# The Mysteries of Pi and e

Fundamental Constants?

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*!

## Natural Logarithms

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.

## A Rabbinical Tradition

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.

### Genesis 1:1

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.

### John 1:1

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!

## Significance?

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!