dmb@morgoth.UUCP (David M. Brown) (08/23/87)
The purpose of a theory is to simplify. Seemingly disparate phenomena are unified, or integrated, into one. The purpose of this is similar to the need for modularity in programming - to hide details. If I am basing a theory upon some other theories, I want to use the ones which have less assumptions to check, preferably none! Therefore, Occam has given me good advice. But what, someone asks, if the simpler theory is not the "right" one? Perhaps you philosophers avoid this question. If so, then you need not consider Occam's Razor as anything more than advice. If not, then we are entering the realm of "Truth" (absolute, relative, whatever). One argument given recently was that simplicity has an aesthetic component, which touches our innate ability to directly sense Truth. I agree with this, but others were not convinced that this sense is accurate. Because we are talking about matters of the mind, it might be appropriate to discuss the origin of the mind. Basically, minds have evolved because they have survival value. The ability to generalize, to hide detail, and therefore to deduce, to look ahead, to imagine, has given us the ability to survive. I submit that if we had generalized, etc., in the wrong directions, we would have died (probably many did). Our process of generalization (ie, simplification) gave us survival value only because it was in the right direction. For example, it was absolutely correct to consider the leaves, branches, trunk and root as one entity, the tree. That was the *correct* simplification. As our thought processes encompassed more and more phenomena, and as we questioned things we previously took for granted, formal theories evolved, along with formal method(ologie)s. However, let's remember that these formalisms are based upon assumptions so innate that they are practically hard-wired. When a theory becomes too complex (at any one particular level), when it has loose ends, when it has jagged edges, when it is not simple, our aesthetical sense, derived from millions of years of being right, tells us it's wrong. Did you have a picture in your mind of 'loose ends', etc.? What is that a loose end of? What are those lines? I can't answer that exactly, but I think they are really *there*. Where? Somewhere you can only see/be with your mind. Somewhere where conception differs but little from perception. Another discussion in this newsgroup concerned Taoists. I think their symbol, the Yin-Yang, is relevant here. Among other things, the Yin-Yang is a symbol of the process of simplification, or generalization, of abstraction. The black and white represent specific details, the circle into which they combine represents the general. As such, it can be mapped into an upside-down letter Y: | <- simple | / \ / \ <- complex This is the basic structure of the hierarchy of dependencies and conclusions which comprise any theory. Multi-branched nodes can be represented as sets of binary branches. The universe, of course, isn't as simple as this. It's not a simple hierarchy, except locally. Note that the duality represented by the binary branching can ba mapped onto the duality between duality and oneness. The tree becomes a graph. Self-reference is encoded at the highest level. Does this have something to do with Godel? Anyway, I have strayed from my original intentions. Trust your mind. It got you this far. David Brown {harvard | ll-xn | mirror}!adelie!morgoth!dmb GZA, 320 Needham St., Newton Upper Falls, MA 02164 (617) 969-0050 WE CHALLENGE our traditions BECAUSE we believe TRUTH without questioning IS FALSE
kube@cogsci.berkeley.edu (Paul Kube) (08/24/87)
In article <433@morgoth.UUCP> dmb@morgoth.UUCP (David M. Brown) writes: >One argument given recently was that simplicity has an aesthetic >component, which touches our innate ability to directly sense Truth. >I agree with this, but others were not convinced that this sense is >accurate. Are you counting me among the `others'? I don't doubt that our intuitions about what's true are sometimes right, and even reliable over some domains. I do doubt, though, that these intuitions are reliable when applied to anything as complicated as a serious scientific theory; do you really mean to suggest that you can tell if a serious empirical theory is true just by thinking about it? >I submit that if we had generalized, >etc., in the wrong directions, we would have died (probably many did). >Our process of generalization (ie, simplification) gave us survival >value only because it was in the right direction. That we have survived as a species shows at most that we have not got it so wrong as to have been put to serious disadvantage with respect to our ecological competitors; it does not show that we have got it right. So far as physics goes, our innate endowment seems to have left us stranded somewhere pre-Aristotle: good enough given our niche and maybe more useful than the correct theory given the computational limitations of our wetware, but wrong nevertheless. I would think that the kinds of cognitive capacities that tend to enhance reproductive success are primarily things like being able to tell if a mating candidate is fertile or whether the thing you're looking at is edible. Our intuitions are bad enough here; what reason is there now to think that we have evolutionarily honed intuitions for detecting correct mathematics, or quantum mechanics, or astrophysics? --Paul kube@berkeley.edu, ...!ucbvax!kube
myers@tybalt.caltech.edu (Bob Myers) (08/24/87)
In article <433@morgoth.UUCP> dmb@morgoth.UUCP (David M. Brown) writes: >The purpose of a theory is to simplify. Seemingly disparate phenomena >are unified, or integrated, into one. The purpose of this is similar >to the need for modularity in programming - to hide details. Yes. But why do you hide the details? So it's easier to think about, I would say. >But what, someone asks, if the simpler theory is not the "right" one? >Perhaps you philosophers avoid this question. If so, then you need >not consider Occam's Razor as anything more than advice. If not, then >we are entering the realm of "Truth" (absolute, relative, whatever). I really don't think that science deals with "Truth" or "right"ness. It does deal with accuracy and explanatory power. Explanatory power has two halves: simplicity, so we can understand it, and generality, so it covers more than a narrow range of phenomena. >One argument given recently was that simplicity has an aesthetic >component, which touches our innate ability to directly sense Truth. >I agree with this, but others were not convinced that this sense is >accurate. I'm not sure what Truth you're talking about here. Do you mean scientific truth, as in the likelyhood of some scientific theory being accurate to such and such a degree, or are we back to some sort of innate philosophical truth? I don't think we can sense directly the accuracy of a scientific theory. >Because we are talking about matters of the mind, it might be >appropriate to discuss the origin of the mind. Basically, minds have >evolved because they have survival value. The ability to generalize, >to hide detail, and therefore to deduce, to look ahead, to imagine, has >given us the ability to survive. I submit that if we had generalized, >etc., in the wrong directions, we would have died (probably many did). >Our process of generalization (ie, simplification) gave us survival >value only because it was in the right direction. For example, it was >absolutely correct to consider the leaves, branches, trunk and root as >one entity, the tree. That was the *correct* simplification. Nonsense. That was the *useful* simplification. *Useful* in that it increased survivability. There is nothing to make any simplification any more "correct" than any other, other than degree of accuracy. And the usefulness of such simplifications varies *greatly*, depending on your purposes. >When a theory becomes too complex (at any one particular level), when >it has loose ends, when it has jagged edges, when it is not simple, >our aesthetical sense, derived from millions of years of being right, >tells us it's wrong. Hmm. For whatever it's worth, I don't think this is right. I think there is a failure to comprehend a theory that gets too complex -- comprehend on an intuitive level -- which is of course yet another simplification. I feel that the isomorphism between my mind and physical reality is not very good. I don't think we're told it's wrong, but that we don't understand it well. A theory is only "wrong" insofar as it is inaccurate. But it is only useful insofar as it is accurate AND understood. >Did you have a picture in your mind of 'loose ends', etc.? What is >that a loose end of? What are those lines? I can't answer that >exactly, but I think they are really *there*. Where? Somewhere you >can only see/be with your mind. Somewhere where conception differs >but little from perception. I think this is more of a psychological problem. Some people (including me) think in pictures. Images come to mind when I think about things. I think it's just another way of representing within your mind what goes on around you. Another way of making the isomorphism between reality and your mind. Many people have a good understanding of what they can picture. It's just a simple step beyond that to represent concepts within your mind as pictures, too. If the brain is hard-wired for anything, it`s hard-wired for dealing with perception. Hundreds of millions of years in the making. Why not make use of that hardware? ------------------------------------------------------------------------------- Bob Myers myers@tybalt.caltech.edu {rutgers,amdahl}!cit-vax!tybalt.caltech.edu!myers
sarge@thirdi.UUCP (Sarge Gerbode) (08/25/87)
In article <20264@ucbvax.BERKELEY.EDU> kube@cogsci.berkeley.edu.UUCP (Paul Kube) writes: > >what reason >is there now to think that we have evolutionarily honed intuitions >for detecting correct mathematics, or quantum mechanics, or astrophysics? Only that it seems to be a psychological fact that we have a kind of "built-in computer" that operates unconsciously (or maybe we get messages from God, or whatever). From this source (or Source) we get hunches and "feelings" about things. These hunches and feelings often form the basis for scientific hypotheses that later turn out to be true. I don't go along with the radical form of "If it feels good, do it!" that was mandated in the '60s counter-culture, but I think, as Aristotle did, that pleasure is a sign of the good (and the true). Therefore, all else being equal (and it usually isn't), one should (and does) pick the choice that gives one pleasure, or, alternatively, that appeals to one aesthetically. -- "Absolute knowledge means never having to change your mind." Sarge Gerbode Institute for Research in Metapsychology 950 Guinda St. Palo Alto, CA 94301 UUCP: pyramid!thirdi!sarge
smoliar@vaxa.isi.edu (Stephen Smoliar) (08/25/87)
In article <3733@cit-vax.Caltech.Edu> myers@tybalt.caltech.edu.UUCP (Bob Myers) writes: > >I really don't think that science deals with "Truth" or "right"ness. >It does deal with accuracy and explanatory power. Explanatory power >has two halves: simplicity, so we can understand it, and generality, >so it covers more than a narrow range of phenomena. > I think it may be useful to recall Marvin Minsky's definition of the term "model:" To an observer B, an object A* is a model of an object A to the extent that B can use A* to answer questions that interest him about A. Thus, we may say that science is concerned with the development of models which answer questions about different bodies of phenomena, and such models are generally called theories. However, the important part of Minsky's definition which is often overlooked is that part about "questions that interest him." Not only is it necessary to scope out the particular body of phenomena which are under study (A); but also one must scope out the nature of the questions one wishes to pose about those phenomena. Indeed, one way of looking at Kuhn's paradigm shift is that it entails a major change in the nature of the questions being posed.
flash@inference.ee.qmc.ac.uk (Flash Sheridan) (09/24/87)
In article <20264@ucbvax.BERKELEY.EDU> kube@cogsci.berkeley.edu.UUCP (Paul Kube) writes: >In article <433@morgoth.UUCP> dmb@morgoth.UUCP (David M. Brown) writes: > do you really mean to suggest that you can tell if >a serious empirical theory is true just by thinking about it? > According to Einstein, yes. He claimed he developed Special Relativity for its harmony with Maxwell's equations, _before_ Michelson-Morley.
cik@l.cc.purdue.edu (Herman Rubin) (10/04/87)
In article <294@sequent.cs.qmc.ac.uk>, flash@inference.ee.qmc.ac.uk (Flash Sheridan) writes: > In article <20264@ucbvax.BERKELEY.EDU> kube@cogsci.berkeley.edu.UUCP (Paul Kube) writes: > >In article <433@morgoth.UUCP> dmb@morgoth.UUCP (David M. Brown) writes: > > do you really mean to suggest that you can tell if > >a serious empirical theory is true just by thinking about it? > > > According to Einstein, yes. He claimed he developed Special > Relativity for its harmony with Maxwell's equations, _before_ > Michelson-Morley. Certainly William of Ockham, and until recently most philosophers, believed that it is easy to find "true" theories, and that it is not difficult to test these theories. Now it may be that the speed of light in vacuum is constant, but there is no way to directly test it. In fact, according to most of what I read in modern physics, there is no vacuum! Thus the real problem is "when should we accept a theory which we cannot completely test, or which we may even know to be false." Since there is no vacuum, the Special Relativity transformations, if we could obtain sufficiently accurate data, would not agree with Einstein's predictions exactly. There is no question that the Lorentz-Fitzgerald transformations were obtained as the set of transformations which preserve Maxwell's equations before Michelson-Morley, and that Special Relativity follows from these equations if the speed of light is assumed constant. However, while the development does not involve any empirical observations, Maxwell used, possibly indirectly, empirical results. On the other hand, I completely disagree that one infers natural laws from empirical observations! One only chooses which mental construct to use among those which the mind can conceive on the basis of observations. -- Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907 Phone: (317)494-6054 hrubin@l.cc.purdue.edu (ARPA or UUCP) or hrubin@purccvm.bitnet
franka@mmintl.UUCP (Frank Adams) (10/06/87)
In article <588@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes: >On the other hand, I completely disagree that one infers natural laws from >empirical observations! One only chooses which mental construct to use >among those which the mind can conceive on the basis of observations. I will certainly agree with that second sentence. But I think it is also indisputable that those observations may cause us to conceive mental constructs which we would not otherwise have conceived. If that isn't "inferring natural laws from empirical observations", I don't know what is. If, on the other hand, you mean to say that we don't *deduce* natural laws from empirical observations, I will quite agree. -- Frank Adams ihnp4!philabs!pwa-b!mmintl!franka Ashton-Tate 52 Oakland Ave North E. Hartford, CT 06108