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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

#91

Post by Cobord »

arketyp wrote: post #44
_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.

Gödel was motivated by convictions about meta-mathematics, motivated by his Catholic fatih. Perhaps a purely mechanistic world view would have eventually generated the same result, e.g. Turing's halting problem, but who knows.

Gödel spacetimes to fuck with your intuitions.

Re: The Octonion Math That Could Underpin Physics

#92

Post by Cobord »

ansible wrote: post #75
atonalfreerider wrote: post #56

Earlier quoted context omitted.

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…

There's been some criticism of his work, back when it first came out. I'm fuzzy on the details now, but the criticism was along the lines of "mixing things together that don't make sense".

I remember something about being unable to do any CP violation.

Re: The Octonion Math That Could Underpin Physics

#93

Post by Cobord »

sigstoat wrote: post #57
fifnir wrote: post #32

Earlier quoted context omitted.

> 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?

Thank Richard Borcherds (R.E.B.) for a lot of that.

Re: The Octonion Math That Could Underpin Physics

#94

Post by gowld »

Maybestring wrote: post #7
anaphylactic wrote: post #3

> There the game stops. Proof surfaced in 1898 that the reals, complex numbers, quaternions and octonions are the only kinds of numbers that can be added, subtracted, multiplied and divided. 1. I think they meant "the only kinds of numbers constructed in this way ". 2. Sedenions can still be added, multiplied, subtracted and divided. it's just that multiplication and division lose most of their useful properties. Wit…

>it's just that multiplication and division lose most of their useful properties. Specifically they lose the property of not having zero divisors. There exists sedonions a,b != 0 such that ab = 0

Are there 32-onions that lack power associativity?

https://en.wikipedia.org/wiki/Power_associativity

https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_constru...

Re: The Octonion Math That Could Underpin Physics

#95

Post by AnimalMuppet »

sigstoat wrote: post #57
fifnir wrote: post #32

Earlier quoted context omitted.

> 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?

Something that covers abstract algebra rather well if you don't already know abstract algebra well enough to know what all the terms mean?

I mean, I suppose you could try to walk the graph of definitions of terms in Wikipedia to try to understand one of the articles. But I'm pretty sure that's not an acyclic graph, and it's not clear where to start in that process.

Re: The Octonion Math That Could Underpin Physics

#96

Post by gowld »

_bxg1 wrote: post #15
ianai wrote: post #2

I think the following quote is the QED for academia ruining any chance at actual research: “What I had was an out-of-control intuition that these algebras were key to understanding particle physics, and I was willing to follow this intuition off a cliff if need be. Some might say I did.”

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.

Thought experiments, not intuition. Thought experiments are kind of theoretical physics: Making an assumption ("c is the universal speed limit"), and thinking about the implications ("addition of velocity cannot be linear"), even though available experimental tools are not powerful enough to demonstrate the implications in a way observable to the though-experimenter.

Re: The Octonion Math That Could Underpin Physics

#97

Post by 77pt77 »

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…

unital -> there is a multiplicative identity 1 such that 1.a = a for all a.

normed -> there is a norm. A way of saying how big an element is. In the reals |x| - x if x is positive and -x if x is negative. In the complex numbers |a+bi| = (a^2 + b^2)^(1/2)

Division -> Division (except possibly by zero) is always possible. That means for a and b not zero there exists c such that a=cb (c is a divided by b)

I could be wrong about these things since I'm quite rusty

Re: The Octonion Math That Could Underpin Physics

#98

Post by firethief »

whatshisface wrote: post #4

I think that maybe if you lock a mathematical physicist in a box forever with an x-TeV collider without letting them upgrade it, they will eventually find a theory that hits all of the datapoints and depending on their philosophical weakness then declare it "final."

Well they will and they won't, until you open the box

Re: The Octonion Math That Could Underpin Physics

#99

Post by simcop2387 »

sannee wrote: post #76
danbruc wrote: post #60

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 al…

> In the approach from the article it seems as you are picking a mathematical structure in the middle of nowhere Quaternions were very popular way of expressing the "classical" physics around the 19th century (and the vector algebra we know today is in some ways just a derivative of quaternion algebra). Complex numbers are extremely useful in many fields even today. It's hardly in the middle of nowhere.

Yep complex numbers get used extensively for doing calculations with electronics when doing analysis.

https://www.khanacademy.org/science/electrical-engineering/e...

Re: The Octonion Math That Could Underpin Physics

#100

Post by yedawg »

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?

Decrease the number of variables and conditions to any physical system; say to something binary and you end up with a 50/50 argument, which means at worst means you can always fall back on trial and error, and at best you might discover something you didn't see before. Simple theories are better than "holistic" theories, because they act as a starting point for many more testable simple theories. Knowledge at it's most primitive form is ultimately somewhat binary, completely testable and scalable.
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