I was joking with a colleague today about replacing Mathematica (a symbolic math program) with an abacus, and it started me wondering: how would one go about making a "symbolic abacus"?
Let's just limit it to finding roots of polynomials, for example. Could you make a mechanical device that lets you slide/fold/twist "x^2 = x+a" and then slide/fold/twist to get "x = (+/- sqrt(4a+1) + 1 )/2" ?
(Edit: To emphasize symbolic, not numeric solutions)
@catselbow You can generate roots for solvable polynomials just by straight edge and compass constructions; the general n-th degree polynomial equation can be solved in terms of modular forms ( see Thomae's formula for instance) so one might try to translate those functions into a physical machine, similar to how square roots can be dealt with by compass constructions.
@fabian There isn't one, even historically, as far as I know (I am a mathematician, but not a historian of mathematics). The reason, I suppose, is historical happenstance. Most mathematical functions don't get their own symbol (sin, cos, tan, tanh, cosh...) and the log family is no exception; I think it is the square root that is the exception, whose first symbol was invented by Regiomontanus probably for his convenience.
Yesterday, before going to bed, my son explained to me the mathematical rules of life that he saw on YouTube. I understood what he was talking about, I was amazed that he saw the video once and remembered the variety of figures. Today we read a wiki article about it and found a cool online simulator
@cazabon Indeed, these buzzwords are just 21 Century versions of the 90s Clipper chip arguments.
That being said, "encryption is math" is a weak argument in the court; of course a copyrighted song in flac form is also just math, but that does not prevent it from being legislated. There are much better arguments for E2EE, both or practical and foundational character; the cryptography stack exchange has an extensive list of questions related to these issues.
I am a mathematician working in homogeneous dynamics and number theory; I came here from Reddit looking for an alternative and still trying to get the hang of things. I see there is little mathematics activity at kbin.social at this moment, but hopefully this will change.
It seems that the administrator is currently swamped with the influx of users, but I am wondering if in the foreseeable future we can look forward to enabling some sort of LaTeX rendering in the threads, putting us far ahead of reddit in capabilities. Currently, I know only one federated place with LaTeX rendering, which is mathstodon.xyz. I wonder if the methods they are using can be transferred to kbin.
Right now we insert mathematical symbols on kbin.social directly from the list on the magazine column, but this is awkward and limited. Without any meaning to offend, I can see that r/math discussions tend to be less about mathematics and more "around" mathematics, and I have a pet theory that the lack of easy LaTeX input contributes to this phenomenon.
I would love it if this place could host a forum for mathematical discussion at all levels, and would like to hear other people's thoughts on this.
I'm not sure I understand why "Threads" and "Microblogs" are separate entities in kbin. From my understanding, "Threads" are like Reddit's link/image posts and "Microblogs" are like text posts. Why are these only viewable in separate tabs? It seems like a bad thing to completely separate certain content from the same Magazine and make it unable to view everything at once. Am I misunderstanding something?
I am a little confused; so, if I want to make a text thread with threaded replies/comments etc. like in a normal forum, do I select microblog? In particular, how was this thread created, where the first post is text?