this post was submitted on 09 Dec 2024
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But we still have a number system where 10 is the sum of 5+5.
I want a number system where 10 is the sum of 6+6, and 12 is the sum of 7+7. A number system with two more single-digit numbers: one representing the sum of 6 and 4 as a single digit; and another representing the sum of 6 and 5. A system where 10*10 is 100, and 100 is the product of 6 * 2 * 6 * 2. A number system where 10 is evenly divisible by 2, 3, 4, and 6.
A metric system developed from that number system would be stunningly gorgeous.
I’m curious how you could make that work as it’s a basic contradiction. For 6+6 to equal 10 6 couldn’t equal itself which makes the entire premise invalid.
If you want more single digit numbers hexadecimal aka base 16 is even better than 12. But I can’t see how 10 can be evenly divided by all of 2,3,4,6 without being a multiple of the set.
I think they just mean base 12. So "10" isn't ten, it's 1 * 12^1^ + 0 * 12^0^; xyz is x * 12^2^ + y * 12^1^ + z * 12^0^.
Like sixteen in hex is 10 (commonly written 0x10, to differentiate it from decimal 10)
Edit: oof, my client is trying to be clever with the mathematical writing and bungling it, I'll try to fix... Hmm, hope that makes it better not worse
Exactly. I am trying to describe a duodecimal number system without using a decimal number system. "Ten" is a single-digit number. "Eleven" is a single digit number. "10" is pronounced "Twelve".
In duodecimal, 10 is, indeed, the sum of 6+6. Add up 6+6 in your number system. The number you reach equals "10" in the number system I described.
Hexadecimal is a wonderful base, as it is the composite of 2 * 2 * 2 * 2.
But, it does not allow for even division by three or six, and that is a problem. The simplest regular polygon is an equilateral triangle. The angle of an equalateral triangle is 1/6th the angle of a complete circle. Hexadecimal cannot represent 1/6th of a circle without a fractional part. Geometry in hexadecimal would require something like the sexagesimal layer (360 degree circle) we stack on top of decimal to make it even remotely functional.
Duodecimal would not require that additional layer: The angle of a complete circle is "10". The equilateral triangle angle is "2". A right angle is "3". A straight line is "6".
With duodecimal, the unit circle is already metricated. Angles are metric. Time is metric.
Let me put it a different way: Our base is the product of 2 and a prime number. A 12-fingered alien who came across our decimal number system would think it about as useful and practical as we think of base-14, another number system with a base the product of 2 and a prime number.
You mean base 12.
Of course. But I'm saying it in such a way that doesn't require the use of numbers in a base that is the product of 2 and 5.
In any given number system, the base of that number system is 10.