Subject:      Re: Words borrowed from mathematics
Author:       John Conway <conway@math.Princeton.EDU>
Date:         Tue, 24 Oct 1995 19:06:16 -0400



On Tue, 24 Oct 1995 math-history-list-owner@maa.org wrote:

> Most of the vocabulary in mathematics seems to be borrowed from other 
> domains of activity. I think the reverse migration is rare. For example, 
> ANALOGY comes from the mathematical terminology for proportion (i.e., the 
> equality of two ratios) in ancient Greek, ANALOGIA. Plato, I recall 
> reading, was responsible for the borrowing to describe comparisons (or 
> oppositions?) that arise in thinking. In THEAETETUS (186 C) he speaks of 
> comparisons in this manner [cf., J. Klein, GREEK MATHEMATICAL THOUGHT AND 
> THE ORIGINS OF ALGEBRA, p. 78.].
> 
> Are there other such words that have been borrowed from technical 
> mathematics by the vernacular?
> 
> Charles V. Jones,
> Ball State Univesity
> Muncie IN 47306
> 
     The words "analogy", "proportion", "ratio", "symmetry", and
"commensurability",  have an interesting, and intertwined, history.

    The first three originally were almost synonymous, as were the last
two.  The numbers  3,6,30   are  "analogous" to  5,10,50,  the "analogy"
here being what we should now call the "ratio"  3 to 5.  As Mr Jones
remarks, the word "analogy" was later taken over for other analogies.

    The non-mathematical uses of the words "rational" and "irrational"
were also taken over from the mathematical ones.  Irrational numbers
were hard to understand, so "rational" and "irrational" acquired the
meanings of "reasonable" and "unreasonable".  The word "surd", for a
particular type of irrational number, has ultimately the same 
meaning as "absurd".
    
     Dionysus of Alexandria introduced the aesthetic meanings of 
"proportion" and "symmetry".  Nowadays, "commensurable" means, to
the mathematician "measurable by integral multiples of the same unit"
but it can also just refer to things that one might measure in the
same way.  "Symmetric" had the same meanings, but, after Dionysus,
it also meant for example, that the two sides of an object "measured
the same", so that that object was what he (and we) call "symmetric".

    I believe that it was Aristotle who took over the mathematical
words that have now become "hyperbola","ellipse", "parabola"  into
rhetoric, where they have become ""hyperbole", "elliptic speech"
or "ellipsis", and "parable".

    The Greek originals mean

   [hyperbola]  "thrown beyond"

   [ellipse]    "falling short"

   [parabola]   "thrown beside"

and for the curves probably refer to the fact that the distance
to the focus  exceeds,  falls short of, or equals,  that to the
directrix.   [It may however, instead refer to the fact that the
plane we take to cut the cone, either "goes beyond" so as to hit
the other portion of the cone, or "falls short of " hitting that
part, or "runs parallel beside" a generator of the cone,  as some
dictionaries think.]

    In rhetoric, "hyperbolic" speech is the kind that goes beyond
the facts, "elliptic speech" falls short of them, while a "parable"
is a story that axactly fits the facts.

    I might add, that the word "parabola" became "parler" in
French, meaning any kind of talk, and has given us the English
words "parlor"  and "parliament"; while in Portuguese it suffered
a metathesis to "palabre", which has given us the English "palaver".

    It is amusing [to me, at least] to contemplate the facts that
"parable", "parlor", and "palaver"  are all etymologically the
same word as "parabola".

    I could go on about the etymologies and history of many mathematical
words for ages, but will stop here before I bore too many readers.

    John Conway