Quantization commutes with reduction

Imagine you have a bunch of marbles, and you want to organize them into different piles of different sizes. When you do this, you are "quantizing" the marbles - you are dividing them up into specific, discrete groups.

Now imagine that you want to take away some of those marbles - maybe you want to give some to your friend. When you do this, you are "reducing" the number of marbles you have.

The idea of "quantization commutes with reduction" means that these two processes - dividing the marbles into groups (quantization) and taking away some of the marbles (reduction) - can be done in any order you want, and you'll end up with the same result.

So if you first divide the marbles into groups and then take some away, it will be the same as if you first took away some marbles and then divided the rest into groups. No matter what you do first, you'll end up with the same total number of marbles and the same number of piles.