Categories and fuzzy causality

Much of our description of the world is in terms of categories, not individuals.  If you see a red light you stop.  If you see a green light you go.  The exact shade of green or red doesn't matter.  It just has to be red.  In a computer anything in the range of 0 to 0.8 Volts is considered a "0".  Anything in the range from 2.0 to 5.3 Volts is considered a "1".  Its the categories that matter.  In quantum theory we talk in terms of the probability that an electron is in the range between x and x + dx.  That's all we can say about its position.  When you measure anything you'd like to have an average and a standard deviation, not just a single measurement.  Reproducibility is then not as simple as one might have thought.  Two measured numbers are "the same" (the same category) if they are within a standard deviation or so of each other. We do not, however, use this as an excuse for being careless or lazy. Students find this difficult.  It's not as simple as they would like it to be.