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Mathematicians hunting prime numbers discover infinite new pattern

scientificamerican.com

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Re: Mathematicians hunting prime numbers discover infinite new pattern

#21

Post by A_D_E_P_T »

seanmcdirmid wrote: post #8
_feus wrote: post #3

Earlier quoted context omitted.

and it will be something so trivial and obvious, those who were looking for it will be kicking themselves for missing it

It’s a huge refrain that shows up again every 20 years or so. Wolfram wrote a huge book with this premise, but I don’t think it’s gone anywhere even though it’s surely 25 years old by now.

It's arguably ~2500 years old, dating back to the Pythagoreans, who believed that "all is number" and had a very large and complex system of musical rituals.

The modern manifestation is mostly the intellectual product of Konrad Zuse, who wrote "digital physics" in 1969.

> https://en.wikipedia.org/wiki/Digital_physics

Wolfram, Tegmark, Bostrom, etc. are mostly downstream of Zuse.

Re: Mathematicians hunting prime numbers discover infinite new pattern

#23

Post by Kaijo »

seanmcdirmid wrote: post #8
_feus wrote: post #3

Earlier quoted context omitted.

and it will be something so trivial and obvious, those who were looking for it will be kicking themselves for missing it

It’s a huge refrain that shows up again every 20 years or so. Wolfram wrote a huge book with this premise, but I don’t think it’s gone anywhere even though it’s surely 25 years old by now.

Wolfram came to our evolutionary biology department to preach that book about 20 years ago. We all got our heads into cellular automata for a while, but in the end they just don't have the claimed profound explanatory power in real biological systems.

Re: Mathematicians hunting prime numbers discover infinite new pattern

#24

Post by e1ghtSpace »

lukan wrote: post #18
e1ghtSpace wrote: post #15

Earlier quoted context omitted.

Did you listen? The audio is different yet it still works.

No, I did not download a big movie and likely won't to get a point on HN.

All you want is points on HN when you comment? Anyway, try to only focus on the top middle screen in this video. https://www.youtube.com/watch?v=T_dLx_J2oVs

Re: Mathematicians hunting prime numbers discover infinite new pattern

#25

Post by isaacfrond »

Sniffnoy wrote: post #7

I'm a little confused at the significance here. Before I read the definition of the M_a, this seemed crazy, but on actually reading it, M_1 is just the sum-of-divisors function (usually denoted sigma). So, n is prime iff M_1(n)=n+1. That's much simpler than the first equation listed there! Indeed, looking things up, it seems that in general the functions M_a can be written as a linear combination (note: with polynomi…

The M functions are the MacMahon’s partition functions (see the paper [1]). They were not known to relate to the sum of divisors. The M_a function counts partitions in a parts but weighing multiplicities in the partion.

[1]: https://arxiv.org/abs/2405.06451

Re: Mathematicians hunting prime numbers discover infinite new pattern

#26

Post by lukan »

e1ghtSpace wrote: post #24
lukan wrote: post #18

Earlier quoted context omitted.

No, I did not download a big movie and likely won't to get a point on HN.

All you want is points on HN when you comment? Anyway, try to only focus on the top middle screen in this video. https://www.youtube.com/watch?v=T_dLx_J2oVs

Your point of argument/information. Not karma points.

Re: Mathematicians hunting prime numbers discover infinite new pattern

#27

Post by robin_reala »

seanmcdirmid wrote: post #8
_feus wrote: post #3

Earlier quoted context omitted.

and it will be something so trivial and obvious, those who were looking for it will be kicking themselves for missing it

It’s a huge refrain that shows up again every 20 years or so. Wolfram wrote a huge book with this premise, but I don’t think it’s gone anywhere even though it’s surely 25 years old by now.

You can read it for free at https://www.wolframscience.com/nks/ if you’re interested.

Re: Mathematicians hunting prime numbers discover infinite new pattern

#28

Post by amelius »

_feus wrote: post #3
wewewedxfgdf wrote: post #2

This sort of thing makes me feel there is some deep understanding of reality only inches away from us, we glimpse it through these patterns but the secret remains hidden.

and it will be something so trivial and obvious, those who were looking for it will be kicking themselves for missing it

Or someone proves that there is no pattern and they will be kicking themselves for wasting their time searching.

Re: Mathematicians hunting prime numbers discover infinite new pattern

#29

Post by mensetmanusman »

amelius wrote: post #28
_feus wrote: post #3

Earlier quoted context omitted.

and it will be something so trivial and obvious, those who were looking for it will be kicking themselves for missing it

Or someone proves that there is no pattern and they will be kicking themselves for wasting their time searching.

The experience gained along the journey is more valuable than the result.
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