Children differ substantially in their mathematical abilities. In fact, some children cannot routinely add or subtract, even after extensive schooling. This new paper proposes that math disability arises from abnormalities in brain areas supporting procedural memory. Procedural memory is a learning and memory system that is crucial for the automation of non-conscious skills, such as driving or grammar. (1)

We learn rules.

We then learn math based on rules which we memorize.

Failure to do so makes us “bad” at math. And yet why should that be a problem? Why should we “learn rules” and memorize them? Why should we interpret or measure the cosmos based on these rules?

In a world where everything is One and non-dividable we try to learn the rules of division. In a world made out of oblivion, we try to base our civilization on remembering…

We can assume that children learn to count starting with one and followed by the lists of numbers in ascending order of cardinality (one, two, three). But besides numbers, in languages there are more words that express quantity such as all, some, most, none, etc., the so-called quantifiers.

A recent study into childhood language in 31 languages, in which UPV/EHU researchers have participated, has reached the surprising conclusion that in all the languages studied, children acquire the quantifiers in the same order, irrespective of the properties of the language in question. The children acquire the words referring to totality earlier than the ones covering only one part of the set. (1)

Babies learning the notion of total. Then growing up. Learning the notion of numbers. Then the notion of infinite. How logical is that sequence? We learn numbers and we only meet “infinite” when we are graduate students. And yet, we accept it with no effort against all odds. We find it difficult to understand numbers and yet easy to accept a notion that is not even close to be observed or experienced by our “limited” nature. And yet here we are. Talking about the One, about infinite. Infinite is supposedly a “difficult” advanced notion which is part of university curriculum and yet we had already learnt it. When we were kids. When we thought about “totality” as a notion only because we already knew it…

We are hardwired to see the One.

We are then forced to see the parts.

We fight against ourselves every day.

We learn to deny our nature every day.

In order to learn, we must unlearn what we have learnt.

It’s easy to understand why natural selection favors people who help close kin at their own expense: It can increase the odds the family’s genes are passed to future generations. But why assist distant relatives? Mathematical simulations by a University of Utah anthropologist suggest “socially enforced nepotism” encourages helping far-flung kin.

The classic theory of kin selection holds that “you shouldn’t be terribly nice to distant kin because there isn’t much genetic payoff,” says Doug Jones, an associate professor of anthropology and author of the new study. “Yet what anthropologists have observed over and over is that a lot of people are pretty altruistic toward distant kin”.

Jones seeks to expand the classic theory with his concept of socially enforced nepotism, which he calls a “souped-up version of the theory of kin selection” in his study published June 15, 2016, by the Public Library of Science’s online journal PLOS ONE.

Socially enforced nepotism “depends on the moral regulation of behavior according to socially transmitted norms”, he writes in the study.

The findings suggest that “a lot of why you help your kin, including distant kin, isn’t necessarily because you like them so much but because it’s your duty, your responsibility, and other people care whether you do it”, he says. (1)

Mathematics to calculate compassion. Numbers to measure ethics. Some years ago this would be considered blasphemy. Now we are gods and nothing is considered blasphemy. Now we are gods. Because we have killed God. Not with weapons or philosophy. But with sheer stupidity. We simply chose to believe in equations. We simply chose to believe in numbers.

Now nothing exists.

Except numbers.

One. Zero.

Well, mainly zero.

All other numbers are simply additions to zero.

In the old times philosophers believed in One. Once upon a time we started believing in Zero. And mathematics were created.

Alexander Grothendieck, who died on Nov. 13 at the age of 86, was a visionary who captivated the collective psyche of his peers like no one else. To say he was the No. 1 mathematician of the second half of the 20th century cannot begin to do justice to him or his body of work. Let’s resist the temptation to assign a number to a man of numbers. There are deeper lessons to be learned from this extraordinary human being and his extraordinary life.

In mathematics, he revolutionized the field known as algebraic geometry. (1)

Once upon a time there was a wise man. Who burned 25,000 pages of manuscripts before disappearing from the face of the Earth.

Once upon a time there were people who were important.

Not for what they published but for what they did not.

We lack those people today.
Burn all the bookstores.
Discover yourself…

Srinivasa Ramanujan presented two derivations of “1 + 2 + 3 + 4 + … = −1/12” in chapter 8 of his first notebook. The simpler, less rigorous derivation proceeds in two steps, as follows.

The first key insight is that the series of positive numbers 1 + 2 + 3 + 4 + · · ·can be transformed to the alternating series 1 − 2 + 3 − 4 + · · ·. The latter series is also divergent, but it is much easier to work with; there are several classical methods that assign it a value, which have been explored since the 18th century.
In order to transform the series 1 + 2 + 3 + 4 + · · · into 1 − 2 + 3 − 4 + · · ·, one can subtract 4 from the second term, 8 from the fourth term, 12 from the sixth term, and so on. The total amount to be subtracted is 4 + 8 + 12 + 16 + · · ·, which is 4 times the original series.
These relationships can be expressed with a bit of algebra.

Whatever the “sum” of the series might be, call it c = 1 + 2 + 3 + 4 + …
Then multiply this equation by 4 and subtract the second equation from the first:

The second key insight is that the alternating series 1 − 2 + 3 − 4 + · · · is the formal power series expansion of the function 1/(1 + x)2 with 1 substituted for x.

So it seems that -3c = 1 − 2 + 3 − 4 + · · · = 1/4. Now make another small calculation and voila!

But can this really be true?
Can the sum of POSITIVE numbers equal a negative one?
Can the sum of INTEGERS be a fractional number?

We tend to rely too much on assumptions. The whole science is based on assumptions. And when we rely too much on them, we tend to forget they even exist.

Watch closely. See the “proof” more carefully once more…

Srinivasa Ramanujan presented two derivations of “1 + 2 + 3 + 4 + ⋯ = −1/12” in chapter 8 of his first notebook. The simpler, less rigorous derivation proceeds in two steps, as follows.

The FIRST key insight is that “infinity” exists.

The SECOND key insight is that the series of positive numbers 1 + 2 + 3 + 4 + · · · (we CAN put these dots because of the first assumption) can be transformed to the alternating series 1 − 2 + 3 − 4 + · · ·. The latter series is also divergent, but it is much easier to work with; there are several classical methods that assign it a value, which have been explored since the 18th century.
In order to transform the series 1 + 2 + 3 + 4 + · · · into 1 − 2 + 3 − 4 + · · ·, one can subtract 4 from the second term, 8 from the fourth term, 12 from the sixth term, and so on. The total amount to be subtracted is 4 + 8 + 12 + 16 + · · ·, which is 4 times the original series.
These relationships can be expressed with a bit of algebra.

Whatever the “sum” of the series might be, call it c = 1 + 2 + 3 + 4 + …
Then multiply this equation by 4 and subtract the second equation from the first:

The second key insight is that the alternating series 1 − 2 + 3 − 4 + · · · is the formal power series expansion of the function 1/(1 + x)2 with 1 substituted for x.

So it seems that -3c = 1 − 2 + 3 − 4 + · · · = 1/4. Now make another small calculation and voila!

It seems as if c = 1+2+3+4+… = -1/12!
But this result is not logical!
So the same process could be actually proof that infinity does not exist!

Infinity…

What is that infinity which we all seek?
What is that infinity to which we all pray?
What made us think about it in a finite cosmos?

Are we humans thinking as Gods?
Or Gods thinking as humans?

Seek the finite.
And you will see the infinity staring back at you…