Whence these zeroes? I suspect when proto-humans were counting things, they didn’t start with zero.
Also, decimal is the most common base but we shouldn’t imply it is the only one in use.
e.g. hexadecimal (base-16) is common in computing contexts.
It is not as error prone for humans to read and write as binary, but is much easier to convert from/to binary than decimal.
We could have picked any power of 2 as our “lingua franca” between us and computers, but hex has stuck more than the alternatives.
The Babylonians used base 60. One hesitates to imagine what sorts of unshoed ménages à trois were involved when they needed to calculate.
Okay, you got me. I shouldn’t have used the term “decimals” as that implies a base of 10. But we would still have fractions, and I think they would be much cleaner and neater in a base-8 system. Especially when dividing things by two.
Of course, if we found it more common to divide things by three, a base like 9 would have made things more convenient.
Octimals, perhaps.
As a great philosopher once said:
[QUOTE=Tom Lehrer]
Base eight is just like base ten really - if you’re missing two fingers.
[/quote]
I’ve heard “oits” used.
But not widely, for obvious dignity-related reasons.
Well, if you’re counting, see, and you get to 9, then go one more, then where do you go from there? With this base, what we do is give it that extra push over the cliff, one more, to put it up to eleven.
Counting in 12s is easy to do with the finger bones on one hand. There’s no need to remove the bones and count them individually. Count the tips, then the knuckles by using the thumb. 16 works if you go all the way from the tip to the palm.
Dern tootin’. Can’t have that, especially since I’m a fan of “Good 11.”
And the Mayan system wasn’t quite a pure base-20 system, either. It’s also partly base 18, to accommodate 360 (an approximation of the number of days in the year).
Maybe, but then it probably didn’t take long to notice that they didn’t always have at least one of every conceivable object. Sometimes you run completely out of stuff.
The concept of zero is a surprisingly modern invention. That is not to say that early peoples didn’t have a concept of “nothing,” just that the idea that a number could be analogous to nothing is not obvious.
I think he means counting to two places, one hand for 1 to 5 and the other to keep track of up to 5 sets of 5s, hence up to 25 (or arguably 30) on two hands. Base ten does not leave you another hand to keep track of the how many groups of tens.
Now of course, as I pointed out in that past thread, that’s why some cultures have used dozens and 60s - it works better for larger groups numbers on your hands: count the 3 phalanges of the 4 fingers with the thumb of one hand - that’s 1 dozen, keep track of up to five dozens with the fingers and thumb of the other hand - that’s 5 dozens, 60.
An advantage of finger counting is that it is easy to keep your place and not worry about being distracted causing you to have to start all over again - leave the three fingers on one hand up and the thumb on the second phalange of the third finger (second finger not counting the thumb) and if distracted you know you had gotten up to three dozens five and can keep going.
Learn to count in base two and you can count to 1023 with both hands. Sadly it is physically very difficult verging on the impossible, but a nice idea in concept.
It’s slightly misleading to think that every counting system has a “base”. Take Roman numerals. What base are they in? They simply don’t have a positional system like our modern numbering system. They have symbols for 1, 5, 10, 50, 100, 500, and 1000. So they had an idea that multiples of 5 and 10 were important numbers. But this isn’t a “base 10” numbering system. It’s clearly derived from a simpler tally marking system, where collections of small numbers are grouped.
Roman numerals is not what makes their number system base ten. Spoken numbers going 1-10, 10 and 1, 10 and 2, …, 10 and 9, 20, … 100, two 100, however, makes it base ten.
Is that how the Romans said numbers? They’d see MCMXII and say, “One thousand nine hundred and twelve”? Or, the latin equivalent?
The way we say numbers in the modern era is a consequence of our positional numbering system.
Base 16 is the answer to all of life’s problems. It makes sense if you’re a pirate. Or a laser printer.
No, not really. Most Indo-European languages developed verbal expressions for numbers combined from multiples of the powers of ten beginning with the highest power (e.g., “three thousand four hundred and twenty-two”) long before they adopted a positional system for writing numerals.
For example, Old English texts are full of expressions like “an þúsend & feower hundred & feowertig”, i.e., “one thousand four hundred and forty”.
It’s true that pre-modern languages did have more variety in their ways of verbally expressing numbers: e.g., “fourscore” for 80 or “thrice seventy” for 210 (in Vedic Sanskrit, for example) or “three-and-twenty” for 23. Some of these variant forms are still in use, like “nineteen hundred” for the more standardized form “one thousand nine hundred”.
But there is absolutely nothing new about the current “standard” form of expressing numbers verbally as a sequence of multiples of successively decreasing powers of ten. Nor was it developed in imitation of the decimal place-value notation for numerals: it already existed in pre-modern and even pre-literate forms of the languages that use it.