Tripod: Messages from the Staff

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what came out was somewhat different, though no less of a message from me to you. It happens that I've been thinking for years about the underpinnings of knowledge, specifically scientific knowledge, and frankly, the time was right to summarize where the investigation currently stands.<br><br> Little effort has been made to structure the following observations and arguments, though it's probably better that way. You are always free to create the structure for yourself. In a fundamental way, that's what I might be driving at.<br><br> <b><font size="+1">PHILOSOPHICAL BRAINSTORM</b></font><br><br> <b>I.</b><br><br> A theory attempts to predict, in a general way, the future state of a system. ("Theory" is too weighty a word; at times "model" is more appropriate.)<br><br> Science is a process that generates an evolving corpora of successively better theories to explain "natural" phenomena.<br><br> Paradigm shifts can be said to occur when a theoretical system is undercut by a major change in the foundation of the system. This is the most radical form of scientific change, as currently formulated.<br><br> Science historically has experienced many paradigm shifts. There is no reason to believe this pattern will stop recurring.<br><br> While scientific theory (normally) attempts to explain nature, it is not determined by nature. It can be argued that scientific theory is non-unique.<br><br> This is so because we can not observe all of the facts in the system. We must abstract away the details that we are not able to observe. 1) The details that we do observe can either be recombined differently to form the basis of an alternative model/theory (Copernicus), or 2) newly observed, or conceptualized, details can alter the fundamental equations (Einstein, et al).<br><br> Natural laws can be thought of as "superb theories" (Roger Penrose's <b>The Emperor's New Mind</b>). Superb theories have long lives and are very easily taken for truthful explanations of nature.<br><br> Even hitherto superb theories have had to be reworked or replaced. Given the pattern of paradigm shifts, how much reason is there to believe that any of our scientific beliefs will stand? For example, recent developments in the theory of EPR particles make it clear that action at a distance is possible, perhaps because the universe isn't as discrete as we had thought. (Certain particles that once interacted remain "connected" in such a way that a change to one instantaneously affects the other, no matter how far apart the particles are.)<br><br> Abstraction is a <b>process</b>  a useful one  that misses a lot and never ends. It's a good bet that unacknowledged dimensions of X, neglected to date, will nonetheless eventually precipitate a rewriting of our most superb theories.<br><br> What did you know yesterday? And what will you know tomorrow? (Paraphrase of <b>Men in Black</b>)<br><br> We could digress into what constitutes (scientific) progress. Progress, as generally understood, occurs within the context of a given system. When the system becomes suspect, the progress that was made can become irrelevant. However, it is possible that the process of elaboration/negation (and I don't mean Hegel) could lead somewhere (cf. mathematical random walk). It probably always appears to lead somewhere.<br><br> <b>II.</b><br><br> Perhaps we can imagine an additional model for the evolution of scientific theory. Theories that have not been refuted within a given system have a truth value (fractional or whatever) and influence the development of the system. These evolving theories influence one another, via people!, but are commonly conceived of as competing for unique status on the pedestal of natural law.<br><br> Kurt Gödel's incompleteness theorem suggests that there are propositions which will never be demonstrated to be true or false within the context of arithmetic (and, more generally, sufficiently complex systems that obey similar rules). Do these propositions have truth values? In my world, they do. The act of wondering about the validity of such propositions influences the evolution of the system.<br><br> For instance, if we added an axiom to fill one of the Gödelian holes, just for kicks, could we find a use for the resulting mathematics? Prior experience suggests that given a model and a little creativity, we can find, or build, an application.<br><br> Systems are frequently evolved by the addition of axioms that permit the handling of phenomena that were previously outside the scope of the system. Compare with (1) above. E.g., the extensions of mathematics introduced to deal with infinity. And even Cantor's seemingly insane transfinite arithmetic has been applied to some good in the realm of mathematical analysis.<br><br> <b>III.</b><br><br> Negating axioms to grow the system.<br><br> The possibility that a fundamentally different formulation of scientific theory could be developed has a truth value. (The image of the scientist with a palette, "something to paint on", and a brush. You choose your canvas, your system, even your metaphysics.)<br><br> Even within the context of established mathematics and general relativity, there is still room for alternate cosmologies. The accepted conception of the universe is non-unique. For instance, Gödel (again) formulated a model that is completely consistent with general relativity in which each point in space revolves around every other point. We can not, using currently established scientific theory, prove this to be false. Couterintuitive as it may seem, the theory has a truth value. It has certainly influenced theorists, most of whom weren't hoping for such a possibility.<br><br> It is problematic that math is so well behaved that we commonly assume the universe works according to mathematical laws. At the limit, however, it is not clear that the equations are accurately modeling the universe. (TO DO: Dig up the recent NY Times article.)<br><br> Math has evolved in pieces. You can see this in the various axioms that take pages to enumerate. Decisions and educated guesses are always being made in math and science, based on incomplete information: Nature works like this, but not like this. These add up to a way of understanding the world.<br><br> These decisions and educated guesses are a way of telling a story; they are not necessarily how the universe really works, assuming the universe works a certain single way to begin with! It seems as if our models are the universe. Instead, our models are the limits of our universe. Unnecessary, perhaps, but we have wired our minds to work this way under the crushing load of accumulated theory. Shoveling out from under that theory can be a Herculian task.<br><br> I can envision a universe that responds to and is shaped by collective thought, and not restricted to human thought. ("Thought" is really a substitute for a more fundamental thingness; one for which I haven't found a word.) A universe in which a shared hallucination explains why our theory so accurately reflects the world around us so much of the time. Re-assert that we can find an application for this model, given a little creativity. This cosmology, too, has a truth value.<br><br> <b>IV.</b><br><br> So what?<br><br> We could embrace the process of coming to terms with the omnipresence of our theory, of accepting the fundamental relativism of the corpora, and of choosing to work with a model or within a given theory when appropriate.<br><br> This way of thinking fosters open-mindedness and (hence) creativity, and empowers individuals to develop a personal understanding of the world. As I argued in <a href="../../../www_subdomain/tripod/letters/jeff2.html">my last letter from Tripod</a>, the elaboration of personal understanding elevates consciousness and begets personal answerability.<br><br> I think this is where we are headed. At the very least, the hope is never far from my mind. </blockquote> <br> <ul> <a href="../../../www_subdomain/tripod/staff/tech-html/anchor_jeff.html">Jeff Vander Clute</a>,<br> Director of Internet Technology (6/5/98)</ul> <hr width="330"> <br><br> <center>Read more "Letters from Tripod" in the <a href="../../../www_subdomain/tripod/letters/archive.html">archive</a>.</center> <br><br> </td> </tr> </table> </td> </tr> </table> </body>