Answers to Foundational Questions

(Part One - as completed May 10, 2005)

by Jonathan J. Dickau
©2005 – all rights reserved

The Foundational Questions in Physics and Cosmology, posed by the people at the Metanexus Institute, give insight into how far we have come in learning about reality and our place in it, and just how far we have yet to go before we truly understand things. To some degree, we have yet to formulate the right questions, in order to find the real foundations of Physics and Cosmology. To get the ball rolling, the people at the Institute created a list of some of the current Really Big Questions, and they plan to inaugurate a multi-year process at a symposium in Berkeley, this October. As most of these areas of inquiry are subjects I have already grappled with at one time or another, I would like to offer brief insights I have on the answers to each question. Where they are available, and appropriate, I will also provide other references for further study.

Q #1 - What is the ultimate nature of reality?

A - To paraphrase Paul Twitchell; There is no Truth greater than the No Truth the seeker knows at the end of all seeking. The exciting thing we are learning is that even beyond form and phenomena, evolution is still possible. Taoist philosophers have talked about this for thousands of years, telling of a region beyond the grand ultimate or Tai Chi (which is still in the realm of comparisons). The idea of Wu Ji, a land of pure process beyond hot and cold, light and dark, or large and small, has been a well preserved secret, but the concept of Wu pervades China’s culture, such that their term for Physics is Wu Li. New insights of what lies in this region ‘beyond the highest’ are coming more quickly, these days, as we can examine this state and the evolution of dimensionality directly using the tools of Noncommutative Geometry, Spin-Foam Networks, and M-Theory. Mathematician Alain Connes declares “Noncommutative measure spaces evolve with time!”[] and this is an exciting confirmation of my earlier statement about evolution in the absence of form. It would seem therefore that the ultimate nature of reality is to evolve into something greater than it was, even if the starting place is nothing at all.

Q #2 - How many dimensions of space are there and why do we experience only three dimensions?

A - The answer to this question needs to be broken down somewhat, because the same answer does not apply at all levels of scale, nor in certain locations (such as near a black hole). It would seem that there are more than three dimensions, and that some are inaccessible, or hidden from view for anyone within a 3-dimensional space, so we should first examine why this is. Our perceptions and measurements derive largely from the properties of light and what is called Optical Geometry. Using the range of scale defined by what is visible to the naked eye; we are prompted to imagine a fixed framework in three dimensions of space, moving through a larger volume over time, having a specific orientation within what we imagine to be a larger 3-dimensional space. This is the framework that is strongly suggested by making optical measurements with limited magnification, but extending the range of our observation and measurement to the extremes suggests a view that is far more interesting and detailed. However, we haven’t had the capability to probe the realms of the vanishingly small, or incredibly large, scale for very long at all, and they are our windows into the nature of dimensionality. What we have learned in the last five or ten years far exceeds all that we knew on this subject before then.

Using modern instruments to reveal the realms of the extremely large and the extremely small gives us a picture very different from a static 3-dimensional view. Space, at the extremes of scale, appears to be evolving dynamically. We know that for volumes of space larger than the universe was at the moment of decoupling (when the Cosmic Microwave Background energy was released), the expansion of space itself becomes a factor, dwarfing all other forces and movements at the largest levels of scale. This expansion also appears to be accelerating. On the other end of the spectrum, in the world at the Planck scale, it would appear that reality opens up into a domain that requires us to use at least 10 dimensions to describe, but it remains to be seen whether they could properly be called dimensions of space. These extra dimensions can be inferred from what we see at the extremes of energy, either in the ultra-high range in particle accelerators, or in the ultra-low range, for temperatures near absolute zero. There appear to be a number of compact dimensions within a volume of expanded space, but that volume may also be embedded in a larger dimensional space. However, we know that a 3-dimensional expanse of space is very special, in its own right.

A universe with 3 expanded spatial dimensions presents unique opportunities because it allows the creation of self-contained and independent, or free-standing, forms. This property seems to derive from the fact that knots in three dimensions can’t untie themselves. This allows energy to form a bundle that wraps around itself, which is what we imagine sub-atomic particles to be. All of this refers to utilized degrees of freedom for forms in a particular range of scale, and not to all of the available degrees of freedom, or to all possible and theoretical dimensions. In my opinion, the underlying question can only have a definitive answer when we remove the requirement that we are examining only whole-numbered spatial dimensions, but the basic question remains. As creatures made from matter, using photonic exchanges for measurement; we must see space 3-dimensionally, as dimensionality itself is defined by the varieties of observable form contained within a given space. So, from our view as humans, or on the scale of what we can see with the naked eye, there are 3 spatial dimensions, but when we consider the bigger and smaller picture, we may need to use 10, 11, or perhaps even more, to represent what we see.

Q #3 - Are we alone in the universe?

A - Each individual is most decidedly alone, but we co-exist with all that is. The question of other sentient beings out there is an interesting one, however. For my part, I feel certain that humans are not the only sentient beings in all of reality, and I am confident that there are other races in our galaxy which are at least as highly evolved as we are today. On the other hand, this does not guarantee that we will ever see any of them, so the question of being alone begs a definition which allows us to quantify what degree of separation we equate with alone-ness. This is not to say that we have enough clear and unequivocal scientific evidence to support the notion of extra-terrestrials who are similar enough to us so that they can be friends and companions, or allies rather than natural enemies of humanity, and so on. Should we discover that there is other life, originating elsewhere in the universe, but find that it is radically different from what we have come to know on Earth; we will still feel very much alone, and it is arguable that this is actually true.

I think the real answer to this question lies more with where we draw the line between living and non-living, between intelligent cultures and primitives or worse, and so on. For us to feel that we are not alone, discovering ancient ET viruses on another planet will not be enough. What we are looking for is satisfactory evidence that there are other human-like species who desire to communicate with us, perhaps to visit, and so on. In my mind, this search goes hand in hand with our efforts to ‘leave the cradle’ ourselves, and to walk beyond the boundaries of our own planet and solar system. I think that the perspective gained from our experience with traveling in space greatly aids our ability to deal with global problems, but we need to do more with what we know. Only if we can put aside our petty differences, and work together to conquer the world’s ills, can we bring something of value to the larger community, if there is other intelligent life out there. On the other hand, if we don’t acknowledge the great opportunities afforded by the endless horizons of space, and utilize some of those resources, we may not survive. Ergo, it seems we are compelled to explore, and this makes the question of others poignant indeed, but I believe it is more a question of our learning to communicate, rather than a matter of whether there is anyone, anywhere, to communicate with.

Q #4 - Where did we come from?

A - In my view; the qualities of consciousness and creativity, that characterize both life and divinity, emerge identically with dimensionality itself, and with the qualities giving rise to the natural forces. Our individual awareness may, therefore, have an origin in the birth of the cosmos. For this question, however, a more detailed answer is necessary, as again there are many parts to examine. If by ‘we’ it is meant that part of us which is purely physical, the obvious answer is that we came from the cosmos, as most of the matter we are made of came from the heart of long dead stars, which spilled out their guts for us (so to speak), when they went supernova after producing the heavy elements. Some of the rest is older still. Most of the Hydrogen in our H2O, and elsewhere in our bodies, is left over from the Big Bang itself. In this sense, the Earth too is a product of the cosmos it is still a part of. If the question is meant to imply an inquiry about the origin of the human species, I feel that we almost certainly evolved on Earth, along with the rest of the life forms we find here. I think the idea of a ‘seed’ from space, or influences from other planetary ‘visitors’ is quite reasonable, though, if we consider the full range of possibilities.

I believe that it’s almost certain that ET viruses have swept the planet again and again, with a definite impact on the evolution of life here on Earth. I greet other scenarios with increasing degrees of skepticism, however, where I regard it as possible that intelligent ETs had a more direct role in human evolution, at some point in Earth’s history, but extremely unlikely that we were ‘engineered’ by aliens. This leaves the broader question of; why did life evolve, or why did human life evolve as it has? Recent work in Physics and Math would imply that the Observer Effect may have played a part in the universe’s birth, and that even the possibility for observation may be enough to influence how things evolve. Thus we are prompted to wonder if there is, perhaps, a primal observer helping to direct universal evolution (as implied by Wheeler-DeWitt), or whether this requirement can be spread out over many observers (as suggested by Fotini Markopoulo-Kalamara[])? In my opinion, there was evolution of both dimensionality and consciousness before the Big Bang, and some spark of our own awareness also sprang from that process, but this will probably long remain difficult to prove.

Q #5 - Is the universe self-explanatory?

A - The universe is an open book and a profound mystery. If the question is whether examining what’s obvious lets us have insights into all that is hidden, we must say that our universe is most certainly not self-explanatory. Nor are the mysteries of the cosmos going to be understood by anybody who thinks they know the answers already. The universe will reveal itself to individuals who have an open mind, and are not going to jump to conclusions prematurely. Reality has enough to reveal that there are sometimes layers upon layers to peel back, before the most essential qualities can be seen at all. Nor does knowing all about the innermost workings necessarily give clear insight into the larger scale structure, or the way that things function at that scale. Each level within a hierarchy, and every level of scale, brings with it a unique perspective that demands attention. The wonderful thing about our universe, however, is that is does have rules and patterns that seem to apply across categories, and repeat at different levels of scale, such that a unifying order can be found. This is why Science has been such a fruitful pursuit, and why we have gotten this far, in understanding the universe.

In order to go much further, however, we must acknowledge that there may be other unifying principles, perhaps another Relativity or Quantum Mechanics, waiting around the next corner. We might find that we are already studying some of these things, without realizing their true significance, but we will one day be putting them on a par with the other ‘Pillars’ of Science. Despite all we know, and all we understand, there are many things we know about the universe that we clearly do not understand. I do think that our universe wants to be understood, on some level, and that living beings are the result of the cosmos’ attempts to see itself more clearly, but we must also want to understand it. We need to observe and explore. We are, in effect, the universe trying to get a better look at itself and to show itself, and life evolving to better understand and deal with its surroundings, at once. Of course; the universe is self-explanatory. All that we know about the universe was shown to us by the universe. It can explain many things, or the same thing a million different ways, but it would be nice to explain some things more clearly, and succinctly, as well. There is a deeper answer to this question, however.

The idea of similarity among patterns developing within different systems, and similar principles that can be applied across disciplines, may give insight into various fields at once. Stephen Wolfram’s “A New Kind of Science[]” suggests that there may be computational mechanisms at work in even the simplest form-building systems which are universal. The holographic principle and the idea of self-similar forms complement this notion, and provide natural mechanisms by which common elements of form or form-building might arise among the different manifested entities within our universe. Physicist Paola Zizzi has shown that these few dynamics, along with the basic fecundity of noncommutative spaces, are sufficient to give rise to the universe, and constitute a ‘Minimal Model’[] (aka Computational LQG) - a system by which our universe might emerge, at the first instant of the Big Bang. Is the universe a quantum computer? If so, perhaps we should alter Descartes’ maxim, and say “It computes, therefore it is.” to describe it. This is an exciting development, in terms of the ways we can answer our question. If the evolution of the universe proceeds by the flow of information, and contains the ‘fingerprint’ of universal processes at work, then the universe is most definitely explaining itself, on some level, but it also provides the only means by which it can be understood.

Q #6 - Is our universe the only universe?

A - In the broadest sense of this question, the answer is almost certainly no, but that doesn’t mean that we’ll find another physical universe just like ours, only different. There are almost certainly other dimensions beyond the physical, but that realm may not qualify as a universe, or a collection of universes, per se. Instead of being another space, it is Hyperspace. There is a high probability that there are alternate realities too, or alternate timelines pertaining to a single reality, but the evidence for this is only suggestive, not conclusive. Still, there is nothing to use as proof that the universe we appear to inhabit is indeed the only one there is, nor that the dimensions we can readily observe are the only ones we interact with. It seems that assuming there are multiple universes is a far simpler explanation for some of the things we observe, than some of the convoluted work-arounds we have developed for things we do not yet understand, but this does not amount to proof they exist either. The real question here is what qualifies, or what precisely are we looking for when we examine the possibility of another universe? In one sense, the universe encompasses all that is, by definition. In another sense of the word, the universe encompasses only the 3-dimensional world of our common perceptions, and anything beyond this is in another universe entirely.

So the question of other universes remains a reasonable matter to pursue. Many physicists now take the possibility of parallel, or alternate, physical universes quite seriously, but they point out that some of those places would be quite inhospitable. Alternate universes with even small changes in the physical constants would be uninhabitable by humans, even if they do exist. But the question of whether ours is the only universe must surely be answered no, at this point, if we take a broad enough view. It may not mean much, however. Theoretical dimensions abound, and our imagination can take us there, but that doesn’t mean all the places we can go in our imagination are (realistically speaking) alternate universes. If they are indeed that, or if there are places yet more real out there to be explored, we are still left with a quandary. There are almost certainly real dimensions beyond the familiar three dimensions plus time that we observe in ordinary experience and Science has almost proven this, in my opinion. I also regard it as likely that some of these spaces correlate with other realms visited by seers and mystics, but I question whether this is germane to our query. The real question then becomes; are there other physical universes accessible to human beings, which might be worthwhile for us to study or visit? Perhaps there are, and we are quickly accumulating scientific evidence that may tell us more about this, but the jury is still out.

Q #7 - How do we account for nature's proclivity to produce complexity even to the degree of the truly astonishing reality of intelligent life?

A - The truth is that even a very simple computational system can produce great complexity, if the parameters are carefully chosen. Stephen Wolfram’s book “A New Kind of Science” devotes hundred of pages to showing how even the most simplistic automata can generate patterns of immense complexity, when given the proper seed formula, documenting how a range of complex behaviors can emerge from simple rules-based systems with different seeds. The Mandelbrot Set is a particularly compelling example of how an exceedingly complex form can arrive through simple means. Its endless range of elegant Fractal forms is a delight to the mind and eye, but all sorts of form can be created by repeating simple formulas enough times. Michael Barnsley discovered that many natural shapes like trees and ferns belong to another class of Fractals[], distinct from objects like the Mandelbrot Set, but again deriving complex form from simple formulas, repeated again and again. In general, fractal shapes are much more true to life, when modeling natural forms, than structures made using only conventional geometry as a basis. This would suggest that nature is fractal, on some level, but also seems to support the view of a computational model of reality and formation. It is as though nature is working to create a level of complexity and organization sufficient to create the means for understanding as well as expressing itself.

We have recently learned, however, that even such a tremendous level of organization and complexity can arrive by simple means. To some extent, it would seem that such a level of complex organization must emerge, as this is the nature of process itself. In my view, Chaos emerges from and depends upon Order, but once there is a certain level of evolution in orderly form, chaos must emerge. It seems that complexity and chaos actually build upon order to exist. It is true that complexity often develops from processes that can rightly be called chaotic, but this doesn’t mean that there is no sense to things, once they do get complex. Instead, complexity is bounded by, as well as inspired by, simplicity. The working of complementarity principles creates limits to complexity that life exploits in order to survive. It also creates boundary conditions by which the foreground aspects can be defined. The most exciting place, you see, is in the boundary region between the orderly and the chaotic, just as the shoreline of the ocean fosters an abundance of life. Intelligent life emerges where things get complex, as evolution gives life forms an edge when they understand reality better. Thus, the boundaries between orderly and chaotic form tend to be a breeding grounds for intelligent life forms.

Q #8 - And what is the final fate of the universe?

A - It appears clear that our universe is expanding, and that the space it is embedded in is itself expanding. In a universe whose expansion is accelerating, it is hard to imagine an end that is anything but bleak. Thus many scientists are now predicting a cold dark end to the universe. Yes, the local space we inhabit appears to be entering its middle age, rather than old age, but that just puts the end a little farther off. The final fate of the universe may be cold indeed, with everything so far apart that light from distant stars could no longer be seen, but I suspect we don’t have the final answers yet. Of course the real answer to this question depends upon our having a far more precise understanding of what the geometry of space is. This is difficult, because we ride on and with the fabric of space, and therefore its shape and its motions are concealed from us, somewhat. On the other hand, we have gained insights from various sources, including the Cosmic Microwave Background radiation, that are helping us to devise better theoretical models.

At this point, we can only narrow down the candidates, for delineating the shape of space at the largest and smallest scales, but we are getting closer to understanding this matter. Space itself appears to be expanding, even accelerating, and this may force a cold dark end, but it may be that once there is enough space extended so that even the possibility of observation no longer exists, the cycle of creation must start over. A number of years ago, physicist Andrei Linde proposed a ‘Self-Reproducing Inflationary’ model[], a Fractal cosmology that suggests such a view where budding universes proliferate when the vacuum energies are great. My own research into fractal cosmologies yields a similar result. There could be a re-start, or cyclical re-birth to the universe, though it appears like the universe will simply expand indefinitely. This may not be the right answer either, as we can’t decisively prove things that can’t be observed, or measured. At this point our answers are more speculation than Science, but this may soon change. We may find that our concepts of size and distance are challenged once we do know the true shape of space, because familiar concepts like size and distance, as well as those of interiority and exteriority, relate to assumptions we make about that space. When we ask “Where did the Big Bang happen?” for example, we are told to point everywhere. Perhaps we will find out one day that the universe is simply inside out, and that it is being stretched back into a tiny point, which appears like space is expanding to us.

Q #9 - What is the nature of reality in the quantum world?

A - The quantum realm is quite different from the experience of life at a normal scale of size. The consensus reality in the world of aggregate objects consisting of millions, or billions, of atoms (or more), has a very different set of rules than the ones that sub-atomic particles must play by. There is, of course, the basic attribute that gives things the term ‘quantum,’ as all interactions within the quantum world must take place in multiples of some fundamental constant, and units of form must themselves be discrete ‘quanta’ (as with photons of light), but there is far more. When we examine things at the level of individual atoms or smaller, we see some truly remarkable things. We often find particles in two places at once, in different orientations simultaneously, and in different levels of excitation at the same time. These are all examples of what is called superposition, or the simultaneous occupation of multiple states. Typically, superposed states last only until there is an interaction or measurement, but lately scientists have been making some of these phenomena manifest on a much more macroscopic level, and have devised clever ways to manipulate the quantum world, including the formation and manipulation of Bose-Einstein Condensates, or collections of particles that are all in the same quantum state and therefore act as a single unit.

At this point, researchers using ultracold and lasers can create BECs on a single bench top, but it is expected that we will see a simple and extremely small apparatus to study arrays of BECs very soon. Being able to study quantum effects outside of the realm of high-energy particle accelerators makes quantum research much more accessible, as new technologies have put this study within the reach of almost any laboratory. While we have learned much about the quantum world, I suspect that we have only scratched the surface, as compared to what we have yet to learn about the subject. The nature of reality in the quantum world is an elusive subject, because so much information is lost when we make a measurement about any one thing definitively. Although there has been some research into Interaction-Free Measurements of quantum systems[], the general rule seems to be that even the possibility of measurement is enough to affect the outcome of quantum interactions. Beyond this, we must choose what we want to know, as we can only learn one thing or another, and not both.

If we stop a particle (for example), we will know exactly where it is, but any information we might have about its motion or energy is lost, at that point. It may have been in more than one place beforehand, as well, but it will appear to be a localized object once you measure its position. It would seem that this is typical, as the nature of things in the quantum world is to be constantly vibrating, or oscillating between possibilities. Even space itself appears to be grainy, or frothy, when we observe it at a small enough scale, becoming a quantum spin foam. This makes quantum reality very hard to precisely define, yet all the more interesting for its magic and the wonder it inspires. It is a world where things can disappear and appear elsewhere, or be in two places at once, or appear only long enough to be ’almost’ real (as with virtual particles). Compared to the observable realm at the human scale (without any technological enhancement), the quantum realm is a very magical place indeed, but we must remember that it is the underpinning of the macroscopic realm, and not something separate from it. Ergo quantum reality is the magical part of the universe, or the magic inherent in reality itself.

Q #10 - What is the origin of space and of time?

A - Time appears to be the precursor of space, and though it might be simply the yardstick by which the evolution of space is measured, it appears to symbolize the dynamic element either way. In a sense, time is identified with the realm of process, and the evolution and unfoldment of processes, as they progress through stages. Although we perceive time as a progression through a linear series of identical movements forward, with a constant and even tempo, it is simply not that way on the smallest scales of size, where time seems rather fickle. If we believe the story told by Noncommutative Geometry and Loop Quantum Gravity, time proceeds forward automatically, however. In my view, the reason is simple. Dimensionless spaces have magical properties, giving them a sort of fecundity. A universe with no contents is hungry to become something, and without form to induce separation it has no boundaries, no limits, but seemingly no power to evolve – or does it? The earlier quote from Connes seems to apply here as well. If noncommutative spaces evolve with time, what does this mean? A noncommutative measure space has a built-in time dynamic that Connes goes on to describe as “God-given,” and though I suspect he meant merely that this dynamic is naturally-occurring, I think there is enough reason to favor the other interpretation, as well.

Or it may be the other way, where natural processes which bring time and space into being are the origin of what we know as divinity too. That is to say that I, and others, feel there are good reasons to believe that an initial observer of sorts may be involved, who either resulted from, or helped to catalyze events at the time of origin. Still, the idea that a 0-dimensional space must be non-commutative, and that such a space tends to unfold or evolve with time, could explain why space exists at all. Quantum variations at the smallest levels of scale expand into minimal areas only as large a few Planck lengths on a side, according to Loop Quantum Gravity, forming a quantum spin foam. The ambiguity of the quantum realm extends to space itself, and to time whose arrow points down several vertices, to recombine later, only resolving into a unified flow when averaged over the course of many propagations within a spin foam network. In my view, this evolution of spin foams expanding every which way in a compact space of 10 or 11 dimensions reached a certain critical value, making 3 of those dimensions large enough to keep them expanding indefinitely. At the point where the universe was still quite small, and very energetic, the familiar laws of Physics took over and the Big Bang scenario, or one of its many variations, tells us the rest of the story up to the present.

Q #11 - Where does the arrow of time come from?

A - This is a fun question for me. Basically, time is identified with the evolution of processes, or arises from unfolding processes, but there is much more to say. In answering the last question, I spoke of the idea that noncommutative measure spaces evolve with time, and I think that understanding this concept is important to discovering the origin of time itself, as well. To some extent, time is meaningless without anything manifested to observe the evolution of, but we can now study the mechanisms of evolution in the pure abstract, even in the absence of manifested form, using what should properly be called differential noncommutative geometry. NCG, as it is commonly called, is the study of spaces where normal laws of size and distance don’t apply, because we can’t add or multiply length values with simple arithmetic. In studying the realm of the infinitesmal, including the universe during its earliest moments, NCG is greatly more appropriate to use, as it aptly incorporates the ambiguity and changeability that the quantum reality possesses. By replacing simple numbers with complex matrices, NCG allows us to accommodate the full sense of quantum superposition, and to incorporate this into our models of space itself. When we do the math, and replace our normal framework with the quotient space equivalent of a NCG, the magic of time’s evolution comes out automatically. The great thing is that, as we approach normal levels of scale, the matrices which allowed additional degrees of freedom at the level of the infinitesmal become uniformly diagonal matrices, which do commute and can therefore be replaced with ordinary numbers.

So the story goes like this, in my view. If things truly started from nothing, it was a dimensionless and/or empty space, but undefined. In the absence of all form, dimensional spaces are ambiguous and noncommutative in their geometry. A space that is noncommutative evolves with time when measure theory is applied, but this seems to take place automatically, even where no kind of measurement or even observation is possible. Apparently, the ongoing evolution of spaces toward the observability of manifested form continues until this property is realized in more conventional spaces, where the commutative law does apply to sizes and distances. The road the arrow of time takes to get here is an interesting one, however. Loop Quantum Gravity predicts that space evolves through a stage, or state, where it is a spin foam network, and time proceeds down the vertices of this network, forming tiny areas up to a few Planck lengths on a side. From my view of this subject, time is more like a wind moving through the fabric of space, at this point, rather than being like an arrow at all. That is; time is not like an arrow, as we move from the Planck scale into the sub-atomic realm, yet it approaches a linear progression when averaged over larger and larger areas or volumes of space. But there is yet more.

The manifested properties of time derive, in part, from the fact that matter is comprised of sub-atomic particles which have a specific duration. The binding of energy into forms of specific geometry or dimensionality requires a specific relationship with the rest of reality, giving them a lifetime, which translates into a half-life, when viewed from relativistic frameworks. This is distinct from measured intervals of time, though, as relativity shows us that observers with different frames of reference rightly perceive events of the same duration occurring over different measured intervals. So we can observe that duration and interval are distinct properties of our motion through time. Again, this observation is easily explained since optical geometry determines how information from distant events arrives at our eyes, or our instruments. Therefore, the properties of light also help to define time’s arrow, and our perception of the passage of time. In my view, time is not linear, but the planet has a regular motion through an ocean or atmosphere of time, moving in stately spirals through space over the years. This gives us the illusion that time is linear, when in fact it is not. Perhaps the wind of neutrinos in the cosmos plays a part in how time unfolds, as well, but this is not clear, and not the whole picture either. Time appears to have an arrow, and to move along a straight line, but the reality of time is considerably more complex.

Q #12 - Why are there laws of nature?

A - In my view; the evolution of dimensionality and of the qualities leading to identity and consciousness proceeds down the same road. I think this applies to Mathematics, as well, or involves it along the way. To my way of thinking; there is an unavoidable link between mathematical reasoning and the science of observation. Where we are used to thinking about Science this way, as it relates directly to what is empirically measurable or observable, it has become a hidden part of what we assume in Math, and it is time we examined this dynamic. In discovering the laws of Mathematics, therefore, we’ve also revealed clues about the nature of consciousness, natural limits on the process of observation, and so on. The “unreasonable effectiveness” of Math, in helping us to make sense of the world, is real in part because it lets us characterize what is observable so well. In a recent paper, I suggest that Mathematics has the form it does because of the manner in which the universe evolved, and that the prior evolution of Math by the universe dictates, or influences, how our understanding of Mathematics evolves.

To explain the emergence of natural law, we must first note that in the absence of form there is no specific frame of reference, making dimensionality ambiguous, and dictating that we assume a noncommutative geometry. If we then trace the steps that make that make commutative spaces and conventional arithmetic possible to evolve, we can gain insight into what made the laws of the universe appear, as well. Being unbroken emptiness, the zero state is oneness, but if we introduce the idea of a point as a center of focus, or a definition of locality, we have a starting place for the familiar laws of Math to evolve. But one infinitesmal point alone is not enough to define (or discover) the dimensionality of a space. To evolve the tools for counting, comparison, and measurement, we need to first distinguish one from none, inward from outward, inside from outside, then one from many, and so on. That is; some of the concepts of geometry and topology have to be evolved before counting and measurement become possible. One can’t count until there are multiple independent objects to count, but once there is multiplicity counting follows naturally. In my view, we can look at the emergence of physical law the same way, as a natural evolution where the utilization of what is possible creates the form of the next phase of creation. I believe, in fact, that all of creation is similar, in this regard.

Big Bang cosmology teaches us that familiar forms were not even possible during the decoupling era, when matter and energy were closely mated, but the specific nature of our form depends on what happened during that cosmological epoch. Ergo; the natural laws as we know them are seen to result from the specific route that was taken by our universe from what is possible to what is actual. In my opinion; the necessary factors for evolving each new concept in the development of Mathematics, when starting from an empty but ambiguous origin, follows a similar sort of development that greatly influences this process. In effect, what is possible to determine mathematically is seen to be closely related to what can be created in a universe of form, as the creative or evolutionary process is similar for both. Likewise, it seems that our existence is predicated on the universe’s ability to compute its own evolution. Ergo, there are aspects of the evolutionary process that derive from questions of computability, and aspects deriving from questions of observability too. So my view is that a framework of Math exists apart from our knowledge of it, and serves as a conduit for creative processes to utilize, as they evolve.

The order in which the concepts of Mathematics can be determined sets the tone for natural law, and nature tries to use all of it, but it has only so fine a grain. I believe that the specific graininess we have here is tuned by natural processes, but any scheme by which things can be quantized leads to certain limitations of how much detail can be represented in any free-standing form. Physical forms can approximate the mathematical ideal of their generating pattern, however they must also be self-consistent, or balanced within themselves, and the specifics of that balance fine-tune the natural laws to their familiar forms. This is to say that reality comprises a balance between form as an emergent aspect of determining forces, and form as a determining element in its own right, or the agent of forces, and so on. Once any sort of substantial form makes an appearance on the scene, it sets the tone for all future development. This may relate to the subject of the elusive Higgs Boson, or to the appearance of mini Black Holes, as these could be the entities which can bear the highest energy as free-standing forms. Thus, the specific natures of these entities, and the process of their formation and breakdown, set the tone for forces that have ‘hardened’ into natural ‘laws’ by virtue of their existence.

[] Noncommutative Geometry – Year 2000 by Alain Connes:

[] Planck Scale Models of the Universe by Fotini Markopoulo:

[] A New Kind of Science by Stephen Wolfram: 2002 – Wolfram Media, Inc.

[] A Minimal Model for Quantum Gravity by Paola Zizzi:

[] Fractals Everywhere by Michael Barnsley: 1998 – Academic Press, Inc.

[] Prospects of Inflationary Cosmology by Andrei Linde:

[] Interaction-Free Measurements – The Ins and Outs of Quantum Interrogation by Paul Kwiat and A.G. White:

Jonathan J. Dickau '05,'06 - all rights reserved

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Article completed
May 10, 2005

page first posted
August 11, 2006