> I'm pretty sure you have misunderstood what he was talking about in terms of what sparsey does

That is quite possible.

> It's pretty clear what you meant, to be honest.

What I meant was exactly what I said: evaluating Sparsey makes a good exercise. I believe it is bogus, but I could be wrong. I am basing my judgement on very sparse (no pun intended) data.

> I'll let him comment on what you guys were talking about

Here are the relevant quotes from our correspondence:

Gerard: I just watched your 2011 "Quantum Conspiracy.." talk and thought you might be interested in an idea I've had concerning quantum theory and how information is represented. The core idea is briefly described in my 2012 paper. "Quantum Computation via Sparse Distributed Representation". I have to related Medium articles as well, "Quantum Computing in the Offing" and "Not Copenhagen, not Everett, a New Interpretation of Quantum Reality". The essential idea is this. To my knowledge, in all quantum theory (QT) and quantum computing (QC) models published to date, prob. amplitudes (PAs) are represented in localist fashion. That is, each PA is represented in its own physically unique memory location (e.g., 64-bits, 32 for real, 32 for imag.) that is physically disjoint from every other PA. In principal, the number of PAs needed to describe a system is of exponential order, so a localist representation requires exponential memory. BUT, if instead, PAs are represented as sparse distributed representations (SDRs), i.e., small subsets of binary units chosen from a much larger field, then they can all exist (be physically stored) in physical (and classical superposition): each PA is just a different subset of the units and the subsets can overlap. Thus, the exponential number of PAs can be represented in sub-exponential (polynomial) memory, Basically, we're leveraging a third fundamental resource, "code space", which is formally orthogonal to the other two, time and (physical) space (i.e., amount of memory). That is, the code space of an SDR coding field is of combinatorial (exponential) order.

Me: Thanks for bringing this intriguing work to my attention. You say "the exponential number of PAs can be represented in sub-exponential (polynomial) memory”. This makes it sound as if you claiming that SDRs allow you to achieve quantum supremacy in a classical machine. Am I reading you correctly? Because if that’s what you’re claiming, then you are almost certainly wrong. Since you don’t seem like a quack, it seems more likely that I’m just misinterpreting what you’re saying, so I thought I should get that cleared up before going any further.

Gerard: Actually, you are interpreting correctly and thank you for being open to the possibility that I'm not a quack :) [Lots of details about Sparsey elided.]

Me: OK, but in the interests of full disclosure you should know that my Bayesian prior on this [not being a quack] is still not very high :-) So let me ask you another “top-level filter” type question: can Sparsey run Schor’s algorithm? If so, have you done it?

Gerard: No I've never tried to run Shor's algorithm. [Lots more details elided.] What d'ya think?

Me: I think you should try to run Shor’s algorithm, because if you succeed that will be a slam-dunk proof that your claims are correct.

Gerard: Well, I don't really understand Shor's algorithm (from wikipedia). I'd have to study it. I never really have so far.

I never responded to that because at that point I was pretty convinced he was a quack. It's possible I'm wrong about that. But I'm very confident that he doesn't understand quantum supremacy, and that his claims about it are wrong.