The original champions of distributed processing, the connectionists, have faced just this issue. Many connectionist models feature hidden layers in which localist interpretation breaks down. (Whence all the bruhaha about distributed processing.) When localism fails, connectionists turn to multivariate statistics for help. A variety of analytical techniques all work to reduce the dimensionality of a target domain. Suppose, for example, we want to understand the various patterns of activation of a hidden layer of eighty units. Multivariate thinking begins with a simple conceptual shift: Regard each activation value as a magnitude along an axis or "dimension." Eighty units, in this way of thinking, represent a space of eighty dimensions, and the eighty activation values are interpreted as coordinates in that space. In other words, the pattern of activation with its eighty coordinates is reconceived as a single point in 80-d space. This 80-d space is thus a handy container for many patterns of activation -- each reappears as a specific point in a high-dimensional map.

At this point the analysis proper begins: An 80-d map is not something we can look at, but it is definitely something whose geometry we can measure. No matter how high the dimensionality, the notion of distance between points can retain its usual non-boggling one-dimensional sense. Euclidean (linear) distance between any two points is easy to calculate, or one may calculate similarity between points with many other algorithms. The result is a matrix of distances (or dissimilarities), not unlike a matrix of mileages between cities. Having extracted the distance matrix from the 80-d mapping, it is now possible to survey and interpret the activation space via several different techniques, each of which can reveal aspects of the structure of the galaxy of points in activation space. One appealing analysis of this type is multidimensional scaling (MDS). MDS uses the distance matrix from points in a high-d space to build a new mapping in a space of fewer dimensions. The MDS condensate can be of arbitrary dimensionality. In choosing the degree of shrinkage, one faces a tradeoff between accessibility and accuracy of the resulting low-d map. More dimensions afford a better fit between the new map and the actual distances, but remain hard to interpret, while fewer dimensions (two or three) are easy to visualize but, depending on the data, could be too procrustean, yielding a new map that wildly misplaces points. One sets the balance of accessibility and accuracy according to taste.

Let us suppose that our 80 unit hidden layer computes 80 functions in a completely localized, modular way; that is, each unit specializes in one function, and is active only when the network computes that function, and inactive otherwise. (For this example, assume that units are either on or off, 1 or 0 in activation value.) In that case, the 80-d activation space is studded with points that lie exactly on its 80 axes, each orthogonal to all the others. If we were to attempt MDS analysis of this space, we would encounter a double disappointment. First, as we shrunk the dimensionality of the space, we would be forcing points on orthogonal axes onto single new axes, resulting in a very bad fit, ever worse as the amount of shrinkage increases. Second, the activation space would be without structure. That is, every point is equidistant from every other. Any grouping of points will be completely arbitrary, not supported by underlying order in the space.

Now let us suppose that the hidden layer is a sparsely distributed processor. In this case, a subset of units work together to compute each function, and these subsets partially overlap from function to function. If we scale this space to fewer dimensions, the overlap means that axes can coalesce without as much forcing, and that the overlaps might reveal a meaningful structure in activation space. That is, where we judge two functions to be antecedently similar, we may expect the activation space to somehow reflect that similarity, and our new MDS'd map to reveal some of that structure.

Over the last two years I've been focusing the lens of MDS on the accumulated PET studies in Brainmap and in the PET literature in general. My goal has been to use MDS as a crude probe of brain activation space. If MDS works without excessive procrustean stress, and if the structures detected by MDS are meaningful, this will offer another line of evidence that the brain is indeed a distributed processor.

As with any meta-analysis, this approach requires careful registration of the original experimental observations in a common format. The PET studies themselves already encourage comparisons in many ways. Individual brains differ strikingly in size and shape, so a routine part of PET processing is the morphing of one's personal brain into the shape of a standard brain, so that points of activation can be localized to comparable anatomical structures. In addition, PET studies always involve multiple subjects. The resulting patterns of activation are averaged (and peaks tested for significance), washing out stray activations, whether due to idiosyncrasy or to a subject's straying off the task. Beyond that, however, the studies differ from one another in one important way: As mentioned above, the reported patterns of activation are generally "difference images," created by subtracting a baseline or control pattern from the test or task pattern. These baseline controls are not uniform in the literature. For example, in a study of semantic processing, study A might image a brain during reading aloud, and subtract from that a control task consisting of reciting the alphabet. The point of this subtraction would be to isolate the subsystem involved in processing word meaning, while factoring out that involved in simple vocalizing. Study B, meanwhile, might also image a brain during reading aloud -- the same test task -- but subtract from it a control task consisting of reading silently. In this case, the function of interest is vocalizing itself. Both studies might display patterns of activation labelled "reading aloud," and indeed the underlying activation in the brains involved might be very similar, but the divergent subtracted control states would yield divergent difference images.

As a result, any PET meta-analysis must rest on a collection of experiments that share a common control state. There are a few such familiar baselines in the literature. One of the most common baselines is simple rest with closed eyes. A full review of hundreds of PET papers yielded 36 experiments where the difference image was based on a control state where subjects rested quietly with eyes closed. (Another common control condition has open-eyed subjects focus on a fixation point on a blank screen. This will be reviewed in a future study.) In these 36 experiments, points of activation were assigned using a brain atlas (as well as published anatomical assignments) to approximately 50 discrete brain areas, chosen to minimize overlaps and thereby minimize double-counting of points of activation. To wax multivariate, individual patterns of activation in the brain were conceived as points in a 50 dimensional space. From here, multi-dimensional scaling generated maps in fewer dimensions. Surprisingly, the procrustean stress, or badness of fit, was quite low even at 3 dimensions.

MDS did reveal the crude outlines of the structure of brain activation space. The largest regional affinities in brain space were determined by the modality of input. Tactile, visual, auditory, and no input conditions tended to group. The groupings were not compact clusters, however, but rather rough ellipsoids. In other words, in many cases similarity of input modality leads to collinearity of resulting points in brain activation space. Within the modalities, there is some indication of further structure, and this seems to be in part a reflection of the response made to the various tasks in the map.

The figures below reveal this collinearity and internal structure. Each is a view through a 3-dimensional MDS space, based on the 36 experimental points in 110 dimensions. The figures are paired, showing two views of the same set of points. The first view rotates the space so that the ellipsoid space of points is seen from the end -- what appears to be a tight cluster is in fact points deployed along an axis through brain space. Then in a companion figure the space is rotated to look at the point set from the side, displaying its internal structure. Each pair labels a different set of points. All 36 task points appear in each of the figures. However, a different subset is labelled in each pair, for ease of interpretation.

Only the relative position of points is meaningful; The XYZ axes are arbitrary. Nor do the positions of points bear any one-to-one relationship with anatomical or physical points in the brain. Each point represents an activation pattern of ten or more anatomical components, and point proximity indicates similarity among patterns. In short, the images that follow condense a large quantity of data -- many experiments, many subjects. Here then is a first multivariate survey of "brain activation space," and a brain-based window into the mind.

[The Inner Light Theory
of Consciousness
by Steven W. Smith, Ph.D.
California Technical Publishing

ISBN 0-9660176-1-7 (2001)




--------------------------------------------------------------------------------

A Brief Overview

Look around and concentrate on what you experience. Perhaps it is a warm summer day and you are sitting on an outdoor patio. You see a deep blue sky and smell the fragrance of the flowers in bloom. Wind blowing through the branches of a nearby tree provides a soothing melody. You feel the texture of these papers in your hands, and can still taste the last sip of your beverage. Of course, your experience will be different; you may be in a university library, at your desk at work, or relaxing on the couch in your home. You may be smelling the fragrance of flowers, the sweetness of newly baked cookies, or the lingering odor of disinfectant. You undoubtedly will be experiencing many things from your five senses, plus an introspective view of your mind's operation. These are the things you perceive, and are therefore the things that define your reality.
But now imagine that you suddenly awake and realize it was only a dream. The things you had been experiencing can now be seen from an enlightened perspective. Before you awoke, you justifiably believed that the sights and sounds you experienced were genuine, originating in an external physical universe. The tree, papers, and patio seemed more that just your perception of them; they were real objects with an independent existence. Or so you thought. But now that you are awake you have gained a greater knowledge, the knowledge that your previous reality was not genuine. The things that you had been perceiving exist only in your mind, and nowhere else.

The lesson here is extraordinary: the low-level activity of the brain is capable of placing its high-level activity into an artificial reality. We know this for a fact; it is clearly demonstrated to us each night as we dream. It is undeniable that the machinery to accomplish this feat is present in each and every human brain. The nature and extent of this "subreality machine" remains for us to determine; but one fact is indisputable, it is there.

The Inner Light theory takes this a step farther, asserting that this "subreality machine" is also activated during our waking hours, just as during our dreams. The unconscious processes that create our dream reality, also create our waking reality. This is not to suggest that the external physical world is an illusion. On the contrary, when we are awake and perceive an apple, we have every reason to believe that the universe contains such an object. However, we do not, and cannot, experience the physical apple directly. The best we can do is to capture clues about the object's nature. These clues come in the form of light photons, sound waves, molecules of various chemicals, and mechanical interactions. These are the physical principles that underlie our five senses, resulting in neural signals being sent to our brains. These indirect clues are all we know about the physical universe, and the only things we can know about it.

But of course, our conscious perception of an apple is nothing like photons, sound waves, or neural activity. We see an apple as red, feel it as smooth, and taste it as sweet. This is our introspective experience, because this is the representation that the subreality machine has created for us. Our unconscious mental processes fused the multitude of sensory data into the thing we recognize as an apple. Everything that we are conscious of has been created in this way. Our consciousness exists in this inner reality, not the physical world. When we are awake, the inner reality is constructed to mimic our external surroundings. When we dream, the inner reality exists on its own, without regard for anything outside of our brains. But either way, all we can consciously experience is the inner reality created for us by the subreality machine in the brain.

Are life and consciousness connected to the funda-mental level of reality?


Quantum Mind 2007
July 16-20, 2007
Salzburg, Austria
Toward a Science of Consciousness 2007,
July 23-26, 2007
Budapest, Hungary

Toward a Science of Consciousness 2006


Consciousness defines our existence and reality, but the mechanism by which

the brain generates thoughts and feelings remains unknown.

Most explanations portray the brain as a computer, with nerve cells ("neurons") and their synaptic connections acting as simple switches. However computation alone cannot explain why we have feelings and awareness, an "inner life."

We also don't know if our conscious perceptions accurately portray the external world. At its base, the universe follows the seemingly bizarre and paradoxical laws of quantum mechanics, with particles being in multiple places simultaneously, connected over distance, and with time not existing. But the “classical” world we perceive is definite, with a flow of time. The boundary or edge (quantum state reduction, or ‘collapse of the wave function”) between the quantum and classical worlds somehow involves consciousness.

Ever since Emil Du Bois-Reymond demonstrated in 1843 that electricity and not some supernatural life force travels through the nervous system, scientists have tried to explain mental life biologically. It's been a long, slow haul. An important step was taken in the early 1940's when the neurologist-philosopher Warren McCulloch and the teen-age prodigy Walter Pitts showed how webs of neurons exchanging electrical signals could work like little computers, picking out patterns from the confusion buzzing at our senses. Inspired by this metaphor, neuroscientists have been making the case that memories are laid when the brain forms new connections, linking up patterns of neurons that stand for things in the outside world.

But who, or what, is reading these neurological archives? The self? The ego? The soul? For want of a theory of consciousness, it is easy to fall back on the image of a little person -- a homunculus, the philosophers call it -- who sits in the cranial control room monitoring a console of gauges and pulling the right strings. But then, of course, we're stuck with explaining the inner workings of this engineer-marionette. Does it too have a little creature inside it? If so, we fall into an infinite regress, with homunculi embedded in homunculi like an image ricocheting between mirrors.