6 ms·

The Tau Manifesto

82 points by acjohnson55 12y ago

lkbm 12y ago
Numberphile also has a really fun debate on Pi v. Tau: https://www.youtube.com/watch?v=ZPv1UV0rD8U https://www.youtube.com/watch?v=ZPv1UV0rD8U
- thomasahle 12y ago
  But changing our number system to base 12 would destroy pi day!
  - lkbm 12y ago
    Yeah, but as Vihart pointed out, Pi = a half rotation, so Pi day is in June. :-)
- pdkl95 12y ago
  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 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 https://www.youtube.com/watch?v=jG7vhMMXagQ
hugs 12y ago
I didn't really understand why tau was "better" than pi until I understood the relationship to radians. Figure 8 [1] in the Tau Manifesto was the eye-opener for me. With tau, instead of pi, I now have a more intuitive sense of how to think in radians when doing trigonometry. [1]: http://www.tauday.com/tau-manifesto#fig-tau_angles http://www.tauday.com/tau-manifesto#fig-tau_angles
jackmaney 12y ago
http://www.thepimanifesto.com/ http://www.thepimanifesto.com/
- thomasahle 12y ago
  I like Terence's suggestion of using 2pii as the fundamental constant. Sqrt(pi) could also be useful given how often it appears.
- cplease 12y ago
  Thank you.
giech 12y ago
I think this whole argument is silly. I really do not think one is fundamentally better than the other. Factor of 2 constants will exist no matter which one you choose. Might as well go with pau http://xkcd.com/1292/ http://xkcd.com/1292/
- mfisher87 12y ago
  I don't like to think about it this way. I think it's silly to go all out and insist one is always objectively "better" than the other (it's a tradeoff), but to have this discussion is illuminating. Look through the comments at how many people gained a better understanding of geometry as a whole by reading.
bau5 12y ago
Do not want.
amalcon 12y ago
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 dozens of completely unused glyphs in the non-English non-Greek alphabets (Hebrew, Russian, etc). It seems almost like a parody.
- deleted 12y ago
  [deleted]
- DSMan195276 12y ago
  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 constant tells you that you have exactly '3 / 4' of a circle. With pi, this is less obvious because there are '2 * pi' radians in a circle, but the 2 frequently disappears (like in my example), which leaves you with '3 / 2 of a half a circle', which isn't obvious how much that actually is. pi definitely does have it's uses when you're talking about the diameter, but when you're talking about something like radians, it makes more sense to use the ratio of circumference to radius rather then circumference to diameter. If we were using diameterians then it would make sense to use pi, since there would be exactly pi diameterians in a circle. Having them mismatched like we do creates a mess.
  - tomp 12y ago
    > 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...
fdej 12y ago
Both tau and pi are inconvenient because you often need fractional multiples like 1/6 or 3/4. We should instead take the fundamental unit of angle measurement to be pi divided by a highly composite number, say 2 * 2 * 3 * 3 * 5 = 180. Most common angles will be then be integer multiples of this unit. Let's give this unit a name, say "degree". One full rotation = 360 "degrees" Half a rotation = 180 "degrees" 1/10 of a rotation = 36 "degrees" etc. I can't believe I'm the first person to think of this. It's so simple that even the ancient Greeks could have figured it out. I should write a full internet manifesto and try to convert the world.
- deleted 12y ago
  [deleted]
- wodenokoto 12y ago
  Stuff like signal processing is horrible if you try and use degrees. I'm not even sure if calculating the area of a circle is in anyway better using degrees.
- tomp 12y ago
  What happens when you have 1/7 of a rotation? There's no one multiplier that will solve all cases. In any case, personally I think that fractions are way better, because they tell you exactly what's what.
- sunfish 12y ago
  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 (except 0), even in the most basic of situations. But instead of picking an arbitrary number like 360 or 1337 or whatever, how about we pick 1? Let's give this unit a name, say "turn". One full rotation = 1 "turn" Half a rotation = 1/2 "turn" 1/10 of a rotation = 1/10 "turn" etc. What do you think?
  - 12y ago
ebbv 12y ago
Do we really need to do this every year? Come on.
cplease 12y ago
e^(τi/2) = -1 Didn't think so.
- StefanKarpinski 12y ago
  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.
  - tomp 12y ago
    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".
    - sukilot 12y ago
      That's ambiguous. Which straight line? Forwards or backwards? It's a half-turn.
    - stouset 12y ago
      You mean a vector in the opposite direction. Clear as mud.
- sebastos 12y ago
  ... e^(τi) = 1 so still better.
deleted 12y ago
[deleted]
sunfish 12y ago
I distinctly remember when I was learning geometry that there were some things that never really made sense. Why was pi defined in terms of the diameter when literally everything else we learned about circles used the radius? Why did radian angles feel off by a factor of 2? When I later stumbled upon the Tau Manifesto, it felt like a lot of things fell into place. And by that time, I had also studied calculus and had a familiarity with the kinds of things that happen in formulas which relate lengths and areas, so the discussion of the circle area formula resonated as well. Despite all the cheap dismissals one sees, this feeling of "woah, that would have actually made sense!" is a big part of what makes the Tau Manifesto popular.

82 points by acjohnson55 12y ago

lkbm 12y ago

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

thomasahle 12y ago
But changing our number system to base 12 would destroy pi day!
- lkbm 12y ago
  Yeah, but as Vihart pointed out, Pi = a half rotation, so Pi day is in June. :-)
pdkl95 12y ago
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 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 https://www.youtube.com/watch?v=jG7vhMMXagQ

hugs 12y ago

I didn't really understand why tau was "better" than pi until I understood the relationship to radians. Figure 8 [1] in the Tau Manifesto was the eye-opener for me. With tau, instead of pi, I now have a more intuitive sense of how to think in radians when doing trigonometry. [1]: http://www.tauday.com/tau-manifesto#fig-tau_angles http://www.tauday.com/tau-manifesto#fig-tau_angles

jackmaney 12y ago

http://www.thepimanifesto.com/ http://www.thepimanifesto.com/

thomasahle 12y ago
I like Terence's suggestion of using 2pii as the fundamental constant. Sqrt(pi) could also be useful given how often it appears.
cplease 12y ago
Thank you.

giech 12y ago

I think this whole argument is silly. I really do not think one is fundamentally better than the other. Factor of 2 constants will exist no matter which one you choose. Might as well go with pau http://xkcd.com/1292/ http://xkcd.com/1292/

mfisher87 12y ago
I don't like to think about it this way. I think it's silly to go all out and insist one is always objectively "better" than the other (it's a tradeoff), but to have this discussion is illuminating. Look through the comments at how many people gained a better understanding of geometry as a whole by reading.

bau5 12y ago

Do not want.

amalcon 12y ago

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 dozens of completely unused glyphs in the non-English non-Greek alphabets (Hebrew, Russian, etc). It seems almost like a parody.

deleted 12y ago
[deleted]
DSMan195276 12y ago
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 constant tells you that you have exactly '3 / 4' of a circle. With pi, this is less obvious because there are '2 * pi' radians in a circle, but the 2 frequently disappears (like in my example), which leaves you with '3 / 2 of a half a circle', which isn't obvious how much that actually is. pi definitely does have it's uses when you're talking about the diameter, but when you're talking about something like radians, it makes more sense to use the ratio of circumference to radius rather then circumference to diameter. If we were using diameterians then it would make sense to use pi, since there would be exactly pi diameterians in a circle. Having them mismatched like we do creates a mess.
- tomp 12y ago
  > 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...

fdej 12y ago

Both tau and pi are inconvenient because you often need fractional multiples like 1/6 or 3/4. We should instead take the fundamental unit of angle measurement to be pi divided by a highly composite number, say 2 * 2 * 3 * 3 * 5 = 180. Most common angles will be then be integer multiples of this unit. Let's give this unit a name, say "degree". One full rotation = 360 "degrees" Half a rotation = 180 "degrees" 1/10 of a rotation = 36 "degrees" etc. I can't believe I'm the first person to think of this. It's so simple that even the ancient Greeks could have figured it out. I should write a full internet manifesto and try to convert the world.

deleted 12y ago
[deleted]
wodenokoto 12y ago
Stuff like signal processing is horrible if you try and use degrees. I'm not even sure if calculating the area of a circle is in anyway better using degrees.
tomp 12y ago
What happens when you have 1/7 of a rotation? There's no one multiplier that will solve all cases. In any case, personally I think that fractions are way better, because they tell you exactly what's what.
sunfish 12y ago
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 (except 0), even in the most basic of situations. But instead of picking an arbitrary number like 360 or 1337 or whatever, how about we pick 1? Let's give this unit a name, say "turn". One full rotation = 1 "turn" Half a rotation = 1/2 "turn" 1/10 of a rotation = 1/10 "turn" etc. What do you think?
- 12y ago

ebbv 12y ago

Do we really need to do this every year? Come on.

cplease 12y ago

e^(τi/2) = -1 Didn't think so.

StefanKarpinski 12y ago
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.
- tomp 12y ago
  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".
  - sukilot 12y ago
    That's ambiguous. Which straight line? Forwards or backwards? It's a half-turn.
  - stouset 12y ago
    You mean a vector in the opposite direction. Clear as mud.
sebastos 12y ago
... e^(τi) = 1 so still better.

deleted 12y ago

[deleted]

sunfish 12y ago

I distinctly remember when I was learning geometry that there were some things that never really made sense. Why was pi defined in terms of the diameter when literally everything else we learned about circles used the radius? Why did radian angles feel off by a factor of 2? When I later stumbled upon the Tau Manifesto, it felt like a lot of things fell into place. And by that time, I had also studied calculus and had a familiarity with the kinds of things that happen in formulas which relate lengths and areas, so the discussion of the circle area formula resonated as well. Despite all the cheap dismissals one sees, this feeling of "woah, that would have actually made sense!" is a big part of what makes the Tau Manifesto popular.