Joke or not, the title was unclear.
Ah.
I think it’s the case that we merely don’t know a way yet to do it in base 10, not that it’s been proven impossible. (And that’s actually what I read Chronos to be referring to.)
So you’re the guy who had to set up Nigel Tufnel’s studio.
Not sure if it has been mentioned, but base 12 would link up with time and calender.
For example, 100 months is 10 years. 200 hours is 10 days. (all base 12 numbers, hope this is correct!)
Ooh… that’s interesting; I didn’t think of that. That perfectly explains the efficiency claim; I retract my skepticism.
Of course, abacuses are discrete, so putting this another way, making sense of the continuous aspect: for any event which may or may not occur, we can define the “information it is responsible for” as the information contained in semilearning about the event (learning of the event if it does occur, and learning nothing otherwise). That is, the information an event is responsible for is defined for any particular case as the information contained in learning that the event occurred, in those cases where it does occur, and as 0 in those cases where it does not occur. For example, whenever one learns the value of a random integer between 0 and 999, one learns three decimal digits of information, but different events are responsible for different parts of that information; if I learn that the random number is 538, then “The first digit is 5”, “The middle digit is 3”, and “The last digit is 8” are each responsible for 1 decimal digit of the information I learnt, while “The number is even” is responsible for 1 bit of the information I learnt, and “The last digit is 2” is responsible for none of the information I learnt.
Alright, so this defines information-responsibility. Then, for any event, we can ask, on probabilistic average, how much information is it responsible for? For example, half the time, “The number is even” is responsible for 1 bit of information and half the time it is responsible for 0 information, so, on average, this is responsible for only half a bit of information. (“The number is odd” is also responsible for only half a bit of information on average, and the information contained in learning a number’s parity is the information contained in semilearning both of these, and thus their sum, 1 full bit on average (and, indeed, all the time), as expected). On the other hand, while “The number’s last digit is 4” is sometimes responsible for a full decimal digit, which is much more than a bit, on average, it is only responsible for a tenth of a decimal digit, which is less than half a bit. So an event with probability 1/2 is responsible for more information on average than an event with probability 1/10, even though learning the latter is learning much more information than learning the former. In this sense, base-2 digits are more efficient than base-10 digits.
Of course, the average magnitude of the information an event is responsible for is the event’s probability * the event’s information-magnitude [thus, p * log(p) for an event with probability p, per the previous discussion]. This is maximized when the probability is 1/e and the information-magnitude is 1 nat. Accordingly, nats (i.e., base-e “digits”) are the most efficient information-magnitudes of all, in terms of expected information-responsibility.
(To clarify, when I wrote log(p), I meant the function which sends a probability p to the corresponding magnitude of information. If the base of the logarithm is q, then the information is measured in units of the information magnitude corresponding to a probability of q. So base 1/2 logarithms measure a probability’s information magnitude in bits, and base 1/10 logarithms measure it in decimal digits, while base 2 logarithms oppositely measure it in negative bits, and so on. So perhaps I should’ve just written -log(p) instead.)
Did you actually understand what the thread would be about, without opening the thread? I couldn’t tell if it was about different number systems, or about chemicals with large Ph, or about a computer language, or about military installations, or something else.
I should also clarify that sometimes I write “digit” and such things to mean a quantity of information (e.g., a “digit” as the information in learning which of 10 many possibilities holds) and sometimes I write it to mean a particular event (e.g., taking each of 10 many possibilities as a particular digit; each particular “digit” in this latter sense is responsible for only 1/10 of a “digit” of information, per the former sense). Hopefully, the context should generally make clear which I mean.
I did not know that. Though as a (former) chemist, I’ve only ever encountered it in terms of “per mole” and in calculations done on a molar basis in which unit analysis would require the number to be in mol[sup]-1[/sup], and so in that context, for practical applications, I still maintain that it isn’t exactly dimensionless. As of now, it is a unit in the SI system, and that’s good enough for me, although I can see the reasoning behind the criticism.
So my nitpick has its own nit. Such is life! 
We don’t know a way. It wouldn’t at all surprise me if some day, someone finds a way.
One nice thing about base 10 is that it scales well. 10^8 = 100000000. I have no idea what 12^8 is, or 8^8, etc.
never mind
All bases scale well if you’re not converting the numbers to some other base. 8^8 in base 8 would be written as 10^10, or 100,000,000. Similarly, 12^8 in base 12 would be written as 10^8, which would be 100,000,000 (or maybe 1,0000,0000 )
This is inherent to the base system. 12^8 in base 12 is 100000000, and 8^8 in base 8 is 100000000 as well. You can see this by breaking the number down into digits and multiplying them by the power that they represent (ie 0 ones, 0 tens, 0 hundreds, … 1 hundred-million):
10^8 = 110^8 + 010^7 + 010^6 + … + 010^0
12^8 = 112^8 + 012^7 + 010^6 + … + 012^0
I’m gonna take a wild guess that HoboStew was joking, guys…
Actually no. I wasn’t. I’m just retarded. Move along! :smack:
Fifty-six posts in and nobody has suggested quater-imaginary yet!? The dork quotient really has fallen on this board.
That is one whacked-out system! 100 is exactly halfway between 101 and 203? But it works!
I have got to read that article a few more times!!!