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Principia Mathematica is modern and insightful

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Re: Principia Mathematica is modern and insightful

#81

Post by d4rkp4ttern »

An interesting fact I learned while reading The Dream Machine[1], is that Principia was the basis of Newell, Simon and Shaw’s Logic Theorist (1956), considered to be the “first AI program”. Amusing and amazing to see this in the context of today’s Erdos-slaying LLMs.

Quoting from Wikipedia:

https://en.wikipedia.org/wiki/Logic_Theorist

Logic Theorist is a computer program completed in 1956 by Allen Newell, Herbert A. Simon, and Cliff Shaw.[1] It was the first program deliberately engineered to perform automated reasoning, and has been described as "the first artificial intelligence program".[1][a] Logic Theorist proved 38 of the first 52 theorems in chapter two of Whitehead and Bertrand Russell's Principia Mathematica, and found a new and shorter proof for Theorem 2.85.[3]

[1] https://press.stripe.com/the-dream-machine

Re: Principia Mathematica is modern and insightful

#82

Post by makerdiety »

bulbar wrote: post #49
makerdiety wrote: post #43

So... the ancient childish attempt to prove mathematics using mathematics (Gödel's Incompleteness slew the challenger) can be used to help me be a better TypeScript programmer? I learned something new today.

Why the belittling language? You actually can prove the completeness and consistency of portions of mathematics. While axioms were known in ancient times, only Hilbert started the whole "prove Mathematics" thing. How else would you prove mathematics and why would that be childish to use math? The limitations discovered were quite surprising back then.

Yikes, guys/girls. I got downvoted to -4 points for a misunderstanding or something. Because the author of the website would probably agree with my simple point that although the Principia Mathematica tried to do the impossible, there is still utility for its value as a programming self-teaching resource for serious students of computer science.

Wow. Yeah. You guys ironically didn't just throw out the baby with the bath water thing. You burned me at the stake like a witch for heresy. Due to your cognitive biases and distortions.

You guys are Imperium of Mankind coded or something?

Re: Principia Mathematica is modern and insightful

#84

Post by vixen99 »

futune wrote: post #76
laichzeit0 wrote: post #53

Earlier quoted context omitted.

Two thoughts on someone who went out of their way to learn math: 1. If you can already program, the worst thing you can do is think of mathematics as learning a programming language. It is not, and you will waste your time being frustrated with things like syntax and notation. You get “used to” mathematics by doing it, and it’s something on its own. Just go with it. It’s ok to be confused. 2. Do the exercises, and st…

I think your latter comment is kind of analogous to people writing python (or any high-level language) without understanding assembly. I think maybe that reduces the mystery a bit?

I'm guessing that that's a lot of people you have in mind.

Re: Principia Mathematica is modern and insightful

#85

Post by karmakurtisaani »

blipvert wrote: post #61
karmakurtisaani wrote: post #56

Earlier quoted context omitted.

> the current version is 3.141592653 Another instance of a "clever" joke that becomes annoying very fast.

I suppose that to make it slightly less tedious we could just refer to the version using the number of significant digits: 10

Denote the version with a simple integer? Now that's thinking outside the box!

Re: Principia Mathematica is modern and insightful

#86

Post by WillAdams »

futune wrote: post #76
laichzeit0 wrote: post #53

Earlier quoted context omitted.

Two thoughts on someone who went out of their way to learn math: 1. If you can already program, the worst thing you can do is think of mathematics as learning a programming language. It is not, and you will waste your time being frustrated with things like syntax and notation. You get “used to” mathematics by doing it, and it’s something on its own. Just go with it. It’s ok to be confused. 2. Do the exercises, and st…

I think your latter comment is kind of analogous to people writing python (or any high-level language) without understanding assembly. I think maybe that reduces the mystery a bit?

The antidote for that of course is for folks to read Charles Petzold's _Code_:

https://www.goodreads.com/book/show/44882.Code

Re: Principia Mathematica is modern and insightful

#87

Post by rramadass »

eru wrote: post #41
rramadass wrote: post #37

Earlier quoted context omitted.

Well said. Thanks for calling out these sort of posers and charlatans on HN. We should not tolerate these people if we are to discuss/argue/motivate interesting/hard subjects productively. I automatically discount anybody on HN (until i have looked at their profile/comment history/any personal bio websites etc.) who claim they have read/studied a) Euclid's Elements b) Newton's Principia c) Maxwell's Treatise on Elect…

Einstein's 1905 Annus Mirabilis papers seem like they easiest of the bunch to just read through. I just pulled up 'Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen', the one about Brownian motion, and read the whole thing. It's only 12 pages and fairly accessible; more prose than equations. (Of course, if you don't read German, you should…

My point is that each of the material above (and i forgot to add the original Quantum Mechanics papers) were major watershed moments in science/mathematics and hence are not easy to read/understand. You need a good background in the subject matter(and mathematics) and/or somebody guiding you through them.

So what i do is try and find books which are written for the "educated common reader" by an expert who guides you through the original paper/book. It is still difficult to understand if you do not have the necessary background but at least you have a good starting point.

Some books in my collection;

1) Newton's Principia for the Common Reader by S.Chandrasekhar

2) Maxwell on the Electromagnetic Field: A Guided Study (Masterworks of Discovery) by Thomas Simpson

3) Einstein's Miraculous Year by John Stachel.

4) The Annotated Turing by Charles Petzold.

What we need is for a group of professors to get together and start writing a series on explaining the original papers to the "educated common reader" i.e. not too trivial nor too overwhelming. I think there is a huge market for this since it humanizes how science is done in real life which is fundamental for motivation.

Re: Principia Mathematica is modern and insightful

#88

Post by firmretention »

laichzeit0 wrote: post #53
data_maan wrote: post #50

It always amazes me how a random dump of someone who read the first 40 pages of PM attracts dozens comments on HN. This really must be a very math-starved community of people who wanted to learn math but never quite could.

Two thoughts on someone who went out of their way to learn math: 1. If you can already program, the worst thing you can do is think of mathematics as learning a programming language. It is not, and you will waste your time being frustrated with things like syntax and notation. You get “used to” mathematics by doing it, and it’s something on its own. Just go with it. It’s ok to be confused. 2. Do the exercises, and st…

>Again, I think this is a programmer centric way of looking at things: “how do I know it’s right if I can’t compile it”.

I would argue this would only be true for those without formal education. Writing your code on paper is very common in CS courses. You get used to not being able to compile it.

Re: Principia Mathematica is modern and insightful

#89

Post by [deleted] »

my-next-account wrote: post #68
derrida wrote: post #19

Earlier quoted context omitted.

LLMs giving some people way too much confidence to conceptually shoot from the hip hehe - “effort to refute bullshit is order of magnitude more than to refute it”.

Derrida, go back to your grave, you messed up the quote!

[deleted]

Re: Principia Mathematica is modern and insightful

#90

Post by jhbadger »

igravious wrote: post #62
hasley wrote: post #55

Earlier quoted context omitted.

Of you prefer an even more entertaining approach and a very gentle introduction into the topic, I recommend the comic "Logicomix" which tells Russel's journey (though not historically correct all the time for story telling reasons). https://en.wikipedia.org/wiki/Logicomix

Logicomix is novel, and done well, but flawed … it's deficiencies lie in what it leaves out which may come across as an unfair charge but in this case the charge is warranted. There is a more historically correct and less orthodox work waiting in the wings for whosoever should attempt it.

It's also a bit weird how it makes ahistorical meetings for "drama" -- e.g. Russell and Frege never met in real life -- why show that they did (they do mention this never happened in their notes, but why write such a scene at all?)
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