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The Tau Manifesto

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Re: The Tau Manifesto

#31

Post by sebastos »

amalcon wrote: post #9

This is probably the most pointless math argument. Apparently, some people consider it too cumbersome or confusing to write two glyphs instead of one, and would prefer to replace the whole thing with a single glyph. The chosen glyph happens to be one of the worst possible options, because it conflicts with torque (an angular force, which frequently appears in the same calculations as pi). This despite there being doz…

It's not just a drop-in glyph replacement. The 2 is a number that can, and frequently does, disappear.

e.g. You would never write the area of a circle as (2pi)r^2/2

Are you really saying that he should have chosen a letter from the Hebrew alphabet as a glyph? Sure, it has no collisions, but it's completely bizarre and unlikely to gain widespread adoption, which is the whole point.

Re: The Tau Manifesto

#32

Post by Retra »

sunfish wrote: post #29
sunfish wrote: post #25

Earlier quoted context omitted.

It's bugged me as well. It feels like whenever you have a unit where all your measurements contain a multiplication by a constant factor, you should just pick a more convenient unit. This applies to radian measure regardless of whether one uses Pi or Tau. It's odd that the unit of radian measure is a quantity which one almost never encounters, and that the quantities one most often encounters are all transcendental (…

And as a bonus, this would make sin and cos library functions easier to implement on computers. Typically, to compute sin or cos, one has approximation functions like Taylor series which work for small values, and then one reduces the input down to that small range by doing a modulus, since sin and cos are periodic. This modulus is very complex to get right in practice, and can be very slow, especially for large valu…

Tau is turns. They're the same thing.

Re: The Tau Manifesto

#33

Post by sukilot »

tomp wrote: post #23
StefanKarpinski wrote: post #21

Earlier quoted context omitted.

Yes, which means "a half turn around the unit circle in the complex plane is -1". Try explaining that in words without saying "half" or something equivalent to it.

Opposite of 1 on the unit circle in the complex plane is -1. Pi just means "enough of a turn to get back to the straight line".

That's ambiguous. Which straight line? Forwards or backwards? It's a half-turn.

Re: The Tau Manifesto

#34

Post by pdkl95 »

lkbm wrote: post #2

Numberphile also has a really fun debate on Pi v. Tau: https://www.youtube.com/watch?v=ZPv1UV0rD8U

I also recommend Phil Moriarty's numberphile video about Tau, where he covers the key point about how Tau is better for education, regardless of how it is used by everybody else in "regular use".

https://www.youtube.com/watch?v=83ofi_L6eAo

Of course, there is always Vi Hart's absolutely amazing discussion of the subject:

https://www.youtube.com/watch?v=jG7vhMMXagQ

Re: The Tau Manifesto

#35

Post by stouset »

tomp wrote: post #23
StefanKarpinski wrote: post #21

Earlier quoted context omitted.

Yes, which means "a half turn around the unit circle in the complex plane is -1". Try explaining that in words without saying "half" or something equivalent to it.

Opposite of 1 on the unit circle in the complex plane is -1. Pi just means "enough of a turn to get back to the straight line".

You mean a vector in the opposite direction. Clear as mud.

Re: The Tau Manifesto

#36

Post by DSMan195276 »

tomp wrote: post #22
DSMan195276 wrote: post #12

Earlier quoted context omitted.

I think most of your arguments are valid, especially about the choice of glyph, tau is already used a ton. However, I think there is something to be said for the fact that, by virtue of being the ratio of C/R, there are exactly tau radians in a circle. This really does simplify the math, and gives more meaning to the constants on tau vs. pi. There's more meaning from '3 * tau / 4' vs. '3 * pi / 2' because the constan…

> which leaves you with '3 / 2 of a half a circle', which isn't obvious how much that actually is I like pi. I think it's quite obvious too, but maybe you need to stop thinking about circles and start thinking about planes or lines instead. Pi is simple, straight line, or equivalently the whole half-plane above the x axis. Pi/2 is half the turning needed to get back to the straight line, i.e. right square. And so on.…

I get what you're saying, but you can say the exact same thing using tau and it's simpler:

Tau is a simple, straight line, and stretches the entire length of a circle, starting from the x-axis in the positive x direction, and ending at the x-axis from the negative x direction. So Tau / 2 is the amount of turning needed to go half-way around the circle. Tau / 4 is the amount of turning needed to go a forth of the way around the circle, IE. a right square.

Pi might seem easier or obvious to you because you've already been dealing with it for years, but it still creates a situation that is more complex then it needs to be. Tau creates a simpler unit-circle, because Tau uses the radius, and we're talking about radians. Using something that's calculated using the diameter, when you're talking about a unit that's measured in radius's is asking for a mess.

Re: The Tau Manifesto

#37

Post by lkbm »

thomasahle wrote: post #7
lkbm wrote: post #2

Numberphile also has a really fun debate on Pi v. Tau: https://www.youtube.com/watch?v=ZPv1UV0rD8U

But changing our number system to base 12 would destroy pi day!

Yeah, but as Vihart pointed out, Pi = a half rotation, so Pi day is in June. :-)
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