## Saturday, June 15, 2019

### [ampdlwwk] Saying or spelling out the unit of acceleration

• 9.8 meters per second per second.  Ambiguity is avoided because division is left associative, so units are (meters per second) per second, and not the silly meters per (second per second) which would simplify to just meters.
• 9.8 meter per second per second.  Similar to previous.  We'll elide further substitutions between "meters" and "meter".
• 9.8 meters per second squared.  Ambiguity is avoided because exponentiation has higher precedence than division, so it is meters per (second squared), not (meters per second) squared.
• 9.8 meters per second square.  Similar to previous.  We'll elide further substitutions between the suffix "squared" and the suffix "square".
• 9.8 meters per square second
• 9.8 meters per squared second.  Similar to previous.  We'll elide further substitutions of the prefix "square" and the prefix "squared".
• 9.8 meters second to the negative two.  Ambiguity is avoided because exponentiation has higher precedence than multiplication.
• 9.8 meters second to the negative second.  The two instances of word "second" have different meanings.
• 9.8 meters second to the negative second power.
• 9.8 meters second raised to the negative second power.
• 9.8 meters hertz squared.  Ambiguity is avoided because exponentiation has higher precedence than multiplication.  (We acknowledge "hertz" is typically only used for periodic phenomena, and there's nothing innately periodic about acceleration.  Maybe we imagine a pendulum in gravity.)
• 9.8 meters hertz hertz.
• 9.8 meters square hertz.  This one is ambiguous: (meters square) hertz, or meters (square hertz)?  We want the latter.
• 9.8 meters times square hertz.  Explicitly inserting the multiplication operator removes ambiguity.
• 9.8 meters by square hertz.  Similar to previous: "by" is multiplication as in "2 by 4".
• 9.8 meters to the first hertz squared.  Explicitly giving all the exponents helps decrease ambiguity if it wasn't known that exponentiation has higher precedence than multiplication.
• 9.8 hertz squared meters to the first.  Similar to previous: multiplication is commutative.
• 9.8 hertz squared meters.  Ambiguous again because of unspecified associativity.
• 9.8 hertz squared by meters.  Not ambiguous.
• 9.8 square hertz meters.  Ambiguous: "square" (or squared) as a prefix is more like a function call than exponentiation, but there isn't an established convention regarding the relative precedence between function calls and multiplication.  In Haskell, function calls bind very tightly (high precedence), so this would be (square hertz) meters which is what we want, but in phrases like "sine two pi" the multiplication is done before the function call.
• 9.8 square hertz by meters.  Remains ambiguous for the same reason as above.