The intersting thing is that today's NLP has nothing to do with the manipulation of symbols, as such. Rather, NLP is performed (lately) by neural networks, that learn to optimise the parameters of continuous functions. NLP is possible in this way because by construction, the parameters of the functions to be optimised are associated to the elements of natural language (characters, mostly, but sometimes words). So an NLP "machine" nowadays means a machine that can predict the next character (or word) in a sequence.

Leibniz's ideas on the other hand, of combining symbols to generate and evaluate human language, that's the spirit that permeates Good, Old-Fashioned AI, symbolic, and logic-based artificial intelligence. Today, most NLP researchers would say that the logic-based branch of research, common as it was until very recently, was after all a dead end that did not lead anywhere. It would be interesting to be able to know what Leibniz would have made of that.

Perhaps one day (in the far distant future, when my bones are dust and my memories lost) we'll be able to reproduce the great philosopher's thoughts from his writings and reconstruct his personality, in part or in whole. And then we could pose to him the question: "Master, what do you think of the machine that now houses your intellect"?

It is amusing to imagine the neural network mind growing advanced enough to realize that to help it level up in clarity of thought and communication, it needs to develop a system of automatic symbolic logic...

There are binary/discrete neural networks. :-)

Well, the original artificial neuron by Pitts and McCulloch was a propositional logic circuit- but that strain of research, too, has fallen by the wayside in favour of neural nets that can be trained with backpropagation of error.

One can train binary NN via backprop by using qbits. Samples are taken, and backprop can be done as if the result was X% 1 and (1-X)% 0. It can be noisy and slow but it is a way to do it.

Where do Leibniz's Monads fit into all of this? (Of course, the answer is probably "not at all").

Description of his interest in mechanized reasoning generally ignores the other half of his proposed project, which was to create a database of propositions for the machine to operate on. His idea was along the lines of Doug Lenat's Cyc, to represent all of human knowledge in propositional form. As I recall, in his grant proposal to the French court, he estimated that it would take a small group of clerks about 5 years to complete the job. The French didn't express any interest.

With the early start of 350 years, we could probably have a sizeable compendium going on by now. After all, much of human knowledge only began to be created at that time.

Maybe mathematical notation would also be established earlier―after the clerks would get tired of spelling it out.

Leibniz: 'What a watch is to time, this engine is to thought.'

Daniel Waterhouse: 'Sir! You show me a few gears that add and multiply numbers – well enough. But this is not the same as thought !'

'What is a number, Mr. Waterhouse?'

Daniel groaned. 'How can you ask such questions?'

'How can you not ask them, sir? You are a philosopher, are you not?'

'A Natural Philosopher.'

'Then you must agree that in the modern world, mathematicks is at the heart of Natural Philosophy – it is like the mysterious essence in the core of the snowflake. When I was fifteen years old, Mr. Waterhouse, I was wandering in the Rosenthal – which is a garden on the edge of Leipzig – when I decided that in order to be a Natural Philosopher I would have to put aside the old doctrine of substantial forms and instead rely upon Mechanism to explain the world. This led me inevitably to mathematicks.'

'When I was fifteen, I was handing out Phanatiqual libels just down the street from here, and dodging the Watch – but in time, Doctor, as Newton and I studied Descartes at Cambridge, I came to share your view concerning the supreme position of mathematics.'

'Then I repeat my question: What is a number? And what is it to multiply two numbers?'

'Whatever it is, Doctor, it is different from thinking .'

'Bacon said, ‘Whatever has sufficient differences, perceptible by the sense, is in nature competent to express cogitations.' You cannot deny that numbers are in that sense competent – '

'To express cogitation, yes! But to express cogitations is not to perform them, or else quills and printing-presses would write poetry by themselves.'

'Can your mind manipulate this spoon directly?' Leibniz said, holding up a silver spoon, and then setting it down on the table between them.

'Not without my hands.'

'So, when you think about the spoon, is your mind manipulating the spoon?'

'No. The spoon is unaffected, no matter what I think about it.'

'Because our minds cannot manipulate physical objects – cup, saucer, spoon – instead they manipulate symbols of them, which are stored in the mind.'

'I will accept that.'

'Now, you yourself helped Lord Chester devise the Philosophical Language, whose chief virtue is that it assigns all things in the world positions in certain tables – positions that can be encoded by numbers.'

'Again, I agree that numbers can express cogitations, through a sort of encryption. But performing cogitations is another matter entirely!'

'Why? We add, subtract, and multiply numbers.'

'Suppose the number three represents a chicken, and the number twelve the Rings of Saturn – what then is three times twelve?'

'Well, you can't just do it at random, ' Leibniz said, 'any more than Euclid could draw lines and circles at random, and come up with theorems. There has to be a formal system of rules, according to which the numbers are combined.'

'And you propose building a machine to do this?'

'Pourquoi non? With the aid of a machine, truth can be grasped as if pictured on paper.'

-- Quicksilver, Baroque Cycle (#1), Neal Stephenson

For any fans of the Baroque Cycle and Cryptonomicon, I can strongly recommend Fall; or, Dodge in Hell.

I'm currently reading Fall; or, Dodge in Hell as my first Neal Stephenson book. I will say the plot summary doesn't do it justice. Regarding the setting the in mid-point of the story, with the split between reality-based social media feed individuals and fear/meme-based feed populations - I went from an initial reaction of "that could never happen" to a feeling of a realization "that is already happening". Especially as I was listening to the audiobook while on a long drive through a semi-rural part of the state to visit relatives who would definitely fall into the latter category.

The audiobook version of the Baroque Cycle is also extremely good - quite long though (mind you I've listened to it all at least 3 times).

He missed a great opportunity when he didn't name it Merkistan, home of the Merkans.

There's a great line by the character of Nicola Tesla in The Prestige. "Man's reach exceeds his grasp, and his grasp exceeds his nerve"

People like Leibniz, Babbage and others could imagine and reason about computers, though it was impossible for to even guess at the consequences of them. But things have not changed. Today we can similarly forsee things far beyond our lives, planetary colonization, star travel, uploading brains, etc. But though we can see them, it is similarly impossible to forsee the consequences of these developments. Which is great. The future would be a very boring place otherwise.

Modern logic and set theory meets some of the requirements of this. At the time, he did not have for-all, exists, and so on. Leibnitz himself created some proofs with the limited logic of his day. Nowadays much more can be done. It's not as all-encompassing, but it is a step forward.

I'm getting a 418 for this page (Firefox and Chrome). First time I encountered this :-).

I'm a teapot? That's what 418 is.

Interesting, at what point do we let AI contribute new words to the lexicon, Shakespeare managed 15...

I thought it was a misconception that Shakespeare added so much new words - him being a prolific and very popular writer, and with much of his corpus surviving to this day, his works get cited whenever there's a "first use" mentioned somewhere.

The fact that one of his plays is the oldest written source where a word was seen for the first time in written form doesn't mean that it wasn't in common use before that; indeed it could mean the opposite – because the spectators of his plays should be able to understand what the characters are speaking, not leave befuddled in need of translation.

Sure, it's contentious, what's not contentious is that our lexicon grows over time, how would an AI go about inventing a new word?

The same ways we do: by scissors-and paste with parts of other words. Most if our English words are small alterations of proto-indo-european words.

We have the idea of infinity. It'll take awhile for a machine to calculate that idea.

Calculemus!

artificial language school