Saturday, March 14, 2015

Pi Day - 3/14/15 (π) = 3.1415926...

Today, 3/14/15 at 9:26am was the best date and time to celebrate the most important trancendental number: Pi (π) = 3.1415926..., the ratio of the circumference of a circle and its diameter. There are 2π radians in a circle, and 4π steradians in a sphere.


Today, our local newspaper, The Villages Daily Sun, had a column about Pi Day that included a bit of information about my professional experience with Pi.


Pi is featured in Chapter 3 -The Value of Pi in my free online novel The Hawking Plan" by Ira Glickstein Note: I wrote the novel in 2008 before "Google Glasses" were announced. The novel takes place in 2052 and the "read-WINS" mentioned are the future version of Google Glasses. The Worldwide Information System (WINS) is the successor to the World Wide Web (WWW).

Jim, the narrator, is recalling his discussion with Luke about apparent factual errors in the Bible. Luke is an Engineer, and a Christian who believes the 1611 King James Version (KJV) of the Bible is the literal word of God. Jim is a Rabbi and Historian who is not a literal believer.

Here is the key excerpt:
I put on my serious face. “Luke, you’re an engineer, surely you know the value of Pi?”

“Well, Jim, Pi is the ratio between the circumference of a circle and its diameter. Twenty-two sevenths is a very good approximation to three significant figures. Pi is equal to a bit over 3.14.”

“How about Pi equals three?” I challenged. “Is 3.0 a good approximation for Pi?”

“Well, if you were building a circular pool in your backyard and you had a space of ten cubits by ten cubits to put it in, the outside diameter of the pool would be ten cubits. Given that, it would be a good approximation that the distance around the inside of the pool would be about 3.0 times the diameter, which would be thirty cubits.” Luke emphasized the words “cubits” and “outside” and “inside.”

“Why did you give a pool as an example?” I asked in amazement. “Why are you talking about cubits? Why did you make such a big deal pronouncing ‘cubits’ and ‘outside’ and ‘inside’?”

“Because I happen to know you were referring to 1 Kings 7:23, where King Solomon had a swimming pool made that was ten cubits across and thirty cubits around. Bible critics generally cite that as an example that God didn’t know the actual value of Pi or didn’t guide the hands of those who wrote the scriptures.
"There’s a very easy explanation. When you build a swimming pool, you need to know the outside dimensions so you’ll have enough space to fit the thing in your backyard. You also need the inside dimensions to know how big a circle you can swim inside. The ten cubits was an outside measure and the thirty cubits was the distance around the inside. Look at the verse on your read-WINs:”
1 Kings 7:23 And he made the molten sea of ten cubits from brim to brim, round in compass, and the height thereof was five cubits; and a line of thirty cubits did compass it round about.
“OK, I’ve got it and you are correct about the wording Luke. However, doesn’t the ratio between the inner circumference and the outer diameter depend on the thickness of the pool wall? I happen to know a cubit is a bit less than a half-meter (about 18 inches). Concrete pool walls are a bit less than a quarter-meter thick which is about half a cubit (about nine inches). Let’s do the math and see if the numbers match. OK, I’ve got it on my read-WINs. If the outside diameter was ten cubits and the wall was half a cubit thick, the inside was a bit over twenty-eight cubits around – not thirty! – so God was off by almost two cubits!”
“Jim,” Luke said with a big happy face, “King Solomon's pool was not made of concrete; it was made of brass so the wall could be thinner. Check 1 Kings 7:26 'And it was an hand breadth thick.' Look up a hand breath” in Biblical measures. OK?”
“OK, I’ve got it on my read-WINs. A digit was about two centimeters. A hand was five digits, or ten centimeters (about four inches). A cubit was twenty-four digits, which is a bit less than a half-meter. Given that the outside diameter was ten cubits, and the wall was a hand thick, the inside circumference comes out to be 30.1 cubits. Wow! – 30 cubits around is good to two significant figures. I’m impressed!”
“Jim, I may not know them off the top of my head, but I firmly believe any apparent error or contradiction you or I or anyone else may find in the 1611 KJV has an explanation.”
[Later that day]
"OK,” said Luke. “I’d like to revisit the supposed Pi equals 3.0 issue. I am quite pleased, and I think you were too, with the explanation I gave you this morning, precise to two significant figures. However, if we go back to the original Hebrew, we get an even better approximation! Please don your read-WINs and bring up the English and Hebrew for 1 Kings 7:23.”
“Fine,” I replied, “Here it is.”
1 Kings 7:23 And he made the molten sea of ten cubits from brim to brim, round in compass, and the height thereof was five cubits; and a line of thirty cubits did compass it round about.
כג וַיַּעַשׂ אֶת-הַיָּם, מוּצָק: עֶשֶׂר בָּאַמָּה מִשְּׂפָתוֹ עַד-שְׂפָתוֹ עָגֹל סָבִיב, וְחָמֵשׁ בָּאַמָּה קוֹמָתו וקוה (וְקָו) שְׁלֹשִׁים בָּאַמָּה, יָסֹב אֹתוֹ סָבִיב
“I don’t read Hebrew well,” said Luke, “But I know you do. See the Hebrew word in parenthesis? What does it say and mean?”
“It is Vuv Kuf Vuv, pronounced ‘vikav’ which means ‘a line’.”
“Great!” said Luke, “What is the word before that one?”
“Well,” I replied, “Hebrew is read from right to left, so the word before ‘vikav’’ is to the right of it and is Vuv Kuf Vuv Hay or ‘vikavh.’
"Hey! Look at that, it is the same word but spelled incorrectly. It has the letter Hay, the Hebrew letter for ‘H,’ at the end. The parenthesis signifies that our oldest manuscripts have a spelling error. The letter Hay does not belong at the end of that word.
"Our scribes are forbidden to correct a spelling error, because, according to our literal believers, this may be some special message from God. So they kept the ‘vikavh’ and, in parenthesis, added ‘(vikav)’ which is the correct spelling for ‘a line.’ It would be as if, in English, the oldest manuscript mispelled ‘a line’ as ‘a lineh,’ so it would appear in the printed text as ‘a lineh (a line).’ So, where are we going here?”
"We are going,” said Luke, “To expose the hidden message about Pi from God in this supposed error! What is the numerology, the so-called ‘gematria’ for each of these words?”
“OK, Luke,” I replied, “As you apparently know, in Jewish numerology, Hebrew letters are also used as numbers. Put on your read-WINs and link them to mine. Let me bring up the conversion table for gematria on my read-WINs. Here it is, up to four hundred. Each group is in the following order: Hebrew Letter, Name of Letter, Sound of Letter, and Numeric Value according to Gematria:”
א, Aleph, (silent) = 1; ב, Beth, B = 2; ג, Gimel, G = 3, ד, Daled, D = 4; ה, Hay, H = 5; ו, Vuv, V = 6; ז, Zion, Z = 7, ח, Chet, CH = 8; ט, Tet, T = 9; י, Yud, Y =10; כ, Kaph, KA = 20; ל, Lamed, L = 30; מ, Mem, M = 40; נ, Nun, N = 50; ס, Samech, S = 60; ע, Ayin, (silent) = 70; פ, Pay, P = 80; צ, Tzadik, TZ = 90; ק, Kuf, K =100; ר, Resh, R = 200; ש, Shin, SH = 300; ת, Tau, T = 400.
I figured the values and said, “Vuv Kuf Vuv is 6 + 100 + 6 = 112. Vuv Kuf Vuv Hay is 6 + 100 + 6 + 5 = 117. OK?”
“No,” replied Luke, “It should be 106 and 111.”
“106 and 111?” I asked. “OK, if you leave out the first Vuv, which is equivalent to the word ‘a,’ and just count the Hebrew word for ‘line,’ you get Kuf Vuv which is 100 + 6 = 106. Kuf Vuv Hay is 100 + 6 + 5 = 111. OK? Where are we going here?”
“Great, get a good grip on your chair!” said Luke expectantly, “Now divide 111 by 106 and multiply by 3.0. What do you get?”
“I get 3.141509. WOW! That’s almost Pi, isn’t it? Let’s see, Pi is 3.141593. WOWIE KAZOWIE! The first five figures are the same! But, if you round the numbers, they match to only four significant figures, 3.1415 vs. 3.1416. That’s one significant figure better than the way you showed me this morning and also one significant figure better than twenty-two sevenths. Fantastic!”
“I take that as proof God knew the true value of Pi when the first book of Kings was written in Hebrew and He hid the value in what appears a mere spelling error! Are you impressed or what?” 
"I must admit I am im…press … surprised,” I said very carefully, “But it’s just another coincidence. What I am impressed with is the ingenuity of the minds of human true believers in coming up with these imaginative explanations.”

Ira Glickstein 

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