My latest book * Proving History: Bayes’s Theorem and the Quest for the Historical Jesus* is now available for kindle. It should come available for nook soon (and possibly other formats, whatever past Prometheus titles have come available in: e.g. check

*The Christian Delusion*in any format, and if it’s available there,

*Proving History*will be, too).

**A note for the visually impaired:** I have noticed that some versions of text-to-speech don’t read the upright bar in mathematical statements of probability (the symbol for “given”), or even the tilde (the symbol for “not”). Also, most of the equations in *Proving History* are graphical inserts and thus won’t be visible to text-to-speech readers at all. These problems might be solved if I do an audio book version, but that depends on my audio book publisher being able to afford the audio license from Prometheus, and in any event an audiobook release could be as much as a year away, so even at best this is not a short-term solution.

The first in-text example of both an upright bar and tilde appears on page 66 of *Proving History*, where you will see the equation P(h|~h) = 0, which when read aloud by a human would sound like P, h, bar, not-h, equals, zero; or: P of h, given not-h, equals zero; or just “the probability of h, given not-h, equals zero.” There are many other instances where a tilde appears or an upright bar, and this can make the text confusing when read out by a computer, if the computer doesn’t read out those symbols. All I can say is just be aware of that as you go and I hope it can be managed.

As for the graphical equations, you will miss out on the visuals those provide, but in most cases that just means you have to trust the math came out right. Otherwise, most everything is explained in the text, and you can do all the math yourself (although that is a real challenge, I know), all you need to know are three equations, which I am here writing out for text-to-speech capture:

**The first is the standard long form Bayesian equation:** the probability of a hypothesis, h, given the evidence, e, and all your background knowledge, b, equals the product of the probability of h given only b and the probability of e given b and h, all divided by the sum of that same product (the product of the probability of h given only b and the probability of e given b and h) and the product of the probability of not-h given only b and the probability of e given b and not-h.

Which, as I graphically show on page 50, amounts to saying, in a more colloquial way, that the probability our explanation is true equals “how typical our explanation is” times “how expected the *evidence* is if our explanation is true,” all divided by that same product repeated (“how typical our explanation is” times “how expected the evidence is if our explanation is true”) plus “how *atypical* our explanation is” times “how expected the evidence is if our explanation *isn’t* true.”

**The second is the extended Bayesian equation for more than two competing hypotheses:** the probability of a hypothesis, h-1, given the evidence, e, and all your background knowledge, b, equals the product of the probability of h-1 given only b and the probability of e given b and h-1, all divided by the sum of that same product (the product of the probability of h-1 given only b and the probability of e given b and h-1) and the product of the probability of h-2 given only b and the probability of e given b and h-2, and the product of the probability of h-3 given only b and the probability of e given b and h-3, and so on, for as many hypotheses as you want to compare.

The prior probabilities must all sum to 1. For example, if you are dividing all possible hypotheses into three, then if the probability of h-1 given only b is 0.2, and the probability of h-2 given only b is 0.3, then the probability of h-3 given only b has to be 0.5, so that 0.2 plus 0.3 plus 0.5 will equal 1. The consequent probabilities do not, however, have to sum to anything. The probability of the evidence, e, given the hypothesis, h, and all your background knowledge, b, can be anything, without regard for what the probability of the evidence is given b and not-h.

**The third equation to know is the odds form of Bayes’ Theorem:** the ratio between the probability of a hypothesis, h, given the evidence, e, and all your background knowledge b, and the probability of not-h, given the evidence, e, and all your background knowledge b, equals the product of two other ratios, the ratio of the prior probabilities and the ratio of the consequent probabilities, which means: the ratio of the probability of h given only b and the probability of not-h given only b, and the ratio of the probability of e given b and h and the probability of e given b and not-h.

For example, if the ratio of priors is 2 to 1 and the ratio of consequent’s is 3 to 1, then the final ratio is 6 to 1, since 2 times 3 is 6. So in that event, the odds would be 6 to 1 in favor of the hypothesis. Note that this way, you don’t ever have to ask what any of the probabilities actually are, just what their ratios would be.

If there is anything else I can do to assist the visually impaired in understanding Proving History or Bayes’ Theorem generally, please let me know in the comments and I’ll see what I can do.

## 19 comments

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## The Nerd

August 17, 2012 at 10:10 am (UTC -7) Link to this comment

Thank you for this.

## Dave Mack

August 17, 2012 at 11:34 am (UTC -7) Link to this comment

Dr. Carrier, Wow! Thank you so VERY VERY much for helping folks like me who rely on text-to-speech (TTS). I am enjoying the Kindle version on my Kindle App for PC with TTS plug-in in spite of missing the math on my first go-round. I hope no one is turned off by the math as there is plenty in your initial volume besides just a plea for mastery of Bayes’ Theorem (in case anyone is otherwise frightened away). I am only about halfway through my listening and enjoying it immensely even without Bayesian mastery yet. But thank you again for your thoughtful consideration for free-thinkers in the blind and visually-impaired community! You are my “Bayesian savior”!

## Quixie

August 17, 2012 at 12:09 pm (UTC -7) Link to this comment

Thank you. I just downloaded it and look forward to reading it.

## Ryan

August 17, 2012 at 2:15 pm (UTC -7) Link to this comment

Great to hear it Richard! Coincidentally, I just got through mentioning your book in a blog post I made today. The relevant portion is here:

“[H]ow do we tell the difference between two theories which predict the same evidence equally? After all, for just about any theory we have that predicts the evidence we have, we can come up with at least one alternative, perhaps even an outlandish and unbelievable alternative…

“First of all, crazy theories… make propositions which are highly improbable prior to considering their evidential value. Second, they make multiple assumptions (which lowers the theory’s prior probability of being true, since each new assumption we add to theory has a chance of being incorrect). Last but not least, a theory with few adjustable parameters has less wiggle room concerning what evidence it can predict (and how probable it can make the evidence) than theories with numerous adjustable parameters, which often means that the former (if it accomodates the evidence we have without any ad hoc assumptions) predicts the evidence we have with higher probability, which in turn makes it more probable than the complex theory (all else held equal). On these points, see this paper [link removed] and/or Richard Carrier’s recent book Proving History: Bayes’s Theorem and the Quest for the Historical Jesus.”

http://www.skepticblogs.com/humesapprentice/2012/08/17/stephen-hawking-is-wrong-and-so-is-jason-rosenhouse/

## Richard Carrier

August 17, 2012 at 3:52 pm (UTC -7) Link to this comment

Thanks.

I also criticize (what you describe as) Hawking-style antirealism in

Sense and Goodness without God, II.2.1.2, pp. 31-32 (and elsewhere in various places therein).## Jason Goertzen

August 17, 2012 at 2:17 pm (UTC -7) Link to this comment

Holy crap. The waiting is over.

Looking forward to reading it, Richard. Thank you for the heads-up.

## Rick Dakan

August 17, 2012 at 2:18 pm (UTC -7) Link to this comment

Bought it! Thanks for the heads up, I was just checking a few days ago to see if this was available yet. Can’t wait to dig in.

## Robert

August 17, 2012 at 3:52 pm (UTC -7) Link to this comment

Great book. Going to have to go back and read it 2-3 times to really get the hang of the material, but really, really interesting.

Wishing I’d taken your class with CFI!

## Lord Bishington

August 17, 2012 at 4:48 pm (UTC -7) Link to this comment

On a slightly off-topic note; the two-star review (by R. Conner) of Proving History on Amazon caused me to break my long standing rule of never posting comments on Amazon reviews. I don’t get someone can consider a review of another book to be the best place to promote their own book. But I envisage that any follow up comments will drill back into me that Amazon is not the place for reasonable discussion.

## Richard Carrier

August 17, 2012 at 6:55 pm (UTC -7) Link to this comment

I don’t mind a critic mentioning their work, especially when it’s a work my book referenced. What I don’t get is why he gave his review two stars. He presents no specific criticism and mostly just agrees with everything in the book that he mentions. Weird. He seems mostly just annoyed that I listed him as among the contradictory conclusions that prove the field has no working method (even though I didn’t even explicitly say his conclusions were false).

(The one star reviews, by contrast, are pure comedy gold.)

## SC (Salty Current), OM

August 17, 2012 at 6:47 pm (UTC -7) Link to this comment

Reading it now!

A tangential note (but since it relates to probabilities, probably worth mentioning): You state a couple of times in the early pages that while it’s rare for people to be struck by lightning hundreds are every year. This sounded quite low to me. Wikipedia suggests that “An estimated 24,000 people are killed by lightning strikes around the world each year and about 240,000 are injured.” The linked article, on my cursory reading, isn’t entirely clear but seems to me to imply that it’s talking about estimated injuries and deaths from direct strikes (rather than, e.g., fires or falling tree limbs); in any case, those estimates look quite high if those directly struck number only in the hundreds, and more what I’d expect in the global population. Were you referring to the US specifically?

## Richard Carrier

August 17, 2012 at 7:17 pm (UTC -7) Link to this comment

Yes, I had in mind U.S. numbers (where it’s been in the low hundreds per year). The actual number wasn’t relevant, of course–the only point being that it happens a lot.

But on that tangent (just FYI), the studies estimating higher numbers worldwide are taking into account regions with large rural populations that lack good buildings to hide in (e.g. China, Africa), and from fragmentary data inferring an overall rate (not an actual body count), which by that reckoning is many times higher than the rate in the U.S. where we have plenty of safe places to duck in a storm. That is plausible. But their estimates look overly high to me.

## Brian

August 18, 2012 at 4:56 pm (UTC -7) Link to this comment

Got it last night. And going over BT chapter now. Thanks for the heads up Richard. Very good book so far…

## Joshua Bennett

August 18, 2012 at 11:25 pm (UTC -7) Link to this comment

Of course, it would become available the day after I ordered a hard copy. >_<

## Skepticali

August 19, 2012 at 7:42 pm (UTC -7) Link to this comment

Bought it!

Chapter 2 – The Basics – ought to be taught to everyone!

## Shin

August 22, 2012 at 1:23 am (UTC -7) Link to this comment

Awesome! I’ve clicked the “Tell the publisher you’d like this book on Kindle” button a few times now, once for each time I go back to check to see if it’s been made available yet. Very glad it finally happened.

## jwthomas

August 23, 2012 at 10:59 pm (UTC -7) Link to this comment

Thanks to Prometheus for wising up to the potential of Kindle sales. Now I can finally buy and read your book.

## gunter

September 1, 2012 at 9:35 pm (UTC -7) Link to this comment

Dear dr Carrier. In NtIF you state that there is “none [referring to archeological evidence] of a Christian presence until the 3rd century” (p 23). Don’t you then ignore the inscription from Pompeii, made in 79 CE, mentioning Christians? This is very early evidence, proven by a charcoal examination made in 1995. Read Paul Berrys treatise on the inscription, before claiming there are no proofs of early Christian presence in the Roman Empire.

## Richard Carrier

September 3, 2012 at 5:25 pm (UTC -7) Link to this comment

The inscription’s content is unfortunately debatable. The inscription itself is lost and only survives in the drawings of two 19th century artists, drawings which do not agree with each other, and the whole sentence transcribed is barely intelligible as Latin (“Hear the Christians the fierce swans” was what one thought it said, but both drawings fail to present coherent Latin–they frequently don’t even form wholly intelligible words, much less a sentence). If the artists erred in what they thought they saw (and you can imagine a 19th century Italian would have a strong verification bias for “seeing” the word “Christians” in ambiguous strokes), or the letters were not Latin (one scholar suggested it was Roman letters writing Aramaic, although that doesn’t fit well either), then the identification of the word “Christians” in the graffito is suspect. Unfortunately, without the ability to re-examine the original, we can’t make anything of this.

Berry, on the other hand, is something of a crank, infamous for trying to argue that the Letters of Seneca and Paul are authentic correspondence (when they are patently, obviously, a late antique fake). And his book on the inscription at Pompeii is almost entirely not even about this inscription at Pompeii. Just FYI.