“Babylonians used the Pythagorean theorem 1,000 years before it was ‘invented’ in ancient Greece”
If you know me, you’ll know that I think this finding is cool, but not surprising. I believe that advanced mathematics were widely known in the ancient world. How else could the Giza pyramids have been built as a model of the stars of Orion’s belt (using pi in their proportions) … the temple complex at Teotihuacan been built as a model of the solar system (with the pyramids there also using pi in their proportions) … Stonehenge been built as an astronomical observatory that also functioned as a calculator … or the circular chambers at Gobekli Tepe been laid out forming a perfect equilateral triangle?
This doesn’t mean that every people group since the dispersion of mankind has had a knowledge of advanced mathematics. Obviously not. But either it was known to a central civilization and then lost in many cases, or else human beings are so clever that they are capable of discovering mathematical principles independently, whenever they have the need and the interest. Or both.
People are probably going to tell you that crediting the Pythagorean theorem to Pythagoras (through whom we first heard about it), rather than to the Babylonians, is racism. It’s not. In one sense, the fact that we credited Pythagoras was harmless. It was ignorance, not a cover-up. That was the farther our knowledge went; now, it goes a little farther.
But if we are super duper surprised that this theorem was in use 1,000 years before we thought it was, then we might be dealing here with an equally wrongheaded attitude. Instead of looking down on some peoples based on their skin tone, this is looking down on them based on the fact that they lived and died just too long before we were born. It’s the assumption that modern people are better at abstract thought, science, and technology than ancient people. Though self-flattering, this belief isn’t just an irrational prejudice. It’s a consequence of the evolutionary presupposition that people started out as animals, and that we had to slowly develop things like language, music, art, religion, mathematics and all kinds of higher thought. Thus, by definition, modern people should be smarter and our technology and mathematics more advanced than those of ancient people. The silent testimony of megalithic monuments all around the world belies this.
Out of Babel 
That is interesting. I wonder why we created such complex math… I studied a lot of primitive tribes (I use that term denotatively) and many of them don’t count past two or five, seeing no need for it. I wonder what inspired the creation of such complicated math.
BTW, if you know anything about math 75,000 years ago, with early man tribes, let me know. I have no idea where they were on the math spectrum.
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I lived with a small people group in rural Borneo, and they had numbers up to at least ten. Actually, two sets: they had one number vocab system that was derived from the Malay language family, and an older one. But I know some peoples just have “one, two, three, many.”
I personally think mathematics is a perceptual ability that humans have, but how much it is developed depends upon the needs and opportunities presented by their lifestyle. It’s just like colors: not every people group “needs” a lot of color words. If a language has only two, it’s usually “red” and “black.” When a language has more color words, the Crayola 8 get added in a predictable order.
I think it would only take a generation of catastrophic population collapse, followed by a generation or two of hardscrabble survival living, for a lot of mathematical knowledge to be lost. Unfortunately, this makes it hard to infer what a given people had in the deep past, because we don’t know what happened in the intervening millennia (or even centuries). Unless, of course, they left us a monument.
75,000 YA is out of my bailleywick, and it also depends upon trusting the conventional dating going back that far. I will say that Gobekli Tepe was built supposedly by hunter-gatherers, and that some people have argued that the Giza pyramids and sphinx are much older than conventionally believed. Graham Hancock once argued for a date of about 20,000 B.C., which gets you a third of the way there.
Basically, I’ve never seen an archaeological project that discovered ancient people knew less than we thought. They all seem to go the other way. So IMO you can give your 75K people as much mathematics as you like, and you probably won’t be proved wrong. Worst case, you’ll be a few years ahead of the science.
Hope this helps.
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Hmm. We must listen to different people. I can’t remember any of my friends or relatives mentioning Pythagoras or his theorem. However, you make some very interesting points. I’ll go for the multiple discovery explanation.
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Wait a minute … aren’t you an engineer?
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How many engineers have you talked to?
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Hmm … I can tell I’m being mocked some way, but not sure in exactly what direction …
Trattray is an engineer, before he joined the dark side and started writing novels. He’s the only engineer that I know for sure that I know, though I am also acquainted with an architect, a woodworker, and a plumber. All of them much smarter and more capable than I am.
I was taught the Pythagorean Theorem in high school math, so I figure that Trattray probably uses it so often that he mutters it in his sleep. So I didn’t think it would be very obscure. I figured it’s something everyone who graduated from high school is familiar with, and that we all heard it came from Pythagoras. But perhaps his point was that it’s not an everyday topic among friends and family.
I like to look at history-nerd type pictures (photographs of megalithic monuments, for example, which look remarkably the same the world over), and attached to an obscure, interesting fact on these, you’ll often see the comment, “How come they never told us that …” with the implication being that it is some kind of nefarious cover-up. That’s the attitude I was responding to in this post.
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I was actually mocking engineers. I’ve worked with and for engineers for the last 20 years and they are all alike, in certain areas.
To the point where I’ll be talking with someone and think to myself, “I bet they’re an engineer” and lo and behold, they were. They’re a type, as it were.
To be fair, I tend to like engineers, except when they get fixated on their specialty and start talking my ear off about the density and tensile strength of concrete with or without rebar, etc, etc, etc.
The thrust of my comment was that an engineer doesn’t need anyone else to be interested in a subject to frequently talk about it 😀 (and to be clear, I was referring to engineers as a mass, not to Tattray in particular).
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Ah yes, like the joke about the hot air balloon and the engineer.
Trattray is rare gem, to be sure. An engineer who writes cozy mysteries and squeaky-clean action novels.
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Yep, sure am. Still true.
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