Saturday, March 14, 2015

Happy Pi Day! 03 14 15

Your humble author, working on pi-cutting skills: West Point, 1987.

Since it is the fourteenth day of the third month (which can be abbreviated 3.14), this day is often playfully referred to as "pi day," in recognition of the fact that the transcendental number pi (which goes on forever and has no discernible pattern to its endlessly-unfolding decimal sequence) begins with 3.14 . . .

And, because this is the year designated AD 2015 (which means that this day in this year can thus be abbreviated 3.14.15), this particular "pi day" is the only one since 1915 that has reflected the "first four digits of pi" after the decimal place (the first 9 digits of pi after the decimal place are 3.141592653 . . .

Mathematically, of course, pi relates the diameter of a circle to its circumference: the circumference of a circle can be expressed as πd, where "d" is the diameter of the circle.

Because of pi's intimate relationship with the shape of the circle -- a shape with great symbolic significance, representative of the heavens above and hence of the world of spirit -- pi has long been treated with reverential honor and respect.

At the ancient monastic academy of West Point, for example, the act of cutting any pie or cake was once treated as a ritual of tremendous importance, as can be witnessed in the photograph above (which was not staged), in which a circular dessert pie is being inscribed with a knife-line across its diameter, while gentle coaching and advice is offered in order to ensure that the ceremony is done precisely in accordance with tradition.

This level of attention to detail is appropriate, because the act of placing a dividing line across the circular space of the pie is symbolically akin to coming into contact with the infinite.

Mathemagician Marty Leeds, who is very attuned to the symbolic significance of number, and especially of the transcendental number pi, explores the profound spiritual significance of pi in his book The Peacock Tales, reflecting:
I was spellbound by pi's infinite digits, its powerful trinity and its mysterious transcendence. [. . .]
[The] cosmic birth was the act of a great try-unity, first manifesting itself within itself and then releasing that potential by dividing itself; and pi is the ratio and geometric symbol given to us to help us remember and understand this story. God manifesting itself in the beginning of time as the sphere of creation is recognized in the circumference of pi, the division of itself recognized in pi's diameter, and the expansion of our universe recognized in pi's ever-unfolding, infinite digits.
In short, the mathematical constant of pi is a representation of the creation of our expanding universe.
15 - 17. [Italics and boldface type in the original].
Later in the same book, Marty dives deeper and deeper into the profound meaning of pi:
In the study of sacred geometry, the circle represented Heaven and the square represented Earth. This motif is seen within the Freemasonic Square and Compasses (the compass being Heaven and the square being Earth), within the ancient Chinese cosmographic concept known as Gai Tian (the square earth is a chariot, the round heaven its canopy) as well as utilized by the Buddhists in the building of the sacred, mound-like or semi-hemispherical structure known as the Buddhist Stupa. It is important to note for our study that the place where God resides, Heaven, is geometrically symbolized by the circle. If one takes a length of string and makes it a triangle, a square, a rectangle, or any other sort of a polygon, the amount of space that string creates will always be smaller than if one makes it a circle. The circle encapsulates the most amount of space with the least amount of effort. Bringing the circle out into three dimensions to make it a sphere will encapsulate the most volume. This geometric fact is one of high symbolic value. The circle is expressing something about the nature of its own being. It is speaking to you. It is representing, within its own essence and qualities, the limit or sphere or creation. [. . .]
The circle also leads us to the first number in existence, zero. If we were to attribute zero to a geometric form, the most obvious form we could equate it to would be the circle. The number (or non-number) zero expresses the concept of nothing. [. . .] The circle, by encapsulating the most space, yet simultaneously being a representation of the zero, or NO THING, condenses all time and all space into one geometric form. Put simply, the circle represents the concept of all or nothing. As far out into the abyss we wish to go, and as close to nothingness as we may conceive, the circle represents both. 125 - 127.
Pi connects the finite to the infinite, in that it relates a finite linear diameter (or radius, which is half the diameter and which is the distance between the points of a compass used to sweep out a circle, the compass thus being symbolic of the circle which it creates when it is used) to the shape that represents the infinite and the ineffable.

The architects of the Great Pyramid incorporated pi into the very structure of that massive monument, which has a perimeter around the base that is 2π times the height of the pyramid.

Similarly, the monument we know today as the Pyramid of the Sun at Teotihuacan in modern-day Mexico has a base perimeter which is 4π times the height of the pyramid.

These structures can thus be understood to symbolically unite heaven (the circle) with the earth (the square) and to act as symbolic link between the finite and the infinite, between the material realm and the realm of spirit.

In the second passage above from The Peacock Tales, Marty Leeds also mentions the Square and Compasses of Freemasonry, which can be seen to point to the same connection between heaven and earth, material and spiritual, finite and infinite. The right-angle square tool clearly evokes the square, while the compass device evokes the circle: Heaven and Earth.

Interestingly enough, there is an important part of the heavenly sphere which contains two constellations that can be seen as evoking the very same profound concept of connection between heaven and earth, the infinite and the finite. These two constellations are the Great Square of Pegasus and the constellation known as the Triangulum, or Triangle, which is located close by. 

The Great Square, of course, evokes the square which represents bounded, limited, physical space: the earth (which goes around the sun in an annual circuit that is bounded by the "four pillars" or the "four corners" denoted by the two solstices and the two equinoxes). 

The Triangle evokes the instrument of the compass which is used to sweep out a circle. Hence, the two constellations, providentially located in the sky so close together, evoke the connection between Heaven and Earth, spiritual and material, infinite and finite.

The Triangle is actually also located very near to the critically-important constellation of Aries the Ram, whose brightest stars are also three in number (and which in fact are not quite so bright as those of the Triangle, making the Triangle a very useful tool for locating Aries, as discussed in this previous post).

Below is a screen-shot of the sky showing the position of the Great Square (outlined in green) and the Triangulum (outlined in red), both of which are outlined along with Aries (also outlined in red, only the brightest three stars being connected in this illustration).

As you can see from the above diagram, which I created using the outstanding open-source planetarium app Stellarium (available at, on this particularly significant "pi day," the earth is located on the opposite side of the sun from the portion of infinite space containing the stars which make up the constellations of the Great Square and of the Triangulum. 

This means that in order to "look towards" the Square and the Triangulum on this 3/14/15 day, one must look towards the sun itself. You won't be able to see these constellations in the night sky on this day, because when we are on the "night side" of the earth (the side turned away from the sun) we will be facing an entirely different sector of the heavens.

This seems somehow appropriate and even significant, since the calendar day itself that we designate as 3/14/15 is a date on the solar calendar (and the year AD 2015 itself is a year which commemorates the year of the Lord, the Christ, who can be shown to have strong connections to our sun, the enabler of all life on earth and the single most-essential intermediary through which or through whom we relate to the heavens beyond).

Ultimately, one of the most important messages of this mysterious and transcendental number pi is what it tells us about ourselves: that we ourselves, like pi, at once touch both the finite and the infinite, occupy the interstices of Heaven and Earth, matter and spirit. 

Pi day can help remind us of this truth -- a truth which the exigencies of the physical world often work to obscure. 

It is a perfect day to pause and meditate further on these truths.

And, once we become aware of it, pi can continue to remind us of these concepts more than just once a year -- whenever we encounter a circle in the form of a sacred drum, for example, or consider the infinite vastness of the night sky that opens up within the circle of the horizon.

Happy Pi Day!

For those interested in previous posts which touch on the concept of pi, see also:

Also, in light of the photo above, it is interesting to note that the Chinese character for "knife" is: