Shortly before all financial support for the old guard in Silicon Valley -- even from their wealthy compatriots like Federico Fagin (Boundary Institute)) -- evaporated under the combined weight of the DotCon collapse and simultaneous mass immigration to Silicon Valley from Asia, Tom Etter (attendee of the 1956 Dartmouth AI Summer with Solomonoff) wrote this summary of where his life had brought him.
Whether you believe it was a good thing guys like Tom were dumped or not, it is probably a good idea to keep this essay around -- just in case it turns out to not have been such a great idea. Outline of a New Science <https://web.archive.org/web/20130511033418/http://www.boundaryinstitute.org/bi/articles/Outline_New_Science.pdf> Tom Etter Boundary Institute Jan 16, 2002 Abstract To be written. Section 1. The old science Why would we want a new science? What’s wrong with the one we’ve got? According to John Horgan, author of “The End of Science”1, nothing. The big discoveries have all been made, and all that’s left to do is fill in the details, a job we’ll eventually pass on to our smart computers. We’ve heard this kind of talk before, usually just before a scientific revolution. The feeling that we've come to the limits of the world creates in some people the restless urge to venture beyond these limits, to take on something bigger. Suddenly it becomes apparent that the supposed edge of the world is really the limitation of our understanding. We become aware not only of our ignorance but of our confusion. In working to achieve greater clarity we discover essential simplifications, which in turn increase our power to deduce important and surprising consequences from what we know. Eventually the whole intellectual landscape is transformed and expanded. That was the story of the new science that arose in the 17th Century. On a lesser scale it has been the story of 20th Century science. I believe that on an even greater scale will be the story of the science of the 21st. Before turning to the new science, let’s briefly pay our respects to the old, and in so doing remind ourselves of some lessons we should take with us into the new territory. The primary categories of the old science are *space, time and matter*. These concepts, in their modern sense, were abstracted from the flux of human experience over a period of several thousand years, beginning in earnest with the pre-Socratics, and coming to a high point with Newton. This abstraction was an enormous achievement, and the explanatory power of purely physical thinking eventually became so impressive that it led some people to imagine that we can reduce everything to matter in motion. Such reductionism has lost much of its appeal today, however, partly because quantum mechanics has made both matter and motion more problematical, and partly because of the rapid growth of information science, to which we’ll turn in Section 2. The laws of Newtonian mechanics, unlike the laws of chemistry or genetics or quantum mechanics, can be easily observed in the behavior of everyday objects like billiard balls. In this we were lucky. Simple Newtonian objects don’t exist under water, so dolphins or cephalopods, no matter how intelligent, would find mechanics very much harder than we did. Air is close enough to empty space so that mechanical things can easily be isolated and studied in small combinations. Under water it's a far different story; there the medium is a much bigger part of the action, and mechanical interactions are never simple. Smart cephalopods would discover complexity theory long before they hit on f = ma. It was our good fortune that the deep laws of mechanics lie so close to the surface, so-to-speak. Is this kind of good fortune a thing of the past? Has the surface gold all been mined? In this series of papers I shall try to show that, on the contrary, there is almost enough surface gold left for a whole new science. A few necessary items do require some deeper digging, and have only come to light thanks to certain esoteric discoveries in modern physics. But the good news is that the most important job is simply to pay more attention to what is before our eyes. Of course we must pay the right kind of attention. That Newton’s laws lie close to the surface does not mean we simply stumbled across them. On the contrary, people have been observing Newtonian phenomena for thousands of years without any inkling that that’s what they were observing. Aristotle, who was an excellent observer, got them all wrong. Their discovery involved something else besides observing accurately and seeing the patterns in what we observe, and this something else, which Galileo almost single-handedly brought to bear on the science of motion, is what the Greeks called theory. So what is theory? Basically, it means staying focused on what is essential. This is the art of theory, and there are no simple rules for it. Why was it right in Galileo's time to carefully study falling cannonballs but to ignore falling sticks and feathers? Never mind why, it was right. Though it’s essential to pay attention to the right objects, we must also make the right distinctions. Many of Galileo’s contemporaries talked about acceleration, but it was only Galileo who carefully distinguished between acceleration as change of velocity with time and acceleration as change of velocity with distance. Without this distinction, his law of falling bodies cannot even be stated, much less tested. When we stay focused on what is essential, it’s much easier to draw out the consequences of what we know. Of course we must not only draw them out but also publish them and stand up for them, which can sometimes be a nuisance. Theory leads us from what is exposed to what is hidden. The Greeks speculated that matter is made of very small objects called atoms, but it was only after the development of Newtonian theory that it became possible to think about the essential properties of these small objects in a way that leads to important and useful knowledge. Though the Greeks never discovered mechanics, they invented theory itself, and the high point of theory in ancient times was Euclidean geometry. Galileo was very conscious of the Greek genius that went into this invention, and brought its spirit to bear on dynamics. Aristotle, in his physics, had taken a very different course, which is to observe and catalogue the motions of various kinds of objects, much as he had observed and catalogued the properties of plants and animals. The empiricists of the Middle Ages and Renaissance followed suite. Galileo, however, realized that the only way to gain real understanding of motion is to concentrate on its simple “points and lines”, so-to-speak. We must study the ideal falling body, the ideal projectile, starting with the simplest cases and working with systematic precision toward the more complex cases. This was a brand new idea at the time, but it caught on fast, and was only forty years before Newton’s Principia, the modern counterpart of Euclid’s Elements, appeared on the scene. It’s important to realize that geometry for the Greeks was about actual physical things and places; after all, geometry literally means measuring the Earth. The axioms of Euclidean geometry are apparent to the eye as well as to the mind; in this sense geometry is an observational science (the fifth postulate was an exception; its axiomatic status was under suspicion from the start, and finally lost all claim to that status with the invention of non-Euclidean geometry in the 19th century). The genius of the Greeks was to treat what is obvious in what we see as something not quite of this world, something that is an ideal simplification of what the eye actually takes in. The eye sees an edge, but the theorizing mind sees a line. The eye sees a corner, but the theorizing mind sees a point, and in so doing notices that two straight lines can meet in at most one point. The mechanics of Galileo and Newton was of course built on the foundation of Euclidean geometry, and Newton, though he had used his new calculus to actually derive his results, first presented them to the world in the language of geometry. Geometry has a modern analogue, which is not so much a system of results as a style of thinking, but to give it a short name I’ll call it structure theory. This new style of mathematics came into its own in the last century with the move toward greater abstraction and generality, and led to a wealth of new mathematical forms: an arithmetic of infinite numbers, new kinds of algebras such as group theory and vector algebra, new kinds of “spaces” such as nonEuclidean geometries, topologies, spaces of mechanical states, spaces of wave functions (Hilbert space) etc. The new style was even applied to logic, which gave us for the first time a precise general definition of mathematical proof. Structure theory, as described above, resembles the diverse body of geometric discoveries made by the early Greeks rather than the tight axiomatic system of Euclid. Russell and Whitehead, in their book “Principia Mathematica”, tried to become the Euclid of their time by capturing the essence of structure theory in a single axiomatic system they called Relation-arithmetic. Their version had serious bugs, however, and never caught on. It turns out that some of these bugs are easily fixed, and I see the fixed version becoming an important tool of the new science9. We’ll see in Sections 3 and 4 how an axiomatization of structure theory based solely on the concept of identity can be used to unify and clarify the key concepts of our new science. But first we’ll turn to something closer at hand, which is the science of information Section 2. *Structure, process and information* Beginning in the early 20th Century, *space, time and matter* began to encounter competition from another basic trio of categories, namely structure, process and information. We have already met structure as a kind of generalized geometry. We can think of process as structure in motion. Process adds to structure the dimension of time, and process philosophers like Whitehead made considerable use of the new style of structural thinking; indeed, Whitehead tried to interpret space-time as an aspect of the structure of process. The third member of the trio, information, was surface gold un-mined until Shannon turned the theorist’s eye on its ground and realized that its essence, at least in the context of information storage and transfer, is simply the narrowing of a range of possibilities. Today information in this sense has come to occupy a large part of the ecological niche once filled by matter, thereby giving its name of our so-called information age. Information is a new kind of stuff, parceled out in bits rather than in pounds or grams, and shaped and transformed by information processing devices. So is information science the new science? A lot of people think so. My own answer is a qualified no. Information science is certainly a new science, but to take the place of the old science of matter in motion it would have to give it a more fundamental grounding. This means that, among other things, it would have to make sense of quantum mechanics, which it has not done. The basic problem here is in its overly narrow conception of process. This topic is covered in detail in a number of the other papers (e.g. 5), so I’ll be brief here. For information science, a process is a structure that evolves probabilistically with fixed transition probabilities. If these transition probabilities are confined to 0 or 1, as in the case of a computer, we call the process deterministic. The more general process is called a Markov chain, or more exactly, a homogeneous Markov chain. It’s safe to say that for the vast majority of scientists, even those who have never heard of Markov chains, to explain something is to present it as a homogeneous Markov chain. This is why Bell’s theorem created such a flap; it showed that there are physical processes, specifically the so-called EPR process, that cannot possibly be Markov chains unless information can travel faster than light, something that physics has declared to be impossible. The reason my answer was a qualified no is that there is a way to generalize the mathematical definition of homogeneous Markov chain that in fact does encompass quantum phenomena like EPR, without any nonsense about fasterthan-light signaling5. When we do so, it turns out that the core of quantum mechanics can be factored out of physics as a purely mathematical feature of these new Markov chains, much as the second law of thermodynamics can be factored out of physics as a purely mathematical feature of ordinary Markov chains. Like the second law, this quantum core says nothing about space, energy or matter. In effect, it belongs to information science. However, it has emigrated from physics to information science, so-to-speak, bringing with it very important knowledge, among which is just that part of quantum physics needed for the logical design of quantum computers. Let’s call the science of these generalized Markov chains New Science One. There is now reason to believe that New Science One can absorb not only the quantum core but much if not all of present-day theoretical physics. Does this make it the new science? It’s certainly a step in the right direction, and I believe that had this step not been taken the new science would remain out of sight. But New Science One still doesn’t directly address the greatest failure of the old science, which is its inability to bridge the gap between our understanding of matter and our understanding of mind (we’ll return to this in the next section). However, New Science One does have something to say about a related failure of the old science, which is its inability to deal with so-called psi phenomena, those strange physical phenomena that seem to reside in an almost dreamlike borderland between matter and mind. The observational and laboratory evidence for these phenomena, or at least for their physical side, is by now overwhelming; that they are still ignored or dismissed by mainstream science is a scandal. Why has science so badly lapsed from its empiricist credo? The kindest answer is that the phenomena make no scientific sense. They are unthinkable, and therefore negligible. To put it more bluntly, science as we know it isn’t up to the job. I’m hardly the first person to say so, nor for the same reason. The physicist Pauli, one of the pioneers of quantum mechanics, was deeply aware of the conceptual problems presented by psi. He developed a close friendship with the psychologist Jung whose lifelong interest in psi had led to his break with Freud (Freud, curiously enough, finally came around to Jung’s way of thinking and said that if he had his life to live over again he would devote it to parapsychology). Jung challenged Pauli to create a new science that would unite physics with psychology at a fundamental level, a level deep enough to make sense of psi. Unfortunately, Pauli left no systematic record of his thoughts on this subject, but there are some intriguing fragments in his letters to his protégé Fierze2. In one such letter he made the extraordinary claim that quantum phenomena, the deepest and most universal manifestations of matter, are in fact a special kind of psi phenomena. In his words "… the quantum is that domain of synchronicity that lies closest to causality". The word “synchronicity” was Jung’s term for a postulated domain of acausal order within which he located psi. At the time of Jung’s and Pauli’s exploration of these matters there was no formalized concept of acausality. Pauli’s vision, however on target, didn’t have much of a chance of becoming a mathematical science. That situation, at least, has been changed by New Science One. This point is discussed at length in 5, and is beyond the scope of the present paper. Suffice to say here that causality, in so far as it is formalized at all in the old science, is given by the structure of the transition matrix in standard Markov theory. New Science One extends standard Markov theory in two basic ways: First, it introduces a new formal concept into process theory that is analogous to velocity in mechanics3. One result of this step is to make the general laws of process symmetrical in time, just as the laws of mechanics are symmetrical in time. Markov chains in the old sense are analogous to moving bodies whose velocity always decreases exponentially. Seen more abstractly, this kind of exponential “slowing down” is the second law of thermodynamics. For Markov “chains” in the new sense, entropy is the sum of two parts, one increasing in time and one decreasing in time; such processes so-to-speak evolve both forward and backward in time simultaneously4. Just how this extends our ordinary notions of causality is discussed in detail in 5; to sum it up in one sentence, adding a velocity component to the chain state is equivalent to putting independent boundary conditions on the beginning and end of the process, just as it is in mechanics, except that now the conditions are on probabilities. The second step is simpler but more radical: probabilities are allowed to go negative. Both steps are necessary to make sense of quantum phenomena as processes. The first, at least, would seem to be necessary to make sense of precognition, and is a crucial first step in going beyond causality in the direction envisioned by Jung and Pauli. Thus I believe that adding “velocity” to the concept of process will be necessary to get our new science started, just as adding velocity to the concept of state, which happened in the early 17th Century, was necessary to get mechanics started. Necessary does not mean sufficient, however. The mathematics of the new process theory is simple and straightforward, but it doesn’t tell us much about what the above-mentioned departures from the chain law mean for experience. For this we need the deeper science that Jung proposed to Pauli, a science that not only unites matter with information but with mind. Section 3. Phenomenology as theory Psi is more than just a physical or informational anomaly – it points to the need for a fundamentally better understanding of the place of mind in nature. The physical sciences, if they are to meet the challenge of psi, must enter into some kind of union with psychology. How should we proceed toward this goal? One thing we cannot do is simply lump the discoveries of physics and psychology together. As they stand, these two subjects have too little in common to mix into a coherent whole. Physics is without question the more impressive of the two sciences. For a while it was the fashion to try to “reduce” psychology to physics, physics being understood rather loosely as our knowledge of material things. In more recent times this has given way to the idea that psychology belongs to information science. In its most extreme form, this new fashion would have it that the mind is a program running in a computer called the brain. We’ll pass here on both of these options, and start out with a much cleaner slate by availing ourselves of certain insights of that philosophical movement known as phenomenology. Phenomenology began in Germany at the end of the last century as a school of psychology whose best-known member was Brentano. Husserl later gave it a more philosophical turn, and it has since become, in one form or another, the dominant philosophical movement on the continent, in contrast to the analytic school of philosophy that has prevailed in England and America. The guiding insight of phenomenology, which dates from Brentano, is known as the doctrine of intentionality. Here is a quotation from Introduction to Phenomenology by Robert Sokolowski6, a recent and very good book to which I’ll refer often in this and other essays: “The doctrine of intentionality … states that every act of consciousness is directed toward an object of some kind. Consciousness is essentially consciousness “of” something or other. Now, when are presented with this teaching, and when we are told that this doctrine is the core of phenomenology, we might well react with a feeling of disappointment. Why should phenomenology make such a fuss about intentionality? Isn’t it completely obvious to everyone that consciousness is consciousness of something, that experience is experience of an object of some sort? Do such trivialities need to be stated?” I should add that this triviality resembles the triviality that two straight lines can meet in at most at one point. What is not trivial is the body of consequences that follow from such “trivialities” in the right context. To return to Sokolowski: “They do need to be asserted because in the philosophy of the past three or four hundred years, consciousness and experience have come to be understood in a very different way. In the Cartesian, Hobbesean and Lockean traditions, which dominate our culture, we are told that when we are conscious, we are primarily aware of ourselves or our own ideas. Consciousness is taken to be like a bubble or an enclosed cabinet; the mind comes in a box.” [ibid p11] In contrast, phenomenology, when properly understood, bursts this bubble, opens this box: “Phenomenology shows that the mind is a public thing, that it acts and manifests itself out in the open, not just inside its own confines. Everything is outside.” [ibid p 12] I’ll not dwell on this issue here; for an in-depth treatment, read Sokolowski. Let me only bring up one point in this connection, which is that it is just as natural to say “We are aware” as it is to say “I am aware”. The conscious subject can be plural as well as singular; consider “People know better” and “The common man knows better”. We hardly notice the difference (I hardly notice the difference, you hardly notice the difference, the common man hardly notices the difference). Clearly who knows better is the same in both statements. We’ll return to singular and plural subjects shortly. “Intentionality”, and its cognates “intending”, “intention”, “intentional act”, etc. are technical terms in phenomenology, and as such they can be confusing. Again, Sokolowski: “The phenomenological use of these words is somewhat awkward because it goes against ordinary usage, which tends to use “intention” in the practical sense. However … there is no way of avoiding them in the discussion of this philosophical tradition. We have to make the adjustment and understand their meanings as primarily mental or cognitive, and not practical. In phenomenology, “intending” means the conscious relationship we have to an object.” [ibid p 8, slightly reworded] Note that intending is characterized here as a relationship. Let’s visualize this relationship as an arrow from subject to object. We ordinarily think of the subject and object as things that preexist the arrow of intending. As I understand phenomenology, it reverses this order, taking the arrow of intending to be primary, the subject and object being its tail and head, so-to-speak. To make an analogy, we don’t start out with a husband and a wife and then marry them; rather, it is by marrying them we make them into husband and wife. By the same token, it is the intentional act that makes two things into subject and object. Husserl and his followers have made an extensive and impressive investigation of the many varieties of intentionality. Our present enterprise is not investigative, though, but theoretical, in the sense discussed in Section 1. Our first problem is that the theoretical tools available to the scientist of mind are very primitive, much more primitive than those available to the physicist or geometer. We should not try to pretend otherwise. Let’s then imagine ourselves to be pre-Socratics, still wandering around in a new intellectual territory, curious but bewildered, and happily alighting on simple essences like points, lines and circles. I believe that phenomenology has already handed us our lines as the arrows of intentionality and our points, which are now of two kinds, as the “heads” and “tails” of intending. It’s worth pursuing this analogy. In section 1, points and lines were introduced as otherworldly abstractions from corners and edges. But points and lines are also abstractions from many other kinds of worldly things. A point can be a corner, but it can be a small object, where small depends on context – in cosmology a star is a very small object. A line can be an edge, or a line-of-sight, or a rigid rod, or a plumb line, or any other kind of taught string. One is tempted to say that there are many kinds of points and many kinds of lines, as if the relationship between the idea and its manifestations is one of genus and species. But this is not quite right. “Point” and “line” are simple words for simple ideas, even though they can be brought into diverse contexts in diverse ways. One should not confuse the diversity of these ways with a variety among possible meanings of “point” and “line”. So it is with subject, object and intention. The investigative phenomenologist may find that there are many varieties of intention, and also of other basic ideas like presence and absence that we’ll come to soon. But the theorist sees the situation differently; precisely what makes these ideas so valuable for theory is that they are simple. That the subject of an intention can be either singular or plural, for instance, means that the simple idea of intention can brought into a real-world context in these two ways. It’s not that the investigative phenomenologist is wrong. His discoveries are perfectly valid. It’s just that where he sees variations on the simple concept, the theorist tries to see a variety of ways in which the simple concept can relate to other simple concepts. Another basic concept of phenomenology is the contrast between presence and absence. Sokolowski speaks of this as one of three structural forms that occur constantly in phenomenological analysis, the other two being parts and wholes and identity in a manifold. The latter two are found in all of philosophy, but presence and absence are new: “However, the theme of presence and absence has not been worked out, in any explicit and systematic way, by earlier philosophers. The issue is original in Husserl and in phenomenology.” [ibid p 22] Presence and absence are also technical terms, though their technical meanings come closer to the vernacular than the technical meaning of intentionality. Like intentionality, they get their philosophical status through “trivial” truths, such as that we can think about things that are out of sight. Husserl distinguished between so-called filled intentions, in which the intended object is present, and empty intentions, in which the intended object is absent. To illustrate this distinction, Sokolowski gives the example of looking at a cube. We can see at most three sides of a cube; these are the sides that are present. To see them is to have filled intentions. Since we are seeing the cube as a cube, however, we also implicitly intend the sides we can’t see, the absent sides. As Sokolowski puts it, our perception of the cube is a blend of filled and empty intentions. There are many varieties of absence: things hidden, things far away, things remembered, things anticipated. There are also gradations of presence and absence, e.g. foreground, middle ground, background. And then there are questionable cases. Is the house I plan to build absent, even if I never build it? Is the present king of France absent? Can something be absent if it cannot possibly be present? Is the rational square root of two absent? As I understand phenomenological, its answer would be yes, since the “intentional object” is to be regarded as “bracketed” against all considerations concerning its worldly status. And yet it’s not clear to me that one can bracket an object of consciousness against a complete breakdown of rational coherence. But be that as it may, the concept of an intentional object, like that of a point, has an essential simplicity that is not affected by problems about borderline cases, and it’s this essential simplicity that makes it a good candidate for a key technical concept. The value of technical concepts comes from their ability to bond with other technical concepts to reveal structure that may otherwise be inaccessible. There is a crucially important bond of this sort between the pair presence-absence and the concept of identity. To quote Sokolowski again: “There is a dimension of presence and absence, of filled and empty intentions, that we have not yet examined. It is the fact that both the empty and the filled intending are directed toward one and the same object. One and the same thing is at one time absent and at another present. In other words, there is an identity “behind” and “in” presence and absence. The presence and absence are “of” one and the same thing. … If I talk to you about Leonardo’s painting, you and I intend one and the same painting, the same one that we will see directly when we walk into the room where it is present. The presence is the presence of the painting, the absence is the absence of the same painting, and the painting is one and the same across presence and absence. … The presence and absence belong to the being of the thing identified in them. Things are given in a mixture of presences and absences, just as they are given in a manifold of presentations. We should also notice that it is this identity, this invariant in presence and absence, to which we refer when we use words to name a thing.” Another key technical idea, identity, has made its first brief appearance on stage. It will now temporarily exit while we continue with the first two, but it will be back in force in the next section. We have called subject and object the “points” of our new “geometry”. There is a problem here. To speak of the subject is to make it the object of our intention, which is of course to make it into an object. And yet we have already introduced the subject as the opposite pole of the object in the intentional act. It is the intentional act itself that creates the polarity of subject and object. It would thus seem that to make the subject into an object is nonsense; it’s like making right into left. Does this mean that we should not even try to speak about the subject? In fact phenomenology exercises a good deal of restraint in this regard; Sokolowski often uses indirections such as “the dative of awareness”. Still, there is a serious need in our theorizing to face the subject directly, as we do in everyday life when we say “me” or “you” or “him” or “her”. Furthermore, there is a natural way to do so. To understand this way requires a brief excursion into another topic, which is the contrast between singular and plural. Phenomenologists tend to favor the singular case; they speak of the object of an intention rather than the objects of an intention. And yet there are certainly times when we are aware of two or more things at once. Our language is full of smooth gradation between singular and plural: sand – gravel – rocks, overcast – cloudy – clouds. Consider “The crowd cheered” vs. “The people cheered”. Our awareness of the crowd cheering has the same intentional object as our awareness of the people in the crowd cheering. Identity can cross the divide of singular and plural, just as it can cross the divide of presence and absence. Singular and plural apply to the subject as well as the object – we’ve already taken note of this above. There can be a kind of identity between “I” and “we” that results from these being the same subjective pole of an intentional act. I and we can be aware of the same thing or things; indeed, this is why the intentional object is public. But if it is the arrow of intentionality that creates the object as its head, the identity of different presentations of that object should carry over to an identity of the datives of the presentation, to use Sokolowski’s term. The identity of “I” and “we” can come and go, and when it fades, objects called “you” or “him” or “her” emerge that are the “others” in the “we”. I propose that this fading out is the birth of the so-called subject. A subject is an object that has faded out of “we” and can potentially fade back in. This definition of subject will do for family and friends, but it does not have the generality of a basic theoretical concept, which is what we need. We must be able to extend the concept of subject to strangers and foreigners and animals, at least higher animals, and if we hope to gain a basic theoretical understanding of the relationship between mind and matter, we must be able to extend it into nature at large, perhaps even into inorganic nature. The key to making this extension is the recognition that there can be several “we’s” that overlap without merging. It may happen that I form a “we” with Bill and at the same time Bill forms a “we” with Mary, but the three of us together do not form a “we”. However, when Bill fades out of our “we”, his status as a subject enables me to grasp his subjective identity with Mary within their “we”, thereby transferring to Mary the status of subject. This indirect way of seeing objects as subjects is transitive; it can in principle be extended indefinitely by means of overlapping “we’s”10. Whether it can be extended in practice is another matter, but that is not really the point. Just as Einstein made free use of galaxy-sized rigid measuring rods in his thought experiments, we’ll avail ourselves of galaxysized chains of overlapping “we’s”. Presence and absence apply to subjects as well as to objects, but in a complementary fashion. That is, when Bill is fully present as an object, his subjective identity within “we” is absent; he is merely a thing. Conversely, when Bill is fully merged into “we”, he is absent as an object, the only present objects being those that we together fully intend. His identity as Bill is preserved across these presences and absences, however; Bill the object and Bill the subject are one and the same. The subject as presented here is clearly a very different kind of being from the Cartesian subject, the “I” of cogito ergo sum. And yet our construction of the subject started out with “I”. Why shouldn’t it simply end there? What about selfawareness? Doesn’t that reveal the subject directly? If we can’t even get started without “I” and “we”, isn’t our definition circular? Indeed it is circular, but unavoidably so. This circle is not an unpaid debt, however, but a progressive recursion. First we use “I” and “we” to construct the direct subject as he or she who drops in and out of “we”. Next we chain overlapping “we”’s to construct indirect subjects. This enables us to describe and empirically study the formation of “I” in a social setting, which in turn reveals a far richer and more complex being than that which appears in the snapshot called introspection (William James once said that introspection is like trying to turn the light on fast enough to see the darkness), The eye can only see itself in a mirror. An essential component of self-awareness is a certain kind of “third person” reflection back from others. I and Bill form one “we”, Bill and I form another “we”, and by chaining these two “we”’s, I become better acquainted with a subject called “me”. We cannot leave the topic of phenomenology without remarking on a split within the movement between those who see it as a “transcendental” science whose truths do not overlap those of the natural sciences, and those who, like myself, see it as an essential part of what natural science must someday become if it is to live up to its promise. Sokolowski, following Husserl, is of the first school. I believe he is clearly right in distinguishing between the so-called transcendental and natural attitudes (see 6, pp. --). It does not follow, however, that we must, as he claims, sharply divide human inquiry into two separate disciplines called philosophy and natural science. How these two activities can and should relate to each other remains to be worked out, but to break off all relations between them is to doom both to sterility and oblivion. Section 4. Identity theory (out for revisions) Section 5. Summary and speculations (Rewrite.) Enough of the axiomatic and the oracular – it’s now time for the arcane. As I said in Section 1, most of the new science will grow out of things that are under our very noses, things that we have simply neglected. But there are a few miracles that must happen before these neglected things can begin to grow into science. Actually, some of them have already happened. Twentieth Century physics took some truly miraculous leaps. So, in fact, did Nineteenth Century physics, one of which was Hamilton’s amazing discovery that subject and object, in the mathematical sense, are interchangeable within the mathematical formalism of Newtonian mechanics. What Hamilton discovered was a big generalization of the relativity of position and of uniform motion. By the early nineteenth century, physicists were working on very difficult problems in multi-body mechanics, and picking the right coordinate system was often the key to their solution. Hamilton pushed this method to its ultimate limit. In keeping with the new abstract spirit, he generalized the concept of space to that of so-called phase-space, which is a many-dimensional space in which every degree of freedom of position and momentum in a mechanical system is a coordinate, and the state of the system is a single moving point. He discovered the most general class of coordinate transformations that would preserve the laws of mechanics, which he called canonical transformations. He then showed, to his and everyone else’s surprise, that the time evolution of the state of the mechanical system can be described as the unfolding of a one-dimensional group of these canonical transformations. In other words, the evolution of the objective state of the system, however complicated, is indistinguishable from a continuous uniform change in the viewpoint or “state” of the subject. This subject-object symmetry carries over to quantum mechanics, where it actually takes a much simpler and more general form. In a quantum context it is sometimes called the equivalence of the Schrodinger and Heisenberg representations, though in deference to its originator I’ll continue to refer to it as Hamilton’s symmetry. What it says in a nutshell is that, for a mechanical system, it is matter of viewpoint whether the appearance of change results from a change in the state of the object or a change in the viewpoint of the subject. We have no grounds for extending Hamilton’s symmetry beyond mechanics, and indeed it would seem to have no analogue for irreversible processes like Markov chains. Still, the question remains whether, within the context of mechanics, it might apply to itself. Might it be that the change of viewpoint from regarding the change in an object J as objective to regarding it as subjective has an objective counterpart in the change of some binary state variable of the object J? The physicist Pauli, though he didn’t do much actual work on Jung’s proposed project to unify physics and psychology, had a powerful vision toward the end of his life that the secret of this unification lay in the imaginary number i [ref and ref]. Pauli was hardly a new-age airhead, and his judgments as to what is worth pursuing in physics were so highly regarded that they earned him the title “the conscience of physics”. It would therefore seem advisable not to dismiss this vision out-of-hand. What could it possibly mean? We calculate the probability of an event in quantum mechanics by squaring the modulus of a complex number called the amplitude of that event. The mathematician George Mackey showed that the quantum-mechanical use of complex amplitudes can be regarded as shorthand for a kind of symmetry imposed on a more general form of quantum mechanics in which the amplitudes are always real8. An equivalent way of stating this is to say that all objects in “real” quantum mechanics have a certain binary quantum variable in common, call it C, whose state is unobservable. Now the binary variable that we hypothesized to be the objective manifestation of Hamilton’s symmetry, call it B, would of course have to be unobservable. Could it be that C is B? This hypothesis does in fact pass one mathematical test that might have shot it down. However, to put it to an empirical test, we would have to move into a broader domain of process than that of standard complex quantum mechanics. Within quantum mechanics as it stands, such a domain is not even conceivable. Fortunately, the enlarged domain of Markov processes mentioned in Section 2 does give us the necessary mathematical room. Within this enlarged domain, quantum processes are a very special case, distinguished from the others by certain basic symmetries5. Such symmetrical processes can coexist with and fade into less symmetrical processes, much as the (almost) flat parts of empty space, as portrayed by general relativity, can fade into regions warped by gravity. What this shows is that we can imagine matter as an extended field-like structure that is mostly quantum-symmetrical with respect to subject and object, but which is modulated by regions of broken symmetry in which the subject-object arrow has a preferred direction. I propose that this is the bare beginning of an intelligible conception of the relationship between matter and mind. It is a very bare beginning, however. The image of a “subject-object” field with lumps of broken symmetry rests too heavily on physics. It scarcely reaches out to psychology at all. For that to happen, we need something deeper. My best present hope for this deeper thing to emerge is the prospect that identity theory will provide a conduit between physical science and phenomenology. Freud once remarked that our best psychologists are our novelists and dramatists. One of the reasons why phenomenology is so attractive is that we can at least begin to see our beliefs and doubts and confusions and hopes and dreams within its austere abstract categories. A purely mathematical “field theory” of subject and object offers no such attractions. In support of this hope I can report that the enlarged notion of process that provides room for the “subject-object field” is very naturally grounded in identity theory8. In particular, identity theory reveals that the seemingly odd step of allowing “negative probabilities” is a consequence of the symmetry among the several varieties of identity that are needed to describe a process as an identity structure. In conclusion, let me briefly return to the society of my cells, and of yours. Each of these cells, and there are many billions of them, is presumably a sentient being. This means that each of them has in some way broken the perfect subject-object symmetry that characterizes dead matter. But how do these minute individual breaks in subject-object symmetry add up to anything more than a soft hiss? As an intended world, a blend of presence and absence, what could be the intended objective counterpart of their collective subjectivity other than a slightly restless void? I said I would enter the arcane mode. Now I’ll wade even deeper into it, and become oracular again too. You’ve probably heard of the “entangled” state of a pair of two-state quantum particles that exhibit the “paradox” of EPR. One feature of these two particles is that if you measure their states from any (quantum) viewpoint, these measurements always agree. Now there is also a similarly entangled state for three or more two-state quantum particles. However, for many-particle entangled systems there turns out to be only one viewpoint from which their measured states are perfectly correlated. Curiously enough, there is also a complementary viewpoint on such systems from which their measured states are almost completely independent, the only departure from independence being that one of them is either the odd or even parity of the others, depending on whether the number of particles in their group is odd or even. Now if any member of a set of binary variables is the parity of all the others, then every member of that set is the parity of all the others, so this departure from independence is a symmetrical property of the set as a whole. Notice that in case the group has only two members, this departure from independence is complete, i.e. the two members are perfectly correlated, which why the EPR pair is such an interesting special case. “We are one for all and all for one and we are happily busy together”. So think the busy bees as together they calculate where to find today’s sugar water. And together they can calculate very well; experiments have shown that they can even catch on to the human experimenter’s plan of moving the sugar water further away every day in a geometric progression [ref]. Perhaps our cells are like that. Suppose that together they are in something resembling a quantum-entangled state. The viewpoint called “I” is, in quantum terms, part way between the cell’s eye view in which “we cells” are perfectly correlated, seeing as one and marching as one in perfect synch, and the crowd’s eye view of a featureless blur that “we cells” would see from the viewpoint that has each going its own way. This middle viewpoint would have to be the subjective pole of the broken subject-object symmetry in the macro-region of offquantum matter that I call my body. This symmetry would be broken in such a way as to create a subject-object polarity that is literally an objective feature of my body, just as the polarity of “up-down” is an objective feature of space in the neighborhood of a massive body. From this middle viewpoint, my cells would act with just the kind of organized independence necessary to create a “supersubject” who can think, namely me. Perhaps there will someday be a physics of the “subject-object field” capable of carrying out experiments that reveal this polarity. This would make it possible in principle to construct a chain of overlapping “we’s” that reveal my inner life to the scientific community at large, even if I were an alien blob. The people who talk about smart computers may have an intimation of this, but computers are not where it’s at, and we can now see why. Which brings us back to psi. Of course psi is a grab-bag term, covering a variety of things we don’t understand which may have little in common. What does seem to be common to many of the frequently reported psi phenomena is that they resist causal explanation. This is what led Jung to coin the term “synchronicity”, meaning an acausal ordering principle. In today’s science, to explain an event literally means to find its causes. “Why did that happen?” “Because of such-and-such”. And yet when you ground a causal explanation at the level of structure theory or identity theory, you find that it has a very specialized “shape”, which is that of a Markov chain. But Markov chains do not even cover quantum processes, let alone the myriad of more exotic processes that result from breaking strict quantum symmetry. We have briefly seen how the need to generalize the concept of process, which in turn comes from the need to incorporate the insights of phenomenology into natural science, forces us to take “acausality” be the norm. Causality is the organizing principle of the everyday practical world, but the everyday practical world is a very special place. Today’s conception of psi phenomena will seem quaintly archaic in the new science. Perhaps we should retain the word “psi”, however, for that horizon of mystery that will always belong to the quest for understanding. References 1. Horgan, John The End of Science, Helix Books, 1996 2. Reproduced in: Lorikeinen, Paavo, Beyond The Atom 3. Tom Etter, Digram States in Markov Processes, work in progress 4. Tom Etter, On the Occurrence of Familiar Processes Reversed in Time, 1960, www.boundaryinstitute.org 5. Tom Etter and H. Pierre Noyes, Process, System, Causality and Quantum mechanics, Physics Essays, Dec. 1999, also on Boundary Institute site 6. Robert Sokolowski, Introduction to Phenomenology Cambridge University Press, 2000 7. W. V. Quine, Philosophy of Logic, Harvard University Press, 1955 8. George W. Mackey, Mathematical Foundations of Quantum Mechanics, W. a. Benjamin, Inc., 1963 9. Tom Etter, Relation Arithmetic Revived, project report for Hewlett-Packard E-Speak project, 2000, also on Boundary Institute website. 10. Tom Etter, Third Person Presence, work in progress. 11. Suppes etc. OUT TAKES Consider a very simple language. It contains the words “and”, “or”, “not”, and the phrases “for some” and “for all”, together with parentheses and an inexhaustible supply of pronouns (“it”, “this”, “that”, “these”, “those”, “this2”, “this3”, etc.). It also contains the word “Red”, though with a new syntax; instead of saying “This is Red” we say “Red(this)”. The grammar of this language is the normal minimal grammar of these words and phrases in English, supplemented by parentheses for grouping. Thus “(For all these)(Red(these) or not Red(these))” is a sentence, and a true sentence. Subject-object, in a mathematical context, is the contrast between the manner in which a thing is represented and the thing itself that is being represented, e.g. the coordinate system and the space. There is only one mathematical subject, however, which is the “we” so dear to the mathematician, the “we” who understand what he is saying. Etc. Appendix. The fundamental theorem of identity theory By an axiom system we’ll mean a system formalized in first-order logic (predicate calculus) with an identity predicate that satisfies the principle of substitution for the other predicates, i.e., if x=x’ then P(x) iff P(x’). We’ll assume that there are no primitive constant terms, and that other terms are only introduced as notational conveniences, which can be eliminated by definite descriptions. We’ll also assume there are a finite number of primitive predicates. These plus formulae constructed from them using AND, OR, NOT, SOME , ALL and “=” will be referred to collectively as statements. By a sameness predicate will be meant a two-term predicate that satisfies the three axioms of an equivalence relation, namely • Sameness 1. x is the same as x. • Sameness 2. If x is the same as y then y is the same as x. • Sameness3. If x is the same as y and y is the same as z then x is the same as z. By a pairing predicate will be meant a three-term predicate Pair(p,x,y), read “p is the ordered pair <x,y>”, that satisfies the following three axioms: • Pairing 1. Pairing is universal in x and y. More formally, ∀x,y∃p(Pair(p,x,y)). • Pairing 2. p is a function of x and y. More formally, ∀x,y,p,p’( Pair(p,x,y) ⇒ Pair(p’,x,y) ). • Pairing 3. x and y are functions of p. More formally, ∀x,y,p,p’( (Pair(p,x,y) and Pair(p’,x,y)) ⇒ p = p’.) A rough statement of the fundamental theorem is that any axiom system with the power to define a pairing predicate also has the power to define three sameness predicates that can completely replace its original primitive predicates. Here is a more precise statement: Fundamental theorem. Let S be an axiom system with primitive predicates P1,P2,P3…Pn and identity x=y. If it is possible to define a pairing predicate Pair(p,x,y) in terms of the Pi together with identity, then it is also possible to define three sameness predicates R, C and V in terms of the Pi together with identity, such that the Pi and x=y can in turn be defined in terms of R, C and V. Let’s briefly discuss the meaning and implications of this theorem before turning to its proof. The main thing to notice about this theorem is that it gives us the ability to translate any axiomatized branch of mathematics into a language whose only concept is sameness. Every statement, be it an axiom, a theorem or a defined predicate, is translated into a statement about sameness. Let’s call this an RCV translation. Whether an RCV translation leads to new insights or is useful for solving mathematical problems has to be decided in particular cases. But, as we’ll see, the RCV translation procedure is quite natural, and there is reason to hope that it will strip away some of the arbitrariness that mars the set-theoretic “encoding” of concepts like function and relation and invariant. Another thing to notice, and this is rather strange, is that there seems to be a certain minimum of expressive power required in a system for it to have an RCV translation. I say “seems” because we don’t yet know what that minimum is; all we know is that the ability to define ordered pairs is sufficient. What is strange is that it’s not the other way around; you’d think that weaker languages would be easier to translate. It would appear, though, that in order to translate certain simple concepts at all, a certain complexity of “entanglement” is required among the sameness predicates, and this is only found when they are abstracted from a relatively expressive language. Of course a simple system S can always be translated by first translating a more complex system of which it is a part. However, when this is done, R, C and V are not intrinsic to S, and there is no direct way to translate S without first rising to a more complex level. What sort of systems can define pairing? For a start, any reasonable version of set theory can. In most versions, <x,y> is defined as {{x,y},{x}}. However, other set-theoretic encodings are possible; for instance, Suppes11 defines an ordered n-tuple as a function on the first n natural numbers, which would make <x,y> a function on {1,2}. Arithmetic can also define pairing; for instance we can define Pair(p,m,n) to mean 2m3n . Clearly this encoding satisfies the functionality axioms for pairing, and the fundamental theorem of arithmetic guarantees that it satisfies Pairing 3. Conversely, what kind of systems can’t define pairing? Axiomatic Boolean algebra almost certainly can’t. Similarly, other austere systems like linear orders. There are certain partial orders, though, that can. ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T52749d62f73acb31-Mc3874483fc53c023e3793b13 Delivery options: https://agi.topicbox.com/groups/agi/subscription
