5 ms·

Leibniz's Explanation of Binary Arithmetic (1701)

84 points by caiocaiocaio 8y ago

nanna 8y ago
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...
- f00_ 8y ago
  I copped Cybernetics awhile ago and just kinda skimmed it anything about Leibniz in there?
  - nanna 8y ago
    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.
  - nanna 8y ago
    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?
    - f00_ 8y ago
      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
nanna 8y ago
Lloyd Strickland's "Leibniz's Monadology: A New Translation And Guide" is an excellent way to get into Leibniz.
olooney 8y ago
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/Stepped_reckoner https://en.wikipedia.org/wiki/Leibniz_wheel 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: https://en.wikipedia.org/wiki/Arithmometer https://en.wikipedia.org/wiki/Arithmometer He also wrote extensively on the concept of artificial languages and what we today recognize as Boolean algebra: https://en.wikipedia.org/wiki/Characteristica_universalis https://en.wikipedia.org/wiki/Characteristica_universalis https://www.iep.utm.edu/leib-log/ https://www.iep.utm.edu/leib-log/ His work on these subjects was explicitly cited by Frege as the inspiration for his own seminal work on formal logic.
- pron 8y ago
  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 https://pron.github.io/computation-logic-algebra [2]: https://www.youtube.com/watch?v=2oNmR0q1uA0 https://www.youtube.com/watch?v=2oNmR0q1uA0
schoen 8y ago
More on Fuxi's figures mentioned by Leibniz: https://en.wikipedia.org/wiki/Bagua https://en.wikipedia.org/wiki/Bagua
- goldenkey 8y ago
  Are these just the names of the hexagrams in the I Ching?
  - schoen 8y ago
    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.
YeGoblynQueenne 8y ago
>> 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".
- nanna 8y ago
  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...
  - YeGoblynQueenne 8y ago
    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.
dosy 8y ago
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.

84 points by caiocaiocaio 8y ago

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...

f00_ 8y ago
I copped Cybernetics awhile ago and just kinda skimmed it anything about Leibniz in there?
- nanna 8y ago
  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.
- nanna 8y ago
  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?
  - f00_ 8y ago
    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

nanna 8y ago

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

olooney 8y ago

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/Stepped_reckoner https://en.wikipedia.org/wiki/Leibniz_wheel 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: https://en.wikipedia.org/wiki/Arithmometer https://en.wikipedia.org/wiki/Arithmometer He also wrote extensively on the concept of artificial languages and what we today recognize as Boolean algebra: https://en.wikipedia.org/wiki/Characteristica_universalis https://en.wikipedia.org/wiki/Characteristica_universalis https://www.iep.utm.edu/leib-log/ https://www.iep.utm.edu/leib-log/ His work on these subjects was explicitly cited by Frege as the inspiration for his own seminal work on formal logic.

pron 8y ago
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 https://pron.github.io/computation-logic-algebra [2]: https://www.youtube.com/watch?v=2oNmR0q1uA0 https://www.youtube.com/watch?v=2oNmR0q1uA0

schoen 8y ago

More on Fuxi's figures mentioned by Leibniz: https://en.wikipedia.org/wiki/Bagua https://en.wikipedia.org/wiki/Bagua

goldenkey 8y ago
Are these just the names of the hexagrams in the I Ching?
- schoen 8y ago
  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.

YeGoblynQueenne 8y ago

>> 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".

nanna 8y ago
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...
- YeGoblynQueenne 8y ago
  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.

dosy 8y ago

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.