Now You Can Wear Even More Bayes’ Theorem!

Picture of the Odds Form Bayesian mug (white mug with artsy black text) offered at Richard Carrier's Marvelous Amusements shop at Cafe Press.Did you say Odds Form? Shirt? Car Flag? Panties? Hell yeah.

I just finished loading my old Cafe Press store with tons of different shirts and other odds and ends featuring my Bayesian graphic, which uses imaginative rather than standard mathematical notation (as I reported last week, you can get jewelry with it from SurlyRamics).

I also duplicated most items with a cool graphic design of the Odds Form of Bayes’ Theorem (in standard mathematical notation, but artful font). Because a lot of people are fans of the Odds Form. No joke…it has actual vocal fans. It’s also the form I use to run the math in my upcoming book On the Historicity of Jesus. If you want to know what the difference is and what the Odds Form equation means and how to use it, see Proving History (index, “Bayes’ Theorem, Odds Form”). Like with the other graphic (as I explained last week), you have to assume b (background knowledge) is in the givens of every term (a common assumption mathematicians allow).

Picture of women's cap-T shirt with Odds Form Bayesian graphic across the chest. White shirt with black shoulders and neckline.Above right is a pic of the Odds Form mug I’m selling. It actually looks pretty awesome. Likewise the women’s Cap-T (below right).

To check out the full range of products, and help support my work by buying some, visit Richard Carrier’s Marvelous Amusements. Note that many items actually have color options at the purchasing page (so it’s not just all black or white). If you have ideas for other products I could develop and offer there, feel free to recommend them in comments here. Just note that I’m limited by the stock and capabilities of Cafe Press.

I have also included some Solon’s Commandments materials, as some fans requested I do many months ago, after I wrote about them in That Christian Nation Nonsense (Gods Bless Our Pagan Nation). Cafe Press doesn’t offer the option of an inscribed plastic plate, so you would have to get the mini-poster and put it in a hard plastic casement or sheath from a local office supply store–or else buy the expensive framed print option (although that does look quite nice). Junior high and high school students who feel like living dangerously can even bring a Solon’s Commandments lunch bag to school.

Two Bayesian Fallacies

At INR3 in Kamloops I spoke on applying Bayesian logic to the study of Jesus along with the same principles we apply to dead religions (so as to avoid the “don’t offend the Christians” reaction to controversial claims…claims that would not be controversial if Jesus was not the object of worship of billions of loud, influential people). In Q&A philosopher Louise Antony challenged my application of Bayes’ Theorem to historical reasoning with a series of technical complaints, especially two fallacies commonly voiced by opponents of Bayesianism. I was running out of time (and there was one more questioner to get to) so I explained that I answered all her stated objections in my book Proving History (and I do, at considerable length).

But I thought it might be worth talking about those two fallacies specifically here, in case others run into the same arguments and need to know what’s fishy about them. [Read more...]

Understanding Bayesian History

So far I know of only two critiques of my argument in Proving History that actually exhibit signs of having read the book (all other critiques can be rebutted with three words: read the book; although in all honesty, even the two critiques that engage the book can be refuted with five words: read the book more carefully).

As to the first of those two, I have already shown why the criticisms of James McGrath are off the mark (in McGrath on Proving History), but they at least engage with some of the content of my book and are thus helpful to address. I was then directed to a series of posts at Irreducible Complexity, a blog written by an atheist and evolutionary scientist named Ian who specializes in applying mathematical analyses to evolution, but who also has a background and avid interest in New Testament studies.

Ian’s critiques have been summarized and critiqued in turn by MalcolmS in comments on my reply to McGrath, an effort I appreciate greatly. I have added my own observations to those in that same thread. All of that is a bit clunky and out of order, however, so I will here replicate it all in a more linear way. (If anyone knows of any other critiques of Proving History besides these two, which actually engage the content of the book, please post links in comments here. But only articles and blog posts. I haven’t time to wade through remarks buried in comment threads; although you are welcome to pose questions here, which may be inspired by comments elsewhere.)

Ian’s posts (there are now two, A Mathematical Review of “Proving History” by Richard Carrier and An Introduction to Probability Theory and Why Bayes’s Theorem is Unhelpful in History; he has promised a third) are useful at least in covering a lot of the underlying basics of probability theory, although in terms that might lose a humanities major. But when he gets to discussing the argument of my book, he ignores key sections of Proving History where I actually already refute his arguments (since they aren’t original; I was already well aware of these kinds of arguments and addressed them in the book).

[Read more...]

Bayesian Blogging

This is a request to all fans of Bayes’ Theorem out there: I’m looking for the best blogs and websites substantially devoted to discussing all things Bayesian.

Of course I know about Less Wrong, the brainchild of Eliezer Yudkowsky, which often discusses Bayesian reasoning and is a fabulous website for learning about human reason, and cognitive biases and how to overcome them, and other related subjects (it should be regular reading for most people keen on those subjects). But I also just discovered the awesome blog Maximum Entropy by Tom Campbell-Ricketts (since he asked me about the famous anecdote of Laplace, “Sir, I have no need of that hypothesis,” which might be apocryphal, but I directed him to what evidence there is for it). This blog is a Bayesian paradise of great posts, often quite advanced (so not for beginners or mathphobes)–but for people getting into the groove of these kinds of things, a fun resource.

The Wikipedia article on Bayes’ Theorem has already become too advanced to recommend to beginners. The Stanford Encyclopedia of Philosophy entry isn’t any better that way, but at least it discusses the application of the theorem to philosophy (epistemology in particular) and has a more extensive bibliography. My own Bayesian Calculator page (which is continually in development) will perhaps be more helpful, with more plain English explanation and some actual calculators you can fiddle with to see what happens. And total beginners should start with my Skepticon video Bayes’ Theorem: Lust for Glory! (that blog article gives the links plus additional resources about the video). Lots of good links are also assembled at Alexander Kruel’s A Guide to Bayes’ Theorem.

But none of these are blogs or websites that regularly produce discussion and articles about Bayesian reasoning. And I’m looking for the best of the latter. I’m looking for more stuff like Less Wrong or Maximum Entropy. If there is any. It can be basic intro level stuff, or advanced, but it should be good reading either way, the kind of place a general Bayesian might want to visit monthly to see what’s going down. So if anyone reading this has recommendations, please plop them in the comments section!

[I should add that I think all Bayesians should also familiarize themselves with the lists of cognitive biases and logical fallacies at Wikipedia, to contemplate how these can model misuses of Bayes' Theorem or be corrected or avoided by using Bayes' Theorem. FallacyFiles also has a useful taxonomy of logical fallacies. But I'm also interested in lists or sites dedicated to common errors or fallacies in reasoning about probability specifically.]

Limited Comments Policy: Because this post is a resource request, only comments that supply relevant hyperlinks (or names of websites) will be posted. Everything else will be deleted. Comments on other subjects should be posted within an appropriate blog thread (see the topic index for my blog down the right side of this page).

New Bayesian Calculator

Thanks to Cam Spiers (who has produced an interesting selection of free javascript Bayesian Calculators), I have updated my own Bayesian Calculator page using the most basic of those. This might be updated again in coming months. Right now it only allows running calculations with two-digit probabilities from .01 to .99 (or 1% and 99%), so you can’t use it for odds outside that range (for example, you can’t see what happens when the prior is 1 in 1,000 or 1 in 1,000,000 or when a consequent is even closer to 100% than 99%). But future versions of the page might have those features.

For people new to the whole idea of Bayes’ Theorem and Bayesian reasoning, you should first check out my talk at Skepticon last year: Bayes’ Theorem: Lust for Glory! For a more thorough treatment (using historical reasoning as a running example), which is also aimed as much as possible at lay readers, there is now of course my book: Proving History: Bayes’s Theorem and the Quest for the Historical Jesus.

The Jesus Tomb and Bayes’ Theorem

Finally, a mathematician actually gets the math right on the Jesus Tomb hypothesis. Conclusion? We have not found the tomb of Jesus. For those who already know the backstory and want to jump right to it, read Bayes’ Theorem and the “Jesus Family Tomb” by physicist Randy Ingermanson. He approached the problem like a physicist dealing with any old problem in data analysis (the problem is not so much different from how particle accelerator data are analyzed). He was assisted by political scientist Jay Cost, another who has good experience running Bayesian models like this. This expands on Ingermanson’s work on this published under peer review as Randall Ingermanson, “Discussion of: Statistical Analysis of an Archaeological Find,” Annals of Applied Statistics 2.1 (2008): 84-90 (responding to Feuerverger).

Backstory: James Tabor and some others have been pushing the claim that a tomb uncovered in the Talpiot district of Jerusalem (hence now called the Talpiot tomb) is the actual burial place of Jesus (and we not only have his “coffin,” but his DNA! As well as evidence he had a child named Judas by Mary Magdalene, also buried therein, also with her DNA!), and they published a book and a documentary arguing their case. (I’m just being colloquial. The tomb’s not full of coffins, of course, but ossuaries, a cultural analog). They had a mathematician backing them (Dr. Andrey Feuerverger), but his math has been consistently bogus from day one. For example, even though we have vastly better odds of randomly getting a name in a group of ten-to-thirty bodies than in a group of five, he kept running the math for five, even though there were ten-to-thirty bodies buried in that tomb. He also adopted a number of dubious (and some outright refuted) factual assumptions (for example, regarding the names of the women in the tomb: see, as one instance, the penultimate paragraph of my previous article on this tomb). By these devices, he found the odds were 600 to 1 in favor of this being the actual tomb of Jesus.

What happened: Ingermanson and Cost apply the correct math (Bayes’ Theorem, valid historical premises, proper treatment of variables, and correct mathematical models, e.g. acknowledging that more than five people were buried there). They find that by standard historical assumptions, the odds are 1 in 19,000 against the Talpiot tomb being the tomb of Jesus, and even by more generous assumptions the odds are 1 in 1,100 against (I put my own assumptions into their model and came up with 1 in 200 against), while even the most fanatical “I desperately want this to be the tomb of Jesus” estimator can only get odds of 1 in 18 that the Talpiot tomb is the tomb of Jesus. Thus, it probably isn’t, even if we are ridiculously generous to the hypothesis that it is.

So much for that. Done and dusted.

The Lame That Would Not Die!

What is The Lame? Unfortunately no one can be told what The Lame is. You have to see it for yourself. No, just kidding. It’s the claim that “Science Requires a Christian Worldview.” JT just blogged that, responding reasonably enough to a repeat of a standard Christian apologetic shibboleth (and, as he callously and shamelessly threatened therein, did indeed email me the link in question as if to annoy me, like the gangster cad that we all know he is; for shame). I realized I should probably collect a resource list of all I’ve written in refutation of it. This is that list.

First, I pretty much kick the legs out from under it with the extensive historical argument (since non-Christians invented science, and that centuries before Christianity even existed, obviously science does not require a Christian worldview) in “Christianity Was Not Responsible for Modern Science,” The Christian Delusion (2010), pp. 396-420. You really don’t have to read anything else on the subject, frankly.

Second, I refute one component of the philosophical case, the claim that the universe must have been designed to be understood or the human brain designed to understand it, in “Neither Life Nor the Universe Appear Intelligently Designed,” The End of Christianity (2011), pp. 279-304 (key pages: pp. 298-302). That’s a short but compact and effective refutation, with references.

Third, I take on the entire Argument from Reason (which is a kind of umbrella argument that includes the claim that science only makes sense if Christianity is true, by arguing that reason would not exist but for God) in an extensive philosophical critique of Victor Reppert’s Argument from Reason. But the most pertinent sections of that are my refutation of the original version of the “Science Needs Christianity” argument from (Surprise!) C.S. Lewis. Those are the sections on where the “Five Axioms of Science” came from, and preceding that, on why “Our Mind Is Reliable Enough for Inductive Logic to Work.” And following both, I refute the more general claim that “Only Theists Can Invent Science” (although I give an even clearer answer to that in the Christian Delusion chapter, item 1 above).

Fourth, I have refuted the claim that the mathematical nature of the universe entails it was intelligently designed, in my critiques of Steiner and Howell. But of those, my refutation of Steiner (Fundamental Flaws) is less fun to read than my refutation of Howell (Our Mathematical Universe), in which I refute Howell’s attempt to rehabilitate Steiner; and really, if you’ve read the latter, you don’t need so much to read the former (unless you are really geeking out on the ontology of scientific theories, which is totally cool if you are).

Now you can add to all that JT’s response, which covers a lot of the most common sense rebuttals. The only weakness of which is that he doesn’t give the best response to the claim that “the atheist worldview cannot account for the uniformity of nature on which to base the scientific process.” He rightly points out that an argument from ignorance is a fallacy, and that Christians don’t really believe in the uniformity of nature (remember those miracles they keep going on about?), and if anyone is going to suss this, it’s going to be actual cosmological scientists, not hack armchair theologians.

But there is one argument one can make that kind of dodges those otherwise obvious points: the evidence e is “the uniformity of nature,” and the explanation h “God made it that way” makes e highly probable whereas one might suppose ~h “a god did not make it that way” does not make e highly probable, therefore e is an argument for god. Not that this must be a conclusive argument; having evidence for something is not the same as that something being true. For example, you can have evidence for someone committing a crime that in fact they didn’t commit–like fingerprints on a murder weapon, which could have gotten there in other ways besides having used it to kill the vic. But still.

The real problem is that ~h is a stand-in for all other theories of the evidence. Because h and ~h together must include all logically possible explanations of the evidence. And since h is only one of them (“God did it”); then necessarily ~h contains all other explanations. Many of which do make e highly probable. We don’t have to pick one, either. We can say “I can think up ten different explanations, other than God, which all guarantee that e will obtain” (for ten such examples see below). And if those all have a higher prior probability than “God did it,” then God is no longer the better explanation. In fact, it then becomes one of the worst. Note that we don’t have to know or even claim that any of those explanations is true. It’s still the case that more probably one of them is true, than that h is true, regardless.

I outline several of these possible explanations in Sense and Goodness without God (especially in section III.3 on “The Nature and Origin of the Universe,” pp.  71-96, and most especially, pp. 86-88), and all of them are more plausible than “God did it,” which means, all have a higher prior probability, because all of them are based on established precedents or simpler assumptions (on this point in general see my End of Christianity chapter again, item 2 above, pp. 282-84). Accordingly, I’ll count this as my fifth listed resource.

So there you have it. A complete kit for battling The Lame.

Proving History!

My new book is finally done and available for pre-order at Amazon: titled Proving History: Bayes’s Theorem and the Quest for the Historical Jesus. Yes, that’s the one (or one of the two) that everyone has been asking me about. It’s been years in the making, and in the waiting, but we completed its academic peer review, I made all requested revisions, proofed the galleys, finished the index, and it’s all ready to go, at the printer’s being typeset now. It’s being published by Prometheus Books, my first sole-author title with them.

Backstory

This all started long, long ago, four years in fact, when my wife and I were buried under student loan debt and I offered myself up to complete any hard core project my fans wanted in exchange for as many donations as I could get to fund my work. They all unanimously said “historicity of Jesus” and came up with twenty thousand dollars. Which cleared our debt and really saved us financially. It was a huge boon and I am extremely grateful for everyone who made that happen. And I’ve been tirelessly working to make good on the project ever since. I wanted the result to be superb and unassailable, nothing half-assed, but thoroughly researched.

Then I discovered that the field of New Testament studies was so monumentally fucked the task wasn’t as straightforward as I had hoped. Very basic things that all scholars pretend have been resolved (producing standard answers constantly repeated as “the consensus” when really it’s just everyone citing each other like robbing Peter to pay Paul), really haven’t been, like when the New Testament books were written (I blogged about one long rabbit hole I got lost in on that question, as just an example of countlessly many, in my Ignatian Vexation). And the relevant literature, so much of it tantalizingly pertinent, is vast beyond reckoning, over forty years of valuable papers and books, leading to discoveries I never expected (for example, real evidence of a pre-Christian expectation of a Dying Messiah). I’ve personally collected and read over 500 articles and 50 books for this project, and skimmed or read over ten times that number at the UC Berkeley and Graduate Theological Union libraries or via JSTOR and other access nodes.

The end result was that I realized this was going to have to be two books: one resolving the problem of method (because the biggest thing I discovered is that every expert who is a specialist in methodology has concluded, one and all, that the methods now used in Jesus studies are also totally fucked), the other applying my reformed method to the question. That second book will be On the Historicity of Jesus Christ, and it is near completion (spoiler: I conclude he most probably didn’t exist, but that it requires a very deep and detailed examination of the evidence to realize that). The first book became Proving History, which I finished last year and has been going through the usually long production and peer review process at the publisher, and is now on track for a late April release. Yes, there will be e-versions as well as print.

What’s It About?

The promo copy prepared by Prometheus Books is really very good, and describes the book quite well. Basically, it aims at two particular objectives, and one broader objective: (1) to show why the methods used to study Jesus are illogical or inapplicable, and to replace them with a method that is neither; (2) to show why, once we use the correct method, every conclusion reached about Jesus so far is not defensible on any previously championed argument (requiring a total, field-wide do-over); and (3) to use these particular examples to make a general point about the entire field of history: that all valid historical argument is and must be Bayesian, and any methods or arguments that are not, are not logically valid or sound.

Historians will want to read the book even if they aren’t interested in Jesus, because it all applies equally to whatever they study, too. Philosophers will want to read the book, because it makes a groundbreaking contribution to the logic and epistemology of history. Fans of Bayes’ Theorem, and anyone who wants to finally find out what that is and why everyone is getting into it all of a sudden (but has found everything written about it so far to be unintelligible or uninformative), will want to read the book because I designed it as a textbook for people in the humanities and not scientists or ivory tower mathematicians. And Jesus scholars (in fact anyone interested in Jesus or the origins of Christianity) will want to read the book…well, for obvious reasons.

To learn more about all this, John Loftus interviewed me about the book just recently and produced a really good article about it on his blog: An Interview with Richard Carrier about His Book “Proving History”. Loftus was one of the few lucky reviewers who received an early pre-publication draft from Prometheus–which contained the text as it was before it was peer reviewed; in response to that peer review it underwent a lot of improvements and corrections, though nothing fundamental. For those who want a primer on what the hell this “Bayes’ Theorem” thingy is, check out my Skepticon talk from last year: Bayes’ Theorem: Lust for Glory!

Common Questions

Since I am applying a mathematical theorem to the logic of historical argument, it’s often asked what my qualifications are in mathematics, since my primary field (my Ph.D.) is ancient intellectual history (philosophy, religion, and science), and my secondary field (self-taught but professionally published) is philosophy. The answer is, I had the book formally peer reviewed by a professor of mathematics, and consulted with a few other professors of mathematics during its development. I also, of course, researched the hell out of Bayes’ Theorem for this book. My more general qualifications are some 20 or so college semester credits in mathematics and mathematical and engineering sciences, and a career background in electronics and the history of science. But the peer review and consults were more important.

Another common question is how “out of the mainstream” my conclusions are. Actually, in this book, they are fully in the mainstream, with the exception of the groundbreaking idea of structuring the logic of historical argument on a foundation of Bayes’ Theorem, which is in many ways a natural progression of what’s already been going on in expanding the applications of that theorem. I’m just the first expert in the humanities to come along who also loves math and knows enough about it to introduce it there. But the rest of the book’s conclusions simply reaffirm what countless insider specialists have already been saying (and I name and cite plenty of them to prove that), and using Bayes’ Theorem to show why they’re right.

Finally, it is often asked if this book argues that Jesus didn’t exist. No. It is necessary to build that case one piece at a time rather than trying to prove everything at once. This book takes no position on that question, but merely shows how the methods used to argue for his existence are illogical and therefore the question must be examined anew, with new methods, methods that are valid. But lest you think that’s the same thing as proving Jesus didn’t exist, you should know that that would be the fallacy fallacy, the fallacious assumption that if an argument for x is fallacious, that therefore x is false. If the same facts are examined correctly, as for example with my new method, we may yet vindicate the conclusion that Jesus existed. So what the correct conclusion is requires that new look, and that is what I accomplish in my next book.

Final Word to My Benefactors

Earlier this week I sent out an email to everyone who donated $250 or more to fund my research grant, which was overseen by Atheists United. Per my contract with you all, anyone in that golden category has earned free copies of Proving History, and I need to work out where to send them, among other details. But many of those email addresses have bounced, no longer active. So if you are in that donor category, and did not receive my email, then please email me at once ([email protected]) so I can update my contact info and see to it that you get your copies of the book when it comes out in a few months. Even if you don’t want your free copies, please contact me anyway, so I at least know not to keep looking for you.

Bayes’ Theorem: Lust for Glory!

My talk at Skepticon IV on the importance of Bayes’ Theorem to skepticism is now available on YouTube (Bayes’ Theorem: Lust for Glory!). (My slides in that on the UFO case don’t show the whole text because I had to use Darrel Ray’s computer at the last minute [thx D!] which didn’t have the right font; but I speak most of it out, so you don’t miss anything. There were some other font goofs, but that’s the only one you’ll notice. Oh, and the slide near the end that everyone laughs at but you can’t see on the video, says “Ockham’s razor will cut a bitch.” Oh yeah she will!)

Dr. Carrier at Skepticon IVFor a handy web page on using and understanding Bayes’ Theorem (which I’ll soon be improving with an even more versatile applet) see my Bayesian Calculator. And besides my book  Proving History: Bayes’s Theorem and the Quest for the Historical Jesus which has since become available (and is now the first place you should go to learn about Bayes’ Theorem and Bayesian reasoning), the other books I recommend in the video are: Innumeracy: Mathematical Illiteracy and Its Consequences by John Allen Paulos (I also recommend his Beyond Numeracy and A Mathematician Reads the Newspaper); Proofiness: The Dark Arts of Mathematical Deception by Charles Seife; The Theory That Would Not Die by Sharon Bertsch McGrayne; Math Doesn’t Suck by Danica McKellar (this is the only one of her series that you need, and everyone should buy, but if you want to gift her higher grade math books to a teen you know, she also has Kiss My Math and Hot X: Algebra Exposed!, and more to come; I didn’t have time to also mention another woman who advocates for wider math literacy, so I will here, although it’s less useful than McKellar’s, since it doesn’t teach math but only why you might like learning it more than you thought: The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse by Jennifer Ouellette); and The Mathematical Palette by Ronald Staszkow and Robert Bradshaw (get a used one, since new copies are priced at “textbook robbery” levels; you might get stuck with an old edition when buying used, but they’re all good) and 101 Things Everyone Should Know About Math by Marc Zev, Kevin Segal and Nathan Levy.

The Christian Delusion (ed. John Loftus)In addition to Proving History, which is now my most comprehensive treatment of Bayesian reasoning for laymen, the books in which I also discuss and apply Bayes’ Theorem are The Christian Delusion (TCD) and The End of Christianity (TEC), both edited by John Loftus. In TCD, in my chapter “Why the Resurrection Is Unbelievable,” I only mention Bayes (and show the math) in the endnotes, but you can see how those translate what I otherwise say in that chapter in plain English, and thus see an application of Bayes’ Theorem in action. That chapter refutes previous attempts to use Bayesian reasoning to prove the miraculous resurrection of Jesus (by Swinburne and the McGrews, for example), by showing the correct way to do it, and how using the correct facts changes everything. (TCD also has my chapter explaining why Christianity isn’t responsible for modern science, contrary to a popular claim of late, but I don’t translate my argument there into Bayes, though I could.)

The End of Christianity (ed. John Loftus)In TEC I have two chapters deploying Bayes’ Theorem, and both explicitly discuss and use it from the get go. One proves the entire Christian religion false just from considering how it began, and that gives you a good look at how Bayesian reasoning opens your eyes to things you might have overlooked before, or confirms what you intuitively knew but couldn’t articulate the logic of. The other uses Bayes to prove every design argument false, including creationism, divine biogenesis, and the fine tuning argument (among some others). In fact, I show how the fine tuning of the physical constants actually proves God doesn’t exist. Quite conclusively in fact. And in saying that I’m just explaining in ordinary language what two independent teams of expert mathematicians already proved (I cite their work in the chapter). (TEC also has my most controversial chapter, peer reviewed by several professors of philosophy, proving my theory of godless morality correct, and Christian morality defective, but I didn’t translate that into Bayes, though again I could have.)

Although I might punt a lot to Proving History, this is the place to ask questions about my Skepticon talk or my use of Bayes’ Theorem in TCD, TEC, or elsewhere. Feel free to query me on any of that here.Skepticon IV