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.
Monday, March 22, 2010
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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!
ReplyDeleteOne 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.
ReplyDeleteThe 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.
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.
ReplyDeleteA significantly better approximation has been known for at least 1500 years, so...
ReplyDeletehttp://mathnuggets.blogspot.com/2009/04/pi-by-fractions.html
http://en.wikipedia.org/wiki/Isopsephy
ReplyDeletebtw, michtav m'eliyahu somewhere puts a providential spin on the radak about kri uktiv, if someone can please post the address.
ReplyDeleteHoreyot 12B mentions a Gematriya.
ReplyDeleteTosafot in Shabbat (in the 130's) about circumcision mentions Gematrya for source that it was the eighth day.
As a Rabbi in my yeshiva said:
ReplyDeleteA huge coincidence is a simple "kah-incident" :)
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.
ReplyDeleteWhat 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.)
"A significantly better approximation has been known for at least 1500 years, so..."
ReplyDeleteNot exactly. What we're discussing here, is not an approximation of pi, but an approximation of the ration pi:3.
Anonymous, I said "barely" any in the Talmud. The Talmud was written more than a thousand years after the Tanach.
ReplyDeleteIf 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.
ReplyDeleteCall me skeptical :) but how is a single instance significant?
ReplyDeleteTrue, 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])
ReplyDeleteAnyway...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.
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.
ReplyDeleteI 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.
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.
ReplyDeleteThat'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.
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!
ReplyDeleteI probably need a control...
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.
ReplyDeletealso 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.
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).
ReplyDeleteThe result is 3.1416 x 10^17.
Great, now what?
When you look at 3.14 in a mirror, you see the word "PIE".
ReplyDelete"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).
ReplyDeleteGematria 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.
According to Ephraim's computer program, 111:106 is the third best ratio for numbers under 10,000.
ReplyDelete..........
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
You originally wrote:
ReplyDelete"Then, even if one wants to claim that Pi is encoded in kav/kaveh, does this reflect a supernatural encoder? The value of Pi was known in ancient times to several decimal places, and a human could encode it in this way. There is a Greek Pythagorean motto "God is ever a geometer" (ἀεὶ ὁ Θεὸς ὁ μέγας γεωμετρεῖ) — the number of letters in each of the six words are the first six digits of pi."
This isn't so simple:
First off, we don't know when this "motto" was formed.
Even if it did come from Pythagoras himself, he only lived from 569 - 475 BCE. Jeremiah, who wrote Kings 1, lived from 655 - 570. (Even if you reject the traditional authorship of Jeremiah, academics still claim Kings 1 was written 600 BCE). At worst, Jeremiah died as Pythagoras was born. Its a long shot to say Jeremiah got it from Pythagoras.
Furthermore, Archimedes (250 BCE), also from the Greek camp, stated that 3.1408 < π < 3.1429. So wee see that centuries later the Greeks only had 2 decimals of pi solidified albeit closer than before.
From wikipedia:
The best known approximations to π dating to before the Common Era were accurate to two decimal places; this was improved upon in Chinese mathematics in particular by the mid-first millennium, to an accuracy of seven decimal places. After this, no further progress was made until the late medieval period.
If true, it seems divine...
Sorry for bumping an old post, I just started reading your blog and want to read it as it develops.
ReplyDeleteA: The attribution of this admittedly clever idea to the Gra is likely wrong. A friend of mine searched the otzar for this and found no mention before the 1950s or so. Maybe he's a bad searcher. Another friend from Golders Green beith midrash (aka Munk's) said he knew the guy who came up with it; it was a "clever Munk's fellow". He didn't give me the name. If this idea happens to be found in Gra's writings, I stand corrected (and will correct these two friends).
B: Pi is unusually easily approximated by fractions. This is due to its continued fraction expansion starting with 3, 7, 15, 1, 292, 1, 1, ... Since this is not a mathematical forum, I can only say: Big numbers mean small corrections to the previous value, which means the previous value is unusually good. Therefore, if you only go with 3+1/7 you're unusually good because the next value is 15. But if you add another two terms, you're getting much better because the next value is 292. Wikipedia knows how this better, I fear.
The word קו appears many times in Tanach (with the meaning "line") and only a few places seem to have the kri and ktiv. (Also Yirmyahu 31:38)
ReplyDelete