The nice thing that happened in class today:
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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 -
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 wish I had that “math” class that inspired “zero indignation” -
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@futurebird I wish I had that “math” class that inspired “zero indignation” -
@dahukanna @futurebird But Dawn, Myrmi, we kinda did, dint we? Like, how would we know, otherwise?
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@dahukanna @futurebird But Dawn, Myrmi, we kinda did, dint we? Like, how would we know, otherwise?
@dahukanna @futurebird I was once asked what book a 13yo should read about math. I said "give'em Eric Bell's _Men of Mathematics_".
The book is well-written, and it's full of scurrilous gossip and silly legendary bullshit.
But at 13, we don't really need to know the truth of everything. We need to know that math really *matters*, we need to know that actual *people* made math.
Bell's a great story-teller, and at 13 we need to know we are part of a story.
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@dahukanna @futurebird I was once asked what book a 13yo should read about math. I said "give'em Eric Bell's _Men of Mathematics_".
The book is well-written, and it's full of scurrilous gossip and silly legendary bullshit.
But at 13, we don't really need to know the truth of everything. We need to know that math really *matters*, we need to know that actual *people* made math.
Bell's a great story-teller, and at 13 we need to know we are part of a story.
@GeePawHill - 1,000,000%
@futurebird has me remote attending her class making cards right now for that exercise, engaging my curiosity and play. I would be literally skipping iin to class, waiting in anticipation for “math-drama” challenge.
I’m NOT doing the work because of “standard” test and I was not thinking about “inventing zero” pre-university.
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@GeePawHill - 1,000,000%
@futurebird has me remote attending her class making cards right now for that exercise, engaging my curiosity and play. I would be literally skipping iin to class, waiting in anticipation for “math-drama” challenge.
I’m NOT doing the work because of “standard” test and I was not thinking about “inventing zero” pre-university.
@dahukanna @futurebird Yep. Cuz we're an us.
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@futurebird
I've been in the late-capitalist dystopia long enough that "new zero" sounds like "now you need an app and a subscription to do math".@silvermoon82 @futurebird Non-Fungible Zero
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@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.
@ersatzmaus @lapis @futurebird
The Romans used an abacus or similar for arithmetic. Or slaves that used other number systems.
Roman Numerals were only used to record numbers.
Read Georges Ifrah
"From One to Zero" revised as "The World's First Number-Systems" (The Universal History of Numbers 1).
The ancients knew about zero, but the big breakthrough was using it for place number system instead of a gap.
The Romans invented concrete, bureaucracy & some war machines. Most else was copied. -
This student wants to "invent a new zero" so. Watch out everyone. Math is about to get a lot more... IDK ... but MORE.
@futurebird C has at least four kinds of zero. I’m sure there’s space for at least one more.
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@ersatzmaus @lapis @futurebird
The Romans used an abacus or similar for arithmetic. Or slaves that used other number systems.
Roman Numerals were only used to record numbers.
Read Georges Ifrah
"From One to Zero" revised as "The World's First Number-Systems" (The Universal History of Numbers 1).
The ancients knew about zero, but the big breakthrough was using it for place number system instead of a gap.
The Romans invented concrete, bureaucracy & some war machines. Most else was copied.@raymaccarthy @lapis @futurebird I'm aware, I was using the roman numeral system as an example. I did mention place-value as the key innovation.
