Comment by azim

I like the way you've phrased this, so let me give a contrived but quasi-realistic example: I have a network of nodes which calculates and returns some floating point value. I then accumulate those in the arbitrary order in which they come back from in the network. (According to Google) 1111.0000000000001 * 2 * 1111.00000000000001 = 2468642 BUT 1111.0000000000001 * 1111.00000000000001 * .2 = 246864.2. By using floating point we've already decided it's OK to give up some precision, however by applying the commutative property of multiplication now we've also given up determinism.