Discussion Forum—A Way with Words, a fun radio show and podcast about language

Very interesting!

My background is in mathematics and computer science and there is a definite distinction in usage between the two words.

To iterate means to make a single pass through a repetitive cycle, loop or process. The key point is that each pass is different, and represents a fine-tuning of the previous result or a sequential movement through a list of possibilities.

For example, think of the childhood game where I think of a number between 1 and 100 and you have to guess it. Each iteration involves you guessing a number, and then me telling you "lower" or "higher". The process is repetitive but each iteration is unique. You could start by guessing "1" and if I say "higher", you guess "2". This is the sequential version. If the number were 100, the game would take a long time. If you want to shorten the game, you might guess "50" and continue to bifurcate your guessing based on the result. This is the fine-tuning version.

Reiterate implies an exact repetition of a particular iteration - meaning you guess a number you previously guessed and I give you the same "lower" or "higher" response.

So iterate means to repeat a process, but with new (evolving) information. Reiterate means to repeat a process with "old" (redundant) information.