I am pretty sure that my understanding of something (or lack of) is not encoded into words and probabilities. It's more like a feeling of "I got this figured out" or "I haven't grasped this".
Words seem more like a protocol to express some internal model/state in the brain and can never capture the entire actual state, only a small part of it. But since we're not telepaths, we obviously need to use words to exchange information.
If brains aren't a complex probability machine, how is it possible that people get the same sort of math problems right and wrong in an inconsistent manner? Or mis-speak?
It is undeniable that human reasoning is a stochastic process. Otherwise it wouldn't be reasonable for people to make mistakes after learning something. Especially inconsistent mistakes, like when we give people 10,000 addition problems to do in a row it'd be reasonable for them to get a few of them wrong.
> It is undeniable that human reasoning is a stochastic process
It can still be a deterministic process. If anything came out of the whole LLM story for me it is that I am even more convinced that it is.
My (somewhat educated, but still naive) idea why it looks like a stochastic process is that the brain gets incredible amounts of random input. We literally get bombarded with particles and energy ever instance we live, from photons hitting out retinas , molecules transferring "heat" energy into our skin to sound waves hitting our ear drums.
Ever noticed that you get more productive when you get up from your screen? Or how some people work better while listening to music? How you find your answer just as you start to explain it to a colleague?
I would argue that this is due to a limited "entropy" pool available to the brain. Just changing the input to the system replenishes the pool.
Are you saying this because quantum mechanics is random in some interpretations and is our most fundamental theory?
That’s a bit of a stretch when we don’t actually know if QM is objectively random, but it could be sure. But then what about things like, is it random that 1+1=2. No…what are you really saying is random when a human answers this? I think even if you make the assumption QM is objectively random, thought is the hard problem after all and we might not want to jump so far head. Math certainly isn’t random and we can think about it.
Food for thought: randomness is in the eye of the beholder. It’s only random to you if you don’t know how to predict it. So can a mind ever truly be stochastic? Perhaps to the minds of others, but never to itself.
Brains are complex probability machines but doesn’t work only on language. It interacts with and learns from the environment, sets its own objective functions and tries to learn better.
Sounds very much like {Matilde Marcolli, Noam Chomsky, Robert Berwick}’s brand new paper on the mathematics of Syntactic Merge [0]:
workspace :: nested forests of binary trees of syntactic structures (with no label order) (= here, thoughts and meanings are assumed to be composites of mental syntax objects that can be re-combined with others. Big assumption? Maybe)
externalization process :: some mental faculty that decides the order to use when outputting thoughts into ordered strings (eg vocalization of thoughts into sentences)
The thing is, you can put a probability theory onto anything that you can count or record states of. Of course, counting the external observations may lack the richness of the internal process. I feel that this linguistic program will work its way into a lot of future LM tooling, in some incarnation or another.
That human thought can't exist without language has been proposed by many great thinkers in the past. Someone who studies linguistics (or philosophy?) can probably cite examples.
As a crude anecdote, certain words when I learned them allowed me to think differently. Gestalt is one of those words.
Words seem more like a protocol to express some internal model/state in the brain and can never capture the entire actual state, only a small part of it. But since we're not telepaths, we obviously need to use words to exchange information.