I know it was known in China at least before Pythagoras https://en.wikipedia.org/wiki/Zhoubi_Suanjing
Perhaps it was, but the article you link denies the certainty of that statement.
Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
221–230 of 248 posts
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#222Earlier quoted context omitted.
I know the top one is generally considered to be Euler's Equation. e^(i * pi) + 1 = 0 It's considered incredibly elegant because it manages to combine multiple fundamental mathematical concepts into a single equation. 1 is the multiplicative identity, 0 is the additive identity, pi is the circle constant, e is euler's number, i is the square root of -1, the basic building block of complex numbers.
IMO, it’s better with tau. e^(i * tau) = 1 You lose the 0, but isn’t it a bit odd the 0 is there in the first place? Normally we’d reduce it to: e^(i * pi) = -1 Which obviously isn’t as nice in this case. And hey, if we’re allowed to break the conventions, you can have the 0 back easily. e^(i * tau) = 1 + 0
That might be because it should be written:
e^(i*θ) = cos θ + i*sin θ
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#223Earlier quoted context omitted.
I'm pretty confused. How do you think an average 8 year old would feel?
They would be fascinated. I have one at home and a 12 yr old. This is the kind of stuff they’re always interested in.
We should all be intrigued by this. Young or old.
Not reels and shit….
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#224Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#225Earlier quoted context omitted.
How useful are universal truths compared to getting shit done? I only see theorems as useful for complex societies. The son of a gem dealer would have the time to work out universal truths. The reputation of everyone doing it without numbers would reveal the pattern of the universal truth. Finally this looks like it was all done using cuneiform. Which brings up questions of notation and the language to describe a squ…
What everyone is talking past here is that the Babylonians discovered what engineers call a "rule of thumb", and engineering is focused on getting things done using rules of thumb. The best possible rule of thumb is a mathematical proof or a scientific discovery, but it's by no means necessary. . Observing that something always holds and even having a formula for it is not the same thing as having a proof, and the pr…
I think what you might be touching on is that the "rules of thumb" may have been so integral of the culture as to be hidden.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#226Earlier quoted context omitted.
I've personally worked on a project where we used a 3-4-5 right triangle to lay it out on the ground. Straight lines alone do not get you right angles.
You can get right angles with a straightedge and compass, both of which you can make on a construction site with string and pegs in the ground. It's just an instance of bisecting the angle. Which is more convenient in practice is situational.
Fair, I didn't realize they were using the string as a compass.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#227Earlier quoted context omitted.
Well, they continue to introduce Pythagorean theorem through many stages of elementary math, so 8 is pretty early. But.. here could be a section of a textbook: Pythagoras & The Pythagoreans: Mathematics, Music, and Mystery Pythagoras was an ancient Greek mathematician and philosopher who lived around 500 BC. He traveled widely and gathered knowledge from diverse cultures, like Egypt. He also founded his own school of…
I have thoroughly enjoyed all of your comments! You’re great at showing how learning can be fun. Do you have a blog where you compile these stories and anecdotes?
That’s very kind. I put work at https://Derek-Lomas.com
(My Pythagorean math blog is yet to be, but I do have some Pythagorean blog posts at https://aixd.substack.com)
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#228Earlier quoted context omitted.
I'm actually curious if "digging in the tunnel" is a euphemism for using psychedelics, which would have been severely frowned upon at the time. The elves are known for their wisdom in helping you see the world and solve problems in unique ways. https://maps.org/2004/08/08/nobel-prize-genius-crick-was-hig... > FRANCIS CRICK, the Nobel Prize-winning father of modern genetics, was under the influence of LSD when he firs…
DMT is pretty famous for, oddly, inducing hallucinations of Machine Elves in people. Don't discard the building tunnels part though, it is a weirdly popular hobby among the very male-brained.
Funny enough DMT is the only psychedelic that's ever given me real, true insight and legitimately changed my life after a single breakthrough dose, 99.5% of which I didn't remember even immediately after 'coming to' (and still don't). I was suicidally depressed and had been for a number of years, struggling with drugs and depression, had all but given up on life. I did it alone not meaning to break through.
Immediately after my breakthrough, I was so overjoyed and happy and couldn't help but bellow out "there is so much love in the universe!!" over and over -- right after a run to the washroom to purge a rainbow from my mouth. Thankfully I was home alone. I immediately called my loved ones to talk to them and tell them how much I loved them. My sister (psych major) thought I was going to end my life soon because I was suddenly so happy and unburdened. Suicidal ideation ceased for over 5 years, and still has only come out in the rare circumstance I was under extreme emotional distress. The majority of the lessons I learned -- many obvious in retrospect, I feel I was almost purposely blinding myself from seeing them because it was easier not to -- came in dreams and waking daydream 'visions' in the days after my trip, and my sudden ability to notice my problems weren't so serious, I just needed to look at them from a different viewpoint, of which there are many.
The only person who noticed (or mentioned) any difference right away in me, was the wife of a client -- a devout Hindu woman. As soon as she saw me a few days after my trip she said "MyName, are you alright?" with a concerned look on her face. I still wonder what she noticed or what concerned her.
I haven't felt the need to do it or any other psychedelics since, but for some reason I felt I'd share a quick tale of my story since the topic of machine elves and insights came up.
I was also, coincidentally (common as it is, apparently?) obsessed with digging a tunnel as far as I could as a 12-13 year old boy until it collapsed on me after about 5ft because I'd started on an unstable hill. That was the end of my tunneling, although I suddenly have a strange urge to grab a shovel.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#229Pythagoras was specifically known for accumulating the wisdom of diverse cultures—supposedly he met Thales, was initiated as Egyptian priest in Hermopolis, spent time in Babylon after being captured, and was initiated into every mystery cult he could. And as a boy on his home island of Samos, he would have been exposed to the building of the largest stone temple in Ancient Greece (to Hera) and the incredible engineer…
> "The relationship between math and spirituality was very strong back then!" Seems to me this connection is having a resurgence now as people attempt to project the capabilities of computers beyond human capabilities, where the implications are necessarily bordering on spiritual. Examples include transhumanism, Yudkowsky-style absurdly extrapolated rationalism (Basilisk etc), the simulation hypothesis, AGI salvation…
Similarly, sometimes practitioners of technical analysis for financial securities treat it spiritually.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#230Earlier quoted context omitted.
I'm pretty confused. How do you think an average 8 year old would feel?
Well, they continue to introduce Pythagorean theorem through many stages of elementary math, so 8 is pretty early. But.. here could be a section of a textbook: Pythagoras & The Pythagoreans: Mathematics, Music, and Mystery Pythagoras was an ancient Greek mathematician and philosopher who lived around 500 BC. He traveled widely and gathered knowledge from diverse cultures, like Egypt. He also founded his own school of…
This is probably appropriate for 10 year olds. Your last comment was not close, IMO. And really, I think we're both overestimating the average 8yo.