Questions

Things I want to learn more about

David Deutsch made a questions page on his blog in 2000, so I thought of doing the same. If you know any of the answers, or could guide me to interesting reading material, please email me at malhar.manek@gmail.com and earn my eternal gratitude. I will keep updating this page over time.

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AI for Math and Science Research

It seems to me that AI will tremendously accelerate math research. Math is a highly formal, verifiable system (like chess or Go, but with a much larger combinatorial search space) and seems perfect for RL to work its magic. So I would not be surprised if, by [insert-time-frame-depending-on-how-AGI-pilled-you-are], there is an order of magnitude increase in the number of new theorems proved per unit time. Some questions pertaining to this:

1. Suppose we get to the point where models run for long times (kind of like the computer in The Hitchhiker’s Guide to the Galaxy that runs for millions of years and outputs “42”) and prove new theorems in math — how valuable would this be, and in what way? Suppose an order of magnitude more theorems are proved per year than current levels. How exactly will this impact the world? Will it just be a vast collection of arcane, abstruse math theorems, or will some of them find applications in say physics or computer science?

2. Will the companies that create these AI-enabled-math-research-juggernauts even publish the most profound theorems, or keep them private? Will math research remain a collaborative endeavour (as it is today, with human mathematicians who publish their results for others to build upon) or become a competitive one?

Note: I really enjoyed reading this vision by Math Inc.

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Deep Tech and Manufacturing

1. From a first-principles standpoint, multi-junction solar cells seem like the obvious successor to monoPERC and TOPCon for breaking past the Shockley-Queisser limit on the efficiency of a single-layer solar cell (~33%). Yet they remain a niche, space-only technology. Why is this? Why aren’t multi-junction solar cells, which have far greater efficiency, more widely produced and used?

2. If every computational task reducible to an unstructured search or optimization problem becomes quadratically faster (Grover’s algorithm in quantum computing), what are the economic effects? Forget implementation of Shor’s which would create whole new categories of value, just sqrt(n) speed up by Grover’s algo would sharply reduce logistics and supply chain costs for physical manufactured goods, causing a deflationary supply shock: what are the percolation effects of this in the economy? How much would GDP be impacted by a square-root speedup in every relevant algorithm?

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Intelligence and Espionage

1. In his essay series on Situational Awareness, Leopold Aschenbrenner writes:

   There’s a lot of low-hanging fruit on security at AI labs. Merely adopting best practices from, say, secretive hedge funds or Google-customer-data-level security, would put us in a much better position with respect to ‘regular’ economic espionage from the CCP. Indeed, there are notable examples of private sector firms doing remarkably well at preserving secrets. Take quantitative trading firms (the Jane Streets of the world) for example. A number of people have told me that in an hour of conversation they could relay enough information to a competitor such that their firm’s alpha would go to ~zero — similar to how many key AI algorithmic secrets could be relayed in a short conversation — and yet these firms manage to keep these secrets and retain their edge.

How do private intelligence networks work, from quant hedge funds to big tech? (Any good reading material on private intelligence/corporate espionage - blogs, books, papers, etc.?)

2. It seems like a lot of China’s technology sector — from solar to EVs to batteries — has been built off of US technology. What is the nature of this techno-industrial espionage? How does it work?

3. The textbook Quantum Computation and Quantum Information by Michael Nielsen and Isaac Chuang says:

   Rather remarkably, public key cryptography did not achieve widespread use until the mid-1970s, when it was proposed independently by Whitfield Diffie and Martin Hellman, and by Ralph Merkle, revolutionizing the field of cryptography. A little later, Ronald Rivest, Adi Shamir, and Leonard Adleman developed the RSA cryptosystem, which at the time of writing is the most widely deployed public key cryptosystem, believed to offer a fine balance of security and practical usability. In 1997 it was disclosed that these ideas — public key cryptography, the Diffie–Hellman and RSA cryptosystems — were actually invented in the late 1960s and early 1970s by researchers working at the British intelligence agency GCHQ.

   And Michael Nielsen also writes in his essay Quantum computing for the very curious:

   This ability to break encryption has made the world’s intelligence agencies very interested in factoring, and they’ve poured enormous sums of money into quantum computing research since the mid-1990s. Indeed, there’s a good (as yet unwritten) history book to be written about how the rise of quantum computing was caused by the interest of the world’s intelligence agencies in accessing humanity’s private thoughts.

   This is another example of why I find myself fascinated by intelligence agencies and their workings. What are some other technological innovations that intelligence agencies pioneered but kept classified? I would love to read the book that Nielsen calls “as yet unwritten”!

4. What exactly is open source intelligence? Best resources to learn more about it?

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Miscellaneous

1. There is this interesting bit about Srinivasa Ramanujan and G. H. Hardy in Gödel, Escher, Bach. Hardy writes:

   I remember once going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. “No,” he replied, “it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways.” I asked him, naturally, whether he knew the answer to the corresponding problem for fourth powers; and he replied, after a moment’s thought, that he could see no obvious example, and thought that the first such number must be very large.

   Then Douglas Hofstadter goes on to write:

   It turns out that the answer for fourth powers is: 635318657 = 134 + 1334 = 1584 + 594. The reader may find it interesting to tackle the analogous problem for squares, which is much easier.

   It is actually quite interesting to ponder why it is that Hardy immediately jumped to fourth powers. After all, there are several other reasonably natural generalizations of the equation u^3 + v^3 = x^3 + y^3 along different dimensions.

   For instance, there is the question about representing a number in three distinct ways as a sum of two cubes: r^3 + s^3 = u^3 + v^3 = x^3 + y^3.

   Or, one can use three different cubes: u^3 + v^3 + w^3 = x^3 + y^3 + z^3.

   Or one can even make a Grand Generalization in all dimensions at once: r^4 + s^4 + t^4 = u^4 + v^4 + w^4 = x^4 + y^4 + z^4.

   There is a sense, however, in which Hardy’s generalization is “the most mathematician-like.” Could this sense of mathematical esthetics ever be programmed?

   My question is, why does Hofstadter believe that Hardy’s generalization is “the most mathematician-like”? What makes him think this?

2. What does the future of reading and writing look like in a world with AGI? Is reading and writing books valuable? Will the future Dostoevsky’s and Kafka’s be humans or AIs (or both?) Will the legendary books of the future — the GEBs, the LoTRs — be written by humans or AIs (or both?)

3. There are these ‘trilemmas’ (three-sided dilemma problems) that show up in many fields. For example, interest rates, exchange rates and inflation in monetary theory: you can choose to control any 2 out of the 3, and the third will be a consequence. Similarly, the CAP theorem in data science says that a distributed data store can simultaneously provide only 2 out of the following 3 guarantees: consistency, availability and partition tolerance. There is also the bandwidth-error-power trade-off in information theory. Is this genre of trilemma theorems simply an interesting coincidence or is there more to it (e.g., does it imply something about the dimensionality of our world/the ‘Fabric of Reality’?)

4. What if we take the multiverse seriously? What would be some non-trivial implications of subscribing to the multiverse interpretation?

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Other People’s Questions

I also want to echo some questions that other people have posed, that I find interesting to think about.

1. Dwarkesh Patel asks -

   What real world impact should we expect from the current batch of AI for math projects? What are the fields of technology where people are going, “Ah we could totally solve quantum computing (or fusion or AGI) only if we had more theorems!” But maybe problems in biology and physics and materials and so on reduce down to math in a way I’m not foreseeing, and automating formal math alone is enough to unlock a bunch of progress.

2. Luke Gromen asks -

   A macro question that is not being asked yet:
   
   “How much were gold prices capped historically by the expansion of credit (unallocated paper) gold?”
   
   Many opining on the gold/oil ratio (GoR), but few seem to be asking if GoR would've been far higher had credit gold not capped GoR.

“I would rather have questions that can’t be answered than answers that can’t be questioned.” — Richard Feynman