Bootstrap
Bootstrap is a term that has appeared frequently on these pages. (In this last link I am using the Google site search, which necessarily includes all of comcast.net. I encourage anyone to make liberal use of this feature, but please note that my address is changing from http://mywebpages.comcast.net/dantsmith/ to http://home.comcast.net/~dantsmith/.) [6/18/04 - Please note that I often use ouroboros (ext. ref.) or ouroboric circuit as being nearly interchangeable with bootstrap. (Google still references the old address.)]
At the end of the previous page I was about to launch into a discussion of cycles, but upon further reflection I have decided to include the bootstrap in that discussion as an important addition. I would first like to review some other uses of this term, particularly in physics.
It was Geoffrey Chew who introduced this term to physics in 1968. Geoffrey's interesting anti-materialist attempt to eliminate the notion of elementary particles from physics, quickly ran afoul of the ascendancy of quark theory. From a purely technical perspective the theory attempted to use only the self-consistency and symmetry requirements of the quantum scattering matrix to derive the properties and interactions of all the strongly interacting particles. But from a more philosophical perspective, Geoffrey's vision included a strongly relational cosmology which included consciousness as a fundamental part of the universal bootstrap. Fritjof Capra's The Tao of Physics (1976) made liberal use of this idea to support a Zen based model of physics.
John Wheeler's Participatory Anthropic Principle (1983) carries the bootstrap idea further in the direction of the BPW hypothesis, but it maintains an otherwise physical cosmology in a curious dualism:
The early multiverse can perhaps be thought of as a massively parallel quantum computer which explored all of possibility-space until it was able to generate a living body, which became the habitation of an observing, sentient being. At that moment the multiverse collapsed into the actuality of that one alternative environment.
A more mainstream version of the bootstrap idea in physics refers to the duality of particles and forces in the inherent symmetry of Richard Feynman's diagrammatic formalism. Here the swapping of the space and time coordinates appears to switch the roles of forces and particles, especially if one is not too particular about the fermi-bose distinctions.
In general, duality principles (3,500 hits) play a very significant role in math and physics. There is an inherent dialectical aspect to them, which in its turn may suggest an underlying bootstrap process as we see with Hegel. It is along these lines that I would like to include the bootstrap idea in a generalized concept of circuits and cycles, especially when they are viewed from an ontogenetic perspective.
[10/11]
While on the subject of circuits and bootstraps, I can hardly avoid mentioning Doug Hofstadter's 'strange loop' (33,400 hits). Here is the Math World entry:
A phenomenon in which, whenever movement is made upwards or downwards through the levels of some hierarchical system, the system unexpectedly arrives back where it started. Hofstadter uses the strange loop as a paradigm in which to interpret paradoxes in logic (such as Grelling's paradox and Russell's paradox) and calls a system in which a strange loop appears a tangled hierarchy.
Douglas Hofstadter, in Gödel, Escher, Bach (1979) and several later books, uses this esoteric concept mainly in service to materialism. His intention was to resolve the mind-body problem, in favor of the material side of the dichotomy, using this device. Daniel Dennett, Consciousness Explained, collaborated with Hofstadter in Mind's I (1981).
The Godelian aspect of the strange loop is a non-starter for Doug's purpose of bootstrapping consciousness. Godel's self-referential arithmetic construction presupposes a self-aware interlocutor, but should not be construed as contributing to that awareness. Also it is strange that Doug discounts the quantum observer loop as having any relevance to his strange loop. His commitment to the classical computing paradigm seems to be a marriage of convenience.
From a more qualitative, less technical perspective, there are aspects of the level shifting, tangled hierarchy which name the larger issues that any systematic cosmology will have to address. There is also a digital version of Pythagoreanism here which warrants our attention. Such a scheme might also be called 'information mechanics', but Doug's version is irreducibly loopy. To this significant extent does Hofstadter depart from materialism and even physicalism.
[10/12]
Those of us on the Microsoft side of the world are all too familiar with rebooting. Recall that the booting being referred to here is not a swift kick to the hard drive, but, rather a bootstrapping process of first loading lower level and then higher level components of the operating system to the active memory. Thus does the computer wake itself up in stages when it starts from scratch. Can any of this simple process be related to the problem of Creation? Probably not, but it's worth keeping in mind.
Probably what most people have in mind with bootstrapping is a spontaneous process of self-organizing emergence. As far as I am aware, the most complex, non-biological system that we know to exhibit this feature is the Belousov-Zhabotinsky oscillating chemical reaction. As long as chemical energy is pumped in, the reaction continues to oscillate around an equilibrium point. This is a long way from even the simplest of Manfred Eigen's hypercycles:
In addition, his name is linked with the theory of the chemical hypercycle, the cyclic linkage of reaction cycles as an explanation for the self-organization of prebiotic systems, which he described 1979.
Living systems are replete with such autocatalytic networks (5,400 hits), but I see no reference to any that exist in vitro. Actually, this is a potentially important piece of evidence against the materialist thesis, and warrants further checking: autocatalytic bootstrapping occurs only in vivo. The only exceptions seem to involve computerized systems of 'artificial life': shades of digital Pythagoreanism and information mechanics.
We have covered the related territory of complexity theory and self-organizing systems at considerable length on previous pages: here and here. The upshot was that what was once thought to be a very promising avenue of research has gotten bogged down while shedding very little new light on the nature of life. Strong emergence and vitalism remain unscathed by the best and brightest of science.
Instead we find that the proteomists and biosemioticians are exploring what for them is the brave new world of scientific non-reductionism, or, simply, scientific realism, i.e. realism about the irreducible existence of their theoretical entities.
In examining the idea of the bootstrap I am attempting to locate the essential element of Creation. This has the potential to be deconstructive of our notion of the Creator, but I don't think you need to hold your breath on that score. I am rather trying understand the relation between the numerical and vital aspects of Creation, using the 'bootstrap' as the possible missing link. What I think is mainly missing from our notion of the bootstrap is its necessarily teleological nature.
Teleology ('mywebpages' url) is frequently mentioned on these pages, but nowhere is it discussed at length. It is anathema to the scientific establishment. It is a conversation stopper. There is very little to be said about it, other than to opine on its existence. The teleological explanation is widely considered to be simply a non-explanation. Nonetheless, any hint of irreducibility must be considered as a possible manifestation of final causation, if there is to be any cause at all.
A less inflammatory substitute which may be applied to individuals is 'intentional'. Daniel Dennett has made a career out of deconstructing intentions: The Intentional Stance (1989). Another substitute is 'downward causation', which I have examined (and here) at some length.
[10/13]
With this hasty review of bootstraps behind us, we can readdress the original intent. That intent was to focus on cycles and circuits, with the bootstrap concept as a late addendum. The renewed focus on cycles was motivated in part by the replacement of the Monster Group with Pi in the 'Big Six'. The Big Six constitute the main logical hurdles in our attempt to understand Creation. Outside of science, two models of Creation present themselves. The irony is that the 'mystical' model of Creation seems more rational than the theistic version. In fact, the pantheist version is just a bootstrap model.
In some sense, I am attempting a synthesis of the theistic and pantheistic cosmologies, by way of rationalizing the 'mystery' of Creation as it is viewed prophetically. The purpose of the Millennium is to allow us to prepare for the Omega. In that preparation we will be taking advantage of the A&O symmetry to better choreograph our participation in the Omega event of our metanarrative.
I am exploring the possibility that Pi could have played a key role in Creation. We are now simply trying to square the circle of Creation, and to that end we can recall, among other things, our formula.
Previously I have speculated that the logical origin of numbers might be tied to the symmetry breaking inherent in the 'small group dynamics' of the primordial cosmic intelligence. Thus they would be a part of the creative logos. Thus there is at least a symbolic rationale for equating Pi with the quantitative aspect of the logos.
Pi could even play the role of the Zim-zum: it is the number of the diametrical fission in the primordial symmetry of the cosmic self-potency. This could also by symbolized by the transition from unipolar circle to bipolar ellipse. The only problem then is to upgrade the numbers from a representational to a functional status.
One thing we are lacking is the discrete precursor that we have in the transition from the discrete exponential, phi, to the continuous form of 'e'. There is no particular number to associate with the polygonal approximations to the circle. We will have to make do with the three-way comparisons between e, pi and phi that we have already introduced, and again here in an attempted transition from network to space, or here in analogy with quarks. At another point I suggested a trinitarian analogy for e^i*pi.
After reviewing these last two pages, I'm inclined to think that our focus on Pi suggests its role as that of a logical bootstrap. It may be the logical key to the coherent substance of our world. But I would have to go further than that. Pi could only have evolved into that role. Its precursor would have been a vital aspect of the cosmic intelligence, indeed, one of the primordial pantheon. I doubt that even science fiction has ever ventured into such a fantasy. Only thus does Pythagoras make sense. We need not let ourselves be forced into numerological extremism. I only want to tentatively put forward the obvious proposition that, even according to Occam, we ought not to make a logical distinction between our notions of a pantheon and the Big Six. Why should these groupings be logically distinct? Animism is not likely to run and hide just because I raise the scepter of rational theism. Why not simply invoke a Solar deity or logos, along with a Pi logos, as a logically necessary stage of Creation. Extreme monotheism is inherently incoherent, and may be blamed as the logical precursor of analytical materialism. We have gone merely from trinitarianism to sexagenarianism which is precisely where I will be one day next month, perish the thought. In retrospect it is almost amusing how long it took me to make this logical connection. So much for the Protestant abhorrence of the flesh of its Gods, despite the overwhelming evidence of its own tradition. Yes, when we get out our Pi enhanced calculators we may as well be passing around the communion wafers. So let's forget the Tarot deck and send out for the crackers. The gods aren't crazy, they're just fully occupied. They took their work so seriously that you can no longer distinguish them from the product of their labor.
You are witness to my honorable attempt to avoid animism. May we now get on with the program?
This is a large step here. If we want to stick with it we will have to hash it over a bit. Already I was in the process of identifying A&O with the past and future aspects of God. That seems relatively uncontroversial. And surely there might be a god of fertility standing in for our reproductive cycle. That just leaves us with math and physics to account for: SAP, i.e. sun, atom and pi.
Sun and Pi stand out in their respective categories. Not so, for any atom. We can easily, however, revert to the elementary particles, which I believe was the intent all along, and relate these to certain numbers as we have already done. This could be seen as precursor of associating particles with symmetries. Not a great leap.
That leaves us with the Sun as a unique case among the Six. We'll need a solar strategy in our animation scheme. We'll, let's see... haven't we all heard of the person with the sunny disposition? A bit of a stretch, but we have to start somewhere. But now I am reminded of heliotropism. How do we fit that into our animation?
You see that each time we come up with a new aspect of cosmology we have to test, and then adjust it against all our other components, and, hopefully, achieve a more coherent configuration. This is an iterative process which ought to converge on the BPW if we're lucky, darned lucky!
If nothing else, our helios-heliotrope causal loop is a bootstrap, par excellence. Where resides the 'animus', or animating spirit, more formally speaking? Are we going to have to invent a god of the bootstrap? Already, Occam is looking askance.
But timeout. I am being reminded that even in monotheism, the creative logos need not be singular, and so we have the logoi as the intermediaries between God and Creation. In Christianity, Jesus, as Logos, is just the first among the archangelic logoi. It appears that my attempted paganism may be short-lived.
[10/14]
One might well wonder what one would have to avoid doing if one were not desirous of ending up as an atom. Reincarnating as an atom would have to be about the bottom rung on the hierarchy of being. On the other hand, ending up as every atom might not be such a bad fate. How might one go about arranging this more auspicious outcome? Surely we will face a prodigious cloning.
We wish to combine pantheism and Pythagoreanism in a logical manner so as to produce respectable atoms. In this case it is metabolism that acts as our telos. Helios and heliotrope would be side show, with photons serving as the metabolites, and in both cases we'll have to do some serious bootstrapping.
Numbers seem to have little difficulty with cloning. They are able to rely on logic for their reproductions. It's not a bad trick if you really need to get around. How might atoms follow suit? Words are noted for a similar ability, with much less reliance on logic. Words are characteristically seminal. That is their charism which we try to capture with the Logos. Is the message in the medium? Is it about currency? How does one set about becoming a medium of exchange?
OK, again. The tack I am pursuing here is simply personalism. The logos and logoi are just that: persons, one and all. Reality is of, by and for persons. Recall also that Leibniz, with his monadology, was an early advocate for personalism and panpsychism, and so I will need to review the connection of that with his BPW hypothesis, later.
How are atoms unlike words, with an organism likened to a text? Organisms occupy space-time, while a (spoken) text occupies time. Individual words come to the fore only in the parsing or analysis of the text. There is no Galilean symmetry of spatial translation that leads to a conservation of atomic mass. Nonetheless there is a contextual conservation of the function or meaning of a text, independent of particular verbal content. There is a similar contextual continuity which preserves organisms. In the study of memetics there are further attempts to draw out this analogy in a Darwinian direction.
The point with words is that they exist in the gray area between mind and matter, between subject and object. My intent is to exploit their ambiguous status to create the slippery slope on which atoms will be seen to be capable of sliding, with a little nudge, over into the realm of mind. The ontological status of persons is ambiguous likewise, and it may be possible to exploit that ambiguity in a similar fashion, bringing us back to the usefulness of the concept of the logos. The thesis of personalism is that the substantiality of atoms and everything else is derivative from the substantiality of persons. This simple point warrants emphasis.
There is nothing else in the world with which we can have more direct contact than with our own personal identity. No other identity can be more substantial to us. The closest contender for some of us might be our automobile, which might be thought to be more tangible than anyone's persona. Tangible, perhaps. Identifiable, certainly not.
How about which one is more real, me or my car? Is this just a semantic issue? Yes, indeed. My point is that reality logically has to begin somewhere, and that somewhere has to be at home with the self. Only a few centuries of scientific abstraction might convince us otherwise, but where then does the scientific reality begin? There seems no longer to be agreement on this point, if ever there was. As we have seen, scientific realism has become a very thorny subject.
Reality begins with persons. If we wander too far beyond that simple truth we are liable to get into a whole lot of trouble: witness Descartes. This observation is the beginning and end of personalism. Thus do atoms and numbers become persons? Quantum theory might best be interpreted as a big reminder that we cannot take the observer out of the quantum loop. Does the observer have to be a person? This is more controversial, and certainly remains open. This is just to say that reality is relative to observing persons.
A car in my dream could seem every bit as tangible as in waking. Thus is mere tangibility not a good measure of substantiality. Let's face it, reality is a contextual game, which none of us can avoid playing. No one else can play it for us. Of course, our cultures have a great propensity to school us in 'reality', but you and I would not be here if that were the end of the story. In the prophetic tradition, it is we prophets who must take our cultures to school and then to task.
If reality were not a relational network of, by and for persons, then what could it possible be? Atoms and numbers show little propensity to escape from this network. This is not to say that I am liable to be reborn as an atom. It is to say that we own the very idea of atoms, and if you try to take our ideas out of the atom, you sure won't have much left over to show for your trouble.
Atoms and numbers are integral to the logical fabric of existence. They behave as they do, because otherwise the fabric would threaten to tear, and that is not logically possible. Paranormal phenomena can occur only on the fringes of that fabric. Yes, this is a social reality, but it goes much deeper than we are won't to imagine.
There is a mutuality between us and our atoms. There is a mutual habituation. It is not wrong to think of atoms as the teleologically projected idea of a society of atomic physicists. Only in the end will this society own up to its creative role. This is a scary thought because that very same teleology also entails an eschatology. We have only to remind ourselves to fear not.
As a teleological social construct, we should expect that Pi will have much to tell us about ourselves. It is just one of us in a peculiar extremis. With patience we may see our own history reflected in its structure and its functional relations.
[10/15]
There must be something holding mathematics together. This something appears to be Pi. This is not the only entity doing so, but it appears to be the preeminent one. If that were the case then it would be fair to say that the role of Pi among other such objects reflects the role of the traditional God in the pantheon that is cosmic intelligence. This pantheon might, in turn, be considered the polyandrous consort of the Matrix. I put this forward merely as a talking point at this time.
The hope of procuring such insights is just the reason that we engage in this multilateral approach to cosmology.
[10/16]
It would be of considerable interest, and not terribly surprising, if mathematical structures reflected cosmological structures. Thus might mathematics work on both the micro and macro levels simultaneously without logical conflict. I'm suggesting an extended structuralism that would mediate the vital primordial processes. One could also imagine a universal grammar at work. Do the structures and grammars have a common source? One suspects that sacred geometry and archeoastronomy point to such a source.
From the Britannica:
[...] Levi-Strauss adopted the so-called distinctive feature method of analysis, which postulates that an unconscious "metastructure" emerges through the human mental process of pairing opposites.
So, we are looking for the metastructure that is the source of the metanarrative. That it would also be the source of logic and math is a more speculative extension. Logic could not be psychologically fundamental, it is much too abstract. We seek the Ur-logic, the pre-geometry, etc. We are hardly alone in that endeavor. In doing so I am running up against the many venerable objections of the positivists and behaviorists to holding mental contents to be real, and not merely abstract. This is the alleged 'fallacy' of psychologism as stated by Frege and many others: Keeping psychologism in mind -- Anthony Newman (MIT).
[10/17]
It is a far reaching claim that the explicit structures in the world reflect deeper implicit structures. This claim must include mathematics, especially. Otherwise we are saying that the Monster Group comes from nowhere, which is less than credible. Saying that the MG may be derived entirely from a handful of axioms is a statement that, I gather, is widely held, but it is also a statement that has not been critically examined from any global perspective. This constitutes a curious lack of wonder on the part of, what may be, an overly professional establishment.
Roughly speaking, I am asking if there can be anything new under the sun. I am also asking about the information explosion. Consider then: conservation of information (1500 hits). The first entry is from that digital mechanic, Edward Fredkin, but his most recent publication deals only with microscopic phenomena. The third entry asks about the source of biological information. There is also the issue of the objectivity of information. The plain fact is that information remains incompletely defined. There is the issue of quantity vs. quality. Can there exist either unobserved or unobservable information? But even these topics do not touch on the information content or source of mathematics.
The discovery of the Mandelbrot (demo) set was a big surprise for mathematicians. I am not aware of anyone who has attempted to measure its information content, or speculate as to its source. Does it not remain an object of great mystery? I suspect that it does point to the holographic, holistic nature of all information. As I mentioned before, even a partial understanding of the meaning of the binary set {0,1} would require a PhD. in the history of ideas. The Mandelbrot is just one possible manifestation of the information contained in that construct.
Many of the entries indicate that it is only the Intelligent Designers who have the temerity to make an issue of the problem concerning the conservation of information. It is not considered a polite question by the establishment. We hear a lot about the limits to knowledge, but perhaps the more basic question concerns the existence of a limit to our ignorance! Frankly, I wouldn't bet on it.
[10/18]
The generating formula, z' = z^2 + C (C -> Mandelbrot if z' remains 'small' after many iterations), gives no hint of the complexity contained therein. What is the explanation for this complexity. Let us look at this question from both a theoretical and a sociological perspective. Here is a useful starting point: Investigating The Mathematics of Complexity. The Mandelbrot may serve as a microcosm for the larger issues being raised here.
Karen points to Robert's Fractal Geometry of the Mandelbrot Set. In past years I have spent some hours playing with the Mandelbrot. I had also heard of the Julia sets, but not until a few minutes ago did I realize they were intimately related: Exploration #3. In fact the Julia sets are just an infinite ramification of the underlying Mandelbrot. Go to Julia Set Applet to see for yourself, and see Exploration #4, and The Julia Set Computer. With the Mandelbrot, I thought I had seen everything, and now I am blown away again. What are we to make of this? Julia published his work in 1918, making a brief sensation, but then it was forgotten until Benoit started his computer explorations of it in the late '70's. Note how the Fibonacci shows up in the Mandelbrot.
10/10/03