Any geometrical form, infinitesimal/fractal and then point

[bahman]

I am not confusing anything. What you said is also valid and mathematically explains that the reality is made of infinitesimal and not from zero.

It explains nothing. For all we know the whole cannot be understood by chopping it up into parts. Let alone infinitesimal ones.

The whole is sum of its parts. No more. No emergence.

You are just over-indexing on reduction/decomposition/analysis.

What do you mean?

Graviton is the quantum space-time.

If gravitons exist, then their respective quantum fields exist - ergo - distance between gravitons.

Gravitions make space-time. Distance is a measure of length which length is a dimension of space-time. There is, however, distance between gravitons.

So there is a gap between two states of affair. You cannot physically have something than infinitesimal.

It's just a fencepost error. You keep switching between digital (discrete) and analog (continuous) perspectives.

No, I am not switching. The reality of space-time is discrete on short scale.

I mean, it is physically impossible. You, however, can abstract it: 1 apple plus another one is equal to one apple.

No. You can't. I know what it means to add numbers. I have no idea what it means to add apples.

Apple + Apple = ?

AppleApple? (String concatenation)
[Apple, Apple] ? (List construction)
[Apple]? (Set construction)

The plus-operator is Overloaded

I think I was clear.

[Skepdick]

The whole is sum of its parts. No more. No emergence.

Fine. So which part of the whole is the observer?

What do you mean?

I mean you disregard holism/emergence.

Gravitions make space-time. Distance is a measure of length which length is a dimension of space-time. There is, however, distance between gravitons.

OK. So how long is a graviton?

No, I am not switching. The reality of space-time is discrete on short scale.

This is circular. You are yet to define "short".

I think I was clear.

I showed you why you weren't. Language (mathematical, or otherwise formal) cannot describe reality without also describing the observer.

[bahman]

The whole is sum of its parts. No more. No emergence.

Fine. So which part of the whole is the observer?

The observer, experience and cause and make sure that the reality is coherent.

What do you mean?

I mean you disregard holism/emergence.

I have an argument against emergence. This is off topic. I might open another thread shortly on the emergence.

Gravitions make space-time. Distance is a measure of length which length is a dimension of space-time. There is, however, distance between gravitons.

OK. So how long is a graviton?

The length at which the energy for the creation of a graviton with smaller length becomes infinite.

No, I am not switching. The reality of space-time is discrete on short scale.

This is circular. You are yet to define "short".

The shortest is graviton size.

I think I was clear.

I showed you why you weren't. Language (mathematical, or otherwise formal) cannot describe reality without also describing the observer's meaning.

You can use for all sorts of different things. I was talking about reality.

[Skepdick]

The observer, experience and cause and make sure that the reality is coherent.

Reality doesn't need you to validate its coherence. Reality is coherent to itself.

I have an argument against emergence. This is off topic. I might open another thread shortly on the emergence.

There is an argument for or against everything. None of it matters if you can't determine which argument is right and which argument is wrong.

The length at which the energy for the creation of a graviton with smaller length becomes infinite.

What if that length is zero?

The shortest is graviton size.

So zero.

You can use for all sorts of different things. I was talking about reality.

Reality doesn't care about our descriptions of it.

In the end, you end up with an argument for Superdeterminism + Free will.

Theists rejoice.

[bahman]

The observer, experience and cause and make sure that the reality is coherent.

Reality doesn't need you to validate its coherence. Reality is coherent to itself.

Reality without an observer is incoherent. That is true since reality without an observer is indifferent.

I have an argument against emergence. This is off topic. I might open another thread shortly on the emergence.

There is an argument for or against everything. None of it matters if you can't determine which argument is right and which argument is wrong.

You are welcome to join my other thread on emergence when I open it.

The length at which the energy for the creation of a graviton with smaller length becomes infinite.

What if that length is zero?

It cannot be, as you illustrated. The quantum field theory puts a finite limit on it. Uncertainty principle.

The shortest is graviton size.

So zero.

No. It is not zero as I and yourself illustrated.

You can use for all sorts of different things. I was talking about reality.

Reality doesn't care about our descriptions of it.

In the end, you end up with an argument for Superdeterminism + Free will.

Theists rejoice.

I don't understand how what you said is related to what I said. By reality, I mean physical which is coherent.

[Skepdick]

Reality without an observer is incoherent. That is true since reality without an observer is indifferent.

So make up your mind then. Does the whole of reality (being the sum of its parts) include or exclude the observer?

It cannot be, as you illustrated. The quantum field theory puts a finite limit on it. Uncertainty principle.
No. It is not zero as I and yourself illustrated.

I have illustrated no such thing.
You said that a graviton's length is the length at which its energy becomes infinite. That's a limit. Calculus.
It becomes infinite at 0. For any other length >0 its energy is near-infinite.

I don't understand how what you said is related to what I said. By reality, I mean physical which is coherent.

What is the limit of coherence for you?

[bahman]

Reality without an observer is incoherent. That is true since reality without an observer is indifferent.

So make up your mind then. Does the whole of reality (being the sum of its parts) include or exclude the observer?

The observer is irrelevant in our discussion since it just guarantees the coherence when there is a change.

It cannot be, as you illustrated. The quantum field theory puts a finite limit on it. Uncertainty principle.
No. It is not zero as I and yourself illustrated.

You said that a graviton's length is the length at which its energy becomes infinite. That's a limit. Calculus.
It becomes infinite at 0. For any other length >0 its energy is near-infinite.

Yes, so we agree?

I don't understand how what you said is related to what I said. By reality, I mean physical which is coherent.

What is the limit of coherence for you?

It is so high that reality with a good approximation can be explained in terms of laws of nature.

[Skepdick]

The observer is irrelevant in our discussion, since it just guarantees the coherence when there is a change.

Eh? You and I are observers. We aren't 'irrelevant' - without us there is no discussion.

You said that a graviton's length is the length at which its energy becomes infinite. That's a limit. Calculus.
It becomes infinite at 0. For any other length >0 its energy is near-infinite.

Yes, so we agree?

I don't know. Is the definition of an "infinitesimal" as "x>0" sufficient for you or not?

To me it's not - It practically refers to the entire number-line. Except 0. But This doesn't really solve anything.

0 is as arbitrary a fixed point as any other. If you take the open interval (-∞, +∞) you can't even find 0.

If infinitesimal exist (x), the positive (+x) and negative infinitesimals (-x) exist, then -x <0 < +x

It is so high that reality with a good approximation can be explained in terms of laws of nature.

Rinse, repeat. What are the limits of approximation? Explanation?

[bahman]

The observer is irrelevant in our discussion, since it just guarantees the coherence when there is a change.

Eh? You and I are observers. We aren't 'irrelevant' - without us there is no discussion.

We are talking about form rather than motion.

You said that a graviton's length is the length at which its energy becomes infinite. That's a limit. Calculus.
It becomes infinite at 0. For any other length >0 its energy is near-infinite.

Yes, so we agree?

I don't know. Is the definition of an "infinitesimal" as "x>0" sufficient for you or not?

To me it's not - It practically refers to the entire number-line. Except 0. But This doesn't really solve anything.

0 is as arbitrary a fixed point as any other. If you take the open interval (-∞, +∞) you can't even find 0.

If infinitesimal exist (x), the positive (+x) and negative infinitesimals (-x) exist, then -x <0 < +x

My understanding now tells me there is a physical infinitesimal at which nothing smaller than that can exist. Infinitesimal of space-time is the graviton for example that has a specific size. Mathematically you can abstract everything. But that doesn't mean that it could be real, like real number.

It is so high that reality with a good approximation can be explained in terms of laws of nature.

Rinse, repeat. What are the limits of approximation? Explanation?

The good approximation is when you are certain about your theory to an extended limit. You say my theory is valid with this level of approximation by which that means the error bigger than specific is not allowed.

[Skepdick]

We are talking about form rather than motion.

My understanding now tells me there is a physical infinitesimal at which nothing smaller than that can exist. Infinitesimal of space-time is the graviton for example that has a specific size. Mathematically you can abstract everything. But that doesn't mean that it could be real, like real number.

Fine. You are talking about form, hence formalism.

The form of an infinitesimal is still a geometric concern. It's still an atomist perspective and it goes as far back as Democritus.

https://en.wikipedia.org/wiki/Democritu ... hypothesis

The theory of Democritus held that everything is composed of "atoms", which are physically, but not geometrically, indivisible

The good approximation is when you are certain about your theory to an extended limit. You say my theory is valid with this level of approximation by which that means the error bigger than specific is not allowed.

Towards quantifying uncertainty/measuring things there's nothing more to add here except to point you to a book.

https://en.wikipedia.org/wiki/Quantum_C ... Democritus

There is an important passage there...

But if quantum mechanics isn't physics in the usual sense -- if it's not about matter, or energy, or waves, or particles -- then what is it about? From my perspective, it's about information and probabilities and observables, and how they relate to each other.

The "atom" you are seeking is information (classical or quantum - doesn't matter much). It's up to you to decide the location of its "existence". Is information epistemic or ontological? I don't even know if there is a difference.

[bahman]

We are talking about form rather than motion.

My understanding now tells me there is a physical infinitesimal at which nothing smaller than that can exist. Infinitesimal of space-time is the graviton for example that has a specific size. Mathematically you can abstract everything. But that doesn't mean that it could be real, like real number.

Fine. You are talking about form, hence formalism.

The form of an infinitesimal is still a geometric concern. It's still an atomist perspective and it goes as far back as Democritus.

https://en.wikipedia.org/wiki/Democritu ... hypothesis

Infinitesimal is empty, otherwise, it would have structure.

The theory of Democritus held that everything is composed of "atoms", which are physically, but not geometrically, indivisible

The good approximation is when you are certain about your theory to an extended limit. You say my theory is valid with this level of approximation by which that means the error bigger than specific is not allowed.

Towards quantifying uncertainty/measuring things there's nothing more to add here except to point you to a book.

https://en.wikipedia.org/wiki/Quantum_C ... Democritus

There is an important passage there...

But if quantum mechanics isn't physics in the usual sense -- if it's not about matter, or energy, or waves, or particles -- then what is it about? From my perspective, it's about information and probabilities and observables, and how they relate to each other.

The "atom" you are seeking is information (classical or quantum - doesn't matter much). It's up to you to decide the location of its "existence". Is information epistemic or ontological? I don't even know if there is a difference.

True. An atom is an information on the surface of the infinitesimal, graviton for example.

[Skepdick]

Infinitesimal is empty, otherwise, it would have structure.

If it didn't have structure it wouldn't exist.

[bahman]

Infinitesimal is empty, otherwise, it would have structure.

If it didn't have structure it wouldn't exist.

The structure is on the surface but not within.

[wtf]

The structure is on the surface but not within.

You seem to be thinking of infinitesimals as physical rather than abstractly mathematical. In which case, how do your infinitesimals relate to standard physics? Are quarks and electrons and muons and such made up of infinitesimals? How do infinitesimals interact with 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.

[Skepdick]

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.