The present is the past rolled up for action, and the past is the present unrolled for understanding. —Will and Ariel Durant, The Reformation
THEOREM 5. In any finite automaton (in particular, in a McCulloch-Pitts nerve net), started at time 1 in a given internal state S1, the event represented by a given state existing at time p is regular. —S. C. Kleene, Representation of Events in Nerve Nets and Finite Automata
The program neglects to test if fopen returns a valid handle: b or not b, that is the question. This article considers whether 'tis nobler in the mind to suffer the slings and arrows of outrageous fortune, or to take arms against a C of troubles, and by opposing end them.
— Conor McBride, Kleisli Arrows of Outrageous Fortune
(what is the equivalent in the languages of Goethe or of Molière?)
In all these difference methods one is impressed by the number of cards which must be punched by the machine and used only once or twice. ... The newer models of the multiplying punch offer possibilities ... to transfer from one counter to another and to punch progressive totals. With slight modification one of these multipliers might become a remarkable "Difference Engine." — W.J. Eckert, Punched Card Methods in Scientific Computation
(NB "progressive totals" in 1940 were what we would now call "prefix sums"; this technique was already, as Eckert alludes to, exploited by Babbage a century earlier)
From: Voltaire
To: M. le comte d'Argental
Date: 5 mai 1741
Subject: sub umbra alarum vestrarum
... without Lemaure's voice and Vaucanson's Duck, you would have nothing to remind you of the glory of France. ...
I suppose the picture of computing is of a topsy-turvy growth obeying laws of a commercial "natural" selection. This could be entirely accurate considering how fast it has grown. Things started out it a scholarly vein, but the rush of commerce hasn't allowed much time to think where we're going. — James Thornton, Considerations in computer design - leading up to the Control Data 6600 (1963)
Δός αὐτῷ τριώβολον, ἐπειδὴ δεῖ αὐτῷ ἐξ ὧν μανθάνει κερδαίνειν — attr. to Euclid
... τοὺς τῶν ἐγκυκλίων παιδευμάτων μετασχόντας, φιλοσοφίας δὲ ἀπολειφθέντας ὁμοίους ἔλεγεν εἶναι τοῖς τῆς Πηνελόπης μνηστῆρσι ... — Laertius on Aristippus, Lives Ch8-79
Here are two thoughts on water … I wonder if Dumas' René d'Herblay might have a third to add?
Be like water making its way through cracks. Do not be assertive, but adjust to the object, and you shall find a way around or through it. ... be formless. Shapeless, like water. If you put water into a cup, it becomes the cup. You put water into a bottle and it becomes the bottle ... Now, water can flow or it can crash. Be water, my friend. — Bruce Lee
The theorem to be known appeared to me as some stretch of ... hard marl, resisting penetration ... the tide rises in silence, nothing seems to happen, to move, the water so far off one can barely hear it ... yet it finally surrounds the resistant substance ... submerged and dissolved by some more or less vast theory, going well beyond the results originally to be established. — Alexandre Grothendieck
La plupart de mes camarades plus brillants sont d’ailleurs devenus des mathématiciens compétents et réputés. Pourtant, ... [i]ls ont fait des choses ... dans un contexte déjà tout fait, auquel ils n’auraient pas songé à toucher. Ils sont restés prisonniers ... dans un milieu et à une époque donnée. ... il aurait fallu qu’ils retrouvent en eux cette capacité qui était leur à leur naissance, tout comme elle était mienne : la capacité d’être seul. — Alexandre Grothendieck, Récoltes et Semailles, §2.2
This principle can be applied to the process of checking a large routine but we will illustrate the method by means of a small routine viz. one to obtain n! ... — AM Turing, Checking a Large Routine (1949)
I don't know if this is the earliest example of fac as a running example in CS literature, but Turing does tackle a slightly more complex problem than the modern usage:
... without the use of a multiplier, multiplication being carried out by repeated addition.
Computer processes have traditionally been specified by means of procedural languages. That is, a computer program is generally expressed as a sequence of steps. ... A non-procedural programming language may be defined as one in which a computer process is expressed solely in terms of the results of the process, rather than in terms of a procedure by which the results are to be produced. In engineering terms, the non-procedural language allows the programmer to define the final state ... as a function of ... initial states. — Katz & McGee, An Experiment in Non-Procedural Programming (1963)
with the benefit of hindsight, we can also appreciate their prediction that:
The extent to which procedural languages are now ingrained makes it certain that they will be with us for many years to come.
beside the point in the XIX
Now, the calculus of distributive operators is a subject of great extent and importance, but Grassmann's view is the more comprehensive ... . For every quantitative operator may be regarded as a quantity, i.e., as the subject of mathematical operation, but every quantity cannot be regarded as an operator; precisely as in grammar every verb may be taken as substantive, as in the infinitive, while every substantive does not give us a verb. — JW Gibbs, On Multiple Algebra (1866)
... in which we learn that Iverson had antecedents in linguistic parallels, and Gibbs lays some groundwork for Backus' 1977 Turing Award lecture.
- (incidentally, Gibbs' lecture, published in the XIX and digitised by Google in the XXI, was apparently very popular, having been borrowed for consultation multiple times during the course of the XX: once in 1937, and once in 1963...)
to be ⇐ to be — Simon Garland (but then again, how many princes operate in Bool?)
« Toute nation a le gouvernement qu'elle mérite. » — Joseph de Maistre (not exactly the most optimistic of philosophes)
It was on one of my journeys between the EDSAC room and the punching equipment that "hesitating at the angles of stairs" the realization came over me with full force that a good part of the remainder of my life was going to be spent in finding errors in my own programs — Sir Maurice Vincent Wilkes FRS, FREng, DFBCS
Tandis que les siecles s’écoulent, la masse des ouvrages s’accroît sans cesse, & l’on prévoit un moment où il seroit presqu’aussi difficile de s’instruire dans une bibliotheque, que dans l’univers, & presqu’aussi court de chercher une vérité subsistante dans la nature, qu’égarée dans une multitude immense de volumes ; il faudroit alors se livrer, par nécessité, à un travail qu’on auroit négligé d’entreprendre, parce qu’on n’en auroit pas senti le besoin. — Denis Diderot, L’Encyclopédie (1755) ENCYCLOPÉDIE
The potential problem with the PM: Like all inhabitants of 10 Downing Street, he wants to take his place on the world stage. But people on stages are called actors. All they are required to do is look plausible, stay sober and say the lines they are given in the right order. Those that try to make up their own lines generally do not last long. — Sir Humphrey Appleby, GCB, KBE, MVO, MA (Oxon)
It would appear that Sir Humphrey is somewhat more optimistic than de Maistre.
is from "On the cruelty..." and while unicode fonts now give us the opportunity to easily play the syntactic games of the immediately prior paragraph, replacing {True,False} with the less-interpreted {◉,◎}, I have to admit that, some two decades after having first encountered this passage, I am increasingly convinced of Dijkstra's approach, in this paragraph, to semantics.
(the distinction between functional and imperative is largely [cf Hehner] moot at such a low level; his description of the procedure call as a matter of taste is correct insofar as it "merely" provides a shorthand for formulae; and I'd even be tempted to more austerity: booleans are to integers as characters are to strings, while skip is a derived notion, as the identity for the semicolon.
Then again, I am an unregenerate purist: while I can understand that the modern applications programmer might be happy to call libraries, finding bit-twiddling and finite-state machines to be things of a musty past, I don't see how anyone can claim to be a hacker without a fundamental grounding in bits and machines sufficient to abstract to information and automata.)
Ved å studere mesterne, og ikke deres elever — Niels Henrik Abel
(who did, in fact, commute ... to Berlin and Paris)
They're still findin' out what logics will do, but everybody's got 'em. — Murray Leinster
(in a story published in the mid-XX: well after Pandora's; slightly before Kleene)
Peano, anticipating both Dijkstra
and Shannon,
in his 1888 "Calcolo geometrico secondo l'Ausdehnungslhere di H. Grassmann"
Correction: Darius Bacon points out that Boole was before Peano in pointing out the connection to Taylor:
("An Investigation of the Laws of Thought", Ch.5 p.52 ... and I failed to find any mention of Taylor's 1715 result in De Morgan)