This is less math and more physics - which is math with rules

Ooh, I kinda want to 3dprint that

Not a mathematician but here's my guess:

Not sure how to prove rigorously, infinities always confuse me a bit when it comes to what is and isn't allowed.

1 + 1 + 1 + 1 + 1 + 1 + … = 1 + (-1) + 2 + (-2) + 3 + (-3) + 4 + (-4) + 5 + …

You forgot -5+6 on purpose.

You know I never liked the name Twitter either, let's rename it X! That will stick

The theorem of all time.

Theorem McTheoremface

They only ever use the face bit of the photo. If they never knew the source was Playboy, they would have been completely fine with it. Rampant Puritanism, like people can't be free to be body positive and model if they please

This is one of those things that you wouldn't believe if it happened in a fictional story but it completely fits with what we know about Newton's personality.

It's not clear if the "solution" was worked out by modern scholars or if Newton told someone the answer? I bet he didn't.

Pour ses cours au Collège de France

https://www.college-de-france.fr/fr/enseignements/audios-videos?f%5B0%5D=chair%3A3547

Solid ending. Worth it.

The correct term is reductio ad absurdum.

Sorry for being so pedantic.

Out of.. binary 10?

I give it 22 out of 10

It's baffling how many civilizations adopted the abacus, but kept using numeral systems that weren't representations of the abacus. Writing numbers by repeating symbols was definitely a thing in the middle east. Babylonians had a sort of dual positioned numeral system, counting up to nine 1s and five 10s, and calling that cluster a single digit. The Egyptians had a separate symbol for each position and wrote as many as they needed. But several systems were like Greek numerals, where there's different symbols for 1-9, and then for 10, 20, 30, etc., and for 100, 200, 300, etc. The Romans... sheesh.

I'm not aware of any written numbers that simply reflect the state of an abacus. It would be trivial - a stack of maybe four dots, sometimes a bar over top, and a vertical line for zero. People already have to think in these terms, to use an abacus. Teaching the number system teaches people how to use an abacus, and vice-versa.

And if little Egalmah gave one digit six dots and two bars to avoid a long carry, eh, close enough.

The simpler explanation is, a logarithm is how many times you've multiplied a number.

This is easy to see with bases like 1.1, where 2 is about 7 times, and 5 is about 17 times. So doing it 7+17 times, for 1.1^24^, gives you 2x5≈9.8.

Ratios happen to be the same in any base. log(5) will always be about 2.3 * log(2). If your base is 2, then log2(5) is about 2.3. You are scaling all measurements such that log2(2) is 1. To turn any base into log10, you simply find log(10), and divide by that.

Finding log(10) for bases closer to 1 can be easy, because squaring a number doubles how many times you've multiplied your base. 1.1 squared is 1.21, squared is 1.4641... two steps, but four times. For 1.00001, getting past 10 takes 18 steps. That's 2^18^ times, which is 262,144, and the result is closer to 14 than 10. The 15th step was pretty close to 1.4, though, so you can divide by its exact result, and subtract 2^15^ times. Finding the closest integer power this way needs only dozens of longhand operations.

And yet: it took until the 1600s.

The ancient Babylonians had something they called logarithms. They figured out a * b = 1/4 * ( (a+b)^2^ - (a-b)^2^ ), so they had lookup tables for 1/4 * x^2^.

The Romans understood compound interest, well enough to ban it entirely. Even with their goofy numeral system, they'd been repeatedly multiplying fractional values.

At any point in recorded history, someone could have scribbled out powers of two at even distances, copied that onto two sticks, and gone "... Huh." But it never happened! It wasn't until after the Renaissance that a mathematician fell backwards onto what would define calculation until well into the industrial revolution. It's maddening! Three millennia of people playing with numbers, before anyone noticed this, and then only two decades between Logarithmorum and the invention of the slide rule.

This was awesome, thank you! Not sure if it’s a voyager client issue, but the bolded numbers in the diagonal proof did not show as bolded for me.

Wonderful post thank you!

Wait, no, it is in the new building! Level 3, East side, section "Droit, Économie, Sciences", just next to the librarian’s desk. Still in its case, ha ha. I guess I missed it the last time I was here — unless it hadn’t been installed yet.

There used to be one displayed at the BPI library in Paris, but it hasn’t been moved to their temporary new building, as far as I can see. I always wished I could play with it, but unfortunately it was protected from idiots like me by a clear case. :-)

We used to be a country.

I saw this as a child, and it was inspiring! Check it out, you might really enjoy it!

I don't have time to read, let alone understand this, but, very cool!

i thought about this pretty long, not really understanding it until it made click: my 1/3 probability for choosing a door didn't change, but the total probability always has to be 3/3, so the other choice HAS to be worth 2/3.