4 ms·

Why would sleeping time be a fraction of 2pi? > I'd guess that you're using rational numbers in the actual calculation anyways. Well, actually one uses float

Why would sleeping time be a fraction of 2pi? > I'd guess that you're using rational numbers in the actual calculation anyways. Well, actually one uses floating point arithmetic, which isn't rational numbers either (as shown by the classic example a = 1/3, b = 3*a, then b != a)

ReleaseCandidat 3y ago
> Why would sleeping time be a fraction of 2pi? The rotation of a hand of the clock, expressed as the arc length of the curve of its endpoint :) A sleeping time of 0 is always a problem, though.
- red_trumpet 3y ago
  But why would the second factor be a rational?
867-5309 3y ago
https://en.wikipedia.org/wiki/Turn_(angle) https://en.wikipedia.org/wiki/Turn_(angle)
saalweachter 3y ago
I mean, we could be measuring time in radians. We already subdivide degrees into minutes and seconds, might as well call the day 2 pi radians. We sleep for 2/3 pi radians of the day in that case.
- red_trumpet 3y ago
  The whole argument started when somebody above claimed that we probably do not sleep exactly 8 hours, but some weird irrational number. That problem persists even if you measure in radians...
  - Rayhem 3y ago
    Do the physicist thing and just define all your constants to be one. "How long is a day? 1 day." "I slept for .37 days." This nicely unifies things with the tao manifesto[1] people since 1 day = 1 turn = 1 tau = 2 * pi radians and reinforces the periodic nature of these things. [1]: https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto
    - PawgerZ 3y ago
      Yes, but in reality, you slept .37827387654329617345987613475130465019873458612386459012374587203475. . . days
      - saalweachter 3y ago
        Doesn't that depend on whether time is quantized?
        PawgerZ 3y ago
        Yes, but with no viable theories of a minimal unit, I'll assume that no such thing exists until given proof otherwise.
nyrikki 3y ago
Base 12 being 3-smooth, any number with 2 or 3 as a factor has a reciprocal with a terminating expansion. base 60 is 5-smooth, so any number with 2,3,5 as a factor has a terminating expansion. Just as SI has to add in deg min sec for fields like astronomy. As the practical numbers are quite dense up to 60, they could divide by multiplication of the reciprocal for many more numbers. Floating point is more complicated than just the base as the radix also matters. C(++) finally got decimal radix support this year in the standards and IBM has had decimal floats for a long time. FFT and encryption often use mixed radix despite being a binary base too. It is a far more complicated subject than it appears on the surface. But there are problems that aren't easily solvable in base 10. The degrees of a circle are an example and why navigation uses the nautical mile, where 1 nautical mile= 1 minute of latitude is an example. 12,60,360 are Superior highly composite numbers and 12 is the smallest 3-smooth and 60 is the smallest 5-smooth. This also means that with using 360 degrees one can divide a circle or semicircle in 12 sections with just a square, 345 triangle and equalatrral triangle. Where decimal or even radians requires the square root of 2, pi, etc... I am a fan of universal units of measurement, but had they been base 12 it would have been better IMHO. SI could be more broadly adopted if it has been base 12.
- xigoi 3y ago
  Base 6 is better than base 12. https://www.seximal.net/ https://www.seximal.net/
  - nyrikki 3y ago
    Pretty light on details, but if it works for you that is great. Quartiles and hand counting would be my argument for 12 but am probably biased based on familiarity.
    - xigoi 3y ago
      Seximal is actually great for hand counting. You can use fingers the classical way for one digit per hand or base 6² compression for two digits per hand, allowing you to count up to 1296 with two hands.

ReleaseCandidat 3y ago

> Why would sleeping time be a fraction of 2pi? The rotation of a hand of the clock, expressed as the arc length of the curve of its endpoint :) A sleeping time of 0 is always a problem, though.

red_trumpet 3y ago
But why would the second factor be a rational?

867-5309 3y ago

https://en.wikipedia.org/wiki/Turn_(angle) https://en.wikipedia.org/wiki/Turn_(angle)

saalweachter 3y ago

I mean, we could be measuring time in radians. We already subdivide degrees into minutes and seconds, might as well call the day 2 pi radians. We sleep for 2/3 pi radians of the day in that case.

red_trumpet 3y ago
The whole argument started when somebody above claimed that we probably do not sleep exactly 8 hours, but some weird irrational number. That problem persists even if you measure in radians...
- Rayhem 3y ago
  Do the physicist thing and just define all your constants to be one. "How long is a day? 1 day." "I slept for .37 days." This nicely unifies things with the tao manifesto[1] people since 1 day = 1 turn = 1 tau = 2 * pi radians and reinforces the periodic nature of these things. [1]: https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto
  - PawgerZ 3y ago
    Yes, but in reality, you slept .37827387654329617345987613475130465019873458612386459012374587203475. . . days
    - saalweachter 3y ago
      Doesn't that depend on whether time is quantized?
      - PawgerZ 3y ago
        Yes, but with no viable theories of a minimal unit, I'll assume that no such thing exists until given proof otherwise.

nyrikki 3y ago

Base 12 being 3-smooth, any number with 2 or 3 as a factor has a reciprocal with a terminating expansion. base 60 is 5-smooth, so any number with 2,3,5 as a factor has a terminating expansion. Just as SI has to add in deg min sec for fields like astronomy. As the practical numbers are quite dense up to 60, they could divide by multiplication of the reciprocal for many more numbers. Floating point is more complicated than just the base as the radix also matters. C(++) finally got decimal radix support this year in the standards and IBM has had decimal floats for a long time. FFT and encryption often use mixed radix despite being a binary base too. It is a far more complicated subject than it appears on the surface. But there are problems that aren't easily solvable in base 10. The degrees of a circle are an example and why navigation uses the nautical mile, where 1 nautical mile= 1 minute of latitude is an example. 12,60,360 are Superior highly composite numbers and 12 is the smallest 3-smooth and 60 is the smallest 5-smooth. This also means that with using 360 degrees one can divide a circle or semicircle in 12 sections with just a square, 345 triangle and equalatrral triangle. Where decimal or even radians requires the square root of 2, pi, etc... I am a fan of universal units of measurement, but had they been base 12 it would have been better IMHO. SI could be more broadly adopted if it has been base 12.

xigoi 3y ago
Base 6 is better than base 12. https://www.seximal.net/ https://www.seximal.net/
- nyrikki 3y ago
  Pretty light on details, but if it works for you that is great. Quartiles and hand counting would be my argument for 12 but am probably biased based on familiarity.
  - xigoi 3y ago
    Seximal is actually great for hand counting. You can use fingers the classical way for one digit per hand or base 6² compression for two digits per hand, allowing you to count up to 1296 with two hands.