3 ms·

I like this idea of choosing a representation for numbers based on the use case. Like, "ints" and "floats" but even more specialized. For example, what would b

I like this idea of choosing a representation for numbers based on the use case. Like, "ints" and "floats" but even more specialized. For example, what would be the most efficient binary representation of probabilities values between 0 and 1? In the future, I can imagine hardware + software that is specialized for examples like this.

dr_dshiv 4y ago
Makes me wonder about quantum computing possibilities.
js8 4y ago
I feel like probabilities are best stored as inverse logistic function, because the closer the probability is to 0 or 1, the less you care about significant digits, because the events are going (not) to happen anyway. (That's why I am proponent of LNS.)
- jbay808 4y ago
  I'd agree with this suggestion. Furthermore this does not need a new number format, as IEEE floating point is already pretty ideally distributed. https://en.wikipedia.org/wiki/Logit https://en.wikipedia.org/wiki/Logit
- planede 4y ago
  I feel that it's actually the opposite. There is a world of difference between 0.0...01 and 0.0...001 , where ... represents the same number of 0s in the two cases. Same applies for the other end. edit: Do I really want more resolution between 0.41 and 0.42 than between 0.01 and 0.02?
  - daniel-cussen 4y ago
    You're dead on. Metals are sold by how fine they are, so .999%, .9995% (should end in a 7 numeral not a 5, whole industry is fucking up right there, but at any rate) .9999%, more nines more purity better experimental results. When they talk about 4 nines or 5 nines the actual measurement is of the f(x)= - log(1 - x). That is the purity. Negative of the log of the complement. And that's why 4.5 nines should be .99997% not fucking .99995%, so stupid (it's almost exactly .99997%). Mining engineers, come on! Such impressive degrees! PhD's all over the place! Professors even! I'm sorry, don't mind me with my math. Some experiments like with liquid crystals early on required purities that what chemical company was it, Merck I think, around the year 1900, complained like they felt insulted. Told the inventor of liquid crystals because it was an absurd amount of purity required to get them actually working. But look at them go! Right in front of your very eyes!
- teo_zero 4y ago
  Isn't it the other way out? The logistic curve becomes denser close to 0 and 1. Which makes sense: you will want to tell apart 1 defect per million from 0.01 dpm, and 5-sigma process (99.977%) from 6-sigma (99.99966%), much more than tell apart 30% from 30.001%.

dr_dshiv 4y ago

Makes me wonder about quantum computing possibilities.

js8 4y ago

I feel like probabilities are best stored as inverse logistic function, because the closer the probability is to 0 or 1, the less you care about significant digits, because the events are going (not) to happen anyway. (That's why I am proponent of LNS.)

jbay808 4y ago
I'd agree with this suggestion. Furthermore this does not need a new number format, as IEEE floating point is already pretty ideally distributed. https://en.wikipedia.org/wiki/Logit https://en.wikipedia.org/wiki/Logit
planede 4y ago
I feel that it's actually the opposite. There is a world of difference between 0.0...01 and 0.0...001 , where ... represents the same number of 0s in the two cases. Same applies for the other end. edit: Do I really want more resolution between 0.41 and 0.42 than between 0.01 and 0.02?
- daniel-cussen 4y ago
  You're dead on. Metals are sold by how fine they are, so .999%, .9995% (should end in a 7 numeral not a 5, whole industry is fucking up right there, but at any rate) .9999%, more nines more purity better experimental results. When they talk about 4 nines or 5 nines the actual measurement is of the f(x)= - log(1 - x). That is the purity. Negative of the log of the complement. And that's why 4.5 nines should be .99997% not fucking .99995%, so stupid (it's almost exactly .99997%). Mining engineers, come on! Such impressive degrees! PhD's all over the place! Professors even! I'm sorry, don't mind me with my math. Some experiments like with liquid crystals early on required purities that what chemical company was it, Merck I think, around the year 1900, complained like they felt insulted. Told the inventor of liquid crystals because it was an absurd amount of purity required to get them actually working. But look at them go! Right in front of your very eyes!
teo_zero 4y ago
Isn't it the other way out? The logistic curve becomes denser close to 0 and 1. Which makes sense: you will want to tell apart 1 defect per million from 0.01 dpm, and 5-sigma process (99.977%) from 6-sigma (99.99966%), much more than tell apart 30% from 30.001%.