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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

#91

Post by IAmBroom »

random3 wrote: post #55
hausrat wrote: post #44

Earlier quoted context omitted.

The very notion of discreteness depends on subjective definitions of "objects". We take concepts of objects for granted because they make interacting with the world tractable, but it's really hard to define them outside of minds.

No, the discreetness comes from physical experiments. I do see a problem defining something outside of one’s mind or outside the universe though :)

Discreetness only comes from experiments carried out in secret laboritories.

Pronounce "lah-BORE-i-tories", obviously.

Re: Mathematicians hunting prime numbers discover infinite new pattern

#92

Post by IAmBroom »

random3 wrote: post #52
giardini wrote: post #50

Earlier quoted context omitted.

As far as we know, the universe is a single unity, and any discrete units and any other type of math are human distinctions overlaid upon that unity.

Can you explain what you mean here? I mean yes there’s a universe so it can be see as a unit. There’s also quantum mechanics, telling us we can only distinguish discrete objects at the bottom of the scale. Can you give an example of a non-human distinction, or explain what you mean by that concept?

I assume the post is missing its "/s".

Re: Mathematicians hunting prime numbers discover infinite new pattern

#93

Post by datameta »

Keyframe wrote: post #88
datameta wrote: post #78

Earlier quoted context omitted.

Where could you recommend I read more about how they are derived scales?

Wikipedia is a good start, but if it's too terse/advanced there's always simple wikipedia which seems to have an explanation as well https://simple.wikipedia.org/wiki/Planck_units

I suppose it was pointless of me to ask if what I received was a wiki link, no offense. Thanks.

Re: Mathematicians hunting prime numbers discover infinite new pattern

#94

Post by Keyframe »

datameta wrote: post #93
Keyframe wrote: post #88

Earlier quoted context omitted.

Wikipedia is a good start, but if it's too terse/advanced there's always simple wikipedia which seems to have an explanation as well https://simple.wikipedia.org/wiki/Planck_units

I suppose it was pointless of me to ask if what I received was a wiki link, no offense. Thanks.

you received a link to simplified wikipedia, which is not wikipedia. https://simple.wikipedia.org/wiki/Simple_English_Wikipedia

Re: Mathematicians hunting prime numbers discover infinite new pattern

#95

Post by FredPret »

cwmoore wrote: post #75
FredPret wrote: post #42

Earlier quoted context omitted.

> If I handed you 1 apple, At this point I hold one object that we agree to label "apple". Note that even seeing it as a single object is a layer of abstraction. In reality it's a clump of fundamental particles temporarily banding together > and then handed you another apple, What's "another apple"? What does it have in common with the thing I'm already holding? We label this thing to be also an apple, but it's a tot…

I’m not sure I am intended to understand what your problem is.

Personally, I suffer from whatever it is that drives a person to think about what numbers mean.

The numbers themselves aren't a problem, I'm just pointing out that our cognition involves many overlapping layers of abstraction, and we're doing mathematics and every other mental activity in one or more of those layers.

That this seems to correlate strongly to real-world phenomena speaks well of the types of abstraction that nature has equipped us with.

Re: Mathematicians hunting prime numbers discover infinite new pattern

#96

Post by datameta »

Keyframe wrote: post #94
datameta wrote: post #93

Earlier quoted context omitted.

I suppose it was pointless of me to ask if what I received was a wiki link, no offense. Thanks.

you received a link to simplified wikipedia, which is not wikipedia. https://simple.wikipedia.org/wiki/Simple_English_Wikipedia

I can't tell now if you're being intentionally condescending.

Re: Mathematicians hunting prime numbers discover infinite new pattern

#98

Post by coderatlarge »

coderatlarge wrote: post #97

just this quote from the article shocked me: “In 1976, Jones, Sato, Wada, and Wiens (2) (…) produced a degree 25 polynomial in 26 variables whose positive values, as the variables vary over nonnegative integers, is the set of primes.“

here’s an explicit formula:

https://mathoverflow.net/questions/132954/the-jones-sato-wad...

Re: Mathematicians hunting prime numbers discover infinite new pattern

#99

Post by coderatlarge »

coderatlarge wrote: post #98
coderatlarge wrote: post #97

just this quote from the article shocked me: “In 1976, Jones, Sato, Wada, and Wiens (2) (…) produced a degree 25 polynomial in 26 variables whose positive values, as the variables vary over nonnegative integers, is the set of primes.“

here’s an explicit formula: https://mathoverflow.net/questions/132954/the-jones-sato-wad...

just to clarify this is well beyond my ability to verify or even situate in larger context.

Re: Mathematicians hunting prime numbers discover infinite new pattern

#100

Post by giardini »

random3 wrote: post #52
giardini wrote: post #50

Earlier quoted context omitted.

As far as we know, the universe is a single unity, and any discrete units and any other type of math are human distinctions overlaid upon that unity.

Can you explain what you mean here? I mean yes there’s a universe so it can be see as a unit. There’s also quantum mechanics, telling us we can only distinguish discrete objects at the bottom of the scale. Can you give an example of a non-human distinction, or explain what you mean by that concept?

Yes. It was a parody of yunwal's post (which I possibly should have cc'ed). . Reread yunwai's post and mine together and you will understand.

Endless "unity...discrete" discussions have arisen in both science and philosophy since the beginning.

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