Solving problems. To see there are none…

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In a future characterized by algorithms with ever increasing computational power, it becomes essential to understand the difference between human and machine intelligence. This will enable the development of hybrid-intelligence interfaces that optimally exploit the best of both worlds. By making complex research challenges available for contribution by the general public, citizen science does exactly this.

Researchers developed a versatile remote gaming interface that allowed external experts as well as hundreds of citizen scientists all over the world through multiplayer collaboration and in real time to optimize a quantum gas experiment in a lab at Aarhus University. Surprisingly, both teams quickly used the interface to dramatically improve upon the previous best solutions established after months of careful experimental optimization.

But why could players without any formal training in experimental physics manage to find surprisingly good solutions? One hint came from an interview with a top-player, a retired Italian microwave systems engineer. He said, that for him participating in the experiment reminded him a lot of his previous job as an engineer. He never attained a detailed understanding of microwave systems but instead spent years developing an intuition of how to optimize the performance of his “black-box.” In this view, the players may be performing better not because they have superior skills, but because the interface they are using makes another kind of exploration “the obvious thing to try out” compared to the traditional experimental control interface.

“The process of developing (fun) interfaces that allow experts and citizen scientists alike to view the complex research problems from different angles, may contain the key to developing future hybrid intelligence systems in which we make optimal use of human creativity” explained Jacob Sherson. (1)

Intuition.

Fun.

Silence.

These have collectively produced more science than any combination of analysis, data gathering, careful structured thought ever have during the history of mankind. Feyerabend said that the scientific method has nothing to do with what we think it has. He was right and yet, scientists think he was wrong. Because scientists today like to be called scientists. And whoever likes to impose himself is never himself…

Look at Newton.

Or Einstein.

They weren’t scientists because they said so.

But because others acknowledged them as such.

Solving problems has never solved any problem.

The key to progress is not progress per se.

The key to science is not making science.

Look at this equation. But don’t try to find a solution. Try thinking of another equation instead. And then another. And then another. Until you have nowhere else to go. Until A equals A. And then wonder.

Was there anything to solve in the first place?

Gödel’s incompleteness theorem: The non-Cretan way out…

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Gödel’s incompleteness theorem is well known for proving that the dream of most mathematicians to formulate foundations for a complete and self-consistent theory of mathematics is a futile exercise.

Gödel proved that any set of axioms you could posit as a possible foundation for math will inevitably be incomplete; there will always be true facts about numbers that cannot be proved by those axioms. He also showed that no candidate set of axioms can ever prove its own consistency (1).

In essence, the incompleteness syllogism by Gödel starts from talking abour logical propositions (or mathematical propositions if you like) and ends up with a proposition that talks about the validity of… itself. This proposition which we might as well call reads something like “I cannot be proved”.

This leads to a dead-end.

If it can be proved, then it means that it cannot.

And vice versa.

So it is essentially a logically true proposition (since indeed it cannot be proved) but which cannot actually be proved within the axiomatic system at hand.

Hence, the incompleteness.

Essentially this is something the ancient Greeks have thought of thousands of years ago; something which they formulated in the famous Epimenides paradox. Epimenides was a man from Crete who said the following simple thing: “All Cretana are liars”.

Well, this ends up in the same dead-end as the proposition mentioned above. If Epimenides is truthful, then he is a liar since he is Cretan and all Cretes are liars. If he is a liar, then he is telling the truth! And, thus, he is a liar!

A self-reference paradox which essentially destroys the hope of mathematicians around the world for a consistent and full way to formulate mathematics. It is weird, but also important to mention here, that self-reference is the basis of our existence. Consciousness, our ability to speak about our self and our own existence and being, is the foundation of our essence as human beings. Without that, we would be nothing than complex machines.

But how can this dead-end be surpassed or perhaps by-passed?

Well, it cannot actually.

Unless…

You ctu right through it.

I was in a discussion the other day about the above topics and when the Epimenides paradox was mentioned, one immediate reaction that I got was the simple “So the solution is that he is not from Crete” (!)

What?! I answered. But I told you he was a Cretan.

Sure. He was.

But…

What is he wasn’t?

Then there wouldn’t be any paradox!

In the same sense…

What if the logical proposition…

“I am false”

is not a… proposition?

Then all problems would be solved!

But if it is not a logical or mathematical proposition then what is it? Well, as I said above, self-reference is not mathematics per se. It is more of a metaphysical reference to existence and being. A proposition talking about… itself is no more a proposition but an attempt to speak with the abyss. It is more God talking to humans than humans trying to talk with God. Such a thing could be many things, but ‘simply’ a logical (mathematical) proposition not.

But this is gibberish, one might counter-argue.

Sure, it can be.

(Gibberish like the Russel way out of his paradox?)

If you really think a Cretan would ever call himself a liar.

Sure, it can be.

If you accept that a proposion can ever referto itself.

But it cannot.

In a cosmos where only humans can talk for themselves.

Gibberish.

In a cosmos where mathematics cannot prove themselves.

Gibberish.

In a world where endless-loop paradoxes exist.

Paradoxes.

In a life which is full with nothing but them.

Paradoxes were the end of the hopes of mathematicians. They alone can be the ones which will instil hope in the once again.

Look around Cretan.

Tell me.

If you cannot prove that there is a sea…

Will you ever lie that you are swimming?

Learning the foundations…

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Contrary to widely-held opinion, taking high school calculus isn’t necessary for success later in college calculus – what’s more important is mastering the prerequisites, algebra, geometry, and trigonometry – that lead to calculus. That’s according to a study of more than 6,000 college freshmen at 133 colleges. (1)

Great line of reasoning. Except that we chose to stop it at a point of our choosing. How do you learn algebra, geometry, and trigonometry? Is it important to learn those or do you just need to learn their prerequisites as well?

Go back in the beginning.

To see that there is no prerequisite…

Based on nothing…

A cosmos was born…

You try to keep him alive.

But it really wants to die.

Don’t be sad.

Let that tear flow down your cheek…

Your life will soon end.

And that is the one and one prerequisite you will ever need to Be…

Measuring the cosmos… Ghosts and numbers…

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A groundbreaking experiment in physics has for the first time provided a precise measurement of a force between electrons and protons called the weak nuclear force. The value 0.0719 (give or take 0.0045) won’t mean much to most of us, but the way they did it makes way for some exciting possibilities for pushing physics beyond the scope of the Standard Model. (1)

We want to measure things in order to believe them. But it is only the truly blessed who believe things without measuring them.

The cosmos is not in numbers.

The essence of the cosmos lies in the irrationality of the numbers’ existence itself. Nothing in the universe is measurable, besides the things which do not belong in it. Only ghosts need tangible “data” for them to exist. Everything else just Is…

Look at π. It does not exist.

And yet, it governs everything…

A man draws circles on the ground.

He will never be able to measure its circumference.

And yet… Here it is…

(the circle, not the man)

Counting till the end… Numbers… Infinite… Water and fire…

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Gisin, of the University of Geneva, debates the physical reality of real numbers.

His main problem lies with real numbers that consist of a never-ending string of digits with no discernable pattern and that can’t be calculated by a computer. Such numbers (like π for example) contain an infinite amount of information: You could imagine encoding in those digits the answers to every fathomable question in the English language — and more.

But to represent the world, real numbers shouldn’t contain unlimited information, Gisin says, because, “in a finite volume of space you will never have an infinite amount of information”. Instead, Gisin argues that only a certain number of digits of real numbers have physical meaning. After some number of digits, for example, the thousandth digit, or maybe even the billionth digit, their values are essentially random.

This has big implications for the seemingly unrelated concept of free will. Standard classical physics leaves no room for free will. But if the world is described by numbers that have randomness baked into them, as Gisin suggests, that would knock classical physics from its deterministic perch. That would mean that the behavior of the universe — and everything in it — can’t be predetermined, Gisin says. “There really is room for creativity”. (1)

The nature of the world is hidden in shadows.

Behind the coldness of empty space.

Concealed by the massive planets dancing between the stars.

Hidden at the outer rim of the universe.

There lies the source of all numbers.

The source of all existence.

Infinite.

Don’t be afraid of it.

Because even the smallest drop of water.

Came out of the primordial abyss…

You are the son of water. The daughter of fire.

Sibling and mother and father of chaos.

You can only count because you know the end.

1, 2, 3, …