Three interesting tidbits for those of you who are, like me, newbs to numbers.
1) According to this episode of the Radio Lab podcast human babies are born thinking in logarithms, and if it wasn't for education we'd never bother learning how to count by 1s. I really didn't know what "logarithm" meant before I listened to this show. What's the half-way point between 1 and 9? — could be 5, could be 3, depending how you think. What about the step between 1 and 2? — is it the same amount as the step between 8 and 9? Maybe yes, maybe no. Listen to show and find out why.
Some things vary in a stepwise fashion — the number of people in a family, the number of sheep in a flock, the number of pebbles in a pouch. These are groups of discrete things about which we can ask, "How many?" Other things vary smoothly — distance, age, weight. Here the basic question is, "How much?"
The first kind of magnitude might be called spotty and the second kind called smooth. The study of spotty magnitudes leads to numbers and arithmetic, while the study of smooth magnitudes leads to notions of length and geometry.
The word "complementarity" was first introduced into philosophy by the quantum physicist Niels Bohr. He used this expression to sum up his belief that basic physical reality is both spotty and smooth. An electron, according to Bohr, is in some respects like a particle (like a number) and in some respects like a wave (like space). At the deepest level of physical reality, things are not definitely spotty or definitely smooth. The ambiguity is a result of neither vagueness nor contradiction. The ambiguity is rather a result of our preconceived notions of "particle" and "wave" not being wholly appropriate at very small scales.
One might also ask whether a person is best thought of as a distinct individual or as a nexus in the web of social interaction. No person exists wholly distinct from human society, so it might seem best to say that the space of society is fundamental. On the other hand, each person can feel like an isolated individual, so maybe the number-like individuals are fundamental. Complementarity says that a person is both individual and social component, and that there is no need to try to separate the two. Reality is one, and language introduces impossible distinctions that need not be made.
3) And here is how I learned to count. Sesame Street - those evil geniuses - somehow devised a counting song that is super catchy but also nearly impossible to sing. I caught on to the counting along bit about 40 years ago, but the singing along bit still causes me stress.
An understanding of logarithms is important for getting the punch line of what I consider to be the best joke ever:
After releasing the animals from the ark, with the instructions to "go forth and multiply", Noah got to relax for a bit. After a few days, however, the snakes came back, and confessed that they were having a bit of trouble with the multiplying bit. "Don't worry", said Noah, "I'll fix you up", and he proceeded to cut down some trees, and hammer together a rough-hewn table. "Hop up on here, and I'll leave you to it", he said.
After a bit, the snakes came back, together with all their new baby snakes, to thank Noah. "But what's the secret?" they wanted to know.
"Easy", said Noah,"Even adders can multiply on a log table!"
- rob (guest) 10-06-2010 3:31 pm
Oh god! I think we need to have a shaggy dog story open mike night and get all this out of everyone's system. Y'all should read the stuff M. Jean sends over email. - sally mckay 10-06-2010 10:50 pm
Heisenberg is speeding through the streets of London, late for a lecture. A cop pulls him over and asks; "Do you have any idea how fast you were going?"
"No," says Heisenberg, "But I know exactly where I am!" - joester (guest) 10-07-2010 4:34 pm
Electric company - base twelve, but MUCH easier to sing.
- joseter (guest) 10-07-2010 4:37 pm
Thanks Joester. I was looking for this. The whole counting to 12 thing was a bit of a challenge, if I remember correctly. But hey. If you want to build anything in North America you're gonna need the imperial system. By the way, it says Sesame Street right on it.
- sally mckay 10-07-2010 6:17 pm
Someone must have put the Sesame Street logo over the Electric Company for some reason. Weird. - joester (guest) 10-07-2010 6:37 pm
And then there's base 8, which is just like base 10, if you happen to be missing a couple of fingers on one hand:
http://video.google.com/videoplay?docid=-7841878207694220233# - Rob (guest) 10-07-2010 8:15 pm
There is a reason why carpenters prefer imperial to metric. When you extend your tape measure up into a rafter in a dark dusty basement, is it easier for the eye/brain to perceive the half of a half... rather then calculate the digit of a centimetre?
Also, because the Babylonians liked it. Is there any other reason why the time showing on your clock/watch/cell/thingy is in base 12?
- VB 10-09-2010 1:23 am
Law and Order Special Letters Unit .
- VB 10-09-2010 2:01 am
The whole 12 thing may come from worshiping Jupiter. Jupiter moves about 1/12 of the way around the sky per year- this is probably the reason that there are 12 astrological signs. Once you've broken the sky up into 12ths, it makes sense to base everything to do with timekeeping and circles on 12s, rather than 10s. - rob (guest) 10-09-2010 5:34 pm
If we were looking at Venus instead of Jupiter, we might have ended up with a Mayan Calender, and then the world would end in around 800 days, give or take a few.
"Girls go to Venus..."
(VB via MJ).
- M.Jean 10-10-2010 4:05 am
Mayan were base 20. Plus they had a place holder zero - very cool.