I can so picture him doing this.
If only I was eligible for tenure.
And just in case you were wondering 4444 in base 5 really is 624. Only a math dork would check.
I always ask my classes a couple of questions on the first day of class.
“What is math?” Even though these students have been taking math classes since they were in grade school they rarely have an answer to this question. It’s a language.
“Why do we use the base 10 system?” Occasionally a student will get this one. I hold out my hands and say “Unless you were a careless meat packer, or born with a mutation, you have ten fingers.”
You do understand that the Mayan and Aztec used a counting system based on 20? I believe the reason the Greeks, Hindus, and ancient Babylonians went for base 10 (as opposed to base two, we after all are symmetrical) was that the addition of an extra zero at the end of the number was a logarithmic increase. The ancient Babylonians had counting and measurement systems that used 2, 5, 12, 20. We still measure circles based on the 12 system. The “10” system ended up the preferred one because of its utility in trade accounts.
We didn’t “invent” math for science or knowledge enhancement, math was created to enhance wealth and to establish prestige and status.
Adding zeros is an exponential increase which is the inverse of logarithmic. And this is true of any base system. The number of digits needed to represent a given number N increases logarithmically with N. Again true of any base system. You would just use a different logarithmic or exponential base.
The reason computers give odd results sometimes is because internally they represents numbers in base two. You get different round off errors with base two because some numbers that can be represented exactly in base 10 can’t be represented exactly in base two. And visa versa. This is because for example the base two logarithm of 100 is an infinite sequence of non repeating digits and the base ten logarithm of 100 is two.
There is no special utility for using base 10 in trade accounts unless you use your fingers to count. And have ten fingers.
You are of course correct, although onkelbob’s comments about the Mayans and the Aztecs using base 20 are interesting.
In my classes I joke that if chimpanzees ever develop a number system it will be base twenty, since they are pretty good with their feet.
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