A Bayesian Brief on Comments at TAM

I was asked about remarks made by Chris Guest (President of the Australian Skeptics, Victorian Branch) at this year’s TAM. He gave a quick twenty minute talk on Bayesian reasoning and its abuses, with which I entirely concur. (This talk begins with Guest’s introduction at timestamp 48:30.) He criticizes my work briefly at the end, but understanding his remarks there require understanding his remarks throughout the talk. His only mistake is that when he gets to my work, he makes one crucial mathematical error that invalidates his entire critique…
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Knitting Fans, Behold Some Awesome Ancient Roman Tech!

There’s this guy, you see, who knitted his way to a solution to an infamous problem in Roman history. This might be a bit premature (since academic journals haven’t weighed in yet), but I am persuaded that the mystery of the ancient Roman dodecahedrons has been solved. And why I’m persuaded affords a handy example for teaching how Bayesian reasoning works in making good historical inferences. [Update: This case likewise shows how Bayesian reasoning can incorporate new facts so as to change what’s likely: experts in the comments to this article subsequently persuaded me that a full accounting of the facts in my Bayesian model does not get as positive a result for this thesis as I had initially thought.]

A What?

Photograph of a bronze dodecahedron recovered from the ancient Roman Empire, described in the text.I suppose I should begin by explaining what a “mysterious ancient Roman dodecahedron” is. It’s not just any dodecahedron from ancient Rome (I’ll show you an unrelated example shortly), but a very peculiarly consistent oddity that no one has been able to explain (mainly because no writing survives mentioning it). It’s a common object. Some hundred or so have been found, originating in the 2nd century A.D. and spanning a couple of centuries afterward. But only in France and northern and eastern Europe. It’s weird looking. And has peculiar features. Some are of stone manufacture, but most are cast bronze.

Another example like the one above, this one lacks the grooves mentioned in the text.Some typical examples (one from Wikipedia, another from the Birmingham Musem) are shown to the right. Each is a twelve-sided hollow object, the sides generally symmetrical (an isohedron, so it looks a little like a twelve-sided die, something old-school role-playing-gamers will recognize), but every side has a circular hole in it, and the holes are different sizes, but the pattern of sizes (the sequence and arrangement) is the same on every object, even though the size of the object (and thus size of the holes) varies considerably, from kind of tiny (one and a half inches total diameter) to about the size of what would have then been a large adult fist (a little over four inches). The holes also sometimes have a sequence of parallel carved rings around them (sort of like gutters or guidelines in the face of the object), but many do not, so these appear to be a decorative flourish (a typical accent found in Roman tech of the time, where common utilitarian objects can be prettied up with some artsy flourishes like that).

But importantly, every corner of these objects has a solid knob sticking out of it, a bollard narrower at its base than at its tip (many of these just look like attached spheres), for twenty knobs in all. This most of all prevents the twelve-sided die analogy from quite being right, that plus the fact that the holes being of different size means each face has a different weight. They also aren’t inscribed with anything…a fact that is far more crucial to determining their purpose than you might at first think.

Just search “Roman dedocahedron” in Google Images and you’ll find dozens of examples. And yet…

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If You Learn Nothing Else about Bayes’ Theorem, Let It Be This

There are two things one learns from Bayes’ Theorem that are the windows to everything else Bayesian reasoning can ever teach you. And there is a lot it can teach you besides these two things. But here I’m cutting to the chase of the two that are most essential: theories cannot be argued in isolation, and prior assumptions matter.

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A New Bayesian Calculator

Bill Seymour has developed a new, more advanced Bayesian calculator for public use, and he would like people to beta test it and offer advice, or even develop it further.

For this open-source Bayes’ Theorem calculator, Seymour writes:

My intent was to find the middle way between, on the one hand, highly technical (and expensive) commercial software used in the sciences and statistics, and on the other hand, the toy Bayes’ Theorem calculators that abound on the Web. Some features of my calculator are:

  • Hypotheses can be saved in permanent storage so that users can work on several at once as part of a larger project.
  • Complete hypotheses can have any number of alternates.
  • Priors and consequents can be almost any arithmetic expression that evaluates to a probability between 0 and 1.
  • Prior and consequent expressions can contain terms that refer to other hypotheses.
  • Probabilities can be entered, and displayed, as decimal numbers, percentages, or odds.
  • The program happily works with what Carrier calls a fortiori probabilities: ranges of values like “20% to 40%”.

If you’re interested, here are some links:

I’ve given the code the open-source Boost Software License which isn’t viral like the GPL and others are said to be; so if you’d like to use some of my ideas in a program of your own, the open-sourceness (if that’s a word) of my code won’t infect yours.

And I explicitly invite others to help with this project. In particular, I think it really should be a downloadable executable that can be run off-line. Unfortunately, writing GUIs isn’t in my wheelhouse (my failing, not GUIs’).

If anyone would like to create a Windows or OS X version; have at it. I’ll even host your source code on my Web site if it’s open-source and high-quality. (But be warned that I’m a professional programmer, and also an old fart, with some curmudgeonly ideas about how quality code should be written.) You’ll find my e-mail address at the end of the documentation.

So if you are interested, check that out. I have also added a link to these materials on my old calculator page so users have the option of both.

Lataster on Mythicism and Theism: A Request for My Readers

Cover of Raphael Lataster's new book There Was No Jesus, There Is No God. Cover art looks like an artist's rendering of blue spacedust and a black hole sucking everything in.I have a request for all my readers. There is a new book summarizing a case that Jesus might not have existed, which has received some positive reviews (from the Arizona Atheist and John Loftus; also reader reviews at Amazon), and some predictably negative ones (from the nefarious Christian apologist J.P. Holding, whose promised Part 2 does not seem to have materialized yet, and an even longer harangue by Nick Peters).

The book I’m talking about was published by a doctoral student in religious studies, Raphael Lataster (more on the soon-to-be Dr. Lataster here), and entitled There Was No Jesus, There Is No God: A Scholarly Examination of the Scientific, Historical, and Philosophical Evidence & Arguments for Monotheism, based on his master’s thesis. The finished book you can buy for a very reasonable price [print] [kindle]. I have not had (and likely won’t have) the time to thoroughly vet the book, much less check it against the copious Christian apologetical attacks on it (by Holding and Peters, linked above). I did read enough to note that there were some problems with it, but I’m curious to know if those were the only ones, and if anyone else would notice them (so I won’t mention them now).

The book actually is in two parts, despite being quite a short read. The second part summarizes a case against traditional arguments for theism generally (not the historicity of Jesus specifically), and some of the approaches there are novel. And humorous. So even if you aren’t interested in the historicity debate, you might be interested in Lataster’s approach to debunking theism and theistic apologetics more generally. Moreover, in both parts he adapts my work to argue from a Bayesian perspective, which may interest yet more readers keen to test that out.

So I’d like as many of my readers as seem inclined to read either or both parts of Lataster’s book and comment here on what they think, positive or negative. Though if negative, please give Lataster a hand by being specific so he has a chance to revise the work for a second edition, which I know he is interested in doing. This is basically my way of crowdsourcing an opinion and assessment of this book, since I haven’t the time to study it thoroughly myself. I’d especially love it if anyone compared their reading of Lataster’s book with its Christian critics, as linked above (quite a task, as their critiques are very long, and possibly tedious and frustrating, if history serves, so I’ll be especially impressed by anyone who voluntarily endures that and reports back here on their findings). Are the Christians being fair? Or are they doing a hatchet job? Specific examples of either would be helpful to Lataster.

Note: I am about to head out for Skepticon, where I’ll be AFK much of the time, so comments that post here might not go live until middle of next week. But rest assured they will be appreciated, and will post eventually (as long as they are polite and on topic).

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.

Want to Literally Wear Bayes’ Theorem?

Picture of the Bayesian SurlyRamic: shows Bayes' Theorem, graphically arranged in an attractive way, black text in haly of white on black ceramic circle.Surly Amy has kindly met my request to create a SurlyRamic of Bayes’ Theorem. I designed the graphic for her, and she has made the product. You can check it out here, and buy one if you are keen. In the interests of art (to make it look elegant and not a busy mess), I took two liberties: I didn’t put the two expressions in the denominator inside brackets, but just stacked them on either side of a plus sign to indicate that (obviously) the multiplications have to be completed before the addition. I also left out the variable b for background knowledge, though that is commonly done even by mathematicians. You should understand that it’s present in every single term (see my Bayesian Calculator for an explanation of this and the rest of the equation). For example, P(h|e) represents P(h|e & b) and P(h) represents P(h|b), and so on.

Now we can totally geek out the Bayesians.

Craig vs. Law on the Argument from Contamination

In a recent attempt to rebut a peer reviewed philosophy paper by Stephen Law on the methodology of Jesus studies, which challenges the historicity of Jesus (hence my interest), William Lane Craig comes up with something so awful it would be worthy of a young earth creationist website. Maybe I’m just losing my patience with Craig’s specious, fallacious and dishonest method of arguing. Or maybe he really is getting worse at this.

The article I’m talking about is Craig’s recent Stephen Law on the Non-existence of Jesus of Nazareth (n.d.). Which is supposed to be a response to Law’s Evidence, Miracles and the Existence of Jesus (which was published in Faith and Philosophy 28.2 [April 2011]: 129-51). In his inept reply, Craig gets Bayesian reasoning wrong and conceals key facts from his readers. It looks more like a con than a sincere attempt to educate. [Read more…]

A Childish Book Review: Stephanie Louise Fisher and the Travesty of Not Getting It

Another baffle clearing for today, I’m finally getting to an embarrassingly childish review of Proving History by Stephanie Louise Fisher (a doctoral student in biblical studies). Her review (published through that nutter R. Joseph Hoffmann’s website…and I’m not throwing “nutter” around lightly, I genuinely think he might be insane) is ironically titled An Exhibition of Incompetence: Trickery Dickery Bayes. Ironically, because she betrays her incompetence in logic and mathematics and reading comprehension throughout, and yet is claiming I’m the one who is incompetent. Her review is also close to libelous and on at least two occasions overtly dishonest.

The immaturity of the review, with its gratuitous insults and intemperance and slanders and complete failure to actually engage with the book, gave it a low priority for me, since it really just discredits itself to any mature reader. But now I have time to cover it. Even right off the bat, a review written like this demonstrates no sense of irony in its author who opens with the claim that they are the one “drawing attention to [my] unprofessional attitudes and prejudices.” Her absurdly repetitious claims of my alleged incompetence characterize the whole thing, despite my having a Ph.D. in the history of ancient religion and philosophy from a top ranked university, and a published background in mathematical arguments (in peer reviewed journals no less), as well as official training in statistics, calculus and electronics engineering…and despite my book having been formally peer reviewed by a professor of mathematics and a professor of biblical studies. (Note that Fisher, at present, and so far as I can discern, can claim none of these qualifications.)

Certainly, claims of incompetence have to be backed up with considerable evidence in the face of such conditions and qualifications. Fisher provides none. Let’s look at what she does argue. [Read more…]

A Well-Deserved Nod to Aviezer Tucker

Front cover of Aviezer Tucker's book Our Knowledge of the PastAfter I published Proving History a reader said I should check out Aviezer Tucker’s book Our Knowledge of the Past: A Philosophy of Historiography, since it appeared to back up the entire core thesis of my book. I am amazed and ashamed that I did not discover this book sooner. It must not have been indexed well in databases, since my searches for Bayesian historiography did not discover it. I just finished reading it, and while I wait for more opportune times to blog on other issues coming up, I thought I’d post a little about this.

Tucker is a prominent and widely published philosopher (see his bio and cv). We have at least two things in common: we both did graduate work at Columbia University, and we both think historical reasoning is fundamentally Bayesian. As some might know, the subtitle of my book is Bayes’s Theorem and the Quest for the Historical Jesus, and though the study of Jesus is its principle example, the overall thesis is that all history is Bayesian and all historians should learn Bayes’ Theorem and how to apply it to their own thinking to improve their reasoning, research, and argumentation.

Tucker makes the same argument. His approach is deeper and more philosophical, more about making the point that historical reasoning is already Bayesian, and that this explains everything from consensus to disagreement in the historical community. My book makes that argument, too, but is more about the practical application of this conclusion, and providing tools and advice for how historians can make use of Bayesian reasoning to improve what they do. Tucker delves more deeply into philosophy and probability theory and as such his book is essentially an extension of my sixth chapter (which goes into more depth on points made earlier in my book).

That’s why I regret not having known of his book before now. It’s a great shame that Proving History does not cite it, and I am writing this review now to redress that gap. OKP provides solid support for the core thesis of PH, and is the first book I know that makes the case I do (and thought I was alone in making). Others had discussed Bayes’ Theorem in the context of historical reasoning, but always skeptically or inconclusively (e.g. see PH, p. 304, n. 28). Tucker appears to be the first to understand that in fact historical reasoning is Bayesian, and to argue the point explicitly. It thus provides another foundation (and independent corroboration) for my main conclusions. It was also a prestigious peer reviewed academic work, published by Cambridge University Press in 2004 (I had my book peer reviewed as well, but my publisher is less known for that).

Owners of Proving History might want to pen Tucker’s name and book title into the margins somewhere (it should certainly have gotten a nod in note 3 of chapter four, on page 306, and probably in my discussion on page 49 as well, perhaps where I mention the precedents of applying Bayesian reasoning in law and archaeology).

The leading merits of OKP are that Tucker grounds you in the history of historiography and philosophy of history, he treats in greater detail the issues of historical consensus and disagreement (with many erudite examples), he addresses several leading problems in the philosophy of history, and he cites and adapts debates and discussions of Bayesianism in the philosophy of science and applies them to history the same way I do (only he again in more detail): by demonstrating that science and history are fundamentally the same discipline, only applied to data-sets of widely differing reliability.

As Tucker says in his central chapter (ch. 3, “The Theory of Scientific Historiography”), “I argue that the interpretation of Bayesianism that I present here is the best explanation of the actual practices of historians” and that “Bayesian formulae can even predict in most cases the professional practices of historians” (p. 134), and he gives good brief explanations of prior probability and likelihood (what I call consequent probability) in the context of historical thinking, and uses real-world examples to illustrate his point. His chapters 1 and 2 cover the background of the philosophy and epistemology of history, and remaining chapters apply the results of chapter three to address three major debates in that field: explaining disagreement among historians (ch. 4), resolving questions of causal explanation in history (ch. 5), and exploring the limits of historical knowledge and method (ch.6). He then wraps it all up with a conclusion (ch. 7). There is also an extensive bibliography and index. Throughout his book, Tucker aims to refute postmodernist and hyper-skeptical approaches to historical knowledge, and in that regard makes a good supplement to McCullagh (whom I do cite in PH).

For me, the most notable facts are that we did not know of each other, yet we independently came to the same conclusion that all historical reasoning is fundamentally Bayesian, and Tucker is a well-established philosopher and his book is by a major peer reviewed academic press. Both facts add weight and authority to my overall conclusion in Proving History. And that’s always nice to have.