The mathematical constant pi is under threat from a group of detractors who will be marking “Tau Day” on Tuesday.
Tau Day revellers suggest a constant called tau should take its place: twice as large as pi, or about 6.28 – hence the 28 June celebration.
Tau proponents say that for many problems in maths, tau makes more sense and makes calculations easier.
It makes more sense but does it make it easier? Well, not really. I think anyone who can even pretend to be able to hack trigonometry really can cope with a few factors of 2 kicking around.
“I like to describe myself as the world’s leading anti-pi propagandist,” said Michael Hartl, an educator and former theoretical physicist.
I once knew someone who played a sport internationally for England – unicycle polo. You gotta have a hobby.
“When I say pi is wrong, it doesn’t have any flaws in its definition – it is what you think it is, a ratio of circumference to diameter. But circles are not about diameters, they’re about radii; circles are the set of all the points a given distance – a radius – from the centre,” Dr Hartl explained to BBC News.
Yes, admitted. τ does perhaps have that elegance and such thoughts had occurred to me when I were a lad but… nobody who handles π outside the context of Greggs knows that Dr Hartl. There are other logically equivalent definitions of a circle but if you ask any student 999/1000 that is the definition they’ll give despite that evil π.
By defining pi in terms of diameter, he said, “what you’re really doing is defining it as the ratio of the circumference to twice the radius, and that factor of two haunts you throughout mathematics.”
I think “haunts” is putting it a bit strongly. As I hinted before I struggled learning a lot of the concepts and machinery of mathematics as a student (everyone does apart from geniuses and liars) but a factor of 2 kicking about in there was the least of my worries. Indeed in a field such as complex analysis which has more &pis; than John Prescott’s freezer to complain about those pesky factors of 2* when you got poles at infinity (something The Express would approve of) and Laurent series and even the dreaded Bromwich contour to worry about is like complaining about the in-flight meal when the aircraft is at nearly π/2 radians from the horizontal and both engines are on fire. “Stewardess, I don’t think you understand, I specifically requested the vegetarian option at check-in!”.
Dr Hartl reckons people still use degrees as a measure of angle because pi’s involvement in radians makes them too unwieldy.
Er, no. People use degrees because 360 is a very easily divisible number. π or τ aren’t being (a) rather small and (b) transcendental and therefore irrational. In order for Dr Hartl to be right on this point you’d have to imagine this scene on a building site with the foreman upbraiding an underling over a wonky door fitting, “Does that look like τ/4 radians to you pal?” It is not going to happen. Can you even conceive of the mathematical joinery posse? Imagine the discussions! “Well yeah, but that’s only if we accept Euclid’s fifth…” And that’s just applied mathematicians. Let the logicians and set theorists loose and they’d be bijecting the set of screws with the set of holes…
Dr Hartl is passionate about the effort, but even he is surprised by the fervent nature of some tau adherents.
“What’s amazing is the ‘conversion experience’: people find themselves almost violently angry at pi. They feel like they’ve been lied to their whole lives, so it’s amazing how many people express their displeasure with pi in the strongest possible terms – often involving profanity.
“I don’t condone any actual violence – that would be really bizarre, wouldn’t it?“
Well for a certain value of “bizarre” possibly but having met a lot of mathematicians it’s hard to say really. I’d love to see the expression on the face of a beak who was more used to dealing with yobs who got into a barney because someone had called someone’s “pint a puff” deal with a pair of dishevelled looking men with the leather patches hanging forlornly from their torn tweed jackets because one had called the other’s τ a 2π.
The (real, apocryphal, whatever) disagreements of medieval theologians are often mocked by our modern men of science as being an exercise in playing les buggeurs risible but dear me! (I can’t believe this but I’m actually going to start getting serious here). The history of mathematics has indeed seen some massive changes in notation which have dramatically improved the usability of mathematics. The Great Grandpappy of course is Indian numerals rather than Roman and before that even place-ordering (thank you Babylon!). But you also have Leibniz notation over Newtonian for The Calculus*** and things like Boolean algebra and vector and tensor notation**.
Maybe τ is neater (sometimes – τ/2r2?) but Hell’s teeth I’m typing this on a QWERTY keyboard which is hardly ideal is it? It ain’t going to change. Anyway π is a cultural icon par excellence. It symbolises mathematics in a way both subtle and profound becuse it bestrides both the pure and the applied. It is to paraphrase my Grandmother one of the few things that separates use from things “eating shit in the trees.”
And it goes without saying that re-writing the whole corpus of mathematics for τ rather than π would be a monumental and confusing Children’s Crusade. An almost Borgesian endeavour.
Anyway I’d have to stop referring to people I disagreed with totally as being π rads off kilter. τ/2 rads doesn’t have the same kerching.
*What’s wrong with 2? Damn fine number if you ask me.
**I am aware that the last three aren’t just new notation but the idea of tackling Maxwell’s equations without vector or tensor notation is really scary.
***Newtonian is still used in some areas.