Inventive vs Inductive Theories MATH IS NOT REALITY Dewey B. Larson

Transcript

ignition sequence start Euston we have a problem you got a bunch of guys about their blue what you're seeing here is a mirage you but just the going one better I'm going to go still farther back 5,000 years ago when the invention of writing on clay tablets by the Sumerians first gave the human race an opportunity to make a permanent record of its thoughts and actions there was already in existence their rather sophisticated science of astronomy the priests who were the scientists of those days were not only familiar with elementary of astronomical facts such as the apparent movements of the Sun Moon planets but they had also advanced to the point where they were able to predict eclipses and to calculate the length of the year within about a half hour of its present accepted value the premises on which these calculations and others of the same kind were made were the fundamentals of the science of that day in the sense in which I am using the term LED that is they were the most basic of the relations that were used the principles that were used by the science of our day now these principles were originally derived by a simple application of what we now call inductive reasoning that is they were generalizations from experience and that is the most reliable method of arriving at scientific principles fundamental or otherwise but unfortunately it's limited by the amount of empirical information that's available and by the extent to which that information has been analyzed so the result is about an inductive science such as that of the ancient peoples has a tendency to fall behind the progress of M vertical discovery and ultimately it acquires a rather embarrassing accumulation of unsolved problems now that was the situation in Egypt in Babylonia and in the Far East about three thousand years ago the time was clearly right for some new approach and that was provided by a remarkable group of thinkers flourished in Greece during the Golden Age of that country's history the source of order in the universe these men said was mind and the proper way of arriving at general principles was to apply insight and reasoning the result of that change in policy was to concentrate attention on the causes of physical phenomena rather than on the phenomena of themselves or the Egyptians saw only the fact that Iraq Falls if it's released from a height the Greeks looked for the cause of the fall a very reasoned that everything must have its natural place so the rock and falling then was merely looked seeking for its natural place and this way by providing an explanation for what happened they remedied the chief defect of the previous inductive theories similarly they reasoned as professor Meyer indicated that while the earth is obviously imperfect the heavens are perfect and all heavenly motions must then take the perfect form that of a circle so the orbits of the planets are undoubtedly circular now observation and experiment were definitely relegated to a secondary position by the Greeks but they were not disregarded altogether so when the observation showed that the planetary orbits are not exactly circles it was recognized that here is a awkward discrepancy that we have to do something about but one of the strong points of an inventive science such as that of the Greeks is that it can easily accommodate new discoveries simply by more invention so they assumed that the planets moved in small circles called epicycles and these epicycles then move around the main planetary orbit then when further observational refinement the stove's still nor discrepancies those could be taken care of in exactly the same way merely by adding more epicycles now this Ptolemaic theory of planetary orbits his typical of inventive theories in general and since we see it in a historical perspective by taking a look at this Ptolemaic theory we can get an idea of the general characteristics of inventive theories the first point that we need to note is that that theory was mathematically correct within the existing observational limits they then existing limits that is a general characteristic of all inventive theories because they are invented for that specific purpose they are specifically designed to fit mathematics that are already known the second point significant point is that that theory the Ptolemaic theory was conceptually wrong the interpretation of the mathematics was wrong that again is a general characteristic it applies to all inventive theories because of the circumstances under which they're invented as many observers have pointed out of them long-standing problems and science do not continue to exist because of a lack of competence on the part of those who are trying to solve them nor do they continue to exist because of a lack of methods by which to go about solving them they continue to exist because some piece or pieces of information that are essential are missing in the case of the Ptolemaic theory there were two such pieces of information the Greeks did not realize that the planets revolve around the Sun rather than around the earth and they did not know that there is a force of gravitation controlling those movements without those two pieces of information neither the Ptolemaic Theory nor any other theory that was invented to explain the mathematics could have been correct now that is a general characteristic of inventive theories and I'm stressing it at this time because it will be important later on and other connections if the information is available if all the essential information is there then there's no need to invent a theory then we can obtain it by inductive means if the essential information is not there then any theory we invent cannot be conceptually right in view of the practically unlimited opportunity for making ad hoc assumptions that is adding epicycles and inventive theory never comes to the fate of the inductive systems of theories the inventive system may fail to account for a few things at any given time but there's never the big accumulation that characterizes an inductive theory either an inductive system of theory that's fallen behind the progress of discovery but the inventive Theory ultimately in inventing system of theories inventive science I might call it ultimately encounters a fate of its own sooner or later we just have too many epicycles and in the meantime the progress of observation and the construction of inductive theories of lower-ranked is continued so that ultimately we get to the point where the scope of those theories is broad enough to challenge the prevailing inventive theory and then the inventive Theory goes to the boards now that's what happened to the Greek invented system about 500 years ago and at that time the perfection of the heavens and the natural places of objects and the other governing principles that the Greeks had invented were discarded and replaced by other principles that were derived by such - Kepler and Newton from from factual foundations by inductive reasoning now the benefit of the 2500 years of accumulated scientific knowledge the demise of the first inductive theories this new science of Newton and his contemporaries was a vastly improved product and it scored some very impressive successes at one time the practitioners of that science were pretty thoroughly convinced that a knowledge of the entire physical universe was within their grasp but here again the inherent weakness of an inductive theory again asserted itself and Newtonian science found itself faced with a series of problems for which it had no answers so then the present-day inventive science took over Allanon idea or a set of ideas gains general acceptance and becomes a familiar feature of thought its origins recede from view and I wouldn't be surprised but what many of you may be reluctant to accept the idea that the basic theories of present-day physics such as the relativity theory for example belong in the same category as the Ptolemaic theory of planetary orbits but they were all inventive theories [Music] the originators of the present-day theories don't deny that in fact they emphasize it we might even say they glory in it Einstein told us that pure invention is the only way by which these basic principles can be obtained and he was highly critical of Newton's attempt to that to ascertain them inductively here's what he said Newton believed that the basic concepts and laws of his system could be derived from experience the tremendous practical successes of his doctrines may well have prevented him and the physicists of the 18th and 19th centuries from recognizing the fictitious character of the foundations of his system Einstein's own do or is that the basic concepts and laws of physics what I'm calling the fundamentals are quote in a logical sense free inventions of the human mind he elaborates this view in these statements that I have taken from his book the world as I see it since however space perception only gives information of this external world of physical reality indirectly we can only grasp the latter by speculative means the theoretical scientist is compelled in an increasing degree to be guided by purely mathematical formal considerations in his search for a theory because the physical experience of the experimenter cannot lift him into the regions of highest abstraction the axiomatic basis of theoretical physics cannot be an inference from experience but must be free invention [Music] there is a rather general tendency to believe that Einstein and the other architects of modern physics could not have been as casual about the foundations of their system as these words would indicate that they must have been tied into something anchored to something solid somewhere but that's not true Ezra Dolf Carnap puts it they were constructed floating in the air so to speak Einstein gives us enough information about the origin of his own theories to make it clear that when he talks about free inventions he means free inventions nothing else for instance the propagation of electromagnetic radiation plays a very significant part in his theories and the comments that he made about the theory that he invented to account for that propagation have a considerable bearing on what we're talking about now in one of his books he goes on at considerable length about what a difficult problem this is and he concludes with this statement our only way out seems to be take teams to be to take for granted the fact that space has the physical property of transmitting electromagnetic waves and not to bother too much about the meaning of this statement the point of all is is that all invented theories share this same defect they are all mathematically correct but they're all conceptually wrong not because of any errors in the constriction but because of their inherent characteristics now this statement may seem to be in direct conflict with a great many of the confident assertions that we find in present-day scientific literature which tell us that the validity of present-day theories has been established beyond any reasonable doubt but if you look at the evidence in support of those assertions you will find that it is all mathematical what has been done is to establish that those theories are mathematically correct just as I said here all along that they are because of the way they were constructed but be those theories that are mathematically correct are not unique under the most in every case there are other theories that are also mathematically correct and as Richard Feynman tells us we can't distinguish between any two of them on any mathematical base on any scientific basis and say which is correct because as Fineman says they both agree with experiment to the same extent so two theories although they may have deeply different ideas behind them may be mathematically identical and then there is no scientific way to distinguish them how Fineman goes on to say this every theoretical physicist who was any good know six or seven theoretical representations for exactly the same kind of physics what Feynman does let's say is that those statements apply only to the present day and other day inventive theories they do not apply to inductive theories as theories that have been derived by induction from factual premises for example the kinetic theory of gases is a theory that relates the gas laws to the motions of the particles that compose the gas now no one tells us that he has a half a dozen equally valid representations for what the kinetic theory tells us in fact there is not another one alternative because the kinetic theory is an inductive theory that's tied in to the facts both mathematically and physically so that it's both conceptually and mathematically correct or as the invented theories are correct mathematically only now that raises a interesting philosophical question as to whether there's actually any net gain by using these inventive theories during a period when we would otherwise have no theories at all to account for some important physical phenomena actually we don't need them we could equally well use the mathematical relations that we have without any theoretical explanation so the whole thing boils down to a question as to whether there is any with any better to have a wrong theory than no theory at all now there's a very widespread belief that that's true that it is better to have a wrong theory it dates back at least to Francis Bacon the idea behind it is that a plausible theory even if it's wrong may suggest some lines of inquiry that in the end will be productive on the other hand we know that continued adherence to the Greek inventive theories particularly during the last few years of the Greek ascendancy was a very serious roadblock in the way of scientific progress and we have pretty good reason for believing that much the same as going on now in any event the fact that needs to be recognized at the moment is that we have again arrived at the kind of a situation that existed in the Middle Ages they present-day inventive theories have accumulated too many epicycles and at the same time inductive theory has caught up with observation and experiment so that as we enter the 21st century shortly we are in a position to go back from the inventive theory to a solidly based inductive theory again now the imminence of such a change could be deduced simply from the from an examination of the tames involved in the cycle of reversals that i've been talking about the first inductive theories lasted for thousands of years before they were overthrown by the greek inventive science now that the first of the inventive sciences endured for 2,500 years before it that its fate at the hands of Newtonian inductive science the accelerating pace of science is shown by the fact that in spite of its greatly superior character the science that's normally associated with the name of Newton only lasted for 400 years before it in turn succumbed to the second inventive science now if we consider the same rate of acceleration we can see that since another hundred years have passed that we are about to do for another reversal will take us back into an inductive theory and we don't have to depend entirely on inferences of that kind because there's plenty of direct evidence to show that we are again in the same kind of a situation in which Greek science found itself during the Middle Ages in the first place the accumulation of epicycles has reached the point of absurdity and in great many cases the quantum theories for instance have a long history of one ad hoc modification or interpretation after another until it's very questionable now if the theory is even intelligible in fact richard feynman though i've already quoted a couple of times says it isn't vineland says this I think I can safely say that nobody understands quantum mechanics the situation in the field of atomic structure is much the same the favorite pastime there these days is inventing properties for the elusive particles called quarks now nobody has seen or otherwise observed a court or anything that could be a quark in fact the most urgent problem for the theorists right now is to invent some theory by which it can be said that the quarks are inherently in unobservable but nevertheless we are told just what kind of quarks can exist and what their properties are such interesting properties is color charm so long in order to fit this situation into the proper perspective let's bear in mind that not only are the quarks themselves unobservable but the particles that it can suppose to be constructed out of quarks have never been observed either now it's true that those particles are given some familiar names such as electron for instance but the hypothetical electron constituent of the atom has a totally different set of properties from the observed electron then there's actually no adequate justification for calling them by the same name the same is true of the other hypothetical constituents the hypothetical Neutron can stitch you under the atom for instance has to be stable or as the observed Neutron is very much unstable the truth is that there is no definite evidence that the atom is constructed of particles at all now that may seem to be rank heresy but a great many of our formal scientists have said the same thing in different words for instance seizure when trading her once we have become aware of this state of affairs the epistemological question do the electrons really exist in these orbits within the atom is to be answered with a decisive no unless we prefer to say that the putting of the question itself has absolutely no meaning here we have a good example of the difference between induction and invasion in the construction of the theory and since I'm making this my principle point I want to elaborate on it a little such men as Newton and Einstein were very much aware of that difference Newton insisted time and time again that he did not resort to invention Einstein on the contrary criticized Newton for trying to get his theories inductively but I'm afraid that a great many people do not recognize the difference because they both start in the same way they both start with the hypothesis that's the only way we're going to arrive at something more general and what we already have start with the hypothesis what the Loudon's looked upon that hypothesis is something to be tested they test the hypothesis and if it doesn't fit the facts they throw it out and try a new hypothesis or at least a greatly modified hypothesis they test that and if that doesn't work they try another one on the other hand the Einsteins take that hypothesis test it if it doesn't work they invent something to make it work and if that doesn't work quite right they invent something to help the first invention make it work well you may think I'm being funny on this but freidheim Stein himself and he tells you exactly that's thing same thing in different words as he said it has to be pure invention but that's the difference between induction and invention in the one case its hypothesis test discard hypothesis test this card until we finally don't have to discard and the other case it's hypothesis test invent test invent until we get something we don't have to invent anymore when it was first discovered that atoms disintegrate under certain proprietary met particles in so doing it was a very natural hypothesis that the atoms are constructed of such particles but now that we have found out that those particles do not have the properties that are necessary in order to be constituents of atoms we have a totally different situation we no longer have any justification for inventing something that we can find no place oh but the general opinion still stands that this these atoms must be constructed of particles present-day theories are obsessed with the idea that they have to keep on dividing and subdividing until they get to something that they can call an elementary particle in fact the whole situation and with the physical particles is beginning to resemble that state as the flees in that popular little verse there'd be mostly view remember that goes something like this big fleas have little fleas upon their backs to bytom the little fleas still smaller fleas and so on ad infinitum the impetus for this frantic search for an elementary particle matter comes from the present-day concept of the nature of the universe which sees it as one in which the basic entities are elementary particles of matter existing in a framework provided by space and time what they might in discovery that matter can be converted into non matter and vice-versa has completely destroyed that concept it's now obvious that matter cannot be the basic constituent that there must be some common denominator underlying both matter and none matter and since that is the situation there must be some level below which matter does not exist and that which exists is this common denominator whatever it is for the moment less call it eggs this again is nothing particularly heretical some of our foremost scientists have emphasized that quite strongly Heisenberg for instance was very clear on the subject he's tried to figure out what this entity X could be he suggests energy but he has no idea he admits her didn't it how energy could fit the bill so our returning to this question of the identity wrecks a little bit later the meantime let's consider further this question of inventive versus inductive theories of how they stand now at the beginning of this century when modern inventive Theory took over from Newtonian inductive science the necessary information for constructing a an inductive theory that would account for the new discoveries that had been made around that time was entirely inadequate the information that could be collected was not enough to extend the existing inductive theories into what we may call the far-out regions the regions of the very fast the very small and the very large now there were a few of the essential building blocks already in place the discrete nature of the units of energy had already been established radioactivity had been discovered and the state electric current as a movement of electrons had been determined but there was still an immense amount of information that had to be collected before a an inductive theory that was capable of being extended into these far-out regions could be constructed that information has now been accumulated and the final inductive step that was necessary in order to construct a theory that would extend into all these regions has been taken by the development that's the subject of discussion at this conference that development like a great many other results of scientific research was a totally unexpected result of our project aimed at an entirely different objective the original objective was to construct a theory or some means or by physical properties could be calculated from the chemical composition in some respects that's not a very good subject for examination because it's been very thoroughly combed over by previous investigators but on the other hand it's also something that has a definite answer because obviously those chemical property or those physical properties are determined by the chemical composition I want to say at this point but while I may be regarded as a heretical that's not by inclination I started from a purely conventional base and my first work was directed in parallel on conventional lines the base from which I started was the idea that's embodied in the periodic table the idea that the principle principle properties of the chemical elements are determined by two variables represented horizontally and vertically in the tables the first really important advance that I made at least it's important and view of what turned up later on was the finding that one of these variables takes both positive and negative values whereas the other one takes positive values only then after a good deal of additional trial and error I found that there were actually three variables rather than two now while all this these efforts to determine the form of the mathematical relations were going on I was also struggling to determine the meaning of the terms of those relations that's the other essential for an inductive theory one that will be conceptually valid here again I didn't stay off the reservation for quite a while I started from the purely conventional idea that the atom was made up of a group of particles and that the properties the differences in properties between the elements are due to differences in the number and arrangement of those particles but after some years of work I got nowhere exactly nowhere so I had to try some different proach or quit job I tried a number of things and discarded them you know trial and error process that we learn College finally I got the idea that perhaps some of the differences in the properties might be due to differences in motions of the particles rather than in differences in the actual number and arrangement of the particles themselves so I tried bad well I didn't work either but in the process there were some indications that I might be on the right track so I just didn't throw that away immediately I worked some oriented and as I worked on it it became evident that the more emphasis I put on the motions and the less emphasis I put on the number of particles the more these indications were that I was getting some more so finally I simply discarded this idea that the motions might account for some of the differences in the properties and I substituted the idea that they motions account for all of the differences of the properties it's that error that has caused astronomy to far exceed science fiction with all of its collapsed stars its neutron stars its black holes and white holes its wormholes I'm not making that up that's in the literature I know this last week that quark stars have been added to the list it's that conceptual err this but astronomy to that pretty pass we might say our reciprocal system enables explaining all these things without those fantastic ideas it brings the physics of the far-out regions down to the same simple and logical relationships that exist in the more familiar regions of our everyday experience now I'll have to admit that maybe that isn't what you wanted maybe we're merely regarded as heartless destroyers of pleasant illusions and entertaining ideas so be it there's one happy thought I want to leave my associates with and that is that even though we're doing the same thing that our predecessors did in the Middle Ages were challenging a thoroughly entrenched an established system of inventive thought were not likely to meet with the same fate as those people or not likely to get thrown in jail or burned at the stake so thank you small circles called epicycles and these epicycles then move around the main planetary orbit then win further observational refinement the stove's still nor discrepancies those could be taken care of in exactly the same way in merely by adding more epicycles now this Ptolemaic theory of planetary orbits is typical of inventive theories in general and since we see it in a historical perspective by taking a look at this Ptolemaic theory we can get an idea of the general characteristics of inventive theories the first point that we need to note is that that theory was mathematically correct within the existing observational limits they then existing limits that is a general characteristic of all inventive theories because they are invented for that specific purpose they are specifically designed to fit mathematics that are already known the second point significant point is that that theory the Ptolemaic theory was conceptually wrong in this way by providing an explanation for what happened they remedied the chief defect of the previous inductive theories similarly they reasoned as professor Meyer indicated that while the earth is obviously imperfect the heavens are perfect and all heavenly motions must then take the perfect form that of a circle so the orbits of the planets are undoubtedly circular now observation and experiment were definitely relegated to a secondary position by the Greeks but they were not disregarded altogether so when the observation showed that the planetary orbits are not exactly circles it was recognized that here is a awkward discrepancy that we have to do something about but one of the strong points of an inventive science such as that of the Greeks is that it can easily accommodate new discoveries simply by more invention so they assumed that the planets movements were not only familiar with elementary astronomical facts such as the apparent movements of the Sun Moon planets but they had also advanced to the point where they were able to predict eclipses and to calculate the length of the year within about a half hour of its present accepted value the premises on which these calculations and others of the same kind were made were the fundamentals of the science of that day in the sense in which I am using the term led that is they were the most basic of the relations that were used the principles that were used by the science of our day now these principles were originally derived by a simple application of what we now call inductive reasoning that is they were generalizations from experience and that is the most reliable method of arriving at scientific principles fundamental or otherwise but unfortunately it's limited by the amount of empirical information that's available and by the extent to which that information has been analyzed so the result is about an inductive science such as that of the ancient peoples has a tendency to fall behind the progress of empirical discovery and ultimately it acquires a rather embarrassing accumulation of unsolved problems now that was the situation in Egypt in Babylonia and in the Far East about three thousand years ago the time was clearly ripe for some new approach and that was provided by a remarkable group of thinkers flourished in Greece during the Golden Age of that country's history the source of order in the universe these men said was mind and the proper way of arriving at general principles was to apply insight and reasoning the result of that change in policy was to concentrate attention on the causes of physical phenomena rather than on the phenomena of themselves or the Egyptians saw only the fact that Iraq Falls if it's released from a height the Greeks looked for the cause of the fall how they reasoned that everything must have its natural place so the rockin falling then was merely like seeking for its natural place ignition sequence start [Music] houston we have a problem right blue what you're seeing here is a mirage Mirage you but just to going one better I'm going to go still farther back 5,000 years ago when the invention of writing on clay tablets by the Sumerians first gave the human race an opportunity to make a permanent record of its thoughts and actions there was already in existence their rather sophisticated science of astronomy the priests who were the scientists of those days