Book Club: The Edge of Reason, 2, science for humans

Time to go back to Julian Baggini’s book, The Edge of Reason: A Rational Skeptic in an Irrational World, which I have began discussing last month. While the first chapter was about God and the rationality (or lack thereof) of arguments pro and against, the second one is about science and why it is far less rational that we are led to believe (especially by scientists).

The chapter opens with the observation that science is not an objective “view from nowhere” thing, but a sophisticated, yet fallible, human enterprise, fundamentally dependent on human judgment. As in the case of a poll Baggini cites from 1999: when 90 leading physicists were asked which interpretation of quantum mechanics they thought was best, 4 voted for Copenhagen, 30 for Many Worlds, and 50 said either none of the above or undecided. Clearly, which available model is preferable is a question of subjective judgment, not empirical fact (as the very word “interpretation” strongly suggests…).

The point Julian is making throughout the chapter is simple, yet controversial: “My aim is to show how accepting the role of judgement in science in no way undermines it, but it does require us to rethink how we assume reason works.”

One of his best examples comes again from quantum physics, when he notices that Schrödinger’s and Heisenberg’s competing theories were not only equally compatible with the empirical data, but in fact had been shown to be mathematically equivalent. They were, therefore, both empirical and mathematically underdetermined. Which one you preferred came down to subjective judgments having to do with beauty, simplicity, or even, possibly, whether you personally liked one physicist better than the other.

The general idea that theories are never, by themselves, uniquely determined by the evidence is known today as the Duhem-Quine theses, but Baggini points out that the concept goes back at least to John Stuart Mill, who wrote in A System of Logic that a hypothesis “is not to be received as probably true because it accounts for all the known phenomena, since this is a condition sometimes fulfilled tolerably well by two conflicting hypotheses.” Mill thought that this was commonly accepted by “thinkers of any degree of sobriety” (I love the turn of phrase!).

As Julian observes, scientists are often dismissive of the Duhem-Quine theses, charging that it is difficult enough to come up with one reasonable theory to explain the data, let alone dream up multiple alternatives. But “this misses the point. The value of the underdetermination thesis is not to make us seriously consider all alternatives to the most powerful and tested scientific explanations. Its value is that it makes it clear that even when the evidence appears overwhelmingly to support one theory rather than another, there is always a gap, however small, between what the evidence requires we conclude and what we actually conclude.”

Another factor that conjures in hiding the role of human judgment in science is the fiction that there is such thing as a quasi algorithm-like thing called “the scientific method.” While philosophers of the early part of the 20th century kept searching for it, the consensus nowadays is that it doesn’t exist. Yet scientists themselves help perpetuate the myth, both in references to the phantomatic method in introductory textbooks, and also by creating “the false impression of a regular, orderly method by writing up their findings in ways which gloss over the real messiness of discovery.”

Indeed, as Baggini stresses, if one looks at how science is actually done — rather than described in simplistic idealizations — it is a highly messy activity where “quirks and deviations” from the official picture of rigorous experiments and straightforward deduction are not exceptions, but rather the norm.

There are many documented cases in the history of science when a scientist persisted out of sheer obstinate conviction of being right, an attitude we associate instead with pseudoscience. My favorite example among those cited by Julian is Boyle, who was “persistent in holding to his theory when observation refused to confirm it. On 49 occasions he tested his hypothesis that smooth bodies that stuck together in air would come apart in a vacuum, without success, yet succeeded on the 50th attempt.”

What, then, distinguishes a brilliant scientist like Boyle from a crank? Good judgment of his intuitions, arising from experience as well as brilliance. Not much else, really.

Moreover, scientists — especially physicists — tend to rely on theory more than empirical evidence, even when the empirical evidence appears to contradict the theory. Eddington, the astronomer that confirmed Einstein’s theory of relativity in 1919, famously declared that “It is a good rule not to put overmuch confidence in the observational results that are put forward until they have been confirmed by theory,” a striking reversal of the usual idea of how science works.

The temperament and gut feelings of scientists play a major role early on during discovery and initial verification, notable cases include Einstein’s suspicion of quantum mechanics (“God doesn’t play dice”) and Heisenberg finding Schrödinger’s theory “repulsive.”

Here is one gem from the chapter: “Another of Einstein’s remarks is extremely revealing. He once said, ‘I find the idea quite intolerable that an electron exposed to radiation should choose of its own free will, not only its moment to jump off, but also its direction. In that case, I would rather be a cobbler, or even an employee in a gaming-house, than a physicist.'” This is an expression of a strongly emotionally held aesthetic judgment. Nothing to do with physics or mathematics as ordinarily understood, or the quest for truth, for that matter.

And of course beauty and aesthetics are not, in fact, guarantors of truth: “As George Ellis and Joe Silk point out, ‘Experiments have proved many beautiful and simple theories wrong, from the steady-state theory of cosmology to the SU(5) Grand Unified Theory of particle physics, which aimed to unify the electroweak force and the strong force.'”

Scientists — below the surface, mostly in private or informal exchanges — even disagree on major issues of epistemology and metaphysics. For instance, “Bohr … completely rejected scientific realism. ‘There is no quantum world. There is only an abstract quantum mechanical description,’ he said. ‘It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.'” Needless to say, a number of his colleagues disagreed vehemently, thus unwittingly engaging in philosophical debates about the nature and scope of their discipline.

By the end of the chapter, Baggini concludes: “The success of science should not lead us to believe that it provides the model for all reasoning; rather that the domain of science is one which is especially conducive to the use of reason. … We need a more expansive notion of what it means to be rational, one which includes all the elements that are left out when we focus only on the strictly formal and empirical ones. At the heart of this notion we need to place judgement.” Indeed.

292 thoughts on “Book Club: The Edge of Reason, 2, science for humans

  1. Bunsen Burner

    Haulianlal :

    ‘ If you wish to know how fast an ordinary body will fall when dropped from a certain height at a certain place (for example, at Athens from a tower 30 feet up), Aristotle’s theory will give satisfactory results for that particular purpose’

    Do you have a reference for this? From what I remember of historians discussing the limits of Aristotle’s ideas (Julia Barbour’s History of Motion I think has a lot of references) this is far beyond what you can hope to achieve from Aristotle’s physics.

    Robin:

    Coming up with theories that aren’t particularly accurate is not a hard task. Aristotle’s ideas would not be accurate enough to be useful for most basic tasks that you would want a theory of motion for. I also very much doubt that you could even come up with robust error bounds for Aristotle’s physical approximations which would make the applications of his ideas incredibly hit or miss.

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  2. Robin Herbert

    Two millennia, in any case.

    A law which said that an object keeps on travelling in the same direction and speed until another force acted on it, would have failed a qualitative and quantiive analysis ftom their point of view.

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  3. Massimo Post author

    Alan,

    No need to apologize about your comments in the previous post. Your contributions are among the most thoughtful here, and I value them highly.

    Liked by 1 person

  4. Robin Herbert

    Hi Bunsen Burner

    Coming up with theories that aren’t particularly accurate is not a hard task.

    You only think so because you have two and a quarter millennia of development of maths and science behind you which you were taught at school.

    As far as I know the very concept of a law of motion did not even exist at the time and it took the rest of mankind another two thousand years to get from Aristotle’s Force = mass times velocity to Newton’s Force = Mass times acceleration.

    Aristotle’s ideas would not be accurate enough to be useful for most basic tasks that you would want a theory of motion for. I also very much doubt that you could even come up with robust error bounds for Aristotle’s physical approximations which would make the applications of his ideas incredibly hit or miss.

    But the point is they would do as well as, probably better than Newton’s laws of motion applied under the same circumstances. Without accurate time measurement neither of them could produce much useful.

    If you could have experimentally estimated values for Aristotle’s density laws and natural motion laws then you could probably have estimated the path of a projectile using divisions of the path, to a reasonable degree of accuracy. As it happened Aristotle was a lot more interested in biology.

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  5. Bunsen Burner

    Robin:

    Are you seriously telling me that you think you can take Aristotle’s physics and apply it to the path of a projectile – say a weight from a catapult of the day – parameterise the problem by mass and angle of ascent, and get consistent quantitative results to a degree of accuracy that they could not be be differentiated from the Newtonian result by the standard rulers of Aristotle’s day?

    I find this very difficult to swallow? On what do you base this assertion?

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  6. Robin Herbert

    Bunsen Burner,

    As I said, if you could use an accurate timer and experimentally quantify his density and natural motion laws, I don’t see why not. If you could quantify the rate at which the “natural motion” gained speed then I don’t see why a pre-calculus calculation of that trajectory using Aristotle’s physics would give a worse estimate of that path than Newton’s. I don’t see how it would have been significantly different. Aristotle’s “natural motion” was an accelarating motion towards the earth and you would have to add resistance to the Newtonian calculations which would be very similar to Aristotle’s “density”

    The difference between Aristotle’s “force = mass times velocity” and Newton’s “force = mass times acceleration” would not be particularly significant in that particular calculation since Aristotle is referring to “velocity produced by the force”. Aristotle understood velocity as being a change in position divided by a change in time and so the calculation would definitely be possible.

    Keep the technology and the notation the same for both calculations and I don’t see how they would be much different.

    What is the nature of the problem you see with that?

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  7. Bunsen Burner

    Robin:

    The problem I see with it? F=ma and F=mv is the difference between a second order and a first order differential equation. A very significant difference – like between a parabola and straight line. The correct distance traveled by a projectile is proportional to the time of flight, under Aristotle it should be a constant! The difference between the two results would definitely be noticed by the ancient Greeks over the distances covered by a catapult.

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  8. Robin Herbert

    Bunsen Burner,

    As I pointed out before, Aristotle was referring to the velocity produced by the force which is, in a practical situation like this, equivalent to acceleration.

    Once the projectile has left the catapult it is not going to continue accelerating. So under a Newtonian system the catapult is going to accelerate it to a particular speed, under the Aristotlean system we would say that the force of the catapult produced that speed.

    But once it is no longer on the catapult the situation is the same. We just have velocity and direction. We have a first order differential equation in each case.

    And we are not going to cheat and allow 17th century mathematics for one and 3rd century BC mathematics for the other.

    After the projectile has left the catapult the trajectory is changed by – in the Newtonian system the downward acceleration due to gravity and the air resistance. In the Aristotlean system it is altered by the “natual motion”, ie a constant acceleration towards the Earth, and the density of the medium.

    If these values have been established experimentally in both cases I don’t see what the difference would be.

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  9. Robin Herbert

    To clarify, once you had taken the other factors into account, not just the velocity at which the projectile left the catapult, you would have a second order differential equation in each case, although the actual calculation for the comparison would not be done using calculus.

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  10. Bunsen Burner

    Robin:

    Lets ignore air resistance for the time being. Can you actually derive what Aristotle’s equation of motion would be, parameterising on any unknowns? Why can’t we solve both equations using calculus if they are both second order differential equations? Who would stop us?

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  11. Haulianlal Guite

    Coel:

    || If I am genuinely baffled by what you’re saying and ask questions to clarify that, it is just about within the realms of possibility that you haven’t explained your meaning very well, is it not?||

    Its entirely possible that’s because you haven’t read it properly, or seek a way out somehow by seeking out some linguistic point to win the case, as if its about winning. Anyway, lets move on.

    ||The Cosmological Principle is not a theory and not a model, it’s not suggested as an explanation for anything. ||

    Oh no, both claims miss the point. Never once did I suggest it to be a theory or model or an explanation. The point being that the isotropy and homogeneity that the principle alludes to, were believed to be facts till the 1980s, and that this fact required an explanation for why the universe appears to obey this principle. Inflation was theorized to explain this observational fact. Now it turns out this fact is no fact at all. And if the fact a theory sets out to explain turns out to be an error instead, what of the theory?

    || It’s an assumption adopted to make models simpler. ||

    It wasn’t an assumption so much as it was believed to be an observational fact.

    ||Then produce your calculation showing that no version of the inflationary model can be made compatible with the size of the observed structures, if that is what you are claiming. I don’t think you can do that.||

    Now this sleight of hand won’t work. Being not a physicist, I’m appealing to the authorities of those physicists who says the principle is incompatible with large-scale structures. Need source?

    Here:
    http://www.iflscience.com/space/what-largest-object-universe/
    http://www.space.com/23754-universe-largest-structure-cosmic-conundrum.html

    Now as per the “established” science, using inflationary models, the experts have calculated the theoretical limit for large-scale structures to be at a maximum of 1.2b light years across. Assuming this to be the case, we have not one but at least 6 structures which already cross this limit.

    Again that’s not my calculation, and I haven’t the faintest idea in God’s cosmos how they come up with this figure. If however you as another expert believe this figure to be wrong for whatever reason, and that these structures are compatible after all, then you render these other experts wrong; and further, you really need to come up with what counts as “isotropy” if structures billions of light years across are in no way a violation.

    Being a philosopher however, and someone who can tell when even the experts are inconsistent, the question is: if there are 6 other structures that already violate the principle by your own calculations, how much structures do you need to abandon the principle altogether – and by extension, the models that were built to explain this discredited fact?

    ||Indeed, as just explained, inflationary models would naturally predict much larger structures in the observable universe than non-inflationary models.||

    Again your the expert here, and I would take your word for it, normally. Alas, in this particular case, there are other experts who have put the theoretical limits for large-scale structures on the basis of such models. Now, either you have done not too well a job in researching your own field of expertise properly, or the other experts have done a rather lousy job in their case by coming up with such wrong calculations. You can’t have both though, you can’t both be true. So which is it?

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  12. Haulianlal Guite

    ||Do you have a reference for this?||

    Bunsen, what you need to do is pretty simple. You can go to the top of a 5-storey building and measure, in the world world without any experimental controls, what the velocity of a heavy object like an iron ball will be, and the speed of a rubber ball. That is how we know Galileo’s alleged Pisa experiment cannot possibly happen, because when we actually drop something from a tower and place like Pisa, given the aerodynamic conditions, Aristotle’s actually triumph there!

    Aristotle’s equation is this: the speed at which two identically shaped objects sink or fall is directly proportional to their weights and inversely proportional to the density of the medium through which they move.

    Granted of course that in controlled experiments and many natural environmental conditions, this won’t work. But there n-number of natural environmental conditions where it will. And that’s the point: within such tightly-defined domain, Aristotle’s physics will remain valid.

    ||Are you seriously telling me that you think you can take Aristotle’s physics and apply it to the path of a projectile – say a weight from a catapult of the day – parameterise the problem by mass and angle of ascent, and get consistent quantitative results to a degree of accuracy that they could not be be differentiated from the Newtonian result by the standard rulers of Aristotle’s day?||

    Perhaps not as far as THAT. Think of simple everyday examples like the fall of an apple. Yes, you can measure its velocity using his concept of motion for many practical purposes. And its a far simpler theory than even Newton’s laws of motion.

    You are attempting to apply Aristotle’s theory all across the board and test it in all types of natural environments. That is never my intent in presenting this theory. Instead, the purpose is to simply show how even Aristotle’s theory of motion holds – if you will, at least in one domain.

    The reason I introduced Aristotle was to press the point how all scientific theories can be made to work within tightly defined domains, no matter how small those domains are. And because it works in this domain, this shows instrumental usefulness cannot be a criteria for verisimilitude.

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  13. Michael Fugate

    HG, have you actually performed the experiment or are you too just imagining what will happen?

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  14. Haulianlal Guite

    Michael:

    Yep. Everytime I dropped a paper from my office building and pour water out of the window, I can see quite well the paper takes far longer time than water to reach the ground (my office is on the 4th floor, towards a hollow aisle).

    A little more “scientifically” however, while I can’t cite the exact sources, when the alleged Pisa experiment that Galileo was said to perform, was repeated by others, in all circumstances they “confirm” Aristotle instead. For the simple reason in an uncontrolled real-life environment such as that, wind and other factors (which is Aristotle’s “medium” of propagation) played crucial roles. That is how we know the Pisa anecdote that made Galileo famous and lampooned the peripatetics, is one pop scientific fiction and cannot possibly be true.

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  15. Haulianlal Guite

    Oh Michael, as I’m no magician, and not yet telekinetic, how am I suppose to chain water and paper together? But why don’t you try it out yourself at your own home right now, and see if a buck of water and paper falls at the same speed?

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  16. Haulianlal Guite

    Ok Bunsen, I have found a source where the Pisa experiment was actually tried out, as opposed to the anecdote:

    “Mazzoni commits anew two other errors of no slight importance. First, he denies a matter of experiment, that, with one and the same material, the whole moves more swiftly than the part. Herein his mistake arose because, perhaps, he made his experiment from his window, and because the window was low all his heavy substances went down evenly.

    But we did it from the top of the cathedral tower of Pisa, actually testing the statement of Aristotle that the whole of the same material in a figure proportional to the part descends more quickly than the part. The place, in truth, was very suitable, since, if there were wind, it could by its impulse alter the result; but in that place there could be no danger. And thus was confirmed the statement of Aristotle, in the first book of
    On the Heavens, that the larger body of the same material moves more swiftly than the smaller, and in proportion as the weight increases so does the velocity
    .

    Source: Alberto Martinez, Galileo and the Leaning Tower of Pisa, p.6.

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  17. Bunsen Burner

    Haulianlal:

    I don’t dispute that if you reframe Aristotle’s concepts into Newtonian terms (at least those that can be), then you can derive one or more models where you will get quantitative answers within the accuracy of the models’ range. What I very much doubt is that we can take Aristotle’s ideas and apriori know what domains to apply them without checking the Newtonian answers first. This makes it useless as a quantitative theory even if now and then it gives the correct qualitative behaviour.

    I also thought Robin’s formulation was significantly stronger. Namely that any analysis of motion I can give, Aristotle can too within the precision of the instruments of ancient Greece. This would be interesting if true but I am not convinced.

    Also I can’t help but be a bit of a smart arse. The experiment of dropping weights from a height can in fact give you any answer you want. The reason is that you have weights flowing through a compressible fluid and the resistance is highly non linear. Its possible to engineer a set up where the lighter object reaches the ground before the heavier one. Its even possible to have it so that one overtakes the other and then the gets overtaken in turn. This is due to velocity dependence in the coefficients of resistance. But you need the Navier-Stokes equations to figure all this out.

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  18. SocraticGadfly

    Dan, I already noted Kekule’s dream of a snake biting itself leading him to intuit that benzene has a ring structure.

    Some more scientists influenced by their dreams include the very Niels Bohr on the structure of the atom, Mendeleev on the periodic table and more:

    http://www.biofuelnet.ca/2015/04/22/role-dreams-visions-scientific-innovation/

    In turn, this reminds us that science hasn’t yet discovered “the purpose” of dreams. And, it may never fully do that.

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  19. SocraticGadfly

    Massimo, re the adjectival phrase you have with the first mention of “the scientific method,” is “quasi-algorithmic” Baggini’s or yours?

    In either case, I’m not saying I disagree, but more discussion would be good.

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  20. Haulianlal Guite

    Bunsen:

    ||I don’t dispute that if you reframe Aristotle’s concepts into Newtonian terms (at least those that can be), then you can derive one or more models where you will get quantitative answers within the accuracy of the models’ range.||

    You’re missing the argument. There is no reframing as such, but taking Aristotle for his word, and seeing how far it fares in real physical conditions. The moment you couch it in Newtonian language it has become something else; what I don’t know, certainly not Aristotle’s.

    ||What I very much doubt is that we can take Aristotle’s ideas and apriori know what domains to apply them without checking the Newtonian answers first. ||

    This is staw man. Nowhere did I mention taking Aristotle a priori, nowhere did I even appeal to Newton for checking the results. Rather, I’m talking about actually finding out a real, physical restricted (what theory ain’t?) domain where Aristotle’s theory of motion applies. And this applies in circumstances such as the ones I refer. And the result can be quantitative in this sense: lay out your conditions of testing (wind speed of this much, air density of this much, at this height, so on and so forth) and then test the theory, and you can find out the velocity that a ball of iron moves at to reach the ground at, then compare the same with the velocity of the feather. You may generalize this result by saying that, given exactly these conditions, the solutions will also exactly hold.

    ||The experiment of dropping weights from a height can in fact give you any answer you want. The reason is that you have weights flowing through a compressible fluid and the resistance is highly non linear. ||

    Now you’re closing in on the point! As I have been labouring, any scientific theory can be made to hold within restricted domains, provided you carefully define the parameters of testing. Aristotle’s was just one example that got elaborated quite far. I mentioned Ptolemy’s earlier too. And the difference between these theories and Newton’s, in terms of their practical utility, is only in degrees, and the types of domains you use. Aristotle’s theory “holds good” in its domains, as does Galileo’s, as does Newton’s, as does Einsteins. Its simply that we prefer Einstein’s over most of the rest because we want to apply the theory to domains where Aristotle’s or even Newton’s are not applicable.

    Further, that Aristotle’s theory, within the restricted domain, holds far better than any other theory. That is, given the type of conditions we prescribe for Aristotle’s domain – which essentially is a portion of the everyday world that we see and experience – the theory will work even better than Newton’s. All you have to do is take a ball of iron and a piece of paper and drop it from the 5th floor. In THAT particular domain – forget about all developments of modern physics, equations, laws and every other irrelevant matters – Aristotle will triumph. As Newton’s will over Einstein’s in its own domains. As will any other theory.

    So no theory is, strictly speaking, even “better” (that is, more useful) than another. One theory is more useful than another for a particular purpose within a specified domian, while that same theory will be less useful for another purpose in another specified domain. And that’s the entire thrust of my instrumentalism.

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  21. Haulianlal Guite

    I’d think the discussion is quite on topic … just taking other examples to prove the same point the chapter is making: that underdetermination abounds, scientific realism is no good, and so on.

    In any case that’s what I’m pressing on when I say all (or most) theories are useful in their restricted domains, and that usefulness is only a matter of context, not an indiction of its virisimilitude. The example of Aristotle’s physics is taken to show how even his theory of motion is useful in some domain; the example of inflation and cosmological principle to show scientists still cling to refuted theories and therefore, falsification has been made irrelevant in science.

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  22. Michael Fugate

    I get what you are driving at HG, but your examples are all wet. Aristotle’s physics and believing 16th c accounts of “experiments” are not going to fly. In any controlled experiment, it just won’t work.

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  23. Massimo Post author

    Socratic,

    “Quasi-algorithmic” is my phrase, but I do believe it renders Baggini’s idea. He is saying that one cannot simply “apply reason” and be done. There is always going to be an inescapable component of human judgment, which is a combination of reason, biases, gut feelings, experience, etc.

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  24. couvent2104

    Is anyone actually going to discuss the post?

    I’ll take up the gauntlet.
    I agree with much in Massimo’s post. I too believe that “The success of science should not lead us to believe that it provides the model for all reasoning.” And I do think it’s correct tot state that science is a sophisticated, yet fallible, human enterprise, dependent on human judgment. How could it be otherwise?

    However, I was disappointed by some of the arguments that Baggini offers. He asked 90 “leading physicists” which interpretation of quantum mechanics they thought was best. Come. On. Please. 1000s of pages have been written about interpretations of QM, and there’s not a single compelling scientific reason to prefer the one over the other. They all have their difficulties. Of course you’re going to get diverging opinions, and of course these opinions aren’t based on science.

    As I already mentioned, I found the following quote particularly weak:

    One of his best examples comes again from quantum physics, when he notices that Schrödinger’s and Heisenberg’s competing theories were not only equally compatible with the empirical data, but in fact had been shown to be mathematically equivalent. They were, therefore, both empirical and mathematically underdetermined.

    I have no problem with the idea that theories are empirically underdetermined, but this is such a weak argument for mathematical underdetermination that I got annoyed when I read it the first time.
    The concept of “money” may be underdetermined, but pointing out that one can pay for the same gizmo with dollars or with euros, certainly isn’t a strong argument. Baggini could just as well made the argument that QM is mathematically so well-determined by nature that she doesn’t care which particular representation one chooses: Schrödinger or Heisenberg. Just like hyperbolic geometry is so well-defined that it doesn’t matter which representation one chooses: the theorems will be exactly the same.
    Both Heisenberg and Schrödinger (without realizing it in the beginning) stumbled on the same mathematical structure, with Hilbert spaces, Hermitian operators etc. And that’s another point: one can argue that the example of H and S shows that humans and human judgments are less important than Baggini (as quoted by Massimo) suggests. Even with all their human differences and differences of human judgment etc. H and S came – without realizing it – to the same conclusion (if you look at what counts, the mathematical structure, and not at the particular representations of that structure).
    As I already mentioned, one can interpret this as a coincidence of cosmic proportions, or one can conclude that nature – fundamentally – has a voice in the debate too. Perhaps this last point sounds trivial, but it isn’t more trivial than pointing out that science is done by humans, using their human judgment.

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  25. Michael Fugate

    No you don’t get it – your example flat-out doesn’t work. A wadded up paper falls faster than a flat sheet – same weight. A feather weighs more than a grain of sand, sand falls faster.

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