Lambda the Ultimate

Yes, one way or another, we can consider Euclid's algorithm to be the first result in Computer Science. Nature, Vol 162, p. 487, September 25, 1948. reported that "A SMALL electronic digital computing machine has been operating successfully for some weeks in the Royal Society Computing Machine Laboratory" and that "H.C.F. by the standard process" was one of the first algorithms run on it. See also http://www.computer50.org/

I'm not sure what your refering to, could you expand this a bit?

For example, consider the type of triples of X's. We can write this as F[X]=X×X×X=X³. Now consider the type of triples with a 'hole', ie. triples where one of the three elements of the triple is 'missing'. Either the first element of the triple is missing, and we're left with the two other slots in the triple filled, or the second element is missing and the first and third are filled, or the last is missing and the first and second are filled. So a triple with a 'hole' is of type 1×X×X+X×1×X+X×X×1=3×X². Ie. the type of an F[X] with one of the X's missing is F'[X], where F' is the derivative of F. This works for a wide variety of types, as described in the paper. Huet's 'zippers' are the best known example of this at work. It's amazing that Leibniz's rules have a direct interpretation in this way and you might be able to see how my verbal description of making a hole in a triple maps directly to the Leibniz product rule.

And don't forget the Calculus ratiocinator!

Anton Van Straaten: Leibniz was famous for his optimism, such as the idea that we live in the best of all possible worlds (allegedly ridiculed by Voltaire).

Is it considered controversial that Voltaire based his character of Dr. Pangloss on Leibniz? I've understood this to be the case, without contradiction, for decades.

Anton Van Straaten, quoting Leibniz: I dare say that this is the highest effort of the human mind, and when the project will be accomplished it will simply be up to men to be happy since they will have an instrument which will exalt reason no less than the Telescope perfects our vision. It is one of my ambitions to accomplish this project if God gives me enough time.

Anton Van Straaten: But in a very real sense, his optimism was justified when it came to the impact of such languages on our reasoning abilities, although most people couldn't have imagined it at the time. Now that a major part of Leibniz' vision has been realized, and we have both formal logics of various kinds as well as Turing-complete programming languages, it is simply up to us to be happy! (Should that be an LtU principle?)

Actually, yes, I think it should, by which I mean several relatively specific things:

• Progress is real, sustainable, and sustained. Perhaps the best collected elaboration of this observation is John McCarthy's. Yes, that John McCarthy.
• It's no accident that question of the relationship between computing and human intelligence arose concommitantly with the invention of computing. The questions "what is computing" and "what is intelligence" are obvious, and obviously related.
• You can't have progress, and I doubt it's coherent to talk about the concept of "happiness," without intelligence.
• Computing takes on more and more repetitive "intelligence" tasks, freeing mankind to do what only mankind can do (the domain of which constantly shifts—that's my definition of "progress.")
• Eventually, computing will subsume life itself and, in terms of physics, might be the actual path to immortality (cf. The Physics of Immortality: Modern Cosmology, God, and the Resurrection of the Dead)

So to the extent that we can see progress, albeit progress isn't monotonic and there are horrific local minima, e.g. Communism, Islamist totalitarianism, etc. we should indeed be optimistic and happy.

Is it considered controversial that Voltaire based his character of Dr. Pangloss on Leibniz? I've understood this to be the case, without contradiction, for decades.

Dr. Pangloss was certainly intended to ridicule Leibniz' philosophy, but the character and what happens to him seems likely to have been inspired by Voltaire's major ongoing, multi-level rivalry with de Maupertuis. E.g. this page says "Dr. Pangloss was allegedly a caricature of Leibniz, but it is possible that the real model was Pierre-Louis Moreau de Maupertuis (1698-1759), a French philosopher and scientist."

Quotes below are from Voltaire vs. Needham.

While Voltaire was a guest of Frederick the Great in Prussia, Maupertuis was accused of plagiarizing Leibniz by a friend of Voltaire's, German mathematician Samuel König. Maupertuis attempted to use his position as President of the Berlin Academy of Sciences to railroad König. Voltaire jumped at the chance "to discredit Maupertuis once and for all", which he did by writing the Diatribe du Docteur Akakia (1752). This upset Frederick, who ordered copies of the book burned. Voltaire fled Prussia and was forbidden by Louis XV from returning to Paris (in those days, "you'll never work in this town again" was not such an empty threat).

Still, Voltaire ultimately "won" his battle with Maupertuis, after publishing a second book, which opened with Maupertuis' threatening letter to Voltaire about the first book. "Maupertuis became the laughing stock of Europe and he left Berlin embarrassed and ashamed in 1753. He died a few years later, in 1759, broken in spirit, in mind and health."

Candide was published in the same year. In Chapter 4, Candide reunites with Pangloss, who is now "a beggar all covered with scabs..." As with Maupertuis, the "best of all possible worlds" is not working out very well for Pangloss. Given Voltaire's propensity for holding a grudge, and following through on it, it seems quite likely that Pangloss was yet another take on Maupertuis, who after all had allegedly plagiarized Leibniz. Voltaire had no reason to have a personal grudge against Leibniz, who had died 43 years earlier. In a philosophical sense, Voltaire was certainly taking on Leibniz. But the personal aspects seem related to Maupertuis.

Since I'm already off-topic enough, I won't delve into the issue of computing as a route to immortality, except to mention that Asimov's story The Last Question is a must-read for anyone who's interested by that topic.

Leibniz was apparently a Whorfian, if such an anachronism is permitted. Maybe this lies at the very heart of modern intellectual optimism: changing the language will change the man, who will change the universe in tiny steps. This motive is of course older than Whorf, Leibniz et al. but it became central in our culture with humanism and the idea of emancipation. Leibniz progressed in formalizing reasoning and making the inifity accessible to calculus. Maybe one plays down the radicality of "Leibniz dream" when one reduces it to its scientific heritage but doesn't talk about the mentioned utopia of social engineering. Maybe it is the stalinistic newspeak which "silences ignorant people" that causes more horror than positive expectations these days ( at least in democratic societies ). One might ask why Leibniz could not abandon god after all? Maybe a universe of puppets in the void approximated too closely a constructive nihilism of machines gone mad. The optimism needed a second, this time animated, source?