The nice thing that happened in class today:
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I wonder if putting it in an addition table format might make it easier?
I've been wanting to do some symmetry group stuff. Bookmarking this for summer. I'd need to play around a lot to see if I can find a simple angle.
@futurebird @johncarlosbaez addition table, multiplication table, it doesn't matter, its an abstract operation. But yeah, I do call it "addition", not multiplication, at least when introducing this stuff.
I think I have a reasonably simple angle for introducing the symmetry group of the square, and that's (imperfectly) represented in the repo as it currently exists. You should print out the calculator front-to-back and play with it for a bit.
I have somewhat developed ideas about how to move from the intuitive approach of my mechanical number line for D_4 to implementing the arithmetic of D_4 using pencil-and-paper calculations. Namely, I think the semidirect product, the 2x2 integer matrix approach, and the permutation-based (i.e. subgroup of S_4) approach are particularly notable.
I don't know where I'd place the lesson on automorphisms, as honestly it need not depend on anything other than the intuitive approach. On the other hand, I'd probably want to prioritize at least one or two of the pencil-and-paper approaches to performing addition in D_4.
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This student wants to "invent a new zero" so. Watch out everyone. Math is about to get a lot more... IDK ... but MORE.
Introduce them to 10-adic numbers, where there's more than one zero.
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@futurebird More... Zero? They do know what zero plus more zero is, right? 🤭
@faithisleaping @futurebird I mean, nonstandard analysis and infinitesimals are a thing, so maybe they're just really forward thinking.
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This student wants to "invent a new zero" so. Watch out everyone. Math is about to get a lot more... IDK ... but MORE.
@futurebird If there can be multiple infinities...just sayin'.
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This student wants to "invent a new zero" so. Watch out everyone. Math is about to get a lot more... IDK ... but MORE.
@futurebird Dedekind showed that any two models of Peano arithmetic are isomorphic. In laymen's terms, if there is something that works like we expect arithmetic to, it will have just the one zero.
This is not obvious, and your student is to be commended for trying things out!
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This student wants to "invent a new zero" so. Watch out everyone. Math is about to get a lot more... IDK ... but MORE.
@futurebird different from undef, null, positive zero, and negative zero? ... okey...
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@futurebird this story has saved my day from being bleh.
@Unixbigot @futurebird damn warp core runs on taking the local warp constant and dividing by the number of seconds since midnight. It crashes at midnight with an F_DIV_ZERO error.
Kit Bashir (@Unixbigot@aus.social)
“We’re out of warp, what’s wrong?” “Nothing, it happens every morning at this time. Just reset it. You haven’t been getting that on B-shift?” “No, and how long—holy crap!” “What?” “Warp degradation has added three days to our ETA so far. TELL ME if stuff breaks; if we miss the book sale on Rigel Four everybody’s getting Curium ash for christmas.” #Tootfic #MicroFiction #PowerOnStoryToot
Aus.Social (aus.social)
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@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
@macbraughton I love Mastodon.
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F myrmepropagandist shared this topic
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This student wants to "invent a new zero" so. Watch out everyone. Math is about to get a lot more... IDK ... but MORE.
@futurebird your students are so lucky to have you
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The nice thing that happened in class today:
Grade 5 students solve a puzzle where they put cuneiform numbers in order (there is no guidance, just work with the symbols, how do you order them?)
I told them they are like archeologists cracking a code. They did it!
"But where is zero?"
"It wasn't invented yet." I said this seriously. I mean ... it's true.Later that day the same student asked if it was a joke. I got to tell them no! Zero had to be invented. Everything had to be invented!
@futurebird In a more perfect world, I would have had you as a teacher when I was a kid. Even for a few months.
I'm so thankful that there are kids out there, right now, with you as their teacher.
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This student wants to "invent a new zero" so. Watch out everyone. Math is about to get a lot more... IDK ... but MORE.
@futurebird your student has a bright future as a topologist
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@futurebird In a more perfect world, I would have had you as a teacher when I was a kid. Even for a few months.
I'm so thankful that there are kids out there, right now, with you as their teacher.
@futurebird I'm curious...thinking about this...but does the concept of zero in mathematics come from rotational calculations? You can't have Pi without zero. Is the lack of zero, more about the approach to keeping track of grain or other crops?
The numbers we count, are the ones we are tracking?
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This student wants to "invent a new zero" so. Watch out everyone. Math is about to get a lot more... IDK ... but MORE.
@futurebird …and I thought things got complex when multiplying by `sqrt(-1)`.
Then again IEEE-754 defines both +0.0 and -0.0 as distinct values.
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The nice thing that happened in class today:
Grade 5 students solve a puzzle where they put cuneiform numbers in order (there is no guidance, just work with the symbols, how do you order them?)
I told them they are like archeologists cracking a code. They did it!
"But where is zero?"
"It wasn't invented yet." I said this seriously. I mean ... it's true.Later that day the same student asked if it was a joke. I got to tell them no! Zero had to be invented. Everything had to be invented!
I get their surprise, I was already in university when I learnt that the Christian calendar that I use every day (not sure how it's called in English, the one with years BC and AD) doesn't have a year zero between 1 BC and AD 1.
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This student wants to "invent a new zero" so. Watch out everyone. Math is about to get a lot more... IDK ... but MORE.
@futurebird
I hope they name it better than imaginary numbers -
This student wants to "invent a new zero" so. Watch out everyone. Math is about to get a lot more... IDK ... but MORE.
@futurebird less is more in this case
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The nice thing that happened in class today:
Grade 5 students solve a puzzle where they put cuneiform numbers in order (there is no guidance, just work with the symbols, how do you order them?)
I told them they are like archeologists cracking a code. They did it!
"But where is zero?"
"It wasn't invented yet." I said this seriously. I mean ... it's true.Later that day the same student asked if it was a joke. I got to tell them no! Zero had to be invented. Everything had to be invented!
Summer reading
Zero: The Biography of a Dangerous Idea
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This student wants to "invent a new zero" so. Watch out everyone. Math is about to get a lot more... IDK ... but MORE.
@futurebird but in seriousness, there is more actual mathematics in this question (can I have a second zero) than in all the calculations we do in school "maths".
Have them write down rules how to use and calculate with their new zero and have them check if they are consistent, and think about a way to check if indeed the two zeroes are truly different numbers, even if they fail to carry that all out, they'll learn a lot about the spirit of mathematics beyond the very limited confines of school "maths" -
@futurebird Dedekind showed that any two models of Peano arithmetic are isomorphic. In laymen's terms, if there is something that works like we expect arithmetic to, it will have just the one zero.
This is not obvious, and your student is to be commended for trying things out!
@bassthang @futurebird they should definitely try!
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@futurebird
I hope they name it better than imaginary numbers
