Brahman and the Fractal nature of the Universe due to the chaotic
nature of
String Theory: a comparison of Hinduism to Western Science.
by Aaron Smith, aka Yavin Koenigsberg

Original essay available with graphics @
http://members.xoom.com/yavin78/hindu1.html

Over the past couple of decades, there have been several attempts at
comparing
Hindu philosophy and science to Western Science. Some of these attempts
to
compare the two schools of thought have been valid, but unfortunately
there have
also been an overabundance of comparisons which simply did not go into
enough
detail to have any real scientific value. Some attempts at comparison
turned out
to be the attempts by Hindu traditionalists to trump up the so called
ancient
Vedic sciences. In his book, More Light on Less Known, Acharya
Ratnananda tries,
with little success, to show how the majority of Western Science is
little more
than a bad copy of the technologies found within the Vedas. While his
reports of
large 'solar-powered chariots' make good fiction, they do not however
provide any
sound comparison between hard science and Hinduism. Another recent
comparison was
the Tao of Physics, by Fritjof Capra. While his book does go into many
of the
poetical similarities between theoretical physics and the various
mystic
traditions of East Asia, he does not go into sufficient detail for it
to have
true scientific value. Weak as these attempts may have been, they still
managed
to raise the topic to the limelight in the mainstream of science.

The real question which is the root cause for all of this discussion,
is why and
how are these two vastly different subjects interrelated? Any deep,
scientific
analysis of Hinduism and Physics should be done by experts within their
respective fields working together. Admittedly, I am not an expert in
either
field, therefore I will limit my comparison in both depth and scope. I
will try
to point out how, when one compares the Hindu notion of Brahman with
the specific
branch of Theoretical Astrophysics known as String Theory, that gross
similarities appear between these two ideas due to the poetical,
structural, and
mystical nature of these two vastly different subjects.

In order to compare Brahman with String Theory, one needs to aptly
define both
ideas. Due to the intensively mathematical nature of String Theory, I
will only
briefly explain what it is in order to show its relevance to the
comparison.
String Theory is an attempt by Physicists to find a unified description
of all
forces in the Universe (Lederman 393). This is a baffling task at best,
and many
scientist are not satisfied with String Theory's explanation of the
universe due
to its unimaginable complexity. Leon Lederman, the renown director of
the Fermi
National Accelerator Laboratory, called String Theory "a structure that
pushes
the frontiers of mathematics and conceptual limitations of the human
imagination
to the extremes" (Lederman 393). In String Theory, the basic units in
the
universe are not particles (such as neutrons, protons, quarks, and
other sub-
atomic particles) which occupy a single point of space, but things that
have a
length but no other dimension, like an infinitely thin piece of string
(Hawking
159). These `Superstrings', as they are often called, may have ends or
they may
be joined up with themselves in closed loops (159). In String Theory
all the
particles which we have so far discovered emerge as vibrations of these
Superstrings (Lederman 394). In Newtonian physics, a string (such as
one on a
violin) has an infinite number of vibration modes (Kaku 153). Thus in
String
Theory, matter becomes nothing more than the harmonies created by these
vibrating
Superstrings (153). Since there are an infinite number of harmonies
that can be
composed for a string instrument, there are an infinite number of forms
of matter
that can be constructed out of the vibrating Superstrings (153). This
explains
the richness of the particles in nature (153). Out of this cosmic
orchestra all
of the matter, energy, space, and time emerges and becomes all of the
things that
we see around us. Now let us look at the Hindu corollary to this
theory. In an
interview with Swami Muktananda, he gives an interesting interpretation
of the
Upanishads. He comments, that "according to the
Upanishads,...everything has come
from the same source, called pure Being. From pure Being emerges pure
space. When
pure space begins to vibrate, air, the next element, comes into being.
From the
friction of air comes fire, and fire then products water in the same
way that we
begin to sweat when it is hot. And when the sediment from water settles
the
element of earth arises" (Muktananda 127). Here Muktananda points out
two
similarities to String Theory, one: the vibrations of space give way to
the
`elements'. Two: the elements that he mentions, curiously enough, match
the four
different states of matter, which are plasma, gas, liquid, and solid.
Although
his explanation is poetical, it still manages to convey the same
meaning if taken
loosely. According to the Upanishads, "this whole world, verily, is
just food and
the eater of food," (Hinduism 91 the Upanishads Brhad-Aranyaka 1.4,
1-8). Here we
see an example of Newtonian physics. The `food' can be thought of as
energy, and
in physics all action requires energy, therefore this statement holds
valid.
Muktananda later states in the interview that "consciousness has become
matter
and matter is only consciousness, and there was a time when the two
were one,"
(Baba 123). If one considers consciousness to be a form or collection
of energy,
then Einstein's famous formulae E=MC^2 would likewise prove the
validity of the
first half of this statement. In order to test the second half of this
statement,
let us examine the creation of the universe, for we shall see that
there was a
time when matter and energy were in fact one. Physicists believe that
the
universe began with the Big Bang, a time when matter and energy were in
fact one
(Kaku 27). According to String Theory, before the Big Bang, our cosmos
was
actually "a perfect ten-dimensional universe...this ten dimensional
world was
unstable, and eventually it `cracked' in two, creating two separate
universes,"
one four dimensional universe one and a six dimensional one (27). We
inhabit the
four dimensional universe. The four dimensions are three spatial
dimensions and
one dimension in time. In the Hindu Song of Creation from the RgVeda
there is an
interesting poem which describes this state before the Big Bang.

Then was not non-existent nor existent: there was no realm of air, no
sky beyond
it...Darkness there was: at first concealed in darkness, this all was
indiscriminated chaos. All that existed then was void and formless: by
the great
power of warmth was born that unit (RgVeda 10.129).

After the Big Bang, the four dimensional universe expanded explosively,
whereas
the six dimensional one contracted violently in a Big Crunch until it
was almost
infinitesimal in size (Kaku 27). The Big Bang therefore, is only a
minor
`aftershock' of the separation of the two universes (27). In the
Manu-Smrti,
there is an account of the creation of the universe from a `world egg'
which
spits in two causing the creation of the heavens and the Earth (Renou
123). Thus,
even the Manu-Smrti account of the creation of the world is similar to
the
splitting of the original ten-dimensional universe into two separate
universes.
During the Churning of the Ocean by the Hindu Gods, the deity Vishnu
appears in
numerous incarnations at the same time and plays different roles as the
universal
struggle between positive and negative is being played out (Hinduism
169).
Throughout Hinduism, the appearance of numerous divine incarnations, or
avataras,
is a commonplace occurrence. Does String Theory likewise allow for
numerous
manifestations of a form at the same time, as in Hinduism? In order to
find the
answer to this, we must examine how String Theory causes the universe
to act as
one giant Fractal.

One of the ramifications of String Theory is that it dictates that the
entire
universe is an inconceivably large Fractal (Gleick 314). As we shall
see, this
`Fractal universe' is amazingly similar to the Hindu notion of Brahman.
In order
to compare aspects of Hinduism to the Fractal nature of the universe, a
definition of Fractals must be given. A Fractal is a mathematical
system that
appears to be chaotic and random, yet in reality contains a fundamental
order
(223). Within this order, the Fractal `pattern' often emerges on
various levels
in similar forms, yet never as the same exact form. Weather, economics,
ecology,
even aspects of the human body have a Fractal nature. The most famous
of all
Fractals is the Mandelbrot set. The Mandelbrot set is an amazingly
complex
collection of points which are calculated from what is called a
recursive
statement in mathematics. (Gleick 223). Within the set, there is a
chaotic
pattern which emerges from time to time when one magnifies the set. One
could
magnify the set to infinity, and one would still find repeating
structures of the
original, but yet never find the end of all the subsets of points
within the set
(224). Every collection of points within the Mandelbrot set are
connected to each
other in a web that binds all of the parts together, yet this web is
only visible
after extreme magnification (Gleick 228). If the universe itself is a
Fractal
such as this, then a number of interesting similarities begin to
develop. Now
that we have defined Fractals and shown an example, let us give a
definition of
Brahman. In the Chandogya Upanisad, it is said that, "Verily, this
whole world is
Brahman. Tranquil, let one worship it as from which he came forth, as
that into
which he will be dissolved, as that in which he breathes," (Renau 97).
So Brahman
is not only the entire universe, but every object within the universe
is likewise
part of Brahman. Just like in a Fractal, all parts are interconnected,
and
interdependent. Brahman too, is just as varied and complex as a
Fractal. For
instance, in the Bhagavad-Gita, when Sri Krishna reveals his true
Brahmanic form
to Arjuna, he cries out, "Behold...my divine forms, hundreds upon
thousands,
various in kind, various in color and in shape," (91). One could
likewise use
this quote to aptly describe the Mandelbrot set if one applies enough
poetic
imagination. In comparison to the Fractal universe, let us look at more
of Sri
Krishna's words to Arjuna, "this very day you shall behold the whole
universe
with all things animate and inert made out within this body of mine,"
(Bhagavad-
Gita 91). James Gleick, author of the book Chaos, describes the
Mandelbrot set in
equally poetic words when he says, "The Mandelbrot set is the most
complex object
in mathematics. An eternity would not be enough time to see it all, its
disks
studded with prickly thorns, its spirals and filaments curling outward
and
around, bearing bulbous molecules that hang, infinitely variegated like
grapes on
God's personal vinyard," (221). Just as all things in this universe are
Brahman,
all things in this universe have a Fractal nature. When one magnifies a
Fractal,
one sees a smaller version of the set within the main set. Likewise,
even in our
universe, there must be smaller representations of the `main set'.
Nature, for
instance, may be provide a clue to this. Michael Barnsley contended
that nature
must be playing its own version of the chaos game when he observed
that, "there's
only so much information in the spore that encodes one fern. So there's
a limit
to the elaborateness with which a fern could grow," (Gleick 239). So
perhaps each
organism's DNA is like a `subset' of the larger Fractal. And what is
this grand
Fractal? Verily, it must be Brahman. Swami Ram Tirth, who was a
distinguished
professor of mathematics before he renounced the world and became a
sannyasi,
wrote the following poem:

The wind that blows is in me, in me, in me. That water that flows is in
me, in
me, in me. The sun that rises is in me, in me, in me.

Swami Muktananda likewise comments that "the human body is a microcosm;
the
universe is the macrocosm. Whatever you find in the universe, you will
also find
the body," (Muktananda 127). If the universe is a Fractal, then both of
these
poetic descriptions of the world around them hold valid, for all the
information
that is contained in the universe would, due to its Fractal nature, be
contained
within you. Possibly the most poetic descriptions of the universal
Brahman are
given in the Bhagavad-Gita. Sanjaya in the Bhagavad-Gita tries to give
a
description of the magnificence of Arjuna's vision of Brahman when he
said, "Suppose a thousand suns should rise together into the sky: such
is the
glory of the shape of Infinite God. Then the son of Pandu beheld the
entire
universe in all its multitudinous diversity, lodged as one being within
the body
of the God of gods," (Bhagavad-Gita 92). Arjuna, after seeing Sri
Krishna's true
form, beheld, "Universal Form, I see you without limit...and find no
end, midst,
or beginning. Licking with your burning tongues devouring all the
worlds, you
probe the heights of heaven with intolerable beams, o
Vishnu,"Bhagavad-Gita 92).
Yet out of all of the descriptions, Lord Krishna describes himself best
as the
Fractal heart of the universe best when he says:

I am the Atman that dwells in the heart of every mortal creature: I am
the
beginning, the life-span, and the end of all...I am
Vishnu...Marichi...the Sama
Veda...Indra...Shiva...Mt Meru...I am the ocean among the waters...I am
the
sacred syllable OM...I am Time...I am Krishna among the Vrishnis,
Arjuna among
the Pandavas...I am the divine Seed of all lives. In this world,
nothing animate
or inanimate exists without me...There is no limit to my divine
manifestations,
nor can they be numbered...one atom of myself sustains the universe.
(Bhagavad-
Gita 88-90).

Here, in this short excerpt from the Bhagavad-Gita, we see the closest
similarities between the Fractal nature of the universe due to String
Theory most
aptly described in a simple Hindu parable. Yet even these vivid
descriptions of
the universe are not Hinduism's strongest link to String Theory.

Possibly the strangest link between Hinduism and String Theory is the
mathematician who gave us this wonderful theory of everything.
Curiously enough,
String Theory is based off of a set of mathematical functions which
were written
down at the turn of the century by a young Hindu mathematician named
Srinivasa
Ramanujan. Ramanujan was born in 1887 in Erode, India which is near
Madras. He
was born into the Brahmin caste, and probably had read the traditional
Hindu
cannon (Kaku 174). As a youth, he vigorously studied mathematics, where
he began
to excel like no other human being has ever done before. His genius is
only
hinted at when Michio Kaku stated that, "Working in total isolation
from the main
currents of his field, he was able to rederive one hundred years' worth
of
western mathematics on his own" (Kaku 172-73). As a youth he spent all
of his
time thinking about mathematics. His devotion to it was so intense that
he failed
out of his senior year of high school and ended up working in a
low-level
clerical job in Madras. There, he spent all of his spare time working
on
mathematics. Eventually, he sent the results of his work to three
well-known
British mathematicians of the time. Two of them ignored the letters out
of racist
ignorance, but the third, Godfrey H. Hardy realized the genius, and had
him sent
for. After much difficulty, Ramanujan arrived at Cambridge in 1914
where he spent
the next three years working on mathematics in collaboration with Hardy
at
Trinity College in Cambridge. Tragically, Ramanujan died at the mere
age of
thirty-three years old due to Tuberculosis. Yet, in those last three
years of his
life he filled up a volume of notebooks with what are called Modular
Functions, "which are among the strangest ever found in Mathematics"
according to
Michio Kaku (173). In total, he wrote 4,000 formulae on 400 pages
filling 3
volumes of notes, all densely packed with theorems of incredible power,
but
without any commentary on how he derived them, nor proof of their
validity (Kaku
176). Since his death, countless mathematicians have worked on proving
them with
only limited success due to the intricacy of the mathematics involved.
Gofrey
Hardy later recalled after Ramanujan's death that proving some of these
theorems "defeated me completely" (175). He recalled, "I had never seen
anything
in the least like them before. A single look at them is enough to show
that they
could of only be written down by a mathematician of the highest class,"
(175).
Years were spent proving his formulas, but then an amazing breakthrough
occurred.
In 1976, 130 pages of Ramanujan's notes, containing the output of the
last year
of his life, were discovered by accident in a box at Trinity College
(Kaku 176).
Among these notes there is what is called the "Ramanujan Function"
which is the
fundamental backbone of String Theory itself (Kaku 173). This function
has alowed
Physicists to attempt to explain the fundamental workings of the
universe, but
unfortunately the function is still not completely understood (Kaku
173). The
other mathematicians with whom Ramanujan worked often asked how he was
able to
come up with these formulae. It was said that, "Ramanujan used to say
that the
goddess of Namakkal inspired him with the formulae in dreams" (Kaku
174). So
perhaps Ramanujan's upbringing as a Brahmin, and his belief that this
goddess was
inspiring him like a modern day Rsi helped shape String Theory into a
form which
so resembles Hindu philosophy.

In conclusion, perhaps Ramanujan was a sort of modern day Rsi. If so,
then his
understanding of mathematics was directly brought about by his mystical
perception of the universe. Perhaps he was like the many other modern
day Siddhas
who claim that, in the words of Swami Muktananda, "it is quite possible
to see
the different worlds of the cosmos...it is possible to see them
distinctly
through the grace of the inner energy...inside, all the different
worlds are
very, very close once you gain access to the inner space," (Muktananda
119). This
seems quite likely in Ramanujan's case. For Ramanujan's String Theory
and
Hinduism share far too many parallels for the reader not to take
notice. I admit,
that I have not gone into as much detail on this subject that is needed
for the
final evaluation of the correlation. Others will, without a doubt, make
more
detailed comparisons between the two ideas. Perhaps science and
mysticism have an
inseperatable link which we have failed to acknowledge. Perhaps
sometime in the
near future scientific knowledge of the universe will show a clear
picture for
humankind to behold, or perhaps the Rsis of ancient India have already
beheld the
universe. In either case, I think that Muktananda says it best when he
said
that, "the fact is that scientific knowledge and spiritual knowledge
are already
married" (119). How true this statement seems when one looks at String
Theory.

Bibliography

Gleick, James. Chaos. New York: Viking, 1987.

Hawking, Stephen W. A Brief History of Time. New York: Bantam, 1988.

Kaku, Michio. Hyperspace. New York: Oxford UP, 1994.

Lederman, Leon, and Dick Teresi. The God Particle. New York: Bantam,
1993.

Muktananda, Swami Baba, and Harold S. Streitfeld. In The Company of A
Siddha.
Oakland: S.Y.D.A. Foundation, 1978.

Hinduism. Luis Renou, Ed. New York: George Braziller, 1961. "Rg-Veda."
(10.129)
Renou 67. "Upanishads." (Brhad-Aranyaka, 1.4, 1-8), (Chandoya, 3.14),
(Kena, 3.1-
12, 4.1-5) Renou 91-99. "Manu-Smrti." Renou 123. "Puranas." Renou 169.

The Song of God: Bhagavad-Gita. Christopher Isherwood, and Swami
Prabhavananda,
trans. New York: Penguin Books, 1972.

"What is the Mandelbrot set?" fabioc@geocities.com, ed. 1998. Available
http://www.geocities.com/CapeCanaveral/2854/

http://everything2.com/?node_id=662887

Excellent analysis.

Hinduism is not synonymous with Vedic philosophy or with the Upanishads. Hinduism represents an agglomeration and integration of many different traditions and perspectives, with the Vedic philosophy and Upanishads forming just a part of what may be legitimately termed Hinduism. Setting that aside for a moment, I think the relation between String Theory and Vedanta and the Upanishads is rather superficial and to be expected, and here's why: The Upanishads presents us with a monistic worldview; the All is derived from the One. String Theory, in attempting to be a unified theory of physics, must start from the same premise that the Many is derived from the One, but it must also be mathematically rigorous and remain attached to observation. The Upanishads, of course, are not mathematically rigorous. The observation that the Upanishads say that All is derived from vibrations of the One and that frequency of vibration is important, while it's very tempting to compare this with String Theory's claim that all particles in Nature are produced by vibrations on strings, the Upanishadic observation lacks the mathematical precision that String Theory has, and so we may legimately question whether the Vedic sages had the same thing in mind as modern day string theoreticians. I don't think they did. Maybe qualitatively at some coarse level, but I think that there is a fundamental difference between the conceptions of the Vedic sages and modern-day string theoreticians. The former are nothing like sages in the Vedic tradition, so why would you expect them to mean the same thing when they talk about vibrating strings? And even if they were talking about something like the same thing, they certainly had very different conceptions of it. The point I'm trying to make is that I don't think you can legimately compare conceptions between Vedic sages that lived millenia ago and modern-day string theorists. I think the similarities between ideas is superficial at best, and that each group had something different in mind when they were talking about frequencies giving rise to the things we see. If you were somehow lucky enough to place a Vedic sage from 1000 B.C. in the same room with a modern-day string theoretician, I really do not think that they would understand each other. Note that modern-day indian sages are not the same as the Vedic sages from 1000 B.C. They can only be imitators, or forgers of new paths.

and that reminds me. We should have a thread describing String Theory more.

it's hard to imagine what the Vedic sages would have thought of mathematics

I find the author admits to short-comings in understanding (which is refreshing in itself). I think he could have gone further by pointing out that the Mayans developed (and probably shred with India through Barabudur) the mathematical concept of zero that we still use today and Europeans often credit to India.

I could add many other things he could ahve dealt with but his references and quotes are from the best people available who I also quote. I found it fits with my present book and I included it in toto.

Clearly one is limited in how much space to give to any one aspect of any scientific understanding of the spiritual world we live in.

The sages before the Vedic and in Ilavarta were most likely more mathematically aware of Harmonics and able to utilize it in anti-gravity and other ways lost to us and only now being studied by the likes of String Theory.

D'accord


Science is reductionist whereas mysticism is broadly integrative. It would seem that science and mysticism occupy anti-podal positions. They are both concerned with truth, yet go about it differently. Science seeks to objectively and mathematically describe truth, whereas mysticism seeks to experience truth. Science and mysticism are flip sides of the same coin. The greatest scientists have invariantly been deeply mystical. I'm tempted to say that the greatest mystics have invariantly been deeply scientific, or at least had an appreciation for science, but this I'm less certain of. (Though I am certain you are right about the great scientists being spiritual.)