Any geometrical form, infinitesimal/fractal and then point

[bahman]

The structure is on the surface but not within.

You seem to be thinking of infinitesimals as physical rather than abstractly mathematical.

I was looking for a mathematical framework that can explain reality. The reality is measurable therefore it is constituted of small irreducible parts.

In which case, how do your infinitesimals relate to standard physics?

Infinitesimals make our reality.

Are quarks and electrons and muons and such made up of infinitesimals?

Electron, quark, etc. are modes of infinitesimals. For example, space-time is the result of the vibration of the graviton.

How do infinitesimals interact with quantum theory?

It is the true quantum theory.

To put my question in context, before this I've been assuming you are talking about mathematical infinitesimals. But now I see you are talking about the physical world; which is another thing entirely.

I was looking for a consistent mathematical framework.

[bahman]

The structure is on the surface but not within.

1. A 'surface' is still a geometric concept (or topological one - same difference). It can be formalised.
2. If there's a "surface" and a "within" - it has volume, therefore - it has structure.

Think of an empty ball. You can draw anything on the surface, structure. The inside is, however, empty. You cannot possibly divide an infinitesimal to two. It is required for any consistent theory that deals with reality.

[wtf]

I was looking for a consistent mathematical framework.

It is required for any consistent theory that deals with reality.

These two statements contradict each other.

If you have some consistent mathematical theory, it may or may not correspond to reality.

So are you looking for a consistent theory of math? Or a theory of physics?

And you were hand-wavy about whether infinitesimals make up quarks. Are all the physicists wrong?

[Skepdick]

Think of an empty ball. You can draw anything on the surface, structure. The inside is, however, empty. You cannot possibly divide an infinitesimal to two. It is required for any consistent theory that deals with reality.

I can think of a ball. I can also think of a sphere. A hollow one even.

I can also think of two nested spheres with a shared center, where one sphere has a radius that is infinitesimally smaller than the other, thus giving you the "surface" that you seek.

I can also think of a divisible sphere e.g a semi-sphere. And a sphere that if you divide "just the right way" and you re-arrange the pieces you will end up with two, identical spheres.

https://en.wikipedia.org/wiki/Banach%E2 ... ki_paradox

That is the one example I have where math is more unintuitive than quantum physics. At least physics has conservation laws.

[bahman]

I was looking for a consistent mathematical framework.

It is required for any consistent theory that deals with reality.

These two statements contradict each other.

If you have some consistent mathematical theory, it may or may not correspond to reality.

It means that such a mathematical framework can describe a possible reality.

So are you looking for a consistent theory of math? Or a theory of physics?

I am looking for a consistent theory of math. A consistent mathematical theory, so-called physics, can describe a possible reality.

And you were hand-wavy about whether infinitesimals make up quarks. Are all the physicists wrong?

I think I said sufficient about the relationship between quantum particles and infinitesimals. Physicist are saying the same. They are missing the importance of mind in any coherent phenomena.

[bahman]

Think of an empty ball. You can draw anything on the surface, structure. The inside is, however, empty. You cannot possibly divide an infinitesimal to two. It is required for any consistent theory that deals with reality.

I can think of a ball. I can also think of a sphere. A hollow one even.

I can also think of two nested spheres with a shared center, where one sphere has a radius that is infinitesimally smaller than the other, thus giving you the "surface" that you seek.

I can also think of a divisible sphere e.g a semi-sphere. And a sphere that if you divide "just the right way" and you re-arrange the pieces you will end up with two, identical spheres.

https://en.wikipedia.org/wiki/Banach%E2 ... ki_paradox

That is the one example I have where math is more unintuitive than quantum physics. At least physics has conservation laws.

And how that is related to our discussion?

[Skepdick]

I think I said sufficient about the relationship between quantum particles and infinitesimals. Physicist are saying the same. They are missing the importance of mind in any coherent phenomena.

There's actually another way to think about it. The mind is a Turing machine - a language recogniser, so a central philosophical question becomes thus:

Do we ever really talk about the continuum, or do we only ever talk about finite sequences of symbols that talk about the continuum?

[Skepdick]

And how that is related to our discussion?

You are trying to formalise the infinitesimal as a geometrical - empty ball. You are failing because an empty ball has volume.

An object with half the volume of your "infinitesimal" is a smaller infinitesimal.

An object whose volume OR size you can't halve is called a point.

[bahman]

I think I said sufficient about the relationship between quantum particles and infinitesimals. Physicist are saying the same. They are missing the importance of mind in any coherent phenomena.

There's actually another way to think about it. The mind is a Turing machine - a language recogniser, so a central philosophical question becomes thus:

Do we ever really talk about the continuum, or do we only ever talk about finite sequences of symbols that talk about the continuum?

I am talking about a continuum which is constructed from infinitesimal.

[bahman]

And how that is related to our discussion?

You are trying to formalise the infinitesimal as a geometrical - empty ball. You are failing because an empty ball has volume.

An object with half the volume of your "infinitesimal" is a smaller infinitesimal.

An object whose volume OR size you can't halve is called a point.

You cannot divide an infinitesimal because the energy for doing this is infinite.

[wtf]

You cannot divide an infinitesimal because the energy for doing this is infinite.

How much energy does it take to divide 6 by 2 to get 3?

[bahman]

You cannot divide an infinitesimal because the energy for doing this is infinite.

How much energy does it take to divide 6 by 2 to get 3?

It depends on how 6 entities interact.

[wtf]

It depends on how 6 entities interact.

Where are you getting this stuff from? Don't you know how to divide 6 by 2?

[bahman]

It depends on how 6 entities interact.

Where are you getting this stuff from?

Physics.

Don't you know how to divide 6 by 2?

Mathematically 3.

[Impenitent]

the best division is done with an axe

-Imp