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Why I’m not celebrating Tau Day
Tau day, celebrated on June 28th, is almost upon us again. Last year I had great fun making a video about tau and appeared in national newspapers and on radio and TV. Though I had helped kick off a story that went viral igniting millions of pixels across the globe, even I felt that it received more coverage than it merited. Don’t get me wrong, it was great fun. Anyone who watched my video could tell from the sound effects, the newspaper headline about Pi is 5.14 and the code hidden in the digits of pi that for me this was not obsessional rage coming out but was instead a reasonably light-hearted look at an irrational bit of maths. Unfortunately, I received a lot of flak and a fair amount of abuse such as being called “peace of sh*t”[sic], “burro” (it’s a Portuguese insult, shame on you BBC Brasil!) and even, rather strangely, bald-headed. (You can hear the inside story in a Math/Maths Podcast.)
However, it is not insults that cause me to pass on two rounds of pie this year. Insults are not a problem, I’m a grown up and know that sticking my head above the parapet will give at least someone the opportunity to take a shot. Instead I have two main reasons.
1. The issue is controversial and although controversy and debate are vital for any subject it should be about the significant issues. Tau is important but not major league important. I don’t want disagreements between mathematicians to obscure our central message that maths is vital to society (see here for example). One of our responsibilities is the health of our subject and a basic tenet, like a doctor’s, should be “Do no harm”. In this case I think a division over a minor matter with different camps trading insults does no good for the perception and standing of maths. A comment from a student essentially said, this is great, I’m going to annoy my maths teacher by using it all the time. I wanted to say no, no, no, this is not what it’s about. It’s not about deliberately engineered conflict.
2. For me the second, more personal reason, is the important one. Although, I don’t particularly care what people think about me, I found that people assume that tau is my main educational focus. It isn’t. Given the chance to dictate the maths curriculum my first decision would not be to introduce tau. There are many more important issues to deal with, such as making school maths more interesting at school and ensuring that students can solve problems. See other blog posts for details (eg here and here).
As an example of being misunderstood, people criticized me and took my comment “You don’t have to think” out of context. So they berate me, the author of a book called How to Think Like a Mathematician, saying that I should be teaching students to think. Of course the point is that I don’t want them to think about unimportant things like one quarter turn is one half pi radians but instead thinking about important stuff such as why exactly do you need to use radians when doing calculus anyway. [Aside: The tau versus pi issue is important pedagogically as 1/4-circle-is-1/2-pi is a problem that students have trouble with. There is an issue for teachers. They have to chose whether to change the circle constant to tau or explain that we chose the wrong circle constant. It is important for teachers such as myself to have an awareness of why students have difficulties. You’ve got to be aware of the problem but also why it happens. Interestingly, some people suggested we should keep pi as we can use it as a test for identifying mathematicians – if a student can’t handle the strange factor of 2, then they are not cut out to be mathematicians. I.e., we should deliberately make the subject harder than needed to keep the riff raff out. End of aside.]
Interest in tau distracts me from the real issues and furthermore means that people assume I am not serious about them. Although it would be fun to write the first textbook to use tau (and I am sure it would be bring me extensive fame, instant notoriety and piles of money!), I would prefer to get on with significant stuff that interests me. I would much rather work on that rather than chase fame and fortune. Obviously, we all want success. However, I would much rather put a lot of effort into solving a major problem and fail than put a lot of effort into a minor problem and succeed. (In my case, the next step is going to be unveiled soon. It’s a rather special book for me. I can say no more…)
So I feel as though I’ve done my bit for the cause of a rational circle constant. It’s time for me to move on but I wish Bob, Michael, Joseph and Peter all the best. I give my heartfelt thanks to Mark Henderson at the Times and Jason Palmer at BBC Online who covered the original story in a professional way and to Nick Wilmshurst at Radio Leeds for inviting me back a number of times.
I’ll finish with one of my favourite comments following the media furore. It’s an unintentionally funny one from a discussion about tau. [My emphasis]:
In the article, they make a point that a quarter of the circle corresponds to an angle of π/2, two quarters of a circle corresponds to an angle of π, etc… They conclude that this is confusing for children and adults alike that are trying to learn trigonometry. Referring to the point they’re making, I don’t think that the fact that a quarter of a circle corresponds to one fourth of pi is confusing at all. And anyone who has learned the subject learns to accept things like that. Therefore it should not be changed.
Isn’t it great when your critics make exactly the mistake they say can’t be made?
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I feel sorry that you feel that tau distracts you from the real issues. But, is tau a real issue? I don’t know if you look at the change in the Tau Manifesto of adding section 5 in June 2012. But, it shows something to think about. Is there mathematics which because of pi has become “clunky”? By clunky I mean that it adds weight to equations and makes the “real” mathematics hidden. One of the formal things I was taught was 0 and 1 are the most fundamental numbers because they form the number system, all other numbers including 1/2, pi, and tau depend on them and how they are defined. They are not defined by a half-unit of circumference as pi has been since Euler’s time. — John
Dear John,
Sorry for the delay – for some reason I didn’t get notification that there was a message awaiting approval!
I have seen the new section and agree with its conclusion. I’m not against tau, I think it has numerous advantages and pi can be “clunky”, the problem is that I have a finite amount of time and need to spend it wisely. Tau is an issue but not big enough for me to devote lots of time to it.
Kevin
I once made the mistake of saying “I’m her sister” instead of “I’m her brother” because, unconsciously, I was linking “her” with the word that followed it. I think that in the comment you mentioned, the writer mistyped “half” for the same reason.
But there is also the possibility that the writer was thinking in terms of area; in that case, a quarter of a circle really would correspond to one fourth of pi. Maybe he was just waiting for somebody to come along and point out his mistake, and then he would say “Well, actually…” After all, pi was originally defined in terms of area and radius squared, not circumference and diameter.
Or maybe he realized that two intersecting lines never form an angle greater than pi radians, so he was thinking in terms of half-circles (but forgot to convert). When I’m working on a math problem, that’s how I usually manage; I think “This is a quarter of a semicircle, and its radian measure is one quarter pi.” When you think about it, a building standing perfectly straight ought to have a half-angle on either side.
Hi Tim,
I think he made the mistake because the definition used for the circle constant is not natural!
I can see what you are saying about buildings having half-angles and can also see that from an engineer’s perspective the definition of pi is practical because when given an circular object it is easier to find its diameter than its radius. But from a pure mathematician’s perspective the circle constant is simplest when defined as tau. That’s not to say one doesn’t get good formulae using pi or even using 90 degrees as the circle constant.
Kevin