“There is no finer sight than that of the intelligence at grips with a reality that transcends it.”

Albert Camus (The Myth of Sisyphus)



“One cannot help but be in awe when one contemplates the mysteries of eternity, of life, of the marvelous structure of reality.”

Albert Einstein [1]



Before the new world was discovered, a famous legend, first put to pen by Plato, foretold of a magnificent realm whose shores hid in the great void that stretched beyond the Pillars of Hercules (the Strait of Gibraltar). This mysterious Atlantic shire stood as a symbol of harmony. It was described as a place full of transcendent treasures where human potential could expand beyond traditional limits. The gateway to this clandestine land was said to be a port so rich in symmetry that all of its elaborate details came together to form an aesthetic marvel with an unmistakable sense of artistic magic.

The mere possibility that such a golden city existed was enchanting, yet there was something more to this legend, something stirring and profound that resonated every time it was told. The very idea that out there, beyond the mists, an entire continent was still waiting to be discovered was bone chilling. If it were true, it would mean that despite all the knowledge humanity had amassed, there was much more to learn. It would mean that every previous rendition of the world that we had so faithfully relied upon was wildly incomplete; that there was far more to the world than anyone had previously imagined. In the end, it would require mankind to completely rewrite its most trusted maps.

This legend offered a possibility that intrepid explorers could not ignore – the chance to participate in the highest quest. It amplified the dream of connecting to certain and universal truths by offering humanity a way to touch the underlying mystery and to actively extend their perceptions beyond the horizon. To those that would sail off into the glimmering mirages that capture the evening sun, this whisper of hope became the Sirens’ greatest song. Over time, the lure and passionate curiosity characterized by this legend entered the common tongue and became known as the call of Atlantis. Answering this call was to embrace the cherished heart of Plato’s legend. Those who did came to believe that by ascending through the stages of rationality the attainment of enlightenment becomes a real possibility; that ultimately we can escape the cave of ignorance and learn to grasp what lies beyond the shadows.

For the most part, the legend of Atlantis was considered a heretical myth. The very notion that the world contained entire continents yet to be discovered was considered laughable and blasphemous. European maps of the world clearly showed three continents — no more. Faith in the accuracy of these maps had won wars and guided men home from far away places. Consequently, the rulers of every land kept their personal maps under lock and key and considered them their most prized possessions. These maps gave them perspective, framed their world, and defined their place in it. Any claim that their maps were wrong was an attack on their entire model of reality. But the legend of Atlantis lived on.

The boldest pages of our past are colored by the achievements and discoveries of gallant individuals that havedirectly participated in theunwraveling of our world’s mysteries. By challenging convention and following their intuitions toward a richer, more complete map, they bring us new insight. Of the historical figures that have shared in this experience I will mention two that appropriately set the stage for the work herein. These particular explorers have made a poignant impact on the maps that frame our modern worldview. Their insights have led to many of the unexpected discoveries that ultimately motivate the higher-dimensional map we will be introducing and exploring in this book.

The first of these individuals may have secretly believed that the tale of Atlantis was more than just a myth. He may have harbored the intuition that beyond the horizon there was more to be found than his maps resolved; that somewhere in that rhythmic oceanic trance Plato’s city of gold was shimmering in the sunlight. Seven years after Marsilio Ficino translated Plato’s legend of Atlantis into Latin the Queen of Spain agreed to finance his expedition. [2] The recorded goal of that expedition was to find a shorter trade route to the rich continent of Cathay (modern China), India, and the fabled gold and Spice Islands of the East. The man who proposed this expedition and then sailed out into the Atlantic abyss was Christopher Columbus. [3]

It is conceivable that Columbus used a combination of rumors, legends, and the maps at his disposal to secretly calculate where the land of Atlantis was most likely to be. Despite his preparations, his projection contained a fortuitous calculation error that would guide his fate. The size of the Earth, according to his maps, was far smaller than its actual size, because the calculations they were based on had not been converted from Arabic miles — which are significantly longer. As a consequence, Columbus conceived the lands of the East being much closer than they actually were. Nevertheless, his officially proposed route would take him in the general direction of his hidden goal.

History records that while underway Columbus deviated from his proposed India-bound course toward the northwest for several days. This deviation suggests that he was searching for something not on his official itinerary. He was sailing into the unknown, fueled only by a dream, and taking a chance that would forever change mankind’s perception of the world. This risky maneuver almost ended in mutiny.

Although Columbus never found Atlantis, or a shorter route to India, his voyage did show that our most trusted maps can be wildly incomplete. In this, his intuition was wholly vindicated. There was indeed an entire continent beyond the Atlantic waters awaiting discovery. In fact, there was much more to the world than the maps of his era portrayed. More importantly, the portions that were missing from those maps were discoverable. [4]

Hundreds of years later, another incomplete map was confronted. Instead of charting the various lands divided by the waters, this map charted the very parameters of physical reality. The man who challenged the old map had a dream to discover a framework wherein all the laws of Nature were simple, harmonious, and unified. He believed that such a map must ultimately be within intuitive grasp. He recognized that the old map, Newtonian mechanics, was no longer capable of charting the ever-increasing array of human observations. To him, this meant that there must be new parameters waiting to be discovered, and he set out to unearth them. The call of this quixotic quest defined his entire life. The man, of course, was Albert Einstein. He was far more than the father of relativity or the grandfather of quantum mechanics; he was the author of a new legend — the legend of a new Atlantis.

Figure 0-1 Einstein’s Quest


The map that Einstein was searching for — the one that would reveal this new ‘Atlantis’ — is called a unified field theory. Those that could not hear the underlying call of Atlantis often mistook Einstein’s goal to obtain a unified and simplified mathematical representation of gravity and electromagnetism, no small task in itself, but Einstein’s aim was much higher. His was a dream of being able to peer into the fabric of physical reality — to ontologically access and fully comprehend its structure, beauty, and the bounds of its potential. His goal embodied the highest aspiration of experiencing the ultimate connection to Nature and grasping the most elegant understanding of what it means to be.

Einstein poetically wanted to be able to touch what lay beyond the horizon. His intuition told him that this goal was within human reach and his explorer’s spirit endowed him with the passion to continue his quest throughout his entire life. On the day before he died, Einstein called for paper and scribbled some calculations in a last hope to complete the map. “He knew he was dying. He knew he would not be able to complete the calculation. He did it anyway. The problem still mattered, and he still cared.” (Levenson 2004, 45) This was his legend.


Figure 0-2 Last Decoding Breaths


Over the years, Einstein’s legend infused the world. Newspapers heralded each of his publications with enthusiastic anticipation; building the rumors that Dr. Einstein had discovered a key insight that allowed him to unveil some of Nature’s deepest secrets. When his papers were released, people flocked to see the new equations, even though most of them considered the menagerie of symbols to be completely incomprehensible. The Prussian Academy printed a thousand copies of one such paper and released them on January 30, 1929. They promptly sold out. The Academy had to print three thousand more. When one set of those pages was pasted in the windows of a London department store, crowds of people who were drawn to the call of this new Atlantis gathered in the cold, pushing forward for their chance to glimpse the complex mathematical treatise. It didn’t matter that the thirty-three arcane equations were unintelligible to most of them. What mattered was that a great mind was attempting to bring humanity a transcendent treasure — a map of the mind of God.

As it turned out, those equations didn’t complete the map. Nevertheless, as a symbol of the growing recognition of the importance of Einstein’s efforts, Wesleyan University in Connecticut paid a large sum to purchase the handwritten manuscript. The papers were deposited in the University library as a treasure. (Isaacson 2007, 343)

Like Columbus, Einstein never reached his end goal. Nevertheless, his discoveries did show that the Newtonian map was incomplete, that entire dimensional continents were still waiting to be discovered. Einstein resurrected the call of Atlantis and left us with the intrepid task of sailing the tumultuous waters of perception as we attempt to discover those continents.

To help guide us toward our destination, Einstein constructed ‘rubber sheet diagrams’ in an attempt to eportraying curved spacetime (see Chapter 9). Those diagrams are quite useful, but they are also incomplete. They map the curvature of only two space dimensions, and they offer no pictorial explanation for warped time. Nonetheless, the partial picture that comes with general relativity dramatically improves our understanding of Nature. It reveals space and time as relative entities, gravity fields as geometric distortions in the vacuum and, most importantly, it releases us from some of our most longheld assumptions about reality.

Einstein’s collective insights (the discovery of the photoelectric effect, which revolutionized electronics, explaining Brownian motion, which verified the existence of atoms, and his masterpieces of special and general relativity) sired a technological revolution that literally invented our modern world. As a result we now have transistors, atomic bombs, lasers, bar-code scanners, digital alarm clocks, charged coupled devices in digital cameras, broadband Internet access, iPhones, solar panels, GPS, fiber optics, remote controls, televisions, DVDs, cancer radiation treatments, smoke detectors, the chemistry of colloids, which is the progenitor of our modern roads, and many of our modern pharmaceuticals from statins to Viagra and more. His insights also set into motion the science of cosmology, the study of ultimate origins, which produced the Inflationary Big Bang theory and enabled us to comprehend far more about the evolution of our universe and our place in it than ever before.

Despite the dramatic effects these things have had on our every day lives, it is important to recognize that all of these advancements were simple pit stops toward Einstein’s true destination. They were the fabled spices, not the city of gold.

Because of the clarity he attained by peering into the fabric of reality further than anyone had before him, Einstein never wavered in his belief that a deeper truth was attainable. He had glimpsed the edge of that truth by ‘lifting a corner of the great veil.’ Because of this, he spent his life in opposition to those whose goal was to define reality as incomprehensible. They aimed to reduce Einstein’s legend into mere myth, and claimed that the human mind has inbuilt limitations that can never be overcome. Einstein’s opponents declared that even if a complete map of Nature exists in principle, it would be forever beyond our ability to comprehend in practice. What is worse is that those figureheads developed the self-destructive notion that ‘good science’ cannot be mixed with emotion or spirituality — that emotion and spirituality can only be grounded in the supernatural. Somehow they never heard the music. They never felt the call of Atlantis.

Above all else, Einstein’s life stands to refute this restrictive view. He once said,the serious scientific workers are the only profoundly religious people,” because “science can be created only by those who are thoroughly imbued with the aspiration toward truth and understanding.” (Isaacson 2007, 390) He profoundly understood that the path of science is ultimately driven by the desire to attain a deeper connection to Nature, to discover a clearer, more comprehensive description of reality, to unveil the causal story. Without this passionate desire scientific progress comes to a screeching halt. “When this feeling is missing, science denigrates into mindless empiricism.” [5]

Realizing that this spiritual fuel, this emotional fire, is required by the goals of science, Einstein embraced and fanned this flame. Because of this he grew to see reality in a way that surpassed the vision of all those who had come before him. Consequently, he was the first to touch a deeper clarity — an experience that connected him with the divine.

“… the cosmic religious experience is the strongest and the noblest driving force behind scientific research.”

Albert Einstein [6]


To differing degrees, many people have felt echoes of the deeper connection that Einstein talked about. We experience them in moments scattered throughout our lives. The first time a child beholds the fossil of a ferocious dinosaur, or gazes into the Trapezium of Orion’s Great Nebula through a telescope, a powerful connection with the vastness of time and space is experienced as an overwhelming feeling of awe and exhilaration. The first time we witness the mesmerizing rhythm of a comb jellyfish, and even when we first hear the melodic trill of a Meadowlark, our intellectual horizon expands and our intuition becomes charged with potential to grow.


Figure 0-3 Childish Wonderment


Whenever we lose track of our physical boundaries, whether we grasp a piece of the Moon in our hands, or experience the ambrosial touch of love, we catch a glimpse of that deeper connection — and a flicker of our ‘magnificent insignificance.’ Einstein’s ‘cosmic religious feeling’ is not inherently limited to punctuated intervals. As a direct link to the divine it has the potential to asymptotically increase until it reaches a constant level of clarity. This is the goal: our quest is to discover the ultimate map of reality and to meld our intuition with Nature’s true form. From this union we will discover that physical law itself is divine, and God will be unmasked as the ultimate manifestation of Nature’s order. The trade winds of Einstein’s efforts blow us in this direction, they motivate us to continue the quest. This journey is more than a dream to complete the map of Nature; it is more than an aesthetic desire for symmetry and mathematical beauty. The scientific quest is about obtaining a direct link to the divine — to touch God, and to understand truth.

Since this quest unavoidably guides us into uncharted waters, our journal entries tend to seek clarity by making use of poetic reference. As a consequence, our discoveries are often confused (by those not on the quest) with something supernatural. But they are not supernatural. Such a misconception would be selling the experience of the quest, and Einstein’s ‘religious’ foundation, short. Einstein was not a theist, nor was he a deist. His ‘cosmic religion’ reflected his devotion to the task of discovering Nature’s hidden structure and his sense of adoration and awe for the infinite potential of that process. (Today many would consider him a Pantheist. [7]) He said, “I believe in Spinoza’s God who reveals himself in the orderly harmony of what exists, not in a God who concerns himself with fates and actions of human beings.” (Dawkins 2006, 18) [8]

Einstein’s repeated use of the word God, despite his knowing that many would be unable to comprehend his intended meaning, was unavoidable. He was as incapable of speaking of the Cosmos in a technical connotation as a young boy is of recounting his first kiss in monotone. His connection to this deeper reality — to God — was the entire point. Those who miss this message, but still try to follow the path of discovery are, as Lee Smolin writes, “reaching for a beautiful flower but missing the beauty of how it is that the flower came to be.” (Smolin 2004, 40)

This quest embodies the preeminent mystery. By definition, it aims to surpass the restrictions that stem from fundamentalism. It is the search for a vivid unfurlment of Nature’s secrets unfettered by dogma. It is the quest to attain a new form of common sense, an elevated intuition by which an intimate understanding of the foundations of the mysterious naturally bestows upon us a fellowship with the infinite.

Einstein invited us to make his dream our universal quest. He blazed a new path and made it possible for all of us to take part in the great intellectual adventure, but like all adventures it has its perils. If we partake in it we will be required to face our ignorance. We will have to brave the thick fog of chaos and drift across a sea of confusion. Eventually we will even need to challenge our most fundamental beliefs about the realm we mean to understand. But by doing this we will be part of a timeless voyage, pursuing an echo of the most ancient intuition, and actively searching for the underlying mystery. This, in and of itself, is reason enough to join the quest, for it is exquisitely human to search for a philosophical truth. As Nietzsche said, “It is time for man to set himself a goal. It is time for man to plant the germ of his highest hope. His soil is still rich enough for it.” (Nietzsche 2005, 13)

Those considering joining this journey should first heed one warning. Threads of an underlying mystery have already been discovered. They have revealed wonders that challenge the imagination and opened chasms that defy empiricism. But the map that connects all of these discoveries is still missing. We are currently lost and confused. Because of this many people have begun to abandon the journey. They have outright given up. They say that if what we are searching for exists, it cannot be grasped by human imagination. To them, additional dimensions, uncertainty, wave-particle duality, and nonlocality are destined to be forever beyond our grasp.

This attitude continues to grow because, for the most part, the sails of our ship have remained slack. Since the death of Einstein no one has presented an idea that has been capable of bringing the mysteries of our modern world within the reach of human intuition. What we are after is intellectual transcendence. The fact that we have not yet achieved it is no reason to give up. There is always a chance that an imaginative insight will restore the wind to our sails. A new picture of reality, the map we have been after, might simply be waiting for someone to challenge an assumption that has never been challenged before. If this is the case, then the conceptual portal we have been searching for might be just one fathom away.

In memory of the dying wish of a great dreamer, and in honor of his intuition, adventurous spirit, and passionate belief in a deeper truth, now is the time to hoist our sails. Now is the time to join the voyage. It is up to us to continue the quest, to brave the dimensional cascades, and to challenge an old map. It is up to us to set out to discover the holy grail of modern physics—the new Atlantis.


“The supreme task of the physicist is to arrive at those universal elementary laws from which the cosomos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them.”

Albert Einstein [9]


In the spirit of Einstein’s intuition, let us launch our intellectual quest from daring shores – starting from the assumption that the axiomatic structure of spacetime is far richer than we have presumed it to be. Let our voyage of discovery be based on careful examinations of the mysteries of modern physics, creative attempts to get beneath assumptions that might be holding us back from understanding those effects, and the process of sifting through a flurry of new ideas by checking our new axioms against the mysteries we mean to explain. Although this book will carry us through that process by exploring the depths of a specific geometric proposal (that spacetime is a superfluid with a fractal structure), the end goal of our investigation will be to fill the sails of our ship with many new and imaginative ideas, and to teach us how to realize the full power of those ideas by learning how to properly trim the sails that capture them.

As we explore new isles of thought we are looking for ones that give us a way to visualize Einstein’s curved spacetime in a richer way. We are searching for a perspective that will allow us to marry the brilliance of Einstein’s intuition with the paradoxical, and sometimes nonsensical, visions of quantum mechanics; creating an intelligible, visualizable system that facilitates a deep understanding, both ontologically and epistemologically, of what is actually going on behind the veil. The treasure we seek is a geometric description of spacetime that can be shown to be deductively responsible for the mysterious effects of both general relativity and quantum mechanics.

Despite the fact that we will be exploring a particular set of assumptions in this book about the geometric structure of space and time (the axioms that lie at the foundation of quantum space theory) and investigating whether or not those assumptions carry us toward our goal of obtaining a greater understanding, my hope is not to convince you beyond any reasonable doubt that Nature actually adheres to the structure proposed herein. Rather my hope is that this investigation encourages you to personally join the quest, to challenge assumptions that you have always taken for granted, to immerse yourself in the unknown, to actively participate in the great mysteries, and to devote yourself to making sense of them all. This book chronicles how I have begun that quest for myself. Should it be a useful guide in your intellectual journey, I shall consider it a success.





[Continue to Chapter One]


From the forthcoming book:

Einstein’s Intuition

by Thad Roberts

Represented by

Sam Fleishman

Literary Artists Representatives

New York, New York



[1] Einstein to William Miller, quoted in Life magazine, May 2, 1955, in Calaprice, 261; Walter Isaacson, “Einstein,” p. 548.

[2] With fastidious resolve Columbus had to make proposals, and switch his allegiance, several times. First to the duke of Anjou in France, then to the king of Portugal, the duke of Medina-Sedonia, then count of Medina-Celi, and finally to the king and queen of Spain. All of these proposals were denied, but after appealing their first rejection, the king and queen of Spain eventually granted him three ships. Jared Diamond, Guns, Germs and Steel — The Fates of Human Societies (New York: W. W. Norton & Company, 2005) p. 412.

[3] In 1485 Marsilio Ficino translated Plato’s works into Latin. Columbus made his first formal proposal to John II, King of Portugal that same year. Seven years later Columbus sailed to the Americas. Whether or not Columbus was actually motivated by a desire to discover Atlantis, or even whether or not he read Plato’s story has been debated. There simply is no reliable record. VNevertheless, von Humboldt, “whose intellectual portrait of Columbus remains unrivalled” notes the absence of any mention of Atlantis from Columbus’s writings but nevertheless maintains that Columbus “took pleasure in Solon’s reference to Atlantis.” (von Humboldt, Historie de la géographie du nouveau continent, 1:167). Pierre Vidal-Naquet and Janet Lloyd, Critical Inquiry, Vol. 18, No. 2 (Winter, 1992), “Atlantis and the Nations,” p. 309. Columbus was not very secretive about how he felt about gold. “Gold is the most exquisite of things,” said Christopher Columbus. “Whoever possesses gold can acquire all that he desires in this world. Truly, for gold he can gain entrance for his soul into paradise.” (New Scientist, Nov 30, 1978 ‘The gold of El Dorado’ by Christine King, p. 705.) This was not an uncommon opinion. The Spanish Conquistadores were prepared to commit genocide to fing the city of gold know as El Dorado. (Ibid.)

[4] Vikings such as Lief Eriksson had visited North America five centuries before Columbus’ voyages, and the Polynesians had been trading their chickens for sweet potatoes with Native Americans for at least a hundred years before Columbus (which is verified by DNA analysis of buried chicken bones in the Americas dated between 1300 and 1424 AD that are clearly of Polynesian, not Spanish, origin). But these encounters did not significantly affect European maps of the world. The enrichment of the European maps is Columbus’ great achievement. See: Elizabeth Matisoo-Smith, University of Auckland, 2007, and Proceeding of the National Academy of Sciences, DOI: 10.1073/pnas. 0703993104.

[5] Einstein to Marice Solovina, January 1, 1951, in Solovina, 119; Walter Isaacson, “Einstein.” pp. 462-463. Einstein also said, “…I maintain that the cosmic religious feeling is the strongest and noblest motive for scientific research.” (Ideas and Opinions, 1954)

[6] From “Religion and Science,” New York Times Magazine, November 9, 1930, 1-4. Reprinted in Ideas and Opinions, 36-40; The New Quotable Einstein, Collected and edited by Alice Calaprice, (2005) p. 199.

[7] “Pantheists don’t believe in a supernatural God at all, but use the word God as a non-supernatural synonym for Nature, the Universe, or for the lawfulness that governs its workings.” Richard Dawkins, The God Delusion (New York: Houghton Mifflin Company, 2006) p. 18.

[8] He also said, “I have never imputed to Nature a purpose or a goal, or anything that could be understood as anthropomorphic. What I see in Nature is a magnificent structure that we can comprehend only very imperfectly, and that must fill a thinking person with a feeling of humility. This is a genuinely religious feeling that has nothing to do with mysticism.” (Dawkins 2006, 15)

[9] Principles of Research, address by Albert Einstein (1918), Physical Society, Berlin, for Max Planck’s sixtieth birthday.