Numbers don't lie, but what do they mean? Last week's article connecting solar flares and Jewish prayers kindled the curiosity of statistician Aaron Dukes to dig deeper. Here's what he found.
Aaron, I'm so pleased you took the time to get into this. I'll weave in my comments point by point below. - AG Hi Aryeh,
So I've just read Praying with Fire, and I have some comments
I have an alternative (or perhaps complementary) hypothesis:
1. It appears from the information in the graph and your beautiful essay that the month with the highest activity throughout the 40 year period was November of the same Jewish year 5741, which then consisted of the period 22 Cheshvan through 22 Kislev. This includes several Chassidic celebratory days: 1, 9, 10, 14, 19-20, two of which are among the most significant days of the Rebbe's history, his wedding and his recovery from the heart attack three years prior, and the last of which is termed the Rosh Hashono of Chassidus. [AG replies] I like your conjecture. Although it fits well with the time of year, it doesn't seem to fit in with the particular year among the 40 years as these dates are annual events and the solar intensity peak was once only. I too, have a hypothesis about this, and that is that probably the Rebbe was redacting the prayer service and associated laws and commentaries that he published for the occasion. Note that never before in history has such a big deal about the blessing of the Sun. The previous cycles were relativelly unsung (sic) affairs involving a few Torah scholars making a blessing and studying a little more about the matter. Here, there were no less than 200,000 people at the Western Wall (I was there at the time) and a big 'hooha' instigated pretty much by the Rebbe in anticipation. I estimate that the Rebbe would have waited to work on this until after the High Holiday season (Tishrei) was over and would have completed his preparations well in advance as is his style. That would make the most likely time for his efforts November 1980 (Cheshvan-Kislev 5741), the time of the largest peak of the 480 months. Because that relates directly to the sun and to the leader of the generation who is considered equivalent to the entire generation (See Rashi on Numbers 21:21), it follows that just as the generation created a big stir with their prayers, the leader of the generation would have created an impact as great or even greater (see the Rebbe's commentaries on that Rashi). 2. The peak in April 1981 included the period 26 Adar II through 26 Nissan, the center day of which is 11 Nissan, the Rebbe's 79th birthday and the beginning of Shnas HaShmonim (v'im biGvura, Shmonim Shanah).
3. As amazing as these two highest peaks in 40 years coming so close together are, and that the whole smoothed cycle reaches a peak of about 20 flares per month centered between these dates, what is striking is that would have been expected to be the peak, the month of January 1981, actually had the fewest flares, less than 10, over the four year period it centers. The center of that month is 10-11 Shvat, the 30th anniversary of the Rebbe's leadership.
4. The first month with an extremely high rate of flares relative to its surrounding months appears to be month 83 or 84 which would correspond to Kislev 5738, the time when the Rebbe recovered from his heart attack. This high rate is a precursor to all the glowing activity to come...
5. If we celebrate Rosh Hashono in TIshrei, why do we celebrate Bircas haChama in Nissan? There is a disagreement between two Rabbis regarding when the world was created. According to one opinion, in the days prior to Rosh Chodesh Tishrei. According to the other (Rabbi Yossi), in the days prior to Rosh Chodesh Nissan (which is itself known as Rosh Hashono liMelochim). Tishrei begins the Natural Order of the Year, whereas Nissan begins the Miraculous Order. Kings, Miracles and Redemption are the themes of Nissan.
6. Moreover, Light, Miracles and Redemption are the themes of the month of Kislev, which contains the Rosh HaShono of Chassidus.
7. The extreme peaks and valleys of the Solar Flare distribution therefore might correlate well with Judaism's recognized seasons of transcendence of the natural order of existence, with will imposed externally by Hashem and His representatives on earth, Kings of the House of David. The smoothed trend would indicate seasons more governed by Hashem indirectly through the natural laws He created the world with. [AG replies] Thank you for expanding the discussion and shedding so much light on it. I also have a quibble:
Your subtitle: p=.002 has lots of problems:
1. A statistician from the frequentist school of statistics would ask you, where is your repeatable experiment? [AG replies] A posteriori statistical analyses are not uncommon in the literature when dealing with historical phenomena. There are several techniques to generate pseudoreplications, for example bootstrapping the data, but I'm not sure that would have helped. What do you think? 2. You don't really have independent results from one month to the next. [AG replies] Granted. And therefore one cannot speak of the probabilities? But I had an a priori hypothesis and a month is a month. From that perspective they are all equivalent. 3. Even ignoring the quibbles 1 and 2, wouldn't you have found it just as significant if all months had flares, but April 1981 had been the calmest with no flares? (So a 2-sided test is perhaps more appropriate than a 1-sided test.) [AG replies] Absolutely not. My guess was along the lines of "Kara lashemesh vayizrach or", ie, calling out a response from the sun. Just as calling is an expression of what is within, the opposite of a status quo calmness, so too the result was expected along the same lines. In fact I alluded to this in the article itself. Hence a 1-sided test is what I did expect. 4. Also, .002 =1/480 would have made sense if April 1981 had been the highest in 40 years, not the second highest. [AG replies] Correct. I'll fix that mistake in the article. Thank you. 5. Given 3 & 4, the only reasonable p-value to quote is .008, [AG replies] (or with a one-tailed test p=0.004) even still with caveats such as "assuming all other things equal", ie. there are no other factors at work (whether spiritual ones such as I delineated above, or scientific causes we haven't taken into account). Even still, the frequentists would still argue that it is invalid. [AG replies] So according to frequentists, would such a problem as the one I posed remain without statistical methodolgy to address it? That would be strange indeed. What normative statistical methods would you have used given my question? 6. You might get more respect from the frequentists if a solar flare peak occurred every (or almost every) time Bircas HaChama took place... Lets revisit in 2 years.. [AG replies] I expect that Moshiach will be long here by then. What role will statistical analysis have then? Have you been following the consciousness research at Princeton (PEAR) and at the Institute of Noetic Sciences? In principle shouldn't the sun be as responsive to concentrated collective prayer as Random Number Generators are to masses of couch potatoes watching the Olympics or the OJ trial?
Nonetheless, I really enjoyed the article.
Your friend,
Aaron Leib Dukes.
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