if, then

June 17, 2024 1:59 PM

George Boole tried to "create a calculus to reduce all logical syllogisms, deductions, and inferences to the manipulation of mathematical symbols, and to cast a precise foundation for the theory of probability. This resulted in his greatest work: An Investigation of the Laws of Thought, [on which are founded the Mathematical Theories of Logic and Probabilities. (Gutenberg, pdf)] a book that laid out the rules of his new symbolic logic and also outlined, in the opening chapter, his grand intention to capture, with mathematics, the language of that ghost that whispers within the tortuous pathways of our minds." [Harper’s]
posted by HearHere (24 comments total)

George Boole, midway through the 19th century, for anyone curious about the missing subject of the first sentence.
posted by Pickman's Next Top Model at 2:47 PM on June 17 [10 favorites]

"He subjected these statements to logical analysis, by replacing them with symbols, and combined them in different ways, through mathematical operations, till all he had left was a result that, according to his system, was categorically true: absolute evil does not exist and pain is an instrument of good."

Gödelian incompleteness is simultaneously a kink and a kind of kink-shaming and I will be taking no questions at this time.
posted by mhoye at 3:04 PM on June 17 [22 favorites]

absolute evil does not exist and pain is an instrument of good

Boolraiser: We have such sights to show you
posted by Jon Mitchell at 3:08 PM on June 17 [18 favorites]

All computers (well terneray chips are really rare) does all this clevers stuff in buffers that apply boolean operations to build up addition, words, all math/all software/3D/web, everything. All just AND, OR, NOT. Fancy chips may hide helper functions but underneath AND,OR,NOT. Boole knew.

One book I had once could reduce AND & OR to a clever sequence of NOT's. Or claimed, way beyond me.

So in a sense, all computing is NOT, repeated like a quark or string.

(mebe)
posted by sammyo at 3:32 PM on June 17 [4 favorites]

Almost certainly a clever sequence of either NANDs or NORs, which are themselves each functionally complete. NOT doesn't work that way (it's a 1-input, 1-output gate that just flips the incoming bit), you can't compose them to get anything other than either the input (2 NOTs in a row) or its negation (1 NOT, obviously).
posted by axiom at 3:52 PM on June 17 [17 favorites]

If the idea presented here interests you but the thought of reading 300 pages of it dissuades you, I found Ideas That Created the Future a good guided tour through the front half of CS history. It always surprises me that the idea for neural networks predates Turing's computers, to the point where he cites them as inspiration for his own work.

Unfortunately as alluded to above, Gödel kinda blew a hole in Boole's goal that all questions of morality can be reduced to logic and computed perfectly, by demonstrating that any such system either systems can't prove all true statements, or proves false ones. Of course, there's plenty more reasons why it was impractical, but we did at least get a decent notation system for Shannon to expand upon when formalizing the modern computer.
posted by pwnguin at 3:52 PM on June 17 [5 favorites]

For a visceral experience of building an entire computer from fundamental logic gates, there is the NAND game. The gestalt-switching from "this is a circuit" to "this object is computing" happens at a different place for me each time I have gone through it — probably three times over about six years.
posted by fantabulous timewaster at 5:04 PM on June 17 [11 favorites]

“undecidability simply means that the axioms do not force the truth value of the proposition” is a Quora comment which best addresses the Boolean intersection with Gödel, imo. yet, if that topic interests anyone further, there are other threads previously. a good adjacent resource is Gödel’s Theorem: An Incomplete Guide to Its Use and Abuse [American Mathematical Society, 4 page pdf] reviewed by Panu Raatikainen.

please also feel no need to read Boole’s linked primary source! the FPP just seemed incomplete otherwise. the FA in the second link is much more current & succinct.

thanks for the game, fantabulous timewaster
posted by HearHere at 6:12 PM on June 17 [1 favorite]

I've been programming for 35 years and did not know that the data type bool was named after the guy who invented the YES/NO logic that all computers use to do work. The connection with his great-great-grandson and the creation of AI is like something out of a Neal Stephenson novel.
posted by jabah at 8:39 PM on June 17 [2 favorites]

pain is an instrument of good

to be fair this is an appropriate description of bit-shift trickery
posted by They sucked his brains out! at 9:52 PM on June 17 [4 favorites]

Mod note: Edited to add Boole's name to the post
posted by taz (staff) at 12:27 AM on June 18 [1 favorite]

AND. .
posted by HearHere at 1:18 AM on June 18

Essay on the life and marriage of George and Mary [Everest] Boole. Alicia was the mathiest of their 5 daughters.
posted by BobTheScientist at 1:21 AM on June 18 [1 favorite]

The Harper's article linked is written by Benjamin Labatut, who is an interesting writer.

Highly recommend When We Cease to Understand the World (Link to Guardian review) and I'm anxious to read his new book which is described by Wikipedia as:

"a fictionalised biography of the polymath John von Neumann. The book was published in 2023 and received mostly positive reviews. It is centered on the life of von Neumann, though the first part of the book is about physicist Paul Ehrenfest, and the last one is about Lee Sedol's Go match against DeepMind's artificial intelligence program AlphaGo."
posted by vacapinta at 1:49 AM on June 18 [2 favorites]

vacapinta, thank you, the title of the first chapter of When We Cease to Understand the World [gbooks] reminded me of cancer-curing possibilities of Prussian blue nanoparticles [Journal of Materials Chemistry B; National Library of Medicine]

BobtheScientist, Alicia’s work neatly builds on Jamnitzer’s (recently & previously) thank you
posted by HearHere at 2:30 AM on June 18 [1 favorite]

the axioms do not force the truth value of the proposition

is as good a description as any of that property of a symbolic system that allows it to be about something.

A work of similar ambition to Laws of Thought, though lesser known and much less well received, is George Spencer-Brown's Laws of Form (full text PDF; Philosophy Forum discussion; Wikipedia). It's a good read despite (and sometimes even because of) the distinct whiff of mania. If Boole is plain brown bread and Gene Ray is a one-note Carolina Reaper, Spencer-Brown is a really good peri peri.
posted by flabdablet at 2:34 AM on June 18 [2 favorites]

logical/"formal"/inorganic paradoxes tend to resolve, in organic studies like D'arcy Thompson's On Growth & Form [Gutenberg]
posted by HearHere at 3:00 AM on June 18 [2 favorites]

Oh that NandGame thing is cool. Back in the late 70s I was gifted a "logic" trainer of a sort which consisted of a series of multi-pole, 2-throw switches (the inputs) that you'd wire up to get the desired logic functionality. It was a very clunky way to simulate and teach gates and logic. NandGame blows it away.
posted by Artful Codger at 7:35 AM on June 18 [1 favorite]

My digital computation and boolean math classes at MIT were amongst my favorites. Just to see how you can go from something do damn simple to something complex in the course of a few Ands, Ors, Nots.
posted by drewbage1847 at 9:29 AM on June 18 [1 favorite]

I got grar with the NAND Game for giving me two relays to make my first NAND gate - the first relay implementing AND, and the second inverting the output of the first - and then telling me that an inverter built out of a whole NAND gate was optimal, as was an AND gate made by using one of those bloated inverters to undo the effect of the inverting relay inside another NAND. That's four relays to do the job of one! Optimal my fat arse.

Removing the low level tools from my toolbox just because I've successfully made some higher level ones is bullshit.
posted by flabdablet at 3:54 PM on June 18 [1 favorite]

Oh that NandGame thing is cool.

It is, I just played it again last night when reminded by this post. I must have lost interest at some point the previous time, because when I "finshed" it in a few hours, I discovered there's a whole second page of software puzzles. Now it's got me programming in a weird assembly code. It's really fun for now, but I suspect when it starts to get hard and seem like more of a job, I'm probably going to give up.
posted by ctmf at 4:55 PM on June 18 [2 favorites]

For a visceral experience of building an entire computer from fundamental logic gates, there is the NAND game.

It's too bad Flash is dead, or you could go one layer deeper! Per a contemporary review:

The key to designing successful circuits is understanding how NPN and PNP gates work.
posted by pwnguin at 8:24 PM on June 18 [1 favorite]

Along the lines of NandGame, if you haven't watched Ben Eater's series where he builds an 8-bit computer on breadboards it's a treat. He starts from component logic, then graduates to chips when the time comes, similar to NandGame.
posted by ctmf at 9:53 PM on June 18 [2 favorites]

I got grar with the NAND Game for giving me two relays to make my first NAND gate - the first relay implementing AND, and the second inverting the output of the first - and then telling me that an inverter built out of a whole NAND gate was optimal, as was an AND gate made by using one of those bloated inverters to undo the effect of the inverting relay inside another NAND. That's four relays to do the job of one! Optimal my fat arse.

Their scoring of optimal is pretty shallow - it only counts using the pallette of objects provided at that stage.

I had no trouble solving the early stages, but my solution wasn't always optimal, so it was fun to try to get to the minimal correct solution. All the stuff I've forgotten...
posted by Artful Codger at 8:21 AM on June 19 [1 favorite]