Fundamental Constants?The Mysteries of Pi and eby Chuck Missler |
The recent discovery that the speed of light is not a constant has created quite a stir—and rethinking—in both physics and cosmology. (Although the spate of recent articles always fails to credit Barry Setterfield for calling this to our attention over a decade ago!) However, there does appear to be at least two intrinsic constants in the universe: π and e.
We all met π (“pi”) in school when we had to deal with the circumference of a circle and similar matters. “Pi are squared” sounds like bad grammar, but it is correct geometry for the area of a circle, πr^{2}. We approximated it with 22/7, until we got into engineering circles where we learned that, more precisely, it was 3.141592654… (It has recently been calculated to a trillion decimal places!^{1}) As we have previously mentioned in several of our materials, π is also a “hidden treasure” in the Hebrew text of 1st Kings 7:23.^{2} When one corrects the letter values for a variation of the spelling, the 46-foot circumference of Solomon’s “molten sea” is specified to an accuracy of better than 15 thousandths of an inch!
Perhaps less well known to most of our less technical subscribers is the base of Naperian (“natural”) logarithms, e . It shows up in myriads of places in advanced engineering and mathematics such as:
In wave mechanics, | X = Ae^{kt} |
Or electrical theory, | Q(t) = Qe^{-t/RC} |
In advanced math, | E^{ix} = Cos x +iSin x, where i = (-1)^{1/2} |
And the distribution of prime numbers: | A(x) = x/log_{e}x |
It is defined by | e = lim (1 + 1/n)^{n} ^{n}-> |
and it is usually approximated by 2.718281828.
The ancient Hebrew sages believed, of course, that God created the heavens and the earth. However, some of them believed that the Word of God was the very template with which He did it. This strikes some of us as simply a colorful exaggeration that goes beyond any direct evidence. There are hints here and there. There are two well-known references to the creation in the Scripture: Genesis 1:1 and John 1:1. Let’s look “underneath” the text of each of these.
In the beginning God created the heaven and the earth.
In Hebrew:
If you examine the numerical values of each of the Hebrew letters, and the numerical value of the words (see chart), and apply them to this formula:
The number of letters x the product of the letters
The number of words x the product of the words
You get 3.1416 x 10^{17}. The value of π to four decimal places! Hmm.
In the beginning was the Word, and the Word was with God, and the Word was God.
In Greek:
This time if you take the numerical value of each of the Greek letters (see chart), and the numerical value of the words, and apply them to the same formula:
The number of letters x the product of the letters
The number of words x the product of the words
You now get 2.7183 x 10^{40}, the value of e. Curious!
Each of these is another of those puzzling ostensible “coincidences” that are too astonishing to dismiss, and yet present challenges in suggesting any real significance.^{3} And taken together, they do evoke some conjectures. There are, however, at least two problems: why just four decimal places (they both deviate from the fifth place onwards) and what do you do with all the “extra zeroes”?
I frankly don’t know. Nevertheless, I thought it would be an excellent conversation piece as we return to our academic schedules this month. The rabbis would suggest that each of these may simply be a remez , a hint of something deeper.
Let me know if you have any suggestions. Meanwhile, let’s continue to praise our Creator-Savior for His marvelous Word!