Molecules, atoms, quarks, and so on

[ƒ(x)]

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?

 

[ƒ(x)]

Of course, if pi isn't irrational (which it is) then this little thought tells us nothing about the divisibility of matter.

 

[micromass]

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

 

[pergradus]

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

This.

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

 

[lisab]

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 .

 

[rootX]

In the real world, pi is 3 but in math world no one knows what pi is ...

 

[ƒ(x)]

Soo...we're saying no because of semantics? It was more of a thought experiment.

 

[middlj]

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.

 

[ƒ(x)]

Ok, I see your point.

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

 

[pergradus]

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.

 

[dlgoff]

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.

 

[Astronuc]

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 ____?

 

[ƒ(x)]

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.

 

[ƒ(x)]

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?

 

[Dr Lots-o'watts]

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.

 

[ƒ(x)]

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.