Why are complex numbers not called duonions then?
And why are the real numbers not called "onions"?
The Octonion Math That Could Underpin Physics
71–80 of 192 posts
Re: The Octonion Math That Could Underpin Physics
#72Earlier quoted context omitted.
As a current PhD student, I'd say the vast majority of researchers aren't anywhere near that enthusiastic about their research.
Many marriages fail in the time it takes to complete a phd. If academia can’t find a way to fund people with actual interest then somethings wrong.
Yet they have no trouble raising tuition every year.
Re: The Octonion Math That Could Underpin Physics
#73I’ve been exploring this idea as well however I have a hunch it’s not actually octonions but dual quaternions as they are the perfect formalism for representing 3d movement over time. And to add to that, the are a Lie group I.e. they are anticommutative I.e. AB=-BA. I’ve also been exploring this relationship between dual quaternions and linear logic. It’s pretty wild. I’m curious if anyone has any opinions on this.
Incidentally, I've also been thinking about dual quaternions for modeling rigid objects in 3d. For anyone who's curious about the topic, these seem to be a decent set of notes: http://web.cs.iastate.edu/~cs577/handouts/dual-quaternion.pd...
Linear logic always reminded me of the no-cloning property in quantum physics, where a resource can only be used once -- no copying for multiple use.
Can you elaborate on the sense in which you think of linear logic as "squaring to zero"? UPDATE: A little googling throws up this: http://www.seas.upenn.edu/~sweirich/types/archive/1999-2003/...
Re: The Octonion Math That Could Underpin Physics
#74I think this is the first article I've ever read about the octonions that didn't include the following John Baez quip: "There are exactly four normed division algebras: the real numbers ($\R$), complex numbers ($\C$), quaternions ($\H$), and octonions ($\O$). The real numbers are the dependable breadwinner of the family, the complete ordered field we all rely on. The complex numbers are a slightly flashier but still…
For the curious, John Baez has written about octonions pretty extensively: http://math.ucr.edu/home/baez/octonions/
happy to see John Baez fans on here, i like his series on his favorite numbers https://www.youtube.com/watch?v=vzjbRhYjELo
Re: The Octonion Math That Could Underpin Physics
#75How 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…
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".
Re: The Octonion Math That Could Underpin Physics
#76In 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.
Re: The Octonion Math That Could Underpin Physics
#77It's rather amusing that the author assumes that non-associtiave objects are "weird" for physicists (or at least that was my reading), since the velocity addition formula is in general non-associative and that has been extensively studied. (I remember three separate occasions in my undergrad particle physics class where we actually went through all the calculations involved with the velocity addition formula and fina…
Not to mention operator calculus. Operators do not, in general, associate. Feynman developed his own notation for operator calculus.
Re: The Octonion Math That Could Underpin Physics
#78Earlier 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…
> 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.
> the amount of technical detail present in math classes
You misspelled "gatekeeping".
Re: The Octonion Math That Could Underpin Physics
#79In 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…
The article briefly alluded to this, that C, R, H are both already seen in features of the universe, so it's not "middle of nowhere."
Re: The Octonion Math That Could Underpin Physics
#80Earlier 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?
Volumes have been written about this topic (principle of least assumption, parsimonious representation, Occam's razor, etc.). It underlies all statistical learning theory and information theory of which science is a special case.