3 ms·

360° in a full circle That's one of the things tau can help solve. I suspect the main reason that people still use degrees so much is because using pi undermin

by mhartl 14y ago

360° in a full circle That's one of the things tau can help solve. I suspect the main reason that people still use degrees so much is because using pi undermines the beauty and intuitiveness of radians.

cygx 14y ago
No, the main reason why degrees are still in use is because most people have an easier time with 51° instead of 1/7 τ.
- waterhouse 14y ago
  51° is not 1/7 τ. 1/7 τ is (51 3/7)°, or 51.428571...°. If you round that to 51°, then presumably you're doing something where inexact numbers are fine, in which case you might then use "0.89 (radians)". My intuition is better for degrees here, but I think that would change if I spent ten minutes doing calculations involving real radian measures.
  - cygx 14y ago
    51° is the latitude of the city I'm living in, and I chose 1/7 τ because it comes pretty close. I could have used 0.14 τ to make my point as well: If you want to avoid fractions in common cases, you'll need to multiply with an arbitrary number like, say 100 (which has obvious benefits in a base-10 system), but arguments could be made for something like 400 (in which case we end up with gon) or, say 360, which has the benefit that it's the established standard (even though it's not the most obvious choice). Actual radians (ie not expressed as fractions of 2π) are pretty user-unfriendly in a base-10 system.
    - blahedo 14y ago
      > Actual radians (ie not expressed as fractions of 2π) I think this is the source of your problem: you view an expression like "τ/8" or "π/4" as less an "actual" radian measure than the inexact ".785". That's a function of how a lot of us were taught math, I think, and I'm quite sure that it's only made worse by the fact that the use of π camouflages the fact that this is related to fractions of a circle. But your premise is faulty. Of course radians expressed in decimal are user-unfriendly, but radians expressed in decimal are no less "actual" than radians expressed as fractions of τ or π.
      - cygx 14y ago
        A physical quantity is given by numerical value and unit of measurement. Giving angles as fractions of τ changes the unit of measurement from radians to turn. There are applications for which neither radians nor turn are a good fit. Similarly, oftentimes the 'messy' SI units are a far better fit than any 'more fundamental' system of natural units.
        oelewapperke 14y ago
        That's true to a degree. But when you think about it, there does not exist any physical quantity that can be specified as an irrational number (because every measurement is quantized, so you could argue even a whole number. Rational numbers and whole numbers are models of eachother however, so there is arguably no "fundamental" difference). As to why people can calculate better/easier with relatively low numbers compared to irrational fractions ... does that really need explaining ? How much is 1+1 vs how much is 1/7 tau + 1/3 tau. Degrees are very useful and quick indeed.
waterhouse 14y ago
I, for one, speak in terms of degrees as a sort of compatibility mode--when talking to people who aren't familiar with tau and when I don't feel like pressing the point with them. (I have almost completely avoided mentioning "pi" except in meta-discussions since I read the Tau Manifesto two years ago.)
louis058 14y ago
The main reason people still use degrees is because the majority of the population only know degrees, can't be bothered to change, and the majority of the population will continue to only know degrees, unless radians start getting taught at a much younger age. People can't be bothered to change, except radians are much more mathematically easy to use, so people who need to do advanced maths will use it. However, laziness is also the reason why people don't change to tau. tau is just a multiple of pi. Confronted with such a small change, people will just think that they can't be bothered to change, especially since pi is already widely supported and implemented in any of the tools that we use, and tau is not. There's no way that changing to tau will make more people use radians.

by mhartl 14y ago

cygx 14y ago

No, the main reason why degrees are still in use is because most people have an easier time with 51° instead of 1/7 τ.

waterhouse 14y ago
51° is not 1/7 τ. 1/7 τ is (51 3/7)°, or 51.428571...°. If you round that to 51°, then presumably you're doing something where inexact numbers are fine, in which case you might then use "0.89 (radians)". My intuition is better for degrees here, but I think that would change if I spent ten minutes doing calculations involving real radian measures.
- cygx 14y ago
  51° is the latitude of the city I'm living in, and I chose 1/7 τ because it comes pretty close. I could have used 0.14 τ to make my point as well: If you want to avoid fractions in common cases, you'll need to multiply with an arbitrary number like, say 100 (which has obvious benefits in a base-10 system), but arguments could be made for something like 400 (in which case we end up with gon) or, say 360, which has the benefit that it's the established standard (even though it's not the most obvious choice). Actual radians (ie not expressed as fractions of 2π) are pretty user-unfriendly in a base-10 system.
  - blahedo 14y ago
    > Actual radians (ie not expressed as fractions of 2π) I think this is the source of your problem: you view an expression like "τ/8" or "π/4" as less an "actual" radian measure than the inexact ".785". That's a function of how a lot of us were taught math, I think, and I'm quite sure that it's only made worse by the fact that the use of π camouflages the fact that this is related to fractions of a circle. But your premise is faulty. Of course radians expressed in decimal are user-unfriendly, but radians expressed in decimal are no less "actual" than radians expressed as fractions of τ or π.
    - cygx 14y ago
      A physical quantity is given by numerical value and unit of measurement. Giving angles as fractions of τ changes the unit of measurement from radians to turn. There are applications for which neither radians nor turn are a good fit. Similarly, oftentimes the 'messy' SI units are a far better fit than any 'more fundamental' system of natural units.
      - oelewapperke 14y ago
        That's true to a degree. But when you think about it, there does not exist any physical quantity that can be specified as an irrational number (because every measurement is quantized, so you could argue even a whole number. Rational numbers and whole numbers are models of eachother however, so there is arguably no "fundamental" difference). As to why people can calculate better/easier with relatively low numbers compared to irrational fractions ... does that really need explaining ? How much is 1+1 vs how much is 1/7 tau + 1/3 tau. Degrees are very useful and quick indeed.

waterhouse 14y ago

I, for one, speak in terms of degrees as a sort of compatibility mode--when talking to people who aren't familiar with tau and when I don't feel like pressing the point with them. (I have almost completely avoided mentioning "pi" except in meta-discussions since I read the Tau Manifesto two years ago.)

louis058 14y ago

The main reason people still use degrees is because the majority of the population only know degrees, can't be bothered to change, and the majority of the population will continue to only know degrees, unless radians start getting taught at a much younger age. People can't be bothered to change, except radians are much more mathematically easy to use, so people who need to do advanced maths will use it. However, laziness is also the reason why people don't change to tau. tau is just a multiple of pi. Confronted with such a small change, people will just think that they can't be bothered to change, especially since pi is already widely supported and implemented in any of the tools that we use, and tau is not. There's no way that changing to tau will make more people use radians.