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/

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