“What’s worse than biting into an apple and finding a worm?… Finding half a worm.”
Considering the question quantitatively, however, finding something less than half of a worm is even more disgusting… a quarter of a worm, or a tenth, or one-hundredth, or some infinitesimal speck visible only by close inspection. The less one finds, the greater the “yuck” factor. So it would seem that the worst, worst possible case must be at the mathematical limit, which is zero. So the maximally-worst possible case would be finding… no worm at all!
Hmmm…
My university research project predecessors had discovered a worm in their apple. An unpredictable pattern had entered their measurements, and it seemed to appear in random places. It was as if something in the process that was so subtle as to be indiscernible was causing sudden departures into utter chaos.
After months of work, they had quantitatively concluded that there was simply no practicable way to assure a reliable measurement. I was sitting in a mathematics class when it suddenly occurred to me that they were wrong.
It’s not that the tiniest bits of worms can’t eat the guts out of things. There was a time when I worked with machines that spun like washing-machines-from-Hell, far faster than jet-engines, and precipitously near their structural limits. Merely keeping them from flying explosively to pieces amounted to an entire discipline in itself. And yet, there was an incentive to get them spinning ever faster. A new type of titanium metallic-glass seemed like a promising route.
One early test exploded with such violence as to destroy the instruments that were monitoring it. Others both worked and failed without any apparent pattern. One test would look good for awhile, and then make a sudden “departure”. Another would simply shatter long before reaching working speeds.
It took months for engineers to determine that microscopic scratches in the material were causing the failures, with many of the flaws visible only under a very powerful microscope. Smaller imperfections would simply result in a higher velocity before a more spectacular failure. Only a flawlessly perfect part would have no worm at all.
Bristol University Physics Professor, Micheal Berry, discussed such worms (or in his case, “maggots”) as mathematically “discontinuous limits”. These are cases where the mathematics simply don’t work out to the value of the function at its limit. That’s to say that the worm ceases to exist at the point where it reaches the extreme.
A real-world example of this is found in the measurement of “viscosity” (the “gooey-ness” of a fluid) and the amount of “turbulence” (chaotic movement) that it will exhibit. The lower the viscosity of a fluid, the higher the turbulence. Put simply, this just means that water moving over rocks will be more splashy than the same flow of thick Maple syrup. Mmm…
However, when viscosity reaches zero (as in “superfluid” helium), the turbulence does not rise to some super-splashy maximum. Rather, it disappears entirely.
Likewise, what my predecessors had actually discovered was how to determine exactly what they were measuring by finding the point at which it became wormy. Below this limit, the worm disappeared entirely. And then, all they had really needed was to adjust to a measure appropriate to that kind of non-wormy produce.
To be fair, the problem was a little more complicated than I’m making it out, and it took me more than a year to work out its solutions. But the misinterpretation of a discontinuous limit had left me with a whole bunch of delicious, low-hanging fruit.
Images from, Clipart Library:
Worm!
Fruit Cocktail Tree.



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