Tolstoy Loves Meby Brendan McKay |
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Given two words w,w', a complicated procedure in [WRR] defines a "distance" c(w,w') in the range 0-1 (though sometimes it is "undefined"). To good approximation, random words w,w' will produce a value of c(w,w') uniformly distributed between 0 and 1. Also in [WRR] are several procedures by which a set of numbers in the interval [0,1] are converted into a single number in the same interval. These procedures are called P1 and and P2. P1 and P2 cannot be correctly interpretted as probabilities, but in [WRR] they are used as measures by which several different sets of numbers can be compared. Small values of P1 and P2 indicate "close matching", and large values indicate lack of matching.

) = Alef B = Beit G = Gimmel D = Dalet H = Hey W = Waw Z = Zain X = Chet + = Tet Y = Yud K = Kaf L = Lamed M = Mem N = Nun S = Samech ( = Ain P = Pey C = Tzadi Q = Kuf R = Reish $ = Shin T = TavMy name is Brendan McKay, which in Hebrew is most correctly written BRNDN MQYY. With regard to spellings, there is no question about BRNDN, as the final "a" of Brendan is not pronounced at all, and certainly is not "o" or "oo". The name McKay can conceivably be spelt in other ways, but the use of only one K or Q correctly reflects the pronunciation, which is not Mc'Kay but M'Kay. In any case, the spelling MQYY was the one independently chosen by the Israeli newspaper Maariv, on the single occasion that I have been named in the Israeli press (May 29, 1997).

My place of residence for the past 14 years has been Canberra, Australia. The Hebrew spellings of these names according to the Encyclopedia Hebraica are QNBRH and )WS+RLYH.

My date of birth was October 26, 1951. In the Jewish calendar, that was 26 Tishri 5712.

To perform the experiment, we must convert the data into words, limiting ourselves to the range 5-8 letters as in [WRR].

Firstly, following [WRR], we make a list of appellations. There are only two obvious ones: BRNDN and DR MQYY. Others are too long (BRNDN MQYY, DR BRNDN MQYY) or too short (MQYY). (The method of [WRR] requires 5-8 letters.) The use of DR for representing my title is common in Israel; for example it appears on office doors in university departments. I do not hold the rank of Professor according to the rules of my University, and so am not entitled to use appellations with that title.

To make the date 26 Tishri 5712 into words, we use precedents from earlier experiments. Firstly, we follow [WRR] in writing 26 Tishri as KWT$RY, BKWT$RY and KWBT$RY. Secondly, we follow [HNGM] in writing 5712 as BT$YB, HT$YB, BHT$YB, $NTT$YB, B$NTT$YB, and $NTHT$YB. (The other two, T$YB and B$NTHT$YB are outside the 5-8 length range.)

w = BRNDN DR MQYY w' KWT$RY 0.1120 0.0480 BKWT$RY 0.2542 0.1441 KWBT$RY 0.1557 0.1393 BT$YB 0.3200 0.4160 HT$YB 0.0720 0.0160 BHT$YB 0.0240 0.0720 $NTT$YB 0.1368 0.0211 B$NTT$YB undef undef $NTHT$YB 0.7500 0.8750 QNBRH 0.0880 0.0081 )WS+RLYH undef undef

Values marked "undef" are undefined according to the rules of [WRR].

The values of P1 and P2 are:

Date only Date and Place P1 : 0.0000326 0.00000252 P2 : 0.0002415 0.00001971The first method of obtaining a significance level will be to try alternates to the two appellations, namely rearrangements of the letters. For example, instead of BRNDN we try BNNDR, NDBRN etc.. This approach was used in [M] to analyse the famous Aaron cluster.

Since the calculation of c(w,w') uses words running both forwards and backwards, and each appellations contains one letter twice, there are 30 distinct permutations of BRNDN and 180 of DRMQYY. In combination, there are 30*180 = 5400 distinct pairs of appellations. We tried every one of these appellation pairs and calculated the P1 and P2 scores. Here are the results:

- Using the date only
P1 P2 Best: BRNDN, DRMQYY 0.0000326 0.0002415 Next best: DBRNN, DRMQYY 0.0002476 0.0008575 Best derangement: DBRNN, RDQYMY 0.0070036 0.0030297

The correct spelling wins by a factor of 7.6 for P1, and by a factor of 3.6 for P2. The third line shows the best combination of two misspellings. It is worse by a factor of 215 for P1, and a factor of 12.5 for P2. - Using both the date and the place
P1 P2 Best: BRNDN, DRMQYY 0.0000025 0.0000197 Next best: BRNDN, RYQDMY 0.0000224 0.0000767 Best derangement: BDRNN, RYQDMY 0.0009109 0.0006115

The correct spelling wins by a factor of 9.0 for P1, and by a factor of 3.9 for P2. The third line shows the best combination of two misspellings. It is worse by a factor of 364 for P1, and a factor of 31 for P2.

Using the date only Using both date and place P1 P2 P1 P2 4 9 2 2Here again we see consistent significance levels below 1 in 1000, completely confirming our expectations.

Did it happen by chance? **Yes!**

[M] D. Michaelson, Reading the Torah at Equal Intervals, B'Or Torah, 1987.

[HNGM] D. Bar-Natan, A. Gindis, A. Levitan and B. McKay, Report on new ELS tests of Torah, 1997, here.

The image at the top of the page shows "Canberra" and "Dr McKay".

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Copyright Brendan McKay (1997), bdm@cs.anu.edu.au.

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