Excerpts Note & Synopses


A sneak peek of ‘Einstein’s Intuition: Visualizing Nature in Eleven Dimensions’ is avail­able here, which includes the preface and chap­ters one through four. Select a chapter or the syn­opses from the book excerpt menu at the top of this window or by clicking the links below.


Preface Chapter One Chapter Two Chapter Three Chapter Four


The full book is avail­able in hard­cover full color, soft­cover full color, iBook and audio­book here.




Chapter Synopses:


Humanity has always yearned to glimpse what lies just beyond the horizon, to touch that which is just out of reach. Our curiosity guides us to seek what lies beyond our senses and to make sense of a world con­tra­dic­tory in char­acter. Great explorers of the past filled in the map of our world. Their charts enriched our con­cep­tual access to the great beyond. But this was only the begin­ning. The world is only a small part of what needs to be mapped. The struc­ture of reality, the Universe, the laws of physics, and the deep under­lying char­acter that sup­ports it all needs to be mapped if we are ever to have intu­itive answers to our biggest ques­tions. Einstein was the last great cham­pion of the quest to obtain this com­plete map. He took our barren notions of phys­ical reality and filled in details that no one before him had imag­ined. He reached deep inside him­self, touched the great beyond, and called the expe­ri­ence “lifting a corner of the great veil.” It is time for us to lift the remainder of that veil. It is time for us to dis­cover the rest of Nature’s hidden struc­ture and to learn how to simul­ta­ne­ously con­cep­tu­alize eleven dimensions.

Part 1 – Returning to a Conceptual Approach

Chapter 1 – Seeing the Problem

This chapter intro­duces the reader to the his­tory of how our con­cep­tual map of the cosmos has changed over time. Our ear­liest maps depicted the earth as a flat disk sur­rounded by a giant rotating sphere that was embedded with thou­sands of tiny points of light. With more obser­va­tions the world switched from being described as flat to round. To account for the motions of the sun and moon three dis­tinct spheres, three celes­tial levels, were added to the map. Then when the motions of the five vis­ible planets were noticed the map of the heavens evolved into one with seven levels inside the orig­inal sphere of stars. Today all of these notions have been replaced by a map that places our world orbiting around an average star that is located in a rather average looking galaxy. The best cur­rent map we have of the cosmos (gen­eral rel­a­tivity) was authored by Albert Einstein. His map revealed a char­acter of space­time that had never before been accounted for. But despite the improve­ments, Einstein’s map is still not com­plete. There are many obser­va­tions that it does not explain or pre­dict. In fact, the entire realm of the super-small entirely con­tra­dicts the rules of gen­eral rel­a­tivity. Quantum mechanics is the set of math­e­mat­ical equa­tions that are used to sta­tis­ti­cally explain occur­rences in that micro­scopic realm. These equa­tions have not been com­bined into any useful or intu­itive map. They have also not been rec­on­ciled with the require­ments of Einstein’s map. Today we stand with an incom­plete map in hand as we peer into the struc­ture of Nature.

Chapter 2 – Rethinking Space and Time Again

In order to con­tinue our quest for the final map of phys­ical reality we need to be willing to com­pletely rewrite the foun­da­tional struc­ture of that map. The foun­da­tions of every map are the assump­tions within it that define the struc­ture of space and time. All higher-order geo­metric rules, struc­tures and inter­ac­tions stem from those base assump­tions. Since we have been unable to explain the mys­teries of Nature through the lens of our cur­rent assump­tions we need to revisit those assump­tions and con­sider the pos­si­bility of a new struc­ture under­neath it all. We need to chal­lenge our most basic assump­tions about space and time.

Chapter 3 – Dimensions

To restruc­ture our con­cep­tion of phys­ical reality we need to make sure that we under­stand what a dimen­sion is. The dimen­sional para­me­ters of a given map form the basis and struc­ture for every­thing else that fol­lows. This chapter dis­cusses exactly what physi­cists mean by the word ‘dimen­sion.’ It then explores the con­nect­ed­ness of spa­tial dimen­sions and explains how those descrip­tors are part of our map of phys­ical reality. Next we examine the idea of curved spa­tial geome­tries, which leads us to the pos­si­bility of addi­tional dimen­sions. The dimension(s) of time are also briefly intro­duced in this chapter.

Chapter 4 – The Quantized Nature of Spacetime

This chapter intro­duces some very impor­tant clues that we will use to piece together our new foun­da­tional struc­ture of phys­ical reality. Some of the biggest mys­teries of Nature come from the quantum nature of the micro­scopic realm. Quantum mechanics has taught us that there is a min­imum dis­crete unit of both space and time. Fundamental elec­tric and mag­netic inter­ac­tions are all based on dis­crete quantum units. Light even exists in quantum packets called pho­tons. Somehow all of these quantum packets travel through the fabric of space as a mys­te­rious wave but they also retain their quantum char­ac­ter­is­tics. All of this brings us to the sug­ges­tion that the foun­da­tion of our new map of phys­ical reality must incor­po­rate a quan­tized struc­ture for the fabric of space and time.

Part 2 – The Framework of Quantum Space Theory

Chapter 5 – Absolute Volume

In this chapter, the reader is intro­duced to the basic frame­work of quantum space theory (qst). They learn how to con­cep­tu­alize nine spa­tial dimen­sions simul­ta­ne­ously and dis­cover how it is pos­sible to move about from one loca­tion to another without changing x, y, z posi­tion. The three types of volume (inter­spa­tial, spa­tial, and super­spa­tial) are intro­duced and the con­cept of two time dimen­sions is fore­shad­owed. This new geom­etry reveals many char­ac­ter­is­tics of space­time that are ignored in the familiar four-dimensional descrip­tions. These addi­tional geo­metric para­me­ters are where the mys­te­rious effects of quantum mechanics and gen­eral rel­a­tivity come from. Elevating our com­pre­hen­sion of the struc­ture of Nature (the map in our head) to include all of the eleven dimen­sions that make up phys­ical reality has the effect of bringing us into sync with its actual form. In doing this we gain access to the intu­itive solu­tions of the greatest mys­teries of modern physics.

Chapter 6 – Space

The con­cept of space has always been elu­sive. Humans are accus­tomed to con­cep­tu­al­izing space as noth­ing­ness – what you have if you remove every­thing from a region. Yet we have always known that space is imbued with prop­er­ties. For example, dis­tance and volume still remain once we remove every­thing else from a region. This mea­sur­able quan­tity is not noth­ing­ness – but what exactly is it? What is it made of? What other prop­er­ties does it have? How do we extract a def­i­n­i­tion of dis­tance from the geom­etry of Nature? What are the geo­metric assump­tions that lie beneath our answers to those ques­tions? These ques­tions and more are tackled in this chapter. Based on our new eleven-dimensional geom­etry we come to a con­clu­sion on what dis­tance really is, how the struc­ture of space com­poses the four dimen­sions of Nature that we are familiar with, and why space only exists in a dis­crete sense.

Chapter 7 – Time

The notion that time passes at a uni­versal rate in all loca­tions throughout the uni­verse seems obvious to us. 100 years after Einstein proved this idea to be false the majority of the world still thinks that trav­eling through time at dif­ferent rates is some­thing that is found only in sci­ence fic­tion movies. The sur­prise is that time travel is a sci­en­tific fact. This fact vio­lates our familiar four-dimensional intu­ition, it comes with a glut of philo­soph­ical ques­tions, but it is a fact nonethe­less. Long ago physi­cists set out to account for this char­acter of Nature. In this chapter we dis­cover that from the eleven-dimensional van­tage point this fact is not only intu­itively explained, it is also required by the geom­etry of space­time. The pas­sage of time is defined uniquely at each loca­tion in the sea of space­time. As the char­acter of that sea changes, from one region to another, the rate at which time passes reflects these changes. All of this can be read from the key of our new eleven-dimensional map. It explains the arrow of time that we expe­ri­ence, and it resolves the philo­soph­ical conun­drums of time travel.

Chapter 8 – The Speed of Spacetime

Many people know that physi­cists say that the fastest any­thing can go through space is the speed of light. People often respond to this state­ment by asserting that with better tech­nology we will one day find a way to go faster than the speed of light. They fail to rec­og­nize that the speed of light is not a reflec­tion of our tech­no­log­ical capa­bil­i­ties. Instead it is more akin to saying that you cannot go fur­ther north than the North Pole. The geom­etry of space­time dic­tates this con­di­tion. It is inscribed in the tex­ture of phys­ical reality. This chapter explores that tex­ture and explains why this con­di­tion nat­u­rally fol­lows from the eleven-dimensional geom­etry of Nature.

Chapter 9 – Warped Spacetime

Here, we dive into the mys­teries of gravity. The mag­ical force that pulls the moon toward the earth has, like an end­less riddle, long echoed through the minds of humankind. Einstein con­nected gravity to a geo­metric dis­tor­tion that extended into higher dimen­sions, but he never granted us with a full pic­ture of these addi­tional dimen­sions. Now that we have learned how to con­cep­tu­alize these other dimen­sions, our map of the Universe nat­u­rally accounts for the effects we credit to gravity. Throughout this chapter we prac­tice switching our intu­ition from the four-dimensional view we grew up with to the eleven-dimensional view of qst. As we do this we dis­cover that gravity’s rid­dles readily trans­form into acces­sible con­di­tions of the struc­ture of Nature.

Chapter 10 – The Bucket

The ancient philo­soph­ical debate about the nature of accel­er­a­tion versus time and posi­tion rests on whether or not an under­lying ref­er­ence frame exists in Nature. In this chapter we dis­cover a unique solu­tion to this bitter debate. We find that from within the eleven dimen­sions that define our uni­verse, there is an under­lying ref­er­ence frame – one that we call absolute volume – but from the ulti­mate per­spec­tive (any higher-dimensional resolve) that ref­er­ence frame is as fluid as the rest. The reason that time and posi­tion are mea­sures that can only be defined in com­par­ison to some other time or posi­tion, while accel­er­a­tion needs no com­par­ison to be defined, is a direct result of the quan­tized struc­ture of space­time. This con­di­tion is also required by the geom­etry of Nature.

Chapter 11 – Dimensional Analysis

This chapter reviews the dimen­sions that we have explored in this part of the book. It then intro­duces the curious con­cepts of spinors and the require­ments of lim­ited dimen­sional freedom that gravity sets in the uni­verse. After explaining how these con­di­tions are con­se­quences of the quan­tized geom­etry we have been exploring we examine the philo­soph­ical require­ments for extending the rules of that geom­etry. We dis­cuss where these rules take us, and how they open the next great door of human imag­i­na­tion. It is here that the heart­strings of our per­sonal life are con­nected to the external world and the infi­nite is found in the finite.

Part 3 – Physical Reality in Eleven Dimensions

Chapter 12 – The Questions of Quantum Mechanics

In order to under­stand how mirac­u­lous it is that we can solve the big mys­teries of the small realms simply by changing our geo­metric assump­tions about space­time we need to be familiar with those mys­teries. To that end this chapter dis­cusses the enigmas of quantum mechanics: particle/wave duality, the non-locality of the uni­verse, and the pho­to­elec­tric effect. After each mys­tery is devel­oped we then turn to view each of them from the eleven-dimensional per­spec­tive that we have been exploring. Every time we do this, the process becomes a little easier and the mys­teries of advanced physics go from imposing frus­tra­tions to delightful and acces­sible parts of Nature’s geometry.

Chapter 13 – Beneath Quantum Mechanics

In this chapter we explore a deter­min­istic expla­na­tion of the double slit exper­i­ment (Bohm’s inter­pre­ta­tion), and come into pos­ses­sion of a clear ontology for the state vector.

Chapter 14 – Quantum Tunneling & Entanglement

This chapter is ded­i­cated to an explo­ration of the mys­teries of quantum tun­neling and entan­gle­ment. We start from a con­cep­tu­ally his­tor­ical approach and then reex­amine the data from the geo­metric per­spec­tive of our new map. What we find is that although all of these effects are mind bending from our four-dimensional per­spec­tive, they are all nat­ural and simple aspects of Nature when we frame it in eleven dimensions.

Chapter 15 – Black Holes and Elementary Particles

One of the most pro­found mys­teries of our time may turn out to be cen­tered on the ques­tion of what black holes are like inside their event hori­zons. By def­i­n­i­tion no light escapes a black hole to reveal its inte­rior struc­ture. For this reason, the insides of black holes have been assumed to be for­ever beyond our grasp. As it turns out, that lim­i­ta­tion only exists when we frame phys­ical reality as being four-dimensional. In this chapter, we dis­cover exactly what a black hole is, what its full geom­etry looks like (even within its event horizon), and how black holes are related to entropy and the dis­crete pieces of space. We even learn how and why black holes form. All of these dis­cov­eries are auto­matic require­ments of our new geometry.

Chapter 16 – The Constants of Nature

The phys­ical quan­ti­ties that appear over and over in all of our equa­tions in physics, chem­istry, biology and so on are often taken as brute unex­plain­able values. The anthropic prin­ciple is often used (in prac­tice) to squelch ques­tions about how these values came to be as they are. The uni­verse, they say, acquired these values ran­domly and since only the com­bi­na­tion that we have in this uni­verse leads to the for­ma­tion of life, the fact that we are here asking the ques­tions shows the out­come of the universe’s ini­tial dice roll. This is not a pro­found solu­tion. Even a random mech­a­nism capable of set­ting the values of the con­stants of Nature needs to be explained. In this chapter, we dis­cover the expla­na­tion for how the con­stants of Nature have come to have the values that we mea­sure. We also dis­cover that there is a non-arbitrary scale within Nature. All of this dras­ti­cally reduces the math­e­mat­ical com­plex­i­ties of the equa­tions we have become familiar with and it gives us a solid under­standing as to why the uni­verse is the way it is.

Chapter 17 – Deterministic Versus Stochastic Models

Is the uni­verse deter­min­istic or sto­chastic? Do things evolve strictly in accor­dance with cause and effect? Or is there a part of the uni­verse that ulti­mately is not bound by cause and effect? This has been a time­less debate. Today’s physi­cists are divided on the matter because the two main branches of physics do not clearly come to full agree­ment on this issue. General rel­a­tivity is deter­min­istic. Most of quantum mechanics is also deter­min­istic. The ad hoc inter­pre­ta­tion of state reduc­tion that we use today is decid­edly sto­chastic. That is the only part of quantum mechanics that is sto­chastic. The inter­esting thing is that the pre­dom­i­nant inter­pre­ta­tion of state reduc­tion is not the only con­sis­tent inter­pre­ta­tion avail­able. So the answer to our ques­tion boils down to our jus­ti­fi­ca­tion of the inter­pre­ta­tion we select for quantum mechanics. But how do we decide which inter­pre­ta­tion is cor­rect? In this chapter we explore these issues. In the end we find that our new model depicts a uni­verse that is fully deter­min­istic. The seem­ingly sto­chastic equa­tions of state reduc­tion used in the stan­dard inter­pre­ta­tion are revealed as solu­tions that are based on only part of the dimen­sions in the uni­verse. When the full dimen­sions of Nature are con­sid­ered the system regains deter­minism. This means that every action has a cause. The philo­soph­ical impact this can have on how we choose to live our lives is quite prophetic. What this means is that the geom­etry of Nature is a very per­sonal issue.

Chapter 18 – Emergent Reality

The com­plex struc­tures around us are always emerging and evolving. Where do they come from? What deter­mines their struc­ture and for­ma­tion? What does it all depend upon? And what drives the evo­lu­tion of these sys­tems? Understanding the emer­gence of form from the under­lying geo­metric foun­da­tion of Nature is the focus of this chapter. We explore the con­cept of super­ve­nience and dis­cover that the KD map elim­i­nates the present day prob­lems with illog­ical infin­ites that quantum mechanics cur­rently wres­tles with in their maps.

Chapter 19 – The Hierarchy Problem

A pop­ular ques­tion today asks why the force of gravity is so infin­i­tes­i­mally weaker than the other three forces. By com­par­ison the strong nuclear force, the weak nuclear force and the elec­tro­mag­netic force are roughly all the same strength. How is it that gravity is so dif­ferent? Where does this dif­fer­ence come from? This ques­tion is called the hier­archy problem. In this chapter we learn that there is a dif­fer­ence in the ori­gins between the three sim­ilar forces and gravity. Gravity is the effect of a small inelas­ticity in the quanta of space. This inelas­ticity is what sets up space­time den­sity gra­di­ents or the cur­va­ture of space­time. The reason that the force of gravity is so very weak is that this inelas­ticity is many powers smaller than the degree of elas­ticity in the quanta. From this we dis­cover that the four forces are all expres­sions of the inter­ac­tive prop­er­ties belonging to the geom­etry of Nature. Exposure of that full geom­etry brings unification.

Chapter 20 – Beyond Forces

If we were to look up and watch an astro­naut orbit the earth in nothing but his space­suit we would say that the force of gravity is what is respon­sible for her ellip­tical path. By doing this we are asserting that a force is acting on the astro­naut. But when a force acts on an object that object is accel­er­ated. Whenever someone is accel­er­ated they can feel it. So does our astro­naut feel some force pulling or pushing on her and accel­er­ating her toward the earth? The answer is no. The astro­naut is not being accel­er­ated at all. Instead she is going straight through curved space. As it turns out, forces are often titles we give to our mis­char­ac­ter­i­za­tions of the world. We form expec­ta­tions for how things should work based on the four dimen­sions we believe in. Then, when we observe occur­rences that do not fit within that set, we make up ‘mag­ical’ forces that exist over and above the rules we assumed in order to explain the obser­va­tions we made. Therefore, forces are little more than shadows of the mis­takes we made when we were orig­i­nally framing the geom­etry of the uni­verse. Once we see the uni­verse in its full geo­metric form these forces dis­solve and the mys­te­rious effects of these “forces” are readily acces­sible. Nature’s true geom­etry should already include the effects we blame on forces.

Chapter 21 – Quantized Vortices

Expanding on Lord Kelvin’s beau­tiful idea we explore the rules of for­ma­tion for vor­tices in a super­fluid and dis­cover that these sonons nat­u­rally match up with the fun­da­mental par­ti­cles of mass in our uni­verse. The for­ma­tion of these “super­fluid smoke rings” offers us a new under­standing of the Higgs mech­a­nism and opens up the pos­si­bility of under­standing even mass in terms of geometry.

Chapter 22 – Superfluidity

In this chapter we enrich our explo­ration of what it means to be a super­fluid and we find that the mere assump­tion that the vacuum is a super­fluid auto­mat­i­cally leads to the expec­ta­tion that its dynamics are con­trolled by the Schrödinger equa­tion. We also explore how space­time cur­va­ture can be explained in terms of ana­logue gravity.

Chapter 23 – Illuminating Dark Matter

Dark matter haloes sur­round galaxies increasing the amount of grav­i­ta­tional dis­tor­tions in these outer regions. But no one has been able to explain where this extra grav­i­ta­tional energy comes from. What causes these haloes to form? Why don’t we find the cul­prits in our lab­o­ra­to­ries here on earth? How do we explain the struc­tures we see in our largest tele­scopes? These are the ques­tions we address in this chapter. What we dis­cover is that the dark matter haloes sur­rounding galaxies are the effects of phase changes in the sea of space­time. Since space­time is par­tic­u­late, just as water is, it can have dif­ferent phases. These phases cor­re­spond to dif­ferent geo­metric con­nect­ed­ness just as the phases of H2O do. When we account for the varying geo­metric arrange­ments of these space quanta with a depen­dency on tem­per­a­ture we nat­u­rally get the dis­tor­tions that we have been attributing to dark matter.

Chapter 24 – Bohmian Mechanics

This chapter is for the math­e­mati­cian that wants to dive into the set of equa­tions that best express the intu­itive geom­etry that we have been exploring throughout the book. (Although the full math­e­mat­ical set has not been com­pleted at this point.) The math is explained in words and equa­tions. A dis­cus­sion on the his­tory of Bohmian mechanics, which is the foun­da­tional set of equa­tions, is also included. Then a sug­ges­tion is given for the direc­tion in which the final for­malism will come from – a  sug­ges­tion that is based on the insights our our new eleven-dimensional map.

Chapter 25 – Symmetry and Symmetry Breaking

The laws of physics don’t depend on where you are or which direc­tion you are going. Why? Why do all our equa­tions assert that the laws of Nature are time-reverse sym­metric yet they all clearly seem to unfold with a pref­er­ence in time? Is time ulti­mately sym­metric or asym­metric? What other sym­me­tries exist in Nature and why? These are the ques­tions that are addressed and answered in this chapter. The char­ac­ters we call sym­me­tries in Nature all stem from the geo­metric struc­ture that defines the fabric of space­time. By under­standing this struc­ture we come to terms with the sym­me­tries of Nature.

Chapter 26 – Entropy

The second law of ther­mo­dy­namics states that if there ever exists a system that pos­sesses less than its max­imum entropy (dis­or­dered­ness) then it will be extremely likely to have higher entropy both before and after that moment. This has been accepted as one of the most invi­o­late, iron­clad ten­ants of our uni­verse – yet it has never been explained. Why do sys­tems tend toward dis­or­dered­ness? Where does the law of entropy come from? In this chapter, we dis­cover that the par­tic­u­late nature of space leads to entropy because geo­metric mixing is an inherent part of all sys­tems in space­time. We also explore entropy to greater depths and dis­cover its con­nec­tion to evo­lu­tion and the Big Bang.

Chapter 27 – Genesis

In this chapter we come to a topic that some have said lies ‘out­side the realm of sci­ence.’ The first thing we dis­cover is that they were wrong. The ques­tion of what caused the Big Bang, what got the whole thing started to begin, with turns out to be encased by the infi­nite cas­cades of dimen­sional hier­archy that is within the set of our KD map. This means that we can answer the ques­tion of ulti­mate ori­gins. The answer turns out to be very ele­gant and per­haps a bit sur­prising. Nietzsche’s con­cept of eternal recur­rence reemerges through this insight and this reemer­gence pulls humanity into the depths of this ques­tion in a whole new way.

Chapter 28 – Dark Energy

Now that the reader has had some prac­tice seeing phys­ical reality in eleven dimen­sions, it is time to address a mys­tery that is so cap­ti­vating that I had a hard time saving it for last. This is the mys­tery of dark energy. The chapter begins by giving a his­tory of the dis­cov­eries that led to our modern under­standing of the expanding uni­verse, and humanity’s struggle with iden­ti­fying its cause, which we have clev­erly named dark energy. The reader is given the chance to apply their new eleven-dimensional intu­ition to solve this mys­tery. To do this we must each address the ques­tion of expanded space – what does that really mean? Then we must dis­cover what is really causing the light reaching our eyes from dis­tant stars to be red-shifted. As we have come to expect, the solu­tion is sur­pris­ingly clear and delight­fully intu­itive from our higher-dimensional vantage.

Chapter 29 – Intellectual Astronauts

This chapter warms the reader to the philo­soph­ical impact that this new geom­etry has on humanity. A new way of seeing the world around us has always changed the way we interact with it. The respon­si­bility we have with each new improve­ment is the task of absorbing dis­cov­ered truths and incor­po­rating them into our daily lives. Here we find that our entire way of being, our most basic mode of exis­tence (at least in the West) is based on assump­tions that do not ulti­mately hold. Where do we go from here? The KD map has a lot to say about this and our per­sonal lives.

Chapter 30 – The Wilderness of Intuition

Our curiosity often tricks us into falling for solu­tions that are made merely of smoke and mir­rors when a more rigid solu­tion is not avail­able. The enti­ties that profit most from the con­tinued pro­jec­tion of that smoke have led a cam­paign to con­vince us that the truth we seek is not obtain­able by sci­ence, that the quest of sci­ence is not capable of sat­is­fying the deep yearning we have. This is, and has always been, a lie. Now that we pos­sess a richer map of Nature, the appar­ent­ness of that lie stands out in the day­light for everyone to see. In this chapter we dis­cuss how the process of the sci­en­tific quest is the most ful­filling and sat­is­fying human expe­ri­ence. It throws us beyond our­selves and encour­ages us to intel­lec­tu­ally and emo­tion­ally tran­scend any bar­riers that hold us back. The char­ac­ters of sci­ence are the people with pas­sion and vigor for life, the seekers, the explorers and the embracers of wonder. It is through the quest of sci­ence that our humanity is rede­fined and lifted to a new plane.