### Intersections of Probability, Philosophy, and Physics

## bSI Epistemology Camp: 2024

Anthony Garrett delivers a comprehensive lecture, touching on several major themes centered around the principles of probability, scientific methods, and the philosophical underpinnings of science. He discusses his academic journey, encounters with prominent figures like Ed Jaynes, and his exploration into areas such as quantum mechanics, Bayesian probability, and the challenges posed by postmodernist criticisms of science. Garrett emphasizes the enduring utility and necessity of rigorous scientific methods, logical consistency in the application of probability theory, and the importance of rejecting flawed philosophical trends that undermine scientific integrity.

Anthony Garrett has a PhD in physics (Cambridge University, 1984) and has held postdoctoral research contracts in the physics departments of Cambridge, Sydney and Glasgow Universities. He is Managing Editor of Scitext Cambridge (www.scitext.com), an editing service for scientific documents.

## Transcript

Good afternoon.

I’m Anthony Garrett. Call me Anton.

Now, the brief that Greg and Emily gave me was to speak about Ed Jaynes and David Stove, both of whom I knew personally, and the brief was also to talk about the maximum entropy method in general and in what’s called statistical mechanics in particular. All of that in the context of the Broken Science Initiative. These are wide-ranging subjects, and the only common thread, the only common thread I could find, is my involvement with all of them. So this will be something of a selective scientific autobiography.

From age 11 to 18, I went to a grammar school near Manchester in England. In those days, the authorities bought some of the places at private day schools; that’s what a grammar school meant at that time. After a dance with the subject of chemistry, I developed a love for physics. I just wanted to take physics as far as I possibly could, and it turned out that I was able to become a researcher in theoretical physics. I actually preferred the practicals in chemistry; much more fun.

I said that I fell in love with physics. Research is a passionate activity; the outside world sees a bunch of physics or mathematics nerds, but serious researchers are as dedicated as top athletes. That is a more fair comparison, but it’s not one you’ll see on TV shows like “The Big Bang.” There is a beauty in the laws of physics, and that’s what attracts people to it.

I like to ask other physicists why the laws of physics are beautiful. You get some interesting responses. Now, after high school, I went to Cambridge University, where there’s a great tradition in physics. I got my degree and stayed on to research for my doctorate. That was on the physics of ionized gasses in the ionosphere. Up there. Ionized gasses are called plasmas, although it’s nothing to do with blood plasma.

Physics is also important in controlled nuclear fusion, aiming to generate electricity using the same processes that power the sun. Today’s nuclear power reactors use nuclear fission, which is a different process and not as good but it’s easier to solve technologically, which is why it came first.

Now you can view an ionized gas as a type of fluid and look at its flow treated as a fluid. That’s okay, but there’s plenty going on that it can’t explain, and a deeper level of description is needed that looks at what the atoms and molecules and ions in the ionized gas are doing and then constructs the variables that specify the fluid description from what the atoms are doing.

If I knew the positions and velocities of all of the million million million million molecules of the air in this enclosure, I could in principle calculate the pressure, density, and temperature of the air and the wind velocity at every point. But how to do that from all that molecular information?

Now, if you ever heard the phrase “too much information,” you’re facing that problem with a vengeance. Pressure, density, and temperature are, in some sense, averages over those million million million million molecules. But in what sense? What sort of average is it? A time average that’s called ergodic theory, and its mathematics is horribly difficult, even for very simple systems with two or three molecules, let alone all those millions.

Probability is also used to average things, and that’s the way forward in this field, and that’s called the maximum entropy principle. That was championed by Ed Jaynes. He adapted Claude Shannon’s 1948 expression for the information content of a probability distribution. There’s obviously more information in a tighter distribution than there is in a broad one where you’re not really sure what the answer is.

Some of Ludwig Boltzmann’s work in the late 19th century was a particular case of Ed Jaynes’s application of maximum entropy in statistical physics. But how can a probability average be something physical if probability is about information, and different people can have different information?

Well, Ed Jaynes explained that in an underrated paper called “Microscopic Prediction.” The reproducibility of your experimental results is the key, and when two people have both got reproducibility, they’ve got the same information. I can use maximum entropy, I won’t go into how, to model the relation between pressure and density, but experimentally, I find a different relation in the summer and in the winter. That’s because you’ve also got to take temperature into account.

So you use maximum entropy, try again allowing for pressure, density, and temperature this time. That works fine for air, but it doesn’t work for ionized gasses because you also need to know the electromagnetic field. You then apply the maximum entropy principle, taking account of all the variables that you need to measure in order to get a reproducible relation between them, and that’s the way forward in statistical physics.

So how did I first get to hear about Ed Jaynes’s work? Well, one of my friends and colleagues was, and still is, a man called Steve Gull, an astrophysicist, and he had been put on to Jaynes by a man called Jeff Daniel. They saw in maximum entropy a better way of cleaning noise from maps of the radio sky. That’s maps of the sky and the distant universe made by radio telescopes at radio wavelengths. Steve Gull and Jeff Daniel published a paper in 1978 in Nature about how to do this.

You can assign an entropy to the raw data image, and you then want the image having the greatest entropy consistent with there being a certain amount of noise. It worked a lot better than other methods of image processing. Steve Gull has improved it since over the years with another colleague, John Skilling.

So, Steve Gull got me reading Ed Jan’s papers. In the early 1980s, four things happened. First, because of those papers, I took up the Bayesian view of probability. As an undergraduate, I’d learned to do the sums in statistics and probability exercises, but never felt I understood what I was actually doing. After going Bayesian, I did.

Second, in 1983, a book containing a selection of Ed Jaynes’ papers on these subjects was published, and we all seized on it.

Third, Steve Gull and John Skilling invited Ed Jaynes to spend the academic year 1983-84 in Cambridge, and I was privileged to share an office with him. We didn’t coincide all that often in that office because we both preferred to work solo in our accommodation in our respective colleges inside Cambridge University. But I did bump into him on quite a few occasions, and I discovered that Ed was different in person and on paper. On paper, he was extrovert and punchy; in person, he was quite introvert. Steve Gull actually got to know him better than me because they both played Beethoven’s piano sonatas to quite a high standard and loved discussing them.

The fourth thing that happened was that the annual maximum entropy conference series began. The pioneer conference was organized in the late 1970s by Myron Tribus, who was the dean of the engineering faculty at MIT. He also at one time had an office in government in Washington, too. In 1969, Myron had written a very fine book on Bayesian probability and its engineering applications called Rational Descriptions, Decisions, and Designs, and he championed maximum entropy against the other schools of statistical mechanics.

He told me that he had cornered Ilya Prigogine, leader of the non-maximum entropy Brussels School of statistical mechanics, who had been avoiding his difficult questions for years. He finally cornered him in a basement in MIT, but he still got no answers.

Anyway, the annual MaxEnt conference series got going in the 1980s, and I learned a lot from those. After 10 years in Cambridge, getting my first degree, doctorate, and first postdoctoral research contract, I asked Ed Jaynes if I could work with him next at Washington University St. Louis, Missouri, where he was a full professor. To my delight, he said yes, and that was unusual because he preferred to bring on the better ones of his own research students. But he also warned me that his money for 1985-86 was committed, so I should come the year after and find something to do for a year in the meanwhile as my time in Cambridge was up.

I got a contract at the University of Sydney, Australia, in the theoretical physics department there, and that’s where, through a mutual friend, I met David Stove, who is in the philosophy department there. I never got to work with Ed Jaynes because his health collapsed and he retired to work on his probability book, which was the one that Greg flashed around earlier. It was still incomplete at the time of his death, a decade later, and one of his research students who stayed on, Larry Bretthorst, pulled the manuscript into shape and got it published.

Meanwhile, I got extended in Sydney and got to know David Stove better. Most physicists aren’t very interested in the philosophy of science, and those physicists who are interested generally suppose that Karl Popper cleared all that stuff up. If you want to look into it, but me, I just want to get on with thinking about theory and doing my experiments. Now I was skeptical of Popper, but at that time, I couldn’t put my finger on what was wrong. David Stove explained that for me.

He told me that Popper rejected inductive logic, but inductive logic done correctly is the same as probability theory done correctly; i.e., in a Bayesian manner. Both of them are often done incorrectly, so there’s a lot of confusion. Probability is what you need in order to see which theory is correct in the light of experimental data. The theory is testable, meaning that the data shift the probability of the theory being correct toward either naught or one. Meaning it’s incorrect or correct within our best knowledge at that time.

But because Popper rejected inductive logic, he couldn’t use this correct inductive criterion of testability, and so instead, he used the criterion of falsifiability: to be a genuine scientific theory, the theory must be capable of being proved wrong. This is a complete perversion of how scientists work. Did Einstein think of relativity as something to be proved wrong, or is something to be proved right? Do we open champagne bottles when our latest experiment proves our theories wrong? “Hey, come to a party and celebrate, my theory has proved wrong today!” It is complete nonsense, obviously.

Now it didn’t help that Popper rejected inductive logic but accepted probability theory, even though when they’re done correctly, they’re the same thing. It isn’t easy to argue with incoherence. I saw Popper speak a couple of times, and I preferred to keep quiet, but David Stove dissected Popper’s rhetoric acutely in that book that you saw earlier. David was devastating at rhetoric himself. He also took aim at Thomas Kuhn, another anti-inductivist, whose famous book, The Structure of Scientific Revolutions, made popular the phrase “paradigm shift.” An example of a paradigm shift is a transition from the Newtonian description of dynamics to Einstein’s description involving relativity theory. Today we prefer Einstein because the predictions of his theory fit the experimental data better, but that fit is performed using probability theory, which is inductive logic, which is rejected by Kuhn. And that’s why Thomas Kuhn ultimately says that theories come and go as arbitrarily as fashions in clothing.

He concentrates on the differences in the Newtonian and Einsteinian way of looking at the motion of objects conceptually; they’re quite different while ignoring the better fit of relativity’s description to the observational data from experiments. In brief, Kuhn was a good historian of science but a poor philosopher of science. From Kuhn, the path is wide open to science as being just another human activity in which there are power struggles, without any relation to the idea of truth. That’s postmodernism, and the first prominent philosopher of science to embrace it was Paul Feyerabend. This, in turn, led on. Sadly, Feyerabend wasn’t the end of the line; it led on to the science wars of the 1990s, in which postmodernist critics of science subtly conflated the doing of science, which is a human activity and fallible as any human activity. That’s why we’re here today. They postmodernist conflated the doing of science with the laws of nature that science seeks to discover. Those laws are independent of culture, and that is a truth claim. Unlike all truth claims, postmodernists hate it.

They claim that science is just Western culture’s way of describing how the material world interacts. Now, in one sense, it’s trivially true that gravity has a different description in, say, two different cultures, China, and the USA because in China, gravity is described using the Chinese language, and in the US, it’s described using the English language. But science asserts an underlying unchanging reality that is the same in America and in China. If postmodernists really believe that gravity itself is different in America and China – which they never say explicitly but is how they write – then I would ask them to jump out of a high window in China. Let them offer a better description for how long they take to hit the ground.

Postmodern descriptions of science were shown up in a famous hoax in 1996 when the physicist Alan Sokal wrote a spoof paper towards a transformative hermeneutic quantum gravity. He mixed physics terms arbitrarily with postmodern jargon and sent it off to a postmodern journal called Social Text. They published it, and Sokal then blew the gaff and said that it was a spoof.

But don’t think that the science wars only needed fighting once. Today the postmodernists are starting to talk about things like “black mathematics” and “Native American mathematics.” This is nonsense, of course. There is only right mathematics and wrong mathematics, and all races and all cultures are welcome to participate in right mathematics. Postmodernists are following in the footsteps of the Nazis, who were fond of talking about Jewish — not just about Jewish scientists and Aryan scientists — but Jewish science and Aryan science. That is not a good description for the postmodernists to follow.

When the Jesuit missionary Matteo Ricci gained access to the court of the Chinese emperor 400 years ago, he showed the Imperial court mathematicians the idea that you could prove a theorem step by step from axioms, as Euclid had done 2,000 years before. The court mathematicians were deeply impressed. Science and mathematics are gifts from one culture to another, but the postmodernists want to undo all of that. On university-level committees, their aim is to outflank, undermine, and ultimately defund genuine science and mathematics. They do this because they cannot bear the truth claims that are made by science and by mathematics.

And we need a coalition of scientists and mathematicians of all ethnicities to call out the postmodernists and to say this: the price of truth and freedom is perpetual vigilance. But it all started with Popper, Kuhn, and Feyerabend in physical science and Imre Lakatos in mathematics. Biological sciences have other enemies. An early example of that was Lysenko in the Soviet Union. It’s an amusing irony that Popper, Kuhn, Feyerabend, and Lakatos didn’t get on with each other, but they’re no less dangerous for that. They were parasites on science, not symbiotes, and like all parasites, they have done their host no good at all. David Stove debunked all four of them.

Now, David never fully agreed with me about probability. There are innumerable points of view about probability among philosophers, but by putting my understanding of probability theory together with his exposing of Popper’s error, I was able to reach an understanding of the philosophy of science which satisfied me completely. I put it into the proceedings of the 1988 Maximum Entropy Conference, which was organized in Cambridge by Steve Gull and John Skilling. I was back there from Australia by then, and I was on a post-doctoral research contract at the University of Glasgow in Scotland. But let me finish about David Stove.

He was like Ed Jaynes — dynamite on paper, quiet in person. We had wide-ranging discussions weekly over lunch in the faculty club at Sydney University, and his untimely death in 1994 was a tragedy. I mentioned that my view of probability plus David’s view of Popper allowed me to reach a full understanding. So, what is my view of probability? Even “Bayesian” has become too vague a word nowadays. There are many different tunes of Bayesian, and here I want to turn to another of my heroes in the field, one to whom, to my great regret, I never met: Richard Threlkeld Cox of Johns Hopkins University in Baltimore.

In 1946, R.T. Cox derived the laws of probability — they called mathematically the product rule and the sum rule — in a new way. They’d been known since a correspondence between Fermat and Pascal in the middle of the 17th century, but Cox put them on a much clearer footing. He wrote at a time when the frequentist view of probability was dominant. The text of his paper isn’t very clear, but the strategy in it is breathtaking. When we talk about a probability, what is it actually a probability of? Ultimately, every probability is how strongly a binary statement — that’s something that’s either true or false — is implied to be true if you suppose a related binary statement — for example, the probability of rain here tomorrow or not, given that there’s cloud approaching or not.

Now, binary statements — things that are true or false — obey an algebra that’s Boolean algebra, the binary logic used in designing computer circuits. So if a probability is a probability that a binary statement is true, and if binary statements obey an algebra, that means that probabilities must obey a corresponding algebra. That was Cox’s strategy for deriving the laws of probability in 1946, and it’s a lot more cogent than the axioms that most people use today, which are called the Kolmogorov axioms.

When I looked up Cox’s theorem on Wikipedia, as Greg suggested, I was pleased to see that at last there is an entry for it. It took Wikipedia long enough, but I cannot recommend that entry; it does not fully understand the sheer radicalness of what Cox did, and which I’ve explained to you.

Cox’s viewpoint also allows a definitive response to frequentists and other people who take a different view of what probability is. I reckon that probability, to repeat myself, is a number that measures how strongly one statement about the world implies another. Thanks to Cox, we know that this definition obeys what people have called the laws of probability for 300 years. On those grounds, I’m happy to identify how strongly one statement implies another as probability, but if frequentists or anyone else disagree, then I’m not going to take them on head-on because how strongly one statement implies another is what you actually want when you’re tackling any real problem where there’s uncertainty. You want to know how strongly the weather forecast implies rain tomorrow, for example.

So, I don’t waste time disputing the meaning of the word “probability” with frequentists and others. I get on with calculating how strongly the weather forecast implies rain because that’s what I want, and I leave them in their echo chamber.

After I’d been unable to work with Ed Jaynes and had got extended in Sydney, as I said, I did a third post-doctoral stint at the University of Glasgow. After that came a fork in my life: I was head-hunted for a senior position in a university town that I then visited incognito, and decided I didn’t like, so I didn’t proceed with the application and returned to Cambridge, where I started an editing business for scientific documents. I carried on doing research with Steve Gull and others who were still inside the university. I’ve never regretted that choice because the sheer amount of useless paperwork that university scientists have to engage in seems to increase year upon year. It’s a slow process, but after 20 years, it becomes a debilitating one to deal with that paperwork.

In the beginning, universities hired administrators to do the paperwork for academics, so the academics needn’t waste their time on routine tasks when they could and should be doing research. But academics have a motive to reduce paperwork; administrators have a motive to increase it, and they’ve now gained so much power that senior administrators routinely tell full professors and heads of research departments what to do, even as those professors have to spend more time on paperwork than ever. Salaries of those administrators come from money that should go to research. Furthermore, it should be a matter of principle, a declaration of emancipation, that the most junior research student has a higher internal rank within the university than the most senior non-academic administrator. Not necessarily in salary, but in terms of internal rank. I suggest that most of these administrators should be given a year’s notice, and professors should return to do-it-yourself administration. They’d quickly decide what was necessary and what wasn’t.

Back in Cambridge, I started thinking about quantum theory. Compared to the rest of physics, it has two novel features: first, it predicts the outcomes of some experiments only probabilistically, not deterministically. That’s why I got into that, and into probability in physics. It gives only the probabilities of the various possible outcomes. The second unique feature of quantum theory is that its predictive apparatus — if you look at the equations — contain mathematical symbols that you can’t do without but that don’t correspond with anything that you observe experimentally. Now, these two features raise questions of interpretation that never enter classical physics. Don’t enter old Newtonian physics, don’t enter even Einsteinian physics, and these new features, core of interpretation, cause a lot of confusion.

Perhaps the craziest idea I’ve come across is called the many worlds view: that when you do a measurement, the universe actually splits into many replicas of itself, and each possible result occurs in one of those universes. I would ask people who hold to this, how could you ever know? I prefer to call it the many words view.

Another crazy idea is that the experimenter’s own consciousness participates in determining the outcome of those experiments where quantum theory does not predict exactly what will happen. Entire books have been written about quantum theory and consciousness, mostly by people who couldn’t solve the Schrödinger equation for a harmonic oscillator, which is the simplest non-trivial undergraduate exercise. But one or two of those books have been written by people who really should know better.

I take the view that if quantum theory doesn’t predict what happens in each run of an experiment when you do your best to prepare the apparatus identically each time but get different outcomes each time, I take the view that the apparatus actually was different at the start of each run, but different in a way that I haven’t learned to see or to control. In that case, I need a theory that describes what is going on at that deeper, hidden level, and this is called the hidden variables view of quantum theory. It’s very much a minority view, but it’s the only view that stands a chance of improving testable prediction, and that is what physics is all about.

If you self-censor and you refuse to ask the question, “Why does one particle go that way and why does the next particle go that way, even though I set up the apparatus identically, as best as I can see,” if you refuse even to ask the question, it’s no sin not to know the answer. But if you won’t ask the question, then you are betraying the calling of science, which is to improve testable prediction.

Now, I grant you that something called Bell’s theorem — you might have heard of — means that that deeper level of description is pretty wild. I’ve published a Bayesian exposition of Bell’s theorem, which makes it easy to understand. But so what? The task of scientists is to ask hard questions about the physical world, not to self-censor. There are so-called no-hidden-variables theorems, but if you look at them closely, what they say is you can’t have hidden variables of this type or that type. I would say, fine, let’s have them of a wider type.

Now, you can move on from the kind of quantum theory I’ve just described to what’s called quantum field theory, and quantum field theory is, in some ways, a triumph of physics. It can predict certain properties of the electron to better than one part in a thousand million, but I’m not prepared to be told that I can’t answer, I can’t ask the question, “Which of these two slits will the next electron go through?” I’m not prepared to be told that’s 19th-century thinking. Your two slits are really just themselves a bunch of quantum fields.

Well, my answer to that is that I could prepare an automaton that, according to which of the two slits the electron goes through, prepares different states which have different descriptions in Quantum Field Theory. And if I did that, then Quantum Field Theory could never predict which Quantum field description that outcome system has. So, there is still something missing, that is a clear failure, and beyond that, even worse still is string theory.

On that subject, I’ll content myself by recommending a book about it called “Not Even Wrong,” a great title by the physicist Peter Voit, and by quoting an Amazon review of another book on string theory called “The Elegant Universe” by Brian Green. Green’s book is an exposition of string theory for the intelligent layman, and an anonymous review on Amazon ran as follows:

“This book is written at such a level and so well that almost anyone can get an appreciation of what string theory is. Even though the author is a proponent of string theory, he has presented it in such an even-handed manner that anyone with a modicum of scientific wisdom can see that it is one of the biggest scientific boondoggles in history.

“Contrary to the claim of elegance in the title of the book, string theory is an arbitrary mathematical construct with parameters, topologies, and dimensions tacked on at every turn. Let us hope that this excellent book is the beginning of the end of string theory.”

And that’s the end of the quote. A better example of broken science I could scarcely imagine. String theory is more like a drug than anything else.

There’s another situation in which the doing of science is broken, and happily, this is one where there’s a way forward. It’s one that Gerd mentioned this morning. At the 1997 Maximum Entropy Conference, I spoke on an improvement that I’d made to Cox’s derivation of the laws of probability, and I wrote it up for the proceedings volume. But I thought it was important enough also to publish in a peer-reviewed journal. I sent it off to the American Journal of Physics because that’s where Cox had published his paper in 1946. They said it wasn’t physics. No, they’re right, but they had published Cox.

There wasn’t a sympathetic Bayesian statistics journal at that time, and all the other statistics journals were frequentist. I sent it to a maths journal; they said it was statistics. I sent it to a philosophy journal; they said it was mathematics. I was getting the runaround, and at that point, I gave up. Now, today, happily, we have the arXiv, a-r-x-i-v, it’s an internet repository for preprints in mathematics and physics. You write your paper, you publish it in the arXiv, and then you submit it to a journal for peer review, and you put the journal reference onto its arXiv page if it’s accepted. The arXiv page gives the date of uploading, and that establishes your priority because peer review can be a slow process.

Going on the arXiv also allows others to read it sooner. Early on, in the days of the arXiv, scientific publishing houses tried to say that they wouldn’t consider any paper for publication that had been uploaded to the arXiv, but its advantages to scientists were so great that the publishing houses had to give way. Today, some scientists just publish on the arXiv and don’t bother with peer review at a journal. That’s what I’d have done in 1997 had the arXiv, which I think existed by then, but it wasn’t prominent; it wasn’t mainstream in 1997. In 2000, I derived the principle of maximum entropy from the laws of probability, and I didn’t bother with a journal for that; it went in the conference proceedings, but that’s not proper peer review, but the arXiv was available by then.

Now, uh, scientific journals originally had two functions, both valuable. One was dissemination of research results, the other was quality control through peer review. The internet solved the first of those; the arXiv is an example. It could solve the second if scientists reorganize peer review or drop it entirely and just let the arXiv flourish. That hasn’t happened because peer-reviewed papers are needed to get jobs. Scientific publishers make scientists typeset their own work, they get peer review for free, they grab copyright, and then they charge enormous sums either in subscriptions or paid charges in order for the research community to view its own work, work which is often publicly funded. Scientific publishing is twice the size of the recorded music business, and professional institutes of physics, chemistry, etc., have publishing arms that are part of this rip-off, generating a conflict of interest with their members.

These institutes campaign for the present state of affairs to continue, but today, online-only journals are starting to appear. They work in various ways, and one option is an arXiv overlay journal. You put your paper on the arXiv, and you inform the journal’s managing editor that you’re submitting the paper to that to his or her journal. They then arrange peer review if it passes, it goes onto the journal’s webpage with a link to the arXiv page, and of course, you update the arXiv page correspondingly to say you’ve been accepted and peer-reviewed by that journal. The cost of this is very little.

I have just talked about it, but someone here is actually doing this in his own particular field of astrophysics. Peter Coles, over there, is Professor of astrophysics at Maynooth University in Ireland. We’ve published a Bayesian paper together a long time ago, and he’s the founding editor of the Open Journal of Astrophysics. I hope to see more journals like this in the near future, and the great rip-off comes to an end. You would do well to listen to Peter on the subject during tomorrow’s open discussion time.

Physical science, here’s my definition, is a quantitative dialectic between theory and designed interventionist experiment. If I do this here, what effect will it have on that over there? Sometimes theory is ahead, and theoreticians ask experimentalists to test a prediction. Sometimes experimentalists find something they didn’t expect, and they challenge theoreticians to explain it. Designed interventionist experiment is the extra ingredient that the ancient Greeks didn’t have. That’s why their mathematics and their astronomy were brilliant, but why they had no other worthwhile science.

Now, at the research frontier, it’s common to have differing schools of thought. That’s fine; that’s why it’s the research frontier. But science can get set back a generation if one school that turns out to be wrong succeeds in monopolizing all the grant money and consequently all the jobs. Truth will eventually out, but it can be a slow process. Max Planck famously said a new scientific truth does not generally triumph by persuading its opponents and getting them to admit their errors but rather by its opponents gradually dying out and giving way to a new generation that is raised on it. So, it’s important that the scientific community should have a few Mavericks, properly and professionally trained within the mainstream but prepared to think outside the box. The Broken Science Initiative recognizes this. Thank you, Greg and Emily.

Science is also vulnerable to fraud. Science presumes good faith behind any scientific paper. No journal editor, no referee can possibly check papers for fraud as well as for error. Editors hope that the risk of exposure is enough to prevent fraud, the same way you get random ticket inspections on some train systems. But in some fields, there are financial pressures to publish bogus results, that is, to falsify. Also, some academics have such an ideological commitment to their own preferred school of thought that they’re prepared to gamble on being right by changing the data to fit their theory. I think that’s still quite rare.

The vast majority of papers in theoretical physics are completely correct but useless, and that is a problem that’s to do with how research is funded and how researchers get jobs. People, including Feynman, often say that science is based on skepticism. Someone makes a claim, fine, do the experiment yourself to check it. You got an anomalous result, go get others to check it. At a deeper level, though, science is based on the belief that there is order in nature, order out there that we can comprehend, and it is based on a passion to know. Recall that I said serious scientists are as dedicated as serious athletes. Science is based on commitment. If you love science, you will want what’s best for it, and you won’t cheat on it. Science is special, it has transformed our lives in the last 400 years. Let us defend it and keep it special. Thank you.

#### Q&A

[William Briggs]

[I want one comment. Not only do you get to do your own writing, your own typesetting, you pay page charges, you also get to sign away your copyright to the journal, and the journal then goes and charges libraries exorbitant fees to read your paper.]

I’ll add that to the written-up version. Thank you, and I’ll publish it for free. Anything else?

[Dale Saran]

[Where does Claude Shannon’s work fit in here with respect to Jaynes and even Cox?]

It’s quite different from Cox’s work. Claude Shannon’s derivation of the mathematical form of the expression for the entropy in 1948 as part of information theory was ingenious. And Ed Jaynes understood that it could be used in the statistical physics problem of boiling down the information about the million million million atoms in this room and what they’re doing down to work out how fast the wind is blowing at any point in this room. It uses also the Shannon form, minus the sum of P log P, but of course, Shannon derived it in the context of the transmission of information down electrical wires, and it’s valid there too. It’s a remarkable expression.

Excuse me, the P log P form has been around for about 150 years now. Boltzmann used it.

Was there something else over here?

[Greg Glassman]

[I have a question, a comment. The multiple universes bit, I think we’re on the subject of the epistemological vs ontological probability and the absurdities that come out of the belief that the probability is ontological. In Sabine Hossenfelder’s “Lost in Math”, are you familiar with that? Isn’t she moaning about the same phenomenon? Aware of what happened? Yeah, okay. I’d like to talk about that tomorrow; we didn’t just now. I have the photo from the 1927 Solvay Conference; Maggie got it for me, and the original photo was in color. What made the papers was black and white, but what an amazing thing that so many brilliant minds got together and made such a horrible decision in consensus, right?]

[William Briggs]

[Yeah, here we go.]

[Greg Glassman]

[There, prominent physicists are bemoaning the lack of progress in physics, and we’re talking about one in particular, Sabine Hossenfelder, who wrote “Lost in Math,” a great read, but she basically goes to the homes of Nobel laureates in physics, gets invited in, and sits down with them. Over an extended and friendly conversation, she gets them to admit it’s all bullshit. It’s not said like that, but as you watch it unfold, you’re like, “That’s exactly where this is going.” It reminds me of the anonymous review.]

Well, I half agree with Sabine Hossenfelder and half disagree. There’s a tension between wanting to use mathematics to express physics and finding the most beautiful theory. There’s a beauty in some mathematics that isn’t in other mathematics, but in physics, the experiment has the last word. I think you can reconcile the two points of view because it turns out that generally, the most beautiful mathematics is the theory that’s correct, but you can be overly guided by aesthetics, or you can be overly guided by experiment and not allow yourself free rein to think before submitting your thoughts to the next experiment.

[Malcolm Kendrick]

[You know, there is value ???, for example, the Michelson-Morley experiments that disprove the existence of aether and allow or pave the way for Einstein’s theories after that. I still believe falsification can provide stronger improvement, or at least the association proves something to be true. You seem to be suggesting it’s just not correct.]

I would say that’s not falsification in the sense that Popper means it. I would say that the Michelson-Morley experiment drove the probability of the ether interpretation of the results down to 0.000000001, or whatever. That would be my take on it. Popper is really talking about probability zero, and it might not look very different on paper between zero and 0.00001, but it’s very different, conceptually.

[Greg Glassman]

[Popper says that we have good logical reason to believe a theory that has survived against falsifications repeatedly over time, and somehow that’s not induction.]

As David Stove said, Popper rejected induction but accepted probability, and probability done correctly and induction done correctly is the same thing; both are often done incorrectly. Therefore, his view is incoherent, and it’s not easy to argue with incoherence.

[Greg Glassman]

[I have another question. Gerd, go first.]

[Gerd Gigerenzer]

[Uh, when the probability theory emerged, we came up with three different interpretations: frequency from mortality tables, the degrees of belief, and the logical view from law, then propensity from gambling. Do I understand you correct that you are in line with the view of logical beliefs from the law?]

I’ll answer that with a bit more autobiography. For a long time, I used to argue that probability was a degree of justified belief—the key word being justified. Then I realized that it was best to say it as the strength of implication of one proposition by another, and that still obeys Cox’s axioms and therefore obeys the sum and product rules, and that is a definition that I believe is the one you need in any actual problem. So, I prefer not to engage with people who say probability is propensity or probability is frequency. I won’t take them on head-on. I’ll go around them and I’ll solve the problem while they’re still arguing with each other about what probability means.

[Gerd Gigerenzer]

[How does your view about strengths of implication relate to Carnap’s view about probability?]

Carnap, I never found very clear on the subject. His work on inductive logic introduced a parameter Lambda, which I found completely arbitrary and which made no sense to me. It’s the only way I can put it.

[Can you expand a little bit on what you said, that you had a disagreement with Stove on probability? Can we talk about that a little bit?]

Uh, we over when I met him weekly over lunch, we preferred not to talk about probability because we both thought we were experts, and we disagreed with each other, and we liked each other. So today, we’d do it by email; in those days, we did it through the University of Sydney internal mail. I’d like to think that if I were able to explain to him as strength of implication that one statement be true if another one is taken as true, I’d like to think that would have convinced him. But I hadn’t gotten there in 1987; I was still talking about a degree of justified belief. At one point, he proved— he sent me an alleged disproof of that viewpoint, due ironically to Popper. I don’t think it disproved it. I disproved his disproof, to my satisfaction but not to David’s. But I owe an enormous amount to his debunking of Popper, Kuhn, Lakatos and Feyerabend. I miss him.

Okay, I think I’ll leave it at that.