I picked decibels because that’s what I’m getting used to as I try to absorb E.T. Jaynes’ book “Probability Theory: The Logic of Science”.
Lojban is flexible enough to use binary rather than decimal; technically, if you say “ju’u re”, everything you say after that is assumed to be in base 2, with the digits “no” 0 and “pa” (and radix point “pi”). Bei’e is still new enough that I can add a note about the use of binary as an option; I’m less familar with using bits in this sense than I am decibels, so if you could give me a reference (or even just type out a representative sample) of how bits compare to a percentage probability, then I could easily add that to the current definition.
(For precise numbers for the decibels, I use the formula:
decibels = 10 log(10) (LevelOfBelief / (1 - LevelOfBelief))
. So to check how many decibels are equivalent to 64:1 odds, I plug into Google Calculator:
10 log ((64/65) / (1/65))
, getting 18 and change.)
Okay, so we don’t actually have to change the base we’re counting in, we’d be changing the units we’re counting—instead of X number of decibels, it would be X number of bits, and X can be expressed in base 10 either way.
I’d like to take a day or so to think about the best way to approach this—it may very well be as simple as adding a note to the reftext about how to convert decibels to bits by dividing by three.
I’ve tried to take the ‘outside view’ on this, to see if I’d originally come up with the idea of using bits, whether it would be worth switching to decibels. Using decibels, only two digits brings you all the way to the billions-to-one level of odds, which seems sufficient for everyday purposes; and decibels dividing probability-space more finely allows for easy differentiation between some useful probability numbers, such as ‘beyond a reasonable doubt’ and ‘clear and convincing evidence’, which would be blurred if using bits.
So I think that I’m going to keep bei’e as being measured in decibels, add a note to the definition about conversion to bits… and, I think, add a note that anyone who really wants to have an experimental cmavo that uses bits is as free to create and use it as I was to create bei’e. Sound good to you?
I picked decibels because that’s what I’m getting used to as I try to absorb E.T. Jaynes’ book “Probability Theory: The Logic of Science”.
Lojban is flexible enough to use binary rather than decimal; technically, if you say “ju’u re”, everything you say after that is assumed to be in base 2, with the digits “no” 0 and “pa” (and radix point “pi”). Bei’e is still new enough that I can add a note about the use of binary as an option; I’m less familar with using bits in this sense than I am decibels, so if you could give me a reference (or even just type out a representative sample) of how bits compare to a percentage probability, then I could easily add that to the current definition.
So “ju’u re pi no pa” is 1/4?
Exactly so.
To see if I understand this correctly; then in this approach, each increase of 1 bit is equivalent to an increase of 3 decibels?
0 dbs → 1:1 → 0 bits 3 dbs → 2:1 → 1 bit 6 dbs → 4:1 → 2 bits 9 dbs → 8:1 → 3 bits 12 dbs → 16:1 → 4 bits 15 dbs → 32:1 → 5 bits 18 dbs → 64:1 → 6 bits
(For precise numbers for the decibels, I use the formula: decibels = 10 log(10) (LevelOfBelief / (1 - LevelOfBelief)) . So to check how many decibels are equivalent to 64:1 odds, I plug into Google Calculator: 10 log ((64/65) / (1/65)) , getting 18 and change.)
approximately. because 3 bits is a factor of 8 which is approximately 10, and 3 decibels is approximately one third of the way to 10.
Okay, so we don’t actually have to change the base we’re counting in, we’d be changing the units we’re counting—instead of X number of decibels, it would be X number of bits, and X can be expressed in base 10 either way.
I’d like to take a day or so to think about the best way to approach this—it may very well be as simple as adding a note to the reftext about how to convert decibels to bits by dividing by three.
Yeah, number of bits is still expressed in base ten (lol, I just realized that all bases are base 10 in their own base).
I don’t know about this divide by three business. it’s not exactly 3. You should use the correct value.
EDIT: log(10)/log(2) = 3.3219
It seems like divide by 3 should be about right. 2**10 is roughly 10**3, so 30 decibels is about 10 bits. (1024 versus 1000).
You are right, the conversion factor is 3.01.
I’ve tried to take the ‘outside view’ on this, to see if I’d originally come up with the idea of using bits, whether it would be worth switching to decibels. Using decibels, only two digits brings you all the way to the billions-to-one level of odds, which seems sufficient for everyday purposes; and decibels dividing probability-space more finely allows for easy differentiation between some useful probability numbers, such as ‘beyond a reasonable doubt’ and ‘clear and convincing evidence’, which would be blurred if using bits.
So I think that I’m going to keep bei’e as being measured in decibels, add a note to the definition about conversion to bits… and, I think, add a note that anyone who really wants to have an experimental cmavo that uses bits is as free to create and use it as I was to create bei’e. Sound good to you?
sure why not.
I just find bits more natural. People talk about twice as much (+1 bit) often, and bits are the unit used in information theory and computer science.