This is marvellous - since about 14, when confronted with probability, I've stated, with a (sarcastic) confused tone, "It's one if it happens and zero if it doesn't. What are you talking about?" But more seriously - I couldn't agree more with this structure, and now that I'm redeveloping my physics and philosophy, I'm giving serious thought to further formal study, and this would definitely be the field of my choice. For anyone watching that wonders if this matches with formal physics or if it's a fringe theory, it matches perfectly with the formalism of quantum physics, whilst making a damn sight more sense of its interpretation than various other common methods.

This is a most intriguing idea. I am so glad that investigators such as Deutsch are looking into ideas such as this. Excellently explained and well-motivated.

This lecture reveals how little we know about the reality of nature. We need to be humble in the face of uncertainty and painfully accept how little we know and find better explanation to keep the world in motion.

Some personal notes/transcriptions of this talk, posted to act as an approximation (ha!) for those who don't have time to view the full talk: Modes of explanation: "The prevailing mode, which is mistakenly thought to be the most fundamental, is, like this: There are particles, and there are fields in spacetime. And, they obey laws of motion and initial conditions, and once you know those, you can predict the whole of the rest of their behaviour. But there are other modes of explanation in common use in physics and elsewhere. Constructor theory seeks to unify and underlie all those modes of explanation, with a single mode of explanation. Which is, explanation via the dichotomy between transformations that it's possible to bring about accurately, and ones that it's not possible to bring about. Those are, possible and impossible tasks." --> using probability in physics is like using the flat earth theory when gardening. It is useful there, but in looking at the nature of reality, it is absolutely useless. Cardion (1501-1576) - inventor(?) of probability - for use in card games and games of chance. - he did not posit that probability was LITERALLY what was occurring, that the process LITERALLY had properties such as probability. - the theory of probability was a narrow parochial application of a mathematical trick "The reason probability was possible at all, is that it's conclusions don't depend on detailed physics of any game-playing processes. It didn't matter what the orbits of the planets are, what matter is made of, let alone anything deeper about the laws of physics. The theory was directed specifically at modelling a particular human, social behaviour, which even animals don't do, let alone the physical world at large." * "As we discover more and more about the world, we sometimes find that things we thought existed, don't exist. Such as, celestial spheres, and, the force of gravity, and trajectories of particles, and so on. They were all thought to exist, and discovering that they don't exist, was a great advance in understanding. But before we can decide that something doesn't exist, we must explain what the world without that thing is like. And also, preferably, why thinking is terms of that thing seemed to work, and why it was a useful fiction, and why it may still be a useful fiction." * - Compare statements of factual, observable properties of the world, of what WILL happen when poker is played, and specified hands arise, to, probabilistic statements which are NOT about physical facts. - probabilistic statements are consistent with ANY sequence of cards arising in a poker game, and in fact, consistent with ANY physical events, such as, the extremely unlikely probability occurring... "Yes, it was true that that action was very risky, but it doesn't apparently refer to any events that actually happen in that case." "No probablistic statement can EVER imply any factual statement. In other words, assertions about probabilities do not refer to the physical world. They don't assert ANYTHING about the physical world." [2 things you think that make probability a good description: 1. Probability introduces, all outcomes over time. Instead of that present instance, it groups all similar outcomes over time into it's predictions and judgements. 2. There are no separate things. You can't posit the strict, bounded existence of any object, of any player, person, ANY object at all, and therefore drawing outcomes between them may be impossible, because at the most fundamental level they are the same thing. It is like, you are attempting to precisely separate their events, where the most precise and fundamental description is that the world is one event, and you cannot possibly separate objects.] "You could also imagine that probability statements are not about the world at all, they are assertions about our minds. With probability being a measure of ignorance, or of, degree of rational belief. Those are two different subjective theories, called credence. But, that is no good for present purposes, because, you still need something to connect statements about our minds, to statements about physical reality. So, to this end, the philosopher david lewis, proposed his principal principle, which asserts as an axiom that rational agents have the same credences as the physical probabilties." - probability statements could be substituted for magical statements, and hold just as valid. * "The principal principle tells us to adjust our credences to match those numbers, though it doesn't say why. And, probablistic game theory tells us that a rational player should value playing such a machine [more likely to win] the same as if it were guaranteed to produce that expectation value. * And again, it doesn't say 'why'. In general, axioms of stochastic theories are not explanatory, which alone should disqualify them from being part of any scientific theory in fundamental science. But, I digress." "Probability, randomness, is just a feature of the model convenience. By the way, I don't mean that the mathematical formalism of quantum theory isn't sometimes useful. I'm saying that the quantities called probabilities in that formalism, do not refer to any stochastic, random processes in nature. Nor to anything in rational minds, such as degree of belief or credence. Nothing in physics, nor in minds thinking about physics." -- high finance Black-Scholes equation are directly analogous to the theory of brownian motion. * "Now, I hope I have shown you that probability doesn't make sense as a description or explanation of what really happens. It can be a metaphor, it can be a technique for calculation or an approximation in a certain sense. But, an approximation, to make sense, has to be an approximation TO something. So if probabilities are to inform decisions in some approximate way, there has to be explanation, rooted in a description of an actual physical world, in which events and processes happen, not, probably happen. And not just via some adhoc axioms. So I hope I have persuaded you that it is right and proper to try to expounge every trace of probability and randomness from the laws of physics, and from our conception of the world, and from the methodology of science, so that we may fully restore realism, as well as rationality. This is a simplication, a unification, and an elimination of nonsense, and it's true. Now, I bet there are hard-headed instrumentalists in the audience, who might be thinking, 'Ok, so this simplification is all very nice and elegant, but since the principal uses of the mathematics of probability are largely unaffected, what really is the benefit of eliminating it at the fundamental level either? And, well, it's true that fundamental falsehoods don't ALWAYS rear up and bite you. You could believe in a flat earth, as many people did, for a long time. And that falsehood may NEVER have affected your life or your thinking. On the other hand, it might have destroyed the entire human species, because belief in a flat earth theory, as a description of reality, is incompatible with developing say, technology to avert asteroid strikes. * Similarly, a belief in probability in quantum theory, may not prevent you from developing quantum computers, quantum algorithms, in practice. But because probability and the Born rule entail fundamental misconceptions about the physical world, they COULD very well prevent you from developing the successors of quantum theory. In particular, constructor theory is the framework in which, I suspect, successors to quantum theory will be developed. As I said, constructor theory is incompatible with physical probabilities." * ~ Q&A "The situation is very analogous to the flat earth theory. When you assume that your garden is a plane surface, you're not assuming the flat earth theory, you are just assuming that the mathematics of the flat earth theory apply to THIS process. But, there is no way in which you are assuming that the TRUE thing is an approximation to the flat earth. It isn't." (So, my understanding is, you are eliminating the distinction between ontological chance and epistemological chance?) "I'm saying that neither of them exist, but that ontological chance can be a good approximation in some situations. And, epistemological chance really should be dispensed with all together." (There is a justification for probability where, the problem is not computable) "Well, that is a particular situation, again, where the probability calculus may be a good approximation. Rather like, if we think about the distribution of the digits of pi, then it's a meaningful approximation to say that they are going to be random. They are not really random, but, the mathematics of them has enough in common with the mathematics of truly random sequences, for it to be a good approximation for SOME purposes. But obviously not for ALL purposes." (So the common feature is just that, no matter what you call it, it's just unpredictable, whether it's ontological or ?) "Yes. Unpredictability can be MODELLED by randomness, sometimes."

It has always bothered me as a physicist that in quantum mechanics we construct objects so as to obtain and use rigorous probabilistic description, while at the same in mathematics we can only say that probabilities "naturally" appear in quantum mechanics (because classical statistical physics is not really random). I'm glad to learn that probability professors refer to that vicious circle as a "scandal" as well. It cannot be stressed enough that "interpretations" is where we impose the arbitrary connections between reality and a self-contained mathematical theory.

Deutsch does a good job of explaining why probabilities can be eliminated from fundamental physics, i.e. of why we don't need to posit stochastic processes as part of any physical theory, but he is far too quick to dismiss the concept of probabilities as credences. Many theorists, including Jeffries, Savage, de Finetti, Lindley, Adams, Good, Jaynes, Jeffrey, etc., have shown how probabilities can be understood as a measure of uncertainty, and this concept does not have to be arbitrarily assumed using an axiom such as the principal principle, but can be derived from decision theory using a primitive and very weak notion of rationality. To call credences 'subjective' is to use a bogey word - in science we don't like subjectivity - but all it really means is that the credence to be attached to a proposition is a function of the information we possess. Two people with different information will assign a different credence.

Excellent And Brilliantly Explained

🎯 Key Takeaways for quick navigation: 00:00 🎙️ Introduction to David Deutsch - Introduction to David Deutsch, a key figure in quantum information and technology. - Mention of Deutsch's significant contributions, including the Deutsch algorithm in 1985. - Overview of his work and recognition, including becoming a fellow of the Royal Society in 2008. 01:34 🌐 Constructor Theory Overview - Introduction to Constructor Theory and its development with Chiara Maletto. - Explanation of constructor theory as a new mode of explaining physical reality. - Highlighting the aim to eliminate probability and explanatory deadweight from physics. 03:23 🔄 Prevailing Modes of Explanation - Overview of prevailing modes of explanation in physics, focusing on particles, fields, and laws of motion. - Mention of alternative modes of explanation in physics, such as the probabilistic mode. - Emphasis on constructor theory's goal to unify various modes with a single explanation based on transformations. 04:18 🚫 Case Against Probability - Assertion that constructor theory aims to eliminate probability from the foundations of physics. - Emphasis on the illusion of probability in the world and its analogy to the Flat Earth theory. - Clarification that constructor theory is motivated by the non-probabilistic nature of the world, not the other way around. 06:06 🎲 Origins of Probability - Historical context of the invention of probability theory in the 16th century for games of chance. - Explanation of how probability theory was initially a mathematical model for fair outcomes in games. - Discussion on why probability theory was not originally connected to real physical quantities or processes. 08:46 🧠 Subjective Interpretations of Probability - Introduction to subjective interpretations of probability, treating probabilities as attributes of the player's state of mind. - Critique of subjective interpretations and their lack of connection to physical reality. - Emphasis on fairness in games depending on physical properties rather than subjective interpretations. 10:31 🔄 Gamblers' Rationality and Probability - Discussion on the rationality of gamblers and the disconnect between probability statements and physical outcomes. - Critique of attempts to connect subjective interpretations with physical reality. - Assertion that probability statements don't imply anything about the physical world. 12:45 🔍 Applications and Ubiquity of Probability - Overview of diverse fields where probability theory has found applications, from game theory to science. - Questioning the fundamental nature of probability despite its widespread use. - Expressing surprise at the centrality of probability to physics and its apparent effectiveness. 14:07 🧐 Examining Probability as a Useful Fiction - Acknowledgment of the practice of discarding concepts as scientific understanding progresses. - Emphasis on the need to explain the world without probability before dismissing it entirely. - Highlighting the importance of understanding why probability seemed useful and whether it remains a useful fiction. 17:51 🚧 Firewall Between Probability and Reality - Explanation of the fundamental disconnect between probability statements and physical reality. - Critique of interpretations attempting to bridge the gap between probability and factual statements. - Assertion that probability statements do not refer to the physical world. 21:21 ⛔ Scandal in Probability Theory - Reference to David Papineau's characterization of the situation in probability theory as a scandal. - Description of probability concepts forming a closed system without reference to the physical world. - Acknowledgment of the need to explain the world without probability before concluding it doesn't exist. 23:06 🔄 Normative Nature of Probability - Discussion on the normative nature of applications of probability theory. - Questioning the appropriateness of a scientific theory prescribing how one should act based on beliefs in certain probabilities. - Reference to the divide between factual and normative statements similar to the one between factual statements and probabilities. 25:29 🎰 Stochastic Physical Theories - Introduction to stochastic physical theories as attempts to incorporate normative statements about probabilities into fundamental physics. - Critique of the need for additional axioms to connect physical probabilities to decision-making. - Assertion that quantum theory, with its mid-twentieth-century state vector collapse form, is an example of a stochastic physical theory. 28:21 🎲 Decision Theoretic Approach - Introduction to the decision theoretic approach as a way out of the probability scandal. - Overview of the gaming machine analogy and the concept of the dividing line for worthiness of playing. - Emphasis on ordinary rationality guiding decisions without the need for probability or the born rule. 31:18 🎲 Critique of Probabilistic Axioms - Critique of the probabilistic axioms in quantum theory. - Probability lacks explanatory power in fundamental science. - Rationality and game theory are discussed as alternatives. 32:14 🔄 Equal Amplitude Superposition Without Collapse - Examining equal amplitude superposition without collapse. - Deriving the average outcome without relying on collapse theory. - Emphasis on the rational player's valuation of different machines. 34:52 🧠 Dispensing with Probability in Quantum World - Dispensing with probability in the quantum world. - Eliminating stochastic processes and credences in quantum systems. - Decisions derived without introducing unexplained postulates. 37:17 🔍 Applications of Probability Struck Out - Discussing the elimination of probability in various scientific applications. - Striking out quantum theory and credences from fundamental applications. - Probability unnecessary in games of chance, decision theory, and actuarial science. 40:01 📊 Probability in Information Theory - Probability's historical use in information theory. - Constructor theoretic information theory as a unified and clarified approach. - Unifying classical and quantum information, eliminating confusion. 42:02 🌡️ Quantum Statistical Mechanics and Experimental Error - Quantum statistical mechanics doesn't require probabilities. - Analyzing experimental errors and their misconceptions. - Systematic errors and the limitations of probability in error analysis. 46:17 ⚖️ Estimating Error in Experiments - Critiquing the use of probability in estimating errors. - Highlighting the inconsistency of probability in describing unknown systematic errors. - Proposing a different approach to error analysis without resorting to probability. 49:36 🎭 Probability's Lack of Scientific Function - Asserting that Bayesian ISM and subjective interpretations have no scientific function. - Probability dropped in contexts where credences are unnecessary. - Emphasis on eliminating probability from the methodology of science. 51:05 🌐 Restoring Realism and Rationality - Arguing for expunging every trace of probability from the laws of physics. - Restoring realism and rationality by eliminating nonsensical concepts. - Probability's fundamental misconceptions hindering scientific progress. 53:19 📚 Many Universes Interpretation - Discussing the Many Universes Interpretation. - Emphasizing the motion's existence rather than its outcomes. - Addressing subjective interpretations and their relevance. 56:34 ❓ Addressing Subjective Interpretations - Critiquing subjective interpretations and their logical inconsistencies. - Arguing against deriving knowledge from ignorance. - Discussing the use of probability in approximations. 59:19 🎲 Idealized Game Player in Quantum Theory - Clarifying the use of an idealized game player in quantum theory. - Acknowledging the counterfactual nature of the analysis. - Emphasizing the need for arguments that link the idealized situation to reality. 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I've believed that probability theory does not apply to physical reality for many years, but I will still continue to calculate probabilities when gambling.

I don't think I totally understand how David's concept of unitary time evolution in a slot machine is much better than the Born rule. I do appreciate that we can eliminate the _presumption_ of fundamental randomness as a matter of principle, and that the Born rule itself is probably holding quantum physics back, for example by prohibiting physicists from exploring deterministic but chaotic theories or many worlds theories to which the Born rule may be an effective approximation. What I'm seeing is essentially reasoning that the outcome of a measurement is unknown, perhaps even unknowable or uncomputable, but certainly not fundamentally random. That seems ultimately unhelpful, as it removes _all_ predictive power from QM, rather than just _some_ as the Born rule does. If all you're saying is that I shouldn't take the Born rule as a serious fundamental part of nature, well, mission accomplished, I've never been able to swallow it. I don't think anyone can until it's really beat into their heads in uni. However, if this would restore realism to QM, where, then, are we left with the experiments violating the Bell inequalities? They supposedly show that no local hidden variable theories are tenable, i.e. there can be no local realism in a universe with QM. The information about the results of the experiment _can't exist_ until the measurement is made, at least not locally. But without locality, the universe makes no sense, it just has no reason for space or time to be ordered and the concept of distance doesn't work. It almost seems better to abandon realism by forgetting about particles altogether, then stitching the theory back together by thinking of particles as events or exchanges and relying on decoherence to render separate potentialities mutually unavailable. I'm fine with superdeterminism, too, I don't know why that makes people uncomfortable. The point is that particle realism is logically dispensable, but locality is not. Non-locality is a disaster, while non-realism can be explained without breaking anything. What I really, really need in order to jump on the many worlds train is an explanation of how decoherence is mathematically approximated by the Born rule. If I live in a slice of Hilbert space where X has eigenvector aA + bB, why should I expect my amplitude seeing A to be a relative to my amplitude before observing X?

Hello Simon. This talk is set as "unlisted". I'm guessing, it shouldn't be :) (I recommend it a lot and can never find it by searching...unless I go to the Constructor Theory homepage and scroll through the resources there to find the link again...).

David talks about eliminating fundamental falsehoods. There is one possible falsehood in his rationale that he still maintains. Chaos is not based in randomness. It is best described by the phrase "immaculate non-order". David actually hit the most important part of this concept in his paper David Deutsch, Artur Ekert, and Rossella Lupacchini, "Machines, Logic and Quantum Physics". It introduces the "not" function. We find the same mechanism systemically present in all physical and theoretical systems. The significance is that paradox is a fundamental mechanism not an anomaly. The result is that logic, although a valid sub-set of reality, is not its basis. I have written a number of papers on this but when a paper expresses "what we cannot know" instead of "what we can know it" is not likely to receive attention.

I don't like fundamental probability, but I am fundamentally too stupid to explain why, so probably this video will help me.

Gaining knowledge about a hypothetical physical world does not provide sufficient information to make decisions, and without the ability to use information to make decisions, obtaining such knowledge is useful. We can't know if a physical world exists or not, so it does not have importance independent of this wider context. In that sense, an accurate understanding of probability is more important then an accurate understanding of "reality".

How would constructors at the quantum level be different from hidden variables?

Any computer simulation of quantum mechanics *must* make use of a random number generator. There are two ways to introduce the randomness that I can think of. The first is tachyonic Brownian motion which is initially orthogonal to everything else, with the Schroedinger equation being assumed to be an oscillation in the other way to travel faster than light. We need TBM in a simulation which can distinguish the behaviour of nitrogen tri-iodide from that of nitrogen trifluoride. No aetiology is proposed for TBM. Two molecules of nitrogen tri-iodide are all we need for a detector. Unfortunately the simulation of this will need to run in an excessive number of dimensions of phase space, and the simulation of any other detector will be as bad. What we can do instead is to represent TBM as classical Brownian motion for any object heavier than the Planck mass. Classical BM is very disruptive and has tachyonic BM as an aetiology. To simulate an electron in a potential well, we model the electron with the Dirac equation plus TBM. We model the well itself with classical BM. I think David Deutsch’s argument is that all flavours of Brownian motion need an aetiology. I don’t agree.

46:11 What if x1=x2, i.e., the observed value is always the same? It's no longer random but I wonder how this case fits into the story anyway.

It's so strange how probabilities have become so fashionable these days. If probabilities aren't describing anything in the physical world... then why are we even using probabilities?

What type of math must be learned to allow one to understand the arguments and explanations involving the equations in the section dealing with the gambling machine (the quantum casino)? My education only went as far as basic calculus.

Dear Professor, my question relates to slide (minute 35-37) where you refer to Quantum theory as unitary. Does the reference to Unitary imply Total probability of 1 or 100% and thus probability theory again is snuck back into the argument while the very purpose of this slide is to prove that the new theory should discard the need for probabilities? Where am I going wrong / missing the point? I would really like to understand this proof because intuitively I want to agree with your approach (as well as with Einstein's) where probabilities would be redundant in explaining quantum physics. Thanks so much!

Can I see the paper in reference to 33:05

So, Constructor Theory (CT) is trying to deal with the "problem of time". Probability tells us about the whole history of events without time (non-deterministic), but our observation of the universe makes time emerge giving us just a range of that history (quasi-deterministic), and CT suggest we should focus on the deterministic as this is the range of the universe that works for us. Sounds fair, but the flat-earthers comparison doesn't seem appropiate as we should also understand what lies beyond our observable range. Separating time and timeless processes is a good start anyways.

Hey, this doesn't even seem to be about Constructor Theory anyway. It's just a complaint about the Born rule, apparently. But the Born rule is only invoked by the standard (Copenhagen) interpretation, not by Many Worlds or Bohm interpretations. So I'm still looking for a simple explanation of CT, if there is one.

This video really shocked me as I would call mysefl a fan of probability. I have always known that events like coin tosses are not truely random in a fundamental sens and the same with thermodynamics - yet I don't know what the 2nd law could really mean however I do understand the intuition behind it. I'm still a a highschool student with ambitions of becoming a mathematician and one of my main field of intrest is probability so it does not mater for me if probabilities cannot be thought as phyisical "objects", I will still feed my intrenst as I did befor when I realised dice roles are nat really random (but to tell you the truth, the part of quantum theoir suprised me as I have grown up knowing that it's fundamentally random, now turned out to be not. Is it mean that its fundamentally deterministic or I'm losing the point?) And one last thing. I can understand that probabilities cannot be thought az physical things but what can we say abaut other mathematical objects like fields of forces space-time coordinates, wave-functions? Are they physical or an other useful but potentially misleeding thigs like probability? p.s.: Sorry for my bad English.

Constructor Theory is not the first explanation that eliminates probability from fundamental quantum mechanics. As I understand it, the CT view is simply Hugh Everett's "many worlds" interpretation of QM. Why is this preferred over the de Broglie-Bohm interpretation, in spite of several experiments that seem to confirm the latter? Just that it is a bit simpler. But that simplicity comes at a high price: since our experience is always within one particular path through the multi-Universe, many worlds isn't really useful for making experimental predictions. Bohmian mechanics, on the other hand, generates deterministic trajectories for fundamental particles, AND explains the strange behaviors of QM experiments, which is quite helpful. Why do physicists, and CT, resist adding the initial positions of particles to the wave function? It gets rid of probability as an axiom (Born's rule) AND removes the catastrophic "wave function collapse" and the appeal to mysticism (including a supposed effect of human consciousness) that is required by the Copenhagen Interpretation.

What if true randomness is deterministic? (As in Pascal's triangle.) It's unpredictable from within, but it's a simple mathematical function that generates everything.

Given that a deck of cards is finite, isn't the number of games of poker also finite, given some reasonable number of players? I mean, it has to be less than 52, right?

The analogy between "facts" and "probabilities" breaks down because correlation is not transitive, while factual deduction is transitive. The correct way to proceed is ala Jaynes, using Bayesian rules to update beliefs based on observations. This gives entropic time and categorical quantum logic as our fields of study, since categorical logical deduction is also transitive. I will take constructor theory seriously when they can formalize their arguments. The main element missing is *choice*, and the substitute of "rational" reasoning is insufficient.

Is physics without probability, the same as, the universe with certainty?

Einstein will be proud.

23:20 Deutsch is right that probabilities are "in a certain sense... normative." He's wrong to say that this is a problem. I think all theories are normative in this loose, instrumental sense. Theories give you advice about how to act, that's the entire point.

Cool, but why is it unlisted?

at about 20:51 he talks about "a rational gambler".... but there's no such thing!

We need the measurement called temperature to do physics, chemistry, and medicine. Yet temperature is an emergent and statistical result of random processes that actually exist in nature and are called heat. So there is a counter-example to Deutsch's claim that there is no fundamental stochastic process. Another counter-example is chaos, which can result from a deterministic algorithm (such as in cellular automata), and can also result from our inability to determine initial values of physical measures (such as in the prediction of weather). If heat (and Brownian motion) are truly random (having a stochastic distribution), then what is so horrible about quantum mechanics hypothesizing that all measurements near the Planck length are essentially random? It is okay to do away with randomness in our axioms, but let's do it in a way that actually explains experiments in terms of deterministic trajectories (as in the de Broglie-Bohm interpretation) rather than in a way that limits us to one narrow path in a multiverse (as in the Everett Many Worlds interpretation).

There's an awful lot of handwaving going on around the 40-minute mark. Deutsch has good arguments against the idea of "physical" probability, but although he is dismissive of epistemic (Bayesian) probabilities, his arguments are very weak there. He gives one no general method for dealing with incomplete information, which is exactly what epistemic probabilities are for. It has in fact been proven that if you want to reason about degrees of credibility, and you want to do so in a manner consistent with classical propositional calculus, probability theory (or something isomorphic to it) is your only option.

I _knew_ there was a reason I hated Bayesian reasoning. Not as much as I hate the blemish that is the Born rule.

If we are in a deterministic world, no randomness, no free will, hence this (universe) is just a computer that calculates, great. However, if the calculus is soo huge to be computed (and it will be), again we will need the help of statistics to predict. Maybe we are condemned to life in a flat world knowing that is not flat.

Deutsch's supposed proof that "systematic errors can't be bounded" (~45:00) is bogus. He confuses single measurements and averages from repeated measurements. An average of two measurements is not the same kind of measurement as the individual measurements, and hence should be expected to have a different error bound.

The Bayesian theory of probability does not have to assume how things work, nor the so called principal principle in order to be applicable in Physics or the real world in general. As Jaynes and other have shown , a set of rationality rules implies the probabilistic framework. I am curious as to why Deutsch did not include statistical mechanics, the most important application of probability in Physics before quantum theory. I would like to see how he would obtain thermodynamics from the underlying mechanics without any use of probability.

So God doesn't play with dice after all