February 14, 2014

WE ARE ALL DESIGNISTS NOW:

Is the Universe a Simulation? (EDWARD FRENKEL, 2/14/14, NY Times)

Many mathematicians, when pressed, admit to being Platonists. The great logician Kurt Gödel argued that mathematical concepts and ideas "form an objective reality of their own, which we cannot create or change, but only perceive and describe." But if this is true, how do humans manage to access this hidden reality?

We don't know. But one fanciful possibility is that we live in a computer simulation based on the laws of mathematics -- not in what we commonly take to be the real world. According to this theory, some highly advanced computer programmer of the future has devised this simulation, and we are unknowingly part of it. Thus when we discover a mathematical truth, we are simply discovering aspects of the code that the programmer used.



MORE:
Mathematics: Why the brain sees maths as beauty (James Gallagher, 2/12/14, BBC News)

Mathematicians were shown "ugly" and "beautiful" equations while in a brain scanner at University College London.

The same emotional brain centres used to appreciate art were being activated by "beautiful" maths.

The researchers suggest there may be a neurobiological basis to beauty.

The likes of Euler's identity or the Pythagorean identity are rarely mentioned in the same breath as the best of Mozart, Shakespeare and Van Gogh.

The study in the journal Frontiers in Human Neuroscience gave 15 mathematicians 60 formula to rate.

One of the researchers, Prof Semir Zeki, told the BBC: "A large number of areas of the brain are involved when viewing equations, but when one looks at a formula rated as beautiful it activates the emotional brain - the medial orbito-frontal cortex - like looking at a great painting or listening to a piece of music." [...]

Mathematician and professor for the public understanding of science, Marcus du Sautoy, said he "absolutely" found beauty in maths and it "motivates every mathematician".

He said he loved a "small thing [mathematician Pierre de] Fermat did". He showed that any prime number that could be divided by four with a remainder of one was also the sum of two square numbers.

So 41 is a prime, can be divided by four with one left over and is 25 (five squared) plus 16 (four squared).

"So if it has remainder one it can always be written as two square numbers - there's something beautiful about that.

"It's unexpected why should the two things [primes and squares] have anything to do with each other, but as the proof develops you start to see the two ideas become interwoven like in a piece of music and you start to see they come together.

He said it was the journey not the final proof that was exciting "like in a piece of music it's not enough to play the final chord".

He said this beauty of maths was missing from schools and yet amazing things could be shown with even primary school mathematical ability.

In the study, mathematicians rated Srinivasa Ramanujan's infinite series and Riemann's functional equation as the ugliest of the formulae.
Posted by at February 14, 2014 6:40 PM
  
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