this post was submitted on 07 Dec 2023
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Asklemmy

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[โ€“] [email protected] 30 points 11 months ago (10 children)

The metric system should be redone in base 12, and RPN should be the norm for teaching arithmetic.

[โ€“] [email protected] 10 points 11 months ago (2 children)
[โ€“] [email protected] 8 points 11 months ago

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

[โ€“] [email protected] 2 points 11 months ago* (last edited 11 months ago)

twelve phalanges makes four digits, use the thumb to count. Also prettier.

[โ€“] [email protected] 6 points 11 months ago

I've been fully on board with base 12 for years. Didn't know about RPN until this post. I'm convinced.

[โ€“] [email protected] 4 points 11 months ago (6 children)

Base 16 is superior and once you learn binary math, easier to divide and multiply.

[โ€“] [email protected] 12 points 11 months ago

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.

[โ€“] [email protected] 7 points 11 months ago

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.

[โ€“] [email protected] 6 points 11 months ago* (last edited 11 months ago)

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.

[โ€“] [email protected] 3 points 11 months ago

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

[โ€“] [email protected] 2 points 11 months ago

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.

[โ€“] [email protected] 1 points 11 months ago

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

[โ€“] [email protected] 3 points 11 months ago

RPN is a gateway to LISP

[โ€“] [email protected] 3 points 11 months ago (2 children)

What's rpn and how does base 12 work.

Don't you still have "numbers" between 11 and 12?

[โ€“] [email protected] 15 points 11 months ago

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.

[โ€“] [email protected] 1 points 11 months ago* (last edited 11 months ago)

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.

[โ€“] [email protected] 2 points 11 months ago* (last edited 11 months ago)

Yes. Also everyone should be required to learn how to use a slide rule before they ever get given a calculator - I think that seeing how the numbers relate to each other on a physical device can help students conceptualize them better.

[โ€“] [email protected] 2 points 11 months ago (1 children)

If we were supposed to use base 10, weโ€™d have 10 figures and 10 toes!

/s

[โ€“] [email protected] 4 points 11 months ago (1 children)

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

[โ€“] [email protected] 5 points 11 months ago

I have 2 balls so binary is more in line with my interests.

[โ€“] JohnDClay 1 points 11 months ago (1 children)

You'd need to move all numbers to base 12 too for it to be worth it.

[โ€“] [email protected] 2 points 11 months ago* (last edited 11 months ago)

Well, let's get on that, and get some CRISPR stuff going so people grow an extra finger on each hand. Stupid evolution, we have to fix so many mistakes.

[โ€“] [email protected] 1 points 11 months ago

woah RPN is awesome

[โ€“] [email protected] 1 points 11 months ago

Yes, BIPM, this user here.