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Hypothesis testing incompatible with Bayesian approach? Dan-E.Nilsson@cob.lu.se Dec 09, 2008

"As the entire Bayesian approach is completely incompatible with the concept of hypothesis testing in general and rejection regions in particular..."
Can't frequentist hypothesis testing be translated into Bayesian terms by selecting some particular prior? A prior which remains unstated in the frequentist approach but can be inferred from concrete calculations nonetheless?

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Berlinski's fallacious argument Firth, Robert Nov 28, 2008

I have never understood why religious people put forward this argument. Yes, let us suppose every atrocity of the 20th century -- from mass murder
to littering --- was perpetrated by atheists.

So what? Why does that say anything about the possible existence of God? There is no valid reasoning from the premise "P is nasty" to the
conclusion "P is false".

Books such as Berlinski's are written in total bad faith -- their purpose is neither to argue nor to convince, but to intimidate by slander.
That in doing so, they make religion look as bad as atheism, is a point that never seems to occur to them.

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Is this one instance Guy, Piano Nov 27, 2008

I found something interesting that was not discussed in this discussion.

Around 480, the Chinese mathematician Zu Chongzhi gave the approximation π = 355/113, and showed that 3.1415926 < π <
3.1415927, which would stand as the most accurate value for π over the
next 900 years.

He obtained the result by approximating a circle with a 12,288 (= 211 × 6) sided polygon. This was an impressive feat for the time, especially
considering that the only device he used for recording intermediate results were merely a pile of wooden sticks laid out in certain patterns.

The exact ratio of a circle's circumference to its diameter equals pi,
3.1415926535897932384626433832795...etc. In this pasuk, pi = (30/10) = 3. But the deeper reading of the text is saying: if you take 106 (the
numerical value of "kuf" "vav" - the pronounced form of "line") and replace it with 111 (the numerical value of "kuf" "vav" "hay", the written form), you have a correction factor 111/106 (or,
1.0471698113207547169811320754717). To fix up the original ration in the pasuk (30/10, 3) by multiplying by this correction factor (3*1.0471698) we get 3.14150943..., the value of pi to 4 decimal places (an error of 9 parts
in 10^-5)! It turns out that if you analyze the error in the numerator (the error in the pasuk's use of "kuf" "vav" and "hay", or 111), it turns out that this spelling yields the best approximation of pi.

Note the superfluous hei in v'kav. Perhaps it somehow alludes to taking the ratio of v'kav and v'chameish, the value of hei. If you do so, it just so happens that the ratio of the numerical values of v'chameish (355) and v'kav (113) [including one for the word itself] equals 3.14159292...which is precisely six decimal places of accuracy - one part in a million of pi's exact value, 0.00000026 more than pi, and 99.9999915...% similar to pi. It turns out that there is no better approximation for pi as a ratio of the numerical values of any two words, or of any other whole numbers less than
ten-thousand. This calculation is even internally consistent due to the fact that it is veiled within a pasuk containing the ratio of circumference to diameter.

Another thought worth noting, perhaps even stronger than the above: The ratio of the numerical values of kav with and without the hei is 111/106, 1.04716...extremely close to the correction factor (3, the circumference as
it appears in the pasuk, divided into pi), worked out as follows: pi/3 = 1.04719...Hence, due to the extra hei in kav, this pasuk comes to teach us that somehow it "knows" the drawbacks of an approximation - 3 is obviously not accurate. But for all intents and purposes, this approximation is the most succinctly accurate way to teach us the measurement of the "sea". (The Rambam writes in Peirush haMishnayos that pi at 3 is a legal definition that is the legal approximation. The reason that they can use this as the legal value of pi is the pasuk in Melochim.)

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Another response to Mr. Goldstein Makovi, Mikhael Nov 12, 2008

Mr. Goldstein,

You mention that polytheists have by no means had less moral imperative than monotheists. This, however, I would question.

First, it has been noted countless times, that when a pagan wanted to do almost any given activity, he had a god at his disposal to justify. As Rabbi Hertz puts it, a god of high justice and morality could coexist with the god of the most depraved sensuality. With monotheism, there is at least no choosing between alternate imperatives.

(I saw with tremendous satisfaction that Berger (op. cit.) regards the Hertz Pentateuch, for all its shortcomings, as a noble and inspiring source for a truly elevated and edifying view of Judaism. I most wholeheartedly concur, if I may add Rabbi S. R. Hirsch thereto.)

Second, even if a pagan had imperatives, they often lacked moralities very critical to Judaism. Human sacrifice, temple prostitution, to name but a few examples, show that even paganism that included imperatives did not mean that the imperatives encompassed what Judaism would demand.

Obviously, every society has widely varying norms, and there is of course much to discuss about exactly what a gentile should have to profess. What if he professes not to murder or steal, but he still performs abortions and downloads music from the internet? Obviously, there is much to talk about. But I believe it clear that the kinds of gentiles that the
average American Jew meets, for example, are well within what could be considered a decent moral person, whatever the precise parameters.
Moreover, Rabbi Ahron Soloveichik, as brought by Berger (op. cit.) claims that a gentile is judged by the majority of his deeds, like any Jew, and that for the remainder he receives Gehinom. So as long as a given gentile is more than 50% righteous in terms of observing the Noahide laws, this would be enough. Rav Ahron has already exempted them from strict
monotheistic belief, as I have noted previously. I agree with you that there is a desideratum of literature on the subject, but I believe the
groundwork already exists, and I believe that at least Modern Orthodoxy is very much prepared to accept the premises and conclusions of this field. May it soon be that all of Orthodoxy follows in the paths of American, British, and German Modern/Neo-Orthodoxy.

I thank you for your essay, which clearly showed what Modern Orthodoxy is going up against in the traditional literature. The first step towards a
solution is acknowledging the problem, after all.

An aside: In the case of the Jewish and gentile shepherds who may be left for dead, you noted that the Jew in question was certainly a
monotheistic one, obviating an argument that only idolatrous gentiles and not monotheistic ones were included. However, following my (and Berger's and Henkin's) interpretation of the Meiri, the solution is simple: monotheistic or not, the Jews and gentiles in question were not moral ones, seeing as how they brazenly violated the laws of theft.

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Lowell's Problem Burrows, Peter Nov 09, 2008

Poor Lowell sufferred from eye strain due to his constant observations of Mars.

Otherwise he was quite a good observer.

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