EWD963

Visuals for BP's Venture Research Conference

• When we had no computers, we had no programming problem either.
• When we had a few computers, we had a mild programming problem.
• Confronted with machines a million times as powerful, we are faced with a gigantic programming problem.
• The programming problem is gigantic because
  1. viewed as string of operations on a collection of variables, each individual computation is a gigantic object;
  2. the individual computation depending on the input, a single program has to be able to control a gigantic number of different possible computations.
• As a result, programming has become one of our most demanding intellectual activities, requiring great clarity of expression and the utmost economy of reasoning.
• This conclusion has never been refuted; it is, however, regularly denied because of its uncomfortable implications.
• It is vigorously denied by the computer industry, which would sell you its products rather as solutions to your old problems than as the source of terrifying new ones.
• It is vigorously denied by those customers that otherwise would have to admit that their computer manufacturer has fooled them.
• [Remember that computers are preferably sold by dealing with such a high level of the customer's hierarchy that incompetence in computing is assured and objections from the technically competent can be overruled.]
• It is vigorously denied by those in computing that by its implications would be demoted to the rank of amateur.
• [Remember: the surest way of making software design prohibitively expensive is viewing it as a production job to be done by cheap labour.]
• It is denied in those companies whose top management consists of lawyers and accountants, as their management lore has all its roots predating the advent of the high-technology industry.
• It is also denied by the personal-computer enthusiast that fails to distinguish between a barber and a team of surgeons.
• Back to the irrefuted conclusion that programming is very difficult; its acceptance gave rise to Programming Methodology as a topic of explicit scientific concern.
• In 15 years of Programming Methodology we have seen the combination of spectacular progress and sharp limitations.
• Many formerly notoriously opaque algorithms now have "ingeniously simple and effective" explanations, which are jewels of clarity.
• Sophisticated new algorithms are being derived which, 15 years ago, would have been absolutely impossible to conceive. But.....
• Current mathematical style —which grew in response to other challenges— limits the applicability to relatively small programs.
• The circumstances shaping the challenge, we try to redefine Mathematics from "The abstract science of space, number, and quantity" (COD) to "The (art and) science of effective reasoning".
• We have learnt that calculi of all sorts have a major role to play.
• We have learnt that it pays to design, for each calculus to be used, with great care a notation geared to one's manipulative needs.
• We have learnt that most philosophers (those of mathematics included) are eminently ignorable.
• We have learnt that a formalism's major purpose can be to free us from the shackles of our native language and the reasoning patterns induced thereby.
• [Being "counter-intuitive" should not be held against any formalism that enables us to accomplish what is beyond the unaided mind.]
• We have learnt that programming methodology and mathematical methodology in general are not so far apart at all. (For instance, a conscious separation of concerns is equally valuable for both.)
• We have learnt that a purely syntactic analysis of the formal requirement can give heuristic guidance to the point of generating the best possible solution.
• We have learnt that the potential for improvement can be dramatic, e.g. reducing a formal proof of two dozen steps to an equally formal proof of one step.

  (Example.)

• We have learnt that it pays to be ruthlessly pragmatic, but.....
• We have also learnt that it is still very hard to sell to industry the economic value of mathematical elegance.
   

  Austin, 5 June 1986

  prof. dr. Edsger W. Dijkstra
  Department of Computer Sciences
  The University of Texas at Austin
  Austin, TX 78712-1188
  USA

  transcribed by Martijn van der Veen
  revised Fri, 28 May 2010