AI May Be Discovering Kurt Gödel Just as Einstein and von Neumann Did
March 17, 2025
This blog post is the work of a humanoid dino baby. If you don’t know what a dinobaby is, you are not missing anything.
AI re-thinking is becoming more widespread. I published a snippet of an essay about AI and its impact in socialist societies on March 10, 2025. I noticed “A Bear Case: My Predictions Regarding AI Progress.” The write is interesting, and I think it represents thinking which is becoming more prevalent among individuals who have racked up what I call AI mileage.
The main theme of the write up is a modern day application of Kurt Gödel’s annoying incompleteness theorem. I am no mathematician like my great uncle Vladimir Arnold, who worked for year with the somewhat quirky Dr. Kolmogorov. (Family tip: Going winter camping with Dr. Kolmogorov wizard was not a good idea unless. Well, you know…)
The main idea is a formal axiomatic system satisfying certain technical conditions cannot decide the truth value of all statements about natural numbers. In a nutshell, a set cannot contain itself. Smart software is not able to go outside of its training boundaries as far as I know.
Back to the essay, the author points out that AI something useful:
There will be a ton of innovative applications of Deep Learning, perhaps chiefly in the field of biotech, see GPT-4b and Evo 2. Those are, I must stress, human-made innovative applications of the paradigm of automated continuous program search. Not AI models autonomously producing innovations.
The essay does contain a question I found interesting:
Because what else are they [AI companies and developers] to do? If they admit to themselves they’re not closing their fingers around godhood after all, what will they have left?
Let me offer several general thoughts. I admit that I am not able to answer the question, but some ideas crossed my mind when I was thinking about the sporty Kolmogorov, my uncle’s advice about camping in the winter, and this essay:
- Something else will come along. There is a myth that technology progresses. I think technology is like the fictional tribble on Star Trek. The products and services are destined to produce more products and services. Like the Santa Fe Institute crowd, order emerges. Will the next big thing be AI? Probably AI will be in the DNA of the next big thing. So one answer to the question is, “Something will emerge.” Money will flow and the next big thing cycle begins again.
- The innovators and the AI companies will pivot. This is a fancy way of saying, “Try to come up with something else.” Even in the age of monopolies and oligopolies, change is relentless. Some of the changes will be recognized as the next big thing or at least the thing a person can do to survive. Does this mean Sam AI-Man will manage the robots at the local McDonald’s? Probably not, but he will come up with something.
- The AI hot pot will cool. Life will regress to the mean or a behavior that is not hell bent on becoming a super human like the guy who gets transfusions from his kid, the wonky “have my baby” thinking of a couple of high profile technologist, or the money lust of some 25 year old financial geniuses on Wall Street. A digitized organization man man living out the theory of the leisure class will return. (Tip: Buy a dark grey suit. Lose the T shirt.)
As an 80 year old dinobaby, I find the angst of AI interesting. If Kurt Gödel were alive, he might agree to comment, “Sonny, you can’t get outside the set.” My uncle would probably say, “Those costs. Are they crazy?”
Stephen E Arnold, March 17, 2025
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