Asklemmy

See elsewhere in the thread, but basically because of the ease of dividing whole numbers.

You would have numbers 0-9 plus two more digits (could use A and B, but any two symbols will do). The advantage is being able to cut things in thirds and quarters as well as in half. Cutting by a sixth is a bonus, as well.

RPN (reverse polish notation) is a different way of doing arithmetic where the order you write it naturally determines the order of operations. Do you know those Facebook memes where people get different answers for seemingly simple math equations? RPN does away with that. There is one and only one right way to interpret an RPN equation, and you don't have to remember any order of operation rules to do it.

Here's a practical explanation of RPN.

Take the simple expression 1 + 1. The plus sign is between the two operands; this is called infix notation and it's what you're probably familiar with. If we wanted to make this more complex, e.g. 1+(2*3), we'd need parentheses to say which part was supposed to be done first.

Reverse Polish Notation (RPN) means you write the two operands and then the operator, i.e. 1 1 +. Writing more complex equations is as simple as putting another expression in place of one of the numbers: 1 2 3 * +. To see how you'd evaluate this without any parentheses, imagine that as you go through an RPN expression from left to right, you keep a stack of sheets of paper, each with a number written on it, that starts out empty. As you go through, you see:

• 1, put that on top of the stack
• 2, put that on top of the stack
• 3, put that on top of the stack (from top to bottom, the stack is now 3, 2, 1)
• multiply, take the top two numbers on the stack (2 and 3), multiply them, and put the result back on the stack (the stack now has two numbers, 6 on the top and 1 on the bottom)
• add, take the top two numbers on the stack, add them, and put the result back (the stack now only has one number on it: 7)

If we wanted to rewrite that expression to be (1+2)*3 instead, we could write: 1 2 + 3 *

Simply by reordering the symbols, we change the meaning of the expression, so there's never any need for parentheses.

As a bonus, this method of writing equations is a lot easier for computers to parse than infix notation, since they think in terms of stacks anyway. They can be (and often are) programmed to parse infix notation anyway, because infix notation is a lot easier for humans to wrap their brains around, but it's much easier to program them to interpret RPN which is why a lot of older calculators and software (like the programming language FORTH) use RPN exclusively.

Let me know if that explanation made sense.

What base 12 gives you is a lot of common divisors: 2, 3, 4, and 6. Base 10 only has 2 and 5. Base 16 only has 2, 4, 8.

The practical upshot of this is that you can divide things evenly in more ways. Particularly when wanting to divide a board into thirds. Having 12 inches to a foot is actually helpful there, though it falls apart as soon as you get larger.

Base 16 is great when you're interacting with a computer, but aside from that, not much. Only being divisible by 2 is kind of a pain in the real world.

This is incorrect, and you don't understand why base 12 is useful. However for binary operations, hex is great. But not for general counting.

I'm not experienced with RPN but at a glance think there's a solid argument for it.

Both are easily countable on fingers using your thumb and counting up the segments for base 12 and adding the pads for base sixteen. You can reasonably count to 144(gross) or 256 using both hands to create a two digit dozenal or hexadecimal number.

Good points, 12 seems to be superior and I've changed my opinion.

You have 12 finger joints which you can count with the thumb.