The nice thing that happened in class today:

@kbm0 @futurebird the kid is on to a fundamental truth of math, that you can always ask questions with the tools you have that seem to make no sense until we decide, what would have to go in that slot so they did make sense? So we get zero, then negative numbers, then fractions, soon irrationals, and and and and

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@munin @futurebird @Unixbigot

Watman

jz.tusk

@futurebird

Hee-hee, topologist have already got "the line with two origins", but we gotta let this student run free and see what they come up with on their own.

Sarah dreams of beans

@mhoye @futurebird Typography has uppercase and lowercase zeroes, but they are usually called lining and old style figures

ersatzmaus

@lapis @futurebird The concept of "nothing" was known. What people didn't have was place-value number representation.

So there was no easy way to multiply by, say, 10 (assuming your base was 10).

Compare arithmetic with roman numerals versus arithmetic with indo-arabic numerals.

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@futurebird And of all the numbers, zero had to be invented the most!

myrmepropagandist

@SarraceniaWilds

Maybe ϵ would be another "zero at home"

Donnie

@futurebird that's awesome. I don't share my work very often, but especially because you mention cuneiform, I actually have "invented" a new zero, called zo, in a modern base-60 number system, inspired by the Babylonian system and Wu Xing

hyxos_numerals/GRAMMAR.md at main · hyxos/hyxos_numerals

A rust library for working with the Hyxos Numerals - hyxos_numerals/GRAMMAR.md at main · hyxos/hyxos_numerals

GitHub (github.com)

There is a very poorly written and not maintained api to generate the glyphs at https://hyxos.io/docs

I'm plodding away in my spare time trying to turn it into something more usable to make it more accessible for everyone... up to this point it's mostly been used by my wife and I to build card game prototypes.

I'm hoping to release a much more polished glyph builder this year, I really want to make a typeface, and oh boy, that is a deep, deep rabbithole

Hey Gus

@futurebird in all seriousness that’s awesome. They were engaged and interacting.

Most importantly made an awesome joke lol

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@futurebird they say the Roman Empire fell for lack of any way to indicate successful exit of their programs

myrmepropagandist

@hypolite @lapis

Zero makes record keeping nicer and when you start using place value (as cuneiform does) to get more out of your limited symbol set ... zero make things less ambiguous.

One needs a way to show which place the symbol lives in even if you don't have everything written in neat columns.

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@futurebird @SarraceniaWilds algebra with a "bottom element" is fun also

Leon P Smith

@futurebird Actually I have a (very undeveloped) concept of a lesson with respect to the symmetry group of the square.

Basically, after the class has been introduced at least to the intuitive approach to the symmetry group of the square, you give them a problem where they have to "solve" a substitution cipher from {a,b,c,d,e,f,g,h} or whatever to the symmetry group of the square, given the multiplication table of that substitution cipher.

The lesson here is that this problem doesn't have a single unambiguous answer: rather you can solve the substitution cipher for a few elements like the identity element and the "rotate by 180 degrees" element, but you can only classify the rest of the substitution cipher up to the symmetry group of the symmetry group of the square, more technically known as the automorphisms of D_4.

I was thinking maybe there's an angle to develop as like an alien linguist as part of a Star Trek science team, and perhaps even make it a trick question by making it seem like they are expected to find the one "true" solution.

It turns out that the automorphisms of D_4 is isomorphic to D_4, which is definitely a very yo dawg moment, but it turns out this is very much accidental. Groups G that are isomorphic to their own automorphism group include all complete groups, but this is one of a handful of sporadic exceptions of a group that is not complete but also isomorphic to its automorphism group. This includes D_4, D_6, D_∞, and may include a few more unknown examples.

It turns out that all the symmetric groups (i.e. groups of permutations of n elements) are complete except for n=2 and n=6. The n=6 exception actually pretty interesting, and @johncarlosbaez likes to talk about it.