3 ms·

This! I've been posting the manifesto to friends and colleagues every tau day for the past ten years. Let's keep chipping away at it and eventually we won't ob

by snthpy 10mo ago

This! I've been posting the manifesto to friends and colleagues every tau day for the past ten years. Let's keep chipping away at it and eventually we won't obfuscate radians for our kids anymore. Friends don't let friends use pi!

avmich 10mo ago
I wonder how many places we have in modern math symbols which we use for historical reasons, rather than because it's most convenient overall. I guess we are balancing things here.
- yen223 10mo ago
  Arguably, base-10 counting vs base-12 counting is one such example
  - deleted 10mo ago
    [deleted]
  - snthpy 10mo ago
    Which one of those is preferable? It seems to me that they are both historically based. 10 x 10 is also 100 in base-12 (it's only in base-10 that it looks like 144). IMHO, in a modern setting base-16 would be the most convenient. Then I maybe wouldn't struggle to remember that the CIDR range C0.A8.0.0/18 (192.168.0.0/24) consists of 10 (16) blocks of size 10 (16).
    - Sharlin 10mo ago
      There’s nothing particularly convenient about base-ten; for real-world uses base-twelve would be preferable thanks to its large number of divisors (and even larger number of divisors of its multiples like 60). Which is exactly why 12 and 60 historically appear in many contexts. A number theorist would probably want a prime base, so that N (mod 10) would be a field. A power-of-two base wouldn’t be particularly convenient to anyone except a small minority consisting mostly of hardware and software engineers.
      - ses1984 10mo ago
        There is one particularly convenient fact of having ten digits.
        Sharlin 10mo ago
        Fair :P I should've said "inherently convenient".
    - tliltocatl 10mo ago
      > base-16 would be the most convenient That would mean 1/5=0.(3)₁₆ would be an infinite fraction as well. A more convenient would be 6 or 12 because it allows to represent 1/3 exactly.
rmunn 10mo ago
Oh, pi has its place: in engineering, for example, it's much easier to measure the diameter of a pipe than its radius: just put calipers around the widest point (outside or inside depending) and you have the diameter. In fact, you probably wouldn't ever measure the radius; in places where you need the radius, you'd just measure the diameter and divide by 2. But for teaching trig? Explaining radians should definitely be tau-based.
- cbolton 10mo ago
  Do you mean the advantage of writing pi*d for the circumference instead of tau*r or tau*d/2? I wouldn't keep pi around just for this...
  - rmunn 10mo ago
    Yes, though more broadly my point was that the radius is the natural measurement of the circle for most things since most things are center-based. But for some physical measurements, mostly based around pipes, "what is the width of this pipe" is the question you need answering, and that is diameter-based. And pi is circumference/diameter, while tau is circumference/radius. But yes, if the world switched to tau then you wouldn't need pi anymore, you'd just write tau/2 in the rare cases where having the circumference/diameter ratio handy is useful.

by snthpy 10mo ago

avmich 10mo ago

I wonder how many places we have in modern math symbols which we use for historical reasons, rather than because it's most convenient overall. I guess we are balancing things here.

yen223 10mo ago
Arguably, base-10 counting vs base-12 counting is one such example
- deleted 10mo ago
  [deleted]
- snthpy 10mo ago
  Which one of those is preferable? It seems to me that they are both historically based. 10 x 10 is also 100 in base-12 (it's only in base-10 that it looks like 144). IMHO, in a modern setting base-16 would be the most convenient. Then I maybe wouldn't struggle to remember that the CIDR range C0.A8.0.0/18 (192.168.0.0/24) consists of 10 (16) blocks of size 10 (16).
  - Sharlin 10mo ago
    There’s nothing particularly convenient about base-ten; for real-world uses base-twelve would be preferable thanks to its large number of divisors (and even larger number of divisors of its multiples like 60). Which is exactly why 12 and 60 historically appear in many contexts. A number theorist would probably want a prime base, so that N (mod 10) would be a field. A power-of-two base wouldn’t be particularly convenient to anyone except a small minority consisting mostly of hardware and software engineers.
    - ses1984 10mo ago
      There is one particularly convenient fact of having ten digits.
      - Sharlin 10mo ago
        Fair :P I should've said "inherently convenient".
  - tliltocatl 10mo ago
    > base-16 would be the most convenient That would mean 1/5=0.(3)₁₆ would be an infinite fraction as well. A more convenient would be 6 or 12 because it allows to represent 1/3 exactly.

rmunn 10mo ago

Oh, pi has its place: in engineering, for example, it's much easier to measure the diameter of a pipe than its radius: just put calipers around the widest point (outside or inside depending) and you have the diameter. In fact, you probably wouldn't ever measure the radius; in places where you need the radius, you'd just measure the diameter and divide by 2. But for teaching trig? Explaining radians should definitely be tau-based.

cbolton 10mo ago
Do you mean the advantage of writing pi*d for the circumference instead of tau*r or tau*d/2? I wouldn't keep pi around just for this...
- rmunn 10mo ago
  Yes, though more broadly my point was that the radius is the natural measurement of the circle for most things since most things are center-based. But for some physical measurements, mostly based around pipes, "what is the width of this pipe" is the question you need answering, and that is diameter-based. And pi is circumference/diameter, while tau is circumference/radius. But yes, if the world switched to tau then you wouldn't need pi anymore, you'd just write tau/2 in the rare cases where having the circumference/diameter ratio handy is useful.