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Comment by snissn | Hacker News Reader

This joke is starting to get pretty annoying..

There are lots of things we do for conventional reasons, such as having electrons exhibit negative charge.

If you're doing any actual complicated math or physics, the last thing you care about is having a different constant floating around in your terms.

What it is, however, is a great learning tool - This thing called pi, maybe we could get away with, or even be better off calling it 2pi. - Can get lots of people thinking about math and possibly learn something cool like trig. But when used in a psuedo intellectual way, it 'really grinds my gears'.

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Perhaps you're right about people doing "actual" complicated maths simply not caring about a multiplicative constant. However, a lot of people do most or all of the complicated maths they're ever going to do in their lives when they're in university. During this period, the correct symbol makes every formula and equation simpler and easier to learn. Crucially, it's also during this period that people's understanding of complicated maths is most important, as they are judged by letter grades upon which many of life's opportunities depend.

How often do people actually make this error? I make all sorts of errors of that class when doing math by hand, but I've never once been off by a factor of two because the formula calls for 2pi.

It's not about errors but understanding. A lot of math involving trig is abstract enough to be confusing to most people. Tau makes is [slightly] less so. For example, understanding that sin represents the y value of a point on a unit circle is easier when 1 tau is a full circle rather than 2 pi.

That's only a problem when you need to use radians, which is only necessary for calculus. You can do all the explanations with "cycles" (1 cycle = 2*pi radians), and it's actually simpler.

It's not simpler, it's identical. 1 "cycle" = 1 tau = 2 pi.

And in any case, I think using degrees to teach trig is a terrible idea and only causes more confusion later. sin90 = 1 makes no sense, and the fact that that's my first thought when thinking about sin only causes me problems. If I had instead been taught radians first, a lot of stuff would be significantly easier.

1 cycle = 1 "tau" radians. It's important to include units. I don't see how keeping irrational "magic numbers" out of the equation could make it anything but simpler. As an added benefit, it would serve as a transition between degrees and radians, by introducing the idea that there are multiple measures for an angle without simultaneously introducing a unit that has irrational values in every useful situation.

I agree that degrees are terrible, but sin(1/4)=1 makes a lot of sense. Probably even more than sin(1/4 tau)=1. The only reason to use radians instead of cycles is that changing the units breaks the wonderful trig derivative symmetry.

Radians are pure numbers (which is why I left them out). That said, I see what you mean now and I agree. sin(1/4 of a circle) makes more sense than sin(1/4 tau) which makes more sense than sin(1/4 360).

Danger being, of course, that sin(1/4) != 1.

(sin(0.25) = 0.247403959)

If your sin function is calibrated to take radians, then yes. If it's calibrated to take cycles, sin(1/4) = 1.

Ahh yes, of course. My apologies!

You are exhibiting what I call "expert idiocy".

Basic teaching theory states that experts don't think like novices, and further, they are likely to not remember the misunderstandings and difficulties they encountered as novices, because the novice problems are what they now consider simple. This is a being studied a lot in the world of education.

I call it expert idiocy when the expert refuses to accept that his understanding is actually a pretty advanced state of thinking, and not immediately obvious to the beginner. It is this form of idiocy that leads to people feeling that "only freaks can get math" or "I'm not smart enough for physics" or "computer geniuses can only do basic tasks".

Perhaps you are correct. I don't remember the order in which I learned various concepts but I probably learned about degrees before pi and certainly before trig.

Since radians involve irrational numbers I can understand it being more difficult to learn than degrees. However degrees are a completely arbitrary unit that are used for historical reasons.

Getting stuck thinking in degrees hindered my ability to understand trigonometry, and I don't think I'm alone. It is my belief that teaching trig using radians would be less confusing than teaching trig using degrees first, then radians (as was my experience). With degrees there is no direct correlation between 90 degrees and the values of the trig functions which leads to people simply memorizing values. The same is true (to a lesser extent) when using 2 pi.

True, but you are now setting up a false dilemma. The point is not that arbitrary units are hard, nor that any 2 are relatively harder. It is that a consistent unit that is not arbitrary is easier than the arbitrary ones, and usually involves quite a few useful "symetries" (by which I don't mean real symetries, but conceptual linkages).

As for why people think degrees is easier: it is simply because common usage of degrees makes the concept familiar to learners. I totally agree that teaching trig in terms of radians first would be much better.

>>>"...understanding that sin represents the y value of a point on a unit circle..."

Wow, I'm enrolled in a college trig class right now and your comment just made me realize that. Thanks for the heightened understanding :)

For the sake of completeness, cos is the x value, because of the identity sin(x)^2 + cos(x)^2 = 1. You should find a good unit circle trigonometry picture if your class isn't giving it to you.

Wikipedia's picture is frightening (http://en.wikipedia.org/wiki/Unit_circle), but perhaps http://www.themathpage.com/atrig/unit-circle.htm or http://www.snow.edu/jonathanb/Courses/Math1060/unit_circ_tri... will help.

What I find especially ironic is that while I completely understood that I could get the x and y values using rcos(t) and rsin(t) and used it a lot when I worked for a video game company, it's only more recently that the idea "clicked". I always thought about sin and cos in relation to triangles and not circles.

Electrons exhibiting negative charge is something that would be difficult to fix because the fix would result in a lot of confusion. Using tau as the circle constant doesn't cause nearly as many problems. I don't see it as a joke; we should do it.

It strikes me as more analogous to using j = sqrt(-1) so that it doesn't conflict with current: it works fine, but you're never going to get everyone to do it because people want the papers to stay consistent.

Actually, in this case, there's a particular discipline that's especially inconvenienced (physicists, due to the torque conflict). Contrast with j: there's a particular discipline that benefits, and they use j=sqrt(-1) all the time.

As a side note, to a physicist j = sqrt(-1) is also a conflict because we're used to i, j, and k being quaternions.

I'm confused by your statement -- in the quaternions, i, j, and k are all square roots of -1.

If you're doing complicated math or physics, the last thing you want is to be off by a multiple of 2 when you're done. It's happened to me enough times, I almost wish I were still doing physics so I could use tau instead of pi.

For electron charge, I have, at times for intermediate calculations, used 'e' in place of the negative sign from electrons, and then substituted -1 at the end. Being off by a multiple of -1 is just as annoying as a multiple of 2.

Even more annoying since it is even easier. Losing a negative sign is the most common mistake I make working through a complicated problem. Your idea of using something less likely to be overlooked when transcribing intermediate steps in solving a problem strikes me as a really good idea. Thanks.

I don't see it as a joke. Why not strive for the conceptually cleanest possible conventions?

It's pretty plain to me that tau is more deserving of the status of 'conceptual entity' than pi is. It's the number of radians in a cycle. Practically every time it occurs in physics, pi represents 'half the number of radians in a cycle'. Kind of crufty if you ask me.

I'm not so sure it is a joke. The author clearly states it's more for neophytes. And the convention can be explained of using 2π after showing what it all means by explaining Tau

If nothing else, we should at least get a non-separated printing character that looks like 2π connected up, similar to latin dipthongs.

When you're programming something complicated, arbitrary ugliness in the APIs you're using brings you more trouble than when you're programming something simple. Right? So what's different about complicated math or physics?

That's how I realized pi was wrong, back before the manifesto came out -- from looking at math the same way I'd learned to look at programs.

Not to mention that they seem to have chosen one of the worst possible symbols: the one that happens to represent torque. Further, it looks a lot like t, which is often used to represent turns (== cycles == 2pi radians).

There are alphabets out there other than the Latin and Greek ones, with plenty of untapped symbols.

> it looks a lot like t, which is often used to represent turns

I see that as an asset. It makes the correspondence between 2Pi and one cycle even more obvious.

This is something I can't quite wrap my head around. Why would I want the symbol for a unit to be similar to a constant that I will very often use in the same calculations? That has a good chance of ruining my dimensional analysis if I finish up a calculation later. A bathroom break could convert 2 * pi radians into 1 cycle * radian, or 1 cycle into a unitless 2 * pi.

And these conversions would be correct, wouldn't they? Radians are length ratios, and as such dimensionless anyway.

While not technically required, it's pretty convenient to treat radians as their own "angle" dimension. This lets you distinguish an angular velocity from a simple periodic repetition. The latter happen to rarely (never?) occur naturally, but I run into artificial ones often enough.

This is not a joke any more than the dvorak keyboard layout is a joke or the metric system is a joke. It's an objectively better approach whose only drawback is the overwhelming force of tradition.

You cannot compare use of the metric system to use of Dvorak or tau=2pi. While Dvorak and tau may be objectively better, the real world gains to be had by switching to either are slim in reality. I already type upwards of 90 words a minute on Qwerty and I doubt that switching to Dvorak would yield much of a gain to my typing. The problem behind pi is that it is never explained correctly, and this can be worked around by fixing pedagogy without having to introduce yet another physical constant. If the United States switched to the metric system, however, doing business with foreign economies would immediately become easier and we would no longer have to memorize long tables of arbitrary conversion factors. It makes much more sense objectively AND pragmatically to use units that are derived from physical quantities, rather than legends about kings' feet and so forth. With the other two examples, the pragmatic improvement isn't there -- the improvements in quality of life/quality of thought that we would experience simply aren't worth the trouble of switching.

No need to look so far. The area of a circle is πr^2. π without 2 is used everywhere.

But in analogous equations (energy of motion .5mv^2, energy of spring, .5kx^2), there is a 1/2. Basically, anytime you integrate a linear equation, you get a factor of 1/2. Using pi as the circle constant hides this fact.

http://tauday.com/#sec:circular_area

I like that it hides the fraction. I'm a computer scientist. I don't like fractions.

Instead of celebrating tau, we should be celebrating integers. Robust, fast, compact, reliable, easy to understand. With pi I can use more integers. Thank you pi!

Well, as a computer scientist, I'd hope you use pi * r * r, because there's no reason to compute tau/2 every time, and pow() is needlessly inefficient for integer powers (on all languages I know. ~6 times slower in python). I'd expect you to make the same optimizations with the analogous equations, but that shouldn't have any bearing on which constant is better for learning, etc.

You don't think celebrating integer day every day would get a bit repetitive?

Only the first 5 million years, then something interesting happens.

I guess you must support legislation to make pi equal to 3, right?

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