# Math history--was calculus was invented before the concept of taking an average? **URL:** \ **Category:** Factual Questions\ **Created:** [November 23, 2024, 5:06pm UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671 "2024-11-23T17:06:32Z")\ **Posts on this page:** 17\ **Page:** 1
**Author:** ![chappachula](https://avatars.discourse-cdn.com/v4/letter/c/d2c977/32.png) [@chappachula](https://boards.straightdope.com/u/chappachula)\ **Post date:** [November 23, 2024, 5:06pm UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/1 "2024-11-23T17:06:32Z")
Neal DeGrasse Tyson says so. 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." the link [https://youtu.be/WMzgXHhKarY?t=858](https://youtu.be/WMzgXHhKarY?t=858) 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 ) ---
**Author:** ![robby](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/robby/32/11048_2.png) [@robby](https://boards.straightdope.com/u/robby)\ **Post date:** [November 23, 2024, 5:38pm UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/2 "2024-11-23T17:38:57Z")
> [@chappachula](#): > > (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 ) I followed the instructions in this post, and I think I got it to work. It took me a few tries, though. > [@How to avoid the YouTube posting bug](https://boards.straightdope.com/t/how-to-avoid-the-youtube-posting-bug/1007499/1): > > You’re trying to post a YouTube video, but you get a popup saying “You can’t embed media items in a post.” Here’s how to avoid that. There are a couple of minor variations. I haven’t written my post yet Write your post normally but do not include the YouTube link(s). When you are satisfied with the post, hide the preview window (see the \<\< button in the lower-right). Then, insert the links in the desired locations. Note that the links should each appear on a line by themselves. Then post. … Also, I believe the link has to be on its own line: [![](https://img.youtube.com/vi/WMzgXHhKarY/maxresdefault.jpg "Overtime: Neil deGrasse Tyson, Donna Brazile, Andrew Sullivan (HBO)") ](https://www.youtube.com/watch?v=WMzgXHhKarY&t=858) ---
**Author:** ![Snarky\_Kong](https://avatars.discourse-cdn.com/v4/letter/s/a183cd/32.png) [@Snarky\_Kong](https://boards.straightdope.com/u/Snarky_Kong)\ **Post date:** [November 23, 2024, 5:53pm UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/3 "2024-11-23T17:53:32Z")
Wikipedia says it was first formalized in the 1500s while calculus was invented in the late 1600s Also, that the average has evidence for existing thousands of years before calculus. Unrelated to the question, but I vote society stops caring about ndt at all. He’s a blowhard and self promoter above all else. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [November 23, 2024, 8:01pm UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/4 "2024-11-23T20:01:21Z")
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. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [November 24, 2024, 12:29am UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/5 "2024-11-24T00:29:05Z")
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. ---
**Author:** ![Topologist](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/topologist/32/3208_2.png) [@Topologist](https://boards.straightdope.com/u/Topologist)\ **Post date:** [November 24, 2024, 1:42am UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/6 "2024-11-24T01:42:50Z")
Just to say that [someone asked the same question](https://hsm.stackexchange.com/questions/18057/does-the-earliest-known-use-of-an-average-occur-after-the-invention-of-calculu) 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. ---
**Author:** ![robby](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/robby/32/11048_2.png) [@robby](https://boards.straightdope.com/u/robby)\ **Post date:** [November 24, 2024, 2:24am UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/7 "2024-11-24T02:24:20Z")
A [source](https://jse.amstat.org/v11n1/bakker.html) from that linked discussion has a [translated] quote from Aristotle five centuries before Ptolemy: > [@Aristotle (384–322 BCE)](#): > > By the mean of a thing I denote a point equally distant from either extreme, which is one and the same for everybody… For example, let 10 be many and 2 few; then one takes the mean with respect to the thing if one takes 6; since 10-6 = 6-2, and this is the mean according to arithmetical proportion [progression]. That certainly sounds like he understood the concept of an average or mean. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 24, 2024, 2:43am UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/8 "2024-11-24T02:43:11Z")
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. ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [November 24, 2024, 5:06am UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/9 "2024-11-24T05:06:37Z")
> [@robby](#): > > That certainly sounds like he understood the concept of an average or mean. Actually, that is the midrange not a mean … but the midrange is one of many averages. ---
**Author:** ![Mijin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mijin/32/9369_2.png) [@Mijin](https://boards.straightdope.com/u/Mijin)\ **Post date:** [November 24, 2024, 6:24am UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/10 "2024-11-24T06:24:45Z")
> [@Snarky\_Kong](#): > > Unrelated to the question, but I vote society stops caring about ndt at all. He’s a blowhard and self promoter above all else Yep. 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. ---
**Author:** ![scudsucker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/scudsucker/32/14101_2.png) [@scudsucker](https://boards.straightdope.com/u/scudsucker)\ **Post date:** [November 24, 2024, 2:13pm UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/11 "2024-11-24T14:13:22Z")
> [@Snarky\_Kong](#): > > He’s a blowhard and self promoter above all else 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. ---
**Author:** ![P-man](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/p-man/32/3606_2.png) [@P-man](https://boards.straightdope.com/u/P-man)\ **Post date:** [November 24, 2024, 4:03pm UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/12 "2024-11-24T16:03:46Z")
I wonder who first thought, “whoa, that’s a small sample size you’ve got there.” ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 24, 2024, 7:20pm UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/13 "2024-11-24T19:20:28Z")
> [@scudsucker](#): > > I think he got a slightly hostile welcome, and only posted a couple of times. Not because folks were hostile to Neil DeGrasse Tyson, but because they didn’t believe that the poster was actually him. ---
**Author:** ![songsoflovetrouble](https://avatars.discourse-cdn.com/v4/letter/s/9dc877/32.png) [@songsoflovetrouble](https://boards.straightdope.com/u/songsoflovetrouble)\ **Post date:** [November 24, 2024, 10:17pm UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/14 "2024-11-24T22:17:07Z")
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. ---
**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\ **Post date:** [November 24, 2024, 10:22pm UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/15 "2024-11-24T22:22:32Z")
> [@songsoflovetrouble](#): > > 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 It’s like he’d never seen a hamster in a ball. ---
**Author:** ![Lucas\_Jackson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lucas_jackson/32/303_2.png) [@Lucas\_Jackson](https://boards.straightdope.com/u/Lucas_Jackson)\ **Post date:** [November 25, 2024, 12:48am UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/16 "2024-11-25T00:48:41Z")
> [@Mijin](#): > > I used to be a fan, but now… Same here. He’s better when he stays in his lane, but when starts speculating he can veer pretty far off base. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [November 25, 2024, 1:21am UTC](https://boards.straightdope.com/t/math-history-was-calculus-was-invented-before-the-concept-of-taking-an-average/1010671/17 "2024-11-25T01:21:06Z")
> [@songsoflovetrouble](#): > > He was complaining about the 2015 Star Wars movie in which a ball-shaped robot moves by rolling along sand. I thought maybe you were exaggerating, but no: [![](https://i.imgur.com/1km2sXY.jpeg) ](https://i.imgur.com/1km2sXY.jpeg) 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.