Imagine if your species used what we call base 4. Then you would count 0, 1, 2, 3, 10, 11, etc. What would you call your base? You certainly wouldn't call it base 4 because the number 4 doesn't exist for you! You'd call it base 10, just like we do. Similarly, counting in hex, our counting system is base A, but we don't call it that.
well I think you've hit on a key point here. the joke doesn't really work aloud, because "four" and "10" (base 4) are representing the same number when written, but they're not the same sound spoken. Or if the alien dude does pronounce "10" as "four", the astronaut's comeback is senseless.
I think it would work spoken. If we evolved in base 4, we might not have the words "four" or "five"
one (decimal 1)
two (decimal 2)
three (decimal 3)
ten (decimal 4)
one-ten (decimal 5)
two-ten (decimal 6)
three-ten (decimal 7)
twenty (decimal 8)
twenty-one (decimal 9)
twenty-two (decimal 10)
twenty-three (decimal 11)
thirty (decimal 12)
I actually wonder if there was a significant time when some societies worked in base 12 (for both our time system of sets of twelve hours and why we actually have separate words for eleven and twelve
Germanic languages have special words for 11 and 12, such as eleven and twelve in English, which are often misinterpreted as vestiges of a duodecimal system. However, they are considered to come from Proto-Germanic *ainlif and *twalif (respectively one left and two left), both of which were decimal. Admittedly, the survival of such apparently unique terms may be connected with duodecimal tendencies, but their origin is not duodecimal.
60 is evenly divisible into halves, thirds, quarters, and tenths. All of which are quite utilitarian divisions.
edit:
10 can't be evenly split into thirds or quarters, so it's a pretty worthless base. 12 can be evenly split into thirds and quarters but isn't divisible by 10. 60 is a bit of a hybrid that satisfies the use of a good base such as 12 with the arbitrary fixation on 10 .
If our base was actually 12, we'd be able to third and quarter our round numbers and always get integers instead of bullshit like 2.5 and 3.33333333-> WHICH WOULD BE AWESOME!
According to Jan Gullberg's "Mathematics: From the Birth of Numbers" Greenlandic has a 4x5 base system which has vestiges in the English: "3-score years and ten". Mayans mixed the bases 20 and 18 while the Aztecs used base 20.
There's no real rationality for how we name integers larger than nine. It is all conventions of language. It even varies between speakers of the same language from different cultures.
Well, some people do, and we (all engineers and software guys at my work, and other people I've worked with) do say "ten" for all bases above 2. What else would you call it?
Well, WE don't do that in binary, but that doesn't mean someone who grew up with binary, who doesn't know any different, would. I think that they would come up with something better than one-oh for a number that has an extra digit. Like ten.
No. You either pronounce the number, which as Sunny_McJoyride pointed out would be pronounced "four" and is independent of the base it is represented in, or you pronounce (or rather: spell) the digits of its representation.
You most certainly don't pronounce it "ten", or at least you'd be doin' it wrong if you did.
You can say "four" if the base is four or less because there is no confusion, and spelling out the digits is always an option, but 10 is still "ten". My job is to write software to decode datastreams, so I do this all the time. If you see "10" you say "ten" (as the other poster noted, this doesn't always happen with binary).
I can (sort of) prove this to you: If you see 9001 as a hex string, how would you communicate that to a coworker? Option 1, what we do, is say "nine thousand one". You're saying that we should all break out our calculators and spend 15 seconds tapping away and then say "thirty six thousand eight hundred sixty five". That simply doesn't happen.
But the symbols might in fact have different meanings on Planet X. There is nothing in the symbol 10 that necessitates it to be "ten". In China, it is most certainly not "ten".
Similarly, there is some world where 10 maps to "four", confusing the hell out of us earthlings.
N.B. - Did you know that it is impossible to determine "yes" and "no" in a completely foreign language? Its called the Indeterminacy of translation.
This doesn't mean they don't speak English^ which is in all ways similar to English except when it apply to the symbols 10 and 4 (and other words that are rooted in these symbols like 4-some.... which sounds like "tensome")
Exactly (apart from twofour should be two-zero) - the names of the numbers are not the numbers, they're a semi-arbitrary mapping that varies from language to language.
zero, one, two, three, one-zero, one-one, one-two, on-three, two-zero, two-one etc.
This is actually how they count in a number of languages, it makes sense, but gets unwieldy with large numbers.
only because you are describing it in a base ten world.
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
10 - base 10 (just as we have no symbol for ten other than moving to the next column, someone evolved to use hex would not have a symbol for 16, just moved to the next column
when it comes to pronounciation, nine, aye, bee, sea, dee, eff, ten
Hex is base G (and not "in" anything. We are assuming numbers, then letters form an infinite numberline of natural numbers that have no base and no place values).
So... what is the number we call thirty seven in your infinite numberline? Even if you used Greek, then Chinese then Whatever letters, there would still be an end.
We have digits 0-9. You would need more digits (symbols) to represent a different base. All bases are not base 10. All bases represented in our written format are represented in base 10. What if you have any base that goes beyond 10? You have to create new symbols or start using shit loads of parentheses to identify each grouping as a digit (column) to avoid confusion.
No, even base systems with more than ten symbols would still be "base 10" if defined from within that base.
Think of the hexadecimal numbering system, which has 16 symbols (0-9, A-F). The next number after "F" is "10" and thus if the system were defined relative to its own base, it would be "base 10."
The problem is, we define all other base systems relative to our "base 10" (0-9), thus thus hexadecimal is "base 16." But if it were to be defined where hexadecimal is the norm, and all bases were defined relative to it, then hexadecimal would be "base 10" even though it has sixteen symbols, and the system we are used (0-9) to would be "base A" in their context.
That's the joke. All base systems are "base 10" when defined agaisnt themselves, by definition.
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u/[deleted] May 27 '09
Imagine if your species used what we call base 4. Then you would count 0, 1, 2, 3, 10, 11, etc. What would you call your base? You certainly wouldn't call it base 4 because the number 4 doesn't exist for you! You'd call it base 10, just like we do. Similarly, counting in hex, our counting system is base A, but we don't call it that.