In the 17th century, Leibniz dreamed of a machine that could calculate ideas(spectrum.ieee.org)
spectrum.ieee.org
In the 17th century, Leibniz dreamed of a machine that could calculate ideas
https://spectrum.ieee.org/in-the-17th-century-leibniz-dreamed-of-a-machine-that-could-calculate-ideas
52 comments
Right! Unfortunately, because the feud between Catholics and Protestants at that time, the later seldom recognize the influences of the former and it seems that there were these “dark ages” until they arrived.
See, for instance, the School of Salamanca: https://plato.stanford.edu/entries/school-salamanca/
See, for instance, the School of Salamanca: https://plato.stanford.edu/entries/school-salamanca/
Leibniz is definitely an interesting person. I studied about him in philosophy, but in grad school I focused more on his contribution to the ideas of computers. Leibniz and Pascal is a good starting point in history.
What about the other 4 billion years?
What, you’re writing off the other nine?
What, organic computing?
> Leibniz’s central argument was that all human thoughts, no matter how complex, are combinations of basic and fundamental concepts, in much the same way that sentences are combinations of words, and words combinations of letters. He believed that if he could find a way to symbolically represent these fundamental concepts and develop a method by which to combine them logically, then he would be able to generate new thoughts on demand.
To what extent did Leibniz impact Frege and the other architects of analytic philosophy? Isn't Begriffsschrift a similar project?
To what extent did Leibniz impact Frege and the other architects of analytic philosophy? Isn't Begriffsschrift a similar project?
Yes, I first read about Leibniz’s machine from the wikipedia page on the Entscheidungsproblem.
The research on this problem eventually led to the invention of Lambda calculus and the Turing machine (formal languages for computing), which proved that such a project is impossible, as on some inputs they infinitely recurse and can’t output True or False.
https://en.wikipedia.org/wiki/Entscheidungsproblem
The source is Martin Davis, 2000, Engines of Logic
The research on this problem eventually led to the invention of Lambda calculus and the Turing machine (formal languages for computing), which proved that such a project is impossible, as on some inputs they infinitely recurse and can’t output True or False.
https://en.wikipedia.org/wiki/Entscheidungsproblem
The source is Martin Davis, 2000, Engines of Logic
My brain also infinitely recurses on some problems and can't output True or False. Guess my brain is impossible.
???
???
Your brain is not Leibniz’s machine nor the algorithm sought upon in the Entscheidungsproblem.
Your brain also doesn’t infinitely recurse as it doesn’t have infinite time or space.
A machine that given a logical statement outputs whether the statement is universally valid is impossible, ergo all mechanisms that don’t output true or false given a logical statement are impossible??
Your brain also doesn’t infinitely recurse as it doesn’t have infinite time or space.
A machine that given a logical statement outputs whether the statement is universally valid is impossible, ergo all mechanisms that don’t output true or false given a logical statement are impossible??
They're very verbose and dense, and it strikes me that Neal Stephenson more or less wrote the three books just for himself, but it's worth checking out his "The Baroque Cycle" trilogy, culminating with "The System of the World."
It's fiction, but it's very eye-opening and mind-teasing fiction that puts a lot of contemporary moving parts in motion at the same time. And the books basically revolve around the Newton-Leibniz feud over inventing calculus.
It's fiction, but it's very eye-opening and mind-teasing fiction that puts a lot of contemporary moving parts in motion at the same time. And the books basically revolve around the Newton-Leibniz feud over inventing calculus.
We take boolean logic for granted, yet Bool's Laws of Thought do a pretty astonishing job of expressing ideas, though at the same time are so far.
https://wikipedia.org/wiki/The_Laws_of_Thought
Also a direct link to shannon use of binary logic
It suggests that thought is not necessarily generative. That we are not generating ideas. That my ideas are not created out of my head.
An alternative model is that thought is performed by the manipulation of references. References to an idea landscape. Anybody who writes software is familiar.
(Sequences and hierarchies of idea-references give us complex ideas)
> Leibniz’s central argument was that all human thoughts, no matter how complex, are combinations of basic and fundamental concepts, in much the same way that sentences are combinations of words, and words combinations of letters.
An alternative model is that thought is performed by the manipulation of references. References to an idea landscape. Anybody who writes software is familiar.
(Sequences and hierarchies of idea-references give us complex ideas)
> Leibniz’s central argument was that all human thoughts, no matter how complex, are combinations of basic and fundamental concepts, in much the same way that sentences are combinations of words, and words combinations of letters.
> if he could find a way to symbolically represent these fundamental concepts and develop a method by which to combine them logically, then he would be able to generate new thoughts on demand
Reminds me of some recent neurosymbolic work, like "DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learning" [1]
[1] https://arxiv.org/abs/2006.08381
Reminds me of some recent neurosymbolic work, like "DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learning" [1]
[1] https://arxiv.org/abs/2006.08381
Leibniz invented the modern world as a side project. Computer science, relativity, nuclear physics can all be traced to him.
>relativity, nuclear physics
Are those just there because of calculus? that's doubly unfair if so. Unfair beacuse there is a huge amount of work that went into those besides simply calculus, and unfair for all those who contributed to calculus before him.
Frankly, I wouldn't even attribute CS to him, he did have a mechanistic view of logic, but that alone doesn't strike me as revolutionary, it was the age of mechanical machines after all, somebody was bound to apply the idea to symbolic manipualation. CS's father on the engineering side is Babbage, it's father on the mathematics side is Russel or Turing.
Are those just there because of calculus? that's doubly unfair if so. Unfair beacuse there is a huge amount of work that went into those besides simply calculus, and unfair for all those who contributed to calculus before him.
Frankly, I wouldn't even attribute CS to him, he did have a mechanistic view of logic, but that alone doesn't strike me as revolutionary, it was the age of mechanical machines after all, somebody was bound to apply the idea to symbolic manipualation. CS's father on the engineering side is Babbage, it's father on the mathematics side is Russel or Turing.
Leibniz was born one and a half century before Babbage and nearly two and a half century before Russel and Turing.
To compare them is immensely unfair to Leibniz and completely ignores how visionary and far ahead of his time he actually was.
To compare them is immensely unfair to Leibniz and completely ignores how visionary and far ahead of his time he actually was.
Everything you assume is false. I'm refering to the fact he came up with the modern concept now known as energy, which he called vis viva. Why are you making things up, he didn't have a mechanistic view of logic, he invented the concept of possible worlds, but for CS what is important is his side project of charachteristica universalis and his introduction of binary formalization.
>he came up with the modern concept now known as energy, which he called vis viva
I forgot that, but crediting relativity and nuclear physics to Conservation Of Energy still feels like a big stretch to me. Maybe Thermodynamics.
>he didn't have a mechanistic view of logic, he invented the concept of possible worlds
I'm not sure I understand why those two things contradict each other. He envisioned a machine doing reasoning, that's a "mechanistic view of logic" in my book. How is possible worlds related to that and why are they in tension in your opinion ?
>charachteristica universalis and his introduction of binary formalization
Fair enough, those two things are fairly radical for his time and very CSy. But neither is original to him, his charachteristica universalis is based on a misunderstanding of chinese ideographs, and there were people contemporary to him like John Wilkins who worked on very similar things ('philosophical languages'), the idea was in the air at the time.
The binary numerals were also inspired by certain chinese texts, and some claim[1] that he plagiarised them outright from contemporaries. All said and done though, I don't think binary numbers are that important or fundamental to computers, only the idea that numbers (and abstract ideas in general) can be operated on purely syntactically without the slightest clue as to their meaning, and still yield useful results; This is an idea much older than Leibniz. Also Babbage managed to design a perfectly good computer on base-10, and binary was just one system among many in the 1940s.
[1]https://www.researchgate.net/publication/314485403_Who_Disco...
I forgot that, but crediting relativity and nuclear physics to Conservation Of Energy still feels like a big stretch to me. Maybe Thermodynamics.
>he didn't have a mechanistic view of logic, he invented the concept of possible worlds
I'm not sure I understand why those two things contradict each other. He envisioned a machine doing reasoning, that's a "mechanistic view of logic" in my book. How is possible worlds related to that and why are they in tension in your opinion ?
>charachteristica universalis and his introduction of binary formalization
Fair enough, those two things are fairly radical for his time and very CSy. But neither is original to him, his charachteristica universalis is based on a misunderstanding of chinese ideographs, and there were people contemporary to him like John Wilkins who worked on very similar things ('philosophical languages'), the idea was in the air at the time.
The binary numerals were also inspired by certain chinese texts, and some claim[1] that he plagiarised them outright from contemporaries. All said and done though, I don't think binary numbers are that important or fundamental to computers, only the idea that numbers (and abstract ideas in general) can be operated on purely syntactically without the slightest clue as to their meaning, and still yield useful results; This is an idea much older than Leibniz. Also Babbage managed to design a perfectly good computer on base-10, and binary was just one system among many in the 1940s.
[1]https://www.researchgate.net/publication/314485403_Who_Disco...
The paper you link is like garbage, there are plenty of resourcces that are intellectually honest.
Leibniz did take binary form I Ching, where it was used to formalize bones thrown on turtle shells for fortune telling, to consider this 'plagiarism' is idiotic.
The mathematics side of CS would be Gödel probably.
The mathematics of CS is mainly logic, for which Gödel isn't essentially the leading light. Very important theories he contributed, but they don't necessarily define logic. I'd be more inclined to attribute to Russell or any of his influencers (like Frege).
[deleted]
Relativity was one of Galileo's contributions, earlier than Leibnitz: 1632 in his 'Dialogue Concerning the Two Chief World Systems'. See https://en.wikipedia.org/wiki/Galilean_invariance
He was wrong because there are so many systems of thought; because he wasn't accounting for or aware of the existance of subconscious thought; because thoughts are context dependant; and of course because all formal systems of this sort tend to suffer incompleteness. However, I have only the greatest respect, as asking a question that leads to so many deep and interesting answers is far more difficult and important then having a "correct hypothesis".
"Taking the idea a step further, Llull invented what he called a volvelle, a circular paper mechanism with increasingly small concentric circles on which were written symbols representing the attributes of God."
So you are saying that Engineer's Disease is at least 700 years old.
So you are saying that Engineer's Disease is at least 700 years old.
Related from Dijkstra, "Under the spell of Leibniz's Dream"
https://www.cs.utexas.edu/users/EWD/transcriptions/EWD12xx/E...
https://www.cs.utexas.edu/users/EWD/transcriptions/EWD12xx/E...
Everything I learn about Leibniz I continue to be impressed. How many other geniuses are we ignoring in the present?
leibniz' project always reminded me of word2vec
ada lovelace was warned off poetry because her mom hated her dad, and pushed into science, and so she developed 'poetical science' aka general computing. (she was also inspired by embroidery card technology I think)
ada lovelace was warned off poetry because her mom hated her dad, and pushed into science, and so she developed 'poetical science' aka general computing. (she was also inspired by embroidery card technology I think)
Whenever the world seems "known", one must pull back the covers and fin a more bizarre harder to explain version. It wouldn't surprise me in the least that it turns out our entire universe is just an Amoeba.
I kept assembling points I wanted to make in the comments, and then the article would cover them itself, so I'll just quote it:
> He imagined that this machine, which he called “the great instrument of reason,” would be able to answer all questions and resolve all intellectual debate. “When there are disputes among persons,” he wrote, “we can simply say, ‘Let us calculate,’ and without further ado, see who is right.”
> But as today’s data scientists devise ever-better algorithms for natural language processing, they’re having debates that echo the ideas of Leibniz and Swift: Even if you can create a formal system to generate human-seeming language, can you give it the ability to understand what it’s saying?
This is the important part. Having the naivete to assume that a flawed mechanical system represents the whole of Truth, is worse than having no system at all.
> He imagined that this machine, which he called “the great instrument of reason,” would be able to answer all questions and resolve all intellectual debate. “When there are disputes among persons,” he wrote, “we can simply say, ‘Let us calculate,’ and without further ado, see who is right.”
> But as today’s data scientists devise ever-better algorithms for natural language processing, they’re having debates that echo the ideas of Leibniz and Swift: Even if you can create a formal system to generate human-seeming language, can you give it the ability to understand what it’s saying?
This is the important part. Having the naivete to assume that a flawed mechanical system represents the whole of Truth, is worse than having no system at all.
> flawed mechanical system
I don't like what "mechanical" is implying here, it gives the impression that humans have weird magic in their head that makes them understand language or search for truth (whatever approximate version they like anyway).
It's just a flawed system, period. Your brain circuits are a flawed system, and the artifacts produced by the data science craze are flawed. They are not flawed equally, but they are all physical infromation processing systems trying to make sense of the weird jumble of signals coming to it from Outside.
I don't like what "mechanical" is implying here, it gives the impression that humans have weird magic in their head that makes them understand language or search for truth (whatever approximate version they like anyway).
It's just a flawed system, period. Your brain circuits are a flawed system, and the artifacts produced by the data science craze are flawed. They are not flawed equally, but they are all physical infromation processing systems trying to make sense of the weird jumble of signals coming to it from Outside.
The problem comes with rigidity and certainty. Using a flawed system with the acknowledgement that it's flawed is well and good. But "mechanical" components like hard data and logic often give the illusion of being flawless and true in some absolute way. That doesn't make them useless, but it means you have to work extra hard to keep in mind the fact that they are and always will be imperfect.
Humans have a bit of irrationality that is based on their different POVs and experience. So the magic system is just that we have dynamic value systems. Shared culture through interconnected internet is making this less of a problem as the dynamic range is getting smaller or narrow enough to categorize
> Your brain circuits are a flawed system
What a roundabout way to admit limitation both in knowledge and tools to investigate them. Except this one is more sinister because it almost closes the curtain on approaching this natural order (of brain circuitry) with both humility and curiosity.
What a roundabout way to admit limitation both in knowledge and tools to investigate them. Except this one is more sinister because it almost closes the curtain on approaching this natural order (of brain circuitry) with both humility and curiosity.
>What a roundabout way to admit limitation both in knowledge and tools to investigate them.
Why? I view humans (and all biological beings really) as machines, fantastic contraptions of unimaginable complexity that push the materials they are made of to the absoulute limits. Their brains are the pattern-matching subsystem responsible for Command, Control and Communcications. Maybe expressing limitations in terms of circuits is roundabout to you, but it's perfectly natural for me.
>it almost closes the curtain on approaching this natural order (of brain circuitry) with both humility and curiosity
Again, why? is it because "Circuits" somehow imply rigidity or fixity ? that's not true at all, plenty of circuits can change their structure while they're operating. And even fixed circuits can be so complex and of so many signal paths that they seem to have a mind of their own, especially in a dynamic changing enviroment.
I don't know about humility*, but the two grandfathers of neural networks, McCulloch and Pitts, were both very curious about the brain, and they used ideas from logic and cybernetics to study it. The Nobel-prize-winning Hodgkin–Huxley model is another framework that looks at the activity inside a neuron in circuit-theoritic terms such as capacitors and current sources.
* : That said, "All of your views and opinions are the product of a few billion capacitors wired together" seems to me like a pretty humble way to go through life.
Why? I view humans (and all biological beings really) as machines, fantastic contraptions of unimaginable complexity that push the materials they are made of to the absoulute limits. Their brains are the pattern-matching subsystem responsible for Command, Control and Communcications. Maybe expressing limitations in terms of circuits is roundabout to you, but it's perfectly natural for me.
>it almost closes the curtain on approaching this natural order (of brain circuitry) with both humility and curiosity
Again, why? is it because "Circuits" somehow imply rigidity or fixity ? that's not true at all, plenty of circuits can change their structure while they're operating. And even fixed circuits can be so complex and of so many signal paths that they seem to have a mind of their own, especially in a dynamic changing enviroment.
I don't know about humility*, but the two grandfathers of neural networks, McCulloch and Pitts, were both very curious about the brain, and they used ideas from logic and cybernetics to study it. The Nobel-prize-winning Hodgkin–Huxley model is another framework that looks at the activity inside a neuron in circuit-theoritic terms such as capacitors and current sources.
* : That said, "All of your views and opinions are the product of a few billion capacitors wired together" seems to me like a pretty humble way to go through life.
> Having the naivete
Regulative ideals do not constitute a claim of achieved solution. Approximation of an ideal result is already an achievement.
Regulative ideals do not constitute a claim of achieved solution. Approximation of an ideal result is already an achievement.
I can't wait for Apple TV to make a Leibniz biopic series as they did with Asimov's Foundation.
It would be so interesting watching her developing Calculus, thanks to her sightseeing powers while working for the emperor.
It would be so interesting watching her developing Calculus, thanks to her sightseeing powers while working for the emperor.
Maybe they'll just pick up the rights to Stephenson's Baroque Cycle
It’s amazing that no one has done this yet.
Just get Johnny Depp to play Jack Shaftoe.
Just get Johnny Depp to play Jack Shaftoe.
If Snow Crash ever makes it out of development hell, I think it becomes more likely
But would Johnny Depp still be willing to reprise his role of syphillitic Jack?
https://publicdomainreview.org/essay/let-us-calculate-leibni...
https://en.wikipedia.org/wiki/Ramon_Llull