# Interpretation of the Universe through Numbers

The laws of nature are but the mathematical thoughts of God.—Euclid

Geometry or algebra, shapes or numbers, axioms or numeric calculations? Which one is more applicable to the possible interpretation of the universe? After all, can we really use numbers and/or geometry to decipher the mysterious patterns behind the universe? Before I proceed further, allow me to introduce the following concepts:

- Mathematics is the language of nature.
- Everything around us can be represented and understood through numbers.
- If you graph the numbers of any system, patterns emerge. Therefore, there are patterns everywhere in nature. Evidence: sun spot cycles, the wax and wane of caribou populations, the cycling of disease epidemics, and the rise and fall of the Nile.

These are the concepts uttered by Max Cohen, the protagonist of the
movie Pi (π). Directed by Darren Aronofsky, Pi tells a story of a genius
mathematician who set out on a quest to find patterns in the number π.
These patterns, as Max believes, would help us answer questions about
the creation of the universe, as well as the symbolic meanings of
various patterns in nature. Due to this quest, Max has completely
isolated himself from the rest of his community, his family and
neighbors. The only people he has any contact with are his
ex-professor—the fatherly figure for Max—with whom Max shares everything
about his research; then there is Max’s neighbor, who genuinely cares
about his well-being, partly because she is attracted to him, partly due
to her concern for Max’s strange and paranoid behavior; and finally, we have a little
girl (another one of Max’s neighbors) who, aware of Max’s expertise in
mathematics, enjoys in testing his intelligence by asking him to solve
very complex algebraic assignments: things such as 322x491, or 73/22.
Max, of course, always manages to impress the girl, but also the movie
audience, by solving these tasks—in the span of a few seconds
only—without the use of a calculator. Max’s obsessive quest for patterns
in π does not go as smoothly as he had initially expected. Namely, he is being chased
by two different groups of people, who wish to intercept his research
and convince him to disclose the results. On the one hand, we have a
group of highly influential bankers who are convinced that Max’s results
could provide them with a *miracle pattern* for the stock market. This way, they would be
able to control and manipulate the rise and fall of stocks on a
global level. On the other hand, we are presented with the members of a
Jewish, Kabbalistic order, who believe that Max’s research is the key to
solving patterns in the Torah and the True Name of God (216 letters
long, as we are told by one of the members of the order). While Max
refuses to help the bankers in their goal to further generate capitalism
and the crash of the stock market, he does become interested in helping
out the Jewish order, mainly because he becomes very intrigued by the
relationship of numbers and letters in the Torah. Towards the end
of the movie, Max comes to a realization that the road to God is to be
achieved not through a specific pattern of 216 numbers, but through the
conception of beauty and simplicity of our existence in the world, i.e.
through a simultaneous acceptance of all the knowledge and lack of
knowledge of that which resides in the terrestrial and celestial
spheres. As Max says to the Jewish rabbi in the movie: “It’s just a
number. The number is nothing. It’s the meaning, the syntax: it’s what’s
between the numbers. You haven’t understood.”

In Ancient Greece, Pythagoras and his followers held a belief that
the universe itself is a harmonious and ordered entity meant to be
interpreted and understood through numbers and numerical patterns. The
general belief was that literally everything, from the structure of
humans, animals and plants, to the movement of the planets and the
emergence of various natural occurrences, can be expressed through
numbers. Interestingly, the Pythagoreans would also use mathematical
relations to analyze and explain musical relations and harmonics. As
suggested by Sextus Empiricus in his *Adversus Mathematicos*, Book VII,
known also as *Against the Logicians*, Pythagoras and his
followers placed great importance on the *tetraktys* (any coordinated
set of four items) and the number 10: “…by *tetraktys* they mean a
number which, being constituted out of the first four numbers, fits
together the most perfect number, as for instance ten: for one and two
and three and four becomes ten. This number is the first *tetraktys*,
and is described as the *fount of ever-flowing nature*” (Sextus
Empiricus, Book VII, p. 94). In *Metaphysics*, Aristotle reaffirms the
importance of the number ten for the Pythagoreans and Greek mathematics.
As he writes: “…since the number 10 seems to be perfect and to embrace
the whole nature of the numbers, they say that the things that travel
through the heaven are ten; but since those that are visible are only
nine, they therefore make a tenth, the ‘counter-earth’…” (Aristotle).

Number ten plays a great importance in many cultural and religious
traditions worldwide. The Bible, for instance, speaks of the ten
plagues of Egypt, the ten commandments given to Moses, the ten
generations of antediluvian age, the ten trials of Abraham’s faith, and
many other instances. In Hinduism, the number of Vishnu’s incarnations
or avatars is ten, but 10 is also the number that symbolizes the unity
of Brahma and Atman, i.e. the coming together of both the immortal and
mortal, or the celestial and terrestrial aspects in the world. It is
also worth noting that the number of *sephirot*, one of the most
relevant concepts in the Kabbalah, is ten. As Kabbalistic teachings
suggest, the Sephirot are the emanations or manifestations through which
God reveals himself, all of them symbolizing a different spiritual
quality or aspect. In addition to the frequency and importance of the
number 10 in different religions, we could say that its presence on a
global level is quite overwhelming. Is it not interesting that 10 is the
primary number used for marking the passage of time? All of the major
periods we use to track time start with the number 10: decade (10),
century (100), millennium (1000). We should also consider the binary
numbers (numbers made up of only 0s and 1s) which, understandably so,
contain the number 10 in itself! Or the simple fact that humans tend to
count, regularly, on their ten fingers!

Going back to the number π, it is fascinating to what extent this number
appears in the natural world. Scientists and mathematicians have shown
that π, which, by the way, is an irrational number (since it goes on
infinitely, and we can never predict the digit that comes next in the
succession of an endless stream of numbers), is everywhere around us:
first and foremost, in circles which are the natural occurrence in
nature (e.g. the pupil of the eye, the disk of the Sun and the planets
in the solar system, the rain drops, the snail’s shell, flowers,
whirlpools, etc); but, it also “emerges in the shapes of rivers… Rivers
that flow straight from source to mouth have small meandering ratios,
while ones that lollygag along the way have high ones. Turns out, the
average meandering ratio of rivers approaches is *equal to the number
π*” (Livescience: What Makes Pi So
Special?).
For more than 3000 years, π has puzzled numerous generations of
mathematicians, who admired the subtle mystery of its patterns. Unlike
most modern sciences, which place their focus mainly on quantity,
constant change and insistent progress, the mathematicians of ancient
Greece saw mathematics and all other exact sciences in a metaphysical
way. For Pythagoras and Euclid, for instance, mathematics was a means to
understanding the microcosmos of soul and intellect, but it also served
as a method to explain the position of humans in relation to God and His
creations; in other words, it paved the way for the attainment of sacred
knowledge.

One of the major mistakes of modern science was the
separation of mathematics and physics from philosophy and psychology
(psychology, for example, was never treated as a separate discipline,
let alone science, until the emergence of the Scientific Revolution in
the 17th century). Famous Greek, Roman, Byzantine, and Islamic scholars
all treated mathematics and psychology as a part of philosophy, and
philosophy itself as integral to mathematics and physics. As expounded
by René Guénon (French mathematician and philosopher) in *The Crisis of
the Modern World*, “psychology as it is understood today—that is, the
study of mental phenomena as such—is a natural product of Anglo-Saxon
empiricism and of the eighteenth century mentality, and that the point
of view to which it corresponds was so negligible for the ancient world
that, even if it was sometimes taken incidentally into consideration, no
one would have dreamed of making a special science of it, since anything
of value that it might contain was transformed and assimilated in higher
points of view. In quite a different field, one could show also that
modern mathematics represents no more than the outer crust or ‘exoteric’
side of Pythagorean mathematics; the ancient idea of numbers has indeed
become quite unintelligible to the moderns, because, here too, the
higher portion of the science, which gave it its traditional character
and therewith a truly intellectual value, has completely disappeared—a
case that is very similar to that of astrology” (p. 50).

When we speak of mathematics as the only viable language of nature, the
following questions arise: What kind of mathematics? Are nature and its
phenomena meant to be interpreted through algebra (numbers), or through
geometry (various geometric shapes), or perhaps through a combination of
both? While watching the movie Pi, I couldn’t help but wonder whether
Max Cohen’s reason for his failure in finding the patterns in π was due
to his excessive reliance on numbers. What if the universe and our
relationship to it is to be interpreted through geometry, not numbers?
Max, however, does not undermine the importance of geometry, despite his
seeming obsession with numbers and numerical patterns in π. He even
names his computer Euclid (author of *The Elements of Geometry*, known
as the father of geometry and geometric algebra), and relates to the
ever-fascinating Pythagoras’ pentagram and the golden rectangle, which
result in the Golden Ratio. In his famous painting “The Vitruvian Man”,
Leonardo Da Vinci used Pythagoras’ golden rectangle and the pentagram to
illustrate the perfect human body. Likewise, Salvador Dali, in his
painting “The Sacrament of the Last Supper”, used the golden rectangle,
as exhibited in the dimensions of the canvas. When we connect a curve
through the concentric golden rectangles (both the small and large
rectangles), we get a golden spiral, or the Golden Ratio. This same
spiral appears everywhere in nature! Pythagoras noted that the Golden
Ratio or the mythical shape of a spiral is always present in the flower
heads, the Milky Way and many other galaxies, the snail or nautilus
shells, tornadoes and whirlpools, ram’s horns, even our fingerprints! To
get a better understanding of what Pythagoras meant by this, take a look
at the images below:

The golden spiral inside the golden rectangle: As shown on the image, the value Phi or the Golden Ratio is 1.61803…

The nautilus shell displaying the presence of the golden spiral in nature.

As fascinating and mind-boggling as this is, I also find it fascinating how proportional and harmonious objects and the living things in the natural world tend to be. By now, many of you have probably noticed the seemingly perfect and equal shapes of snowflakes, or the equal shape and size of flower petals, but also the intricately shaped parts on a pine cone and a cauliflower, or the proportional lines on a leaf. Also, have you ever paid attention to all of the details and different patterns/motifs on a bird? Take eagles, doves, or blue jays, for example: one can notice all sorts of shapes on their backs and wings, all equal in size. These shapes range from triangles, circles and ellipses, to oval and conical shapes. Note that when birds fly together, they very often form a flock that resembles a triangle. Speaking of other animals, it is very common for all domestic cats to have a pointy pattern shaped like a semi-triangle, each right above their eyes (both patterns are equal in size) and between the sides of the upper part of the nose. These patterns cannot be so easily discerned in purely white or black cats, though. These are just some of the examples that point to the constant presence of geometry, and mathematics in general, in our everyday lives and surroundings. Why do we come across all these fascinating instances of perfect geometric shapes in nature? What is the purpose that these shapes exhibit in the natural world: what are they supposed to remind us of? In line with the teachings of Euclid and other Greek mathematicians, I choose to believe that all of the geometric shapes and numerical patterns in nature are here to remind us of the harmony and order on a macrocosmic level. More importantly, diverse geometric shapes and patterns in nature also exemplify the perfection and unity of divine creations, as opposed to the human attempts to mimic that perfection and soar beyond the beauty and harmony of the natural world. Therefore, everything around us is not necessarily represented and understood through quantity and numbers, as Max Cohen would believe; rather, everything around us can be represented and understood through geometry. Perhaps geometry and its patterns, not numbers, are the true language of nature. In any case, the possibilities are infinite!