Posted by bookofjoe 6 hours ago
The AI was of course trained on existing pre-AI transcriptions of Goedel's shorthand, which he was taught in school around 1920 and which was widespread and only technically "obsolete".
In the second paragraph, we have what appears to be a claim that the model knows how to read Gödel's shorthand because it has been exposed to past examples of that shorthand. What is your point here? I think the model learning to generalize by training on a few examples is a point in its favor.
Ergo all defined axiomatic systems have sentences about the far past and future that cannot be defined in those languages with certainty. Most do not make the connection to physics. Gödel did and would 100% aware the limits exist and will always exist
Scaling laws aren't just for computers; humans cultures do not scale infinitely through time, just approximately 2-3 generations
As I understand immutable physical truth like this played a huge role in his early research and ultimately were the forcing function that led him to incompleteness
This is often misunderstood or misstated to mean that there are some things that are unknowable or unable to be solved. (I'm not saying that's what you were implying, I am referring to the common way I see his theorem being represented)
But what he really proved is that no single sufficiently powerful, consistent, effectively specified formal system can prove every arithmetic truth.
He didn't prove that there are mathematical truths that are unsolvable through any possible extension or alternative framework. It's just that one framework isn't enough to solve all problems.
Scaling issues do not just matter when making bridges and when hosting LLMs.
Back in Gödel's day physicists were like rockstars and all Gödel's output was 100% influenced by Einstein and the rest. Given the group's expertise in the domain the implicitly forever incomplete/never computed did not need to be spelled out explicitly.
Do better.
> On his return to Helsinki he began the process, showing Claude his transcriptions of the workbooks, as well as six books he had previously written on Gödel and other secondary scientific literature.
> “In a couple of days, I got to see a 650-page explanation of the workbooks. It had to be controlled page for page, but it’s basically a work that is impossible to do for human beings,” he said. “Humans read one page at a time and we tend to forget things. It takes us a year to read about 50 pages. We just are not able to keep in mind all the different parts.
> “The AI can connect all the pieces in a thousand pages. It can see all of Gödel’s writings as one piece.”