Here’s a 53-minute podcast that I recorded this afternoon with a high school student named Micah Zarin, and which ended up covering …[checks notes] … consciousness, free will, brain uploading, the Church-Turing Thesis, AI, quantum mechanics and its various interpretations, quantum gravity, quantum computing, and the discreteness or continuity of the laws of physics. I strongly recommend 2x speed as usual.
QIP’2026, the world’s premier quantum computing conference, is happening right now in Riga, Latvia, locally organized by a team headed by the great Andris Ambainis, who I’ve known since 1999 and who’s played a bigger role in my career than almost anyone else. I’m extremely sorry not to be there, despite what I understand to be the bitter cold. Family and teaching obligations mean that I jet around the world so much less than I used to. But many of my students and colleagues are there, and I’ll plan a blog post on news from QIP next week.
Greg Burnham of Epoch AI tells me that Epoch has released a list of AI-for-math challenge problems—i.e., open math problems that are below the level of P vs. NP and the Riemann Hypothesis but still of very serious research interest, and that they’re putting forward as worthy targets right now for trying to solve with AI assistance. A few examples that should be familiar to some Shtetl-Optimized readers: degree vs. sensitivity of Boolean functions, improving the constant in the exponent of the General Number Field Sieve, giving an algorithm to test whether a knot has unknotting number of 1, and extending Apéry’s proof of the irrationality of ζ(3) to other constants. Notably, for each problem, alongside a beautifully written description by a (human) expert, they also show you what the state-of-the-art models were able to do on that problem when they tried.
There’s been a major advance in understanding constant-depth quantum circuits, by my former PhD student Daniel Grier (now a professor at UCSD), along with his PhD student Jackson Morris and Kewen Wu of IAS. Namely, they show that any function computable in TC0 (constant-depth, polynomial-size classical circuits with threshold gates) is also computable in QAC0 (constant-depth quantum circuits with 1-qubit and generalized Toffoli gates), as long as you provide many copies of the input. Two examples of such TC0 functions, which we therefore now know to be in QAC0 given many copies of the input, are Parity and Majority. It’s been a central open problem of quantum complexity theory for a quarter-century to prove that Parity is not in QAC0, complementing the celebrated result from the 1980s that Parity is not in classical AC0 (a constant-depth circuit class that, for all we know, might be incomparable with QAC0). It’s known that showing Parity∉QAC0 is equivalent to showing that QAC0 can’t implement the “fanout” function, which makes many copies of an input bit. To say that we’ve gained a new understanding of why this problem is so hard would be an understatement.
“extending Apéry’s proof of the irrationality of ζ(3) to other constants”. This is not a good problem, there were already extensive attempts to do it and they failed. Better problems in this area would to try to improve Calegari-Dimitrov-Tang’s methods and further progress on Zagier’s Polylogarithm Conjecture.
Scott, this is excellent.
I can’t handle you at 2x speed, 1.25 is plenty fast enough – I suspect that your familiarity with the concepts you cover is making you overestimate how well most people can comprehend them. Maybe 2x is fine for most of your readers on here, I suppose.
I think this is the perfect time for me to ask you a question I’ve been thinking about for a long time now – regarding Newcomb’s Problem. (I’m sure most people here will be familiar with it so I won’t describe the thought experiment other than to give a wikipedia link: https://en.wikipedia.org/wiki/Newcomb%27s_problem )
In this experiment the predictor is supposedly able to know the player’s choice in advance. If we assume that is the case, everything is straightforward.
However, my intuition is that this can not be the case for humans – at least, in general.
I guess I’m starting with the assumption that although, yes, the brain is a computer in the sense that it’s performing physical operations – it’s effectively a computer hooked up to a powerful, unpredictable physical random number generator.
I should say, some people may pre-commit to taking only one box, or be completely naïve about the situation and clearly plan to take both boxes. Those players are easy to predict; I don’t care about them. I’m considering here the people who might waver in making the decision. Furthermore, I think the amounts generally given in the experiment work counter to this consideration – if you’ve got a million dollars, you’re not really that bothered about an extra 0.1%. So I propose reducing the scale to something like $2000 and $1000. Now the option of the second box actually makes a psychological difference – making the experiment actually interesting, rather than just a test of the player’s logical capabilities. I don’t think that changes the theory in any meaningful deleterious way.
To illustrate this, let us suppose then that the predictor is able to read the entire exact state of the player’s brain at some point beforehand, and can simulate it going forward very quickly. What this can’t determine is every following quantum interaction in the brain from then until the choice is made. And this matters as you describe at about 26 minutes into the video – there’s a cascade from molecular reactions up through neuron firing events and chaotic interactions until the brain state is unpredictable.
So my belief is that this will fairly quickly make the predictor unable to reliably guess the player’s choice. But I don’t know for definite. I’m wondering how you feel about that. You do say “on what timescale that happens – I don’t think we know.”
So – do you have any insight on how we could find out?
is there any reason to think that this is more relevant than the old classic “how many angels can dance on the head of a pin?”? Are these problems equivalent?
Yg #1: In that case, I’m sure they’d be thrilled for you to contribute an entry about improving Calegari-Dimitrov-Tang’s methods and further progress on Zagier’s Polylogarithm Conjecture!
Mr_squiggle #2: Yes, it was precisely thinking about things like Newcomb’s Problem that led to many of the views on free will, personal identity, etc. that I explored in The Ghost in the Quantum Turing Machine.
I strongly agree that, even if you knew the complete state of someone’s brain—and even their surrounding environment—predicting their actions beyond a certain time horizon would likely be impossible because of tiny quantum uncertainties that would then get chaotically amplified. Alas, this observation by itself isn’t as helpful for Newcomb’s Problem as many people think. The reason is that, even if the Predictor could merely calculate the probability that someone will take both boxes, and be well-calibrated in its prediction, you get back a version of the same paradox. See for example this old blog post where I explain this point.
To rule out the Newcomb Predictor, you instead seem to need some sort of “Knightian uncertainty” (that is, inability of an external agent even to calculate the probabilities of your choices in a well-calibrated way). And the only source of such uncertainty that I know of, is the external agent’s uncertainty to know the initial state to the requisite precision, since measurements would necessarily disturb the state.
Raoul Ohio #3: I feel like science wouldn’t have gotten very far if, as soon as Maxwell proposed his Demon, Schrödinger his cat, Hawking the black hole information paradox, etc., someone came along to say “you might as well wonder how many angels can dance on a pin!” 😀
Anon #4: There’s very little in QC theory that can be compared to Shor’s algorithm, but I do think that (along with, e.g., the classical oracle separation between QMA and QCMA) this is one of the most exciting quantum complexity results of the past year. And shockingly, I’d somehow totally missed it until colleagues told me about it when I visited U. of Washington.
Certainly that is true, but it might be worthwhile to consider the likelihood of hard thinking resulting in something useful. Consider some examples on the PUC (Problem Usefulness Continuum):
A. Stuff like obtaining an analytic solution for the sphereical pendulum or maybe the Helmholtz clock problem (two good pendulum clocks go bad if placed on the same wall). These problems are challenging but doable, resulting in useful knowledge and some satisfaction.
B. Stuff like the Lorenz equations. These cannot be analytically solved, but you can figure out a lot of stuff, resulting in useful knowledge and some satisfaction.
…
Z. Stuff like Russell’s paradox, the Barber problem, … . These play an important role in logic, showing how the Halting problem works. But how much time do you spend thinking about “solving” the Barber problem, or any of the thousands of equivalent problems? Not much, because you instantly see that it is a waste of time.
Falling in the middle is the key problem of modern science; “what happens when you make a quantum measurement?”. In one sense it doesn’t matter, because SE+BR (Schroedinger eqn + Born Rule, aka “Shut Up and Calculate) always works. But on the other hand, one would certainly like to know what is actually happening. 100 years of hard thinking by many have resulted in plenty of “interpretations” all of which have considerable levels of bizarreness, implausibility, and general WTF-ness. The quantum measurement problem is certainly worth thinking about despite the reasonable chance an answer will never be found, or there is no answer.
So, how does one rate Newcomb’s Problem on the PUC? My rough analysis was that it is an unrealistic idealized model, designed to force some kind of Barber Problem logic, which I don’t find very interesting. A deeper look might reveal connections to something real, which would make the problem a lot more interesting.
Scott #5: I don’t think I can write a proper exposition which will do them justice. I have looked up the submit a problem link and one of their requirements is “Verifiable: solutions can be verified to a high degree of confidence by a typical computer program (not Lean) running on a typical laptop in under an hour.” which explains why they asked for “find analogous recurrences and initializations that can be used to prove the irrationality of other “famous” constants” because it is easy to verify. However what I suggested doesn’t really fit.
Mr_squiggle #2: Even with the payoffs being $2000 and $1000 instead of the usual, it’s not a good idea for the contestant to try to hide the information of what he plans to do (or equivalently to wait and then choose randomly). Omega can just fill box 1 with probability equal to the probability that you one-box, and then your optimal strategy is to increase that probability as much as possible. (I know this is explained at Scott #6’s second link but I wanted to make it explicit.)
Scott #6: Of course, Knightian uncertainty only helps the contestant if you assume Omega won’t react adversarially to it, e.g. filling box 1 with probability p where p is the largest number such that Omega can prove that the contestant one-boxes with probability at least p.
Dacyn #11: My claim wasn’t that Knightian uncertainty would help the contestant, but that it would invalidate the whole starting assumption that the Predictor is physically possible. Of course one could then replace what’s in the problem statement by your “adversarial Predictor,” against whom it would pay to be legible — to cripple one’s own free will, so to speak, do something to pre-commit to one-boxing, like ripping out the steering wheel in a game of Chicken.
Most people assume that learning a new language won’t help them hammer a nail — but in an unexpected way, it actually might. Most things that increases cognitive flexibility, including bilingualism, are known to delay the onset of dementia. So yes: indirectly, it lets you keep hammering nails for more years than you otherwise would.
Understanding Newcomb’s paradox has the same sort of indirect usefulness, but not for the body — for the mind itself. The lesson isn’t about decision theory per se; it’s about training your capacity to notice the invisible assumptions you bring to a problem.
The learning arc typically looks like this.
First, you solve the paradox on your own. You feel confident — perhaps even triumphant.
Then you try explaining your solution to a few people, some of whom simply refuse to understand what seems obvious to you. Frustrating.
Then, inevitably, you begin to doubt your initial certainty and you end up on Wikipedia, only to read:
> *David Wolpert and Gregory Benford point out that paradoxes arise when not all relevant details of a problem are specified, and there is more than one “intuitively obvious” way to fill in those missing details. They suggest that, in Newcomb’s paradox, the debate over which strategy is “obviously correct” stems from the fact that interpreting the problem differently leads to two distinct noncooperative games. Each strategy is optimal for one interpretation but not for the other. They then derive the optimal strategies for both versions of the game — strategies which turn out to be independent of the predictor’s infallibility, and independent of questions of causality, determinism, or free will.*
This is when the real learning starts.
You realize that your initial “solution” wasn’t wrong — it was **model‑dependent**, anchored in a set of implicit priors you hadn’t even noticed.
And when you see this once, something in your mind flips: you begin to notice how many of your most confident intuitions rest on frameworks you never consciously chose.
That awareness — the ability to see your own hidden premises — is a form of intellectual superpower.
It’s the meta‑skill that Newcomb trains: the recognition that disagreements often don’t come from reasoning errors, but from different, unspoken assumptions about how the problem is framed.
Applied to quantum mechanics, the lesson becomes even clearer.
Once you stop believing that your favourite interpretation is the only sound one, you gain immediate access to an entire landscape of alternative conceptual models. They don’t need to be “true” in any metaphysical sense to be useful. Some provide better intuition for particular calculations; some illuminate symmetries; others make certain paradoxes evaporate. In practice, each interpretation is a tool, and different tools solve different problems.
Seen that way, grappling with Newcomb’s paradox is not an intellectual curiosity — it’s a training ground.
It teaches you to switch models when the context demands it, to notice when you’re trapped inside a single interpretive frame, and to appreciate the value of having multiple conceptual lenses available.
Some of those lenses will prove useful to someone, somewhere — and often in domains far removed from where you first learned them.
That is the real utility of understanding Newcomb: not the answer itself, but the expansion of the mental space in which answers become possible.
> Z. Stuff like Russell’s paradox, the Barber problem, …
I can actually name a great deal of practical economic impact those have had! I would argue that, without wrestling with these question, people would not have appreciated the need for “foundations” for set theory (foundations in the sense of well-ordered constructions, not just in the sense that math is foundational to physics). Without that, we would not have developed something akin to modern type theory. Modern type theory underpins all modern computerized theorem provers – there were simpler ones in the last millennium, that e.g. could handle rings or classical logic, but generally doing any “serious” math within those systems was entirely impossible.
And these theorem provers are having a clear, high-dollar-value impact today, powering safer software/hardware, helping verify murky theorem proofs, even being used in the educational setting to teach undergrads analysis… 🙂
The QAC0 vs TC0 result is great. Unfortunately I get terribly lost in the conventions for what the different variants are. AC, NC, TC, sure, those I get – as decision problems. And then there’s their function problem equivalents (technically, FAC, FNC, FTC), which strictly speaking are a different beast, but of course everyone understands what you mean when you write QAC⁰ ∘ NC⁰, that it’s composed with an FNC⁰ precomputation.
But then the quantum setting is so messy. First you have \(QNC_{wf}\) where you allow fanout, as an additional circuit class, and this is what others (unless I’m mistaken) have written as \(QNC_{f}\). Then for each class of circuits, you have E- and B- variants, for exact vs. bounded-error computation. But those are for decision problems. What does that mean for the function problems!? As a class of functions, will BQNC⁰ be those where each bit can be independently computed correctly at least 2/3 of the time, or is it those where the correct output string can be computed at least 2/3 of the time? I’m sure it’s explained in the paper, but it makes me feel tired to think about, and I can certainly write down some cases where these are not the same.
As section C.2 of https://arxiv.org/pdf/2601.03243 points out, there’s even a different notion of “probabilistic computation”, which is an ensemble of circuits that together likely produce the right function on any given input. Which again is irrelevant for poly-size circuits and above, but matters at low depth.
And then in other works, like https://arxiv.org/abs/2508.11487, it gets even worse, because you consider not only languages or function problems, but the circuits are unitaries themselves. Or the class of states you can prepare.
It’s a mess. 🙂 Mostly I’m glad there’s good work being done. But I also really wish we could fix our notations a bit! 😉
Scott,
In the video, you phrase “information” as fundamental to description of physical world. How different is this from, say a mathematical entity like “integral” being fundamental to physics.
Since both are abstract entities, being independent of the physical world, they are in a sense more of a descriptive tools, than fundamental physical entities like mass, time , energy etc ?
Trying to see how Max Tegmark’s view of math being the sufficient and fundamental description of the physical world, than physical entities like matter and energy, is different from this viewpoint
Prasanna #18: That’s what I said in the video! I gave examples of major discoveries in physics that were “really about information” (thermodynamics, no superluminal signaling, the Bekenstein bound), but I also explained why I don’t understand how the laws of physics could be such that we wouldn’t talk about them in terms of information—since “information” is just a name we give to whatever selects one state out of multiple possible states.
If anything about the physical world wasn’t ultimately “about information,” it seems to me that it would need to be what the philosophers call the “quiddity,” “whatness,” “essence,” etc. of physical things—i.e., properties, or alleged properties, that are outside the scope of physics for the very reason of being non-informational.
the only caveat is that, to be practical, information has to be finite. I.e. laws of physics are often about continuums, and most equations (e.g. 3 body problem) don’t have analytical solutions, but have to be solved numerically, as approximations.
So, to be able to digest the world (understand it), we have to chop it in little “bits” (like superimposing a regular grid onto the world and decide what’s in it and what’s not in it based on some property) and those bits can be processed as thoughts (a thought is a unit of thinking).
In that sense reality doesn’t appear to be about information, but information is a tool to approximate it and model it.
Another example is the quantization of continuous fields, where the “bitting” only works in low energy regimes, but at high energies the continuum is just too wild to be tamed and described.
Another point is that there are no “physical things”, all there is are patterns. Information is a tool to try and describe those patterns.
Imagine an opaque fluid mixing in a transparent one, light shines on it, the interface projects a complex shadow, the image of this shadow creates an interface of low and higher temperature, and this heat image feeds back on the original interface, in some subtle recursive loop… very similar of how a brain stores information about the world, and this information modifies the world, etc.
So when we say the world is information, we’re really saying that there are places in the world where this feedback loop between subtle shapes and their shadows is taking place.
Note that there’s no clear causality going on (we just think our brain is in control but it’s not, it’s just one cog that’s part of the complexity medium).
most equations (e.g. 3 body problem) don’t have analytical solutions
I do not think that this is a constructive argument. Is a solution involving tan() “an analytical solution”? Involving the general hypergeometric function? Involving the function solving the Cauchy problem for the three body problem (Cp3BO)?
You “cannot calculate” tan() without a calculator involving such “a button”. But it is not much harder to design a calculator able to solve Cp3BO!
i was trying to say that “symbolic calculus” (mathematical relations for physical laws) is quite different from “information theory” (Shannon, etc). Although I guess there must be ways to connect the two (degrees of freedom, etc), but that’s above my pay grade.
Knightian uncertainty cannot save you from Newcomb’s paradox unless you are willing to completely sacrifice the notion of rational decision-making. If you grant that people sometimes make decisions according to some rational calculation, then at least in those contexts their decision should be mostly predictable (and in particular mostly independent from those Knightian quantum bits). For example, I believe that one-boxing in Newcomb’s paradox is rational and therefore I will almost certainly one-box if I were inside Newcomb’s paradox. There is no reason of principle why it’s impossible for a predictor to exist that can infer this fact about me. Of course, you can also imagine another person who, if they find themself in Newcomb’s paradox, will act according to some Knightian quantum bit in their brain. In this case, the result depends on Omega’s exact algorithm. For the sake of the argument, we can assume that whenever Omega fails to derive a satisfactory prediction, it default to leaving the box empty. If so, it sucks to be the “deferential-to-quantum-bits” person.
My initial snide remark was due to intellectual laziness in not wanting to do that hard thinking. I did not follow my usual plan to “think before clicking Submit”.
Another point is that saying the world is about information is a different way of saying the world is about energy, and there are conservation laws, and how those things propagate in space and time. Basically information theory is a type of abstract accounting method for all those things.
It all works with 19th century physics at the macro state, but then QM, field theory, and GR made those concepts not that clear cut at the edges – how does information escape a black hole, etc.
Ultimately, whenever we say “reality is about this”, we confuse a map with the world.
Regarding the TC0 result, to what extent does the caviat “as long as you provide many copies of the input” weaken the result? If the interesting question is whether QAC0 contains fanout, doesn’t providing multiple copies undercut that result?
She was alive.
That fact had settled into Sean Carroll like concrete. Not as a fragile hope. Not as a probabilistic statement. As reality.
He had slept in a chair beside her hospital bed, neck crooked, spine aching — and happy. He woke in the dim early light to the soft rhythm of the monitor and thought, she’s still breathing. And he smiled into the half-dark.
By the second day, the ICU room no longer felt clinical. It felt almost celebratory.
Flowers crowded the counter. Balloons hovered awkwardly near medical equipment. Paper coffee cups multiplied. Friends rotated in and out. Colleagues from the university. Family members who had cried themselves empty the night before.
Someone called it “a second life.”
Someone else said, “It’s a miracle.”
Plastic cups of orange juice were raised in a makeshift toast.
Sean laughed. And it was real laughter. The terror had drained out of his nervous system. The survival was no longer fragile — it was integrated. His body believed it now.
She spoke in soft fragments. Weak, but lucid. Her voice — the most beautiful sound in the room.
The atmosphere warmed. Relief thickened into celebration.
Mid-afternoon, the door opened again.
A physician entered, followed by a clinical statistician — someone involved in reconstructing the exact chain of events that led to her survival. Not a Many Worlds advocate. Just standard quantum mechanics, standard probability theory. The microscopic cascade had included molecular fluctuations where quantum uncertainty mattered.
“There’s something you might want to know,” the statistician said carefully.
Sean smiled lightly. “She’s stable. That’s what matters.”
“Yes,” the man nodded. “But we finalized the model. The timing of the clotting, the ion channel behavior, the cascade in neural recovery — it hinged on quantum-level fluctuations. Without them, the outcome would have been different.”
He turned the tablet toward Sean.
Survival probability: 0.00000001%
The room reacted instantly.
“That’s unbelievable.”
“She’s a miracle.”
“That’s impossible.”
Someone actually clapped.
Sean took the tablet.
He read.
He checked assumptions. Bayesian structure. Error margins. Sensitivity analysis. It was rigorous. No exaggeration. The chain of recovery genuinely hinged on quantum-scale indeterminacy.
He nodded slowly.
“Yes,” he said. “This is correct.”
Another wave of celebration filled the room. Laughter. Tears. Hugs. Someone said, “She beat the universe.”
But something different happened in him this time.
Not immediately.
Not dramatically.
It seeped in.
Yesterday it was simple: she’s alive.
Today it was: she’s alive against a quantum probability effectively indistinguishable from zero.
And his mind completed the rest automatically.
If the dynamics are unitary…
If the wave function never collapses…
If amplitudes branch rather than vanish…
Then the branch in which she dies overwhelmingly dominates the measure.
He didn’t visualize it as parallel lives.
He felt it as weight.
Around him, the room grew louder. Lighter. Almost festive. Pictures were taken. Someone joked about annual celebrations.
He looked at her — smiling faintly at a niece telling a story.
And suddenly her presence felt different.
Not physically fragile.
Cosmologically marginal.
In the vast structure described by his own worldview, the overwhelming amplitude corresponded to her death.
In almost every branch, this room was silent.
In almost every branch, he was standing beside a body.
The thought did not feel philosophical.
It felt cold.
A friend wrapped an arm around him. “You’re the luckiest man alive,” the friend said.
Sean nodded.
Luck.
In his formal framework, luck meant occupying a low-measure branch.
He looked again at the number: 0.00000001%.
The others saw miracle.
He saw distribution.
A measure space in which her survival barely registered.
The celebration now felt strangely thin — like it was suspended over something bottomless.
His theory had always been elegant. Clean. Free of ad hoc collapse. Beautiful in its simplicity.
But standing in that hospital room, surrounded by joy, he felt something else:
If his cosmology was correct, this happiness carried almost no weight in the full structure of reality.
And yet—
she squeezed his hand.
A small, imperfect pressure. Warm. Immediate.
His heart reacted to that, not to amplitudes.
He set the tablet down.
Sat beside her.
Took her hand more firmly.
While the room continued to celebrate the impossible survival, something inside him shifted quietly and irreversibly:
He understood, perhaps more clearly than ever, that no multiverse could dilute the fact that this branch — this room, this breath, this hand in his — was the only one he could ever inhabit.
It was recently shown that no super-poly advantage exists for quantum communication protocols over classical communication protocols to compute total AND-functions. Isn’t this a biggish development in QC?
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Comment #1 January 29th, 2026 at 4:31 am
“extending Apéry’s proof of the irrationality of ζ(3) to other constants”. This is not a good problem, there were already extensive attempts to do it and they failed. Better problems in this area would to try to improve Calegari-Dimitrov-Tang’s methods and further progress on Zagier’s Polylogarithm Conjecture.
Comment #2 January 29th, 2026 at 7:08 am
Scott, this is excellent.
I can’t handle you at 2x speed, 1.25 is plenty fast enough – I suspect that your familiarity with the concepts you cover is making you overestimate how well most people can comprehend them. Maybe 2x is fine for most of your readers on here, I suppose.
I think this is the perfect time for me to ask you a question I’ve been thinking about for a long time now – regarding Newcomb’s Problem. (I’m sure most people here will be familiar with it so I won’t describe the thought experiment other than to give a wikipedia link: https://en.wikipedia.org/wiki/Newcomb%27s_problem )
In this experiment the predictor is supposedly able to know the player’s choice in advance. If we assume that is the case, everything is straightforward.
However, my intuition is that this can not be the case for humans – at least, in general.
I guess I’m starting with the assumption that although, yes, the brain is a computer in the sense that it’s performing physical operations – it’s effectively a computer hooked up to a powerful, unpredictable physical random number generator.
I should say, some people may pre-commit to taking only one box, or be completely naïve about the situation and clearly plan to take both boxes. Those players are easy to predict; I don’t care about them. I’m considering here the people who might waver in making the decision. Furthermore, I think the amounts generally given in the experiment work counter to this consideration – if you’ve got a million dollars, you’re not really that bothered about an extra 0.1%. So I propose reducing the scale to something like $2000 and $1000. Now the option of the second box actually makes a psychological difference – making the experiment actually interesting, rather than just a test of the player’s logical capabilities. I don’t think that changes the theory in any meaningful deleterious way.
To illustrate this, let us suppose then that the predictor is able to read the entire exact state of the player’s brain at some point beforehand, and can simulate it going forward very quickly. What this can’t determine is every following quantum interaction in the brain from then until the choice is made. And this matters as you describe at about 26 minutes into the video – there’s a cascade from molecular reactions up through neuron firing events and chaotic interactions until the brain state is unpredictable.
So my belief is that this will fairly quickly make the predictor unable to reliably guess the player’s choice. But I don’t know for definite. I’m wondering how you feel about that. You do say “on what timescale that happens – I don’t think we know.”
So – do you have any insight on how we could find out?
Comment #3 January 29th, 2026 at 9:38 am
Mr_Squiggle #2:
First thought on Newcomb’s Problem:
is there any reason to think that this is more relevant than the old classic “how many angels can dance on the head of a pin?”? Are these problems equivalent?
Comment #4 January 29th, 2026 at 10:12 am
The result on TC0 and QAC0 is impressive and somewhat surprising indeed. Congratulations to the authors.
It gives me the vibes of Shore’s algorithm for Factoring, but at lower levels of complexity hierarchy.
Comment #5 January 29th, 2026 at 11:04 am
Yg #1: In that case, I’m sure they’d be thrilled for you to contribute an entry about improving Calegari-Dimitrov-Tang’s methods and further progress on Zagier’s Polylogarithm Conjecture!
Comment #6 January 29th, 2026 at 11:15 am
Mr_squiggle #2: Yes, it was precisely thinking about things like Newcomb’s Problem that led to many of the views on free will, personal identity, etc. that I explored in The Ghost in the Quantum Turing Machine.
I strongly agree that, even if you knew the complete state of someone’s brain—and even their surrounding environment—predicting their actions beyond a certain time horizon would likely be impossible because of tiny quantum uncertainties that would then get chaotically amplified. Alas, this observation by itself isn’t as helpful for Newcomb’s Problem as many people think. The reason is that, even if the Predictor could merely calculate the probability that someone will take both boxes, and be well-calibrated in its prediction, you get back a version of the same paradox. See for example this old blog post where I explain this point.
To rule out the Newcomb Predictor, you instead seem to need some sort of “Knightian uncertainty” (that is, inability of an external agent even to calculate the probabilities of your choices in a well-calibrated way). And the only source of such uncertainty that I know of, is the external agent’s uncertainty to know the initial state to the requisite precision, since measurements would necessarily disturb the state.
Comment #7 January 29th, 2026 at 11:20 am
Raoul Ohio #3: I feel like science wouldn’t have gotten very far if, as soon as Maxwell proposed his Demon, Schrödinger his cat, Hawking the black hole information paradox, etc., someone came along to say “you might as well wonder how many angels can dance on a pin!” 😀
Comment #8 January 29th, 2026 at 11:23 am
Anon #4: There’s very little in QC theory that can be compared to Shor’s algorithm, but I do think that (along with, e.g., the classical oracle separation between QMA and QCMA) this is one of the most exciting quantum complexity results of the past year. And shockingly, I’d somehow totally missed it until colleagues told me about it when I visited U. of Washington.
Comment #9 January 29th, 2026 at 2:21 pm
Scott #7:
Certainly that is true, but it might be worthwhile to consider the likelihood of hard thinking resulting in something useful. Consider some examples on the PUC (Problem Usefulness Continuum):
A. Stuff like obtaining an analytic solution for the sphereical pendulum or maybe the Helmholtz clock problem (two good pendulum clocks go bad if placed on the same wall). These problems are challenging but doable, resulting in useful knowledge and some satisfaction.
B. Stuff like the Lorenz equations. These cannot be analytically solved, but you can figure out a lot of stuff, resulting in useful knowledge and some satisfaction.
…
Z. Stuff like Russell’s paradox, the Barber problem, … . These play an important role in logic, showing how the Halting problem works. But how much time do you spend thinking about “solving” the Barber problem, or any of the thousands of equivalent problems? Not much, because you instantly see that it is a waste of time.
Falling in the middle is the key problem of modern science; “what happens when you make a quantum measurement?”. In one sense it doesn’t matter, because SE+BR (Schroedinger eqn + Born Rule, aka “Shut Up and Calculate) always works. But on the other hand, one would certainly like to know what is actually happening. 100 years of hard thinking by many have resulted in plenty of “interpretations” all of which have considerable levels of bizarreness, implausibility, and general WTF-ness. The quantum measurement problem is certainly worth thinking about despite the reasonable chance an answer will never be found, or there is no answer.
So, how does one rate Newcomb’s Problem on the PUC? My rough analysis was that it is an unrealistic idealized model, designed to force some kind of Barber Problem logic, which I don’t find very interesting. A deeper look might reveal connections to something real, which would make the problem a lot more interesting.
Comment #10 January 29th, 2026 at 5:33 pm
Scott #5: I don’t think I can write a proper exposition which will do them justice. I have looked up the submit a problem link and one of their requirements is “Verifiable: solutions can be verified to a high degree of confidence by a typical computer program (not Lean) running on a typical laptop in under an hour.” which explains why they asked for “find analogous recurrences and initializations that can be used to prove the irrationality of other “famous” constants” because it is easy to verify. However what I suggested doesn’t really fit.
Comment #11 January 29th, 2026 at 5:51 pm
Mr_squiggle #2: Even with the payoffs being $2000 and $1000 instead of the usual, it’s not a good idea for the contestant to try to hide the information of what he plans to do (or equivalently to wait and then choose randomly). Omega can just fill box 1 with probability equal to the probability that you one-box, and then your optimal strategy is to increase that probability as much as possible. (I know this is explained at Scott #6’s second link but I wanted to make it explicit.)
Scott #6: Of course, Knightian uncertainty only helps the contestant if you assume Omega won’t react adversarially to it, e.g. filling box 1 with probability p where p is the largest number such that Omega can prove that the contestant one-boxes with probability at least p.
Comment #12 January 29th, 2026 at 6:27 pm
Dacyn #11: My claim wasn’t that Knightian uncertainty would help the contestant, but that it would invalidate the whole starting assumption that the Predictor is physically possible. Of course one could then replace what’s in the problem statement by your “adversarial Predictor,” against whom it would pay to be legible — to cripple one’s own free will, so to speak, do something to pre-commit to one-boxing, like ripping out the steering wheel in a game of Chicken.
Comment #13 January 29th, 2026 at 8:20 pm
Raoul Ohio #9,
Most people assume that learning a new language won’t help them hammer a nail — but in an unexpected way, it actually might. Most things that increases cognitive flexibility, including bilingualism, are known to delay the onset of dementia. So yes: indirectly, it lets you keep hammering nails for more years than you otherwise would.
Understanding Newcomb’s paradox has the same sort of indirect usefulness, but not for the body — for the mind itself. The lesson isn’t about decision theory per se; it’s about training your capacity to notice the invisible assumptions you bring to a problem.
The learning arc typically looks like this.
First, you solve the paradox on your own. You feel confident — perhaps even triumphant.
Then you try explaining your solution to a few people, some of whom simply refuse to understand what seems obvious to you. Frustrating.
Then, inevitably, you begin to doubt your initial certainty and you end up on Wikipedia, only to read:
> *David Wolpert and Gregory Benford point out that paradoxes arise when not all relevant details of a problem are specified, and there is more than one “intuitively obvious” way to fill in those missing details. They suggest that, in Newcomb’s paradox, the debate over which strategy is “obviously correct” stems from the fact that interpreting the problem differently leads to two distinct noncooperative games. Each strategy is optimal for one interpretation but not for the other. They then derive the optimal strategies for both versions of the game — strategies which turn out to be independent of the predictor’s infallibility, and independent of questions of causality, determinism, or free will.*
This is when the real learning starts.
You realize that your initial “solution” wasn’t wrong — it was **model‑dependent**, anchored in a set of implicit priors you hadn’t even noticed.
And when you see this once, something in your mind flips: you begin to notice how many of your most confident intuitions rest on frameworks you never consciously chose.
That awareness — the ability to see your own hidden premises — is a form of intellectual superpower.
It’s the meta‑skill that Newcomb trains: the recognition that disagreements often don’t come from reasoning errors, but from different, unspoken assumptions about how the problem is framed.
Applied to quantum mechanics, the lesson becomes even clearer.
Once you stop believing that your favourite interpretation is the only sound one, you gain immediate access to an entire landscape of alternative conceptual models. They don’t need to be “true” in any metaphysical sense to be useful. Some provide better intuition for particular calculations; some illuminate symmetries; others make certain paradoxes evaporate. In practice, each interpretation is a tool, and different tools solve different problems.
Seen that way, grappling with Newcomb’s paradox is not an intellectual curiosity — it’s a training ground.
It teaches you to switch models when the context demands it, to notice when you’re trapped inside a single interpretive frame, and to appreciate the value of having multiple conceptual lenses available.
Some of those lenses will prove useful to someone, somewhere — and often in domains far removed from where you first learned them.
That is the real utility of understanding Newcomb: not the answer itself, but the expansion of the mental space in which answers become possible.
Comment #14 January 29th, 2026 at 9:36 pm
Scott #12: Sure, agreed.
Comment #15 January 30th, 2026 at 7:57 am
The supposed photo of Scott Aaronson on that video thumbnail is AI slop that looks nothing like the actual Scott Aaronson. 🙂
Comment #16 January 30th, 2026 at 8:23 pm
Raoul #9:
> Z. Stuff like Russell’s paradox, the Barber problem, …
I can actually name a great deal of practical economic impact those have had! I would argue that, without wrestling with these question, people would not have appreciated the need for “foundations” for set theory (foundations in the sense of well-ordered constructions, not just in the sense that math is foundational to physics). Without that, we would not have developed something akin to modern type theory. Modern type theory underpins all modern computerized theorem provers – there were simpler ones in the last millennium, that e.g. could handle rings or classical logic, but generally doing any “serious” math within those systems was entirely impossible.
And these theorem provers are having a clear, high-dollar-value impact today, powering safer software/hardware, helping verify murky theorem proofs, even being used in the educational setting to teach undergrads analysis… 🙂
Comment #17 January 30th, 2026 at 8:44 pm
The QAC0 vs TC0 result is great. Unfortunately I get terribly lost in the conventions for what the different variants are. AC, NC, TC, sure, those I get – as decision problems. And then there’s their function problem equivalents (technically, FAC, FNC, FTC), which strictly speaking are a different beast, but of course everyone understands what you mean when you write QAC⁰ ∘ NC⁰, that it’s composed with an FNC⁰ precomputation.
But then the quantum setting is so messy. First you have \(QNC_{wf}\) where you allow fanout, as an additional circuit class, and this is what others (unless I’m mistaken) have written as \(QNC_{f}\). Then for each class of circuits, you have E- and B- variants, for exact vs. bounded-error computation. But those are for decision problems. What does that mean for the function problems!? As a class of functions, will BQNC⁰ be those where each bit can be independently computed correctly at least 2/3 of the time, or is it those where the correct output string can be computed at least 2/3 of the time? I’m sure it’s explained in the paper, but it makes me feel tired to think about, and I can certainly write down some cases where these are not the same.
As section C.2 of https://arxiv.org/pdf/2601.03243 points out, there’s even a different notion of “probabilistic computation”, which is an ensemble of circuits that together likely produce the right function on any given input. Which again is irrelevant for poly-size circuits and above, but matters at low depth.
And then in other works, like https://arxiv.org/abs/2508.11487, it gets even worse, because you consider not only languages or function problems, but the circuits are unitaries themselves. Or the class of states you can prepare.
It’s a mess. 🙂 Mostly I’m glad there’s good work being done. But I also really wish we could fix our notations a bit! 😉
Comment #18 January 31st, 2026 at 7:27 am
Scott,
In the video, you phrase “information” as fundamental to description of physical world. How different is this from, say a mathematical entity like “integral” being fundamental to physics.
Since both are abstract entities, being independent of the physical world, they are in a sense more of a descriptive tools, than fundamental physical entities like mass, time , energy etc ?
Trying to see how Max Tegmark’s view of math being the sufficient and fundamental description of the physical world, than physical entities like matter and energy, is different from this viewpoint
Comment #19 January 31st, 2026 at 7:34 am
Prasanna #18: That’s what I said in the video! I gave examples of major discoveries in physics that were “really about information” (thermodynamics, no superluminal signaling, the Bekenstein bound), but I also explained why I don’t understand how the laws of physics could be such that we wouldn’t talk about them in terms of information—since “information” is just a name we give to whatever selects one state out of multiple possible states.
Comment #20 January 31st, 2026 at 10:11 am
Any “system” can be reduced to some state, states can be expressed as bits, and then seen as “information”.
Can someone give an example of a physical process that doesn’t include “information”?
Comment #21 January 31st, 2026 at 11:29 am
Ty-ty #20: Indeed, that’s what I said! 😀
If anything about the physical world wasn’t ultimately “about information,” it seems to me that it would need to be what the philosophers call the “quiddity,” “whatness,” “essence,” etc. of physical things—i.e., properties, or alleged properties, that are outside the scope of physics for the very reason of being non-informational.
Comment #22 January 31st, 2026 at 1:09 pm
Scott #21
the only caveat is that, to be practical, information has to be finite. I.e. laws of physics are often about continuums, and most equations (e.g. 3 body problem) don’t have analytical solutions, but have to be solved numerically, as approximations.
So, to be able to digest the world (understand it), we have to chop it in little “bits” (like superimposing a regular grid onto the world and decide what’s in it and what’s not in it based on some property) and those bits can be processed as thoughts (a thought is a unit of thinking).
In that sense reality doesn’t appear to be about information, but information is a tool to approximate it and model it.
Another example is the quantization of continuous fields, where the “bitting” only works in low energy regimes, but at high energies the continuum is just too wild to be tamed and described.
Another point is that there are no “physical things”, all there is are patterns. Information is a tool to try and describe those patterns.
Comment #23 January 31st, 2026 at 1:32 pm
Scott:
also we forget that we live in a very particular interface where lots of subtle things can happen, what we call complexity.
https://scottaaronson.blog/coffee-lrg.jpg
Imagine an opaque fluid mixing in a transparent one, light shines on it, the interface projects a complex shadow, the image of this shadow creates an interface of low and higher temperature, and this heat image feeds back on the original interface, in some subtle recursive loop… very similar of how a brain stores information about the world, and this information modifies the world, etc.
So when we say the world is information, we’re really saying that there are places in the world where this feedback loop between subtle shapes and their shadows is taking place.
Note that there’s no clear causality going on (we just think our brain is in control but it’s not, it’s just one cog that’s part of the complexity medium).
Comment #24 January 31st, 2026 at 4:58 pm
Ty-ty #22
I do not think that this is a constructive argument. Is a solution involving tan() “an analytical solution”? Involving the general hypergeometric function? Involving the function solving the Cauchy problem for the three body problem (Cp3BO)?
You “cannot calculate” tan() without a calculator involving such “a button”. But it is not much harder to design a calculator able to solve Cp3BO!
Comment #25 February 1st, 2026 at 1:10 pm
Ilya #24
thank you
i was trying to say that “symbolic calculus” (mathematical relations for physical laws) is quite different from “information theory” (Shannon, etc). Although I guess there must be ways to connect the two (degrees of freedom, etc), but that’s above my pay grade.
Comment #26 February 2nd, 2026 at 6:02 am
Scott #6,
Knightian uncertainty cannot save you from Newcomb’s paradox unless you are willing to completely sacrifice the notion of rational decision-making. If you grant that people sometimes make decisions according to some rational calculation, then at least in those contexts their decision should be mostly predictable (and in particular mostly independent from those Knightian quantum bits). For example, I believe that one-boxing in Newcomb’s paradox is rational and therefore I will almost certainly one-box if I were inside Newcomb’s paradox. There is no reason of principle why it’s impossible for a predictor to exist that can infer this fact about me. Of course, you can also imagine another person who, if they find themself in Newcomb’s paradox, will act according to some Knightian quantum bit in their brain. In this case, the result depends on Omega’s exact algorithm. For the sake of the argument, we can assume that whenever Omega fails to derive a satisfactory prediction, it default to leaving the box empty. If so, it sucks to be the “deferential-to-quantum-bits” person.
(If you want to know what I think the actual solution to this sort of paradoxes is, see https://www.alignmentforum.org/s/n7qFxakSnxGuvmYAX/p/E6HwiG6TaZ338ub3t)
Comment #27 February 2nd, 2026 at 9:53 am
Glassmind Duo #13 and Alex Meiburg #16:
Excellent points!
My initial snide remark was due to intellectual laziness in not wanting to do that hard thinking. I did not follow my usual plan to “think before clicking Submit”.
Comment #28 February 6th, 2026 at 10:23 am
Another point is that saying the world is about information is a different way of saying the world is about energy, and there are conservation laws, and how those things propagate in space and time. Basically information theory is a type of abstract accounting method for all those things.
It all works with 19th century physics at the macro state, but then QM, field theory, and GR made those concepts not that clear cut at the edges – how does information escape a black hole, etc.
Ultimately, whenever we say “reality is about this”, we confuse a map with the world.
Comment #29 February 14th, 2026 at 8:10 am
Regarding the TC0 result, to what extent does the caviat “as long as you provide many copies of the input” weaken the result? If the interesting question is whether QAC0 contains fanout, doesn’t providing multiple copies undercut that result?
Comment #30 March 1st, 2026 at 12:23 pm
The first night had been euphoric.
She was alive.
That fact had settled into Sean Carroll like concrete. Not as a fragile hope. Not as a probabilistic statement. As reality.
He had slept in a chair beside her hospital bed, neck crooked, spine aching — and happy. He woke in the dim early light to the soft rhythm of the monitor and thought, she’s still breathing. And he smiled into the half-dark.
By the second day, the ICU room no longer felt clinical. It felt almost celebratory.
Flowers crowded the counter. Balloons hovered awkwardly near medical equipment. Paper coffee cups multiplied. Friends rotated in and out. Colleagues from the university. Family members who had cried themselves empty the night before.
Someone called it “a second life.”
Someone else said, “It’s a miracle.”
Plastic cups of orange juice were raised in a makeshift toast.
Sean laughed. And it was real laughter. The terror had drained out of his nervous system. The survival was no longer fragile — it was integrated. His body believed it now.
She spoke in soft fragments. Weak, but lucid. Her voice — the most beautiful sound in the room.
The atmosphere warmed. Relief thickened into celebration.
Mid-afternoon, the door opened again.
A physician entered, followed by a clinical statistician — someone involved in reconstructing the exact chain of events that led to her survival. Not a Many Worlds advocate. Just standard quantum mechanics, standard probability theory. The microscopic cascade had included molecular fluctuations where quantum uncertainty mattered.
“There’s something you might want to know,” the statistician said carefully.
Sean smiled lightly. “She’s stable. That’s what matters.”
“Yes,” the man nodded. “But we finalized the model. The timing of the clotting, the ion channel behavior, the cascade in neural recovery — it hinged on quantum-level fluctuations. Without them, the outcome would have been different.”
He turned the tablet toward Sean.
Survival probability: 0.00000001%
The room reacted instantly.
“That’s unbelievable.”
“She’s a miracle.”
“That’s impossible.”
Someone actually clapped.
Sean took the tablet.
He read.
He checked assumptions. Bayesian structure. Error margins. Sensitivity analysis. It was rigorous. No exaggeration. The chain of recovery genuinely hinged on quantum-scale indeterminacy.
He nodded slowly.
“Yes,” he said. “This is correct.”
Another wave of celebration filled the room. Laughter. Tears. Hugs. Someone said, “She beat the universe.”
But something different happened in him this time.
Not immediately.
Not dramatically.
It seeped in.
Yesterday it was simple: she’s alive.
Today it was: she’s alive against a quantum probability effectively indistinguishable from zero.
And his mind completed the rest automatically.
If the dynamics are unitary…
If the wave function never collapses…
If amplitudes branch rather than vanish…
Then the branch in which she dies overwhelmingly dominates the measure.
He didn’t visualize it as parallel lives.
He felt it as weight.
Around him, the room grew louder. Lighter. Almost festive. Pictures were taken. Someone joked about annual celebrations.
He looked at her — smiling faintly at a niece telling a story.
And suddenly her presence felt different.
Not physically fragile.
Cosmologically marginal.
In the vast structure described by his own worldview, the overwhelming amplitude corresponded to her death.
In almost every branch, this room was silent.
In almost every branch, he was standing beside a body.
The thought did not feel philosophical.
It felt cold.
A friend wrapped an arm around him. “You’re the luckiest man alive,” the friend said.
Sean nodded.
Luck.
In his formal framework, luck meant occupying a low-measure branch.
He looked again at the number: 0.00000001%.
The others saw miracle.
He saw distribution.
A measure space in which her survival barely registered.
The celebration now felt strangely thin — like it was suspended over something bottomless.
His theory had always been elegant. Clean. Free of ad hoc collapse. Beautiful in its simplicity.
But standing in that hospital room, surrounded by joy, he felt something else:
If his cosmology was correct, this happiness carried almost no weight in the full structure of reality.
And yet—
she squeezed his hand.
A small, imperfect pressure. Warm. Immediate.
His heart reacted to that, not to amplitudes.
He set the tablet down.
Sat beside her.
Took her hand more firmly.
While the room continued to celebrate the impossible survival, something inside him shifted quietly and irreversibly:
He understood, perhaps more clearly than ever, that no multiverse could dilute the fact that this branch — this room, this breath, this hand in his — was the only one he could ever inhabit.
The others kept cheering.
He smiled with them.
But behind the smile, something had gone dark.
Not hysterical.
Not broken.
Just aware.
And permanently altered.
Comment #31 May 20th, 2026 at 2:01 am
It was recently shown that no super-poly advantage exists for quantum communication protocols over classical communication protocols to compute total AND-functions. Isn’t this a biggish development in QC?