Max H

Most of my posts and comments are about AI and alignment. Posts I'm most proud of, which also provide a good introduction to my worldview:

I also created Forum Karma, and wrote a longer self-introduction here.

PMs and private feedback are always welcome.

NOTE: I am not Max Harms, author of Crystal Society. I'd prefer for now that my LW postings not be attached to my full name when people Google me for other reasons, but you can PM me here or on Discord (m4xed) if you want to know who I am.

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My point is that there is a conflict for divergent series though, which is why 1 + 2 + 3 + … = -1/12 is confusing in the first place. People (wrongly) expect the extension of + and = to infinite series to imply stuff about approximations of partial sums and limits even when the series diverges.

My own suggestion for clearing up this confusion is that we should actually use less overloaded / extended notation even for convergent sums, e.g.  seems just as readable as the usual  and  notation.

 In precisely the same sense that we can write


despite that no real-world process of "addition" involving infinitely many terms may be performed in a finite number of steps, we can write



Well, not precisely. Because the first series converges, there's a whole bunch more we can practically do with the equivalence-assignment in the first series, like using it as an approximation for the sum of any finite number of terms. -1/12 is a terrible approximation for any of the partial sums of the second series.

IMO the use of "=" is actually an abuse of notation by mathematicians in both cases above, but at least an intuitive / forgivable one in the first case because of the usefulness of approximating partial sums. Writing things as  or   (R() denoting Ramanujan summation, which for convergent series is equivalent to taking the limit of partial sums) would make this all less mysterious.

In other words, (1, 2, 3, ...) is in an equivalence class with -1/12, an equivalence class which also contains any finite series which sum to -1/12, convergent infinite series whose limit of partial sums is -1/12, and divergent series whose Ramanujan sum is -1/12.

True, but isn't this almost exactly analogously true for neuron firing speeds? The corresponding period for neurons (10 ms - 1 s) does not generally correspond to the timescale of any useful cognitive work or computation done by the brain.

Yes, which is why you should not be using that metric in the first place.

Well, clock speed is a pretty fundamental parameter in digital circuit design. For a fixed circuit, running it at a 1000x slower clock frequency means an exactly 1000x slowdown. (Real integrated circuits are usually designed to operate in a specific clock frequency range that's not that wide, but in theory you could scale any chip design running at 1 GHz to run at 1 KHz or even lower pretty easily, on a much lower power budget.)

Clock speeds between different chips aren't directly comparable, since architecture and various kinds of parallelism matter too, but it's still good indicator of what kind of regime you're in, e.g. high-powered / actively-cooled datacenter vs. some ultra low power embedded microcontroller.

Another way of looking at it is power density: below ~5 GHz or so (where integrated circuits start to run into fundamental physical limits), there's a pretty direct tradeoff between power consumption and clock speed. 

A modern high-end IC (e.g. a desktop CPU) has a power density on the order of 100 W / cm^2. This is over a tiny thickness; assuming 1 mm you get a 3-D power dissipation of 1000 W / cm^3 for a CPU vs. human brains that dissipate ~10 W / 1000 cm^3 = 0.01 watts / cm^3.

The point of this BOTEC is that there are several orders of magnitude of "headroom" available to run whatever the computation the brain is performing at a much higher power density, which, all else being equal, usually implies a massive serial speed up (because the way you take advantage of higher power densities in IC design is usually by simply cranking up the clock speed, at least until that starts to cause issues and you have to resort to other tricks like parallelism and speculative execution).

The fact that ICs are bumping into fundamental physical limits on clock speed suggests that they are already much closer to the theoretical maximum power densities permitted by physics, at least for silicon-based computing. This further implies that, if and when someone does figure out how to run the actual brain computations that matter in silicon, they will be able to run those computations at many OOM higher power densities (and thus OOM higher serial speeds, by default) pretty easily, since biological brains are very very far from any kind of fundamental limit on power density. I think the clock speed <-> neuron firing speed analogy is a good way of way of summarizing this whole chain of inference.

Will you still be saying this if future neural networks are running on specialized hardware that, much like the brain, can only execute forward or backward passes of a particular network architecture? I think talking about FLOP/s in this setting makes a lot of sense, because we know the capabilities of neural networks are closely linked to how much training and inference compute they use, but maybe you see some problem with this also?

I think energy and power consumption are the safest and most rigorous way to compare and bound the amount of computation that AIs are doing vs. humans.  (This unfortunately implies a pretty strict upper bound, since we have several billion existence proofs that ~20 W is more than sufficient for lethally powerful cognition at runtime, at least once you've invested enough energy in the training process.)

The clock speed of a GPU is indeed meaningful: there is a clock inside the GPU that provides some signal that's periodic at a frequency of ~ 1 GHz. However, the corresponding period of ~ 1 nanosecond does not correspond to the timescale of any useful computations done by the GPU.

True, but isn't this almost exactly analogously true for neuron firing speeds? The corresponding period for neurons (10 ms - 1 s) does not generally correspond to the timescale of any useful cognitive work or computation done by the brain.

The human brain is estimated to do the computational equivalent of around 1e15 FLOP/s.

"Computational equivalence" here seems pretty fraught as an analogy, perhaps more so than the clock speed <-> neuron firing speed analogy.

In the context of digital circuits, FLOP/s is a measure of an outward-facing performance characteristic of a system or component: a chip that can do 1 million FLOP/s means that every second it can take 2 million floats as input, perform some arithmetic operation on them (pairwise) and return 1 million results.

(Whether the "arithmetic operations" are FP64 multiplication or FP8 addition will of course have a big effect on the top-level number you can report in your datasheet or marketing material, but a good benchmark suite will give you detailed breakdowns for each type.)

But even the top-line number is (at least theoretically) a very concrete measure of something that you can actually get out of the system. In contrast, when used in "computational equivalence" estimates of the brain, FLOP/s are (somewhat dubiously, IMO) repurposed as a measure of what the system is doing internally.

So even if the 1e15 "computational equivalence" number is right, AND all of that computation is irreducibly a part of the high-level cognitive algorithm that the brain is carrying out, all that means is that it necessarily takes at least 1e15 FLOP/s to run or simulate a brain at neuron-level fidelity. It doesn't mean that you can't get the same high-level outputs of that brain through some other much more computationally efficient process. 

(Note that "more efficient process" need not be high-level algorithms improvements that look radically different from the original brain-based computation; the efficiencies could come entirely from low-level optimizations such as not running parts of the simulation that won't affect the final output, or running them at lower precision, or with caching, etc.)

Separately, I think your sequential tokens per second calculation actually does show that LLMs are already "thinking" (in some sense) several OOM faster than humans? 50 tokens/sec is about 5 lines of code per second, or 18,000 lines of code per hour. Setting aside quality, that's easily 100x more than the average human developer can usually write (unassisted) in an hour, unless they're writing something very boilerplate or greenfield. 

(The comparison gets even more stark when you consider longer timelines, since an LLM can generate code 24/7 without getting tired: 18,000 lines / hr is ~150 million lines in a year.)

The main issue with current LLMs (which somewhat invalidates this whole comparison) is that they can pretty much only generate boilerplate or greenfield stuff. Generating large volumes of mostly-useless / probably-nonsense boilerplate quickly doesn't necessarily correspond to "thinking faster" than humans, but that's mostly because current LLMs are only barely doing anything that can rightfully be called thinking in the first place.

So I agree with you that the claim that current AIs are  thinking faster than humans is somewhat fraught. However, I think there are multiple strong reasons to expect that future AIs will think much faster than humans, and the clock speed <-> neuron firing analogy is one of them.

I haven't read every word of the 200+ comments across all the posts about this, but has anyone considered how active heat sources in the room could confound / interact with efficiency measurements that are based only on air temperatures? Or be used to make more accurate measurements, using a different (perhaps nonstandard) criterion for efficiency?

Maybe from the perspective of how comfortable you feel, the only thing that matters is air temperature.

But consider an air conditioner that cools a room with a bunch of servers or space heaters in it to an equilibrium temperature of 70° F in a dual-hose setup vs. 72° in a single-hose setup, assuming the power consumption of the air conditioner and heaters is fixed in both cases. Depending on how much energy the heaters themselves are consuming, a small difference in temperature could represent a pretty big difference in the amount of heat energy the air conditioner is actually removing from the room in the different setups.

A related point / consideration: if there are enough active heat sources, I would expect their effect on cooling to dominate the effects from indoor / outdoor temperature difference, infiltration, etc. But even in a well-insulated room with few or no active heat sources, there's still all the furniture and other non-air stuff in the room that has to equilibrate to the air temperature before it stops dissipating some amount of heat into the air. I suspect that this can go on happening for a while after the air temperature has (initially / apparently) equilibrated, but I've never tested it by sticking a giant meat thermometer into my couch cushions or anything like that.

Anecdotally, I've noticed that when I come back from a long absence (e.g. vacation) and turn on my window unit air conditioner for the first time, the air temperature seems to initially drop almost as quickly as it always does, but if I then turn the air conditioner off after a short while, the temperature seems to bounce back to a warmer temperature noticeably more quickly than if I've been home all day, running the air conditioner such that the long-term average air temperature (and thus the core temperature of all my furniture, flooring, etc.) is much lower.

Part of this is that I don't share other people's picture about what AIs will actually look like in the future. This is only a small part of my argument, because my main point is that that we should use analogies much less frequently, rather than switch to different analogies that convey different pictures.

You say it's only a small part of your argument, but to me this difference in outlook feels like a crux. I don't share your views of what the "default picture" probably looks like, but if I did, I would feel somewhat differently about the use of analogies.

For example, I think your "straightforward extrapolation of current trends" is based on observations of current AIs (which are still below human-level in many practical senses), extrapolated to AI systems that are actually smarter and more capable than most or all humans in full generality.

On my own views, the question of what the future looks like is primarily about what the transition looks like between the current state of affairs, in which the state and behavior of most nearby matter and energy is not intelligently controlled or directed, to one in which it is. I don't think extrapolations of current trends are much use in answering such questions, in part because they don't actually make concrete predictions far enough into the future.

For example, you write:

They will be numerous and everywhere, interacting with us constantly, assisting us, working with us, and even providing friendship to hundreds of millions of people. AIs will be evaluated, inspected, and selected by us, and their behavior will be determined directly by our engineering.

I find this sorta-plausible as a very near-term prediction about the next few years, but I think what happens after that is a far more important question. And I can't tell from your description / prediction about the future here which of the following things you believe, if any:

  • No intelligent system (or collection of such systems) will ever have truly large-scale effects on the world (e.g. re-arranging most of the matter and energy in the universe into computronium or hedonium, to whatever extent that is physically possible).
  • Large-scale effects that are orders of magnitude larger or faster than humanity can currently collectively exert are physically impossible or implausible (e.g. that there are diminishing returns to intelligence past human-level, in terms of the ability it confers to manipulate matter and energy quickly and precisely and on large scales).
  • Such effects, if they are physically possible, are likely to be near-universally directed ultimately by a human or group of humans deliberately choosing them.
  • The answer to these kinds of questions is currently too uncertain or unknowable to be worth having a concrete prediction about.

My own view is that you don't need to bring in results or observations of current AIs to take a stab at answering these kinds of questions, and that doing so can often be misleading, by giving a false impression that such answers are backed by empiricism or straightforwardly-valid extrapolation.

My guess is that close examination of disagreements on such topics would be more fruitful for identifying key cruxes likely to be relevant to questions about actually-transformative smarter-than-human AGI, compared to discussions centered around results and observations of current AIs.

I admit that a basic survey of public discourse seems to demonstrate that my own favored approach hasn't actually worked out very well as a mechanism for building shared understanding, and moreover is often frustrating and demoralizing for participants and observers on all sides. But I still think such approaches are better than the alternative of a more narrow focus on current AIs, or on adding "rigor" to analogies that were meant to be more explanatory / pedagogical than argumentative in the first place. In my experience, the end-to-end arguments and worldviews that are built on top of more narrowly-focused / empirical observations and more surface-level "rigorous" theories, are prone to relatively severe streetlight effects, and often lack local validity, precision, and predictive usefulness, just as much or more so than many of the arguments-by-analogy they attempt to refute.

a position of no power and moderate intelligence (where it is now)

Most people are quite happy to give current AIs relatively unrestricted access to sensitive data, APIs, and other powerful levers for effecting far-reaching change in the world. So far, this has actually worked out totally fine! But that's mostly because the AIs aren't (yet) smart enough to make effective use of those levers (for good or ill), let alone be deceptive about it.

To the degree that people don't trust AIs with access to even more powerful levers, it's usually because they fear the AI getting tricked by adversarial humans into misusing those levers (e.g. through prompt injection), not fear that the AI itself will be deliberately tricky.

But we’re not going to deliberately allow such a position unless we can trust it.

One can hope, sure. But what I actually expect is that people will generally give AIs more power and trust as they get more capable, not less.

Is it "inhabiting the other's hypothesis" vs. "finding something to bet on"?

Yeah, sort of. I'm imagining two broad classes of strategy for resolving an intellectual disagreement:

  • Look directly for concrete differences of prediction about the future, in ways that can be suitably operationalized for experimentation or betting. The strength of this method is that it almost-automatically keeps the conversation tethered to reality; the weakness is that it can lead to a streetlight effect of only looking in places where the disagreement can be easily operationalized.
  • Explore the generators of the disagreement in the first place, by looking at existing data and mental models in different ways. The strength of this method is that it enables the exploration of less-easily operationalized areas of disagreement; the weakness is that it can pretty easily degenerate into navel-gazing.

An example of the first bullet is this comment by TurnTrout.

An example of the second would be a dialogue or post exploring how differing beliefs and ways of thinking about human behavior generate different starting views on AI, or lead to different interpretations of the same evidence.

Both strategies can be useful in different places, and I'm not trying to advocate for one over the other. I'm saying specifically that the rationalist practice of applying the machinery of Bayesian updating in as many places as possible (e.g. thinking in terms of likelihood ratios, conditioning on various observations as Bayesian evidence, tracking allocations of probability mass across the whole hypothesis space) works at least as well or better when using the second strategy, compared to applying the practice when using the first strategy. The reason thinking in terms of Bayesian updating works well when using the second strategy is that it can help to pinpoint the area of disagreement and keep the conversation from drifting into navel-gazing, even if it doesn't actually result in any operationalizable differences in prediction.

The Cascading Style Sheets (CSS) language that web pages use for styling HTML is a pretty representative example of surprising Turing Completeness:


Haha. Perhaps higher entities somewhere in the multiverse are emulating human-like agents on ever more exotic and restrictive computing substrates, the way humans do with Doom and Mario Kart.

(Front page of 5-D aliens' version of Hacker News: "I got a reflective / self-aware / qualia-experiencing consciousness running on a recycled first-gen smart toaster".)

Semi-related to the idea of substrate ultimately not mattering too much (and very amusing if you've never seen it): They're Made out of Meat

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