he doesn’t make any coherent argument as to why one is more clear or preferred than the other. he simply states it and moves on with this bias. for example, when he compares 2 to 2a, i feel he doesn’t really address anything and just states his preference as the more clear one.

plus, he of course seems to know nothing about lisp (or just ignores it) where you might have:

  (+ a (+ b c)) = (+ (+ a b) c) = (+ a b c)

all three are valid lisp syntax and represent associativity of addition well, including “dropping the parentheses”. the thing is, procedure notation as opposed to infix operators actually make it more explicit by what is meant by associativity. this is because it makes explicit about what comes first because of how procedures are evaluated. this is much more explicit than conventions of what parentheses mean in infix operator expressions. even his python procedure example in (2) demonstrates this property.

the distributive law is:

(* a (+ b c)) = (+ (* a b) (* a c))

that seems pretty clear to me. and with this, you can of course extend the language such that the +, , etc. procedures operate on new data types or heterogeneous data types like ( c v) where c is a constant and v is a vector and you get scalar multiplication.

it is also funny to me that he considers readability over performance. well, i do too, but you can have both. see lisps, schemes, and sml dialects, all languages he seems to ignore the existence of.

another thought is that i recall gerald sussman saying in a talk that mathematical notation is impressionistic, and in general, i think he is right. his point was that procedure notation is much more explicit. he also mentions that prefix notation is inconvient for small expressions versus infix notation but is much more preferred when you have very large expressions with many, many terms.