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Humanist Discussion Group, Vol. 34, No. 68. Department of Digital Humanities, King's College London Hosted by King's Digital Lab www.dhhumanist.org Submit to: humanist@dhhumanist.org Date: 2020-05-29 03:10:44+00:00 From: Douglas KnoxSubject: Iverson on notation as a historical struggle that begins in hand-waving Willard, I appreciate your provocations on ":=" and the subsequent discussion, which led me to look around a bit in the Wexelblat volume from the 1978 History of Programming Languages conference. Ken Iverson, the inventor of the programming language APL, cared a lot about notation, understood math to be embedded historically in language and human culture, and characterized himself as a "renegade mathematician." His closing talk at the conference seems well matched to the generously broad spirit of your provocation while perhaps resisting some premises. I'll sign off here and quote Iverson at length below. Doug Knox What follows is from Kenneth E. Iverson, transcript of presentation, in Wexelblat (1981), pp. 681-682: "In talking about the development of all programming languages, not just APL, I think we tend to make a mistake in thinking of them as starting, ab initio, in the 1940s when machines first came along. And I think that that is a very serious mistake because, in fact, the essential notions are notions that were worked out in mathematics, and in related disciplines, over centuries. I mean, just the idea of a formula, the idea of a procedure -- although in mathematics we never had a really nice formal way of specifying this -- it's clear that this is what we do. In fact, in a lecture, you sort of give the kernel of the thing and then you wave your arms and that replaces the looping and what-not. But the idea of algorithms and so on is very central to mathematics. And so I think it's a mistake to think of the development as starting from the computer. I think it's worthwhile trying to examine this in the following sense: if we look at mathematical notation, say, at the time of the development of the computer we had some very important notations. If you don't think they're important, I would recommend strongly that you take a look at some source like [Florian] Cajori's History of Mathematical Notations; it's just incredible the time and effort that went into introducing what we now just take as obvious. For example, the idea of a variable name: a very painful thing. At the outset you wrote calculations in terms of specific quantities. Then it was recognized that you really wanted to make some sort of a universal statement and so they actually wrote out things like 'universalis' which, because we are all lazy, gradually got abbreviated, and I suppose by the time it reached 'u', somebody said, 'Aha! We've got a lot of letters like that. And now we can talk about several universals,' and so on. "But the serious thing is that this is a very important notion. The idea of identifying certain important functions like addition, multiplication, and assigning symbols to them. These symbols are not as old as you think. Take the times sign for example. It's only about 200 years old; it's too young to die. That's why we resist the things like the asterisk and so on, that happen to be on tabulating machines because of the need for check protection. "There were other things like grouping. It took a long time for what seems now the obviously beautiful way of showing grouping in an expression by parentheses. It was almost superseded by what is called the 'vinculum' -- where you drew a line over the top of the subexpression -- linearization again. I think the main reason that the parentheses won out was because when you have what would now just be a series of parentheses you got lines going up higher and higher on the page, and that was awkward for printing. "The question of representation -- certainly mathematics had long since reached the stage where you don't think about how the numbers are represented. When you think about multiplication, division, and so on, you don't think, 'Ah, -- that's got to be carried out in roman numeral, or in arabic, or in base-2' or anything like that. You simply think of it as multiplication. Representation is subordinated. "And of course, the idea of arrays has been in mathematical notation and other applications for something like 150 years. They still haven't really been recognized, but they've been there. "Now, what happened when the first computer came along? For perfectly good practical reasons every one of these notions disappeared. You couldn't even say 'A + B.' You had to say, 'Load A into accumulator; load B into so-and-so' -- you couldn't even say that. You had to say, 'Load register 800 into the so-and-so and so on.' So all of these things disappeared, for perfectly practical reasons. The sad thing is that 30 years later we're still following that same aberration..." https://archive.org/details/historyofprogram0000hista _______________________________________________ Unsubscribe at: http://dhhumanist.org/Restricted List posts to: humanist@dhhumanist.org List info and archives at at: http://dhhumanist.org Listmember interface at: http://dhhumanist.org/Restricted/ Subscribe at: http://dhhumanist.org/membership_form.php

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