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The Octonion Math That Could Underpin Physics

quantamagazine.org

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Re: The Octonion Math That Could Underpin Physics

#51

Post by raverbashing »

madhadron wrote: post #24
_bxg1 wrote: post #15

Earlier quoted context omitted.

It's my understanding that most of Einstein's theory was the product of intuition, backed up after-the-fact with mathematics and experimentation. Intuition isn't a bad compass, as long as you can set it aside if reality measurably contradicts it. In fairness, Einstein never accepted quantum mechanics because they flew in the face of his intuition, but it still got him pretty far.

This is very false. Einstein's reputation was built on explaining known phenomena such as the photoelectric effect and Brownian motion. Special relativity was heavily motivated by a pile of puzzling evidence and a bunch of existing mathematics.

It's not false, w.r.t. general relativity

And you still need a good amount of creativity to come up with special relativity and to a certain extent, with the photoelectric effect (though we could say that was the 'easy' one)

But yes, the puzzling results and existing mathematics were part of it. But there is a reason we hear much more about Einstein than Lorenz or Michelson-Moreley

Re: The Octonion Math That Could Underpin Physics

#52

Post by RobertoG »

whatshisface wrote: post #35
OscarCunningham wrote: post #19

Earlier quoted context omitted.

Surely what we're looking for is the simplest theory among the theories that hit all the datapoints. That's the theory that's most likely to be the "Theory of Everything" and therefore to continue working when we upgrade our collider.

Why would the simplest theory be the most likely to be true?

Occam's razor is not about the simplest theory being true, but about how from a simple theory you can create infinite more just adding an element.

If you have infinite possible theories, the only logical thing to do is to stay with the most simple theory until it can't explain the world anymore, then you choose the next one more simple.

There is also, I think, a theoretical information argument: when creating a theory you are trying to compress all the observations. The better the compression, the better the theory.

I don't understand why people down-vote you, by the way.

Re: The Octonion Math That Could Underpin Physics

#53

Post by sigstoat »

Micoloth wrote: post #29
fifnir wrote: post #14

A layman's quest to understand wtf this is... >In mathematics, the octonions are a normed division algebra over the real numbers . wtf is a normed division algebra?? >In mathematics, Hurwitz's theorem is a theorem [...] solving the Hurwitz problem for finite-dimensional unital real non-associative algebras endowed with a positive-definite quadratic form. ... right. I have the same problem when I try to understand any…

Well yeah, math books... Jokes aside, i too think we need a new framework for divulgating math that actually tells what you need to know, without just handwaving at it, BUT without the amount of technical details of a mathematics class. What do you know, i think this is Possible, too.. You can communicate a surprising amount of information if you use words properly. Of course, since this has never been done except fr…

> Jokes aside, i too think we need a new framework for divulgating math that actually tells what you need to know, without just handwaving at it, BUT without the amount of technical details of a mathematics class.

oh man, have i got bad news for you about the amount of technical detail present in math classes.

Re: The Octonion Math That Could Underpin Physics

#54

Post by RobertoG »

whatshisface wrote: post #49
tlb wrote: post #43

Earlier quoted context omitted.

That's a big topic, and the definition of simple is subtle. I recommend David Deutsch's book _The Beginning of Infinity_ for an accessible introduction to what makes one theory better than another when they both fit the observations.

One theory might be better than another when they both fit the observations, but you can't say which one is true-er. For example, were Newton been presented with GR but only allowed his contemporary evidence, he should not conclude that classical gravitation is more true than GR on the grounds that he doesn't have any evidence for the additional complexity.

I think you are wrong. If he is following the scientific method, and he doesn't have evidence, he should 'conclude' that.

The key is that in science, you never 'conclude' (in the sense of finalize) anything. Everything is temporal until new evidence deny your current understanding.

Re: The Octonion Math That Could Underpin Physics

#56

Post by atonalfreerider »

imglorp wrote: post #45

How does this tie into E8? Does this work validate Garret Lissi or is it parallel? https://en.wikipedia.org/wiki/An_Exceptionally_Simple_Theory...

I remember hearing Garret Lisi's TED talk on the E8 ToE (link below) years ago and hoping that components of the theory would eventually come to light through advances in particle physics research. Has anyone heard anything supportive or to the contrary since?

TED Talk: https://www.ted.com/talks/garrett_lisi_on_his_theory_of_ever...

Paper: https://arxiv.org/abs/0711.0770

Edit I remember seeing an update from him two years ago where he addresses some of the criticism: https://www.quora.com/What-is-the-status-of-Garrett-Lisis-E8...

Re: The Octonion Math That Could Underpin Physics

#57

Post by sigstoat »

fifnir wrote: post #32
Micoloth wrote: post #29

Earlier quoted context omitted.

Well yeah, math books... Jokes aside, i too think we need a new framework for divulgating math that actually tells what you need to know, without just handwaving at it, BUT without the amount of technical details of a mathematics class. What do you know, i think this is Possible, too.. You can communicate a surprising amount of information if you use words properly. Of course, since this has never been done except fr…

> only do it if it made economic sense What if writing wikipedia articles was treated like publishing on prestigious journals? (somehow)

wikipedia already covers abstract algebra (the subject necessary for understanding the math in this article) rather well. what more do you want?

Re: The Octonion Math That Could Underpin Physics

#58

Post by scotty79 »

> “Because while it’s very easy to imagine noncommutative situations — putting on shoes then socks is different from socks then shoes — it’s very difficult to think of a nonassociative situation.” If, instead of putting on socks then shoes, you first put your socks into your shoes, technically you should still then be able to put your feet into both and get the same result. “The parentheses feel artificial.”

> The octonions’ seemingly unphysical nonassociativity has crippled many physicists’ efforts to exploit them.

I'd say nonassociativity is extremely physical property. And example with shoes and socks, if anything, shows just that. In idealised mathematical model, if you put socks inside shoes and then insert feet into socks you could end up with same thing as if you put feet in socks an then both in shoes. But in real world or just accurate model of physical world you'll end up with very different result.

I feel that nonassociativity is what's missing to take into account time which unidirrctuonality is suspiciously missing from almost all of the physics.

Re: The Octonion Math That Could Underpin Physics

#59

Post by throwaway37585 »

fifnir wrote: post #14

A layman's quest to understand wtf this is... >In mathematics, the octonions are a normed division algebra over the real numbers . wtf is a normed division algebra?? >In mathematics, Hurwitz's theorem is a theorem [...] solving the Hurwitz problem for finite-dimensional unital real non-associative algebras endowed with a positive-definite quadratic form. ... right. I have the same problem when I try to understand any…

Some useful advice: https://math.stackexchange.com/questions/617625/on-familiari...

Re: The Octonion Math That Could Underpin Physics

#60

Post by danbruc »

In the approach from the article it seems as you are picking a mathematical structure in the middle of nowhere with the universe faintly visible at the horizon and then you start wandering around hoping that you will stumble across a path leading to the horizon.

But there don't seem to be many reason to believe that such a path exists, there are countless mathematical objects you could pick as a starting point and almost none of them have a path leading to the universe at the horizon. And even even of those with path going roughly into the right direction many will take a turn before you arrive at your destination.

So it seems much more promising to me to start at the universe and the mathematical structures describing our observations in a straight forward way and then explore from there the surrounding mathematical structures to see if they are a better fit, suggest new ideas, or whatever.

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