Mathematical secrets of ancient tablet unlocked after nearly a century of study (2017)
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Re: Mathematical secrets of ancient tablet unlocked after nearly a century of study (2017)
#2More detailed video of Plimpton 322 from the authors of the paper https://youtu.be/L24GzTaOll0?si=sNdwKiM7uYXbzVfL
Re: Mathematical secrets of ancient tablet unlocked after nearly a century of study (2017)
#3It's probably worth adding the context that Wildberger's agenda is to ground mathematics in integers and rational numbers, eliminating those pesky irrationals Euclid introduced, because reasoning about them invariably involves infinities or universal quantifiers, which everyone agrees are tricky and error-prone, even if they don't agree with Wildberger's radical variety of finitism. So he was delighted to find a kindred spirit millennia ago in the Plimpton 322 scribe and, presumably, the entire Babylonian mathematical tradition.
cf. https://en.wikipedia.org/wiki/Divine_Proportions:_Rational_T...
Re: Mathematical secrets of ancient tablet unlocked after nearly a century of study (2017)
#4It's probably worth adding the context that Wildberger's agenda is to ground mathematics in integers and rational numbers, eliminating those pesky irrationals Euclid introduced, because reasoning about them invariably involves infinities or universal quantifiers, which everyone agrees are tricky and error-prone, even if they don't agree with Wildberger's radical variety of finitism. So he was delighted to find a kind…
How do we do things like electrical engineering without imaginary numbers? Is this method an actual improvement?
Re: Mathematical secrets of ancient tablet unlocked after nearly a century of study (2017)
#5It's probably worth adding the context that Wildberger's agenda is to ground mathematics in integers and rational numbers, eliminating those pesky irrationals Euclid introduced, because reasoning about them invariably involves infinities or universal quantifiers, which everyone agrees are tricky and error-prone, even if they don't agree with Wildberger's radical variety of finitism. So he was delighted to find a kind…
How do we do things like electrical engineering without imaginary numbers? Is this method an actual improvement?
imaginary numbers are not the same thing as irrational numbers
Re: Mathematical secrets of ancient tablet unlocked after nearly a century of study (2017)
#6It's probably worth adding the context that Wildberger's agenda is to ground mathematics in integers and rational numbers, eliminating those pesky irrationals Euclid introduced, because reasoning about them invariably involves infinities or universal quantifiers, which everyone agrees are tricky and error-prone, even if they don't agree with Wildberger's radical variety of finitism. So he was delighted to find a kind…
Thanks for the context - I was baffled at first how the Guardian would run with the tagline "a trignometric table more accurate than any".
But it's because the sine of 60 degrees is said by modern tables to be equal to sqrt(3) / 2, which Wildberger doesn't "believe in", he prefers to state that the square of the sine is actually 3 / 4 and that this is "more accurate".
The actual paper is at [1]:
Re: Mathematical secrets of ancient tablet unlocked after nearly a century of study (2017)
#7It's probably worth adding the context that Wildberger's agenda is to ground mathematics in integers and rational numbers, eliminating those pesky irrationals Euclid introduced, because reasoning about them invariably involves infinities or universal quantifiers, which everyone agrees are tricky and error-prone, even if they don't agree with Wildberger's radical variety of finitism. So he was delighted to find a kind…
Thank you for this expansion. I was about to rabbit hole on how it could be that ratio-based trig (and what is that?) is more accurate than modern calculations.
Re: rationals, I mean there's an infinite number of rationals available arbitrarily near any other rational, that has to mean they are good enough for all practical purposes, right?
Re: Mathematical secrets of ancient tablet unlocked after nearly a century of study (2017)
#8Re: Mathematical secrets of ancient tablet unlocked after nearly a century of study (2017)
#9Earlier quoted context omitted.
How do we do things like electrical engineering without imaginary numbers? Is this method an actual improvement?
imaginary numbers are not the same thing as irrational numbers
He doesn't work with imaginary numbers, either. He treats complex numbers as matrices of rationals.
Re: Mathematical secrets of ancient tablet unlocked after nearly a century of study (2017)
#10Earlier quoted context omitted.
imaginary numbers are not the same thing as irrational numbers
How do you rationalize pi or e?
By fiat, of course. :) (e.g. https://en.wikipedia.org/wiki/Indiana_pi_bill)