Religion and Ethics Forum
General Category => Science and Technology => Topic started by: Nearly Sane on July 21, 2018, 08:48:52 PM
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The Rise of the Octonions. Fascinating stuff.
https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/
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Wow.
Squirrelled away for later study.
Ta
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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.
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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.
???
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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?
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Why would you think that?
I think it might upset the physicalists and materialists somewhat.
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I think it might upset the physicalists and materialists somewhat.
Why?
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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.
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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.
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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?
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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?
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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.
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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?
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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'.
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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.
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Quantum fields give rise to matter but quantum fields themselves are not 'physical'.
I think that bears reposting
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Quantum fields give rise to matter but quantum fields themselves are not 'physical'.
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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.
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I think it might upset the physicalists and materialists somewhat.
Do we have any of those here?
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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.
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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 (https://www.symmetrymagazine.org/article/july-2013/real-talk-everything-is-made-of-fields)
There are no particles, there are only fields (https://aapt.scitation.org/doi/10.1119/1.4789885)
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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 (https://www.symmetrymagazine.org/article/july-2013/real-talk-everything-is-made-of-fields)
There are no particles, there are only fields (https://aapt.scitation.org/doi/10.1119/1.4789885)
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.
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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.
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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.
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That's a rather bold philosophical statement.
No it's just a statement that happens to be true.
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No it's just a statement that happens to be true.
How do you know?
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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.
what you have written is the qualification and clarification I think I can agree on now that you have agreed maths has a wider role.
Physics though seems to dependent on maths in a way maths is not dependent on physics by dint that maths can be used for other things and the physical world might not,as you suggest, be it's primary purpose.
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How do you know?
Good question.
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How do you know?
The physical world is not made of maths. Maths is about abstract concepts and we are just lucky that the physical world can be represented (approximately) by abstract mathematical concepts. For example, there is an equation that describes an electron, but an electron is not that equation and one day we may discover that it doesn't always obey the equation.
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Physics though seems to dependent on maths
If by "physics" you mean the scientific subject invented by humans, I would agree with you. Maths is the language we use to describe the physical world and make predictions about it.
If you mean the physical world, I would disagree with you. Maths is its description, not its prescription.
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The physical world is not made of maths. Maths is about abstract concepts and we are just lucky that the physical world can be represented (approximately) by abstract mathematical concepts. For example, there is an equation that describes an electron, but an electron is not that equation and one day we may discover that it doesn't always obey the equation.
That's just a further statement of your view, not how you know it to be true. I'm not saying you're wrong but I don't see how you can rule out the idea that what you are calling 'lucky' doesn't have a greater significance. How do you know that the ideas of (for example) Tegmark (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis) are wrong?
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If by "physics" you mean the scientific subject invented by humans, I would agree with you. Maths is the language we use to describe the physical world and make predictions about it.
If you mean the physical world, I would disagree with you. Maths is its description, not its prescription.
I mean the physical world. Several physicists and others would disagree with you. Maths has arisen which is not dependent on physical observation. On the other hand no physics or observation of the physical has been made that does not conform to mathematical principles and indeed much of the physical has been predicted by pure mathematics.
I don't think you have grasped the significance of the maths which is not descriptive if anything in the physical world eg the maths used to model simulated universes. Also there is the independence of maths from physics.... a suitable machine calculating the graph of a quadratic equation would yield the same result whether in a freezer or a furnace.
Because of these properties of maths Tegmark et al question a simple defining of maths as a tool or description of the observable.
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On the other hand no physics or observation of the physical has been made that does not conform to mathematical principles and indeed much of the physical has been predicted by pure mathematics.
What mathematical principle does the orbit of the Earth around theSun "conform to"? 150 years ago, people would have said it conforms to Newton's gravitational equation but then Einstein came up with a better theory. Does the Earth's orbit conform to general relativity? OR is general relativity a description of that the Earth does? It would be a brave person who would say GR will never be superseded by a better description. Maybe the real Universe cannot be modelled accurately by maths at all. Perhaps we can only find better and better but ultimately wrong approximations.
I don't think you have grasped the significance of the maths which is not descriptive if anything in the physical world eg the maths used to model simulated universes. Also there is the independence of maths from physics.... a suitable machine calculating the graph of a quadratic equation would yield the same result whether in a freezer or a furnace.
I don't think you grasp the fact that you offered up a false dichotomy.
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Maybe the real Universe cannot be modelled accurately by maths at all. Perhaps we can only find better and better but ultimately wrong approximations.
Maybe so, but equally maybe there is a mathematical theory of everything and maybe what you referred to as "lucky" in #28 (http://www.religionethics.co.uk/index.php?topic=15870.msg740946#msg740946) isn't luck at all and is indicative of some necessary relationship between mathematics and the physical universe.
How are you so sure?
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Maybe so, but equally maybe there is a mathematical theory of everything and maybe what you referred to as "lucky" in #28 (http://www.religionethics.co.uk/index.php?topic=15870.msg740946#msg740946) isn't luck at all and is indicative of some necessary relationship between mathematics and the physical universe.
How are you so sure?
The theory of everything wouldn’t actually be everything, it would just describe everything, perhaps perfectly, but we’ll never know.
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The theory of everything wouldn’t actually be everything, it would just describe everything, perhaps perfectly, but we’ll never know.
I agree we could never know but this is really just another restatement of your position, not the reason(s) why you are so sure.
The relationship between mathematics and the physical universe has been debated for millennia, yet you seem confident enough to proclaim the matter settled.
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I agree we could never know but this is really just another restatement of your position, not the reason(s) why you are so sure.
The relationship between mathematics and the physical universe has been debated for millennia, yet you seem confident enough to proclaim the matter settled.
Maths is a language for describing abstract objects. It's not "stuff" in the sense that the Universe is stuff. It's as nonsensical to say the Universe is made of mathematics as to say that this cup of coffee is made of the English language.
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Maths is a language for describing abstract objects. It's not "stuff" in the sense that the Universe is stuff. It's as nonsensical to say the Universe is made of mathematics as to say that this cup of coffee is made of the English language.
I'm going to put that statement in a safe place - and try to remember where it is - so that I can quote it when appropriate.
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Maths is a language for describing abstract objects. It's not "stuff" in the sense that the Universe is stuff. It's as nonsensical to say the Universe is made of mathematics as to say that this cup of coffee is made of the English language.
Another restatement of your position. The problem is that we have no idea what 'stuff' is and, more specifically, we don't know why there seems to be a close relationship between 'stuff' and mathematics, which have led may people, over the course of millennia, to speculate about some necessary connection or even identity (Tegmark (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis)). Many mathematician feel that mathematics is discovered rather than invented, so we would then have two 'systems' we are discovering with a very close correspondence.
I still have no idea where you get the confidence to dismiss all that and call the relationship between the physical world and mathematics 'lucky'.