The Idea of Number
Nowadays, we take it for granted that whether you're talking about two snowflakes or two chickens, the number "two" is still the same. But this idea wasn't always obvious. The imaginative leap of numbers - after this on Earth and Sky.
Date
(Tape 0:03:04-0:03:07) Number is an absolutely fascinating concept.
JB: This is Earth and Sky, and you're listening to Dr. Robert Osserman of Berkeley's Mathematical Sciences Research Institute. He spoke with us about an amazing idea we take for granted - the idea of number.
(Tape 0:03:49-0:04:16) There's a famous saying by a 19th century mathematician that God gave us the whole numbers and the rest is the work of man, so that fractions and negative numbers and imaginary numbers are things that we invented; but we were kind of "given" the whole numbers. And I find that totally mistaken because the whole numbers were one of the most imaginative and creative notions invented by people. (Tape 0:04:50-0:05:30) One indication that numbers were not given to us is that in many languages there isn't even a single word for a given number. For example, Japanese has different words, different number words when numbers are used in different contexts. They think of like long, thin objects and short round objects and so on and they have different number words for those objects. And the idea of just having a single number "two" which abstracts from all these different things is a very advanced and fascinating idea.
JB: Thanks to Dr. Robert Osserman of the Mathematical Sciences Research Institute for speaking with us. And with thanks to the National Science Foundation, I'm Joel Block, for Deborah Byrd, for Earth and Sky.
Author: Beverly Wachtel
Thanks to the following individual for aiding in the preparation of this script:
Dr. Robert Osserman
Mathematical Sciences Research Institute
Berkeley, CA
Osserman@msri.org
If you enjoyed this program, you may be interested in the following:
Poetry of the Universe, by Robert Osserman. NY: Anchor/Doubleday, 1996.
Mathematical Sciences Research Institute website:
http://www.msri.org