About 340 million years ago, all four-limbed creatures – the ancestors of today’s amphibians, reptiles, birds and mammals – began to “standardize” to five fingers/toes on each limb. Yes, many birds seem to have only three claws, and the horse seems to have a single big hoof, but when you look closely at their anatomy, these variations all turn out to be the result of fused or vestigial digits.
Suppose, just for the sake of argument, that this development in the Lower Carboniferous age had resulted not in pentadactyls, but in tetradactyls – creatures with four fingers or toes on each limb. And suppose that in this alternate universe we humans had evolved anyway, giant brains and all.
I’m thinking we’d have developed binary arithmetic a lot earlier in our history. After all, historical development of mathematics has been hobbled by the need to count in multiples of five and ten. The ancient Babylonians found themselves stuck with base sixty. Such an unwieldy counting system seems quaint until you realize that traces of this system survive today – such as in the number of minutes in an hour, and the number of angular degrees around a circle.
The ancient Romans were hobbled by their need for a number system that had symbols for 5, 10, 50, 100, 500 and 1000. The resulting way of counting rendered as simple an operation as multiplication all but impossible.
But if we had four fingers on each hand, eight fingers in all, sixteen digits between feet and toes, we’d already be well on our way to thinking in binary. Perhaps, in such a world, computers would have been developed far earlier. The whole notion of building complex structures of meaning out of sequences of binary bits would have made sense to even the smallest child.
Of course when you start to play this kind of game, you begin to uncover some disturbing questions. For example, in such a world would there still be Four Horsemen of the Apocalypse, or would there be only three? Would the Holy Trinity become a Holy Duality? Would a picture be worth two hundred and fifty six words, and would Snow White really still be hanging out with seven dwarves? Would there have to be a science fiction series names “Babylon 4”? Could the Beatles still be the Fab Four, or would Ringo have to go?
And then of course there is the question I’m sure you are all asking: In such a world, how many fingers would Homer Simpson have?
Alas, these questions may forever remain unanswered. 🙂
Ha! funny!
The assumption that wasn’t clear is why a base-8 (or base-2) number scheme is the ideal. When considering the exact economical cost of representation, e is the best choice. In general, ternary is less costly than binary (smaller width*radix). Ternary also shows more balance, since 0 is truly neutral. Binary numbers may have led to greater technological innovation for early peoples, but it may be stifling ours without our knowing it, like an inarguable religion.
For ancient cultures, the magic numbers 60 and 360 were nearly ideal for counting the number of days in a year (with the gods providing the remaining days) and was of course easily divided in the head by 2,3,4,5,6.
If we divide the following by factors of 360, we arrive at…
(360 days / 12 / 3 = decan) / 10 = day
(360 days / 12 / 4 = ca. week, a day for each planet) / ca. 7 = day
(30 days / 30 = day) / 12 = ancient hour (1/12 of the lit day)
I’ll admit, it’s hard for me to see anything as more fundamental in general than repeated binary separation, but it may not offer the robustness of a system that encapsulates more-useful constructs of spatial geometry and time.
And how would our musical instruments look like? guitars with 4 strings? recorders with 6 holes? and how would the music of Mozart et al. sound like?
I agree with Dan… and it does make me wonder why we actually don’t define a nibble as being 5 bits, a byte as 10 and a word as 20.
After all, binary doesn’t necessairly imply the 4/8/1/32/64-bit grouping (unless I completely disregarded something, which may well be possible at this time of the day).
I’m afraid to imagine what could have been if we have evolved from snakes.