jessicata

Ah, I was confused by statements such as the following:

Now, imagine if all of those developments were instead compressed into the decade after 1925.

Now imagine all the scientific, intellectual and technological developments that you would expect to see by the year 2125, if technological progress continued over the next century at roughly the same rate that it did over the last century. And then imagine all of those developments occurring over the course of just ten years.

Have edited it to one about training scale-ups. "The biggest training runs can continue to scale for roughly another 10,000x increase before running into power and other limits (likely well within a decade from now)..."

Replying to2025 in AI predictions

End of 2024

Replying toFixed Buckets Can't (Phenomenally) Bind

Fixed Buckets Can't (Phenomenally) Bind

Re pagerank: This looks a lot like eigenvalues / eigenvectors, which show up a bunch in physics. (Eigenvector with high eigenvalue is like a "self-ratifying / stable generalized state".)

Quantum mechanics involves topology of course. In operator algebra theory (Gelfand duality). And in TQFT. However the article seems to be making a leap relating quantum topology to minds and phenomenal binding. This is skipping many levels of abstraction!

I will now summarize a quantum topology approach, relevant to observers, which is not skipping nearly as many abstraction levels. We start by a quantum operator space as a C* algebra. This algebra is in general non-commutative. However, it has commutative sub-algebras. (Sub-algebra here is similar... (read 439 more words →)

Replying toUnderstanding complex conjugates in quantum mechanics

Understanding complex conjugates in quantum mechanics

To disambiguate terminology: By "dual space" I mean the standard meaning in QM; we go from a complex vector space V to a space $V^{\lor}$ of linear maps $V \to C$ , with the bra/ket duality as a special case. Perhaps I should avoid using "dual" but this explains my earlier usage.

By "complex conjugate space" (sometimes abbreviated as "conjugate space") I mean specifically the $¯ ¯¯ ¯ V$ construction, a completely formal mathematical operation. (To avoid confusion I could say "complex conjugate space")

Since "complex conjugate space" is an entirely formal construction, it doesn't necessarily have a physical meaning. Or it could have multiple physical meanings as different isos with V.

OP doesn't try to go lower-level than Hilbert space;... (read more)

Replying toUnderstanding complex conjugates in quantum mechanics

Understanding complex conjugates in quantum mechanics

In terms of goals of OP, I was taking standard QM notation at face value, and trying to peel back one layer of the onion: why antilinear-linear inner product, POVM observables as Hermitians implying quadratic forms, quadratic density matrices, etc? And I think real structure + conjugate spaces basically explains these dualities in the Hilbert space standard formulation, although that doesn't mean this is the deepest symmetry layer (it's not).

field strength tensor

This is not an area I understand well, but, either the field values are expressed as a real number or complex number. If real: OP framework doesn't apply, or applies at a lower level; perhaps applies indirectly through CPT. If complex:... (read 429 more words →)

Replying toUnderstanding complex conjugates in quantum mechanics

Understanding complex conjugates in quantum mechanics

The bilinear form is from the inner product. The inner product is generally defined as 'antilinear in first argument, linear in second'. If replacing the first argument with complex conjugate space, it is now 'linear in first argument, linear in second argument', i.e. bilinear. This is of course for a single Hilbert space (and its complex conjugate). When having multiple Hilbert spaces tensored together, the 'tensor product of Hilbert spaces' yields an inner product for that tensored space. That is implicitly multilinear, although decomposes as usual for tensor product, into multiple bilinearities.

Understanding complex conjugates in quantum mechanics

1mo

Why does quantum mechanics use complex numbers extensively? Why is the inner product of a Hilbert space antilinear in the first argument? Why are Hermitian operators important for representing observables? And what is the i in the Schrödinger equation doing? This post explores these questions through the framework of groupoid representation theory. While this post assumes basic familiarity with complex vector spaces and quantum notation, it does not require much pre-existing conceptual understanding of QM.

Roughly, there are two kinds of complex numbers in physics. One is a phasor: something that has a phase. The other is a scalar: a unitless number representing a combined scale factor and phase-translation. Scalars act on phasors... (read 3545 more words →)

Replying to2025 in AI predictions

Here's an evalution claiming it isn't even true at Anthropic in terms of lines of code (I haven't checked independently)
The kind of thing I don't want to count is that, for example, it would be easy to write a script that generates many many lines of code. It's just not interesting to count "how are most lines of code written" globally. "Code actually merged at particular big tech companies" is much closer and I expect that was less than 90 percent at the time.

Replying to2025 in AI predictions

Ah sorry. Edited.

Replying to2025 in AI predictions

With 10K lines it's not impressive to write 10K lines. I'm thinking of writing software that would be 10K lines if done by humans.
"bug-free" & "reliably" is a high bar!

Inverting qualia with group theory

1mo

Past years: 2023 2024

Continuing a yearly tradition, I evaluate AI predictions from past years, and collect a convenience sample of AI predictions made this year. I prefer selecting specific predictions, especially ones made about the near term, enabling faster evaluation.

Evaluated predictions made about 2025 in 2023, 2024, or 2025 mostly overestimate AI capabilities advances, although there's of course a selection effect (people making notable predictions about the near-term are more likely to believe AI will be impressive near-term).

As time goes on, "AGI" becomes a less useful term, so operationalizing predictions is especially important. In terms of predictions made in 2025, there is a significant cluster of people predicting very large AI effects by 2030.... (read 3002 more words →)

242

Matrices map between biproducts

3mo

David Chalmers describes the inverted qualia thought experiment, in The Conscious Mind, as an argument against logical supervenience of phenomenal experience on physical states:

one can coherently imagine a physically identical world in which conscious experiences are inverted, or (at the local level) imagine a being physically identical to me but with inverted conscious experiences. One might imagine, for example, that where I have a red experience, my inverted twin has a blue experience, and vice versa. Of course he will call his blue experiences "red," but that is irrelevant. What matters is that the experience he has of the things we both call "red"---blood, fire engines, and so on---is of the same

... (read 2136 more words →)

Homomorphically encrypted consciousness and its implications

3mo

Why are linear functions between finite-dimensional vector spaces representable by matrices? And why does matrix multiplication compose the corresponding linear maps? There's geometric intuition for this, e.g. presented by 3Blue1Brown. I will alternatively present a category-theoretic analysis. The short version is that, in the category of vector spaces and linear maps, products are also coproducts (hence biproducts); and in categories with biproducts, maps between biproducts decompose as (generalized) matrices. These generalized matrices align with traditional numeric matrices and matrix multiplication in the category of vector spaces. The category-theoretic lens reveals matrices as an elegant abstraction, contra The New Yorker.

I'll use a standard notion of a vector space over the field $R$ . A vector... (read 1398 more words →)

A philosophical kernel: biting analytic bullets

4mo

I present a step-by-step argument in philosophy of mind. The main conclusion is that it is probably possible for conscious homomorphically encrypted digital minds to exist. This has surprising implications: it demonstrates a case where "mind exceeds physics" (epistemically), which implies the disjunction "mind exceeds reality" or "reality exceeds physics". The main new parts of the discussion consist of (a) an argument that, if digital computers are conscious, so are homomorphically encrypted versions of them (steps 7-9); (b) speculation on the ontological consequences of homomorphically encrypted consciousness, in the form of a trilemma (steps 10-11).

Step 1. Physics

Let P be the set of possible physics states of the universe, according to "the true... (read 3386 more words →)

Measuring intelligence and reverse-engineering goals

6mo

Sometimes, a philosophy debate has two basic positions, call them A and B. A matches a lot of people's intuitions, but is hard to make realistic. B is initially unintuitive (sometimes radically so), perhaps feeling "empty", but has a basic realism to it. There might be third positions that claim something like, "A and B are both kind of right".

Here I would say B is the more bullet-biting position. Free will vs. determinism is a classic example: hard determinism is biting the bullet. One interesting thing is that free will believers (including compatibilists) will invent a variety of different theories to explain or justify free will; no one theory seems clearly best. Meanwhile, hard... (read 3767 more words →)

Towards plausible moral naturalism

6mo

It is analytically useful to define intelligence in the context of AGI. One intuitive notion is epistemology: an agent's intelligence is how good its epistemology is, how good it is at knowing things and making correct guesses. But "intelligence" in AGI theory often means more than epistemology. An intelligent agent is supposed to be good at achieving some goal, not just knowing a lot of things.

So how could we define intelligent agency? Marcus Hutter's universal intelligence measures an agent's ability to achieve observable reward across a distribution of environments; AIXI maximizes this measure. Testing across a distribution makes sense for avoiding penalizing "unlucky" agents who fail in the real world, but use effective strategies... (read 2532 more words →)

Generalizing zombie arguments

7mo

In "Generalizing zombie arguments", I hinted at the idea of applying a Chalmers-like framework to morality. Here I develop this idea further.

Suppose we are working in an axiomatic system rich enough to express physics and physical facts. Can this system include moral facts as well? Perhaps moral statements such as "homicide is never morally permissible" can be translated into the axiomatic system or an extension of it.

It would be difficult to argue that a realistic axiomatic system must be able to express moral statements. So I'll bracket the alternative possibility: Perhaps moral claims do not translate into well-formed statements in the theory at all. This would be a type of moral non-realism,... (read 2469 more words →)

The Weighted Perplexity Benchmark: Tokenizer-Normalized Evaluation for Language Model Comparison

7mo

Chalmers' zombie argument, best presented in The Conscious Mind, concerns the ontological status of phenomenal consciousness in relation to physics. Here I'll present a somewhat more general analysis framework based on the zombie argument.

Assume some notion of the physical trajectory of the universe. This would consist of "states" and "physical entities" distributed somehow, e.g. in spacetime. I don't want to bake in too many restrictive notions of space or time, e.g. I don't want to rule out relativity theory or quantum mechanics. In any case, there should be some notion of future states proceeding from previous states. This procession can be deterministic or stochastic; stochastic would mean "truly random" dynamics.

There is a decision... (read 1884 more words →)