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Humanist Archives: June 8, 2020, 7:03 a.m. Humanist 34.89 - notation, software and mathematics

                  Humanist Discussion Group, Vol. 34, No. 89.
            Department of Digital Humanities, King's College London
                   Hosted by King's Digital Lab
                Submit to: humanist@dhhumanist.org

    [1]    From: Henry Schaffer 
           Subject: Re: [Humanist] 34.88: notation, computation, liberation (?) (96)

    [2]    From: Bill Benzon 
           Subject: Software and Mathematics (64)

        Date: 2020-06-07 16:42:22+00:00
        From: Henry Schaffer 
        Subject: Re: [Humanist] 34.88: notation, computation, liberation (?)

I very much enjoyed

On Sun, Jun 7, 2020 at 5:12 AM Humanist  wrote:

>                   Humanist Discussion Group, Vol. 34, No. 88.
>             Department of Digital Humanities, King's College London
>                    Hosted by King's Digital Lab
>                        www.dhhumanist.org
>                 Submit to: humanist@dhhumanist.org
>         Date: 2020-06-07 08:55:41+00:00
>         From: C. M. Sperberg-McQueen 
>         Subject: Re: [Humanist] 34.85: notation, computation, liberation
> (?)
> ...

 and here are a few thoughts about his ending paragraph:

> When in the late 1970s Susan Hockey and others created the Oxford
> Concordance Program (OCP), it took a year or more to develop the
> program.  When I teach a three-day introductory course in XQuery,
> we sometimes write simple functions for word frequency lists and
> concordances as an exercise on the third morning.  Our functions
> are not, to be sure, nearly as full-featured as OCP.  But still:
> how likely is it that the programmer who wrote OCP had a working
> prototype of the word frequency list routine running by noon of
> his first morning on the project?  One does not need to think
> that Fortran is a bad language in itself, in order to think that
> we can write software for many purposes faster and more reliably
> if we use a different kind of language.

  I've written earlier about the difference in suitability of different
computer languages for different types of tasks. E.g. to handle numerical
processing vs. text processing. Is efficiency of execution a consideration?
This mention of programming to produce a concordance is one in which text
processing is central and where various text conventions must be
accommodated. I'm reminded of an undergraduate English course taught by
Paul Fyfe on my campus when he and I did a workshop on concordances in the
age of DH and "distant reading" (ala Moretti).

  Part of the workshop dealt with the programming needed to produce a
concordance - or at least go half-way towards a concordance. The task was
to extract all of the words in a (digital) text, and then print each of
them out with a count of how many times each one appeared. Here's the

while there is text left to read {
  read in line
  split into words
for each one of these words, increment count
print words with count of each

This led to discussion on what each of these operations meant, how they
need to be unambiguously presented to the computer - and here's the initial
version of the computer program (written in Perl) which we discussed, saw
operate, and discussed the output.

while ($linein = <>) { # read each line as long as there are any

  chomp $linein; # remove line ending character

  @linewords = split (/ /, $linein);      #split line into words

  foreach $word (@linewords) {            #for each word in the line

    $conwords{$word}++;                   #increment (and store)



while (($word, $count) = each (%conwords)) { # for each word/count

  print "$word appears $count times\n";   # format of printing


The discussion included topics such as whether we should eliminate some
words? e.g. the, of, and preserve case.  How to handle spelling errors,
and related words.

And then to a discussion as to who cares about these aspects and why people
might need a full concordance (or today the equivalent via a search) for
biblical and legal study where the context(s) in which a word is used are

We ended with my favorite statement:
*Computers do what you tell them to do, not what you want them to do.*

--henry schaffer

        Date: 2020-06-07 15:30:15+00:00
        From: Bill Benzon 
        Subject: Software and Mathematics

To Willard and fellow humanists:

There's a somewhat diffuse set of conversations going on over the last few
weeks or so. I believe it's been precipitated by remarks Willard made in
Humanist 34.27: punctuation in the assignment statement. Almost at the end
Willard remarked:

So I translate "X is to be MADE equal to the sum of Y and Z". Or, we might say,
"Warning: this is NOT an algebraic statement!" Or, better, I think: "Here we
must stretch our understanding of mathematics to include something new."

It's that very last sentence that interests me, about stretching our
understanding of mathematics. In Humanist 34.39 Willard elaborates on the target
and scope of his inquiry:

I'm looking for evidence concerning the realisation or conviction that software,
though mathematical in some sense, is "mathematics with a difference", as
Mahoney wrote in "Computer science: The search for a mathematical theory".* To
ask whether software is mathematics or is essentially mathematical, expecting a
yes-or-no response even if with arguments, seems to me too crude an instrument.
So, I am wanting to ask, what is software in relation to mathematics? I don't
assume that either is a well-defined (or confined) thing.

So, is software to be considered a kind of mathematics, with that little bit of
notation as evidence bearing on the matter?

I'll leave notation aside. It's the relation between mathematics and
software that concerns me. It seems to me that there's a bit of ambiguity in
the word "mathematics". My dictionary tells me that it's "the abstract
science of number, quantity, and space" That is, it is an intellectual
discipline, something that people do. My dictionary also offers: "the
mathematical aspects of something: the mathematics of general relativity."
That seems a bit different. Here "mathematics" is functioning not so much a
discipline as it is the objects which that discipline is about.

What of "software"? Software is not at all a discipline. Computer
programming is the discipline concerned with software. Whatever computer
programming is, it is not reasonably considered a branch of mathematics. Nor for
that matter does it make much sense to think of computer programs directly as
mathematical objects, though we may subject them to mathematics analysis, which
is a different matter (in principle, we can subject anything to mathematical

So, notation aside, I agree with Willard that "whether software is mathematics
or is essentially mathematical, expecting a yes-or-no response even if with
arguments, seems to me too crude an instrument." Software is something else.
Though it has some kinship with mathematics, it also has some kinship with
natural language. But it does seem to me that we must think of it as something
in itself, different from both mathematics and natural language. It is something
new that entered the world in the decades after World War II.

Bill Benzon



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