The original example of Stigler’s law of eponymy.
Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
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Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#182[dead]
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#183For anyone wondering how they got the approximation sqrt(2)=1+24/60+51/60^2+10/60^3. It's based on the simple idea that: Z = (a + b)^2 = (a^2 + (2a+b)*b) => (2a+b)* b Given an initial estimate "a", we need to find the largest "b" such that the term on the left is less than the term on the right. Therefore our estimate will always be slightly less than the actual answer and we can repeat the process to get slightly cl…
Why do you choose b=x/60 for the first iteration? That isn't obvious to me, but 60 must be an obvious choice to be chosen.
You can choose any integer > 1
For example if you choose 2 you will get the binary expansion.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#184The mainstream is and was _enamored_ with Ancient Greece. Our Western culture made Ancient Greek into the vocabulary root of our sciences. We have a lineage of philosophy from Ancient Greece to the 19th century. Only in the 19th century with archeology (again a neo-word made from Ancient Greek roots – it suggests to the mainstream that the Ancient Greek had a concept of archaeology, which they obviously didn’t have)…
Is it not a simpler explanation that Greece simply did a better job of disseminating its own literature than prior cultures? My understanding is that the “through line” of modern scientific progress begins in Greece because that’s where “trivially-legible to contemporary scholars” written history began. Like, we always knew that it didn’t start with Ancient Greece (the Greeks themselves mention this), but because abu…
> Is it not a simpler explanation that Greece simply did a better job of disseminating its own literature than prior cultures?
That's a simpler explanation but it's not necessarily right.
What we can say for sure is that Greek thought has been easier for Western scientists and pseudo-scientists to learn. Availability and language are parts of that for sure. Geography is, too - it's easier for Europeans to excavate Europe than Iran.
But what does it mean to say "the Greeks" disseminated their knowledge better when virtually all of what we have comes from Roman citizens living centuries later?
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#185For anyone wondering how they got the approximation sqrt(2)=1+24/60+51/60^2+10/60^3. It's based on the simple idea that: Z = (a + b)^2 = (a^2 + (2a+b)*b) => (2a+b)* b Given an initial estimate "a", we need to find the largest "b" such that the term on the left is less than the term on the right. Therefore our estimate will always be slightly less than the actual answer and we can repeat the process to get slightly cl…
Why do you choose b=x/60 for the first iteration? That isn't obvious to me, but 60 must be an obvious choice to be chosen.
Base 60 was the number system for the Sumarians/Babylonians.
> Sexagesimal, also known as base 60 or sexagenary, is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinates.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#186The mainstream is and was _enamored_ with Ancient Greece. Our Western culture made Ancient Greek into the vocabulary root of our sciences. We have a lineage of philosophy from Ancient Greece to the 19th century. Only in the 19th century with archeology (again a neo-word made from Ancient Greek roots – it suggests to the mainstream that the Ancient Greek had a concept of archaeology, which they obviously didn’t have)…
The Greek still did something remarkable that to my knowledge we don’t have record of from before: they started a culture of free thinking that grew into philosophy, logic, and scientific inquiry. They also sentenced some of their free thinkers to death for not worshipping the gods but that’s a separate issue.
> they started a culture of free thinking that grew into philosophy, logic, and scientific inquiry.
Culture of free thinking? Socrates, the most iconic free thinker of all time was forced to commit suicide by the greeks. So much for a culture of free thinking.
> They also sentenced some of their free thinkers to death for not worshipping the gods but that’s a separate issue.
It isn't. It directly contradicts and refutes your assertion.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#187The original example of Stigler’s law of eponymy.
Just curious, who came up with Stigler's law?
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#188Earlier quoted context omitted.
That sounds like he was being figurative. He probably meant that he got ideas while working. Every morning, I get up at 5, and take a 5K walk. During that time, I tend to "triage" the day ahead, and often solve problems that were vexing me, the night before. Part of my walk is around a local high school track. There is a small flock of killdeer birds, that hang out there, and I guess they give me the ideas I have, as…
Cray sounds mildly autistic.
For this particular story, he sounds more like a cynic making fun of some bureaucrats.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#189Earlier quoted context omitted.
The Greek still did something remarkable that to my knowledge we don’t have record of from before: they started a culture of free thinking that grew into philosophy, logic, and scientific inquiry. They also sentenced some of their free thinkers to death for not worshipping the gods but that’s a separate issue.
> they started a culture of free thinking that grew into philosophy, logic, and scientific inquiry. Culture of free thinking? Socrates, the most iconic free thinker of all time was forced to commit suicide by the greeks. So much for a culture of free thinking. > They also sentenced some of their free thinkers to death for not worshipping the gods but that’s a separate issue. It isn't. It directly contradicts and refu…
> Socrates, the most iconic free thinker of all time was forced to commit suicide by the greeks.
See my last sentence.
> It directly contradicts and refutes your assertion.
Maybe Greek society was not a homogeneous mass, and some parts of it nurtured free thinking while others reacted against it?
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#190Earlier quoted context omitted.
When I was 8 I would sometimes watch a Disney VHS tape that had Donald Duck exploring stuff like this. The golden ratio, octaves of sound/music, pythagorean theorem etc. I loved it.
Donald Duck in Mathmagic Land. You can find the whole thing on youtube
Found Pythagoras: https://youtu.be/4m_ROtUQ5Vk?si=0V_Jt9lS_44w2QyL