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Discussion Overview

The discussion revolves around the relationship between the mathematical concept of pi, its irrationality, and the divisibility of matter. Participants explore whether the irrational nature of pi implies that matter can be infinitely divided, considering both theoretical and practical implications.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant suggests that because pi is irrational, matter must be infinitely divisible, using a thought experiment involving a wheel and its circumference.
  • Others argue that the wheel will never be a perfect circle, and thus the argument does not hold, as real-world measurements are approximations.
  • Some participants express uncertainty about the divisibility of matter, noting that it may not be infinitely divisible due to the discrete nature of particles.
  • There is a discussion about the limitations of mathematical models in accurately representing physical reality, with references to the need for experimental validation.
  • One participant mentions that while pi is irrational, this does not necessarily inform us about the divisibility of matter.
  • Another participant points out that practical applications of pi do not require infinite precision, suggesting that the real-world implications differ from mathematical theory.
  • Some participants note that matter may be modeled as polyhedral with point particles, raising questions about the divisibility of these particles in high-energy collisions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the irrationality of pi implies that matter is infinitely divisible. There are multiple competing views regarding the relationship between mathematical concepts and physical reality, and the discussion remains unresolved.

Contextual Notes

Participants acknowledge that real-world measurements are approximations and that the nature of matter may not align perfectly with mathematical models. There are references to the limitations of energy in experimental validation of particle divisibility.

ƒ(x)
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So, I was brushing my teeth and started thinking about pi and how it is irrational. One thing led to another and I remembered Atom, by Asimov (which I haven't yet finished). Now, assuming pi is irrational, if we have a wheel with a radius of 1/2 (units don't really matter), and unroll it so that it forms a strip, that strip will have a length of pi. Suppose we try to measure that strip; we'll never be completely accurate. Since pi is irrational, we'll be able to keep refining out measurement infinitely. Therefore, every bit of matter is composed of smaller bits.

So, because pi is irrational, matter is infinitely divisible, correct?
 
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Of course, if pi isn't irrational (which it is) then this little thought tells us nothing about the divisibility of matter.
 
The point is that your wheel will never be a perfect circle. So spreading out this wheel will not give pi, but some closely related quantity.

I honestly don't know if matter is infinitely divisible or not, but I don't think that your argument really works :frown:
 
micromass said:
The point is that your wheel will never be a perfect circle. So spreading out this wheel will not give pi, but some closely related quantity.

I honestly don't know if matter is infinitely divisible or not, but I don't think that your argument really works :frown:

This.

In fact everything in the real world is only an approximation to the mathematical concept... shadows on the wall.
 
pergradus said:
This.

In fact everything in the real world is only an approximation to the mathematical concept... shadows on the wall.

Mathematical concepts are mere approximations of the real world :wink:.
 
In the real world, pi is 3 but in math world no one knows what pi is ...
 
Soo...we're saying no because of semantics? It was more of a thought experiment.
 
But as a thought experiment it is just that, thought. So the length of the strip will be exactly pi. However, in the real world the length won't be pi, as the strip will be made up of a finite number of particles, which, at some point, become non divisible.

This isn't really a thought experiment, just a question of why the world doesn't 100% comply with mathematical theory.
 
Ok, I see your point.

So, going back to what micromass said, how do you know it isn't a perfect circle?
 
  • #10
ƒ(x) said:
Ok, I see your point.

So, going back to what micromass said, how do you know it isn't a perfect circle?

because its made of tiny little jiggly balls of matter than can never form a smooth surface at the infinitesimal.

Matter is discrete in the real world, there's no way around it.
 
  • #11
ƒ(x) said:
Ok, I see your point.

So, going back to what micromass said, how do you know it isn't a perfect circle?

...elementary applications, such as estimating the circumference of a circle, will rarely require more than a dozen decimal places. For example, the decimal representation of π truncated to 11 decimal places is good enough to estimate the circumference of any circle that fits inside the Earth with an error of less than one millimetre, and the decimal representation of π truncated to 39 decimal places is sufficient to estimate the circumference of any circle that fits in the observable universe with precision comparable to the radius of a hydrogen atom.[22][23]

http://en.wikipedia.org/wiki/Pi"

If you want the circumference past this, you'll need to start thinking in terms of quantum mechanics.
 
Last edited by a moderator:
  • #12
ƒ(x) said:
So, I was brushing my teeth and started thinking about pi and how it is irrational. One thing led to another and I remembered Atom, by Asimov (which I haven't yet finished). Now, assuming pi is irrational, if we have a wheel with a radius of 1/2 (units don't really matter), and unroll it so that it forms a strip, that strip will have a length of pi. Suppose we try to measure that strip; we'll never be completely accurate. Since pi is irrational, we'll be able to keep refining out measurement infinitely. Therefore, every bit of matter is composed of smaller bits.

So, because pi is irrational, matter is infinitely divisible, correct?
The diameter (d) and circumference (c) of a circle are exact. The ratio of circumference to diameter (c/d) is described by an irrational number, pi.

How about 2 and 7. Both are exact, but 2/7 is ____?
 
  • #13
pergradus said:
because its made of tiny little jiggly balls of matter than can never form a smooth surface at the infinitesimal.

Matter is discrete in the real world, there's no way around it.


Now that isn't fair. Yours starting at the end result of what I'm talking about and working backwards. I'd classify that as cheating.
 
  • #14
Astronuc said:
The diameter (d) and circumference (c) of a circle are exact. The ratio of circumference to diameter (c/d) is described by an irrational number, pi.

How about 2 and 7. Both are exact, but 2/7 is ____?

Can you elaborate a little more on what you're saying? I guess I'm a tad slow. Is there something I don't know about irrational numbers?
 
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  • #15
ƒ(x) said:
Of course, if pi isn't irrational (which it is) then this little thought tells us nothing about the divisibility of matter.

Pi IS irrational, and this little thought indeed tells us nothing about the divisibility of matter.

Math is used to model nature. And any math model only has validity if experiments correlates. Whether the model is this concise deduction of yours, string theory or anything in between, someone is going to have to validate with experimental fact, such as what they're up to with the LHC.

General consensus is that matter is polyhedral with a point particle at each vertex. High-energy collisions tell us if these point particles are divisible or not, but energy is a limited ressource.
 
  • #16
Dr Lots-o'watts said:
Pi IS irrational, and this little thought indeed tells us nothing about the divisibility of matter.

Math is used to model nature. And any math model only has validity if experiments correlates. Whether the model is this concise deduction of yours, string theory or anything in between, someone is going to have to validate with experimental fact, such as what they're up to with the LHC.

General consensus is that matter is polyhedral with a point particle at each vertex. High-energy collisions tell us if these point particles are divisible or not, but energy is a limited ressource.

Yo comprendo.
 

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