# Happy Tau Day!

George Box once said “All models are wrong, but some are useful.”  As we build up our understanding of the world around us, we find different parts of our maps fall short of the territory.  Sometimes our predictions end up out of joint with reality, but sometimes we just can’t stand how inelegant our approximation is.  We’re getting the right answers, but we suspect we haven’t actually hit on why yet.  And we suspect that missing the beauty of the big picture will eventually lead us astray.

And I like living in a world where twice a year we get to have a fight about the aesthetics of two different ways of talking about math.  You can read Tau’s side of the story here.

Leah Anthony Libresco graduated from Yale in 2011 and lives in Washington DC. She works as a news writer for FiveThirtyEight by day, and by night writes for Patheos about theology, philosophy, and math at www.patheos.com/blogs/unequallyyoked. She was received into the Catholic Church in November 2012."

• KG

I’m all in favor of tau, but I don’t understand the point you’re making in your first paragraph. How is the choice of pi versus tau going to have any effect on our understanding of “why” math describes nature? Yes, it’s an aesthetic choice for the formulae we commonly use, but that’s about it. It’s a choice of whether we want a symbol to serve as a shortcut for “one turn” or a symbol for “one half turn.” But it’s not a choice between two fundamentally different models. Right?

No antagonism intended, just a request for elaboration.

• LeahLibresco

Not two different models on the level of geocentric vs heliocentric at all. But, as Vi discusses in the video, the choice of constant makes a difference to what intuitions we rely on and which way we translate the math to make it feel tangible/real/etc.

• KG

Sure, I’ve watched the video, and Vi is awesome, no arguments there. It’s just that I still don’t get what new insights this is supposed to give, other than providing us with a symbolic shortcut that means one turn instead of one-half turn. Maybe it will make trigonometry easier for those first learning it (very important!), but no mathematician is in jeopardy of missing the big beautiful picture of geometry because they’ve grown up thinking in terms of pi instead of tau.

• Alexander Stanislav

I wouldn’t be so sure of that, in an alternative universe where tau was the dominant circle constant perhaps more students would have understood the big beautiful picture of geometry and become mathematicians.

• Brutus

The discussion is about whether diameter of a circle is more fundamental than radius. From the engineering point of view, diameter is more important where it exists, because the easiest way to make something circular is to chip away at the largest dimension until it reaches the desired diameter; diameter is easier to measure (using just about any measuring device).

The only thing diameter doesn’t do is apply to anything less than a half-circle or hemisphere. So many arcs, rounds, fillets, and other curved surfaces simply don’t have a diameter to measure.

• JWP

Just making all measured widths equal is no guarantee that the shape you end up with will be a circle. The Reuleaux triangle, for instance, is a curve of constant width that isn’t a circle.

• Brutus

You can’t get something very close to the Reuleaux triangle by chipping away from both sides of the maximum dimension from any initial shape that has no initial point on the surface that is a final point on the surface. You will get something close to a circle or sphere.

Proof: Consider a Reuleaux triangle and the circle circumscribing it, tangent at the vertices. Since the initial shape (by definition) contains the entire circle, for that shape to be reduced by chipping to the Reuleaux triangle, at some point the largest dimension must have been reduced to less than the diameter of the circle; before that chip was taken, the shape was already nearly a circle of that size.

• Alexander Stanislav

That’s interesting but I don’t think that engineers would have affected at all if tau had been proposed instead of pi. The only difference I can see is how intuitive the equations end up being and in that regard I think that tau wins.

Is there a specific engineering problem that you think pi is better for?

• Brutus

Engineers were the first people to describe the ratio of circumference to diameter; they used diameter instead of radius because that’s what made sense at the time.

For modern engineering and math, diameter is used less than radius, so it makes sense that radius becomes ascendent.

• JohnE_o

Is it tau day already? My, how time flies!

• Martha O’Keeffe

I would have understood trigonometry much better if it had been explained to me in school – as this video explains – what a sine wave was measuring. As it was, I just had to learn what to me was a bunch of arbitrary values that I had no clue where they came from or what they related to.

• grok87

i’m a convert to tau! area of a circle as a quadratic form. 1/2 * (Tau) *r^2- i love it.

volume of a sphere 2/3 * (Tau)*r^3, volume of a 4-sphere: 1/8* (tau)^2 * r^4

http://en.wikipedia.org/wiki/N-sphere

• http://last-conformer.net/ Gilbert

• Mariana Baca

I’m convinced but I feel sad. It is like losing a good friend.

• http://last-conformer.net/ Gilbert
• Alexander Stanislav

It’s a shame he leaves out his disagreement over the quadratic form till the end because the entire article is essentially a dispute over whether or not a factor of 1/2 should be there. Most of his arguments boil down to minimizing the number of factors in equations which is a strange goal (intuitive equations are a more sensible one). I think that when comparing linear quantities to squared quantities, it makes sense to have a factor of a 1/2 in there because of how derivatives work, but if the author disagrees then I respect that.

• Alexander Stanislav

He also ignores the strongest argument in favor of tau imo. Tau makes learning trigonometry easier which is as far as I can see the biggest difference between pi and tau.

• Mariana Baca

Nope sorry, it is too late, can’t change my mind again. 😉

Seriously, though, the pi manifesto does not convince — it doesn’t address the issues brought up by the tau manifesto at all.

Can we just build a time machine and convince euler to define pi as 6.28? That will solve everyone’s problems.