2/25/17

INTRODUCTION
When we consider the question, "How can mindless mathematical laws give rise to aims and intentions?", the obvious and necessary role of consciousness jumps out at us. Aims and intentions can only be felt as conscious experiences. And, whether mathematics is invented, discovered, or simply learned and understood, invention, discovery, and understanding cannot take place without consciousness. Once the mathematical laws are discovered or invented, however, they can be rendered "mindless" by reducing them to inscriptions in some physical media such as textbooks. So, we need to explain the structure, location(s), and role of consciousness in the cosmos before we can answer our thematic question.

To develop an answer to the question, we propose the acceptance of Interactionist Cartesian Dualism, (ICD)¹ , and the reality of large, extra spatio-temporal dimensions. After presenting arguments for the plausibility of these ideas, we develop a scenario, along with the necessary mechanisms, which lead to an answer to our question. In short, the answer is that aims and intentions precede mathematics which in turn precedes our Big-Bang-initiated 4D world.

THE STRUCTURE OF CONSCIOUSNESS
Here is a list of some, perhaps not all, of the features or components of consciousness:

Awareness, experience, perception, the ability to notice, the self, thought, feelings, intentionality, attention, free will, purpose, imagination, conception, pattern recognition, memory, self-reflection, logical ability (reason), knowledge, comprehension, understanding, meaning, value, morality, wisdom.

The list is arranged in the order the components would appear in a narrative I might deliver to answer the question, What is consciousness like for you? I might say,

"I am aware that I have experiences, I perceive a world around me which just asked me a question about consciousness, and I notice that I need to use the word "I" frequently just to respond to the question. That "I" is my self.

"I experience thought happening and among the thoughts I experience are many feelings ranging from pain to various other sensations and urges. My attention seems to be focused on one mental aspect at a time. Among the feelings are intentions, which somehow urge me to take some action. I take those actions by exercising my free will to redirect my attention so that I may achieve some purpose.

"I can imagine counterfactuals by an exercise of will. I can recognize patterns and concepts among those counterfactuals. I can relegate those concepts, along with perceptions and other experiences to my memory and retrieve them later. I have the ability to consider concepts and infer new and different concepts as logical implications of the ones I am considering. I can reason.

"In my memory I have accumulated quite a store of concepts along with myriad percepts which, taken together, I count as knowledge. I comprehend many of the interrelationships among the percepts and concepts that I know. Thus, I understand much of what I know. I seem to understand some of the relationships between what I know and the world around me, which gives that knowledge some meaning. Some of those relationships are more important than others, which gives them value. Applying those values to the world constitutes morality. And understanding morality constitutes wisdom."

To determine the structure of consciousness in detail, we need to understand how each of these components is attenuated and distributed across the various locations where they reside. We can only sketch the beginning of that process in the space we have.

THE LOCATIONS OF CONSCIOUSNESS
Obviously, one candidate location is the brain. But to keep an open mind, so to speak, we will consider other candidate places as well. The proposed extra dimensions provide another obvious candidate. Lastly, there is the possibility that we might endow some of our computers with some form of consciousness, thus some of our artifacts will be considered candidates.

THE ROLE OF CONSCIOUSNESS
In order to accept ICD, we not only need to identify some place outside the brain where the seat of consciousness resides, but we also need to solve the mind/body problem, and we need to solve the homunculus problem. We will address those later.

With ICD reestablished, and with the acknowledgment of the existence of large extra dimensions, we will be able to construct a plausible scenario that will explain how mindless mathematical laws can give rise to aims and intentions. That scenario will explain the role of consciousness in the cosmos.

The scenario in broad strokes is that the entity that embodies the primary components of consciousness, let's call that entity "X", exists in higher dimensions. X deliberately and consciously went through the following steps in sequence: 1. X developed the mathematics necessary to define a huge matrix of numbers (think Hilbert Space). 2. X developed a set of theorems which include Schrödinger's equation, Maxwell's and Einstein's field equations, and/or whatever the actual laws of physics are that govern our 4D world and its processes. 3. X populated the huge matrix with an extremely improbable and precise array of numbers. 4. X provided the 4D substrate in which the physical universe was to unfold. 5. X started a process much like a cellular automaton and let it go. That produced the Big Bang and its consequences, which we are just now beginning to understand.

ESTABLISHING PLAUSIBILITY
In the scenario we outlined, since X resides beyond our 4D world both in space and time, there was (is) plenty of opportunity to start many such 4D worlds and many places for the substrates so that they don't necessarily intersect or overlap. Thus, various "many-world" theories could be true within this scenario.

Based on our experience, it appears that X intended to keep the world(s), at least the one we find ourselves in, self-consistent. That would imply that the world(s) remain consistent with the laws of physics². If so, the automaton would run unmolested, driven strictly by the laws of physics—unless, of course, in the implementation of the mechanism that actually applies the equations to the substrate (breathes fire into them), something was added like programmers of The Game of Life often do here in our 4D computers. That is a mechanism that allows for stopping the action temporarily, deliberately changing a cell (meaning an active element of the cellular automaton) here and there, and resuming the action with those changes now taking effect.

Since the laws of physics are nearly causally closed, the only known exception being apparently random outcomes of some (or even most) quantum interactions, the deliberate alteration of cells must stay under the detection threshold (think Heisenberg Uncertainty Principle) of 4D detection instrumentation. Only then would the behavior of the 4D world remain consistent with the laws of physics and still allow for some small, deliberate changes as the world evolves.

In this way, the aims and intentions of X for specific desired outcomes in the 4D world, in addition to the general ones expressed in the initial conditions, might be pursued, however tediously and slowly. This could explain how biological evolution could have started and how it could have occasionally been nudged to pursue goals like reproduction and speciation. It could also provide an easy answer to the very hard problem of the origin of the genetic code³.

This capability also provides for a mind/body interaction mechanism—a transponder in the brain—that solves half of the mind/body problem and which helps make Interactionist Dualism plausible. Francis Crick has identified⁴ a structure in the brain, the claustrum, which appears to be an excellent candidate for just such a transponder, or at least the antenna circuit for the transponder. As in the case of a cellphone, the transponder and antenna circuits probably make up a rather innocuous part of the device (brain) which could be easily overlooked by any investigator who was oblivious to its presence and function. The other half is the 2-way communication link between mind and body which we shall discuss later.

Next, we establish the plausibility of the idea of large, extra dimensions. There are three commonly used arguments meant to dismiss the idea:

1. If they exist why can't we see them?
2. If they exist our inverse square laws should be inverse cube (or higher) laws.
3. By accepting the idea, we would be violating Occam's Razor.

Rebuttals to all three are straightforward:

1. We can't see them because our 4D world is an embedded manifold in a higher-dimensional space and all structures and processes involved in our "seeing" anything are restricted to our manifold.

Oskar Klein's commonly cited explanation, that we can't see the extra dimensions because they are "curled up" too tightly, is absurd. If you analyze carefully any of the many renditions⁵ of "the hosepipe analogy" the absurdity is immediately evident because the analogs do not match up.

2. In the current scientific paradigm, all identified physical forces act in 4D spacetime. The expectation of inverse cube (or higher) laws would come from assuming that the forces involved would also act in the higher-dimensional space if it existed. That may or may not be the case.

It could well be that just like material structures, the forces are also confined to act only in our manifold which would then mean that the familiar inverse square laws would obtain. There is talk of forces "leaking" into higher dimensions, and that is certainly possible. If our 4D phenomenal world is a manifold in a higher-dimensional space, new possibilities for the understanding of fundamental forces may present themselves. There could be, for example, forces that act only in a direction normal to our manifold, in which case all component vectors of the force in our manifold would be zero. Thus, the force would be completely undetectable by our instrumentation or observation. Such a force, however, could provide a mechanism for a communication link between mind and body, helping solve the mind/body problem.

3. Roger Penrose⁶ has cited as one of his objections to large extra dimensions that it would introduce just too much complexity. But we should be careful using Occam's Razor in this way. The examples of Copernicus, Einstein, and Hubbell should caution us against rejecting ideas simply because they seem preposterous or too complex. Moreover, Occam's Razor is only useful in selecting from a set of competing hypotheses, all of which explain the phenomena under consideration. In our case, we have no plausible field of candidate hypotheses.

In addition to answering those objections, we have direct evidence of the existence of extra dimensions. General Relativity has demonstrated that our 4D spacetime continuum is bent. A theorem⁷ from Differential Geometry tells us that a space cannot be bent unless it is an embedded manifold in a space of at least one higher dimension. QED.

THE MIND/BODY PROBLEM
The problem is in two parts. First is explaining a plausible communication link between the separate worlds of mind and body. Second is how processes in either world can cause effects in the other world without violating the laws of physics.

The communication link could be explained as propagation of perturbations in the field(s) associated with a force acting normal to our manifold as described above. Such a force may be coupled to an orthogonal force which acts in our manifold, similar to the coupling of the electric and magnetic forces used in our radio transmission. Obviously, this needs more work, but it seems plausible⁸ .

To avoid violating the laws of physics, we have already explained that the influences of the signal on the detection structures—the transponder in the brain—must stay under the HUP threshold. That would mean that the signal appears as seemingly random quantum outcomes when, in fact, information is carried by those outcomes. From there, Penrose and Hameroff⁹ have provided a plausible explanation for the consequent chain of events leading to physical action.

THE HOMUNCULUS PROBLEM
If consciousness is moved from the brain to X in a higher dimension, then how do we explain consciousness in X? Is it resident in some higher-order entity, say W, "above" X? And, if so, how do we avoid infinite regress?

Our answer is to reject the notion of infinity from mathematics altogether¹⁰ and accept the necessity of a finite set of Xs, which implies a single highest one. We replace infinite regress with a finite set of Matryoshka dolls. We will develop this idea more later, but for our purposes now, a 3-node hierarchy consisting of 1) a single X at a dimensional level above our 4D world, 2) our 4D brains, and 3) a human artifact at a lower level, described below, will suffice to complete our explanation. We will consider how the various components of consciousness might be distributed among these hierarchical nodes. (For an excellent proposal for how such a hierarchical structure might provide A Place for Consciousness, see Gregg Rosenberg's book¹¹ by that name. His proposal also provides an explanation for causality.)

THE EXPLANATORY SCENARIO
We begin by examining the relationship between X and a brain. We can use the analogy of a radio. The radio itself is the analog of the brain, the transmitting station is the analog of X, and the communication link between X and the brain is the analog of the EM radiation channel used by the radio and transmitter.

In this analogy, music coming from the radio is the analog of conscious experience. (Credit for this idea is due to Plato¹² for his analogy of the mind to the music of the lyre.) Some complications are revealed when we ask, "Exactly where is the music located?".

The answer is that it is smeared across several real components. Most proximal to the human listener are patterns in brain states in the auditory regions of the brain, the cortex, and wherever else. Just prior to that, the music existed as patterns in the movements of structures involved in hearing (eardrum, cochlear hairs, etc.), and prior to that as vibrational patterns in the air, then as movements in the radio's speaker, and next as patterns in the flow of electrons in the radio's circuits. Prior to that, the music exists as patterns in the frequency and amplitude of the EM radiation, then in electronic patterns in the transmitter, and so on until we reach the minds of the musicians who performed the music.

The radio is complex, but completely understandable and plausible. We should expect similar complexity and plausibility in the consciousness analog. The analogy suggests that consciousness is similarly smeared across the brain, X, and the communication link between them, muddying the question of exactly where consciousness resides.

As complex as this analogy is, we need to expand it still further to make it more accurate and complete. The traffic between brain and X needs to be 2-way, and we would like the brain and X to reside in completely different worlds. To achieve that, we expand the radio analogy to place the radio inside a Mars Rover and to place the transmitting station in JPL.

The radio traffic is now two-way allowing for information from Mars to be received at JPL as well as for willful commands to be transmitted back to the Rover. The willful commands result in physical and behavioral changes in the Rover that are analogous to conscious acts of free will in humans.

Now let's review our general question in a little more detail. We paraphrase the question using our Rover analogy: "How can mindless mathematical laws, and the mindless design specifications of the Rover, give rise to the obvious (to a parochial Martian observer) aims and intentions of Spirit or Opportunity?" In short, how did the rover come to be and how can it carry out aims and intentions? We know the answer.

The answer is that a colluding group of conscious scientists and engineers at JPL took on the project and carried it out. Together, they applied the laws of physics and geometry to design the rover system. They used their conscious wills to cause their bodies to move in such ways as to cause the construction of the many artifacts that eventually resulted in the launching of a successful Mars rover and its resulting activity on Mars. Until the launch, all the activity was strictly resident on Earth. Mars was out of the picture. Once the rover landed, however, it made its appearance on Mars and began behaving in a seemingly autonomous and intentional way.

From that point on, the rover could only behave strictly per the laws of physics (on Mars). Its behavior could be controlled to a certain extent by the JPL scientists but only via signals to its on-board computers across a communication link that is also bound by the laws of physics.

A parochial Martian, observing the Rover and knowing nothing of JPL or life on Earth, would conclude that this alien machine is conscious and that it deliberately goes about selecting sites, moving to them, drilling holes, collecting samples, etc. Obviously, the Rover has some aims and intentions, but to the Martian, even if he/she/it could completely analyze the physical components of the rover and understand all its physical and electronic structure and behavior (except for radio transmission and reception), the question of what gives rise to those aims and intentions would be a complete mystery.

We humans who have existed more recently than the 19th century could provide the puzzled Martians with a perfectly understandable and plausible explanation, which we have just gone through. But our explanation would be neither plausible nor understandable to, say, Isaac Newton, René Descartes, Plato, or any other brilliant person who lived prior to Maxwell, without them learning much of what we now know. We are fortunate to have the huge advantage we do. We should take advantage of it.

Having developed this story of Mars rovers, we will put it to two different uses. First, we will continue to use the rover as an analog for the human brain-body in our rover analogy. Secondly, we will use the rover as a player in part of the hierarchy of entities we need to explore.

We encountered that hierarchy when we discussed the homunculus problem. Starting with the 2-node hierarchy of a brain being subordinate to X, we speculated that there might be another node in that same relationship above X. We called it W.

Continuing that line of speculation, we would have V above W, U above V, and so on. And, as I briefly mentioned, to avoid infinite regress, we agree to stop at some point, say when we run out of letters, and we then have a top node, we'll call it "A". We have no good reason for settling on any particular number of such nodes except that it must be finite which means that there must be a top node: A. It is interesting that Plato¹³ guessed at the number as being 11 and string theorists guess at numbers ranging from 6 to 26, or so, 11 being one of their favorites too.

The premise is that each of these nodes is somehow responsible for the design, construction, and initiation of the node(s) below. Following this premise, the Mars rover fits right into the hierarchy directly under the human brain node. The rover was conceived, designed, constructed, and sent on its mission by the action of humans-with-brains. And, with our hypothesis, the necessary conscious component was supplied by X in a third node residing in yet another world outside Mars and Earth.

For the moment, we will ignore the nodes from A to W and just concentrate on the lower three: X, brain, and rover. We know a great deal about how the "general features—like information processing, computation, learning, complexity thresholds, and/or departures from equilibrium—allow (or proscribe) [the] agency"¹⁴ exhibited by the rover. We know the role played by the JPL scientists, the rover they built, the radio link between them, and how they work together to provide the rover with the ability to pursue the aims and intentions of...the JPL scientists. Manifestations of those aims and intentions may be found in the onboard computers in the rover and in documentation on JPL bookshelves, but they originated in the minds of the JPL scientists. Which means that they really belong up in X.

HINTS TOWARD AN UNDERSTANDING OF COSMOGONY
In our acceptance of large extra dimensions, we have a lot more to explain concerning the origin of reality than simply explaining the origin of the Big Bang. We have already explained that origin, now we need to explain all that extra space-time and, harder yet, we need to explain A through X. A tall order.

In an acceptable cosmogony, we would like the simplest conceivable origin. Following our premises, A is ultimately responsible for the origination of B and everything else in reality that followed. So, we need to focus on A and explain how it could be ultimately simple yet be responsible for the origination of everything else in reality.

In order to keep A ultimately simple, we can ascribe no magic powers or extremely unlikely initial conditions. A is nobody's God! Even the experience of consciousness itself is too complex to be lodged in A. A must not only be ultimately simple, but unconscious as well. This seems to contradict our premises that led to the hierarchy in the first place. The remedy is in the "smearing". Somehow, consciousness must diminish as you ascend the hierarchy from X to A so that it vanishes at the top.

A simple thought experiment suggests how this might happen. Using one example from our list of consciousness components, knowledge, think about something that you know. For example, I know that there is a cat on my lap. Then consider the following propositions: I know that. I know that I know that. I know that I know that I know that. I know that I know...that I know that.

If you carry this thought experiment out only a few propositions, it becomes clear that the longer the string, the less you can be sure it is true. You really don't know that the assertion is true unless you specifically think about it and realize that yes, you do know that you know that you know, etc. You are most sure about the first assertion: that you know that there is a cat on your lap. The conscious component of knowing seems to diminish as you ascend the hierarchy and we suppose it has vanished by the time you reach A.

Now think about who those personal pronouns refer to. Each of the propositions expresses a fact about a conscious experience. According to our theory, the first proposition expresses the experience of having a cat on my lap. Therefore, since "my" consciousness is located in X, the first "I" refers to X. But since the second proposition is about knowledge of X, the second "I" refers to W, and so on up the hierarchy.

That sort of smearing would imply that there may be some component of consciousness in the physical brain after all, and that there may even be a trace of it in the rover. To examine that more closely we would need to tease apart the components of consciousness. We could start with our list of possible components that we mentioned at the beginning of this essay. Then we would have to ask how are they attenuated and then how might they be distributed among the nodes of our (or Rosenberg's) hierarchy. We have just done that with the example of knowledge.

As another example, consider memory in the context of the rover, JPL, and X. Consider the information in the various memories. The rover's memory, which is part of its on-board computers, is large, maybe on the order of terabytes. and it is extremely fast. Much of its contents might be shipped up to the JPL computers, but maybe not all. Even so, the capacity at JPL probably exceeds that of the rover, but that is in the computers at JPL. The capacity of the brains of the scientists is much smaller and the speed is much slower. The memory in X is probably closer to that of the brain than of the computers. That is, in the minds of the JPL scientists, there is only a small fraction of the information that exists in the computers. Instead there are only fleeting recollections of images of the information that has been viewed by the scientists. So the memory component seems to diminish as you go up.

Another component, concepts, on the other hand, makes little to no appearance in the rover. Concepts appear in JPL as sentences and drawings in various forms within the lab and as fleeting structures in the brains of the scientists, but in X, the consciousnesses of the scientists, they are most acute.

We can't go through the components of consciousness one by one in this short essay, but it seems that most of them exist on a spectrum ranging from acute, intense, or vivid at one end, over to the other end where they are dull, dim, or nonexistent, just as knowing seemed to do in our thought experiment.

Using those examples, and realizing that the distribution up and down the hierarchy needn't be monotonic, it is possible that all the components eventually diminish as you ascend the hierarchy so that the result is that A is left nearly vacant and ultimately simple. It is as if The Wizard of Oz were divinely inspired.

So where, exactly, does consciousness reside? We can refine our answer to say that it is relative to who is asking. From our human point of view, it is smeared from our artifacts, to structures in our brain, up to X, and maybe beyond, but it is most acute in X. If we extrapolate to nodes higher up in our hierarchy, say node M, we would say that consciousness at that level would be smeared from its artifacts at level L, to structures in the level of M, up to N, and beyond, but it is most acute in N.

But that can't be. It would imply that most consciousness would end up in A after all. We must be missing something.

What we are missing is the "illusion" that so many commentators mention in connection with consciousness. To even talk about "illusion" we must acknowledge that illusion is a deception, and that for a deception to exist, there must be someone/something that is deceived. And just who/what is that?

We can make sense of that by considering the bottom two nodes of our 3-node case: the JPL scientist and the rover.

Someday, likely soon, when the computers in the rover are upgraded to levels that can pass the Turing Test and are as smart as Watson, the JPL scientist may get so engrossed in the vicarious experiences of operating the rover, that he/she (the scientist) will come to believe that he/she actually is on board that rover and actually is on Mars. When it is lunchtime and the scientist's colleague shakes him/her by the shoulder and breaks the spell, the scientist will seem to have just awoken from a dream and realized that he/she was not on Mars at all.

So, who experienced the illusion? Well, that experience, like all others was smeared from the rover, to the scientist, to X. And what it means is that the actual experience of consciousness may be bottom-heavy, leaving little or none of it to ascribe to W and the nodes higher up. Without knowing anything about those higher nodes, we can at least imagine that there is some distribution pattern that leaves A simple and unconscious.

SUMMARY AND CONCLUSION
The major changes required to our thinking about our world in order to accept this proposal are the same as those that were required to accept the proposals of Copernicus and Hubble. We need to acknowledge that our world, or galaxy, is not unique but instead one of many similar worlds, or galaxies. Our 4D spacetime continuum, the traditional domain of science, is not the whole picture.

We need to accept the reality of additional temporal dimensions. By doing so, we understand that the temporal dimension in which X operates is separate and distinct from the temporal dimension established by the continuing increase of entropy in our 4D manifold beginning with our Big Bang. From X's point of view, our temporal dimension appears as just another spatial dimension so that our entire 4D "universe" is spread out and exists at once along its temporal axis just as Brian Greene¹⁵ described in his "loaf of bread" picture. By extending our thinking in this way, some difficult questions begin to make sense.

For example, the connections between goals, and their pursuit, are linked one-for-one with the arrows of time in the several different temporal dimensions. The goals harbored by X, for example, are pursued in that "cosmic" time spectrum in which X does the math and establishes the various worlds, among which is our Big Bang "universe". The goals seemingly harbored by us humans, on the other hand, are pursued along our temporal axis and make progress measured and marked by our familiar clocks and calendars. One level below that, is the artificial temporal axis defined by the progress of the execution of a program running in one of our computers.

Whether we attribute any aspects of consciousness to the computer or not, the temporal axis defined by the sequential execution of instructions in the machine may not coincide with our familiar temporal dimension. The computer, for example, may be stopped for a while, or its speed of execution may vary, or it may be restarted back at an earlier point in the instruction stream.

The important cosmological effect here is that in the big picture and in a higher temporal dimension, aims and intentions precede the invention/discovery of mathematics, which in turn, precede the appearance of biology.

That makes it easy to understand some questions, for example how physical systems that pursue the goal of reproduction arose from an abiological world: The abiological world contained X, which deliberately designed and constructed the abiological world of our Big Bang, which in turn evolved to produce the complex structures of life, with some possible yet-to-be-understood nudging by X along the way. That is fairly straightforward.

Some questions, by contrast, become more complex in this context. The question of how to define, ascribe, and measure intelligence becomes an obscure semantic one. It depends on who/what is doing the defining. In addition, the definition of 'intelligence' becomes more ambiguous. For example, we may or may not choose to consider Watson to be intelligent. Or the Turing Test may or may not be useful in measuring the separation of intelligent vs. non-intelligent systems. And at this point in our understanding, we cannot precisely nail down the difference in intelligence between our human brains and X.

Similarly, the question of causality becomes more complex in this scenario. Causality is at work independently in worlds such as our 4D manifold and it is presumably at work, albeit differently, in the hyper-dimensional worlds of X, and higher. As I mentioned, Greg Rosenberg has offered a promising start in understanding the relationship between causality and consciousness which goes beyond the scope of this essay.

Finally, based on the proposal described in this essay, goal-oriented behavior is an imperative cosmic trend steered along its path by the various manifestations of consciousness as they appear from nothing at the very beginning, to successive and various seemingly conscious vehicles remotely operated by seemingly more-conscious designers and builders of those vehicles.

______________________________

1 Chalmers, David J., The Conscious Mind: In Search of a Fundamental Theory (Oxford University Press, 1996) pp. 161-162. See my notes .

2 Stafford, Richard D. Ph.D., has proved what seems to be a theorem which solves Hilbert's 6th problem. If true, he has proven that consistency and mathematics alone imply the laws of physics. His theorem is a differential equation whose solutions include Schrödinger's wave equation, and Maxwell's and Einstein's field equations. His book, The Foundations of Physical Reality, is available on Amazon.com. You may read my interpretation of his result here.

3 See my essay "On the Origin of the Genetic Code"".

4 Crick, Francis C. and Koch, Christof, "What is the Function of the Claustrum?", Philosophical Transactions B, The Royal Society, London, 2005 June 29,

5 See my essay "On Seeing Extra Dimensions" for examples of scientists citing the "hosepipe analogy".

6 Penrose, Roger, from a lecture in Seattle, 2/23/05: "Extra dimensions are likely to be unstable...Extra dimensions are a problem if they are dynamical...Extra degrees of freedom cause trouble."

7 I distinctly remember watching spellbound in a Differential Geometry class 50 years ago, as the professor proved the theorem on the blackboard in front of us. (I think the professor was Gerald Cargo of Syracuse University, but I can't be sure.) To my continuing dismay, all my efforts to find a reference to this "mystery theorem", beginning 20 years after the fact, have been in vain. Yet the "theorem" seems obviously to be true: It says that you can't bend a sheet of paper while it remains lying on a tabletop.

8 Greene, Brian The Fabric of the Cosmos: Space, Time, and the Texture of Reality (Alfred A. Knopf, New York 2004) T. Kaluza showed that 5 dimensions unifies gravity and electromagnetism. p. 382. See my notes

9 Sir Roger Penrose, Stuart Hameroff, M.D., Consciousness and the Universe: Quantum Physics, Evolution, Brain & Mind (Journal of Cosmology, Vol. 14, Cosmology Science Publishers, 2011) "Microtubules as Biomolecular Computers", pp. 5-10 See my notes.

10 See my essay "An Introduction to Practical Numbers" for a proposal for eliminating the concept of infinity from mathematics.

11 Rosenberg, Gregg A Place for Consciousness: Probing the Deep Structure of the Natural World. (Oxford University Press, New York, 2004) See my notes.

12 Plato, "Phaedo", Soul compared to the lyre.

13 Jowett, B., trans. The Dialogues of Plato (Oxford: The Clarendon Press, 1871), "Phaedrus", "Zeus, the mighty lord, holding the reins of a winged chariot, leads the way in heaven, ordering all and taking care of all; and there follows him the array of gods and demi-gods, marshalled in eleven bands;..."

14 Quoted from the rules of the FQXi essay contest.

15 Greene, Brian The Fabric of the Cosmos: Space, Time, and the Texture of Reality (Alfred A. Knopf, New York 2004) Loaf of Bread pp. 132-138. See my notes