In 17th century, Leibniz dreamed of a machine that could calculate ideas (2019)

https://spectrum.ieee.org/in-the-17th-century-leibniz-dreamed-of-a-machine-that-could-calculate-ideas

152 51 3 years ago

spectrum.ieee.org

Unless a symbol is as fuzzy as the bray of a donkey of Buridan.

Also Newtons method/gradient descent + calculus play a big role in backpropagation/ML (Leibnitz was one of the inventors of calculus).

anthk• 3 years ago

I was about to mention Ramon Llull, but it's there.

sublinear• 3 years ago

Swift’s point was that language is not a formal system that represents human thought, but a messy and ambiguous form of expression.

Yep even the greatest minds are susceptible to false dichotomy. We now have linguistics and computer science, yet some aspects of thought remain forever intractably messy.

divbzero• 3 years ago

The Baroque Cycle contains a fun digression describing the combinatorial logic behind this machine.

chrisbrandow• 3 years ago

I loved that section and wasn’t sure how much livery Stephenson might have been taking. Not much, it seems.

moffkalast• 3 years ago

Newton has left the chat

dwheeler• 3 years ago

Leibniz dreamed that we would be able to completrly determine if some claim was true or not. We can't do that for all claims, but at least in mathematics, we can prove with absolute certainty that some axioms will lead you to other claims. So at least a little piece of his dream is a reality.

dvt3• 3 years ago

Leibnitz followed very closely in the footsteps of the Neoplatonists and he was what you'd call a rationalist's rationalist. He would be later rebuked by Hume (the famous is-ought problem made moral—ought—problems fundamentally distinct from rational—is—problems) and Kant would put the nail in the coffin of the rationalist-empiricist debate in the next century (with his earth-shattering Critique of Pure Reason). And if that wasn't enough, as the logical positivists of the early 20th century were still clinging to some form of mathematical completeness, Gödel proved that the project dreamed up by Leibnitz (and more distantly by Plato) was a dead end, to Wittgenstein’s, Russell’s and many others' dismay. Some things (even true ones!) are simply unprovable.

I love this story as it spans more than 2000 years, and even though the idea itself proved to be untenable, this search gave us the enlightenment, the industrial revolution, the computer age, and beyond.

smokel2• 3 years ago

Hmm. Do I understand your comment correctly in that thoughts should be either rational or not?

I think different kinds of thinking have their applications in different contexts. Gödels theorems are hardly ever relevant to most of mathematics and not in the least to computers (which are finite).

I also doubt that industrialism has anything to do with Leibniz or Hume. That part of history is most likely fuelled by greed for money, not for philosophical thought.

routerl6• 3 years ago

Do I understand your comment correctly in that thoughts should be either rational or not?

You didn't understand correctly. "Rationalist", in the OP, is a historical label which can retrospectively be applied to a specific set of thinkers, who defended specific beliefs, from the 16th to the 18th centuries.

None of them were claiming they were the only people who thought "rationally"; rather, they were mostly claiming that only rational thought could reach truth, and empirical evidence need not factor into it.

In modern parlance, the Rationalists believed that all knowledge would end up being deductive, like math.

Gödels theorems are hardly ever relevant to most of mathematics and not in the least to computers (which are finite).

https://en.m.wikipedia.org/wiki/Halting_problem

I also doubt that industrialism has anything to do with Leibnitz or Hume. That part of history is most likely fuelled by greed for money, not for philosophical thought.

In this time period, the intellectual circles that Leibniz and Hume frequented are exactly the circles that gave rise to modern economics, the ability to measure longitude at sea, the ability to calculate rates of change over time, using steam to power machines, etc. In other words, we're literally talking about all of the intellectual developments that directly led to the industrial revolution.

routerl6• 3 years ago

the project dreamed up by Leibnitz (and more distantly by Plato)

More distant than that. It all comes from Euclid. Who, you know, was actually tremendously successful in that project.

dvt3• 3 years ago

More distant than that. It all comes from Euclid. Who, you know, was actually tremendously successful in that project.

I of course know of his Elements, but is there any evidence that Euclid was an axiomatic reductionist? Was he trying to turn everything into an axiomatic system? I regrettably don't know enough about him and should probably rectify that (any book suggestions?).

thomasjv• 3 years ago

Kurt Gödel was a rationalist. https://plato.stanford.edu/entries/goedel/#GodRat

coldtea4• 3 years ago

and Kant would put the nail in the coffin of the rationalist-empiricist debate in the next century (with his earth-shattering Critique of Pure Reason)

Kant was mostly convincing for himself (to whom he was a great fan of) and Kantians. His arguments were hardly definitive.

Some things (even true ones!) are simply unprovable

Within the context of a system with certain algebraic properties.

routerl6• 3 years ago

Kant was mostly convincing for himself (to whom he was a great fan of) and Kantians

This is shown to be false by the historical record. Kant was, unquestionably, the most influential thinker of his day.

Centuries later, Einstein himself felt that it was necessary to write about how Kant was wrong (given modern physics and general relativity), which shows how convincing and influential Kant's arguments were; there's no point to debunking things no one believes.

You're probably looking at Kant with contemporary eyes, thereby deciding that he's obviously wrong and completely unconvincing. But no one looked at Kant with contemporary eyes until contemporary times, and there's a very long road of extremely important and influential scientists/mathematicians/philosophers replying to Kant; which is how our contemporary perspective came to exist.

> Some things (even true ones!) are simply unprovable
Within the context of a system with certain algebraic properties.

Right, that's what "provable" means. There's no such thing as a proof, outside of formal inferential systems.

myownpetard• 3 years ago

Within the context of a system with certain algebraic properties.

This downplays the importance of the set of systems for which his proof holds and makes it sound like it applies to some obscure branch of mathematics.

It applies to a huge set of important systems, not least of which is any system that is sufficiently expressive as to uniquely identify the natural numbers.

data_maan2• 3 years ago

Within the context of a system with certain algebraic properties.

The algebraic properties are those that formalize arithmetic, so this encompasses almost any reasonable system

Reflecticon• 3 years ago

I love your coherence. Can you recommend a book (if you have read it) that explains in detail what you have summarized?

dvt3• 3 years ago

If you want all the details, I can recommend a philosophy degree :P

johndhi2• 3 years ago

What do we dream of now?

I've been reading 70s and 80s sci Fi and loving all of the ideas of the future they had. I don't see them today but I don't know what to read.

gpderetta• 3 years ago

I think cyberpunk was pretty spot on?

johndhi2• 3 years ago

That's the 90s though, right? What about now?

WillAdams5• 3 years ago

Mastering biological processes so that we can ensure that there is enough food for everyone (of a reasonable variety)[1] and that maybe the plants can do well and clean up our environment and make it nicer to live in?[2] Maybe to achieve long enough human lifespans that we can think of interstellar travel?[3]

1 - Hal Clements _Space Lash_, short story "Raindrop"

2 - L.E. Modesitt, Jr's The Forever Hero trilogy (as well as the "The Mechanic" from Space Lash)

3 - Poul Anderson's _The Boat of a Million Years_

climb_stealth• 3 years ago

I'd say Ian M. Banks Culture series [0]. Arguably also written in the 90ies but it draws a bit more of a positive picture. I'd love to live in an environment like that.

[0] https://en.m.wikipedia.org/wiki/Culture_series

cubefox2• 3 years ago

(2019)

Note that this article precedes both ChatGPT and GPT-3. When it was written, Leibniz' idea of a machine reasoning by manipulating symbols was still science fiction. Now it is very much reality.

mensetmanusman2• 3 years ago

Are the billions of parameters all symbols, or are you referencing math manipulation as symbol manipulation?

cubefox2• 3 years ago

Both the inputs and outputs are symbols: text.

WillAdams5• 3 years ago

Does ChatGPT actually manipulate symbols, or does it string together strings of characters based on what most frequently occurs next? I haven't seen anything that indicates actual working w/ symbols/logic/ideas.

gberger• 3 years ago

"string together strings of characters" = "manipulate symbols", no?

kangalioo• 3 years ago

s/frequently/likely

(Large language models are not plain Markov chains, contrary to popular belief)

emmelaich• 3 years ago

Related: Dijkstra's "Under the spell of Leibniz's Dream"

https://www.cs.utexas.edu/users/EWD/transcriptions/EWD12xx/E...

K0balt• 3 years ago

I wonder how his vector math was? Because it sounds like he had the conceptual underpinnings of the altar we’ve all been praying at lately.

It’s really humbling how a fundamentally simple algorithm interpreting a ridiculously complex and vast data set is capable of a simulacrum of thought.

That data set, of course, is the formalisation of human culture, taken from our works. It begs the question of whether our fundamental algorithm for parsing that data is really that much different. We cannot think without tokens, symbols.

We can be, and we can feel, but we cannot think without them. So, where is the intelligence, really? Is it in our heads, or in the data?

Is the data the computation, like an unfathomably vast choose-your-own-adventure book, or is the computation the data, like a one time pad decryption algorithm that creates a universe simulator from the chaotic arrangement of atoms in a beach full of sand?

Is this really “artificial” intelligence, at all? Or just the steam engine of human intellect?

routerl6• 3 years ago

I wonder how his vector math was?

He was born around the same time as the invention of analytical geometry (i.e. the idea that it is possible to do geometry using algebra), and "vector math" (or linear algebra) came several decades later.

So, his vector math was non-existent.

wrp• 3 years ago

Leibniz was envisioning something like Douglas Lenat's Cyc project. In his grant proposal to the French court, his first intended stage was to reduce all of human knowledge to propositional form. He estimated it would take about 5 years given a small clerical staff and a good library.

082349872349872• 3 years ago

I sometimes wonder if Turing picked factorial as the example in his 1949 "Checking a Large Routine"[0] purely at hazard, or possibly as an homage to Leibniz, who was fond of them[1]?

[0] https://turingarchive.kings.cam.ac.uk/publications-lectures-...

[1] see "Dissertatio de arte combinatoria...", 1666 https://ia800906.us.archive.org/BookReader/BookReaderImages....

personlurking• 3 years ago

https://news.ycombinator.com/item?id=21448983 (2019, 25 comments)

https://news.ycombinator.com/item?id=29210099 (2021, 50 comments)

In 17th century, Leibniz dreamed of a machine that could calculate ideas (2019)

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