Saturday, November 12
An argument I often find myself drawn into with adherents of astrology, creationism, dualism or other such fairy tales is the definition of Science. I use the capital letter here because these arguments are about the over-arching structure of the scientific system rather than any one scientist's efforts or any one scientific theory.
To save myself some time, I'll post my argument here, once, so that I can simply point any bewildered netizens I encounter back to it and say, read this.
What is Science? First and foremost, it is an attempt to understand the world. That is not surprising, but even in this there is a buried statement. If you are making an attempt to understand the world, you are making the statement that the world can be understood, that it is not random or arbitrary. This is shared by all attempts at understanding, even primitive concepts like animism and misapprehensions like the Cargo Cults.
Science sets itself apart from other such attempts in that it constructs a system, a rigorous framework, in which we can build our understanding. The framework is based on metaphysical naturalism.
For Science does not permit of just any explanation. Science seeks to explain the world in terms of the world. For any event we observe, Science seeks an explanation in terms of other events we observe. Events that we cannot observe are precluded from our explanations.
So, for example, we observe that if we leave a piece of rotting meat lying about, after a few days we find it crawling with maggots.
Hypothesis: Maggots spontaneously form from meat if it is left undisturbed.
Hypothesis: Maggots are planted in the meat by invisible immaterial demons.
We have two plausible explanations, but they can't both be true. Why does this matter? Well, it matters because we want to know which explanation is the correct one. We can perform tests - experiments - to see if our Theory of Spontaneous Maggotation is true. We can put the meat in a tightly sealed jar and see if our maggots generate.
And, as it turns out, they do not.
We can repeat the experiment, and we find that while maggots appear in unprotected meat, meat in the sealed jar remains maggot-free. We can vary the experiment, and find that even if we do not seal the jar, but merely cover it with a cloth, there are still no maggots.
This means that the first hypothesis is incorrect. This hypothesis required only meat and time, which have both been provided, but with no maggots resulting.
What about our demons then? Well, they are invisible and immaterial, so they clearly would not be stopped by something as simple as a cloth. But a cloth does prevent maggots. What does this mean in demon terms? It means that we have observed intances where demons do not create maggots.
And that's all we can say.
The difference here is that we know the first explanation to be incorrect. We know it for certain. It is wrong. It is false.
The second explanation? Well, maybe sometimes the demons are busy inflicting cholera on the people of the next village. We don't know.
The difference is that the first is a natural explanation, and the second is a supernatural one. Natural explanations derive from natural causes, and we can control natural causes. Supernatural explanations derive from supernatural causes, and we cannot control those.
The meat is there. We gave it time. No maggots appear, so spontaneous generation is false.
The demons may or may not have been there. They are supernatural; we cannot preclude them; we may not even be able to detect their presence. We do not know, nor can we ever know, whether the demons are the cause or not.
The Theory of Spontaneous Maggotification is a scientific theory, and it is wrong. The Theory of Devilish Wormonising is not a scientific theory, because we can never know whether it is wrong.
Science's utility lies in its unique ability to throw out its trash. This is known as falsification, and although it has been acknowledged since the dawn of science, it was not until last century that Karl Popper fully explained its role.
For a hypothesis or a theory to be considered scientific, it must be falsifiable, that is, we must be able to determine if it is false. On the other hand, there is no requirement for a scientific theory to be provable, and indeed they are not. A scientific statement can be provable; the predictions made by theories are a good example of this.
Einstein's Theory of Relativity predicted that gravity would bend light in a certain way and by a certain amount. Observations by Sir Arthur Eddington confirmed this; the prediction was proved correct. This did not prove the Theory itself. It lent support to it, certainly, but that is all.
However, had it turned out that light was not bent by gravity, the Theory of Relativity would have been proved wrong, and discarded. It would have been falsified.
Now, back to our invisible demons. We know that if we cover the jar with a cloth, we don't get maggots. Is the cloth blocking the demons? That would make no sense, since the demons are supposed to be immaterial. Cloth or cork or wax stopper, all prevent the maggots, but none should present any barrier to our demons. (And we can note that wrapping people in cloth does little to prevent cholera.)
We can't say whether the demons are stopped by the cloth or just slacking, because we can't observe the demons. In fact, we have no direct evidence that the demons exist. We have postulated their presence from the existence of maggots, the corruption of wholesome meat. But now we have no maggots. Perhaps that flimsy layer of gauze really is an impassible barrier to maggot-demons.
Only... Now that we have no maggots, we have no reason to postulate the existence of demons at all. We haven't proved they're not there. The only sign we might have had of their presence is gone, but we said from the beginning that they were invisible.
And that's the problem with the Invisible Demon Theory. You can't ever know for sure that you're wrong.
Science, as we have said, is a systematic attempt to explain the world. And we know that for an explanation to be useful, we must be able to depend on it. Knowing that s = ut + ½at2 sometimes isn't really a big help.
But you can't prove that it's always correct. You can't test every situation, because there are infinitely many situations in which any theory might apply. A theory is supposed to tell you what to expect, so if all you ever do is test it, it's not much good.
You can't prove your theory, but what you can do is disprove it. We say, s = ut + ½at2 always. And we look for cases where it isn't. We can't ever hope to prove it true, but just one counter-example will prove it false. And if, over time, we find no such examples, we gain confidence in the theory. We would gain confidence too from a mass of confirming evidence, but there is a critical difference: In one case, we were trying to prove it right, and we didn't happen to stumble across anything to the contrary. In the other, we were actively seeking counter-examples, and despite our best efforts we couldn't find any.
Failure of falsification can offer much stronger support than mere confirming evidence.
So falsifiability inevitably arises as a key requirement if you wish to construct a rigorous system for explaining the world. You have to test your ideas, and this is the only reliable way to do so.
But falsification is impossible for theories deriving from the supernatural. Which means that any rigorous system for explaining the world must be naturalistic. It must preclude all supernatural causes, and forbear trying to explain supernatural events, because the former cannot produce useful explanations and the latter... cannot even be detected.
So Science, from humble beginnings as simply a concerted attempt to get the right answer, turns out to necessarily require both metaphysical naturalism as its foundation and falsification as its primary tool in seeking truth. And it is unique. There is only one Science. A system based on naturalism and using falsification to test ideas is Science. A system that fails of either of these is not.
Posted by: Susie at Saturday, November 12 2005 09:11 AM (a0oF7)
Posted by: Pixy Misa at Saturday, November 12 2005 10:02 AM (QriEg)
Posted by: Steven Den Beste at Saturday, November 12 2005 01:45 PM (CJBEv)
Posted by: Pixy Misa at Saturday, November 12 2005 05:08 PM (QriEg)
Posted by: Bill Beaty at Saturday, November 12 2005 05:46 PM (/7z+c)
Consider the postulate, made in the 19th century, of a luminiferous ether as the medium for waves of light. The ether was not observable itself (because it doesn't actually exist) but scientists believed in it, because they could predict events correctly by assuming it was there. It was when Michelson and Morley tried to measure the Earth's motion with respect to the ether, and got the "impossible" result that the Earth wasn't moving at all, that scientists lost confidence in the ether's existence. The impossibility of observing the ether gave scientists no difficulty; it needed a failed experiment to raise doubts.
The essential part of doing science is to follow out a theory's logical consequences until one reaches an assertion about observable events, and then test that assertion against reality. That is "falsification". But a scientific theory can perfectly well include unobservable causes, provided that everywhere it predicts observable events, those events come to pass -- as with the luminiferous ether. (The spacetime 4-manifold of relativity, and the virtual particles of quantum field theory, are unobservable themselves also; no one denies their existence on that account.) So naturalism, being a limit on the causes one may suggest, is far from necessary to science; and might well prove an impediment to it, by stifling imagination.
A final point. If science were based on naturalism, as you suppose, it would not be evidence for naturalism. There are people who will disbelieve their own eyes rather than admit a favorite theory of theirs is wrong, but they aren't called as witnesses to their theory. It is only if scientists are prepared, given good evidence, to entertain supernatural causes, that their testimony against such causes, when evidence is absent, carries weight.
Posted by: Michael Brazier at Saturday, November 12 2005 08:36 PM (8LTnv)
Posted by: Pixy Misa at Saturday, November 12 2005 08:52 PM (QriEg)
Posted by: Pixy Misa at Saturday, November 12 2005 08:56 PM (QriEg)
Posted by: Pixy Misa at Saturday, November 12 2005 08:58 PM (QriEg)
The real objection is, as I said before, that no inference can be reached from what the demons do to meat to anything else they might be expected to do. The theory yields no testable predictions, except for the one type of events it was built to explain; that is why it isn't scientific. But the supernatural aspect of the theory has nothing to do with that failure. A theory that maggots are generated in meat by interaction with a weightless, odorless gas named frammistine, which is inert to every substance except meat, would be non-scientific for the same reason.
On "science is based on naturalism": let's imagine a haystack, and two men who are asked whether there's a needle buried in the haystack. The first man answers, "A haystack, by definition, is made out of hay, not of needles; therefore I am certain there are no needles in this haystack." The second man says, "I have examined most of the hay in this haystack, and haven't found a needle; therefore I believe the part I haven't examined is not likely to have a needle in it." Which man would you call for to prove the absence of a needle: the first, or the second?
If science presupposes naturalism, it's parallel to the first man. If science is free to consider the supernatural, but hasn't found any compelling evidence of it, it's parallel to the second man. Science is far more convincing an advocate for naturalism if it reaches that position as a conclusion, than if it starts from there as a premise ... Science is utterly impossible under a framework of dualism. You mean, naturalism is impossible under a framework of dualism -- quite true, but not worth saying. But what you said is quite peculiar. One small miracle, however distant it may be from us in time or space, would undermine all our science and prove the cosmos to be irrational and incomprehensible? If we admit one ghost into the world, the laws of physics are a mere comforting delusion? Is it really true that unless all we survey fits into the same pattern, there is no pattern at all?
Posted by: Michael Brazier at Sunday, November 13 2005 05:01 AM (hc1pe)
Posted by: Wonderduck at Tuesday, November 15 2005 12:27 AM (HoSBk)
Posted by: matoko-chan at Tuesday, November 15 2005 02:29 AM (cxYaY)
Posted by: Pixy Misa at Saturday, November 19 2005 01:42 PM (3FPsg)
Posted by: Pixy Misa at Saturday, November 19 2005 01:45 PM (3FPsg)
Posted by: Neal at Saturday, November 19 2005 07:42 PM (pdiJG)
Second: Quantum mechanics, one of science's great triumphs, actually is Dualist as you define it. Systems of quantum particles and "measuring devices" belong to different classes of existence, and while the theory says precisely what happens when they interact, it does not even try to predict where and when interactions occur. Measurements, it would appear, are lawless intrusions into an otherwise determinate world of matter. Going by your definitions, then, quantum mechanics admits the supernatural and thus cannot be Science ...
You are no doubt ready to say "Oh, that just shows you don't understand quantum mechanics!" Please don't. This is exactly the view real working physicists take of quantum mechanics. The attempt to find a law for "measurements" that fits the observed facts is a prominent open problem in physics and a subject of current research. My point is, since quantum mechanics flatly contradicts Naturalism, it can hardly be said to presuppose it, and yet it makes a host of testable predictions, all of which have proved correct; so either one of the most useful theories ever conceived is not science, or science can dispense with Naturalism.
Posted by: Michael Brazier at Monday, November 21 2005 05:08 PM (8LTnv)
Posted by: Pixy Misa at Monday, November 21 2005 07:06 PM (3FPsg)
Posted by: Pixy Misa at Monday, November 21 2005 07:47 PM (7X4Bl)
Posted by: Tanooki Joe at Tuesday, November 22 2005 12:18 AM (loZG3)
Measuring devices are systems of quantum particles. Don't confuse reality with the model of it. Anything we call a "measuring device" is, in fact, a collection of elementary particles -- but, to make any use of quantum mechanics, we pretend our measuring devices are not controlled by quantum mechanics. If we didn't do that, the theory would make no predictions at all. Every interpretation of quantum mechanics is Dualist, because you have to split the universe into the measuring and the measured just to get started.
If you don't believe me, look up Lee Smolin -- who has said:I am convinced that quantum mechanics is not a final theory. I believe this because I have never encountered an interpretation of the present formulation of quantum mechanics that makes sense to me. I have studied most of them in depth and thought hard about them, and in the end I still can't make real sense of quantum theory as it stands.
Posted by: Michael Brazier at Tuesday, November 22 2005 03:14 AM (hc1pe)
Posted by: Pixy Misa at Tuesday, November 22 2005 03:48 AM (AIaDY)
Posted by: Pixy Misa at Tuesday, November 22 2005 03:52 AM (AIaDY)
Posted by: Pixy Misa at Tuesday, November 22 2005 03:57 AM (AIaDY)
Posted by: Pixy Misa at Tuesday, November 22 2005 04:03 AM (AIaDY)
Let's deal with a concrete example of QM in action, the classic two-slit interference effect. We have a source of photons, a sensitive photographic film, and a screen with two pinholes placed between them. If we pose the question "What is the probability that a photon from the source will hit a given spot on the film?" QM gives an answer which (if we turn on the source and observe events) proves to be correct. But by posing that question we are implicitly assuming that, when a photon interacts with the film, it must hit one and only one spot on the film. And, if we take the film to be a system of quantum particles described wholly by Schrodinger's equation, that assumption isn't justified. For the photons in question, at the moment they interact with the film, are in a superposition of states; and when a quantum system in a superposition of states interacts with another quantum system, the result is not to reduce the first system to one of its constituents, but to put the other system into superposition.
The question "What is the probability that a photon from the source will hit a given spot on the film?", thus assumes that the film is not fully described by Schrodinger's equation. The problem with QM, as a conceptual scheme, is that there's nothing in the theory itself which says when, or even whether, you are allowed to make assumptions of that kind. That's what the interpretations are for: they fill a gap in the scheme. (Notice that there were never any "interpretations" for the equations of Newton, Maxwell, or Einstein. Their theories didn't have conceptual gaps to fill before they could be applied to reality.) Wigner had absolutely no basis for claiming that consciousness cannot be in a superposition of states. There is nothing in the mathematics of QM that suggests anything of the sort. Nothing in the mathematics, to be sure; but the mathematics of QM are not -- don't even claim to be -- a complete description of reality. The point of "Wigner's friend" is to bring out just where the mathematics falls short. What's more, if the mind is magical and not subject to the laws of Quantum Mechanics, and yet is able to interact with QM systems, you arrive unavoidably at the same sort of inconsistency that afflicts all forms of Dualism Yes. That's what I meant by saying that QM is Dualist. To justify posing the questions that QM answers, you have to appeal to something that isn't subject to the rules of QM, and the actions of that something are not predictable. And that's also what Smolin meant by saying that QM is not a "final theory". A final theory would characterize the something, in addition to quantum particles.
Which brings us back to the original point. QM implies the existence of a class of being which it does not even attempt to describe, or to predict the behavior of, in order to explain the behavior of the entities it does describe. (The interpretations of QM are attempts to describe this other class of being.) Therefore it implies the falsity of Naturalism. And therefore QM cannot possibly presuppose Naturalism. If science must presuppose Naturalism, as you maintain, QM is not science -- even though it has been tested against reality in a host of ways, and has never been falsified yet.
Posted by: Michael Brazier at Monday, November 28 2005 06:19 PM (8LTnv)
Posted by: Michael Brazier at Monday, November 28 2005 06:41 PM (8LTnv)
Posted by: Pixy Misa at Monday, November 28 2005 08:09 PM (AIaDY)
Posted by: Pixy Misa at Monday, November 28 2005 08:17 PM (AIaDY)
However, having that state does not answer the question "what is the probability of the photon reaching point A on the film?" To do that you take the norm of the amplitude at point A, which is a much simpler procedure in technical terms. But -- note this, please -- that step isn't described by the equations which describe the change from the "photon at source" state to the "photon at film" state! This step, state reduction, bears no resemblance to state evolution, except that both change the current state from one function to another. Moreover, the formalism does not specify when you are supposed to use state reduction, rather than state evolution.
That's the Dualism in QM: two different dynamical laws, exactly one of which applies at any given moment, and no rule saying when to use one or the other. All the interpretations of QM are Dualist because they exist to specify when state reduction is the right law.
The one apparent exception among them, the many-worlds interpretation, turns out to conceal a Dualist premise: for what it says is that state reduction never happens, and our belief that it does is an artifact of our perceptions. The problem is that on that account, as perception is a product of state evolution like all other events, it cannot distinguish pure states from superpositions. (Only state reduction can do that.) This means we should, sometimes, perceive a superposition directly -- a thing which never happens. To explain why this doesn't happen, you have to introduce a theory of perception, which brings the mind/matter version of Dualism back into science. As I said, Dualism asserts two spheres of existence, which do and don't interact. If they interact consistently, they can be described more simply as a single sphere of existence, and it becomes Naturalism. If they do not interact, then the statement is meaningless. Only if the interaction is inconsistent is it Dualism. Here you want "consistent" to mean predictable... ... showing both that QM is not Dualist in nature and Dualism is inherently inconsistent. ... and here you want it to mean not contradictory instead. Sorry, those are not the same thing. There are, for instance, sets of natural numbers with definitions quite free of contradiction, but whose members can't be predicted. If I remember the jargon from the theory of computation, these are the "recursively enumerable" sets. It's true that Dualism postulates a partly unpredictable universe, but the jump from "unpredictable" to "contradictory" is not justified by logic or observation.
Oh, and you're a bit confused about Wigner. Certainly he was arguing for a specific interpretation of QM, in which state reduction is caused by an interaction of mind with matter. But "Wigner's friend" is a sharpening of "Schrodinger's cat", which points out the implausibility of state evolution (as QM describes it) at macroscopic scales. The difficulty it raises is inherent to QM, and isn't confined to Wigner's favorite interpretation.
Posted by: Michael Brazier at Tuesday, November 29 2005 12:18 AM (8LTnv)
Posted by: Pixy Misa at Tuesday, November 29 2005 07:15 AM (QriEg)
Observations, however, show that the basis of nearly-pure states is preferred by real particles. The many-worlds interpretation says this is an artifact of our mode of perception. What we perceive is a projection of the universe's true state into a subspace of the Hilbert space to which it belongs. But the fact that we perceive only along a subspace itself needs explanation. State evolution takes no account of subspaces or projections into them; if perception takes them into account, it cannot be a result of state evolution.
Put differently, if we the observers are only a quantum system, fully predictable by state evolution, then we should perceive the state of the rest of the universe as a whole. Our perceptions could not decompose that state into multiples of states in some basis, because the states in a basis don't physically exist. Decomposition of a state vector requires more information on the structure of Hilbert space than state evolution provides. To account for the fact that we perceive, not the whole state of the universe, but a component of it, we must invoke something outside the universe to provide the extra information.
The question which interpretations exist to answer is, why does observation of quantum systems invariably show those systems in nearly-pure states, and never shows them in superpositions? Or in more formal language: why are quantum systems always observed in states that are multiples of members of a particular basis, and never in linear combinations of these? The many-worlds interpretation "answers" it by transferring it out of the material realm and into a realm of subjective perceptions -- which is not, really, an answer at all. Indeed, not only does it appeal to an immaterial class of being (which makes it Dualist), it does so in a way that precludes any inquiry into that class. Your silly "maggot demon" theory gives more scope for investigation ...
On to the walk-through of Dualism: If they interact in a consistent manner, there aren't two modes of existence, and Dualism has contradicted itself. Substitute "fully predictable" for "consistent", and I agree to this. Only if they interact inconsistently can Dualism even be a coherent philosphy. Because any rule binding the two existences proves the principle of Dualism to be false. Any rule at all. Again I substitute "fully predictable" for "consistent" ... and the argument fails. Where is the contradiction in assuming a rule that specifies effects up to a point, but not in full? That's what state reduction does in QM: "Repeat this experiment many times, and the results follow this probability distribution."
The fact is, you won't accept any description of reality unless it's both comprehensive and deterministic. That drives you to the many-worlds interpretation of QM, because every other attempt to make sense of QM is not deterministic. But many-worlds isn't comprehensive, and can't be extended in any testable way to make it so. Which means it fails the falsifiability criterion. Insisting on absolute predictability is driving you away from interpretations that are open to refutation, and to one that both provokes further inquiry and denies the possibility of any results from such inquiry.
Posted by: Michael Brazier at Tuesday, November 29 2005 06:52 PM (8LTnv)
Posted by: L_Raj at Monday, December 05 2005 10:47 PM (dahsf)
Well, you don't really need Godel's Theorem for this. Mathematics is not science in any case. Mathematics is mathematics.
Posted by: Pixy Misa at Friday, August 18 2006 04:22 AM (FRalS)
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