Humanist Discussion Group, Vol. 34, No. 48.
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        Date: 2020-05-22 05:49:19+00:00
        From: C. M. Sperberg-McQueen 
        Subject: software as applied mathematics

Willard writes:

> A common move is to call software 'applied mathematics',

Perhaps we just hang around with different groups of people, but I
haven't encountered this move before.  Whom are you talking about?  And
what do they mean?  If what they mean is that software is applied
mathematics and 'applied mathematics' is another name for software as a
field, I can only advise you to keep smiling, make no sudden moves, and
back slowly but firmly away. If what they mean is that software
development is a field in which mathematics can be applied, then I
agree:  software development is an activity in the known universe. But
I don't understand why you are hanging around with people who make
portentous statements which, when their meaning is ciphered out, turn
out to be tautologies, and not very surprising ones at that.
I confess to being mildly disappointed by your decloaking.

The question "where did the := of Algol 58 assignment statements come
from?" is fairly interesting, and I have learned some things I found
worth my while, from thinking about it and from what posters to
Humanist have said about it and from attempting to confirm or falsify
various possible answers.

The most promising line of inquiry at the moment appears to me to be
Herbert Wender's observation that := is used in set theory (and, I have
learned, in mathematics more generally) to mark a definition and to
stress that the relation is asymmetric and a matter of definition, in
contrast with the equals sign and the identity or triple-barreled
equality sign, which describe symmetric relations which are matters of
fact about independently defined objects.   (See for example [1] and
[2].)

[1] https://mathworld.wolfram.com/Defined.html
[2]
https://math.stackexchange.com/questions/182101/appropriate-notation-equiv-
versus

If one could establish that := was in use in this way by the 1950s (and
preferably earlier, when those sitting on the Algol working group had
received their mathematical training), it would be very difficult to
resist the conclusion that the Algol symbol was adopted from its
mathematical usage, like a number of other symbols in Algol 58's
reference language.  Unfortunately, the only history of mathematical
notations on my shelf appears not to have an index of symbols.  I can
hardly blame the author, but still it makes it difficult to know
whether he discusses the origin of this particular bit of notation or
not.

If the origin of := is in mathematical notation, then things look bleak
for the proposition that the function of yoking the colon to the equals
sign is to signal that software is mathematics with a difference.

The question "what is software in relation to mathematics?", on the
other hand ... well, if I think of it as a sort of koan, I can just
about see a point in the question, but most of the time I cannot.  So
the only answer I can suggest is one you will I fear find painfully
obvious:  two French hens and a bathtub full of brightly colored
machine tools.


Michael






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