#30. The Russian-dolls--multiverse Part I [physics]

Matryoshka/pupa

PH

Red, theory; black, fact.

The nucleus around which a TOE will hopefully crystallize.

6-03-2017

I usually assume in these pages that the space we live in has an absolute frame of reference, as Newton taught, and which Einstein taught against. Not only that, but that this frame of reference is a condensate of some sort, rather like the water that a fish swims in.

I also assume that the divide-and-conquer strategy that has served science so well thus far can blithely continue with the (conceptual) dis assembly of this space into its constituent particles. At that point the question arises if these particles are situated in yet another space, older and larger than ours, or if you go direct to spacelessness, where entities have to be treated like Platonic forms. In the former case, one wonders if that older, larger space in turn comes apart into particles situated in a still older and larger, etc, etc, ad infinitum.

I am told that infinities are the death of theories. Nevertheless, let us hold our noses and continue with the Russian Dolls idea, merely assuming that the nesting sequence is not infinite and will not be infinite until the entire multi verse is infinitely old, because the "dolls" form one by one, by ordinary gravitational collapse, from the outside in.

What, exactly, is it that collapses? Call them wave functions, following quantum mechanics. In the previous post, we see that wave functions are slightly particle-like in having a centre of symmetry. In the outermost space, previously called #, the wave crests always move at exactly the speed of light.

7-14-2017

This speed is not necessarily our speed of light, c, but more likely some vastly greater value.

6-03-2017

The space-forming particles of # are themselves aggregates with enough internal entropy to represent integers and enough secondary valences to form links to a set of nearest neighbors to produce a network that is a space. This space acts like a cellular automaton, with signals passing over the links to change the values of the stored integers in some orderly way. The wave functions are the stereotyped, stable figures that spontaneously develop in the automaton out of the initial noise mass left over from catastrophic gravitational collapse, or some abstract, spaceless equivalent. 

Gravity would enter as a geometric effect; impossible at 1D, poorly developed at 2D, commonplace but commonly stalled at extended systems in 3D, and irresistible at 4D and higher (The latter conclusion is based on an anthropic argument in "The Universe in a Nutshell", by Steven Hawking). 

Finally, assume that the dimensionality of a space increases steadily over time, suggesting that the number of links emanating from each node in the underlying network increases slowly but surely. Macroscopically, this dimensionality increase could look something like protein folding. This does not yet explain gravity, a task for another day&&, but static nonlinearities in the automaton's representation system may be involved.*

To facilitate discussion, let us label the Russian-dolls universes from the outside in, in the sequence 1, 2, 3,...etc, and call this number the "pupacity" of a given frame of reference. (From the Latin "pupa," meaning "doll.") Let us further shorten "pupacity" to "p" for symbol-compounding purposes. Thus, the consecutively labelled spaces can be referred to as p1 (our former "#"), p2, p3,... etc.

A final, absolutely crucial assumption is that pn can exhibit global motions ("n" is some arbitrary pupacity), such as rotation, in the frame of reference of p(n-1). Yes, we are talking here about a whole, damned universe rotating as a rigid unit. Probably, it can drift and vibrate as well.

Now, by the assumptions of the previous post, these global motions must be subtracted from the true, outer, speed-of-light speed of the wave crest to produce its apparent speed and direction when seen from within pn. Thus, the universe's love of spinning and orbiting systems of all sizes is explained: a spinning, global-motion vector is being subtracted from the non-spinning, outermost one. As the0-pupacity of our frame of reference increases, more and more of these global vectors are being subtracted, causing the residual apparent motion to get progressively smaller. We would assume under current physics that the wave functions are acquiring more and more mass, to make them go slower and slower, but mass is just a fiction in the scenario presented above. However, the reliance of current physics on the mass construct is a golden opportunity to determine the pupacity of planet Earth.

It is three.

Three, because physics knows of three broad categories of particle mass: the photon, leptons, and baryons. The photon would be native to p1, leptons, such as electrons and positrons, would be native to p2, and baryons, such as protons and neutrons, would be native to p3, our own, dear home in the heavens. 

01-09-2019: it is an interesting coincidence that our pupacity equals the dimensionality of our space. Are dimensionality and pupacity linked during cosmological evolution?&&

6-03-2017

Some interpretations follow. The positron atom would be a standing-wave pattern made up of oppositely rotating wave functions, an electron and a positron, both native to p2. A neutron would be exactly the same thing, but native to p3. Note that both are unstable in isolation.

How is it that we observers in p3 can even detect electrons, say, if those are not native to p3? Because p2 is necessarily older than p3 and has had more time to develop extra dimensions. This will give p3 thin dimensions when seen in the frame of reference of p2, and it is along these thin dimensions that the electrons of p2 approach our own, native protons closely enough to participate in our p3 physics.

Neutron stars would be p4, but I haven't figured out black holes. Just big p4s?

*6-05-2017

or an amplitude-speed coupling.

#29. My Second Theory of Everything [physics]

PH

Red, theory; black, fact.

This post comes from considering how wavelike, low-frequency light becomes particle-like, high-frequency light as frequency is smoothly increased. Waves are continuous, whereas particles are discontinuous; how, then, does the breakup occur?

You have to put the source in the picture. Recoil of the source atom sends the wave function off in a specific direction, but the wave function is known to expand (about its center of symmetry?) as it goes. Presumably, it is the vector sum of these two motions that must equal the speed of light; either one is presumably free to take on some lower speed, say, that of a pitched softball. I conjecture that as frequency increases, the particle-like drift of the center progressively dominates the mixture at the expense of the local, wave-like expansion of the wave function about its center. This is how I see waves morphing into particles as the frequency increases. 

These ideas suggest the existence of a unique, watershed frequency at which both motions are equal, and equal to one-half the speed of light when the vectors are aligned. I suspect that this frequency lies in the terahertz range, between radar frequencies and the far infrared, partly on the basis that this seems to be the last part of the electromagnetic spectrum to find technological use. The non-dominance of either the particle or the wave model in this range may translate into a perfect storm of undesirable properties. That comment about the softball, however, suggests the possible existence of easy, classroom experiments with these frequencies that illustrate wave-particle duality.

These considerations brought me to the following set of TOE assumptions, some from relativity theory, some in apparent contradiction of it, and some from quantum mechanics:

• There is an absolute frame-of-reference, which I shall call "#."
• All motions seen in this frame of reference will be observed to occur at the speed of light (c); no more, but no less, and only this frame of reference has this property.
• All speeds lower than c are illusions caused by the motion of the observer's frame of reference.
• That which moves always at c is not a wave function, but a phase marker of some sort within it, such as a zero crossing or a wave crest.
• The local wave function evolution relative to its center of symmetry combined with the drift of that center relative to # always travels at c relative to #.
• If local evolution is an expansion along all wave function radii, you have light; if it is a rotation about the center of symmetry (i.e., motion perpendicular to radii), you have matter.
• Light wave functions will be like nested spherical shells, whereas matter wave functions will have a lobar, angle-dependent structure like a p-, d-, or f-orbital in theoretical chemistry. The lobes are essential to provide a contrast pattern that could, in principle, be observed to spin.
• The presence of one axis of rotation produces the neutrino; two simultaneous axes of rotation produce the mesons; three produce the remaining stable particles, e, p, and n. If the three rotational rates are distinguishable, the resulting structure has a handedness.
• The matter/antimatter dichotomy arises from this handedness, when combined with a law of conservation of spin that would result from space initially being symmetrical. 
• The mesons should have an ability in 3-space to flip over into their corresponding antiparticles.

#28. The Origin of Consciousness [neuroscience]

NE

Red, theory; black, fact.

After perusing Gideon Rosenblatt's blog at the prompting of Google, I finally saw the need for this post.

I theorize that we begin life conscious only of our own emotions. Then the process of classical conditioning, first studied in animals, brings more and more of our environment into the circle of our consciousness, causing the contents of consciousness to become enriched in spatial and temporal detail. Thus, you are now able to be conscious of these words of mine on the screen. However, each stroke of each letter of each word of mine that now reaches your consciousness does so because, subjectively, it is "made of" pure emotion, and that emotion is yours.

Some analogies come to mind. Emotion as the molten tin that the typesetter pours into the mold, the casting process being classical conditioning and the copy the environmental data reported by our sense organs. Emotion as the bulk on one side of a fractal line and sensory data the bulk on the other side. Emotion as an intricately ramifying tree-like structure by which sensory details can send excitation down to the hypothalamus at the root and thus enter consciousness.

The status of "in consciousness" can in principle affect the cerebral cortex via the projections to cortex from the histaminergic tuberomamillary nucleus of the hypothalamus. Histamine is known to have an alerting effect on cortex, but to call it "alerting" may be to grossly undersell its significance. It may carry a consolidation signal  for declarative, episodic, and flash memory. Not for a second do I suppose all of that to be packed into the hippocampus, rather than being located in the only logical place for it: the vast expanse of the human cerebral cortex.

#27. Why Organized Religion? Theory Two [evolutionary psychology]

EP

Red, theory; black, fact.

My last post about proxy natural selection (PNS) has directed me to emphasize emotion more in seeking explanations for human behavior. I now think of emotions as an "endophenotype," to use a term from functional magnetic resonance imaging, that provides a useful stepping stone from evolutionary arguments to explanations of our daily lives. I recently applied this insight to obtaining a second explanation of religion, alternative or parallel to the first one that I give in a previous post.

What is the mood or feel as you enter a place of worship and participate in the ceremonies conducted there? More than anything else, the mood is one of great reverence, as though one is in the presence of the world's most powerful king. Kings are supposed to "represent their race." However, I want to translate that statement into a sociobiological function assignment. My discussion "Proxy Natural Selection from the Inside" suggests a problem: if the emotional outlines of people's behavior is being partly randomized in each generation by recombination-type mutations, a consistent moral code seems impossible if we assume that morality comes mostly from peoples' inborn patterns of emotional reactivity, that is, the sum total of everyones' betes noir. The purpose of a king may be to find or at least coincide with societies' moral center of gravity, around which a formal, if temporary, moral code can be constructed. In a complex society, everyone must be "on the same page" for efficient interaction. 

The same problem no doubt recurs each time organisms come together to form a colony, or super-organism: the conflict between the need of a colony for coordination of colonists and the need of evolution for random variability. Such variability will inevitably affect the formulation and interpretation of the coordinating messages that the colonists exchange, like all their other inborn characteristics. 

Kingship comes the corrupting influence of personal power, leading to destructive, tyrannical governments. Replacing a real king with a pretend-king named "God" would seem to be the solution that accounts for organized religion, but then one loses all flexibility, the flexibility that goes with having a flesh-and-blood king who can change his predecessor's laws based on current popular sentiment.

However, human nature may well have a core-and-shell structure, with an "unchanging" core surrounded by a slowly changing shell. The former would be the species-specific objective function previously alluded to in post #16, and produced by species-replacement group selection within the genus, and the latter would be due to PNS, and would represent the stratagems hit upon by our ancestors to meet the demands of the objective function in our time and place. This shell part may account for cultural differences between countries. The core may be implemented in the hypothalamus of the brain, whereas the shell may be implemented in the limbic system. The core, being unchanging, could be taught by organized religion, whereas the shell could be codified by the more flexible institution of government. Though the core is unchanging overall, specific individuals will harbor variations in it due to point mutations (not part of PNS), necessitating the standardizing role of religion. Synaptic plasticity would then be used to cancel the point-mutational variation in the objective function.

This core  consists of four pillars, or themes: genetic diversity, memetic diversity, altruism, and dispersal. Our energetic investment in obtaining each item is to be optimized. To produce this, the church of my acquaintance is continually emphasizing, respectively, tolerance, creating beautiful things, charity, and justice. It's almost too neat, especially if we adopt the deeply cynical-sounding position that the demand for "justice" only polarizes groups to the point of schism and diaspora.

#26. The Phasiverse [physics]

PH

Red, theory; black, fact.

The nucleus around which a TOE will hopefully crystallize.

3-29-2017

I will be arguing here that our reality, the world of appearances, is encoded in the relative phases of an ineffably large number of oscillators, each of which is a kind of primitive clock.

An early interpretation of the theory of quantum mechanics was that there is a harmonic oscillator somehow assigned to each point in space, and that these account for the matter fields of the universe. Examples of such oscillators (the definition is abstract and mathematical), unsuitable for easy, weekend universe creation, would be masses bouncing up and down on springs, and electronic devices called tank circuits, which are just one capacitor connected across the terminals of one inductor, plus taps on the inductor for getting the energy in. (I am thinking here of the Hartley oscillator, of which I built half a dozen as a teenager.)

If a bunch of such oscillators can communicate with each other (exchange oscillatory energy), this is called coupling, and it can make the oscillators tend to pull each other in to the same, common phase. The Huygens's clocks experiment begins with two old-school pendulum clocks in a case with their pendulums swinging in some random phase relationship. The next day,  mysteriously, the pendulums will always be found swinging in opposite directions. The coupling is evidently due to tiny, rhythmic forces travelling through the common case from clock to clock.

If the coupling is positive, as assumed here, (it's negative in the above experiment), the phase pull-in effect becomes stronger the closer the two phases approach each other, causing a positive feedback effect. This is very reminiscent of Hebb's rule in neuroscience and the tendency of natural attractive forces such as gravity to depend inversely on distance. I have already offered Hebb's rule in these pages as an abstract rule of attraction and binding in a scheme for polymerizing spaceless but noisy "time lines" into a three dimensional network that approximates the space we live in. However, oscillators make better space-forming entities than these "time lines" on a number of counts.

First of all, the phase pull-in effect alluded to above provides a simple answer to questions such as where the organizing principle comes from. All you need to explain is where the oscillators themselves all came from, how they oscillate, and why they are coupled. Since the oscillators begin life in spacelessness, it is hard to see how they could avoid interacting to produce a coupling effect. Second, oscillators need no past or future; they can arise as a succession of causally related nows that alternates between two contrasting forms. (Since we haven't gotten as far as space yet, these would have to be abstract, spaceless entities that smack of yin and yang.) Figures in Conway's game of Life would seem to be examples of this alternation.

What is the time required for such an alternation? The question is meaningless; they just do it. With no past or future, the special status of the present becomes self-explanatory, alleviating some of the cognitive dissonance that goes with the concept of a unified space-time. This space-time, and the even more bizarre idea that it is warped by mass-energy as if embedded in an even higher-dimensional space, starts to look like a device to visualize one's way to solutions to problems that have their origin in unvisualizable spacelessness.

A great many oscillators all with the same phase is not an interesting universe. However, suppose this is impossible because of "train wrecks" happening during the synchronization process that produce frustration of the synchronization analogous to spin frustration in spin glasses. An example would be a cyclic relationship of oscillators in which a wave goes around the loop endlessly. Such cycles may correspond to particles of matter in our universe, and the spiral waves that they would throw off into surrounding space may correspond to the fields around such particles.

A black hole or galaxy would be surrounded by a tremendous number of such radiating fields. The resulting desychronization of the oscillators making up the surrounding space would increase the average phase difference between phasically nearby oscillators, thereby inhibiting their coupling, thereby inhibiting the travel of signals generally through the region. Result: the speed of light is reduced in the vicinity, resulting in the bending of light rays, called gravitational lensing. Notice how easily we derive an effect that formerly required General Relativity.

The next level of description deals with where the oscillators come from.

4-23-2017

Let us jettison the particle model altogether at this point and assume the universe to be made of the waves themselves, with no need for generating objects. These waves might have a tendency to synchronize as a fundamental given. If it is not fundamental, maybe the explanation for it can safely be left to a future generation of physicists. (The image I get at this point is of a series of temporary camps struck during the ascent of some stupendous mountain, for step-wise consolidation of gains, with the grail of the TOE located at the summit.)

As a second thread of this argument, I note that some of the phenomena characteristic of quantum theory can be explained as due to the practicalities of representing functions like waves, practicalities that are always in your face when programming a computer, but never mentioned in the physics I have read so far. In programming, you have to define memory space for all variables, which is always, ultimately, an integer or a set of integers, with both a maximum and a minimum (nonzero) amount that can be represented.

Quantization could be due to the presence of small quantities comparable in size to the value of the least significant bit of an integer-like entity. (Deprecated, Part 4)

#25. Proxy Natural Selection from the Inside [evolutionary psychology, genetics]

EP    GE    

Red, theory; black, fact.

My first post on proxy natural selection (PNS) left open some questions, such as what it should feel like, if anything, when one is fulfilling the species objective function and being deemed "proxy-fit" by one's own hypothalamus.

I conclude that it's just what you would think: you feel joy and/or serenity. Joy is one of Ekman's six basic universal human emotions, the others being fear, anger, disgust, sadness, and surprise. I think that emotions collectively are the operations of the highest-level human behavioral program. (That is, the program in its broadest outlines.) The unpleasant emotions force you to get off the couch until they are taken care of, and joy lets you get back on. Thus, the unpleasant four are the starting emotions, and joy is the stopping emotion. 

Surprise may be a meta-emotion that tells you that your threshold for experiencing one of the other emotions is too high, and immediately lowers it. I also think that each activation of an emotion tends to lower the threshold for activating it next time, which implies a positive feedback loop capable of changing the personality to suit suddenly changed circumstances, especially if the emotion eventually begins issuing with no trigger at all.

To relate this to the mechanism of PNS, the crossing-over events that went into making the sperm cell that made you would theoretically affect brain development more than anything else, specifically connecting some random stimulus to one of the unpleasant primary emotions. This creates your temperament, and thus your personality, which is the unique quality which you have to offer the world, and on which you are being tested by history. If the actions to which your own, special bete noir propel you are what the species objective function is looking for, you succeed, feel joy and serenity, and experience an altered methylation status of the DNA in your spermatogonia, if you are male, which (I conjecture) suppresses further crossing over in the manufacture of your own sperm, so that your personality type breeds true, which is what the population needs. 

PNS is quickie evolution to respond to challenges that come and go on less than a multi-thousand generation timescale, and I conjecture that it explains the complexities of sexual reproduction. You may object that trees, for example, have no behavior, much less personalities, and yet they have sexual reproduction. However, trees probably adapt quickly not by behavioral change, but by changes in their chemistry. The chemistry in question would be the synthesis of pesticidal mixtures located in the central vacuole of each plant cell. In terms of such mixtures, each tree should be slightly unique, an easily testable prediction.

Here is my own self-analysis in terms of PNS theory. My special emotional novelty that is potentially my gift to the world is a morbid fear of social rejection. This has motivated much more than the usual self-criticism of my own creative productions before they are communicated to others, for fear of rejection, leading to the kind of thing you are now reading. Social rejection/criticism hits me like a wall of flame that burns for days, or like some kind of rays coming out of the other person's head. The rejection that goes with the dating game has made it intolerable to me, leading to a lifelong celibacy that has freed all my resources for scientific pursuits. 

My father was a general in the Canadian Armed Forces, and was most unlike this, but my older brother takes after him somewhat. What happened to sour my father's life so radically before my birth in 1953, so that his recombinotype (coined word) no longer bred true? I conjecture that it was the failure of the defeat of Nazi Germany to produce a true, lasting peace, only ushering in the nuclear cold war with the USSR. With this, "God" was telling us: "Don't study war no more."

Each of the four unpleasant "starting" emotions may sub serve one of the four pillars of the species objective function already listed in The intermind: Engine of History?. Thus: sadness, altruism; disgust, genetic diversity (due to point mutations; what is motivated here is the screening of such novelties, screening always being the expensive part); fear, memetic diversity (or motivating prescreening of memetic novelties); anger, dispersal. Each of these emotions seems to have another use, in preserving the life of the individual, as opposed to the entire species. Thus: sadness, unfavorable energy balance; disgust, steering one away from concentrations of harmful bacteria; fear, avoidance of injury and death; anger, driving away competitors for food and mates. 

#24. The Pictures in Your Head [neuroscience]

NE

Red, theory; black, fact.

My post on the thalamus suggests that in thinking about the brain, we should maintain a sharp distinction between temporal information (signals most usefully plotted against time) and spatial information (signals most usefully plotted against space). Remember that the theory of General Relativity, which posits a unified space-time, applies only to energy and distance scales far from the quotidian.

In the thalamus post, I theorized about how the brain could tremendously data-compress temporal information using the Laplace transform, by which a continuous time function, classically containing an infinite number of points, can be re-represented as a mere handful of summarizing points called poles and zeroes, scattered on a two-dimensional plot called the complex frequency plane. Infinity down to a handful. Pretty good data compression, I'd say. The brain will tend to evolve data-compression schemes if these reduce the number of neurons needed for processing (I hereby assume that they always do), because neurons are metabolically expensive to maintain and evolution favors parsimony in the use of metabolic energy.

Ultimately, the efficiency of the Laplace transform seems to come from the fact that naturally-occurring time functions tend to be pretty stereotyped and repetitious: a branch nodding in the wind, leaves on it oscillating independently and more rapidly, the whole performance decaying exponentially to stillness with each calming of the wind; an iceberg calving discontinuously into the sea; astronomical cycles of perfect regularity; and a bacterial population growing exponentially, then shifting gears to a regime of ever-slowing growth as resources become limiting, the whole sequence following what is called a logistic curve.

Nature is very often described by differential equations, such as Maxwell's equations, those of General Relativity, and Schrodinger's Equation, the three greats. Other differential equations describe growth and decay processes, oscillations, diffusion, and passive but non-chemically energy-storing electrical and mechanical systems. A differential equation is one that contains at least one symbol representing the rate of change of a first variable versus a second variable. Moreover, differential equations seem to be relatively easy to derive from theories. The challenge is to solve the equation, not for a single number, but for a whole function that gives the actual value of the first variable versus the second variable, for purposes of making quantitative, testable predictions, thereby allowing testing of the theory itself. The Laplace transform greatly facilitates the solution of many of science's temporal differential equations, and these solutions are remarkably few and stereotyped: oscillations, growth/decay curves, and simple sums, magnifications, and/or products of these. Clearly, the complexity of the world comes not from its temporal information, but from it's spatial information. However, spatial regularities that might be exploited for spatial data compression are weaker than in the temporal case.

The main regularity in the spatial domain seems to be hierarchical clustering. For an example of this, let's return to the nodding branch. Petioles, veins, and teeth cluster to form a leaf. Leaves and twigs cluster to form a branch. Branches and trunk cluster to form a tree. Trees cluster to form a forest. This spatially clustered aspect of reality is being exploited currently in an approach to machine intelligence called "deep learning," where the successive stages in the hierarchy of the data are learned by successive hidden layers of simulated neurons in a neural net. Data is processed as it passes through the stack of layers, with successive layers learning to recognize successively larger clusters, representing these to the next layer as symbols simplified to aid further cluster recognition. This technology is based on discoveries about how the mammalian visual system operates. (For the seminal paper in the latter field, see Hubel and Wiesel, Journal of Physiology, 1959, 148[3], pp 574-591.)

Visual information passes successively through visual areas Brodmann 17, 18, and 19, with receptive fields becoming progressively larger and more complex, as would be expected from a hierarchical process of cluster recognition. The latter two areas, 18 and 19, are classed as association cortex, of which humans have the greatest amount of any primate. However, cluster recognition requires the use of neuron specialist sub-types, each looking for a very particular stimulus. To even cover most of the cluster-type possibilities, a large number of different specialists must be trained up. This does not seem like very good data compression from the standpoint of metabolic cost savings. Thus, the evolution of better ability with spatial information should require many more new neurons than with the case of temporal information.

My hypothesis here is that what is conferred by the comparatively large human cerebral cortex, especially the association cortices, is not general intelligence, but facility with using spatial information. We take it on and disgorge it like water-bombers. Think of a rock-climber sizing up a cliff face. Think of an architect, engineer, tool-and-die maker, or trades person reading a blueprint. Now look around you. Do we not have all these nice buildings to live and work in? Can any other animal claim as much? My hypothesis seems obvious when you look at it this way.

Mere possession of a well developed sense of vision will not necessarily confer such ability with spatial information. The eyes of a predatory bird, for instance, could simply be gathering mainly temporal information modulated onto light, and used as a servo error for dynamically homing in on prey. To make a difference, the spatial information has to have someplace to go when it reaches the higher brain. Conversely, our sense of hearing is far from useless in providing spatial information. We possess an elaborate network of brain-stem auditory centers for accomplishing exactly this. Clearly, the spatial/temporal issue is largely dissociable from the issue of sensory modality.

You may argue that the uniquely human power of language suggests that our cortical advantage is used for processing temporal information, because speech is a spaceless phenomenon that unfolds only in time. However, the leading theory of speech seems to be the Wittgenstein picture theory of meaning, which postulates that a statement shows its meaning by its logical structure. Bottom line: language as currently understood is entirely consistent with my hypothesis that humans are specialized for processing spatial information.

Since fossil and comparative evidence suggests that our large brain is our most recently evolved attribute, it is safe to suppose that it may be evolving still, for all we know. There may still be a huge existential premium on possession of improved spatial ability. For example, Napoleon's strategy for winning the decisive Battle of Austerlitz while badly outnumbered seems to have involved a lot of visualization. The cultural face of the zeitgeist may reflect this in shows and movies where the hero prevails as a result of superior use of spatial information. (e.g., Star Wars, Back to the Future, and many Warner Bros. cartoons). Many if not most of our competitive games take place on fields, courts, or boards, showing that they test the spatial abilities of the contestants. By now, the enterprising reader will be thinking, "All I have to do is emphasize the spatial [whatever that means], and I'll be a winner! What a great take-home!"

Let me know how it goes, because all this is just theory.