LESSWRONG
LW

All of Aidan Rocke's Comments + Replies

Revisiting the Manifold Hypothesis
Aidan Rocke30

Thank you for sharing this. 👌

Reply
Revisiting the Manifold Hypothesis
Aidan Rocke10

Regarding your remark on finding low-dimensional representations, I have added a section on physical intuitions for the challenge. Here I explain how the prime recognition problem corresponds to reliably finding a low-dimensional representation of high-dimensional data. 

Reply
Revisiting the Manifold Hypothesis
Aidan Rocke50

The best physicists on Earth, including Edward Witten and Alain Connes, believe that the distribution of primes and Arithmetic Geometry encode mathematical secrets that are of fundamental importance to mathematical physics. This is why the Langlands program and the Riemann Hypothesis are of great interest to mathematical physicists.

If number theory, besides being of fundamental importance to modern cryptography, allows us to develop a deep understanding of the source code of the Universe then I believe that such advances are a critical part of human intelligence, and would be highly unlikely if the human brain had a different architecture.

Reply1
2Nathaniel Monson
I agree with your entire first paragraph. It doesn't seem to me that you have addressed my question though. You are claiming that this hypothesis "implies that machine learning alone is not a complete path to human-level intelligence." I disagree. If I try to design an ML model which can identify primes, is it fair for me to give it some information equivalent to the definition (no more information than a human who has never heard of prime numbers has)? If you allow that it is fair for me to do so, I think I can probably design an ML model which will do this. If you do not allow this, then I don't think this hypothesis has any bearing on whether ML alone is "a complete path to human-level intelligence." (Unless you have a way of showing that humans who have never received any sensory data other than a sequence of "number:(prime/composite)label" pairs would do well on this.)
Revisiting the Manifold Hypothesis
Aidan Rocke10

Thank you for bringing up these points: 

  1. Riemann's analysis back then was far from trivial and there were important gaps in his derivation of the explicit formulas for Prime Counting. What appears obvious now was far from obvious then.  
  2. I just appended a summary of Yang-Hui He's experiments on the Prime Recognition problem. 

Either way, I believe that additional experiments may be enlightening as the applied mathematics that mathematicians do is only true to the extent that it has verifiable consequences. 

Reply
2Mitchell_Porter
This might interest you: a language model is used to develop a model of inflation (expansion in the early universe), using a Kolmogorov-like principle (minimum description length). 
Aidan Rocke10

Feel free to reach me via email. However, I must note that Sasha and myself are currently oriented towards existing projects of the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation.

If your research proposal may be formulated from the vantage point of that research program, that would improve the odds of a collaboration in the medium term.

Reply
Kolmogorov's theory of Algorithmic Probability
Aidan Rocke10

I agree. I don't think he had to attempt to address this problem, if it may be addressed at all. 

He has since taken into account the work of experimentalists doing related work, that validates his thesis of Quantum Theory essentially predicting what an observer will see next: 

Reply