Nice! The other thing people talk about with these Artin braid groups is actions on free groups, which i'm now understanding as a mapping class group acting on pi_1 of a punctured surface (and the punctures trace out the braids) .. and this pi_1 is a free group (or close to..?)
gives the symmetric swap diagram
You get these from swapping "row major" to "column major" counting array entries, for example this one
And just for fun going to p=5... looks like we get some kind of order (p-1) Sierpinsky triangle.
Here is the p=3 version, counting prime factors equal to 3
What does the SierpiΕski triangle have to do with Pascal's triangle? Here's a pictorial answer; i'm just learning about this from Bowman's "Diagrammatic Algebra" book
wow, the braided symmetric string diagram does have the Coxeter braid relation ABAB=BABA ! what is this magic
A string diagram for an element of the hyperoctahedral group has a symmetry property, from Bowmans book "Diagrammatic Algebra". This immediately suggests a braided version ... hmm..
nice! how do i undo?
I think you are interfacing to a hyperbolic surface code
Wherein philosophy is dragged, kicking and screaming, into the twentieth century.
The word "nothing" is doing a lot of work here and I'm not sure it is up to the task.
I see, good point, thankyou.
People do make superpositions of some very large systems, (i think even a tardigrade?) so what are you saying ? Are you the ket-police now?
I think I am just about ready to make my own search engine.
Ruth Kastner has some things to say about field theories..
It must be so frustrating to have billions of dollars and still be a miserable a**hole.
The principle of "two big ideas": one contains the other, or else they are not big ideas.
If people are going to continue to put the introduction to their paper in the abstract, then i'm going to put my paper's abstract in the title.
Any sufficiently complicated physics paper contains an ad hoc, informally-specified, bug-ridden, slow implementation of half of an idea from algebraic geometry.
Today's OEIS fishing expedition. The only question is how much RAM am i going to need to find the next number... Love these OEIS cliff-hangers! ARGGH
It's *a* graphic framework. I've been using 3d string diagrams for this stuff... Here is a laxator for a monoidal functor, which is the blue string. The monoidal product is the sheet layers... etc etc
it's mostly excel spreadsheets..
Still trying to figure that out, will get back to you.
If by "the completely standard way" you mean, as taught in undergraduate quantum mechanics, then yes. I can't remember the last time i saw the Born rule actually used in the wild. It tends to be only in discussions like this about the foundations of quantum.
Behold! A one-qubit quantum computer:
i don't know if it's really a "need", but here is one way to get probabilities: en.wikipedia.org/wiki/Born_rule
I think it's just as valid saying you get zero-worlds when you don't add anything to the SchrΓΆdinger equation. I happen to prefer this interpretation (the zero-worlds one) on my more transcendent days.
from: canyon23.net/math/tc.pdf
no don't kill it. Yes we need it.
