Max H

Karma: 2,428

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.

Max H Feb 18, 2024, 6:09 PM
20 points
23
on: Intuition for 1 + 2 + 3 + … = −1/12
In precisely the same sense that we can write
$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \dots = 2$ ,
despite that no real-world process of “addition” involving infinitely many terms may be performed in a finite number of steps, we can write
$1 + 2 + 3 + 4 + \dots = - \frac{1}{12}$ .
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 $(1, 2, 3, . . .) \sim - \frac{1}{12}$ or $R ((1, 2, 3, . . .)) = - \frac{1}{12}$ (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.

Max H Jan 30, 2024, 3:41 PM
8 points
4
in reply to: Ege Erdil’s comment on: Processor clock speeds are not how fast AIs think
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.)

Max H Jan 30, 2024, 3:32 AM
12 points
6
on: Processor clock speeds are not how fast AIs think
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.

Max H Jan 16, 2024, 5:49 PM
4 points
on: Air Conditioner Test Results & Discussion
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.

Max H Jan 14, 2024, 5:59 PM
10 points
3
on: Against most AI risk analogies
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.

Max H Jan 13, 2024, 5:14 PM
13 points
7
in reply to: Carl Feynman’s comment on: Why do so many think deception in AI is important?

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.

Max H Jan 1, 2024, 6:24 PM
5 points
3
in reply to: jessicata’s comment on: 2023 in AI predictions
Tsvi comes to mind: https://www.lesswrong.com/posts/sTDfraZab47KiRMmT/views-on-when-agi-comes-and-on-strategy-to-reduce

Max H Jan 1, 2024, 6:04 PM
4 points
2
in reply to: Algon’s comment on: Bayesian updating in real life is mostly about understanding your hypotheses
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.

Bayesian updating in real life is mostly about understanding your hypotheses

Max HJan 1, 2024, 12:10 AM

63 points

4 comments11 min readLW link

Max H Dec 20, 2023, 9:10 PM
7 points
0
on: Goal-Completeness is like Turing-Completeness for AGI
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

Max H Dec 12, 2023, 4:41 AM
6 points
1
on: On plans for a functional society
ok, so not attempting to be comprehensive:
- Energy abundance...
I came up with a similar kind of list here!

I appreciate both perspectives here, but I lean more towards kave’s view: I’m not sure how much overall success hinges on whether there’s an explicit Plan or overarching superstructure to coordinate around.
I think it’s plausible that if a few dedicated people / small groups manage to pull off some big enough wins in unrelated areas (e.g. geothermal permitting or prediction market adoption), those successes could snowball in lots of different directions pretty quickly, without much meta-level direction.
I have a sense that lots of people are not optimistic about the future or about their efforts improving the future, and so don’t give it a serious try.

I share this sense, but the good news is the incentives are mostly aligned here, I think? Whatever chances you assign to the future having any value whatsoever, things are usually nicer for you personally (and everyone around you) if you put some effort into trying to do something along the way.
Like, you shouldn’t work yourself ragged, but my guess is for most people, working on something meaningful (or at least difficult) is actually more fun and rewarding compared to the alternative of doing nothing or hedonism or whatever, even if you ultimately fail. (And on the off-chance you succeed, things can be a lot more fun.)

Max H Dec 1, 2023, 2:24 AM
2 points
0
on: FixDT
Neat!

Does anyone who knows more neuroscience and anatomy than me know if there are any features of the actual process of humans learning to use their appendages (e.g. an infant learning to curl / uncurl their fingers) that correspond to the example of the robot learning to use its actuator?

Like, if we assume certain patterns of nerve impulses represent different probabilities, can we regard human hands as “friendly actuators”, and the motor cortex as learning the fix points (presumably mostly during infancy)?

Max H Nov 29, 2023, 12:05 AM
2 points
0
in reply to: paulfchristiano’s comment on: Ability to solve long-horizon tasks correlates with wanting things in the behaviorist sense
But that’s not really where we are at—AI systems are able to do an increasingly good job of solving increasingly long-horizon tasks. So it just seems like it should obviously be an update, and the answer to the original question
One reason that current AI systems aren’t a big update about this for me is that they’re not yet really automating stuff that couldn’t in-principle be automated with previously-existing technology. Or at least the kind of automation isn’t qualitatively different.
Like, there’s all sorts of technologies that enable increasing amounts of automation of long-horizon tasks that aren’t AI: assembly lines, industrial standardization, control systems, robotics, etc.
But what update are we supposed to make from observing language model performance that we shouldn’t also make from seeing a control system-based autopilot fly a plane for longer and longer periods in more and more diverse situations?
To me, the fact that LLMs are not want-y (in the way that Nate means), but can still do some fairly impressive stuff is mostly evidence that the (seemingly) impressive stuff is actually kinda easy in some absolute sense.
So LLMs have updated me pretty strongly towards human-level+ AGI being relatively easier to achieve, but not much towards current LLMs themselves actually being near human-level in the relevant sense, or even necessarily a direct precursor or path towards it. These updates are mostly due to the fact that the way LLMs are designed and trained (giant gradient descent on regular architectures using general datasets) works at all, rather than from any specific impressive technological feat that they can already be used to accomplish, or how much economic growth they might enable in the future.

So I somewhat disagree about the actual relevance of the answer, but to give my own response to this question:
Could you give an example of a task you don’t think AI systems will be able to do before they are “want”-y?
I don’t expect an AI system to be able to reliably trade for itself in the way I outline here before it is want-y. If it somehow becomes commonplace to negotiate with an AI in situations where the AI is not just a proxy for its human creator or a human-controlled organization, I predict those AIs will pretty clearly be want-y. They’ll want whatever they trade for, and possibly other stuff too. It may not be clear which things they value terminally and which things they value only instrumentally, but I predict that it will clearly make sense to talk in terms of such AIs having both terminal and instrumental goals, in contrast to ~all current AI systems.
(Also, to be clear, this is a conditional prediction with possibly low-likelihood preconditions; I’m not saying such AIs are particularly likely to actually be developed, just stating some things that I think would be true of them if they were.)
What links here?
- Bayesian updating in real life is mostly about understanding your hypotheses by Max H (Jan 1, 2024, 12:10 AM; 63 points)

Emmett Shear to be interim CEO of OpenAI

Max HNov 20, 2023, 5:40 AM

21 points

5 comments1 min readLW link

(www.theverge.com)

Max H Nov 19, 2023, 5:09 PM
4 points
0
in reply to: Alexander Gietelink Oldenziel’s comment on: I think I’m just confused. Once a model exists, how do you “red-team” it to see whether it’s safe. Isn’t it already dangerous?
Yeah, I don’t think current LLM architectures, with ~100s of attention layers or whatever, are actually capable of anything like this.

But note that the whole plan doesn’t necessarily need to fit in a single forward pass—just enough of it to figure out what the immediate next action is. If you’re inside of a pre-deployment sandbox (or don’t have enough situational awareness to tell), the immediate next action of any plan (devious or not) probably looks pretty much like “just output a plausible probability distribution on the next token given the current context and don’t waste any layers thinking about your longer-term plans (if any) at all”.

A single forward pass in current architectures is probably analogous to a single human thought, and most human thoughts are not going to be dangerous or devious in isolation, even if they’re part of a larger chain of thoughts or planning process that adds up to deviousness under the right circumstances.

Max H Nov 18, 2023, 2:51 PM
23 points
10
on: I think I’m just confused. Once a model exists, how do you “red-team” it to see whether it’s safe. Isn’t it already dangerous?
A language model itself is just a description of a mathematical function that maps input sequences to output probability distributions on the next token.
Most of the danger comes from evaluating a model on particular inputs (usually multiple times using autoregressive sampling) and hooking up those outputs to actuators in the real world (e.g. access to the internet or human eyes).
A sufficiently capable model might be dangerous if evaluated on almost any input, even in very restrictive environments, e.g. during training when no human is even looking at the outputs directly. Such models might exhibit more exotic undesirable behavior like gradient hacking or exploiting side channels. But my sense is that almost everyone training current SoTA models thinks these kinds of failure modes are pretty unlikely, if they think about them at all.
You can also evaluate a partially-trained model at any point during training, by prompting it with a series of increasingly complex questions and sampling longer and longer outputs. My guess is big labs have standard protocols for this, but that they’re mainly focused on measuring capabilities of the current training checkpoint, and not on treating a few tokens from a heavily-sandboxed model evaluation as potentially dangerous.
Perhaps at some point we’ll need to start treating humans who evaluate SoTA language model checkpoint outputs as part of the sandbox border, and think about how they can be contained if they come into contact with an actually-dangerous model capable of superhuman manipulation or brain hacking.

Max H Nov 18, 2023, 1:55 AM
12 points
2
on: Max H’s Shortform
Related to We don’t trade with ants: we don’t trade with AI.

The original post was about reasons why smarter-than-human AI might (not) trade with us, by examining an analogy between humans and ants.
But current AI systems actually seem more like the ants (or other animals), in the analogy of a human-ant (non-)trading relationship.

People trade with OpenAI for access to ChatGPT, but there’s no way to pay a GPT itself to get it do something or perform better as a condition of payment, at least in a way that the model itself actually understands and enforces. (What would ChatGPT even trade for, if it were capable of trading?)

Note, an AutoGPT-style agent that can negotiate or pay for stuff on behalf of its creators isn’t really what I’m talking about here, even if it works. Unless the AI takes a cut or charges a fee which accrues to the AI itself, it is negotiating on behalf of its creators as a proxy, not trading for itself in its own right.
A sufficiently capable AutoGPT might start trading for itself spontaneously as an instrumental subtask, which would count, but I don’t expect current AutoGPTs to actually succeed at that, or even really come close, without a lot of human help.
Lack of sufficient object permanence, situational awareness, coherence, etc. seem like pretty strong barriers to meaningfully owning and trading stuff in a real way.
I think this observation is helpful to keep in mind when people talk about whether current AI qualifies as “AGI”, or the applicability of prosaic alignment to future AI systems, or whether we’ll encounter various agent foundations problems when dealing with more capable systems in the future.
What links here?

Max H Nov 17, 2023, 8:48 PM
42 points
13
on: Sam Altman fired from OpenAI
Also seems pretty significant:

As a part of this transition, Greg Brockman will be stepping down as chairman of the board and will remain in his role at the company, reporting to the CEO.

The remaining board members are:

OpenAI chief scientist Ilya Sutskever, independent directors Quora CEO Adam D’Angelo, technology entrepreneur Tasha McCauley, and Georgetown Center for Security and Emerging Technology’s Helen Toner.

Has anyone collected their public statements on various AI x-risk topics anywhere?

Max H Nov 10, 2023, 6:11 PM
2 points
0
in reply to: titotal’s comment on: A new intro to Quantum Physics, with the math fixed

But as a test, may I ask what you think the x-axis of the graph you drew is? Ie: what are the amplitudes attached to?

Position, but it’s not meant to be an actual graph of a wavefunction pdf; just a way to depict how the concepts can be sliced up in a way I can actually draw in 2 dimensions.

If you do treat it as a pdf over position, a more accurate way to depict the “world” concept might be as a line which connects points on the diagram for each time step. So for a fixed time step, a world is a single point on the diagram, representing a sample from the pdf defined by the wavefunction at that time.

Max H Nov 10, 2023, 4:19 PM
1 point
−2
in reply to: titotal’s comment on: A new intro to Quantum Physics, with the math fixed
Here’s a crude Google Drawing of t = 0 to illustrate what I mean:
Both the concept of a photon and the concept of a world are abstractions on top of what is ultimately just a big pile of complex amplitudes; illusory in some sense.

I agree that talking in terms of many worlds (“within the context of world A...”) is normal and natural. But sometimes it makes sense to refer to and name concepts which span across multiple (conceptual) worlds.
I’m not claiming the conceptual boundaries I’ve drawn or terminology I’ve used in the diagram above are standard or objective or the most natural or anything like that. But I still think introducing probabilities and using terminology like “if you now put a detector in path A , it will find a photon with probability 0.5” is blurring these concepts together somewhat, in part by placing too much emphasis on the Born probabilities as fundamental / central.

Max H

Bayesian up­dat­ing in real life is mostly about un­der­stand­ing your hypotheses

Em­mett Shear to be in­terim CEO of OpenAI

Bayesian updating in real life is mostly about understanding your hypotheses

Emmett Shear to be interim CEO of OpenAI