← Starting Henceforth
Episode 3
Why the maths looks backwards
Postfix, and why the stack is the parentheses.
2:03 · Vivaldi · Allegro (RV 293 i)
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What you’ll learn
- ✓ You write the numbers first, then the operation — 2 3 + . That's reverse Polish (postfix).
- ✓ The stack remembers as you go, so 2 3 + 4 * nests without any brackets.
- ✓ Because the last two numbers already sit on the stack, Fibonacci is one little word: : next-fib tuck + ;.
Transcript
- you already know how to add.
- watch how this little machine wants it.
- you put the numbers down first —
- two, then three.
- then you say: add.
- five. the plus reached back and grabbed the two.
- numbers first, then the operation —
- that's reverse polish.
- and it stacks up — no brackets.
- two plus three is five —
- then five times four.
- twenty. the stack just remembers.
- now — one that's a headache in most languages.
- the fibonacci numbers — each one the last two, added.
- python needs a loop and two boxes to hold them.
- but our two numbers already sit on the stack.
- so it's one little word.
- take the pair, make the next one.
- start it with two ones.
- now nudge it forward — again and again.
- and it just keeps climbing —
- a hundred and forty-four — the twelfth.
- fibonacci. in one little word.
- clear the pair —
- and the school way? watch it break.
- no — the plus went looking for two numbers,
- and found nothing behind it.
- numbers first. that's the whole trick.
- henceforth.