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Thursday, August 8, 2013

Scientism redux

Stick or switch?
Some years ago, reading Case Studies in Sample Design by A.C. Rosander and some other books on sampling practice by W. Edwards Deming, TOF was offered this particular nugget of information.  On any particular problem there will be statistical aspects and non-statistical aspects and the practicing statistician's task is to provide advice on the former.  The statistics is not the be-all and end-all of the problem in view.  There may be a wide number of other aspects to it.  A statistical analysis may shed light on some of these, and that is all to the good.  But the important thing to remember is that not all problems are simply statistical problems.

Consider the Monte Hall problem, which puzzled even pros because they forgot that the problem was not probabilistic.  Monte Hall did not use random chance to choose which door he would open.  Let us call this tendency to apply the rules of probability even in non-random situations probabilism.  Which serves as today's lead-in.


There are lots of situations in life that have aspects amenable to the scientific method.  But not all do, and of those that do, those aspects may not be the most important.  Unless you suppose that the most important thing about the Moonlight Sonata is the physics of vibrating strings.  Yet, like the over-eager statistician or the determined probabilist, those enthralled by the success of Science!™ may try to use it where it fits ill.

Natural science in the Modern Ages applies to the metrical properties of material bodies.  It can tell us about wavelengths of light, but cannot tell us about the sensation of red.  (Which is "subjective" and therefore.... perhaps not real, but certainly to be dismissed.)  As such, it is best suited to the domain in which it arose: the physics of local motion.  However, it worked just as well in other areas of physics: optics, acoustics, electricity and magnetism -- all of which you notice deal with motions of some sort.  In the following century, it was extended successfully to alchemy, thus conjuring chemistry.  It applied pretty well to some portions of biology, esp. biophysics and biochemistry, genetics, etc.  But some parts of the Scientific Revolution dropped off.  Biology is not mathematized in the same way as physics and chemistry.  And when it came to the social "sciences" it began to lose traction.
Getting fitted for Science!

Basically: the methods apply most successfully when its objects are inanimate, less well when they are animate, and poorly when they have a mind of their own.  Subjects are, by their nature, subjective.  A sack of potatoes and a human being will fall from a building according to the same laws of physics; but the sack of potatoes is less likely to object. 

A while back TOF wrote a few words on the much maligned topic of scientism.  This is a term taken with much umbrage by devotees of Reason who have evidently never heard of the Genetic Fallacy, since their reason for derogating the term is that it is oft used by... (wait for it)...  creationists!  Oh, the horror!

Of course, TOF remembers how "punctuated equilibrium" once came in for scoffing for the very same reason.  Eldrege and Gould were scolded for giving comfort to the Enemy by implying that a mid-Victorian country squire did not get everything quite right.  Of course, no other theory of that era escaped unscathed, and physics in particular underwent a revolution. 

In the pink
In any case, a sensible if overwrought essay and a hysterical blog posting have recently been brought to TOF's attention.  One of the remarkable things about both is that the response of the echo chamber not only yielded the usual smug denunciations of "faith" but also laid main battery fire on the humanities, whose practitioners were variously describes as "elite," "ignorant," "mandarins," and so forth.  Many of the respondents exhibited blatant scientism as they attacked... humanism!

Yes, it is the age-old war between Science!™ and Humanism, the Game of Spock and Bones.

Coyne of the realm
The most dogmatic practitioners of scientism are often themselves not scientists.  Essay author, Stephen Pinker, is a psychologist and blogger Jerry Coyne is a biologist.

Does this sound provocative?  Does it sound like physics-imperialism?  Yes it does -- let's call it physicsism -- and those on the other end of it may now understand what humanists mean by scientism

In TOF's previous essay on this matter, he used the example of enthusiasts for Statistical Process Control (SPC) who believed in their zeal that SPC was the answer to all problems in the factory.*  This is a common affliction of all those who master a techne.  They come to believe that the techne can be used in all circumstances, and that only that which the techne can address is "real."
(*) factory.  Amazing as it may seem, at one time people used to work at making stuff. 

The First Rhetorical Flourish

Both Pinker and Coyne muddy the water by affecting not to know what "scientism" even refers to.  Coyne writes:
One of the problems has been the definition of “scientism,” which varies from commenter to commenter but is always pejorative.  I take it to mean “science overstepping its boundaries” in the sense of Gould’s Non-Overlapping Magisteria: scientists misusing science or technology to bad ends (racism or eugenics), claiming they will take over the humanities (as in E. O. Wilson’s notion of “consilience”), or making moral and political pronouncements that exceed scientific expertise or ambit.
But this is not a problem if he pays attention to Wittgenstein, Feyerabend, Hayek, Midgley, and others -- all of them, be it noted, atheists or agnostics.  If he wishes to say that creationists are sloppy thinkers, he will get no argument from TOF.  But why rely upon creationists for the definitions of one's terms?

Pinker, at least, cites serious thinkers, which has the benefit of rhyming.  He writes:
The term “scientism” is anything but clear, more of a boo-word than a label for any coherent doctrine. Sometimes it is equated with lunatic positions, such as that “science is all that matters” or that “scientists should be entrusted to solve all problems.” Sometimes it is clarified with adjectives like “simplistic,” “naïve,” and “vulgar.” 

The Second Rhetorical Flourish

After first not defining scientism, or declaring it "anything but clear," the next step is to define Science!™ as "every kind of good stuff."  Coel, a commboxer on the Coynesite, caught up in the fervor of scientism, proposes:
that science — interpreted broadly, as Jerry does, namely reasoned deductions from observed evidence — is indeed the only method of learning and knowing about the universe around us, and that if it is possible for humans to know something then science is the tool that will lead to it. That’s not the same as saying “science has all the answers” since there are many things that we may never be able to know.
 But of course, he has said exactly that, in the sense that the only knowledge science does not provide are in his belief system the things that we cannot know.  Naturally, if "reasoned deduction from observed evidence" is all that is meant by science, then as TOF has said before, a police detective, a building contractor, or a Wall Street bond trader is a scientist. 

In particular, Pinker states:
Scientism … is not the dogma that physical stuff is the only thing that exists. Scientists themselves are immersed in the ethereal medium of information, including the truths of mathematics, the logic of their theories, and the values that guide their enterprise.
But this means he is trying to annex Mathematics into the realm of "Science" as he (and Pinker) have just done with Engineering and Tinkering.  But Mathematics does not proceed from "observed evidence" or "empirical facts."  It proceeds from first principles.  "Science" incorporates Mathematics only if we return to the medieval way of thinking, in which scientia meant "knowledge" of proximate causes.  Given this, we can have Political Science, Military Science, etc. 

Of course, Pinker is trying to capture the term "scientism" by using it in a positive sense for "science."  But we already have the term "science" and conflating the two only muddies the discourse.  Scientism has little to do with what "scientists themselves" are "immersed" in. 

The Third Rhetorical Flourish

By 1) not defining scientism and by 2) defining science in broad generalities, the way is cleared to conflate scientism with science and criticism of the former with criticism of the latter.  Oh, and religion sucks.  In Coyne's case, the invocation of religion is a sine qua non, as it is his particular trailing hound.  But Pinker went to lengths to cite left- and right-wing critiques of scientism, many of them on both sides secular, so his occasional use of "religion" as a "boo-word"* rings a bit like brass. It seems gratuitous. 
(*) boo-word.  Pinker applies this to "scientism," which in certain hands it definitely is; but his use of "religion" as a boo word slips past him because from the center of his coordinate system it looks clearly logical.  Jacques Barzun noted back in the 1950s that "scientific" was already becoming a "success word" and was used in advertizing and such as a synonym for "good." 
We know it is a boo-word by the predictable reaction of commbox zealots shouting Amen! (or Boo!)

Thus, their riposte is:  How can anyone think dark thoughts about Science!™?   Look at all the Good Stuff it's done!  "A litany of achievements," says Coyne, "that theology can’t hope to match, since it’s revealed nothing convincing about the cosmos."*
(*) cosmos.  Those familiar with the original meaning of the Greek are permitted an ironic smile at this point.

Naturally, this is an example of the very scientism that Coyne claims does not exist.  Theology has revealed nothing convincing about the cosmos.  Why  must it be about the cosmos?   

The Pea Beneath the Shell


Thus, Pinker (and Coyne) have shifted the discussion from whether the charge of scientism is valid as against certain people to whether Science!™ as a whole is kool.  Since science definitely is kool, the original issue gets swept under the rug.  Pinker essentially says that "scientists" do not believe such foolish things without noting that most scientists are not in thrall to scientism.  In fact, it may be fair to say that most devotees of scientism are camp followers of Science!™, although the likes of Coyne, Krauss, Dawkins, and their compadres are exceptions.  Mary Midgley, in her book Science as Salvation, gives numerous examples.

Scientism is just what Pinker and Coyne say it is not: the belief in the omnicompetence of science, that the methods of the natural science are the only way to knowledge about reality.  Certainly, enough commboxers responeded in such a way, smuggling unexamined assumptions in through terms like "reality" and "evidence." 

 Aristotle's Revenge

Take the commboxer Coel, previously cited, he (or possibly she) states:
I’d say that physical *is* the only stuff that exists, so long as that is taken to include *patterns* of physical stuff.  
which is silly.  A pattern of physical stuff is not itself physical stuff.  If it were, Coel could deliver twenty kilograms of pattern.   He (or she) is unclear on the nature of the physical!  What he (or... the heck with it) has stumbled upon is the distinction of matter and form, but since ignorance of Aristotelian principles has been cultivated for centuries, he does not realize it. 

A thing is a union of matter and form, and it is the form that gives the thing its powers.  When we see a basketball, we do not see two things, a basketball and a sphere.  The sphere just is the form of the basketball.  Similarly, an atom of chlorine and an atom of sodium are made of the same matter, the same parts -- protons, neutrons, electrons.  What makes one a flammable metal and the other a poisonous gas is the number and arrangement of those parts.  The fact that non-physical stuff like number, arrangement, or pattern are crucial for doing natural science does not make them physical things themselves. It's actually the form of which we have knowledge, not the matter

Try this on for size:  I’d say that mathematical *is* the only stuff that exists, so long as that is taken to include *material instantiations* of mathematical patterns. 

Tahāfut al-Tahāfut

After Pinker (and Coyne) went to great lengths to justify Science via consequentialism, citing all the wonderful fruits of science, Coyne commboxer dcarpenter had to go and spoil it by writing in response to a Green critic of science who complained that science was destroying the planet:
Science - that is, "open debate, peer-review, and double blind methods" is a necessary endeavor for a level of technological progress that could affect the stability of our climate. But that doesn't mean that science caused climate change
One wonders what double-blind methods are used in astronomy.  Perhaps it is not scientific.  Open debate can occur in a kitchen or an art gallery.  And peer review comes from medieval theological panels reviewing for orthodoxy.  But of course if science did not really cause the bad things, then what justification is there for saying it really caused the good?  This sort of cherry-picking and confirmation bias is common (and not only to devotees of scientism).  Miracle drugs and nerve gasses, airliners and ICBMs, etc. -- Science is responsible for both or neither.

Pinker commboxer bpuharic states:

As Pinker points out, the laws of nature admit to no purpose, so their objection is fruitless. And humanity has yet to come to grips with this radical, profound statement. Certainly the humanities haven't. Is there any more radical idea than that the universe doesn't revolve, Ptolemaic-like, around us?
Never mind how he misunderstands how the Ptolemaic model was grasped in its time, but if nature admits no purpose, then human beings, being part of nature, can have no purpose and therefore, including scientists, must act at random. 

Pinker mentions eugenics:
Eugenics was the campaign, popular among leftists and progressives in the early decades of the twentieth century, for the ultimate form of social progress, improving the genetic stock of humanity. 
But eugenics was not scientism because it was wicked -- oops, there's that purpose/value thingie that bpuharic says does not exist -- but because the scientists who advocated it went beyond the bounds of science.  They went from "Darwinism IS true" to "therefore, we OUGHT to breed people like horses."  It does not matter that Fischer wore a white lab coat and assured people that it was scientificalistic to the max.  The scientists were not doing Science when they stepped over into Setting Public Policy.  This would be just as true if eugenics was a great idea instead of a bad one.  The issue of scientism is the pretense that one is doing science rather than politics or philosophy or some other field of human endeavor. 

Instrumentalism

Nope, no God here.
A heretical voice yclept Al_de_Baran tried to explain on the Coyne blog the error Pinker (and Coyne) had made in equating science with scientism by drawing an analogy between the scientific method and a metal detector.  The commboxers then revealed their utter lack of understanding of analogical thinking* and a stunningly stolid literalism.  
(*) analogical thinking.  Some years ago, the College Boards dropped the analogy questions from the general intelligence exam.  Schools then stopped teaching it and now only us Old Farts™ have any grasp of it.

First PaulS responded:
One problem with your analogy is that a metal detector is a physical object and the scientific method is a process.
If the only instrument you own is a hammer
every problem looks like a nail.
Showing that he at least recognizes there are things that are not physical objects, but also that he misses the point of the analogy.  The analogy is instrumental.  The scientific method and the metal detector are instruments, one material the other immaterial, and the point is that an instrument can only detect what it is designed to detect.  The trap of scientism is that the wonderful successes of using that particular instrument can fool the user (Science "Works"!) into believing that there are no aspects of reality other than those which are detectable by his instrument and therefore his instrument is the go-to instrument for any and all "real" problems.  

A second boxer, Sastra, adds:
The scientific method though is not like a metal detector. It’s more like a way of using a metal detector — or a detector of any kind. Careful, cautious, honest … checking against other detectors, digging, consulting with other people using their detectors, building models, making predictions, analyzing results, eliminating bias, changing assumptions with new information, challenging other discoveries and working with others to figure out a consistent answer to the common puzzle what is under the ground? Metal, stone, oil?
This is delicious, since Sastra describes precisely a bunch of folks determinedly using their detector, checking against other detectors, consulting with other people using their detectors, and building models(!) from the data given by their detectors -- apparently they must be trying to do Science!™  rather than, say, look for lost coins and keys.  But she has provided an excellent precis of scientism, which we will call detectorism.  The only way they will discover anything non-metallic is by using some other instrument, such as their eyes, or a shovel. 

The Infiltration of Science

Pinker mentions a bunch of folks -- Descartes, Spinoza, Hobbes, Locke, Hume, Rousseau, Leibniz, Kant, Smith -- some of whom okay, but some of whom were responsible for the most godawful incoherence to afflict the Modern Ages.  Descartes was okay in his science, though Newton trumped him; but he is responsible for the substance dualism that has bedeviled Moderns with silly things like the Mind-Body "problem."(*)  Hobbes was a totalitarian.  Hume undermined efficient causality (and hence Modern Science).  Rousseau concocted the most non-empirical political philosophy that ever erected guillotines.  Oy.  But Pinker supposes that these folks were all crypto-scientists.  Oh well.  One wonders at the absence of Newton, Hooke, et al. 
(*) Mind-Body "problem."  Why does no one ever speak of the Sphere-Basketball problem?  If you don't know why these are parallel, then you don't understand what Descartes screwed up.  

Pinker then lays out the variety of ways science can contribute to the humanities, reminding one of Deming's observation of a professional manager that "he knew everything there was to know about the business except what was important."  Science can of course make contributions to those aspects of a field that are scientific.  Acoustics can help design better concert halls, even perhaps better clarinets.  But that is accidental to music.  Science does not compose the Clarinet Concerto in A

To which the response is: what scientist ever claimed this?  And the answer is that Science then addresses music only peripherally.  When one has understood the acoustics, the physics of vibrating reeds, the effect of lengthening and shortening the air column, one has still not understood the essentials of the concerto. 

Pinker says that Science will aid the humanities:
  • by giving us a better take on human nature, [but Modern Science denies that there are natures or essences!]
  • by the use of statistics and data analysis to settle questions of social and political science, [in which case they better damn well hurry, because for now it falls into two categories: obvious or wrong.  Besides, statistics and data analysis are Mathematics, not Science.]
  • by providing fertile new ground: the study of how the workings of the human brain, as revealed by science, provide more depth to the social sciences, literary analysis, and even studies of music.  [How this will do so is left unsaid.  One may as well say a study of the human arm will provide more depth to golf.  One may doubt the depth while admitting the possible interest.  But any depth at all provided to the social "sciences" would be welcome.]  
He adds that
Intellectual problems from antiquity are being illuminated by insights from the sciences of mind, brain, genes, and evolution. Powerful tools have been developed to explore them, from genetically engineered neurons that can be controlled with pinpoints of light to the mining of “big data” as a means of understanding how ideas propagate.
The mining of Big Data provides models with terms that do not correspond to any physical factor and may as often obscure understanding as anything else.  But that is a separate issue and affects the real sciences as well.

It might be interesting to learn which intellectual problems from antiquity are being illuminated.  In fact, one wonders if any intellectual problems from antiquity are known to the folks opining.  On Coyne's blog, eric tells us that
Yee-haw!  Run, turtle, run!
calculus is highly relevant to Zeno’s paradoxes 
which shows he does not understand what Zeno's paradoxes were all about.  They were problems in physics, to be papered over by mathematical abstractions like "infinitesimals."  One may have a mathematical model that calculates correct answers -- the Ptolemaic model did so for stellar motion for two thousand years -- without a corresponding understanding of the physics, let alone of the metaphysics.  Perhaps there are other examples of illumination.  TOF does not discount the possibility. 

The Techie and the MBA

Joseph Moore comments at Wm Briggs' blog in a manner apropos of this here post.
Perhaps an example from a slightly different area: in the high-tech business world out here in California, I run into many people who are brilliant – at technology. Being brilliant at business requires an entirely different skill set. It is possible, in fact, it is more common than not, that the genius programmer or engineer lacks any hint of business intelligence. But what is really frustrating for us business types: More often than not, the techies are evidently incapable of recognizing that they are NOT experts in business. This leads to all sorts of amusing interactions that are very much akin to the discussions between scientists and philosophers. The techies are absolutely stone-cold certain they understand everything, and that the business people are just being obstreperous; the business folks are flabbergasted by the idea that they would even need to explain some of the ideas that are being dismissed. (Emph. added). 

26 comments:

  1. "Why does no one ever speak of the Sphere-Basketball problem?" Brilliant

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    1. Obviously, because the Orange-Basketball problem and the Rubber-Basketball problem are much more pressing.

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    2. The Orange-Basketball problem was first observed in Syracuse, iirc.

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  2. I would like your opinion, if I may, of my analysis of knowledge, set out in this essay: http://fpb.livejournal.com/481660.html and http://fpb.livejournal.com/481835.html . I warn you that, opposite to your view here, I call mathematics a part of the realm of science. Otherwise, I think what I said is relevant to the points you make here.

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    1. I would encourage all TOFlings to read Fabio's essay. Save for a few minor flourishes - such as, as he says, the conventional inclusion of Mathematics into Science - it is a commendable and insightful summary. Worth alone the price of admission is this gem:
      St.Paul describes the role of this collection of old books with remarkable exactitude: "...from a child thou hast known the holy scriptures, which are able to make thee wise unto salvation through faith which is in Christ Jesus. All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness: that the man of God may be perfect, throughly furnished unto all good works." The purpose of studying the Old Testament is nothing to do with the study of history, or for that matter of science: it helps faith by understanding "doctrine" (theology, philosophy), by rousing a sense of one's inferiority or downright guilt as compared with heroes of old ("for reproof, for correction") and to learn from them and from their collected wisdom ("for instruction in righteousness"). It is for this reason, and for no other, that Paul teaches that "all scripture is inspired by God". Indeed, one has the sense that if he - or the other teachers who, in every tradition and culture, repeat the same concept from Europe to the Far East - were to become aware of the obsession of some moderns with factual authenticity, they would would be shocked. They certainly would regard it as a base and mean ambition: who is interested in squeezing some dumb fact that had ceased to matter four thousand years ago from books whose source of wisdom and inspiration lives for ever?)

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    2. I thought that was pretty good, though I would lob a small objection to the idea that the purpose of studying the Old Testament has *nothing* to do with history.

      Certainly, most of the OT isn't supposed to be read as a newspaper-accurate account of what happened (imagining for a moment that modern news media is anywhere near as accurate as they put on). If you closely examine the story of Abraham, for instance, you can pick up on an elaborate chiastic structure, which implies that the story was carefully arranged, and events focused on or left out, for the purposes of theological meaning and memorization. Most of the stories of the OT are written in epic form, which allows a degree of artistic and literary license and so forth. We shouldn't think we're dealing with exact quotes most of the time, etc.

      But, at the same time, Jesus' claims to be the fulfillment of the promises to Abraham and Moses, or to be the promised root of David, etc, become incoherent if those promises were never made or if those people didn't exist. There are also books like the Chronicles which are certainly meant at least in part to be histories. It's difficult or impossible to learn from the collected wisdom of the heroes of old, or have a correct sense of inferiority and guilt compared to their examples, if they were just outright fictions.

      So while I agree that teachers like Paul would be appalled at the obsession of moderns with factual authenticity, I do think it important to the New Testament message that the OT narrative of Israel's past is broadly historical in the main, and that the OT isn't supposed to be completely uninformative in that regard.

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  3. The nice thing about the business world is that it really is self-correcting to some extent - if you're wrong enough, you get go out of business if you haven't made friends in government. Unfortunately, an Ehrlich and a Gore can go on and on no matter how wrong they are.

    The most common error I see: because a product is believed by the developer to be way cool, we don't need to bother with seeing if anyone out there wants to buy it at a reasonable (for both sides) price - nope, just build it, they will come. For software development, there's even an industry term for this: shelf ware - a product that just sits on the shelf. I would bet that there are billions of dollars worth of shelf ware collecting dust today. Conversely, the greatest advances we see in science (loosely defined to include technology, which seems to be the working definition in the wild) are in areas where there's a potential for profit - which would make Boyle smile, I suppose.

    In more pure science, success today is fundamentally defined as getting funding. You can say that advancing human knowledge is success, but the truth is that, if you don't get funding, you'll probably not get the chance to advance human knowledge. Ultimately, Pournelle's Iron Law kicks in: those good at getting funding run things.

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  4. It's amazing how elastic the definition of "science" becomes in the hands of scientismatics.

    On the one hand, Pinker defines "science" so broadly that Descartes, Spinoza, Hobbes, Locke, Hume, Rousseau, Leibniz, Kant, and Smith were all "doing science" without so much as performing an empirical experiment, and even when they were casting doubt on or even denying the possibility of empirical knowledge!

    Based on this, one would reasonably conclude that by "science" Pinker means basically all possible thought of any sort. But then he contrasts "science" with "religion," which doesn't count as "science" according to him, and which is totally stupid and benighted and the opposite of "science."

    The only way to make sense of this is to conclude that by "science" Steven Pinker means all thoughts which he sees as supporting some part of Steven Pinker's worldview (namely materialism and "Enlightenment" morality), and by "religion" he means all thoughts that oppose it. And having defined "science" as that which supports his worldview, he proceeds to tell us that we should accept his worldview because it is supported by "science."

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  5. What's with the sphere-basketball analogy? We've already proved these guys don't get analogies.

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  6. In University (and a Catholic, heavily-liberal arts university at that), my Calculus text opened with the example of how Calculus proves Zeno wrong. Fortunately, or unfortunately, depending on how you want to look at it, the philosophy department never get wind of that.

    Could you give some more information, or point out a post where you've elaborated on what Zeno's paradoxes really are, and why Calculus doesn't have anything to do with them?

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    1. While it is certainly possible to overlay a continuous function y=f(t) over the motion of an object and treat its derivative as velocity, this is a mathematical abstraction, not a physical reality. In like manner, we can lay a normal distribution over a collection of measurements - say, the nitrogen content of a series of steel billets - but the physical reality is only approximated by the mathematical ideal. The normal curve runs to infinity in both directions, and the nitrogen content of steel does not. So while the math is enough to provide useful answers to physical problems to as many decimal points as may be needed, we must not confuse the properties of a mathematical ideal with those of the physical real.

      When motion is represented by a continuous function y=f(t), we have implicitly conceded the ground to Zeno (and Parmenides). Instead of motion as such, we have a set of static points (t,f(t)) with no explanation of how one actually gets from one to the other.

      Aristotle's answer was that the infinite divisibility of a continuum was only a potential infinity and not an actual one, and thus the problem of traversing it does not arise.

      Parmenides and Zeno wanted to show that assuming a continuum led to contradictions. They were perfectly aware that change (motion) took place, so the other possibility is that space and time are not continua, but rather discrete - what shall we call them? - quanta?

      It's well known that discrete data can be approximately modeled with with continuous substitutes: the Poisson distribution is ofttimes used to approximate the binomial, and the normal curve is well known. For the normal curve, the probability of X=x (where x is any exact value) is always zero, since probability is the integral from x to x, and there is no area above a single point.

      In any case, the question has never been whether the motion can be calculated mathematically, but how the motion takes place physically, given the assumption of an infinitely divisible continuum.

      My own uneducated opinion is that God is a Parmenidean, but humans must be Aristotelian.

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    2. "Aristotle's answer was that the infinite divisibility of a continuum was only a potential infinity and not an actual one, and thus the problem of traversing it does not arise.
      Parmenides and Zeno wanted to show that assuming a continuum led to contradictions."

      I still don't understand. Didn't they want to show that the contradiction was that if there were an infinity of points, then it would take forever to cross them? But calculus shows how that's not true (that would only work if you had an infinity of finite points), so their contradiction doesn't work. Or do you mean that's not what they were really getting at, so if they had known calculus, they just would have formulated their real point differently?

      But then coming at it from the other side I don't get it either. Aristotle said that there aren't an actual infinity of points between Achilles and the tortoise, just a potential infinity, meaning that you could divide the distance at any mathematical point, but the separate points don't all exist just by themselves. So what happens when Achilles crosses the distance? Either he skips and hits only some of the points in between (quanta) or else he passes through every mathematically possible point (I don't know whether this makes them into "actual" points). But surely it's one or the other, I can't see how there's any possible alternative.

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    3. IIRC, Parmenides and Zeno regarded the passage of time as an illusion of the consciousness, so it isn't really a question of an infinite passage requiring an infinite time. And the Achilles example is always stated backward, with Achilles first covering half the distance, then half of the remaining half, etc. But the original formulation was from the tortoise POV: to reach the tortoise, Achilles must first traverse half the distance; but before he has traversed half the distance, he must have traversed a half of that; but before... And hence, not that it would take him an infinite time, but that he could never actually get started!

      This is akin to the medieval problem of first and last moments. There is a last moment at which Achilles is at rest, but there is no first moment at which he is in motion. This can be (and was) applied to the heaviest weight a crane can lift, or the first moment when Socrates begins changing from white to black. Or for that matter, the first moment after the Big Bang. We now regard these as problems involving open sets. In the life of the universe: (0, t) the 0-point can be approached infinitesimally closely, but never actually attained. So we may be able to grasp t=0.00000001 sec, but that always leaves t = 0.000000001 sec, 0.0000000001 sec, etc.

      Instants, infinitesimals, instantaneous change are mathematical phantoms, not real-world entities. They are the epicycles of modern physics: mathematical devices to ensure the calculations work out right.
      This article may be useful:
      Instantaneous Change Without Instants, by David S. Oderberg
      https://docs.google.com/file/d/0B7SKlRTfkUieY3c1ZERGakhNZHc/edit

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    4. Here are two more possibly relevant articles:

      'Temporal Parts and the Possibility of Change
      https://docs.google.com/file/d/0B7SKlRTfkUieZnA2YUlOZEpRRXc/edit

      'Traversal of the Infinite, the “Big Bang” and the Kalam Cosmological Argument'
      https://docs.google.com/file/d/0B7SKlRTfkUieTjQtNjNZaWpmMVU/edit

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    5. I guess I would have taken the calculus answer of "taking forever" to be a mathematical equivalent to "could never get started". But those articles look interesting, thanks!

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  7. Some years ago, the College Boards dropped the analogy questions from the general intelligence exam. Schools then stopped teaching it and now only us Old Farts™ have any grasp of it.

    Whoah! I did not know that. They were my favorite part of the tests. Looking around I see that they were eliminated because they were not the sort of thing that would be used in real life; which I find rather funny, since I'm pretty sure there's no one who doesn't engage in some abstract reasoning about relations among concepts on a regular basis, even if they do so poorly.

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    1. It was because girls did not score as well on the average as boys, and the difference was statistically significant. I do not know what the practical magnitude was. Every question is tested in this manner in order to detect questions with hidden biases, for example in the way things are worded, or prior assumptions by the test writers by which a crystal-clear question is made opaque to a large class of test-takers. Sometimes there are questions that hardly anyone gets right -- or which nearly everyone gets right. Such questions are of little use in evaluations. They also look at which wrong answer gets picked (it being multiple choice), which helps determine what about the question was unclear. "Water fountain" means different things in Philadelphia and Milwaukee, for example.

      The decision was that analogies were gender-biased; although it may as well be argued that the decision was that girls could not think analogically as well as boys. The obvious thing for us engineering types would have been to design curricula that would focus training in analogical reasoning on girls. But that leaves the question of what you do in the meantime.

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    2. That does make somewhat more sense than any reason I could find given. I wonder if they tested alternative formats. After all a:b::c:d, useful as it may be for showing that analogies are related to mathematical ratios, is not the most lucid way of putting an analogy, nor the form that most people would normally come across.

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  8. I'd like TOF to comment on the wrongness of only linking to the First Movement of that concerto, well knowing that it did not include follow up links to the remainder.

    As a service to all, this: http://www.youtube.com/watch?v=u3EWzyFWyBM

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    1. Ah, I had not known of that link! Muy Thanks.
      I like the first movement because of the obligato solos near the end. But the second movement has some appeal because it is the only part that I could even play a little bit. :-(

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  9. A very interesting article, thoroughly enjoyed it. I must confess that I'm unsure exactly what "scientism" is though I do read about it frequently on the blogosphere. While I thoroughly enjoyed your writing I have to disagree on a few points.

    It seems to me quite naive to suppose that biology is not a science, the only reason I can imagine you would want to do this would be so that you can later declare that Pinker and Coyne are not scientists. On this point I have to disagree strongly, and suspect that an educated fellow such as yourself is perfectly aware that both Pinker and Coyne are scientists. On any definition of both biology and science (except yours) biology would be classed as a science, since biologists employ the scientific method.

    Also I think you are in grave error here:

    "but if nature admits no purpose, then human beings, being part of nature, can have no purpose and therefore, including scientists, must act at random."

    What could it possibly mean for nature to have a purpose? Please correct me if I'm wrong, but I imagine that you want to smuggle God in through the back door here. In which case you would have to a) demonstrate God; b) demonstrate how we know the purpose it has bestowed upon nature.

    Nature has no purpose, yet I do not act at random. I, those around me, and various other contingent facts of nature help me to give my life purpose.

    Thanks for a great read!

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    1. That the methods developed for the physics of motion become less and less powerful the further from the physics of motion one gets was an idea I came across in a history of science text covering "Copernicus to the present." It is also tongue-in-cheek to some extent, and meant to point out that when the scientific big boy pants are pulled on, biologists can't suit up with the physicists. Remember, one of the six pillars of the Scientific Revolution was the privileging of mathematics as the primary means of scientific discourse, and the further into the soft end you get the fewer equations you find lying about. Sociologists muddle (usually badly) with statistics rather than with mathematics.

      Now biology is a science in medieval terms -- scientia: knowledge obtained by rational thought -- but then so is a police detective by that criterion.

      Nature has no purpose, yet I do not act at random.

      Then either a) nature does have purpose or b) you are not part of nature.

      What could it possibly mean for nature to have a purpose? Please correct me if I'm wrong, but I imagine that you want to smuggle God in through the back door here.

      People often suppose that once it is shown that nature acts to an end, that God pops out the other side automatically. That was precisely why final causes were banished by the likes of Bacon and Descartes (and why some Late Moderns are trying to banish will, intentions, and even consciousness!) OTOH, Thomas (like Aristotle) thought the teleology of Nature was obvious, but deducing God from it was difficult.

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    2. Some very interesting comments, thank you. However, I must say that I still disagree with you on both points. I think you are in error in the first instance by equating the physics of motion with "science". When we say that biology is a science what we really mean is something like, in order to study biology we have to employ the scientific method. All branches of science use the scientific method. I would not disagree that some sciences are more (I'm unsure of the correct term here, fundamental?) than others. However, this only means that some scientific findings are much harder to falsify than others. While the scientific method is being employed we are, by definition, doing science. Biology is not a medieval science, it is not obtained merely by rational thought. We certainly have to think rationally to do science, but this is a necessary, not sufficient, requirement.

      I'm unfamiliar with the exact process of investigating crime. Certainly some science (e.g DNA analysis. Which is biological, incidentally) will be used in the investigation. Whether the whole process employs the scientific method, I'm uncertain, but this is irrelevant. If the detectives investigation employs the scientific method, it's scientific; if not, it's not.

      As for purpose in nature, I really fail to see how you draw the conclusion you do from my statement. I will of course grant you that b) is patently not true, I am a part of nature. However, I fail to see how this necessarily entails that nature has a purpose. Why must nature have a purpose in order for me to act non-randomly? What is the purpose of nature?

      Thanks again!!!

      (it's knbb147 again)

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  10. Perhaps this cartoon, which I've always liked, is appropriate to this thread:

    http://xkcd.com/435/

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