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Leibniz's Explanation of Binary Arithmetic (1701) (leibniz-translations.com)
84 points by caiocaiocaio 7 months ago | hide | past | web | favorite | 15 comments

Liebniz is something of an unacknowledged grandfather of computer science. Everyone knows Babbage for designing but never finishing a universal mechanical computer, but a century earlier Lienbniz materially advanced the state-of-the-art by designed and actually constructing the first mechanical calculator capable of all four basic mathematical operations: addition, subtraction, multipication, and division.

https://en.wikipedia.org/wiki/Stepped_reckoner https://en.wikipedia.org/wiki/Leibniz_wheel

Liebniz's design was the basis of the first successful mass produced mechanical calculator more than a century later:


He also wrote extensively on the concept of artificial languages and what we today recognize as Boolean algebra:



His work on these subjects was explicitly cited by Frege as the inspiration for his own seminal work on formal logic.

Leibniz plays a central role in a book I composed of excerpts of original sources about the history of computation, logic and algebra[1], and in a talk I gave about it[2].

[1]: https://pron.github.io/computation-logic-algebra

[2]: https://www.youtube.com/watch?v=2oNmR0q1uA0

Also, if the philosophical roots of computing are of interest, then check out

Martin Davis "The Universal Computer: The Road from Leibniz to Turing"

I'm working on an article about Norbert Wiener's cybernetic reading of Leibniz atm...

I copped Cybernetics awhile ago and just kinda skimmed it

anything about Leibniz in there?

Yeah he appears over and over. Eg

  if i were to choose a patron saint for cybernetics out of the
  history of science, i should have to choose leibniz. the
  philosophy of leibniz centers about two closely related
  concepts-that of a universal symbolism and that of a calculus of
  reasoning.  from these are descended the mathematical notation
  and the symbolic logic of the present day. now, just as the
  calculus of arithmetic lends itself to a mechanization
  progressing through the abacus and the desk computing machine to
  the ultra-rapid computing machines of the present day, so the
  calculus ratiocinator of leibniz contains the germs of the
  machina ratiocinatrix, the reasoning machine. indeed, leibniz
  himself, like his predecessor pascal, was interested in the
  construction of computing machines in the metal . it is therefore
  not in the least surprising that the same intellectual impulse
  which has led to the development of mathematical logic has at the
  same time led to the ideal or actual mechanization of processes
  of thought.
- Cybernetics (1961 ed.)

  Leibnitz, in the meantime, saw the whole world as a collection of
  beings called "monads" whose activity consisted in the perception
  of one another on the basis of a pre-established harmony laid
  down by God, and it is fairly clear that he thought of this
  interaction largely in optical terms. Apart from this perception,
  the monads had no "windows," so that in his view all mechanical
  interaction really becomes nothing more than a subtle consequence
  of optical interaction.  A preoccupation with optics and with
  message, which is apparent in this part of Leibnitz's philosophy,
  runs through its whole texture. It plays a large part in two of
  his most original ideas: that of the Characteristica
  Universalis, or universal scientific language, and that of the
  Calculus Ratiocinator, or calculus of logic.  This Calculus
  Ratiocinator, imperfect as it was, was the direct ancestor of
  modern mathematical logic.  Leibnitz, dominated by ideas of
  communication, is, in more than one way, the intellectual
  ancestor of the ideas of this book, for he was also interested in
  machine computation and in automata. My views in this book are
  very far from being Leibnitzian, but the problems with which I am
  concerned are most certainly Leibnitzian.  Leibnitz's computing
  machines were only an offshoot of his interest in a computing
  language, a reasoning calculus which again was in his mind,
  merely an extention of his idea of a complete artificial
  language.  Thus, even in his computing machine, Leibnitz's
  preoccupations were mostly linguistic and communicational.
- Human Use of Human Beings (1954 ed.)

Wiener becomes preoccupied with Leibniz from his youth, writing philosophical entries for the Encyclopedia Americana which are like premonitions of his cybernetics.

He wasn't uncritical though, he especially attacked the pre-established harmony of monads. The argument I'm pursuing is that if you get rid of God, if you let monads actually intercommunicate, if you reinvent Leibniz's continuum of infinite confusion and infinite clarity of knowledge as entropy and information, you're pretty close to cybernetics.

Out of curiosity, what did you make of Cybernetics? It's a pretty unwieldy book, especially today... Did you ever try the Human Use of Human Beings?

i just thought it was interesting if not just for the subjects it covers. information theory before shannon, Henri Bergson's time philosophy, thermodynamics/statistical mechanics, learning machines (neural networks?)

I'll try to get my hands on human use of human beings, probably give cybernetics another run through too

More on Fuxi's figures mentioned by Leibniz:


Are these just the names of the hexagrams in the I Ching?

They're related, but each hexagram contains two of these (which are apparently sometimes written slightly separated and considered separately). As there are 8 of these symbols, there are 64 hexagrams.

>> every reasoning derivable from notions could be derived from these notions' characters by a way of reckoning, which would be one of the more important means of assisting the human mind.

I guess he's saying that symbolic reasoning can be performed automatically ("by a way of reckoning", in the sense of computation). He's advocating for the use of automatic symbolic manipulation as a way to enhance the capabilities of the human mind. That's, like, the soul of logic-based, symbolicist AI. You know - "GOFAI".

Yes! Leibniz thought it would be possible to invent "a kind of alphabet of human thoughts" in which "everything can be discovered and judged by it comparison of the letters of this alphabet and an analysis of the words made from them." These would be essentially arithmetic - every thought would have a numbers. This would "increase the *power of the mind much more than optical lenses strengthen the eyes and which will be as far superior to microscopes or telescopes as reason is superior to sight." This was influenced (but not reducible) to what he had been reading from Chinese philosophy.

In 1679 he said it would take, "five years to complete project with a few select men." Famous last words...

Well, there were a few unforeseen problems along the way...

On the other hand, so many brilliant minds have put in so much great work in this idea that it's just silly to let it die only because we're, well, stuck.

Lloyd Strickland's "Leibniz's Monadology: A New Translation And Guide" is an excellent way to get into Leibniz.

It strikes me that Leibniz would have been right at home in this time. I can see him blogging, sending emails like the posted explanation, writing RFCs.

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