A prefix is a morpheme "fixed" at the beginning of another morephem (often one which has independent wordage) to change the meaning. Thus, the prefix of pre- in "preheat" meaning to heat, say, the oven, before putting in the heatinng dish to bake for food.

A suffix is a morphem "fixed: at the end of another morpheme (often one which has indpendent wordage) to change the meaning and even the grammatical status. Thus, the suffix of -ing transforms an atttribute, such as "heat", into a genund, as in "heating". This is critical in scientific communication. The great mathematician and science writer, Henri Poincaré (x-y), noted that the use of a substantive term, "heat", to describe a familiar process may have motivated scientists to search errantly for a substance, such as "phlogiston" or "caloric" to explain this process of molecular activity, whereas use of a gerund such as "heating" would not have misled them.

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While little used or absent in nonmathematical language, a primary term in mathematical language is the infix, which interconnects two terms. Familiar examples occur in addition, multiplication, etc., as in 2 + 3 = 5, 2 * 3 = 6. There is reason to believe that the impetus for this was the invention of printing, since it often saves spacing. But it can often require extensive use of parentheses to indicate operational ordering, as in the distributivity, 4 * (2 + 3) = 4 * 2 + 4 * 3 = 8 + 12 = 20 .

The Polish logician, Jan Lukasiewicz, showed that prefix notation can preclude the parenthetical need, as in + * 4, 2 * 4, 3 = 20. This notion has attained popularity for several recent decades because of the hand calculators, being known as "prefix Polish". Its converse is "postfix Polish" and is the standard because of the need to enter the division operation only after dividend and divisor have been entered, to avoid the errror of dividing by zero.

However, I am perhaps the only person who notes the "commutativity" problem arising from this form of operational language. To illustrate, let "S" denote the squaring operation, as in S2 = 4, S3 = 9. Consider then (by mixing notation) the following:

• S+x,y = S(x + y) = (x + y)² = x² + y² + 2xy;
• +Sx,y = +x²,y² = x² + y² .

Clearly, the first operation yields a 2xy not present in the second, indicating noncoummutativity of operations.

This becomes critical in quantum mathematics. The two operations involve differences of measurement information. The extra "2xy" corresponds to superposition.

The first big surprise in quantum mathematics was the noncomutativity of operators. Perhaps this could have been anticipated if more attention had been given to the influence of notation -- prefix, suffix, infix forms, etc. -- upon thinking about a subject.

A critical field known as "iatrogenic medicine" concerns "medical problems created by medical practice". (Example: You enter the hospital for a sonsilectomy, and acquire a staph infection.) The prefix "iatro-" is from Greek, meaning "self", so "iatrogenic" means "solf-generated". Elsewhere I speak of "iatromath" and "iatrophysics", dealing with problems created by practice in