Monday, March 22, 2010

Puzzled by Pi Perplexities

After reading through the fascinating comments to my post about Pi, I am left utterly perplexed as to what to conclude about the kav/kaveh gematriya.

On the one hand:
According to Ephraim's computer program, 111:106 is the third best ratio for numbers under 10,000. And it's the best that could be generated from a single letter difference - i.e. a kri/kesiv. Now, of course coincidences happen. But to have such a figure, resulting in Pi to five significant figures, emerging from precisely the word that the Passuk uses for the circumference, seems far too extraordinary to be relegated to coincidence. (This does not prove that God did it - a person could do such a thing too - but it is an ingenious feat of encoding, and the point is that it is a deliberate encoding.)

But on the other hand:

The kav/kaveh kri/ksiv occurs in Zechariah 1:16 too, where it is not referring to a circumference. This would indicate that it is merely a standard matter of confusion as to how the word should be spelled. (Malcolm argued that the fact that in Divrei Hayamim 2:4:2 it says kav without a kri/ksiv indicates that they knew the correct version and the kri/ksiv elsewhere is deliberately introduced, but I find this unconvincing; the existence of a kri/ksiv in Zechariah seems much more significant than the lack of kri/ksiv in Divrei HaYamaim.)

So is this kri/ksiv a deliberate way of encoding a closer value of Pi or not? I don't know what to make of it.

22 comments:

  1. I'm puzzled, too. I'm partial to the theory that there is ingenious encoding, and I'm partial to the theory that the 10 refers to the outer diameter while the 30 refers to the inner circumference. If you say, "you can't be right about both," then you're right, too!

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  2. One must understand what this Kav in Zacharya is, in the context of building the House. B'Pashut it is a line used by the builders to get things straight, but I think it is deeper.

    The House of G-d must be build at the proper location. Zevachim 54b explains how David and Shmuel figured it out. The key is the border between Benyamin and Yehuda. It seems to me that the Kav in Zecharya is the part of the border between the two tribes that is relevant to the location of the Mikdash, the North-South line from the top of the Har Moriah to מי נפתוח (see the border description in Yehoshua 15:7-9), which must be the Gihon. The Braita in Megillah 26a (also Yoma 12a) explains what was East and what was West of the line. It does not mention the Kiyor. Perhaps it was on the Kav itself, and thus shared by Yehuda and Benyamin, and the Kri/K'tiv of the word Kav hint at this.

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  3. Let's be clear about one thing: There's not a hint about gematria anywhere in Tanach. (And barely any, in our sense of the word, in the Talmud.) It's likely adopted from the Greek practice- the name certainly is. At the time Divrei HaYamim was written- and Kal V'Chomer Melachim- it simply didn't exist. So unless the kri/ktiv was added centuries later (it would be interesting to see what the Dead Sea Scrolls read), this is likely a huge coincidence. An incredible one, which maybe even points to the Hand of God all the more, but that's all we can say.

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  4. A significantly better approximation has been known for at least 1500 years, so...

    http://mathnuggets.blogspot.com/2009/04/pi-by-fractions.html

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  5. http://en.wikipedia.org/wiki/Isopsephy

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  6. btw, michtav m'eliyahu somewhere puts a providential spin on the radak about kri uktiv, if someone can please post the address.

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  7. Horeyot 12B mentions a Gematriya.

    Tosafot in Shabbat (in the 130's) about circumcision mentions Gematrya for source that it was the eighth day.

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  8. As a Rabbi in my yeshiva said:

    A huge coincidence is a simple "kah-incident" :)

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  9. I am highly suspicious of the Torah codes as used by Aish and others. Why? Two reasons: 1) the statistics don't necessarily hold up. 2) We have no clear mesorah for this. Rav Weismandl's codes are very different than that used by Aish. I believe his sefer is on hebrewbooks.org. Look it up, it's a work of drush not prophecy. Today's prophectic codes simply do not have a clear and unambiguous tradition.
    What does this approach do for the kri/ksiv in question? Well the math is pretty good as I've shown. If we accept that the vort comes from the Gra, then we're on solid footing as far as mesorah goes. (By the way, the Gaon could easily have verified my results without a computer.)

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  10. "A significantly better approximation has been known for at least 1500 years, so..."

    Not exactly. What we're discussing here, is not an approximation of pi, but an approximation of the ration pi:3.

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  11. Anonymous, I said "barely" any in the Talmud. The Talmud was written more than a thousand years after the Tanach.

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  12. If anything accepting the kri/ksiv here as an item hidden in the text creates more theological problems for a frum person than it solves. A knowledgeable (even omniscient) author might give an approximate result. However, a truly knowledgeable entity would have known that even this ratio was just an approximation. Thus, whoever introduced the kri/ksiv knew a little math but didn't know that much.

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  13. Call me skeptical :) but how is a single instance significant?

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  14. True, it's slightly different (by the way, if you want to play around with irrational numbers this way, the Rationalize[] function on WolframAlpha is fun; e.g. Rationalize[Pi/3,.0001])

    Anyway...calculating a post hoc probability for something like this is not really meaningful--chances are|were that somewhere in the vicinity of a Pi approximation you can figure out a clever way of encoding a more precise approximation...I could probably write out a dozen ways of representing that (different number systems, base systems, continued fractions, series approximation, etc.) and a dozen ways of "hiding" it, so that even if it did not in fact intentionally exist, I could still "find" it.

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  15. However, a truly knowledgeable entity would have known that even this ratio was just an approximation. Thus, whoever introduced the kri/ksiv knew a little math but didn't know that much.

    I don't agree at all. Maybe they also knew that this was an approximation, but put it in because it is much more accurate than the obvious inaccuracy in the passuk.

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  16. chances are|were that somewhere in the vicinity of a Pi approximation you can figure out a clever way of encoding a more precise approximation... I could probably write out a dozen ways of representing that (different number systems, base systems, continued fractions, series approximation, etc.) and a dozen ways of "hiding" it, so that even if it did not in fact intentionally exist, I could still "find" it.

    That's what I suggested in the original post, but it turns out that it doesn't seem to be the case. Go ahead, come up with a dozen ways of finding such an approximation in this passuk! And don't forget, it was hidden in the very word used to describe the circumference.

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  17. Put up or shut up, eh? Well, the question is; if I find such a clever encoding in a relevant location, will that support the argument that it is easy to find that type of signal anywhere, or the opposite--look how amazing! The same pasuk has multiple references to Pi!

    I probably need a control...

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  18. however even if Gra new about approximation of pi, when halacha came he held that it was 3. see RMBM laws of shabbos 17:26 and shulchan aruch 363:19 when kora(beam for eruv) is discussed - if circumference of kora is 3 tefachim then its diameter is one tefach. Gra does not says anything in those places.
    also the Shulchan Aruch 634:2, "If it [the succah] is round, there must be within it enough to square seven by seven [tefachim]." Taz says that "And a string which can encircle twenty nine tefachim and two-fifths can square within it seven by seven." But really sukka has to be not 29 tefachim but rather 31. So we sit in pasul sucah, but Gra again keeps quite.

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  19. Here's an unusual way to get pi from the Torah, which I found online. Take the first passuk, "In the beginning...". In the numerator, put the number of letters times the product of the letters (28 * 2.389 x 10^34). Divide that by the (number of words times the product of the words) (7 * 3.042 x 10^17).
    The result is 3.1416 x 10^17.

    Great, now what?

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  20. When you look at 3.14 in a mirror, you see the word "PIE".

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  21. "Let's be clear about one thing: There's not a hint about gematria anywhere in Tanach. (And barely any, in our sense of the word, in the Talmud.) It's likely adopted from the Greek practice- the name certainly is." (Nachum).

    Gematria is no doubt from the Greek yet there is an underlying numerical structure to Torah which defies what you're saying. It's especially prevalent in Bereshit. I'll have to dig up some examples.

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  22. According to Ephraim's computer program, 111:106 is the third best ratio for numbers under 10,000.

    ..........

    do not quite understand third best ratio comment

    if pi is 3.1415926536 and the kri kesiv 111/106 gives approximation 3.1415094340 then the difference is 0.0000832196. I think there are 14 more accurate fractions under a thousand not 3.

    although as you say what happens if you cannot make a one letter kri kesiv with any of these more accurate fractions

    in ascending order of difference

    355 / 339 ( difference 0.0000002668)
    954 / 911
    821 / 784
    599 / 572
    466 / 445
    843 / 805
    577 / 551
    244 / 233
    688 / 657
    910 / 869
    865 / 826
    621 / 593
    998 / 953
    377 / 360 (difference 0.0000740131)


    if however you are looking for a fraction to add on to 3 then I think there are over 50 more

    fractions that gives a more accurate value less than a thousand than 111/106



    16 / 113
    127 / 897
    129 / 911
    111 / 784
    113 / 798
    95 / 671
    97 / 685
    79 / 558
    81 / 572
    65 / 459
    63 / 445
    114 / 805
    110 / 777
    49 / 346
    47 / 332
    131 / 925
    125 / 883
    82 / 579
    78 / 551
    115 / 812
    109 / 770
    140 / 989
    33 / 233
    31 / 219
    116 / 819
    139 / 982
    83 / 586
    108 / 763
    133 / 939
    77 / 544
    50 / 353
    123 / 869
    117 / 826
    46 / 325
    67 / 473
    107 / 756
    84 / 593
    61 / 431
    101 / 713
    137 / 968
    118 / 833
    135 / 953
    76 / 537
    91 / 643
    106 / 749
    121 / 855
    136 / 961
    17 / 120
    34 / 240
    137 / 967
    15 / 106

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