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Complex Numbers #1080216 added November 20, 2024 at 9:56am
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Powers of Three
From Quanta, and as usual for that source, may not be suitable for numerophobes:
There's been talk of quantum computers being used for that, as well. Difference is, from what I understand, quantum computing is still very much in its infancy.
Three, as Schoolhouse Rock! told children of the 1970s, is a magic number.
Thanks. Now I have an earworm. 
The number 3 also suggests a different way of counting. Our familiar base 10 decimal system uses the 10 digits from zero to 9. Binary, our digital lingua franca, represents numbers using only the two digits zero and 1.
One of my favorite nerdy jokes: "There are 10 kinds of people in this world: Those who understand binary, and those who don't."
The hallmark feature of ternary notation is that it’s ruthlessly efficient. With two binary bits, you can represent four numbers. Two “trits” — each with three different states — allow you to represent nine different numbers.
"Trits?" No. "Bits" is short for binary digits. If you have trinary digits, using the same convention would yield something way funnier.
It turns out that ternary is the most economical of all possible integer bases for representing big numbers.
The article explains why, or we can just take their word for it. But:
For large numbers, base 3 has a lower radix economy than any other integer base. (Surprisingly, if you allow a base to be any real number, and not just an integer, then the most efficient computational base is the irrational number e.)
That doesn't surprise me at all, except the surprise of being allowed to have a non-integer base number. The irrational number e is 2.71828..., which is closer to 3 than to any other integer.
Despite its natural advantages, base 3 computing never took off, even though many mathematicians marveled at its efficiency. In 1840, an English printer, inventor, banker and self-taught mathematician named Thomas Fowler invented a ternary computing machine to calculate weighted values of taxes and interest.
What pleases mathematicians doesn't usually please the rest of us.
Why didn’t ternary computing catch on? ... Binary was easier to implement.
Thus showing once again that "easier to implement" doesn't always translate to "most efficient to run."
How does this affect us? Well, it doesn't, much. Numbers have to be shifted to decimal notation either way, so we can do things like taxes and budgets. Mostly, I'm just disappointed with "trits." |
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