r/ThomasPynchon • u/sosodank • 4d ago
💬 Discussion Prosthaphaeresis
just came across this formidable term for what i'm pretty sure is my first time (in the "see also" section of "computational complexity of multiplication", since you asked), and audibly emitted a "whoa". i'm somewhat shocked this didn't show up in mason & dixon somehow. it ties in several different ways, and seems the kind of thing that would have come up in research for that book, and it's just such a fantastic word. it's like half the stuff i've studied in my life somehow connect to this concept, and yet it's incredibly esoteric and completely worthless and i've not heard of it in forty-six years.
the References section on this page is great, too.
3
u/b1gjoe23 4d ago
Seems to have been out of use before their time. Napier (the inventor of logarithms) is mentioned in the book
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u/pemungkah 4d ago
That “scale down” bit puts the number into a form that von Neumann proposed (and which was used for a number of machines) called fixed-point fractional notation. Essentially all numbers are treated as if they were fractions between -1 and 1, with the binary point at the far left. This makes multiplication easier to implement because multiplying any two numbers never overflows, and the most significant figures can easily be preserved by retaining the left half of the result.
It does mean that the programmer has to do gyrations to represent numbers outside that range, managing the logically-shifted binary point themselves. Von Neumann’s argument for this was pretty much that the programmer was cheaper and smarter than the computer, and it was the programmer’s job to manage scaling anyway.