tanya

In response to Toto's announcement that Richard Carrier would soon be publishing the first of two volumes devoted to use of Bayes' theorem to investigate the historicity of J.C., I shared with this forum, my concern that Bayes' theorem was of little value in attempting to uncover the history of the early Christian movment.

I then offered an illustration of how unhelpful any mathematical procedure would be, in assessing ancient papyrus documents, by citing the three extant versions of Mark 1:1. The rationale for this choice is easy:
Mark is the oldest written text representing Christianity.
There is no agreement about which verse represents the "original" text, authored by Mark.

In response, Andrew Criddle, defending Carrier, wrote

I object to the concept of "real probabilities".

LegionOnomaMoi replied in support of Andrew's comments, suggesting:

My rejoinder that no amount of "fuzzy" logic would provide an answer to this simple question, of which verse of Mark 1:1, if any, represents the ink drying on Mark's first papyrus, irritated Legionaire, who replied:
He had earlier, in the same post, 50, suggested:

Let us refocus on the topic of this thread:
Carrier's forthcoming titles regarding use of Bayes' theorem in the investigation of early Christianity.

Can we employ Bayes' theorem, or any other statistical algorithm, absent knowledge of the conditional priors?

Why should "fuzzy" logic, or the absurdly childish, McCulloch-Pitts 1940's era generalization about neuron this, axon that, synapse here and there, a few dendrites thrown in for good measure, help us to figure out which of the three versions of Mark 1:1, above, represents the authentic text?

A genuine neuron indeed does possess soma, axons, dendrites, and makes synaptic connections with other neurons, in a relatively unpredictable fashion, to date. We know almost nothing about genuine neuronal connectivity, for most of the central nervous system of vertebrates, the retina having been the best studied component. Shouting and hollering about AI and "neural networks" and fuzzy this or that, is a useless waste of time, from the perspective of unlocking the secret of the origins of Christianity.

Go to any military hospital, and ask the wounded soldiers with head injuries which "algorithm" they wish to employ to restore their vision/hearing, or what bit of "fuzzy logic" they wish to purchase, in order to regain their ability to move an arm or leg. If we really knew something about the inter-relationship of specific neuronal synaptic connections, we could help them overcome their injuries by implanting replacement parts performing functions compatible with those which had been lost.

Applying mathematical constructs to analysis of papyrus documents in an effort to identify dates of authorship, or to establish authenticity, is utter nonsense.

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LegionOnomaMoi

This is a complete distortion. Let's look at what I said and was responding to:
That wasn't a "rejoinder" to anything about Mark 1:1, it was a response to your dismissive comment about "folks without credentials in the natural science or medicine" talking about neural networks. Only neural network models and artificial neural networks were both primarily the products of the field I work in (cognitive science) and/or psychology (depending on whether one includes cog. sci. as a subfield of psychology). Neither one is a "natural science." So apparently you "get nervous" when the people who are most qualified to talk about neural network models do so, and the only way I can explain that is that you don't have any idea what you are talking about.

1) I never said anything about using neural networks here. I said that fuzzy bayesian models increased the capacity of bayesian theory to work with non-numerical data. Please stop distorting what I said.
2) Fuzzy probability theory provides a mathematically robust method to translate linguistic terms such as "more likely" or "less likely" into functions or "fuzzy numbers." Which means that one can use bayesian models without numerical data.
3) Formal representation of an argument, apart from any numbers, allows its logic to be more easily followed
4) When Carrier uses numerical data, which is an a fortiori method of reasoning, he reverses the very same methods used in a priori statistical tests. When those measures are incorporated into hypothesis testing, the assumption is that the hypothesis is wrong, and unless it his highly improbable that it isn't, the null is accepted. When Carrier uses bayes, he does the same, only in reverse. He uses extreme probability values in his initial equations, so that if the equation still returns a low probability value, it is essentially the equivalent of p<.01 for a t-test or something like that.

tanya

Mark 1:1 is not the question. It is simply an illustration of my contention regarding the fundamental substance of this thread:

Can one apply mathematical massage, of any sort, (Bayesian, fuzzy, "neural networks", algebra, Euclid, or Hindu arithmetic with or without zero) to our collection of extant papyrus documents, and achieve thereby, superior understanding of:

a. the date of their issuance;

b. the author of the particular publication;

c. the incidence(s) of interpolation of the text;

I deny the validity of this idea.

I claim that mathematics can not provide any clarity in addressing these questions, a,b,c. I cited the three different verses of Mark 1:1 to demonstrate that no amount of "artificial intelligence", applied to the pages referenced (Codex Sinaiticus, Hort & Westcott, Byzantine) will yield answers to a,b,c.

If LegionOnomaMoi, or anyone else, wishes to refute me, the method is simple:

I offered the three Greek verses, in post 51. Please employ your remarkable, self proclaimed, mathematical prowess, to unlock the answers to any one of those three questions, a, b, c, for these three, extraordinarily simple, short verses.

One hopes that it will not be argued that their very brevity, renders these three competing versions of Mark 1:1, ill-suited for the proposed mathematical massage, required to achieve an answer to a,b or c.

Now, where did I put my abacus?

LegionOnomaMoi

This is the problem about dismissing things you don't understand. You ask for a demonstration of a method to solve a particular question, whether or not it is suited for that one, and if not, you act as if that means anything. It's like asking "can anybody use carbon dating to determine what day, month, and year the papyri documents were written?" and then, when they can't, denying "the validity of this idea."

A fair amount of research has demonstrated how badly "common sense" and our natural reasoning abilities fall apart when it comes to logic and probability. For example, when a coin is tossed many times, we don't expect exactly 50% tails, but we do expect something that approximates that. In other words, we would expect a coin toss that looks like this:

HHTHTTTHTTHHTHTHTTHHTTTTHHHTHHHTTHTHTHTTTHTT

(where H is heads and T is tails and thus the above represents a mix of both) rather than this:

TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT

So, assuming that both of the above have the same number of "tosses" (I didn't count) most people would say that the first is far more likely than the second, as the second is CLEARLY highly improbable.

Only they would be absolutely wrong. The probability of both tosses (again, assuming I series has the same number of tosses) is exactly equal.

Bayesian models are not just useful because they provide a robust measure for testing the inference concerning the plausibility of a hypothesis given evidence, but because the formalization of these models is a check against common reasoning fallacies.

Carrier demonstrates the use of Bayes here. The actual example begins on page 16.

tanya

I may have misunderstood this example.

I will rewrite it, to confirm that I have accurately understood your sentence above:

A. A coin is tossed 1000 times, about 50% are tails, without any particular streak of heads or tails.
B. Another coin, of equal weight, minted at the same time, is also tossed 1000 times, each time coming up tails, i.e. 100% tails.

Now you propose, above, that the odds of Coin A being tails, on the next toss, is equal to the odds of Coin B being tails, on its next toss.

If you have only one dollar left, no other possession, and someone proposes that you wager that last dollar, else die, will you gamble that A or B will turn up Tails?

If I have understood you correctly, the odds are precisely 50% that one would win the bet, whether the money gambled has been placed on A or B, because both coins are equally likely to show up tails on the next toss.

Unfortunately, in the case of Mark 1:1, the situation is not so simple. There is only one authentic version, i.e. representing the ink drying on the papyrus, from "Mark's" quill. It may be that NONE of the three versions in our possession, correspond to that original version. The odds that version A, or B, or C corresponds to the authentic, original version, are not calculable.

One reason why we cannot calculate the probability that version A, or B, or C (if any) is the correct version, is that we do not possess the "evidence", required to perform the computation:

In order to TEST anything with Bayes' theorem, one needs evidence. Bayes' theorem depends upon "prior probabilities" in predicting outcomes: its utility is followed, not only in medicine, but also in horse racing, precisely because one has precise, detailed, accurate information about the horses' performance, with times recorded accurately, on different tracks running under distinctive weather conditions.

We lack that kind of detail, in examining the ancient papyrus documents, which form the basis for our understanding of earliest Christianity.

I appreciate your defense of the application of Bayes' theorem, to studies of earliest Christianity, however, I maintain, still, notwithstanding your example of coin tosses, that establishing WHICH extant version of Mark 1:1 represents the authentic version, quilled by Mark himself, cannot be accomplished by any sort of mathematical massage of the text of our extant papyrus documents.

p.s. neither in medicine, nor in horse racing, and certainly not in studies of ancient papyrus documents, does the notion of equal probability arise, as one typically observes with coin tosses, assuming that the coin tossed has the weight distributed uniformly, on both faces.

LegionOnomaMoi

A coin is tossed 40 times, without any particular streaks, with the following results:

HHTHTTTHHTHTHHTTHTHTTHTTHTHHHTHTTTHHTTHT

Another coin is tossed 40 times, and ends up all tails:

TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT

Which is more likely?

The probability of either is exactly equal.

Did you bother to read Carrier's paper? If you don't understand how bayesian logic or probability works, then what makes you think that the question you demand it apply to in order to show its usefulness is in any way relevant? Nobody is saying "look, now that we have bayesian models, all historical questions are solved!" The question is CAN it be used to answer SOME important questions. I've come across several arguments since I joined this and one other forum concerning early christianity and Jesus. So many statements involve things like "if Jesus existed, we would expect to find X" or "if christianity existed before the 4th century, we would expect to find X." That's what Bayes' is for. Testing how likely a particular hypothesis is given the evidence we have. If one states, for example, that if christianity existed prior to the 4th century, we would have X evidence (a "hypothesis" which has been offered on this forum), then we can test this with Bayes' theorem. We take evidence we do have of other religious movements in and around that period. We assign a probability value to how likely it is that, if Y religious movement existed, we would have X evidence for it. We make sure that this value is quite biased against our hypothesis, or in this case that the probability assigned exceeds the evidence we have for religious movements in general. If we then plug into our model what evidence we do have for pre-4th century christianity, and find that it is greater than or almost equal to what we would expect given our assigned probability score (which, again, was selected because it was extreme and thus unreasonably biased against our hypothesis), then we can show that the best explanation for our evidence is that pre-4th century christianity existed.

Again, before bothering to respond with objections, why don't you read the link I provided in which Carrier outlines a Bayesian approach and demonstrates its use. Then, if you have criticisms about his use, you could voice them. Continuing to argue Bayes' theorem can't be used unless someone shows how it can answer a question you came up with is a waste of time. If you look at how historians have used it, and bring up specific criticisms with these uses, then it is possible to have a discussion. Until then, all you are doing is the equivalent of denying carbon dating is useful unless someone can tell you how one can use it to tell the day, month, and year an ancient piece of pottery was created.


papyri documents. Typos and other errors happen all the time (at least to me). But you keep using papyrus rather than the plural.

What exactly is your background in mathematics and science? In particular, how does your work utilize probability theory and statistical models?

aa5874

So probability is meaningless or has NO real significance to determine history if what you say is true.

LegionOnomaMoi

What? How did you go from what I said to that conclusion?

aa5874

You don't seem to understand what you wrote.

LegionOnomaMoi

Or you don't understand probability/set/ statistical theory. If I toss a coin X number of times, each particular toss has a .5 chance of heads or tails. Additionally, each toss is independent from the previous (the first toss in no way influences the outcome of the second, the second of the third, etc.). Therefore, the probability of any sequence of coin tosses is found by multiplying the independent probabilities of each coin toss. If I toss a coin twise, the probability of HH is (.5)(.5)=.25 and if I toss it three times the probability of HTH is (.5)(.5)(.5)=.125 and so on for any number of coin tosses.

This was my point. People can easily recognize that a series of coin tosses like os highly unlikely. However the question was:
I didn't ask whether it was more likely that one would get all tails or a mixture of heads or tails. I gave an exact sequence of heads and tails: HHTHTTTHHTHTHHTTHTHTTHTTHTHHHTHTTTHHTTHT

Hiow do I compute the probability that I would get the above sequence? Every single toss has a .5 probability of landing on heads or tails. To get the total probablity of the sequence above I multiply the number of times that I tossed the coinby .5, which is the probability for H or T given any single toss.

Given a million coin tosses, the probability of getting any specific sequence is equal. It's HIGHLY unlikely that a million coin tosses (without cheating) will result in all tails or all heads. There will be a mixture. However, the precise sequence of this mixture is as probable as getting all heads or tails. I can only say that it is more likely I will get a mixture of roughly half heads and tails. Any specific sequence given a million tosses is exactly equal.