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The concept of "circle" is a human invention, in that a perfect circle has never been observed in the universe. The value of pi follows immediately as a derivat

The concept of "circle" is a human invention, in that a perfect circle has never been observed in the universe. The value of pi follows immediately as a derivative human invention.

justifier 10y ago
I would argue the 'perfect circle' is inherent in every circle, similarly to how it is inherent in your dismissal of it But if you require a more direct understanding I would say there is a perfect circle in every rotation
- kordless 10y ago
  The possibility of a perfect circle exists in this universe, but the last digit we are aware of is definitely a posteriori. In other words, the description of a circle is prior knowledge given it allows calculating pi, but the actual values are post observational knowledge, given they must be calculated and continue to be irrational forever. (At least as far as we know.) It would take an infinite amount of power to calculate every digit in pi, given pi itself is irrational, even while describing how to calculate it is rational.
  - justifier 10y ago
    You are moving someone else's goalposts I answered where circles are in our universe and you then try to change the original intent of omalleyt's question to mean a symbolic representation of pi > It would take an infinite amount of power to calculate every digit in pi Calculating pi is so simple life without nervous systems does it Now, expressing that value in our limited yet overly verbose base ten symbolic representation would indeed require infinite recursion
    - kordless 10y ago
      I'm not aware of a means by which goal posts can exist in a philosophical debate around rational vs. irrational thinking. Both types of thinking are valid, but I can see how and why some tend to argue for absolute rationality at all times.
      - justifier 10y ago
        I apologise, I thought you were implying that what omalleyt 'really meant' was a perfect circle is data we can calculate It seemed to me you were changing the question that was being asked, and a question asked implies an answer, or 'goal post' But if you were just developing new inquiry stead building off omalleyt then I apologise and would hope to encourage like critical thinking in the future .. Thinking on it 'goal posts'.. and 'soap box' elsewhere in this thread.. lacks a timeless quality, I really should have left it out ;P
        kordless 10y ago
        I asked my daughters friend why pi was irrational, and she said "because you have to calculate it". The knowledge of those calculations cannot be given, but the way to calculate it, with a bit of suffering, can.
  - szemet 10y ago
    "It would take an infinite amount of power to calculate every digit in pi" Representation by digits is just one representation. We have plenty of finite representations: http://mathworld.wolfram.com/PiFormulas.html http://mathworld.wolfram.com/PiFormulas.html Base 10 notation also requires a calculation to get the concrete number: You have to sum and multiply and power a lot (Imagine whole numbers described in base 10, now how you get that number of something?)
- szemet 10y ago
  Yes, if you take something like "Minimum Description Length principle", there may exists circles in physical world that are best (most economically) described with a perfect circle + some noise.
tyingq 10y ago
How far from a perfect circle is the event horizon of a black hole? Or, closer...Is the slight bulge in our Sun statistically that far off from perfect?
- komali2 10y ago
  Enough to be considered imperfect.
  - tyingq 10y ago
    But with known reasons for why it isn't perfect. And math that works fine if you round to a reasonable degree. Edit: "Scaled to the size of a beach ball, say scientists, the sun's equatorial bulge would be less than the width of a human hair"[1] And, I assume the defects in the event horizon of a black hole are even more negligible. [1]https://www.theguardian.com/science/2012/aug/16/sun-perfect-sphere-nature https://www.theguardian.com/science/2012/aug/16/sun-perfect-...
    - platz 10y ago
      It is still going to be fuzzy at the Planck length. I'm not sure quantum mechanics and infinite precision are reconcilable
      - tyingq 10y ago
        Yes...I'm having trouble verbalizing what I'm trying to say. Basically trying to say that Pi, to me, doesn't appear to be a man-made construct. Any naturally occurring circle that's near perfect seems to illustrate that. Any deviation from a Pi-derived shape has plausible reasons for the defect, like the one you point out.
nurettin 10y ago
The value of pi is apparent in nature. You can experimentally deduce it by measuring the magnetic permeability or coulomb force without knowing of a circle at all.
- cft 10y ago
  It will still reduce to the length of a circle, otherwise it's just a units convention.
- amelius 10y ago
  As far as we know, only at certain length scales and to a certain precision.
coldtea 10y ago
>The concept of "circle" is a human invention, in that a perfect circle has never been observed in the universe. It doesn't have to be observed as some material manifestation to be a discovery. Notions can also exist outside human intervention and shape the universe. Which is also why humans can discover such things (like pi) in parallel, without one discoverer ever having been in contact with the other. Or why even aliens can discover the same concepts.
- omalleyt 10y ago
  Ok, but how would you define "human invention" if not as "something that didn't previously have a material manifestation"?
wyager 10y ago
> a perfect circle has never been observed in the universe Yeah, that's not true. Many things in the universe have perfectly spherical or spheroid shapes, cross sections, or propagation patterns, like black holes or isotropic EM emissions or (more abstractly) light cones. Pi is baked into the laws of physics in many locations as a consequence of the geometric behavior of our spacetime. It would also be baked into a lot of other plausible spacetimes. It's hard to quantify exactly what causes it to come up so much, but it's probably the fact that our universe is locally Euclidean and therefore uses the L2-norm for distance, which gives rise to circles/spheres as the unit shape and the extrema of a number of optimization problems.

The concept of "circle" is a human invention, in that a perfect circle has never been observed in the universe. The value of pi follows immediately as a derivative human invention.

justifier 10y ago

I would argue the 'perfect circle' is inherent in every circle, similarly to how it is inherent in your dismissal of it But if you require a more direct understanding I would say there is a perfect circle in every rotation

kordless 10y ago
The possibility of a perfect circle exists in this universe, but the last digit we are aware of is definitely a posteriori. In other words, the description of a circle is prior knowledge given it allows calculating pi, but the actual values are post observational knowledge, given they must be calculated and continue to be irrational forever. (At least as far as we know.) It would take an infinite amount of power to calculate every digit in pi, given pi itself is irrational, even while describing how to calculate it is rational.
- justifier 10y ago
  You are moving someone else's goalposts I answered where circles are in our universe and you then try to change the original intent of omalleyt's question to mean a symbolic representation of pi > It would take an infinite amount of power to calculate every digit in pi Calculating pi is so simple life without nervous systems does it Now, expressing that value in our limited yet overly verbose base ten symbolic representation would indeed require infinite recursion
  - kordless 10y ago
    I'm not aware of a means by which goal posts can exist in a philosophical debate around rational vs. irrational thinking. Both types of thinking are valid, but I can see how and why some tend to argue for absolute rationality at all times.
    - justifier 10y ago
      I apologise, I thought you were implying that what omalleyt 'really meant' was a perfect circle is data we can calculate It seemed to me you were changing the question that was being asked, and a question asked implies an answer, or 'goal post' But if you were just developing new inquiry stead building off omalleyt then I apologise and would hope to encourage like critical thinking in the future .. Thinking on it 'goal posts'.. and 'soap box' elsewhere in this thread.. lacks a timeless quality, I really should have left it out ;P
      - kordless 10y ago
        I asked my daughters friend why pi was irrational, and she said "because you have to calculate it". The knowledge of those calculations cannot be given, but the way to calculate it, with a bit of suffering, can.
- szemet 10y ago
  "It would take an infinite amount of power to calculate every digit in pi" Representation by digits is just one representation. We have plenty of finite representations: http://mathworld.wolfram.com/PiFormulas.html http://mathworld.wolfram.com/PiFormulas.html Base 10 notation also requires a calculation to get the concrete number: You have to sum and multiply and power a lot (Imagine whole numbers described in base 10, now how you get that number of something?)
szemet 10y ago
Yes, if you take something like "Minimum Description Length principle", there may exists circles in physical world that are best (most economically) described with a perfect circle + some noise.

tyingq 10y ago

How far from a perfect circle is the event horizon of a black hole? Or, closer...Is the slight bulge in our Sun statistically that far off from perfect?

komali2 10y ago
Enough to be considered imperfect.
- tyingq 10y ago
  But with known reasons for why it isn't perfect. And math that works fine if you round to a reasonable degree. Edit: "Scaled to the size of a beach ball, say scientists, the sun's equatorial bulge would be less than the width of a human hair"[1] And, I assume the defects in the event horizon of a black hole are even more negligible. [1]https://www.theguardian.com/science/2012/aug/16/sun-perfect-sphere-nature https://www.theguardian.com/science/2012/aug/16/sun-perfect-...
  - platz 10y ago
    It is still going to be fuzzy at the Planck length. I'm not sure quantum mechanics and infinite precision are reconcilable
    - tyingq 10y ago
      Yes...I'm having trouble verbalizing what I'm trying to say. Basically trying to say that Pi, to me, doesn't appear to be a man-made construct. Any naturally occurring circle that's near perfect seems to illustrate that. Any deviation from a Pi-derived shape has plausible reasons for the defect, like the one you point out.

nurettin 10y ago

The value of pi is apparent in nature. You can experimentally deduce it by measuring the magnetic permeability or coulomb force without knowing of a circle at all.

cft 10y ago
It will still reduce to the length of a circle, otherwise it's just a units convention.
amelius 10y ago
As far as we know, only at certain length scales and to a certain precision.

coldtea 10y ago

>The concept of "circle" is a human invention, in that a perfect circle has never been observed in the universe. It doesn't have to be observed as some material manifestation to be a discovery. Notions can also exist outside human intervention and shape the universe. Which is also why humans can discover such things (like pi) in parallel, without one discoverer ever having been in contact with the other. Or why even aliens can discover the same concepts.

omalleyt 10y ago
Ok, but how would you define "human invention" if not as "something that didn't previously have a material manifestation"?

wyager 10y ago

> a perfect circle has never been observed in the universe Yeah, that's not true. Many things in the universe have perfectly spherical or spheroid shapes, cross sections, or propagation patterns, like black holes or isotropic EM emissions or (more abstractly) light cones. Pi is baked into the laws of physics in many locations as a consequence of the geometric behavior of our spacetime. It would also be baked into a lot of other plausible spacetimes. It's hard to quantify exactly what causes it to come up so much, but it's probably the fact that our universe is locally Euclidean and therefore uses the L2-norm for distance, which gives rise to circles/spheres as the unit shape and the extrema of a number of optimization problems.