Humanist Discussion Group, Vol. 34, No. 61.
            Department of Digital Humanities, King's College London
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    [1]    From: Norman Gray 
           Subject: Re: Submission emails (122)

    [2]    From: Willard McCarty 
           Subject: that over which blood is spilled (63)


--[1]------------------------------------------------------------------------
        Date: 2020-05-25 14:03:13+00:00
        From: Norman Gray 
        Subject: Re: Submission emails

Greetings.

I stand gladly corrected by Michael Sperberg-McQueen (Humanist 34.54),
and plead poor phrasing on my part.

I hadn't really intended to make any historical point, but instead aimed
to simply stress that notation is and was fundamentally arbitrary.  Thus
I gestured towards 'old keyboards', and the extent to which they are
different from each other and from the roughly standardised keyboard we
are currently familiar with, as an example of the range of ultimately
unimportant contingencies which may have nudged an author towards a
particular choice of notation.  When I said 'they presumably cast around
in their memories...', I was hoping to make clear that I hadn't actually
looked up what keyboards were in contemporary use, but it's clear that
that 'presumably' was being deplorably overworked in that sentence, and
should probably claim overtime rates.

I also had in mind the story of Ray Tomlinson's choice of the '@' sign
for TENEX machine-to-machine email [2], in which he mentions that 'the
at sign just makes sense' (and it was available on the PDP-10 keyboard
that Tomlinson and his colleagues were using), and that 'The at sign
also had no significance in any editors that ran on TENEX', although --
also tangentially relevant to this story -- this turned out not to be
straightforwardly true.

Michael Sperberg-McQueen says:

> Unfortunately, [any dependence on keyboards] can easily be shown false
> by the account given in
> the Algol 58 report itself and by the actual content of the report.

Indeed, and this conclusively demonstrates (top of p.10) that my gesture
towards keyboards was ahistorical.  I'm sorry for leading anyone up the
garden path.

Now I come to read the report (available at eg [1]), which I've never
done before, I see (p9) that having the language be mechanically
compilable was only the third of three objectives for it.  That is
illuminating and unexpected to me -- thank you.

Michael goes on to say:

> Norman Gray's suggestion that Church's lambda calculus might be a
> possible source [for the choice of ':='].

I certainly didn't mean to suggest that!

Instead I meant, firstly, to respond to Gabriel Egan's exclamation
(Humanist 35.45) that the keyword 'let' in BASIC-like languages
'compounds the offence'; and secondly to observe that while we are
discussing notational intricacies of Algol (and thus of essentially all
mainstream current languages), we should recall that there are languages
such as Lisps which have significantly and importantly different ideas
of what is happening in an 'assignment statement' (firmly in
scare-quotes), and thus significantly different notational needs.  Thus
there is a degree of choice even in having the notion of assignment in a
language, before we move on to the choice of deciding how to notate it.

I may have caused confusion by my passing remark at the end, that

> I also observe in passing that the Wikipedia page about the lambda
> calculus [1] uses ':=' with an assignment-like meaning which would be
> read aloud as something like 'taken to be' or 'replaced by'.

That is, this ':=' symbol is being used in a way which doesn't have
'equals' or 'assign' in its natural 'reading'.  I should perhaps have
emphasised that this is a feature of this page's version of some present
notation describing the lambda calculus, and that, notational
instability being what it is, there are no grounds for supposing that
this notation would have been used in the past (for example by Church or
McCarthy), or even that it is universally used now.

Finally, I'm glad that Michael picked up on the suggestion that
notations need 'some level of intuitive affordance'.  Mathematical
notation is just a type of text, and thus falls under the same general
civility requirements as non-mathematical text: as an author you aim to
take the reader with you, and avoid undue whimsy or perversity in
notation by choosing notation the reader is likely to guess the meaning
of; you decide on a text-by-text basis if two notions do or do not need
to be distinguished; it is this (and referees) that enforces 'rules' of
notation.  Mathematical authors are like any other author in being
obliged to make such choices, so are language designers.

So to bring this back to Willard's question, yes, notation is a
reasonable subject for a close reading.  What else were the Algol
designers reading?  What alternative notations were mooted and why were
they voted down?  I may be missing a very significant trick here, but
there may be slimmer pickings here than one might initially hope.


I'll also mention, as a dessert, strictly in parentheses, that when
lecturers in the physical sciences talk of history -- 'Galileo
discovered...', or 'Maxwell said...' -- it is almost always in a
whiggish sense which is cheerfully careless of whether Galileo or
Maxwell actually said any such thing (I exaggerate only slightly).  In
part, this is because the only function of history in this context is to
help teach the present by citing the illuminating or entertaining errors
of the past; and in part it is because Maxwell's actual writing would be
only of antiquarian interest, about as hard to read as Gawain, say,
because of the changes in notation, and changes in the set of ideas
needing to be notated.  As a perverse corroboration of the general
point, I'll mention that it has never in fact occurred me to try reading
anything Maxwell wrote, nor would I know where to start.

Best wishes,

Norman



[1]
http://www.softwarepreservation.org/projects/ALGOL/report/Algol58_preliminary_re
port_CACM.pdf/
[2] http://openmap.bbn.com/~tomlinso/ray/firstemailframe.html



--
Norman Gray  :  https://nxg.me.uk
SUPA School of Physics and Astronomy, University of Glasgow, UK



--[2]------------------------------------------------------------------------
        Date: 2020-05-25 08:00:37+00:00
        From: Willard McCarty 
        Subject: that over which blood is spilled

As a student attempting to put food on the table as well as write 
a doctoral dissertation, I had a job as an editorial assistant 
for the Records of Early English Drama project. There I was 
fortunate enough to come up against practices of scholarship
as it is actually done when it is done with care. A very valuable
experience for a student to have. But I mention this bit of 
personal history because of several instances in which as an 
editorial assistant I participated in arguments over minutae 
(such as marks of punctuation), always the most passionate, where 
if we'd been of a different sort, blood would have been spilled.
  
Now one can chuckle about scholars' murderous passion over trivia, 
but in the cases in which I was involved I learned that meaning can 
be discovered in the minutest of detail. Such disputes often cannot be
resolved conclusively. The meaning that one sees, teasingly suggested 
by some tiny detail, often has to be put aside, alas, in the interests 
of finishing the work. But the irresolvable tease can be worth hanging 
onto. It may suggest a direction that does yield less elusive evidence. 

Someone in the past few exchanges saw that I was engaging in
deliberate provocation rather than trying to hammer home an argument,
take a position, make points and so on. At this juncture I simply do not
know enough to make the argument that is struggling to be born. But 
the question won't go away: what we might be able to do fruitfully with 
the implications of ':='closely read in its historical context. 

Perhaps there's nothing there to be explicated, but I beg to differ. 
I think we can do better than brush these implications aside as 
the product of an arbitrary act (possibly) or as simply unknowable 
(certainly). We do know that the need for an 'algebraic' language was 
felt strongly enough to drive the development of the hugely influential 
ALGOL (short for 'Algebraic Language'). The struggle for a mathematical 
theory of computation was underway. As Philip Kitcher has emphasised, 
the importance mathematicians often place on "perspicuous notation"[*] 
suggests further that we attend with care to what ':=' may be said 
perspicuously to hint at. 

So I wonder -- here the argument peeks out to see how friendly the world 
might be -- if those who set down ':=' were of a mind to think that 
'mathematics' needed stretching to accommodate a new family member? 
We are still using that word as if it were a tightly bounded, clearly 
understood concept. But the tight bounds do not survive the close 
inspection of Hacking's fearless, indeed playful monograph, Why do we
need a philosophy of mathematics at all? (2014). Even more tentatively,
I wonder if the implications of ethnomathematics and other cross-cultural 
practices of 'mathematics' have a place in this discussion.

Comments -- or is this a proverbial dead horse?

Yours,
WM

-----
*Philip Kitcher, The Nature of Mathematical Knowledge (New York: Oxford 
University Press, 1984): 130-1, 170-1.

--
Willard McCarty (www.mccarty.org.uk/),
Professor emeritus, Department of Digital Humanities, King's College
London; Editor, Interdisciplinary Science Reviews
(www.tandfonline.com/loi/yisr20) and Humanist (www.dhhumanist.org)




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