MathCAD


6.9.6. A genuinely optimum fire bucket


(Translation into English by R.Girvin)

(Russian Text)

This optimization task was easily manageable either numerically (see Etude 2) or analytically (see Etude 7). In those, we learned how to maximise the volume of a bucket given a chosen manufacturing technology: cutting a sector from a metal disk and folding the remainder into a cone. But that way the bucket lost not only optimality, but also the status of bucket: it turned into a fire bowl! It was also impossible to put on a floor, and would be useless for any purpose except as a Vietnamese hat. In our rush for Number (the volume of the bucket) we have lost Essence (the function of a bucket, its capacity for conveniently carrying liquid).

The author recalls a cartoon film based on a Norwegian fable about a goat that learned to count, and decided to count all the farm animals: "I am one; the hen is two; the pig is three, etc." But as all the animals were moving around, the process soon turned into uproar. "Oh, have you counted me?!" "Keep still, or else..!" But everything ended happily, both for the goat and the fable.

In this story, as with any other fairy tale, there's a deep wisdom. It's necessary for us to count things, but as we interact with them we can run into a conflict. Not only does Nature dislike sharp corners, but also enumeration, which in a number of cases simply kills her. This can be observed not only in biology and physics, where the tools of knowledge frequently unrecognizably spoil the object of research, but also in computer science. This applies not only when applying computers to natural sciences applications, but also when applying computers to computers.

To establish a diagnosis, a doctor has no need to know the exact numerical value for a patient's body temperature (36.6C, 38.9C, etc). It's enough to express the thermometer indications by ranges, on which 'medics' have agreed beforehand: "low", "normal", "raised", "mild fever", "high fever". The borders of these estimates, though precisely fixed, are nevertheless imprecise – 'fuzzy'. This comes not merely from modern representations in terms of fuzzy set theory (FST) but also in terms of practical reality: thermometer error, measurement technique, and so on. A graduate of a medical school can tell you, without even pausing to think, where the division between high and very high temperature lies. The skilled doctor can decide this without consciously thinking of the number, while diagnosing better than the beginner.




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