In a political panel show (Bill Maher), they were discussing polls and statistics about the election. Neal DeGrasse Tyson said that human beings have trouble understanding statistics, and then stated as an example:
"Look at the history of math. The first time anyone took an average of numbers was after calculus had been invented."
I find this impossible to believe…The formula for taking an average is intuitive, easy to understand, almost as easy to invent as counting. Calculus is hard to understand, and even harder to invent.
Neal Tyson is a serious scientist and educator. Is he wrong here?
When in the history of math was the first time somebody calculated an average?
It seems to me that it should be ancient. In Mesopotamia or in ancient Egypt or China, some military commander would have wanted to decide how much water he need to carry for his men and horses. He would have calculated the average consumption, even if he didn’t use the word “average”.
(Sorry about the link to the video–I tried every trick, adding %1, etc, and it didn’t work.So I typed it as plain text, you may have to copy and paste it in a new tab )
Statistics, as a formal discipline or area of study, is more recent than calculus. The concept of an average as a formally-defined mathematical concept may well be more recent than calculus.
But I would say that the claim “The first time anyone took an average of numbers was after calculus had been invented” is either incorrect, or vague and ill-defined enough that it cannot be considered either correct or incorrect.
Taking an average is so obvious that it is hard to see how it could have been said to have been invented. Ug the caveman probably said something like, “It takes me about five hunts to bring in an okapi.”
Archimedes carried out some computations that were precursors of calculus. If by calculus you mean imagining arbritrarily small intervals. Napier and Briggs invented logarithms long before calculus and the idea that such people could not have worked an average is absurd.
Real statistical inference, however, is newer than calculus. And harder.
Just to say that someone asked the same question today over at the History of Science and Mathematics Stack Exchange site and is starting to get answers. Apparently Ptolemy, in the 2nd century CE, was already using an idea of mean motion in the Almagest.
Although Aristotle’s definition only makes sense for a mean of two values. Or rather, it could make sense for more as well, but in that case it won’t correspond to what we call the mean: The “Aristotelian mean” of 2, 3, and 10 is 6, but the mean is 5.
I would say that a lot of science and maths communicators are self-promoters, and self-obsessed, as people in front of the camera often are (and largely need to be).
However, most don’t let that influence the content of what they are saying, and sadly this isn’t true of NDT. As he’s gotten older he seems to increasingly see himself as a wise sage who can intuit the truth and distill it into a sound bite. I used to be a fan, but now I cringe when I see him being invited on to a show.
And, suprisingly, a member of the SDMB, under his own name, not a pseudonym. I think he got a slightly hostile welcome, and only posted a couple of times.
Tyson loves talking out of his ass, and not just when he ventures into politics. He was complaining about the 2015 Star Wars movie in which a ball-shaped robot moves by rolling along sand. He said this is physically impossible (ignoring the fact that it’s in a movie where people shoot lightning from their hands and lift buildings with their minds so whether it’s “impossible” according to real-world physics doesn’t enter into it). The movie props team pointed out that the way they achieved this effect was by … actually building a ball-shaped robot that moves by rolling along sand, which of course is entirely possible. The double dose of “debunking” a completely fictional scenario and doing so by confidently asserting scientific nonsense is pretty typical for NDT.
I don’t know what’s weirder: his extreme confidence in his own speculation, or that he has almost zero physical intuition for what works or doesn’t in the real world. It’s well below average, even for a typical person, let alone a scientist.
