7 ms·

Why Pi Matters (2015)

72 points by Osiris30 11y ago

deleted 11y ago
[deleted]
chocolateboy 11y ago
s/Storgatz/Strogatz/
mdergosits 11y ago
this should have a (2015) on the title
meta_AU 11y ago
Pi is too small. We should just move to Tau and make things easier.
- labster 11y ago
  Agreed. https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto
- krylon 11y ago
  Tau is too large. We should settle on Pi * 1.5 (or Tau / 1.5), thus making life ... interesting for both Pi lovers and Tau lovers.
  - FreeFull 11y ago
    I object to your use of the arithmetic mean. We should actually settle on Pi * sqrt(2)
    - krylon 11y ago
      Yes, that idea is even better! =D
- vog 11y ago
  There are good reasons to stay with π: | http://thepimanifesto.com/ http://thepimanifesto.com/ There are also good reasons to switch to Tau (τ=2π): | https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto But then, there is also Radical Tauism, proposing to switch to √(2π): | https://cp4space.wordpress.com/2013/02/28/radical-tauism/ https://cp4space.wordpress.com/2013/02/28/radical-tauism/ And of course there is the famous XKCD compromise on that matter: | https://xkcd.com/1292/ https://xkcd.com/1292/
deleted 11y ago
[deleted]
plank 11y ago
Would have loved a discussion on the digits of Pi and whether they have similar properties as those discovered of prime numbers, but this story seems a year old ...
- goldenkey 11y ago
  The gaps between primes are an endless ticker defined by previous primes and convoluted by mirroring and partitioning by future primes. Of course chaos has a pattern. It's as simple as using data as function, and functions as data. What makes sense in one representation is consequently nonsense in a different Head.
  - adrianN 11y ago
    That sounds like you read too much Time Cube.
    - goldenkey 11y ago
      I guess studying prime gaps can do that... But I was actually quite serious. Prime chaos is the result of taking additive modularity and relaying it to multiplicative modularity. Form creating function. Function creating form. Two things hardly related but at a junction through numbers, through counting. If you think my mention of mirror and partitioning has pangs of insanity, you should study how the gaps of primes evolve...its just a waveform defined by previous primes. And yes, it does involve mirroring and partitioning. Primes are just an easy target for bullshit if you dont even understand what belies each prime generating a waveform that then causes interference with the existing sieve waveform (that belies all previous primes.) If this interests you or you have any questions, I'd be happy to do a skype or hangouts call to show you how primes are actually very analagous to 'an endless convoluting ticker.'
    - goldenkey 11y ago
      I should also mention I had been programming in mathematica. So when I said different Head, I just meant different type. Guess it could have sounded kooky without that context
nickm12 11y ago
...and the formula that is given as an example of π's importance has a tau in it.
goldenkey 11y ago
Its a bit coy to call on Pi's significance in a Fourier transform where the Pi is simply the units inside of sin and cos calls. I kind of lost a bit of joy for the article after that gulp.
- Chinjut 11y ago
  What do you mean? In terms of Fourier series, the significance is that a function of period 1 breaks down into a sum of components whose derivatives are integer multiples of 2πi times themselves (or, if you wish to avoid descriptions which make use of complex numbers, whose second derivatives are square multiples of -(2π)^2 times themselves). When people describe sines and cosines by breaking a full revolution down into 2π radians, they don't do it for no reason. They do it because this manifests itself loudly in the differential properties of sines and cosines.
  - goldenkey 11y ago
    I mean that sin and cos are tied to Pi in terms of their period. The antipode and catipode. So one might as well group all 3 quantities as Pi related. And if you merely take sin or cos into your formula because they are continuously differentiable periodic functions, then well, couldnt you have just taken something else and the Pi really loses its 'sanctity'? I'm on my phone but I'm starkly betting that there are Fourier transforms that use diff periodic functions instead of the trig ones. Maybe computable ones instead of symbolic, although I'd have to concede profundity if that is the case
    - avian 11y ago
      You are correct and that point in the article caught my attention as well. Fourier transform works perfectly OK if you redefine sine and cosine functions to have different periods. That's basically equivalent to a variable substitution in the integral. As far as I can see, the transform itself doesn't favor any specific definition and pi has no special connection to periodic functions like the article implies. It's also true that sine and cosine functions are most conveniently defined in terms of radians, which is what I think Chinjut is trying to say. But that is more or less unrelated to the Fourier transform.
acqq 11y ago
My skeptical take is that US has the Pi day only because acknowledging on that level any more modern scientific discovery wouldn't be so easily politically acceptable. Even Babylonians had an approximation of Pi as 3.125, so it's nothing "modern." And it doesn't question the literal interpretation of the Bible, 6000 years and all that. So let's celebrate that innocent number. Well, at least, apparently is in the Bible Pi exactly 3. The creationists probably deny that too (1). And there was that famous https://en.wikipedia.org/wiki/Indiana_Pi_Bill https://en.wikipedia.org/wiki/Indiana_Pi_Bill Edit: 1) This approach here I even like: http://www.purplemath.com/modules/bibleval.htm http://www.purplemath.com/modules/bibleval.htm Still no cigar, 3.139 is still not more a "final truth" than 3. Both are approximations. You just can't learn scientific or mathematical "truths" out of the Bible. God wasn't all-seeing and all-wise enough to inspire the mention the existence of irrational numbers in the Bible. And I still believe Pi matters in sense of having "its official day" mostly for appearing to the legislators as being uncontroversial enough (irrational numbers, nobody cares, "everybody knows" it's 3.14).
- pbhjpbhj 11y ago
  It wouldn't really be a surprise if someone denied your eisegetical interpretation of scripture ("in the Bible Pi [is] exactly 3"). Those creating the "sea" in the passage usually referenced to this end clearly were able to do it, there's no reason for us to consider they didn't have as accurate a definition of the ratio as anyone else. Of note is the tradition of numerology in Hebrew texts and the assertion that the passage on the sea includes an adjustment that renders a better approximation with a fractional percentage of error. http://www.answering-islam.org/Religions/Numerics/pi.html http://www.answering-islam.org/Religions/Numerics/pi.html for example. >"Still no cigar, 3.139 is still not more a "final truth" than 3." Were you expecting a casual observer to give a fully accurate (!) rendering of the exact measurements of an artefact; moreover were you expecting those measurements to reveal a more accurate rendering of pi when the units are "about as long as a forearm" and "about as wide as a hand"?
  - acqq 11y ago
    > Were you expecting a casual observer to give a fully accurate (!) rendering of the exact measurements of an artefact; No, I surely wouldn't, but I would expect from all-knowing God to pass any fact that wasn't commonly known at that time as a proof of his all-knowledge (like, "there are atoms" or "the speed of light is..."). Irrational numbers or some really exceptional (for these times) approximation of some constant would also be a nice "touch". And not to put in one of 10 commandments slaves, women and donkeys together. But He surely knew his priorities. And note that there are enough of people that really consider and study the Bible as the source of such "all-time truths."
extramille 11y ago
Einstein was born on 14 March.
goldbrick 11y ago
My favorite pi formula: https://xkcd.com/179/ https://xkcd.com/179/

72 points by Osiris30 11y ago

deleted 11y ago

[deleted]

chocolateboy 11y ago

s/Storgatz/Strogatz/

mdergosits 11y ago

this should have a (2015) on the title

meta_AU 11y ago

Pi is too small. We should just move to Tau and make things easier.

labster 11y ago
Agreed. https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto
krylon 11y ago
Tau is too large. We should settle on Pi * 1.5 (or Tau / 1.5), thus making life ... interesting for both Pi lovers and Tau lovers.
- FreeFull 11y ago
  I object to your use of the arithmetic mean. We should actually settle on Pi * sqrt(2)
  - krylon 11y ago
    Yes, that idea is even better! =D
vog 11y ago
There are good reasons to stay with π: | http://thepimanifesto.com/ http://thepimanifesto.com/ There are also good reasons to switch to Tau (τ=2π): | https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto But then, there is also Radical Tauism, proposing to switch to √(2π): | https://cp4space.wordpress.com/2013/02/28/radical-tauism/ https://cp4space.wordpress.com/2013/02/28/radical-tauism/ And of course there is the famous XKCD compromise on that matter: | https://xkcd.com/1292/ https://xkcd.com/1292/

deleted 11y ago

[deleted]

plank 11y ago

Would have loved a discussion on the digits of Pi and whether they have similar properties as those discovered of prime numbers, but this story seems a year old ...

goldenkey 11y ago
The gaps between primes are an endless ticker defined by previous primes and convoluted by mirroring and partitioning by future primes. Of course chaos has a pattern. It's as simple as using data as function, and functions as data. What makes sense in one representation is consequently nonsense in a different Head.
- adrianN 11y ago
  That sounds like you read too much Time Cube.
  - goldenkey 11y ago
    I guess studying prime gaps can do that... But I was actually quite serious. Prime chaos is the result of taking additive modularity and relaying it to multiplicative modularity. Form creating function. Function creating form. Two things hardly related but at a junction through numbers, through counting. If you think my mention of mirror and partitioning has pangs of insanity, you should study how the gaps of primes evolve...its just a waveform defined by previous primes. And yes, it does involve mirroring and partitioning. Primes are just an easy target for bullshit if you dont even understand what belies each prime generating a waveform that then causes interference with the existing sieve waveform (that belies all previous primes.) If this interests you or you have any questions, I'd be happy to do a skype or hangouts call to show you how primes are actually very analagous to 'an endless convoluting ticker.'
  - goldenkey 11y ago
    I should also mention I had been programming in mathematica. So when I said different Head, I just meant different type. Guess it could have sounded kooky without that context

nickm12 11y ago

...and the formula that is given as an example of π's importance has a tau in it.

goldenkey 11y ago

Its a bit coy to call on Pi's significance in a Fourier transform where the Pi is simply the units inside of sin and cos calls. I kind of lost a bit of joy for the article after that gulp.

Chinjut 11y ago
What do you mean? In terms of Fourier series, the significance is that a function of period 1 breaks down into a sum of components whose derivatives are integer multiples of 2πi times themselves (or, if you wish to avoid descriptions which make use of complex numbers, whose second derivatives are square multiples of -(2π)^2 times themselves). When people describe sines and cosines by breaking a full revolution down into 2π radians, they don't do it for no reason. They do it because this manifests itself loudly in the differential properties of sines and cosines.
- goldenkey 11y ago
  I mean that sin and cos are tied to Pi in terms of their period. The antipode and catipode. So one might as well group all 3 quantities as Pi related. And if you merely take sin or cos into your formula because they are continuously differentiable periodic functions, then well, couldnt you have just taken something else and the Pi really loses its 'sanctity'? I'm on my phone but I'm starkly betting that there are Fourier transforms that use diff periodic functions instead of the trig ones. Maybe computable ones instead of symbolic, although I'd have to concede profundity if that is the case
  - avian 11y ago
    You are correct and that point in the article caught my attention as well. Fourier transform works perfectly OK if you redefine sine and cosine functions to have different periods. That's basically equivalent to a variable substitution in the integral. As far as I can see, the transform itself doesn't favor any specific definition and pi has no special connection to periodic functions like the article implies. It's also true that sine and cosine functions are most conveniently defined in terms of radians, which is what I think Chinjut is trying to say. But that is more or less unrelated to the Fourier transform.

acqq 11y ago

My skeptical take is that US has the Pi day only because acknowledging on that level any more modern scientific discovery wouldn't be so easily politically acceptable. Even Babylonians had an approximation of Pi as 3.125, so it's nothing "modern." And it doesn't question the literal interpretation of the Bible, 6000 years and all that. So let's celebrate that innocent number. Well, at least, apparently is in the Bible Pi exactly 3. The creationists probably deny that too (1). And there was that famous https://en.wikipedia.org/wiki/Indiana_Pi_Bill https://en.wikipedia.org/wiki/Indiana_Pi_Bill Edit: 1) This approach here I even like: http://www.purplemath.com/modules/bibleval.htm http://www.purplemath.com/modules/bibleval.htm Still no cigar, 3.139 is still not more a "final truth" than 3. Both are approximations. You just can't learn scientific or mathematical "truths" out of the Bible. God wasn't all-seeing and all-wise enough to inspire the mention the existence of irrational numbers in the Bible. And I still believe Pi matters in sense of having "its official day" mostly for appearing to the legislators as being uncontroversial enough (irrational numbers, nobody cares, "everybody knows" it's 3.14).

pbhjpbhj 11y ago
It wouldn't really be a surprise if someone denied your eisegetical interpretation of scripture ("in the Bible Pi [is] exactly 3"). Those creating the "sea" in the passage usually referenced to this end clearly were able to do it, there's no reason for us to consider they didn't have as accurate a definition of the ratio as anyone else. Of note is the tradition of numerology in Hebrew texts and the assertion that the passage on the sea includes an adjustment that renders a better approximation with a fractional percentage of error. http://www.answering-islam.org/Religions/Numerics/pi.html http://www.answering-islam.org/Religions/Numerics/pi.html for example. >"Still no cigar, 3.139 is still not more a "final truth" than 3." Were you expecting a casual observer to give a fully accurate (!) rendering of the exact measurements of an artefact; moreover were you expecting those measurements to reveal a more accurate rendering of pi when the units are "about as long as a forearm" and "about as wide as a hand"?
- acqq 11y ago
  > Were you expecting a casual observer to give a fully accurate (!) rendering of the exact measurements of an artefact; No, I surely wouldn't, but I would expect from all-knowing God to pass any fact that wasn't commonly known at that time as a proof of his all-knowledge (like, "there are atoms" or "the speed of light is..."). Irrational numbers or some really exceptional (for these times) approximation of some constant would also be a nice "touch". And not to put in one of 10 commandments slaves, women and donkeys together. But He surely knew his priorities. And note that there are enough of people that really consider and study the Bible as the source of such "all-time truths."

extramille 11y ago

Einstein was born on 14 March.

goldbrick 11y ago

My favorite pi formula: https://xkcd.com/179/ https://xkcd.com/179/