Monthly Archives: May 2013

The Gambler’s Fallacy


So I’ve been reading some critiques of frequentism and p-value tests, and one thing that stuck out was how the “intuitive” understanding of frequentism will necessarily lead to fallacies like The Gambler’s Fallacy. This is one of those fallacies that is not weak Bayesian evidence since it violates Bayes Theorem. The Gambler’s Fallacy is thus:

The Gambler’s fallacy, also known as the Monte Carlo fallacy (because its most famous example happened in a Monte Carlo Casino in 1913), and also referred to as the fallacy of the maturity of chances, is the belief that if deviations from expected behaviour are observed in repeated independent trials of some random process, future deviations in the opposite direction are then more likely.

Someone subscribing to the Gambler’s Fallacy would think that, since I flipped three heads in a row, the probability of me flipping a fourth heads is 6.25%… since the probability of flipping heads four times in a row is 6.25%. But no, that is incorrect. The coin doesn’t have a memory; the probability of flipping heads that fourth time is the same as flipping tails.

The problem with frequentism is that this leads people to think that probability is part of the essence of an object instead of a description of your internal state of knowledge. So someone who thinks that 50% is a property of the coin being flipped will more than likely subscribe to the Gambler’s Fallacy. The 50% property of the coin builds up some sort of probability equity if you flip too many heads or tails in a row!

On a message board I frequented about 15 years ago, a huge argument that lasted for months on end went on about airplane disasters. One faction on the board argued that since the probability of being in a plane crash is [X%], the more you fly on planes, the probability of being in a plane crash will eventually move to 100%. This makes no sense from a Bayesian point of view (what new knowledge is being input in the system on each flight that increases the probability?), but makes sense from an intuitive Frequentist point of view where probability is based on n number of trials (though an actual Frequentist who used probability regularly would not make that mistake).

The n number of trials being used to establish a fact about the object in question instead of your own subjective state of knowledge.

Thinking of things in terms of n number of trials leads one to believe that in some unspecified point in the future, the improbable thing must happen. This is the one huge critique of frequentism that Bayesians have, that frequentism is based on an infinite set, and relying on infinity abandons empiricism (we will never empirically verify the infinitieth trial).

This is different than some event that is not independent, like picking cards from a deck. In that instance, 1/52 is a fact about the object in question; in that case both your subjective knowledge and a fact about pulling a particular card from the deck are the same. But even so, something like the Monty Hall problem still makes you realize that Bayes Theorem wins the day.


Posted by on May 2, 2013 in Bayes


Public Glory, Secret Agony


So I just read a post by April DeConick where she’s ruminating about the progress on her latest book. In it (it’s a very short post), she writes:

I really find in the fabric of that text [John’s Gospel] Gnostic spirituality merging with Jewish scriptures and nascent Christianity. It is not just later Gnostic interpretation imposed on an orthodox gospel. It is there in the soul of the Gospel.


My next chapter is on Paul… I remember as a young woman really disliking Paul. What I didn’t know then is that what I disliked was not Paul but Luther’s Paul. That is when I discovered Paul the mystic. I read Albert Schweitzer’s book and then Alan Segal’s book, both on Paul the mystic. Suddenly Paul made sense to me. But he wasn’t anyone that contemporary Christians could relate to. What he was saying was way out there. Undomesticated. Wild. He was a visionary who realized union with Christ whom he saw as the manifestation of God. He developed rituals that helped democratize this experience so that all converts could similarly be united.


Of course as I am thinking about Paul the mystic, I am also wondering about Paul the Gnostic. Have we worked so hard over the centuries to domesticate Paul that we have lost touch with his Gnostic aspects too, like with the Fourth Gospel?

That got me to remembering something I thought about a long time ago, but never had any evidence for, other than in a general sense. Mystery religions in antiquity, (of which Christianity was a part of), had public stories and then private stories. Think about Scientology: They have the public story they sell on the streets with their e-meters and Dianetics books but then they have the private story they tell about Xenu and his nuking of humans in volcanoes millions of years ago. The same dichotomy was happening in antiquity. Richard Carrier gives an example with the cult of Osiris:

In fact, Plutarch attests that Osiris was believed to have died and been returned to life (literally: he uses the words anabiôsis and paliggenesis, which are very specific on this point, see my discussion in The Empty Tomb, pp. 154-55), and that in the public myths he did indeed return to earth in his resurrected body (Plutarch, On Isis and Osiris 19.358b).

Although Plutarch does say that in the private teachings Osiris’ death and resurrection took place in outer space (below the orbit of the moon), after which he ascended back to the heights of heaven in his new body (not “the underworld,” as Ehrman incorrectly claims on p. 228), that is irrelevant to the mythicist’s case (or rather, it supports it, by analogy, since this is exactly what competent mythicists like Doherty say was the case for Jesus: public accounts putting the events on earth, but private “true” accounts placing it all in various levels of outer space: see my Review of Doherty). In fact the earliest Christians also believed Jesus was resurrected into outer space: he, like Osiris, ascended to heaven in his resurrection body, appearing to those below in visions, not in person (see my survey of the evidence in The Empty Tomb, pp. 105-232; the same is true of many other dying-and-rising gods, like Hercules). The notion of a risen Jesus walking around on earth is a late invention (first found in the Gospels).

That these kinds of beliefs about Osiris’ death and resurrection long predate Plutarch is established in mainstream scholarship on the cult: e.g. S.G.F. Brandon, The Saviour God: Comparative Studies in the Concept of Salvation (Greenwood 1963), pp. 17-36 and John Griffiths, The Origins of Osiris and His Cult, 2nd ed. (Brill 1980). But we hardly need point that out, because there is already zero chance that the entirety of Isis-Osiris cult had completely transformed its doctrines in imitation of Christianity already by 100 A.D. (I shouldn’t have to explain why such a claim would be all manner of stupid). Ehrman’s claim that Plutarch is making all this up because he is Platonist is likewise nonsense. Ehrman evidently didn’t check the fact that Plutarch’s essay is written to a ranking priestess of the cult, and Plutarch repeatedly says she already knows the things he is conveying and will not find any of it surprising.

It should be that Christianity shares that same pattern. You can see this a little bit in Paul, e.g. 1 Cor 3.1-3. My thought was that the gospel of Mark is the “public” story and the gospel of John (and Paul himself) are part of the tradition of the “private” story. Eventually the public story gained social currency and overshadowed the private story, and the private story fell to the Gnostics to maintain. Of course, there’s no evidence of this, so it will have to remain in the realm of speculation.

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Posted by on May 1, 2013 in early Christianity, gnosticism, jesus myth

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