I think it's a lot more interesting to look for practical markers of simulation than do a teleological thought experiment.
How would a simulated universe differ from a "real" one? How would the simulation cut corners to save resources? Maybe the laws of physics are designed not just to produce interesting results, but also to be efficient to run.
Karl Friston and Steven Wolfram are sniffing around here, with cellular automata and free energy describing ways of partitioning space so it's cheaper to update
The art of rhetoric and human communication involves knowing your audience, and when using idioms and metaphors, you choose those which are shared in common to be immediately recognizable and impactful.
When I was 19, I had a psychologist who employed a lot of baseball idioms. "We'll touch base next week..." and although I am not a baseball fan, my father is, and we're all Americans, and so the baseball references were well-understood by his audience of one.
When an LLM starts going off about a "tractable beachhead" that behavior indicates that it's unaware of its audience, and also ignorant of how to put together a human idiom. That's exciting that emergent behavior is coining new idioms that may be applicable to some situation, and also explainable by dudes on Hacker News, but that wasn't the point of the comment.
The point is that the LLM's audience wasn't a veteran of D-Day in WWII, and even with an understanding of what those words mean individually, neither he nor I recognized "tractable beachhead" as a meaningful idiom for speakers of standard English.
> That's exciting that emergent behavior is coining new idioms that may be applicable to some situation
I dunno, it feels pretty similar to an elementary student blindly swapping words with a thesaurus to increase the sophistication of their writing (which I readily admit I was guilty of doing once). It sounds more intelligent but lacks substance.
FWIW as a humanities nerd, “tractable beachhead” packs a lot of nuanced meaning into two words. It’s probably not the right vocabulary choice for most audiences, but it isn’t empty or arbitrary.
Tractable = you can make it work, but it’s not going to take care of itself, you have to get your hands around it
Beachhead = you’re on a mission, you’re trying to probe to find the right way in to get started to eventually accomplish the whole thing, but first you have to find a little spot to get situated and then expand from there.
It does, but in the same way that LLMs take two paragraphs to make a one-sentence point: by being weirdly specific and also redundant. LLMs don’t have a sense of whimsy in the face of RLHF, so if it’s proposing a solution, the solution is tractable. All implementation plans start with a beachhead.
“A good starting point” is almost certainly all it needed to convey and what it should have written.
This kind of nuance is very suited to a mother tongue and I would probably like it in French, but as a non-native speaker who uses english mainly for professional or hobby stuff, claude-speak is becoming a bit off-putting.
My only exposure to english literature comes from the Brontë sisters at this moment in time.
Thanks. This is the first time I encounter the word "beachhead", and googling a bit made me indeed saw something related to an invasion. But I was so annoyed by the claudeisms that I closed the tab and just asked it to rephrase instead of trying to make another step towards its vocabulary.
It's an indicator of AI progress. The solutions aren't especially revolutionary, but no person had been able to solve them after decades of collective attempts.
To be fair I don’t think there were too many people really trying to. Symbolically, one could make a parameterization of the Jacobian determinant and then brute force a solution, if one had known such a polynomial existed in only three dimensions.
This is not true at all. The parameter space is absolutely MASSIVE. The counterexample is a degree 7 polynomial in 3 variables, which means 360 coefficients. There's no particular way to bound these coefficients or even the degree or number of variables apriori, but assume you somehow did. Also assume you were confident that it would work with integer coefficients bounded from -12 to 12. Now you have to iterate over 360 degrees of freedom, verify that the Jacobian is a nonzero constant, and somehow show uninvertibility of the transformation, which is not a particularly simple task.
If you searched for coefficients from -12 to 12, this would be 25^360 = 2 * 10^503 different possibilities. A common reference point is that there are 10^80 atoms in the observable universe. Sure you could probably reduce this a bit with clever tricks, but the starting point makes the method completely unviable, even with the knowledge: A) a counterexample exists, B) it's in 3 variables, C) it's in degree 7 or less, D) it's in integer coefficients, E) those coefficients are 12 or lower.
Here the search wouldn't have been chosing the coefficients independently. Note that one intermediate variable is a polynomial in the input variables, and it is used in other polynomials. A search over expressions like the ones in the counterexample would have a much smaller search space.
No, I’m not saying you would know in advance that it was possible, but sometimes you visit the crystal cave and the diamond is just sitting there, so why not work out the odds?
I learned from poking around that checking the invertibility of a system in C is a much, much harder problem than I thought. Nonetheless if that were no object, let’s say coefficients from -16 to 15 (5 bits) times eight terms times choosing up to cubes (64) times three equations is searchable, especially since you have only the final combination of coefficients in the determinant. It’s not impossible to generate the equations like this Fizzbuzz style.
Edit: no. 2048 possible monomials, to the 24th power, not times 24. Fine, can’t brute force it.
If I pull out the two terms 1+xy and 3 + 4xy as new variables, then make three polynomials that are <= 3 terms in each with coefficients in the range -3 to 3, then there are something like 10^19 possibilities. Multiply this by the various simple possibilities for the definitions of those two new variables.
The coefficients are mostly 1, so biasing toward that would make it much faster.
Oh yes there were. The Jacobian conjecture is "notorious for the large number of published and unpublished false proofs which turned out to contain subtle errors."
It's not quite the Reimann hypothesis, but many prominent mathematicians have spent years working on this problem. Yitang Zhang wrote his PhD thesis on it.
That’s the counterexample. Low integer coefficients, power 7 in three variables. If someone said it was there, couldn’t we all have written a pretty simple brute force solution for the search space, especially with the constraints that the symbolic determinant had to cancel to a constant?
I don't think you even understand the problem. The determinant needs to be a non-zero constant AND you need to prove that particular map is not globally injective, meaning you have to find at least two points mapping to the same value. Of course it looks easy when someone shows you the counterexample.
Small social sites are just as dangerous in another way, as vessels for a toxic monoculture. Pro-anorexia forums, political radicalization, there was even a famous one that fetishized infecting people with HIV.
To add, a lot of the most infamous Internet subcultures, with the worst effects on the "real world" (think incels, /pol/ types, mass shooters) have their own forums or hang out on places like 4chan/8chan. Where there's no big tech corporation or finely tuned engagement algorithm. Just broken people finding a place where they can reinforce each other.
I think specific, but not archaic. The written word can be beautiful like any other form of art - it's not only about transmitting information but transmitting emotion. Sorta like a photograph, painting, or song.
Yes, as other's have pointed, its just really hard to write well, I have thought that books are just an inefficient medium, but once I started reading more broadly, outside of computer topics, I discovered that engineers are just horrible writers.
Yes, I think so. When you read a book you spend a long time with the ideas it contains. You think about the book when you go about your day: primed by what you're reading, you see new connections. You are in conversation with the book. Maybe parts of the book seep into your dreams. Years later, you might remember what you were doing when you read a particular passage.
Much of this is because reading a book takes time.
I think because good writing is easier to read and understand than bad writing, there's almost an inverse relationship between how easy writing seems and how easy it is to read. So you read something and think "well, this is obvious" but the magic trick is how much work went in to making it so.
Absolutely. One of the major purposes of art is as a way to communicate things that can not be put into words. And if that's the case, how could one ever hope to create it with a prompt?
How would a simulated universe differ from a "real" one? How would the simulation cut corners to save resources? Maybe the laws of physics are designed not just to produce interesting results, but also to be efficient to run.
Karl Friston and Steven Wolfram are sniffing around here, with cellular automata and free energy describing ways of partitioning space so it's cheaper to update