Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Happy Tau Day

bbc.co.uk

Post reply on HN
Print view View original

21–30 of 54 posts

Re: Happy Tau Day

#21

Post by drbaskin »

Jach wrote: post #4
Confusion wrote: post #2

The mathematical world is as full of lonely pi's, as it is of 2*pi's. Now we need to move to tau/2 and tau, only to get a pi-manifesto in a couple of decades. Previous discussions: http://news.ycombinator.com/item?id=1468341 http://news.ycombinator.com/item?id=2322666

I like the compromise of using Tau and its fractions when it makes sense and using a single Pi when it's not so intuitively-connected with a circle. e.g. \int_{-\infty}^{\infty} e^{−x^2} dx = \sqrt{\pi}. Plus Tau Day's a fun excuse to eat two pies.

I'm not a big fan of introducing a new constant (though I believe \pi should have been 2\pi), but I love thinking of the integral you wrote down as \sqrt{\tau / 2} because then the answer practically tells you how to derive it!

How to derive the value of the integral: Square the integral to make it an integral in two variables, introduce polar coordinates, then change variables.

Re: Happy Tau Day

#22

Post by TheOnly92 »

edanm wrote: post #16
TheOnly92 wrote: post #8

If it's not broken, don't fix it. I don't see pi broken as it has been used for _centuries_. Why should we change it all of a sudden? To signify that we're into a new era? The Tau era?

Why did we move from Roman Numerals or other systems of writing down numbers, to the current numerals we use today? Simple - they make lots of things easier. Now, no one is claiming that Tau vs. Pi is even close to the same level of importance. But it makes some things just that much easier.

Of course, if there's proof that the changes from Pi to Tau will accelerate technological advancement even by 0.01%, I'll totally support it.

The fact is that making things easier doesn't necessarily mean improvement.

Re: Happy Tau Day

#23

Post by Jach »

drbaskin wrote: post #21
Jach wrote: post #4

Earlier quoted context omitted.

I like the compromise of using Tau and its fractions when it makes sense and using a single Pi when it's not so intuitively-connected with a circle. e.g. \int_{-\infty}^{\infty} e^{−x^2} dx = \sqrt{\pi}. Plus Tau Day's a fun excuse to eat two pies.

I'm not a big fan of introducing a new constant (though I believe \pi should have been 2\pi), but I love thinking of the integral you wrote down as \sqrt{\tau / 2} because then the answer practically tells you how to derive it! How to derive the value of the integral: Square the integral to make it an integral in two variables, introduce polar coordinates, then change variables.

Yes, it's one of my favorite proofs. (I think I like it more than Euler's formula, especially since many calc teachers will look at e^{-x^2} and say it's un-indefinite-integrable without a second thought at what else it can do.)

But I'm not quite sure how you seeing it as \sqrt{\tau/2} helps you see the proof more easily. Because if you see \tau (ignoring the 1/2) you think "It has to do with circles or polar form." as per my rule of thumb?

Re: Happy Tau Day

#26

Post by drbaskin »

Jach wrote: post #23
drbaskin wrote: post #21

Earlier quoted context omitted.

I'm not a big fan of introducing a new constant (though I believe \pi should have been 2\pi), but I love thinking of the integral you wrote down as \sqrt{\tau / 2} because then the answer practically tells you how to derive it! How to derive the value of the integral: Square the integral to make it an integral in two variables, introduce polar coordinates, then change variables.

Yes, it's one of my favorite proofs. (I think I like it more than Euler's formula, especially since many calc teachers will look at e^{-x^2} and say it's un-indefinite-integrable without a second thought at what else it can do.) But I'm not quite sure how you seeing it as \sqrt{\tau/2} helps you see the proof more easily. Because if you see \tau (ignoring the 1/2) you think "It has to do with circles or polar form."…

I'm sorry I wasn't more clear, but your interpretation is what I meant. Per your rule of thumb, seeing \tau should suggest that it has to do with circles or polar coordinates, and the square root points to how to get the polar coordinates.

Re: Happy Tau Day

#27

Post by jerf »

ianterrell wrote: post #25

Can anyone defend Pi on grounds other than that's the way it's always been , or introducing a new constant is hard ?

I'm a Tauist myself, but it should be pointed out the first one is a legitimately good argument. (Local introduction of a constant is easy, though.)

I don't expect to wake up one day and everybody suddenly agrees "Yes, tau is the winner!" I expect that either things will peter out, or tau will just gradually start showing up in real papers and stuff. Unfortunately, since K-12 mathematical curricula seem to have gotten stuck in 1920, switching the "official curricula" to tau is well down on my list of things that needs to happen to K-12 math education and at the current rate even if formal mathematics did just wake up tomorrow and decide tau was the way to go, it would be at least 50 years before that penetrated back down.

Re: Happy Tau Day

#28

Post by jerf »

TheOnly92 wrote: post #22
edanm wrote: post #16

Earlier quoted context omitted.

Why did we move from Roman Numerals or other systems of writing down numbers, to the current numerals we use today? Simple - they make lots of things easier. Now, no one is claiming that Tau vs. Pi is even close to the same level of importance. But it makes some things just that much easier.

Of course, if there's proof that the changes from Pi to Tau will accelerate technological advancement even by 0.01%, I'll totally support it. The fact is that making things easier doesn't necessarily mean improvement.

"The fact is that making things easier doesn't necessarily mean improvement."

Untrue, and if you're a programmer you ought to know better. Making something that works the exact same way, only easier, is definitely an improvement. Now it takes less of your finite mental reserves to accomplish a task, and you can now go further in the same amount of time. Making something that abstracts away some things and makes the rest easier is often an improvement, when the advantage of being easier outweighs the loss of control.

Or are you still programming in raw machine language?

Programmers live in such a rich ecosystem of things that are improvements merely because they are easier that it is easy to take that process for granted without understanding it. How many orders of magnitude less effective would I be in machine language? Certainly more than one, almost certainly more than two (working on a network + manual memory management = security fail).

Re: Happy Tau Day

#29

Post by ignifero »

scythe wrote: post #18

The Greek letter tau is already used to refer to the period of an oscillation, the time constant of a decay interval (these are intimately related), plus plenty of other stuff. There really aren't any Greek letters left that aren't used for a million things already. tau-as-time-constant is the standard use for the thing, and the confusion with torque and natural temperature is bad enough as it is. Yes, pi shows up as…

Not to mention the tau neutrino. But the bigger question is why would one want to do that?

Re: Happy Tau Day

#30

Post by ignifero »

imurray wrote: post #17

"What Tau Sounds Like" http://www.youtube.com/watch?v=3174T-3-59Q (Yes, we know that Tau doesn't really sound like anything, but this was fun and better than I expected.)

on a related note, tau in greek is pronounced ˈtaff
Post reply on HN