Editing Openai/68a11068-3fe8-8007-bd18-674462ff2b41 (section)

=== Assistant: Ahh, now we’re touching the psychology of notation, not just the rules. ===
Ahh, now we’re touching the psychology of notation, not just the rules. Let’s pin this down carefully.

===== - Multiplication and division have the same precedence. =====
* They are evaluated strictly left to right.

So both are formally unambiguous if you follow that rule:

πr2/r2π=((πr2)/r2)π=π2\pi r^2 / r^2 \pi = ((\pi r^2)/r^2)\pi = \pi^2πr2/r2π=((πr2)/r2)π=π2
ac/bc=((ac)/b)c=ac2b.ac/bc = ((ac)/b)c = \frac{ac^2}{b}.ac/bc=((ac)/b)c=bac2.
No ambiguity if you’re strict. ✅

===== - When people see ac/bcac/bcac/bc, they tend to visually group it as a single stacked fraction: acbc\frac{ac}{bc}bcac because numerator and denominator look like mirror structures. =====
* When people see πr2/r2π\pi r^2 / r^2 \piπr2/r2π, they don’t see matching groups — they see “divide by r2r^2r2, then multiply by π\piπ.” So almost nobody interprets it as: πr2r2π.\frac{\pi r^2}{r^2 \pi}.r2ππr2.

===== - ac/bcac/bcac/bc: Two clean products on top and bottom → our brains map it to a stacked fraction. Ambiguous between “left-to-right” and “stacked fraction.” =====
* πr2/r2π\pi r^2 / r^2 \piπr2/r2π: Uneven grouping → the stacked fraction version feels clunky, so people default to left-to-right. Feels unambiguous.

It’s not that the math rules are different — it’s that the typography of the symbols nudges human intuition differently.

✅ Takeaway:
Both are only unambiguous if you enforce the left-to-right rule.
But in practice:
* ac/bcac/bcac/bc → people often intend acbc\frac{ac}{bc}bcac.
* πr2/r2π\pi r^2 / r^2 \piπr2/r2π → people usually intend left-to-right.

Would you like me to make a side-by-side chart showing (1) strict rule interpretation vs (2) common human “expected” interpretation, for all these cases? That would make the pattern crystal clear.