'The Peculiar Math That Could Underlie the Laws of Nature'

[Nearly Sane]

The Rise of the Octonions. Fascinating stuff.


https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

[torridon]

Wow.

Squirrelled away for later study.

Ta

[Walt Zingmatilder]

All good stuff
But I feel many on this forum would be most disappointed if it turned out that the physical was dependent on the mathematical rather than the other way round...no problem of course for the neo Platonism or Platonism of course.

More importantly, why does this mathematician resort to cliched mysterious poses and where does the yoga mat come in.

[Maeght]

All good stuff
But I feel many on this forum would be most disappointed if it turned out that the physical was dependent on the mathematical rather than the other way round...no problem of course for the neo Platonism or Platonism of course.

More importantly, why does this mathematician resort to cliched mysterious poses and where does the yoga mat come in.

 

[Stranger]

But I feel many on this forum would be most disappointed if it turned out that the physical was dependent on the mathematical rather than the other way round...

Why would you think that?

[Walt Zingmatilder]

Why would you think that?

I think it might upset the physicalists and materialists somewhat.

[Rhiannon]

I think it might upset the physicalists and materialists somewhat.

Why?

[jeremyp]

But I feel many on this forum would be most disappointed if it turned out that the physical was dependent on the mathematical rather than the other way round.

Huh?

Neither is true. The physical world just is. Mathematics only comes into it as the tool that we humans use to describe the way the physical world behaves.

[Walt Zingmatilder]

Why?

Because according to them the physical is all there is. Imagine if it were the case that in some way mathematics becomes material and has an independent existence not dependent on it but the physical very much beholden to mathematics for it's existence.


There could not also be the same reservations expressed against other ontologies becoming physical.

If maths, whatever it is incarnates in physical form for instance.

[Walt Zingmatilder]

Huh?

Neither is true. The physical world just is. Mathematics only comes into it as the tool that we humans use to describe the way the physical world behaves.

So you dismiss the article?

[Walt Zingmatilder]

Huh?

Neither is true. The physical world just is. Mathematics only comes into it as the tool that we humans use to describe the way the physical world behaves.

Why then pure and applied maths?
What about maths which does not describe the way the physical world behaves?

[jeremyp]

So you dismiss the article?

If the article, which is not a peer reviewed technical article but a journalist's attempt to describe something for lay people, is claiming that the World is really based on octonians rather than that octonians are a good tool for describing the fundamental building blocks of the World, then yes, I reject it. That wasn't the impression I got though.

[jeremyp]

Why then pure and applied maths?

What about them? Pure maths is about finding new maths. Applied maths is about applying maths to other problem domains.

For example, people were exploring the mathematical properties of quadratic equations long before anybody realised they could be used to model the movement of objects in Earth's gravitational field.

What about maths which does not describe the way the physical world behaves?

What about it? Why do you think all maths needs to describe the physical world?

[torridon]

Because according to them the physical is all there is. Imagine if it were the case that in some way mathematics becomes material and has an independent existence not dependent on it but the physical very much beholden to mathematics for it's existence.

Quantum fields give rise to matter but quantum fields themselves are not 'physical'.

[Walt Zingmatilder]

What about it? Why do you think all maths needs to describe the physical world?

I don't....but you it seems do...here is what you said

 

Mathematics only comes into it as the tool that we humans use to describe the way the physical world behaves.

[Walt Zingmatilder]

Quantum fields give rise to matter but quantum fields themselves are not 'physical'.

I think that bears reposting

[Sebastian Toe]

Quantum fields give rise to matter but quantum fields themselves are not 'physical'.

[Udayana]

Quantum fields give rise to matter but quantum fields themselves are not 'physical'.

"give rise" is probably not a good choice of words here.

I don't think anyone here is arguing that maths causes or becomes matter - that includes Furey and the writer.

[Stranger]

I think it might upset the physicalists and materialists somewhat.

Do we have any of those here?

[Stranger]

Neither is true. The physical world just is. Mathematics only comes into it as the tool that we humans use to describe the way the physical world behaves.

That's a rather bold philosophical statement.

[Stranger]

Quantum fields give rise to matter but quantum fields themselves are not 'physical'.

I really don't know what you mean by that. The term matter is not well defined and you put physical in scare quotes.

As far as I know the ontology of quantum theory (QFT and plain old QM) is still a matter of some debate. Those who study QFT are likely to tell you that fields are all there is (particles are excitations or particle-like phenomena due to the quantisation of the fields).

See for example:
Real talk: Everything is made of fields
There are no particles, there are only fields

[torridon]

I really don't know what you mean by that. The term matter is not well defined and you put physical in scare quotes.

As far as I know the ontology of quantum theory (QFT and plain old QM) is still a matter of some debate. Those who study QFT are likely to tell you that fields are all there is (particles are excitations or particle-like phenomena due to the quantisation of the fields).

See for example:
Real talk: Everything is made of fields
There are no particles, there are only fields

Well, yes.  I'd understand 'physical' as pertaining to matter interactions within the spacetime domain, but according to many, spacetime is not fundamental. In the effort to reconcile quantum theory with relativity, spacetime is becoming killed off as a fundamental description of reality, and quantum fields, from which spacetime emerges, are seen as the fundamental description of reality.  Quantum fields therefore do not exist in any place, or at any time; there is no sense of up or down or long or short or quick or slow or before or after; no matter, no speed, no direction, no 'physical'; all of these intuitive concepts have no real meaning and only exist as emergent properties within the context of spacetime which emerges from the interactions of covariant quantum fields.   This is where my head starts to hurt.

[Stranger]

Well, yes.  I'd understand 'physical' as pertaining to matter interactions within the spacetime domain, but according to many, spacetime is not fundamental. In the effort to reconcile quantum theory with relativity, spacetime is becoming killed off as a fundamental description of reality, and quantum fields, from which spacetime emerges, are seen as the fundamental description of reality.  Quantum fields therefore do not exist in any place, or at any time; there is no sense of up or down or long or short or quick or slow or before or after; no matter, no speed, no direction, no 'physical'; all of these intuitive concepts have no real meaning and only exist as emergent properties within the context of spacetime which emerges from the interactions of covariant quantum fields.   This is where my head starts to hurt.

You seem to be talking about the various hypotheses that (as you say) attempt the reconcile existing QFT with General Relativity (it already copes with Special Relativity) whereas I was talking about the well established QFT as used today, in which the fields are defined on a (flat) space-time background.

I'm not sure I'd agree about your definition of physical in either case. "Matter" is a pretty useless term because what it refers to depends on the context. If it turns out that space-time is emergent (Loop Quantum Gravity, for example; at least some of the versions of String Theory start with a, space-time plus other dimensions, background), I don't think that I'd then think of the more fundamental fields as not physical.

[jeremyp]

I don't....but you it seems do...here is what you said

How does my statement that we use maths as a tool to describe the physical world mean that all maths has to describe the physical world?

Maths can be used as a tool to describe the physical world, that doesn't mean it can't be used for other things or even that its primary purpose is to describe the physical world.

[jeremyp]

That's a rather bold philosophical statement.

No it's just a statement that happens to be true.