10 ms·

I think the basic idea is that highly composite numbers [1] make good bases. It's a trade off between the number of divisors of the base and the number of digit

I think the basic idea is that highly composite numbers [1] make good bases. It's a trade off between the number of divisors of the base and the number of digits we want to learn. Note that both 12 and 60 are such numbers. [1] https://en.wikipedia.org/wiki/Highly_composite_number https://en.wikipedia.org/wiki/Highly_composite_number Also it looks like the Babylonian is a composite system, where the 'digits' are represented in base 10 (the 10s use a different digit, but it doesn't matter). They could alternatively use base 12 for this digit.

kutkloon7 9y ago
Yes, composite numbers have many advantages. Working in base 60 = 2^2 * 5 * 3, has advantages of working in base 2, base 5, and base 3. In base 10, you can quickly spot multiples of 2, 5, and ten (or alternatively, reduce any number module 2, 5, or 10).
- vog 9y ago
  > base 60 = 2^2 5 * 3, has advantages of working in base 2, base 5, and base 3.* ... and 4 and 6 and 10. (and 12, 15, 30, 60)
  - kutkloon7 9y ago
    And 120, 180, 240, ... ;)
heycam 9y ago
Firefox and Servo use 1/60 as the smallest layout unit for the same reason. http://searchfox.org/mozilla-central/source/gfx/src/AppUnits.h http://searchfox.org/mozilla-central/source/gfx/src/AppUnits... http://doc.servo.org/app_units/ http://doc.servo.org/app_units/ https://bugzilla.mozilla.org/show_bug.cgi?id=177805 https://bugzilla.mozilla.org/show_bug.cgi?id=177805
- microcolonel 9y ago
  It's cool and all, but keeping that decision has led to some pretty annoying bugs in SVG (and other) transforms. https://bugzilla.mozilla.org/show_bug.cgi?id=844258 https://bugzilla.mozilla.org/show_bug.cgi?id=844258
schindlabua 9y ago
psh, it's 2017. Clearly we should switch to hex, ditch scientific notation and decimal points and all that difficult junk, and just use IEEE 754 double precision notation for all our calculations. Granted the sign bit in front makes hex notation a bit awkward but I believe it will give us a nice kickstart for when we will inevitably be subsumed by our AI overlords.
- eadmund 9y ago
  Sixteen doesn't have 3 as a factor. IIRC, it's not possible to represent .1 (or is it .2) accurately in IEEE 754. Better to use duodecimal.
  - JadeNB 9y ago
    > IIRC, it's not possible to represent .1 (or is it .2) accurately in IEEE 754. > Better to use duodecimal. Assuming you mean the decimals 0.1 and 0.2, they can't be represented as terminating duodecimals (which is different from not being represented accurately!), either. Whatever base you choose, someone's favourite fraction won't have a terminating expansion.
  - SAI_Peregrinus 9y ago
    IEEE754 includes two decimal floating point basic formats: decimal64 and decimal128. 0.1 can be accurately represented. Of course in any base there will be some non-terminating representations of rational numbers, so changing the base of the floating point system changes which numbers these are but does not eliminate them.

kutkloon7 9y ago

Yes, composite numbers have many advantages. Working in base 60 = 2^2 * 5 * 3, has advantages of working in base 2, base 5, and base 3. In base 10, you can quickly spot multiples of 2, 5, and ten (or alternatively, reduce any number module 2, 5, or 10).

vog 9y ago
> base 60 = 2^2 5 * 3, has advantages of working in base 2, base 5, and base 3.* ... and 4 and 6 and 10. (and 12, 15, 30, 60)
- kutkloon7 9y ago
  And 120, 180, 240, ... ;)

heycam 9y ago

Firefox and Servo use 1/60 as the smallest layout unit for the same reason. http://searchfox.org/mozilla-central/source/gfx/src/AppUnits.h http://searchfox.org/mozilla-central/source/gfx/src/AppUnits... http://doc.servo.org/app_units/ http://doc.servo.org/app_units/ https://bugzilla.mozilla.org/show_bug.cgi?id=177805 https://bugzilla.mozilla.org/show_bug.cgi?id=177805

microcolonel 9y ago
It's cool and all, but keeping that decision has led to some pretty annoying bugs in SVG (and other) transforms. https://bugzilla.mozilla.org/show_bug.cgi?id=844258 https://bugzilla.mozilla.org/show_bug.cgi?id=844258

schindlabua 9y ago

psh, it's 2017. Clearly we should switch to hex, ditch scientific notation and decimal points and all that difficult junk, and just use IEEE 754 double precision notation for all our calculations. Granted the sign bit in front makes hex notation a bit awkward but I believe it will give us a nice kickstart for when we will inevitably be subsumed by our AI overlords.

eadmund 9y ago
Sixteen doesn't have 3 as a factor. IIRC, it's not possible to represent .1 (or is it .2) accurately in IEEE 754. Better to use duodecimal.
- JadeNB 9y ago
  > IIRC, it's not possible to represent .1 (or is it .2) accurately in IEEE 754. > Better to use duodecimal. Assuming you mean the decimals 0.1 and 0.2, they can't be represented as terminating duodecimals (which is different from not being represented accurately!), either. Whatever base you choose, someone's favourite fraction won't have a terminating expansion.
- SAI_Peregrinus 9y ago
  IEEE754 includes two decimal floating point basic formats: decimal64 and decimal128. 0.1 can be accurately represented. Of course in any base there will be some non-terminating representations of rational numbers, so changing the base of the floating point system changes which numbers these are but does not eliminate them.