheless, axioms or principles are a basic and fundamental element for science. They offer the foundations on which theories are built and evolved. Without these foundations observations are just set of meaningless data. Axioms offer the context in which a theory is built; the basic building blocks on which the whole structure of the theory is erected upon. Change those axioms and you end up with a different theory based on exactly the same observational data. It may be the case that some new evidence disprove one axiom/ principle, but in that case another axiom takes its place for the whole structure of theories to still be able to stand tall. Needless to say that this is neither a bad nor a good thing. It is just how science works. Any journey needs a starting point and these axioms offer that point of reference from which one can watch the cosmos and derive meaning from it.

This section will first examine the use of such axioms and principles in various cases of scientific endeavor. I will then show that such axioms cannot be reliable foundations for the philosophical quest for the truth.

Important Notes

  • The term ‘axioms’ and ‘principles’ will be used interchangeably in this paper depending on the context. In essence, even though the former are used in mathematics and the latter in exact sciences, they denote the same thing: unproven assumptions that we use as a starting point to build a theory.

4.1.1 The case of the 5th axiom

The fifth axiom of Euclid (also known as the “parallels’’ postulate”) was accepted for centuries as self-evident [2]. Why shouldn’t it be anyway? It is self-evident (this is a key phrase used for all axioms) that parallel lines never meet. And it is also self-evident that from one line only one parallel line can be drawn. It is quite interesting though that people – from the very beginning – felt quite uneasy with that axiom (and not the other four). Somehow, they felt (intuition?) that something was wrong with this axiom. That is why there were many attempts to deduce it from the other four as a theorem, with all the efforts failing. So the years passed and for centuries after centuries this axiom was part of the geometry everyone knew and used.

What is important in the case of the Euclidian geometry, is that geometry was not just ‘geometry’ back then. It was the tool used for doing math as well. Long before algebraic notation, mathematicians used geometry to calculate the squares and cubes of number simply by designing… squares and cubes. In that sense the Euclidian geometry and its validity was often correlated with the axiomatic validity of the known mathematics. This idealistic picture was soon to change with changes not only in mathematics, but in geometry as well.

Eventually, it was proved that the 5th axiom cannot be proved, i.e. that it was indeed an axiom and not a theorem based on the previous axioms. This opened the path towards other types of geometries in which we either have more than one parallel lines to a certain straight line, or no parallel line at all. Non-Euclidian geometries soon gained momentum and many practical applications to various sections of science, like in the Theory of Relativity in physics, were revealed. Again, the details of the other geometries are mute. What is of essence here is that the change of an axiom is not a matter of change in the observable phenomena, but purely a matter of choice. Can you imagine of a geometry where there are only three parallel lines to a straight line? There you go! Congratulations on your new geometry!

Axioms turning into dogmas.

What does the above example show us? In short, the obvious: The more one thinks of something as self-evident the harder it is for him to discard it. It took us literally thousand years to change the 5th axiom of Euclid and yet, the moment we did, the new way of thinking bred many new children. What was initially the basis of scientific thinking, ended up hindering scientific thinking. This is expected and totally human in nature. Our mind is very prone to prejudice. One needs to actively pursue being open-minded in order to be so.

How can we change axioms though? This is a question that could baffle people outside the domain of science and yet it is one of the easiest questions to answer. Quite simply, an axiom can change if you just change it. There is no other way to select a different starting point for your theories besides selecting a different starting point for your theories. It sounds tautological in nature and it is; tautology is anyway the only truth we can be certain about from a philosophical point of view. This way of changing an axiom was used when the 5th axiom of Euclid dead-end was reached: In an extreme simplification of the story, people simply decided to see what would happen if they opted for a different thesis regarding the existence of parallel lines and new geometries emerged based on these new options. The new axioms were as unproven as the old one. And yet, they too helped build a new theory which seemed consistent (waiting for Gödel to prove otherwise – see below) and had practical applications.

The open questions regarding what is valid and what is not valid were just made more intense with the new ‘discoveries’. If it is so easy to change a basic axiom and produce equally valid theories, then what does that imply for the truthfulness of the axioms per se? Are they just ad hoc selected cornerstones for the theories we want to build and which can be changed with others at will? Are we limited in any way regarding their selection? If such a change can easily happen in one of the most important and fundamental areas of science what does this mean for other areas where the basic principles are still in open debate? One could argue that other areas of science – like physics – are based on evidence; but again wasn’t the parallel lines axiom based on purely empirical evidence that two parallel lines never meet? And let us not forget the practical applications of the (now) three different geometries we have, indicating a strong connection of the theory to actual life which cannot be easily ignored.

Having in mind all of the above, it is important to examine the other basic cornerstone of science besides mathematics: Logic.

We must forget how to think in order to think!

 ~ Harmonia Philosophica

4.1.2 Logic as Organon

Aristotle founded Logic as an Organon (Όργανον, Greek for ‘tool’) in his work with the matching title (“The Organon”) for the first time [3]. In this work he managed to document the basic types of logical syllogisms and formulate the basic rules with which these syllogisms could produce valid conclusions based on some initial premises. This work helped formulate the basis of mathematical logic for the next centuries, only to be amended with new elements rather recently. Even today when we think logically we instinctively use these rules, which are generally so much accepted and embedded in our thinking that are almost automatically seen as valid. However, as in the geometry axioms mentioned above, extra caution should be exercised whenever something is seen as self-evident.

Despite the extensive use of logic from the time of ancient Greece until today, the actual usefulness of logic eludes us. Even Aristotle himself did not know how this ‘organon’ would be used for. For some it would be seen as a linguistic instrument to drive conclusions without any relevance to the philosophical concept of the “truth” whatsoever; a merely game which allows us to create new conclusions based on the (potentially erroneous) input we give to its mechanism. Anyway, it is true that logic is as good as its premises. For others, logic is the basic tool to reach the truth and the high peak of human thought throughout our history on this planet. To understand what is the case we need to take a step back and see logic from a different perspective.

If we examine logic more carefully, we will discover that even logic has axioms on its own. For example, the Law of Excluded Middle (LEM) is one of the basic laws used not only by Aristotle but also today by modern mathematics: In essence this law (remember, people have the bad habit to refer to axioms/ principles as “laws”) states that a logical proposition is either True or False (but never both or neither). This sounds like very logical and common sense, however in science nothing is (or should be) common sense. That is why this principle is used as an axiom in logic; it was also the basic element of Peano arithmetic, which is what we essentially use today in mathematics. Brouwer however chose not to accept this as self-evident in his intuitionistic mathematics and in this way attempted to build a different area of mathematics, even though historically this did not work out as intended due to mainly non-mathematical reasons.

4.1.3 Axioms in modern mathematics

As mentioned above, modern mathematics are based on axioms; with the more important ones being related to mathematical logic. Those axioms played (and still play) a major role in the attempts to formulate the foundations of mathematics in logic, an attempt the beginnings of which many trace back to Russel (Logicism). These efforts – regardless (or perhaps because) of their inconclusiveness – were very fruitful in seeding the scientific thought with perspective regarding what is or what could qualify as a founding principle for a specific field of knowledge.

This debate over the foundations included many other principles of mathematics. For example regarding set theory – initially proposed by Cantor and regarded as one of the building blocks of modern arithmetics – there were (and still are) many discussions regarding the overall validity of the set theory and its premises. Cantor started his quest for the theory by doing what every scientist should to: Question the obvious. And the obvious in this case stated that the whole bigger than the parts. This simple and ‘self-evident’ truth was at the end discarded; we now ‘know’ that the set of e.g. integer numbers is not larger than the set of positive numbers which are just a part of the first set. The counter-intuitive basis of Cantor’s theory caused great dispute, with the most infamous one being the dispute between Kronecker and Cantor. The results of their clash resulted in the modern set theory being accepted across the mathematics society, something we today take for granted. It is interesting to note here that foundations forming with a bang usually end up being accepted in silence by the generations to come.

Questioning the obvious is hard in the context of this silence. After the foundations of algebra took shape, modern mathematics based on the set theory were also formulated. But the Set theory – as any other – has axioms. Axioms leading into paradoxes (see Russel’s paradox). In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell’s paradox. Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics. Zermelo–Fraenkel set theory with the axiom of choice included is abbreviated ZFC, where C stands for “choice”, and ZF refers to the axioms of Zermelo–Fraenkel set theory with the axiom of choice excluded [4].

There are many equivalent formulations of the ZFC axioms; for a discussion of this see Fraenkel, Bar-Hillel & Lévy 1973. For illustration purposes only, a set of ZFC axioms is documented below. The following particular axiom set is from Kunen (1980). All formulations of ZFC imply that at least one set exists. Kunen includes an axiom that directly asserts the existence of a set, in addition to the axioms given below (although he notes that he does so only “for emphasis”) [4].

ZFC axioms list [4]

  • Axiom of extensionality
  • Axiom of regularity (also called the axiom of foundation)
  • Axiom schema of specification (also called the axiom schema of separation or of restricted comprehension)
  • Axiom of pairing
  • Axiom of union
  • Axiom schema of replacement
  • Axiom of infinity
  • Axiom of power set
  • Well-ordering theorem (the Axiom of Choice is equivalent to that)

One can easily find out the axioms of any other theory; they are indeed a fundamental element for every theory anyway. As mentioned already, their existence per se implies nothing regarding the validity of the theories built upon them. All theories which have their foundations on such unproven theses can and do have practical applications.

After someone realizes the plethora of axioms used by a theory, some ‘simple’ and ‘obvious’ questions come to mind: Can there exist a theory that is based on arbitrary axioms and not have such practical applications? Should we choose the axioms with a specific ‘common sense’ (or instinct) so as to have ‘valid’ theories? Is there a limitation on how we choose axioms or is it that ‘everything goes’, to paraphrase Feyerabend when he was talking about the anarchy which rules the scientific method?

By examining other realms of science and, especially, evidence-based ones will allow us to easier detect the methodological limitations (or even worse, the inexistence of such) of modern science.

4.1.4 Axioms in modern physics

For many, mathematics is simply a tool and not a science per se, at least not as physics is. The first can be based on arbitrarily selected axioms but the latter is based on observations and evidence. This picture is totally false. By examining how physics formulates and adheres to specific principles it will be made evident that physics also has its own axioms that can be changed much more easily than many people believe. To exhibit that, we first need to show the way physics selects these principles and show how potential changes in those principles can indeed lead to equally valid pictures for the cosmos, in a similar way as the change of axioms in geometry resulted in equally valid geometries.

To begin with, physics is – as geometry – based on several assumptions. These assumptions, when used widely are promoted to what we call ‘principles’, which play the similar role that axioms play in mathematics. Some of these principles are difficult to detect since most of them (especially the fundamental ones) are used in every piece of research without any explicit reference to it. These principles usually reflect specific philosophical dogmatic beliefs, which for many – especially those who adhere to them – seem self-evident.

As a side note, it must be noted that the principles on which modern science is based are often called ‘presuppositions’, like in the PEL (Presuppositions, Evidence, Logic) model [5]. The nomenclature though does not have any effect on the essence of the matter in hand. These presuppositions/ principles/ axioms are all some unproved statements which are taken for granted and on which we build the theories we build. From here on this paper will refer to the presuppositions as either axioms, assumptions or principles, recognizing that the word ‘axiom’ is mostly related to mathematics and geometry. The reader should be aware that what we are trying to do here is to examine the essence of the connection between science and the truth. In that quest, words are a hurdle that we must sooner rather than later overcome.

Terminology note No. 3: Principles, axioms, assumptions or presuppositions are used interchangeably in this paper from hereon – all implying unproven assumptions that we take for granted when developing a scientific theory.

Assumptions that underlie any science – and physics in particular – may include:

  • A world external to mind exists;
  • This external world is not chaotic, it is organized;
  • The external world is knowable (intelligible), including the world beyond appearances; and, last but not least,
  • (iv) This external organized world is only material. [6]

These principles need to be accepted in physics in order for any scientific endeavor to have meaning. One cannot start measuring things in a lab if he does not believe that all things are measurable. There is no reason for the scientist to start analyzing the cosmos if he does not believe that there is some kind of order in what he is analyzing. There is no meaning in doing physics (and science in general) if you do not believe that your limited view of the cosmos has any validity whatsoever. There is no point in analyzing matter to discover how the universe works, if you do not believe that the universe is created by matter and matter alone.

If these seem very similar to specific philosophical ideologies, you would be right.

Philosophy is in any case the mother of science.

And the latter, as any spoiled child, want’s to ignore (or kill, if possible) its parents and behave as if it has done everything on its own. However it is this oblivion of the foundations of science which makes it so arrogant as to believe that it is founded on nothing more than ‘facts’; a current worldview which gives birth to the monster of modern scientism. Taking the abovementioned principles one by one, one can see that the basis of science is faith. Not faith in a supreme being, but in everything that makes the existence of such a being necessary: The existence of eternal universal laws, a universe in order and the ability of tiny humans to understand and comprehend the above. Newton did believe that he could understand the cosmos and he blatantly admitted that what he did was nothing more than reading the mind of God himself.

Planck did mention that if religion aims at finding God, science starts from the belief that God exists. The principles selected are selected based on nothing more than philosophy and saying otherwise would just blatantly ignore the elephant in the room: There is no way to ‘prove’ that the universe is comprehensible (intelligible) and that our limited view (via our limited senses) is correct or not. There is no way to ‘prove’ or consider as ‘self-evident’ that us ‘unimportant’ (based on the modern materialistic view) humans can in any way confer any truth from what we see with our limited senses and limited brains. Science accepts that our senses work properly. Every aspect of science accepts that the cosmos is intelligible [7]. All scientific work is based on our belief in the intelligibility of the cosmos [8] and (this goes without saying) our ability to comprehend the cosmos [9]. If we didn’t believe in that intelligibility, there would be no starting point at all to collect evidence on which science is based upon. If we did not believe that the cosmos is intelligible there would be no sense in trying to understand it anyway. And yet, for philosophers, the very notion of our ability to sense the cosmos is under scrutiny with no specific conclusion drawn yet. Such principles make as a whole the idea of scientific realism [5] which is currently the ‘dark matter’ of modern exact sciences.

The principle that all things we need to know are measurable is yet another axiom (principle) on which modern science (especially exact sciences) is almost explicitly based upon. But who can verify that what we need to know is indeed measurable? This idea is strongly related to the notion of materialism which transcends all modern science. Still, many – if not most – physicists today work in experiments while taking this principle as obvious. Another principle strongly related to the previous one is the mechanistic view of the cosmos. Even though it is centuries old and obviously not in any way proven, all scientists today look at the cosmos as if it was a well-designed machine the inner workings of which we can understand by analyzing its parts. And let’s not even go to more fundamental principles for which philosophers still debate: For example are our senses a valid window to the cosmos? Do they work in a valid manner that could lead to our truthful understanding of the universe? Or are they a distraction from the truth of the cosmos, a distraction which makes us focus on phenomena rather than the essence of existence? The catalogue could go on forever.

And there are many more principles to add to the above. The fact that science today does not mention them explicitly makes it extremely hard to detect them, but they are there. Poisoning our thought to the point that we believe that it is not poisoned. Take for example the simple notion of ‘Things change’. If Parmenides was alive he would argue that this is an assumption we should not take lightly[3]. But science does believe in the notion of ‘change’. If it did not there would again be no meaning in doing science. (Religion on the other hand is very close to the eternal view of One made by Parmenides – this will be examined further in the latest chapter) The existence of time is another basic axiom (principle) used by modern physics. Even though time is one of the most elusive philosophical notions stirring wide debates among philosophers on its existence, physics takes it for granted and attempts of scientists to disprove its validity (e.g. Gödel who eliminated time in one of his proof for General Relativity in a revolving universe) are just considered as interesting and yet meaningless games.

The basic idea that all the above try to illustrate should be evident to the reader at this point. Non-proven philosophical principles are currently driving the quest for knowledge and we should be very careful as to how we use those principles.

Humans should try to think freely. But is this possible? Can we ever think without any axioms? Can we formulate science without principles? The thesis of this paper is that we can by using science. Although this science was not actually called that way a long time ago…

4.2 Questioning the assumptions

How axioms/ principles change in order to give birth to a new theory is a matter of debate. Some believe that the changes can only happen within a very limited frame set by our experiences and the observational data at hand. Extreme voices speak about our ability to arbitrary select axioms. The truth – despite to what one might expect – lies not in the middle.

4.2.1 Which assumptions? There are no assumptions!

As already mentioned, axioms are not provable principles which we use so, by definition, they cannot be not related to what we call truth. The notion of truth for philosophy has been referring to eternal certainties and one can never be certain if the axioms he uses are related to anything true. It might be the case that in a specific case an axiom is accidentally related to the truth, but this would only be accidental. There is no way to systematically and scientifically know whether a specific axiom/ principle holds any special connection to the notion of truth whatsoever. And what is important is that the non-existence of this relationship does not affect at all the use of the theories built on those principles.

Some examples will better illustrate this.

4.2.2 Questioning the obvious

Science today is based – as mentioned already – in many assumptions. These assumptions (presuppositions) are so fundamental that rarely do people question them. Isn’t it obvious that you see a table? Isn’t it obvious that crossing the street without looking for incoming cars might get you killed? Do you need more evidence or proof to say that “this chair that you see with your own eyes” exists? Discussions about such things usually end up in arguments using the ‘obvious’ as evidence of the obvious. Science is based on some very few presuppositions which in any case are closely related to what we call ‘common sense’ [5]. Can or should we question common sense? Even children have it [5].

But the obvious can be a trap for free thinking.

Are we to trust a kid’s opinion on the cosmos because it is pure? Fine. But let us also trust its opinion that unicorns exist (by the way, as Parmenides said, we wouldn’t be able to even talk about them if they did not exist). Are we to trust common sense on the evidence we have and their interpretation? Should we trust this common sense when it cries out that someone must have created this cosmos? Are we to trust our sensory input? But what happens if someone else has a different sensory input? Are we just going to discard people with different common logic as ‘crazy’ so as to verify our own perception? Can we say that our senses reveal anything about the cosmos when they are so limited? Touch a table. Feel it. And yet, the table is consisted of atoms which are essentially empty. What does that say about the validity of the sensory input that we get? Touch that table again. Do you sense the bacteria crawling on it? If not, what does this mean about the validity of this sensory input? Are we to trust our belief into an objective cosmos and laugh at those who claim that this cosmos is just an illusion? If we have no solid proof, there is no room for laughter. What is common sense today is history tomorrow. Quantum mechanics has provided many counter-intuitive examples which totally break down what we would call ‘common sense’. And no, we cannot use the argument ‘if we question our senses then we do not have science’ as an argument. We cannot have the result (science) as an argument to justify itself.

Let us continue the analysis by questioning some more obvious premises of science.

4.2.3 Are there axioms of higher validity?

As already mentioned, axioms do not hold any special connection to the notion of truth. Having said that, one would wander what could be the limitations in selecting those axioms be. And if he is unable to find such, he would be right: There are no limitations. Any set of whatever axioms or principles can help us build a new theory (by logically deriving theorems and theories from those axioms). However, can arbitrarily selected axioms lead to anything of use? Could randomly selected axioms lead to the formulation of a useful theory?

Even though axioms and principles are seen as non-provable propositions, nevertheless there has always been a common belief among scientists that they must have some connection to nature and reality. (by the way, the belief in the existence of an objective reality is another major assumption of modern science) For example, when recently three physicists discovered a way to connect eigenvectors and eigenvalues [10], thus contributing in a major way in the field of mathematics, this was hailed as another proof that mathematics must in any case be connected with nature. The same applies for physics, which is much more interrelated to nature than mathematics.

To examine the validity of the proposition “All axioms must have a connection with nature to produce useful theories” (where by nature we mean the connection with reality) we must find some counter-examples. If we do find cases of theories which do not have any connection whatsoever to nature and yet produce useful theories, then we would have shown that having a connection with nature is not a required component for a practically useful theory.

Such examples were already analyzed in the previous section and we can easily find more. For example the mathematics we know have multiple practical applications and they contain negative numbers, which we learn to handle from first grade. The mathematics we know have multiple practical applications and contain irrational numbers, which we learn to handle from fifth grade. And yet, there is nowhere in nature that one can find -1 oranges…

Besides the above, it is true that if we follow the modern scientific paradigm on the value of random processes in producing valid results (e.g. random mutations play a vital role in the creation of life, at least according to the main paradigm in biology, always through the rules of natural selection) or on the possibility of creating the whole cosmos from random fluctuations (see for example the theories which want the cosmos to be created from random quantum fluctuations of the void of space), we can easily think of random axioms being the seed to create something really powerful and magnificent. If random fluctuations can produce a cosmos with universal laws science can discover, why deny the possibility that randomly selected axioms can create a useful theory? (something which in any case is much less difficult to exist than a cosmos so finely tuned and with so universal laws as our own)

To this, we must add another important note: The notion of ‘usefulness’ is something that is subjective. Even the most useless of theories for me could be extremely useful for someone else and vice versa. Surely today’s materialistic civilization finds modern science theories as useful, but again a more spiritual civilization could render all those theories as completely and utterly useless. Having accurate GPS signals does not solve human everyday problems anyway.

Last but not least, why in any case should we use the criterion of the ‘usefulness’ in the first place? (remember, questioning everything also entails questioning yourself) The most critical and important things in life are useless. Or at least we do not currently know their usefulness. Are our grandparents useful? Are we useful to anyone else in the cosmos? Is life per se useful? Why should an axiom be judged scientifically based on its usefulness? Would that be a scientific argument to begin with?

4.2.4 Research and intuition

For Husserl, it is clear that the ultimate principles must be epistemological principles that are a priori eidetic laws (Husserl 1984, 235–36). Husserl used a rather unambiguous terminology in order to point out that there is one principle that is more fundamental than all the others. This is his principle of all principles. As Husserl said, “No conceivable theory can make us err with respect to the principle of all principles: that every originary presentive intuition is a legitimizing source of cognition, that everything originarily (so to speak, in its “personal” actuality) offered to us in “intuition” is to be accepted simply as what it is presented as being, but also only within the limits in which it is presented there”. In other words: Every originary presentive intuition is a source of immediate justification [11]. This is very close to what was briefly mentioned in the beginning regarding the epistemological anarchy proposed by Feyerabend. And was also the cornerstone of the vision of Brouwer regarding the foundations of mathematics.

Poincare was also a proponent of the use of intuition in science [12]. The pre-intuitionists (in which Poincare was included, others use the term semi-intuitionist [12] [13]), as defined by Luitzen Egbertus Jan Brouwer, differed from the formalist standpoint in several ways, particularly in regard to the introduction of natural numbers, or how the natural numbers are defined/ denoted. For Poincaré, the definition of a mathematical entity is the construction of the entity itself and not an expression of an underlying essence or existence. This is to say that no mathematical object exists without human construction of it, both in mind and language [14].

This sense of definition allowed Poincaré to argue with Bertrand Russell over Giuseppe Peano’s axiomatic theory of natural numbers. For example, there had been discussions on whether the property of induction is valid or not.

The five axioms of Peano are [15]:

  1. Zero is a natural number.
  2. Every natural number has a successor in the natural numbers.
  3. Zero is not the successor of any natural number.
  4. If the successor of two natural numbers is the same, then the two original numbers are the same.
  5. If a set contains zero and the successor of every number is in the set, then the set contains the natural numbers.

The fifth axiom is known as the principle of induction because it can be used to establish properties for an infinite number of cases without having to give an infinite number of proofs. In particular, Peano’s fifth axiom states [15] [14]:

  • Allow that; zero has a property P (= it belongs to natural numbers);
  • If every natural number less than a number x has the property P then x also has the property P.
  • Therefore every natural number has the property P.

This is the principle of complete induction, which establishes the property of induction as necessary to the system. Since Peano’s axiom is as infinite as the natural numbers, it is difficult to prove that the property of P does belong to any x and also x + 1. What one can do is say that, if after some number n of trials that show a property P conserved in x and x + 1, then we may infer that it will still hold to be true after n + 1 trials. But this is itself induction. Hence, the argument is a vicious circle. From this Poincaré argues that if we fail to establish the consistency of Peano’s axioms for natural numbers without falling into circularity, then the principle of complete induction is not provable by general logic. Thus arithmetic and mathematics in general is not analytic but synthetic. Logicism thus rebuked and Intuitionism is held up [14].

To cut the long story short, the issues debated by intuitionists and constructivists in relation to the validity of long held assumptions in mathematics are well-known [16]. The discussions surrounding this matter are extremely interesting for someone to follow; there have been for example cases where there is debate of whether using the Platonic system of numbers we use (instead of the intuitionistic one) results in our difficulty in describing the notion of time in physics [17]. The purpose of this paper is not to describe them all, but just to document the very existence of such debate even for many self-evident and widely used principles.

No principles can be accepted without faith in their validity (again, this is not an argument but a tautology actually). And this faith by itself is based on intuition. If we are to trust the intuition we have however, then we must come in terms with some very uncomfortable truths regarding science that could lead us – temporarily – away from it. Truths which can result from the decomposition of science as we know it, based on the various tools we currently know (like induction) and its re-composition based on a much ‘cleaner’ view of things as they are. In metaphysics, we anyway deal with things that exist ‘as they are’. And the main sector of human thought which deals with metaphysics has always been religion [18].

It could be that the correct path is not to discard science, but to rediscover it.

The next lines of this paper will discuss how this can be performed.

4.3 Irrationality as the path to follow?

The question is simple. And, thus, as all simple questions, exceptionally difficult to answer.

How can mathematics and science progress and change paradigm in order to be able to reach the truth? The answer could be more irrational than we might have thought, but because of this, much more logical than it could ever be if we chose to follow logic. Because in any case logic will have rules, which you will have to accept on the irrational basis of belief in them. Whenever you start using assumptions then the whole system you have developed will always be in question. But the truth cannot be in question. If you use axioms and principles that cannot be proved, then your theorems will never be proved as well. But can the truth be left unproven?

Modern man understands that the above lead to a different path than the one we have taken thousands of years ago. And he is just afraid to follow that path because of the uncertainty it poses. (do not underestimate the more practical reasons which have a lot of times hindered scientific progress: the fact that all science and scientists today are based on these assumptions that we now question! It is hard to get funding to research on why all current research could be obsolete…)

Questioning things is a difficult path that few can or are willing to take. It is much easier to stand behind unproven assumptions and then move on with confidence as if you have proved everything. Modern civilization’s arrogance along with deep hostility towards anything religious, have fed the monster of scientism to a level that it is no longer distinguishable from science per se.

And we must kill the beast if we are to go back to the right path…

4.3.1 Untrustworthiness of axiomatic-founded science

All justifications of science using assumptions like the ones mentioned above are essentially using the same reasoning: “These things are common sense. If we cannot trust them, what can we trust? Even kids can understand that these things are true”.

But are we really ready to go to kids for the foundations of science? Children, with their raw wisdom, can be truly terrifying for modern scientists. Because kids can be irrational. And as they can “know” that 1 + 1 = 2 (something which took more than 300 pages to Whitehead and Russell to prove by the way, again based on unproved assumptions/ axioms) they can also easily know that unicorns exist.

People today do not believe in unicorns or miracles.

Because we are too logical to know life.

But we do believe in assumptions which lead to research funding…

Because we are too vulgar to know death.

Others could also argue: “We could not even have science if we questioned such fundamental things as the input of our senses”. This especially is a very common and popular argument against any attempt to question the assumptions of science. This argument is based however on the dogma that science (as this term is referring mainly to the ‘exact sciences’ today) is and should be the only tool to search for the truth (a.k.a. ‘scientism’, which we must remember that it is a dogma and by no means a proven position).

The answer this argument is simple: So?

Why should we not accept the obvious because we could not then have science? Yes, the fact that we cannot prove the validity of our senses for sure makes us more anxious. But, so what? Should that make us not accept the elephant in the room?

It is crucial that we not lose sight of the questions science cannot ask, let alone the ones it cannot answer [19]. If we try to free our thought from axioms and dogma’s, then perhaps we should also try to remove the biggest dogma of them all: that science, as we know it today, is the only method of thinking that can lead to answers.

Searching for the “new” science that could overcome the limitations of existing science is the next logical step in our quest.

4.3.2 The vision of Brouwer revisited

In mathematics, the battle between Platonists, formalists and constructivists/ intuitionists in mathematics still rages on. Even though the formalists have officially won (there is no school today questioning the law of excluded middle or teaching that formal mathematics may not lead someone to valid proofs), specific elements of other ways of thinking still persist. We are still taught that we should construct our proofs, we are still watching in awe when a mathematician finds out a new theory or develops a new idea (see for example the Riemann hypothesis [28]) by intuition alone and others struggle for centuries to prove his thesis (see for example the Riemann hypothesis). Despite the use of irrational numbers and negative numbers every day, we still discuss about philosophy and the idea of truth and reality, regardless of the practical usefulness of such constructs.

Platonists – Constructivists – Formalists definitions: Platonists believe that the ‘truth’ is somewhere ‘out there’ for us to discover. On the other hand, constructivists believe that only what we can practically construct is worth analyzing and talking about (that is why for them the notion of infinite has no meaning – the same goes for irrational numbers). Last but not least, the formalists care for neither of the above! They only care about the rules of the game. And as long as you set the rules, then you can play… [20] [24] [26]

In Brouwer’s original intuitionism, the truth of a mathematical statement is a subjective claim [21] [25]. Accepting this should be our first step towards realization of the need for a new science. What is obvious is the source of all potential errors. The presuppositions one uses are really dangerous. You cannot easily question what you have been taught to take for granted.

However, the vision of Brouwer is limited. It reaches up to a point, but fails to reach the final destination. For us to reach our destination, we must let go of all the restraints put on us by thinking in general. As for Brouwer the Pre-Intuitionists failed to go as far as necessary in divesting mathematics from metaphysics, for they still used principium tertii exclusi (the “law of excluded middle”) [14], we must say the same for Brouwer himself.

Even though he goes a long way in discarding basic assumptions, he still uses the most basic of all assumptions: That thinking itself is something that can lead to valid conclusions! Brower and his followers afterwards tried to formulate arithmetics without the axiom of the excluded middle [22]. In the same way, we must try to formulate science in general without the axiom that scientific thinking itself is what is needed to understand the cosmos!

It is a daring attempt, but true philosophy should not be deterred in the face of difficulty. I would say that the opposite is true: Whatever seems like the hard path, this should be the path we should try to follow.

4.3.3 Credo quia absurdum! (Shestov)

Shestov, one of the greatest thinkers of modern time, spoke eloquently about the irrational. His objections to logic were all too logical to deny. “If someone requires you to adhere to his logic in order to understand his arguments, then what value can those arguments have?” he wandered [23]. This is something so obvious that we tend to forget it as we speak about science today. Every theory we have is based on axioms and yet we always fail to truly understand what this simple fact means.

What is logical for you could be illogical for me and vice versa. And if this happens, this will not be due to a caprice, but due to fundamental differences in the assumptions we make when we start analyzing the problem at hand.

For Shestov the motto “Credo quia absurdum” holds more truth than one can ever realize at first glance. There is nothing logical in logic, whereas there is deep wisdom in the irrational. For while the former tries to build castles on moving sand, the latter digs deep inside the depths of existence itself in order to build on the most concrete foundations that there can be: the cosmos itself. And in that sense, one can only believe something not because it is not irrational (i.e. it is rational) but exactly because it is irrational!

What I mean with that will be more evident later on.

For the moment, just keep the idea lingering in your head…

To go back to the problem of the scientific foundations, it seems we are in a stalemate since there is no way to determine which assumptions are the best to use. Yet, this is one of the cases where the difficulty to answer a question denotes a third option we rarely consider in today’s knowledge-addicted civilization…

4.3.4 Religion as non-axiomatic Science

When a question – like the one above – is hard to answer, one should consider the obvious. Besides the various possible answers to the question, there might be another solution to the problem: Perhaps the question itself is wrong! Science is a way to interrogate nature [5]. And this can and should be done with no constraints whatsoever. Many people claim that science is great because it is based on so few assumptions [5]. Why not make it even greater and base a new science on zero assumptions?!

At the end, the meaning and the purpose of the cosmos are not to be analyzed with science. The truth is not to be seen with our eyes or sensed with our touch. As Jung wisely pointed out, our self is the only element of the cosmos that we experience without the mediation of anything. And this is the only truth we can ever lay our hands onto. Could it be that this is the only truth worth pursuing? Only time will tell. If time exists after all. At the end, what is certain is that we must question everything in order to reach the truth – if such a notion even exists. And this questioning should consider nothing as self-evident, not even our logic or senses. This seems like a heavy toll to pay. And it is. But the destination is of such importance that this toll is relative small in exchange.

Religion is a way to view the cosmos without assumptions or presuppositions. In that sense, it is much more scientific than science as we know it today. It just entails accepting the cosmos (weirdly enough in the same way science today accepts the intelligibility of the cosmos). Pure thought can only be possible without thought. As Shestov once explained, whenever we try to understand something we destroy it in our effort to make it fit into those little boxes we have built in our brains.

Religion is about accepting what we know. It is not about analyzing and understanding, but about being part of the cosmos as it is. Every scientific theory is based on unproven axioms, thus nothing. And this ‘nothing’ is nothing more than our acceptance of the obvious: The cosmos is here for us to know. And we can know it only because we are part of God himself! Religion has said that a long time ago. We have believed in our godly nature for thousands of years. Until we started denying our self. And resulted in a cosmos void of any meaning, except the comical belief in our science. There is no logic entailed in believing. Only the acceptance of the things your heart has already seen. We seek to understand the cosmos, but to paraphrase Pascal, we wouldn’t be searching for understanding the universe if we hadn’t already known it…

The eternal mystery of the world is its comprehensibility…

The fact that it is comprehensible is a miracle!

~ Albert Einstein [27]

5. CONCLUSION

I went for dinner with some friends from work once. At some point someone mentioned that a university did some empirical research to determine whether a tree falling in a forest void of humans will actually make any sound. I do not know whether that was a true story. I do know that everyone laughed at that though. And then, they kept on eating. But I wanted to cry. We are so much accustomed to our assumptions that even at the slightest hint of them being wrong we just… laugh!

Imagine two small worms living all their lives inside the earth. Discussing about philosophy. Being so positive that their senses are telling them all they need to know about the cosmos. Laughing at the possibility that this is not the case.

Questioning the validity of science or even our very senses seems like an exaggeration. But so is the quest for truth. If we want to play ball in the big league, then we should be prepared for some heavy loses. At the end, we might lose what we cherish the most (science), only to discover that all this time we missed something much more important.

Plato once told us about a cave. And we laughed at those inside the cave. But we never understood that we should also laugh at those outside the cave. If those inside are not getting valid inputs, what makes us so certain that those outside do? Why should the shadows inside the cave be invalid but the shadows outside it valid?

We have used to see science as the only way out of the cave.

But we have forgotten that it was originally called religion…

We have accustomed to think that thinking is the only way to reach the truth.

But we have forgotten that thinking is based on non-thinking…

Yes, the cosmos we live in is irrational.

Yes, the fact that it is intelligible seems like a miracle.

If we try to analyze it, we will end up denying it.

For there is nothing which can be said to prove it.

Accept it we must!

For we are part of it.

And believe it, exactly because of its irrationality!

We can understand the mind of God.

Only because we are part of Him!

Remember?

Credo quia absurdrum!

Science is (was) based on it! (or should we say Religion?)

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[1] The term “phenomena” is the right term and not “fact” which is widely used in science-related articles. We can never be certain of the truthfulness of what we can experience via our senses. This is an important question that is outside the scope of this paper.

[2] Geometry and mathematics were inherently connected up to very recently.

[3] According to Parmenides, change is just an illusion. For the great thinker there is no way for A to change to B, for if it does then it wouldn’t still be A. And there is no way for something which does not exist at all to come into existence or for something which exists to perish into nothingness.