bahman wrote: ↑Fri Mar 27, 2020 11:31 pm
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.

wtf wrote: ↑Sat Mar 28, 2020 5:01 am
In which case, how do your infinitesimals relate to standard physics?

Infinitesimals make our reality.

wtf wrote: ↑Sat Mar 28, 2020 5:01 am
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.

wtf wrote: ↑Sat Mar 28, 2020 5:01 am
How do infinitesimals interact with quantum theory?

It is the true quantum theory.

wtf wrote: ↑Sat Mar 28, 2020 5:01 am
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 wrote: ↑Fri Mar 27, 2020 11:31 pm
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.

bahman wrote: ↑Sat Mar 28, 2020 7:53 pm
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.

bahman wrote: ↑Sat Mar 28, 2020 7:47 pm
I was looking for a consistent mathematical framework.

bahman wrote: ↑Sat Mar 28, 2020 7:53 pmIt 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.

wtf wrote: ↑Sun Mar 29, 2020 12:45 am
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.

wtf wrote: ↑Sun Mar 29, 2020 12:45 am
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 wrote: ↑Sat Mar 28, 2020 7:53 pm
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.

bahman wrote: ↑Sun Mar 29, 2020 7:04 pm
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?

bahman wrote: ↑Sun Mar 29, 2020 7:04 pm
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.