Take the simple expression 1 + 1. The plus sign is between the two operands. 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 this works, 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 the stack
2, put that on the stack
3, put that on 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 the equation to be (1+2)*3 instead, we could write: 1 2 + 3 *
Simply by reordering the symbols, we change the meaning of the expression, and there’s never any need for parentheses.
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.
I like base 12 a lot, but Reverse Polish Notation is a mess when you get up to working with polynomials.
With polynomials, you’re moving around terms on either side of an equation, and you combine positive terms and negative terms. In essence, there’s no such thing as subtraction. (Similarly, division is a lie; you’re actually just working with numerators and denominators.)
Reverse Polish Notation makes that a mess since it separates the sign from its term.
Also, RPN draws a distinction between negative values and subtraction, but conceptually there is no subtraction with polynomials, it’s all just negative terms. (Or negating a polynomial to get its additive inverse.)
But, yeah. It’s a shame we don’t use base 12 more.
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 really break down the conceptual barrier of how they relate to each other.
The metric system should be redone in base 12, and RPN should be the norm for teaching arithmetic.
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Here’s a practical explanation of RPN.
Take the simple expression
1 + 1. The plus sign is between the two operands. 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 this works, 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:If we wanted to rewrite the equation to be (1+2)*3 instead, we could write:
1 2 + 3 *Simply by reordering the symbols, we change the meaning of the expression, and there’s never any need for parentheses.
Let me know if that explanation made sense.
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.
I like base 12 a lot, but Reverse Polish Notation is a mess when you get up to working with polynomials.
With polynomials, you’re moving around terms on either side of an equation, and you combine positive terms and negative terms. In essence, there’s no such thing as subtraction. (Similarly, division is a lie; you’re actually just working with numerators and denominators.)
Reverse Polish Notation makes that a mess since it separates the sign from its term.
Also, RPN draws a distinction between negative values and subtraction, but conceptually there is no subtraction with polynomials, it’s all just negative terms. (Or negating a polynomial to get its additive inverse.)
But, yeah. It’s a shame we don’t use base 12 more.
That’s super interesting. I adore RPN on caclulators and had never heard any drawbacks well-articulated.
RPN is a gateway to LISP
Base 16 is superior and once you learn binary math, easier to divide and multiply.
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.
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 really break down the conceptual barrier of how they relate to each other.
If we were supposed to use base 10, we’d have 10 figures and 10 toes!
/s
You have 12 finger joints which you can count with the thumb.
I have 2 balls so binary is more in line with my interests.
Base 60 was good enough the Babylonians and it’s good enough for me!
Why base 12?
twelve phalanges makes four digits, use the thumb to count. Also prettier.
See elsewhere in the thread, but basically because of the ease of dividing whole numbers.