Archive for the 'Science' Category

The divisibility trick

January 7, 2014

You might have learned the “divisibility trick” in grade school. It says that if you want to know whether a number is divisible by 3, there is a shortcut: if the sum of its digits is divisible by 3 then the number itself is divisible by 3. For example, is 459 divisible by 3? Well, 4 + 5 + 9 = 18, which is divisible by 3, so 459 is divisible by 3 as well.

This trick also works with the number 9. Again, you can try it with 459.

A week or two ago I was reading Anthony Esolen’s “Word of the Day” blog in which he stated a result about the divisibility trick generalized to a base-X number system; namely, in a base-X number system the divisibility trick works for X-1 and its factors. I was intrigued, and, as I had given some thought to the divisibility trick a few years ago and had some notes on it, I sat down last night and came up with what I think is a sound proof of the claim.

I am sure there is a nice way to formulate the argument — my approach leans heavily on modular arithmetic, which is closely related to the elegant theory of cyclic groups — but I went about it in the most simpleminded way imaginable. You can read my argument here:

DivisibilityTrickBaseX [pdf, Updated]

An amusing application of this result is in a binary (base-2) number system. The claim simply says that any binary number for which the sum of its digits is divisible by 1 (which is all of them, since every positive integer is divisible by 1) is itself divisible by 1 (which is all of them, for the same reason). So the claim is almost empty in that case.

Elemental boating

June 18, 2013

The topic this week at the What If? blog is a novel one:

What would it be like to navigate a rowboat through a lake of mercury? What about bromine? Liquid gallium? Liquid tungsten? Liquid nitrogen? Liquid helium?

I spent a few days last week on a boat in a lake of water, and after reading the entertaining and instructive responses to the questions above — not neglecting to watch the illustrative videos — I will say this: thank goodness for water!

Notes on neuroscience

June 6, 2013

I am in no respect an expert in neuroscience, but naturally I am aware of the main technical developments of the past few decades — especially functional MRI — which now provide neuroscientists with amazing imagery related to brain activity. I am also aware of the broad effort in the field to establish correlations between brain activity and mental states.

I will not deny that I am mildly discomfited by this effort, not because there is anything suspect about such correlations but because they are so often conjoined with a strange presumption that somehow brain scans are particularly probative windows on human behaviour, whereas in fact they are usually just fancy proxies for things we already know by other means (as has been convincingly argued). One also routinely runs into a tacit neurological reductionism according to which minds are “really just” brains, and you and I are, at bottom, “really just” fleshy computers processing stimuli. In this view of things, the notion of persons as bearers of freedom, dignity, and moral responsibility tends to become, at best, occluded.

My discomfort is only mild because I am aware that, whatever the merits of any particular scientific study, the minds-are-brains view is plagued by conceptual problems and, at least within the ambit of the reigning philosophy of nature in which matter is defined to be devoid of mental properties, is doomed to failure.

But, quite apart from the question of how we should interpret findings of correlations between mental states and brain activity, there remains the question of whether we should believe that such correlations exist in the first place. It seems that we should, but with reservations, for the evidence is not as strong or as straightforward as one might think.

For instance, a few years ago an important paper identified problems with common analysis techniques in fMRI studies. The authors showed that using such techniques they could produce nice correlations using data that were pure noise. Studies which avoided such confused methods uniformly showed comparatively low correlations. The authors speculated that a significant number of the findings claimed by the field might be illusory. I do not know what revisions resulted when (or if) the data were analyzed again.

And now, in this month’s Nature Reviews, comes another paper that criticizes the results of a wide swath of neuroscience work. The authors argue that a significant fraction of neuroscience studies suffer from low statistical power, meaning that both the sample sizes and the effects being studied are generally small. The problems with low power studies are many: the probability of missing true effects is fairly high, as is the probability of falsely “discovering” something that isn’t there. Even when a finding is true, low power studies tend to exaggerate it. Here is a popular level summary of the paper and the issues at stake.

Obviously it is up to the specialists to sort these issues out, and I have no doubt that they will. But there does seem to be warrant for wariness the next time you hear a claim that the neural correlate of this-or-that aspect of your mental life has been found. Sometimes things are just not that simple.


Planck results

March 21, 2013

Big science news today: the Planck experiment has released a huge raft of results based on cosmological observations made during 2009-10. Planck is a satellite-based experiment that has been making precision measurements of the cosmic microwave background (CMB) radiation, the details of which tell us a great deal about the history and structure of the universe. Planck is a truly spectacular project.

I remember that when I was an undergraduate physics student — which was quite a long time ago now — we heard rumours of this satellite, which was then in the planning stages. The hope was that it, and to a lesser extent its predecessor WMAP, would usher in an era of “precision cosmology”, in which cosmologists would have a wealth of high quality measurements against which to judge their theories about cosmic structure and evolution.

Based on the results published today, I would say that those hopes have been triumphantly vindicated. For instance, consider this paper on cosmological parameters; look at Tables 1 and 2. These are amazing results: baryon density is about 2.2%, cold dark matter density about 12%, dark energy density about 68%, Hubble constant about 67, and the age of the universe about 13.8 billion years (with an uncertainty of only about 100 million years!).

There is a lot here for non-specialists to digest — and I certainly count myself in that group. The BBC is on the case.

Planet Mole

July 24, 2012

There is a new physics blog at xkcd called What If? Each week it discusses a question of pressing scientific interest for a general audience. If one loses the train of thought one can always consult the diverting illustrations, which feature those lovable xkcd stick figures.

The issue this week is particularly pressing — if you’ll forgive the pun — as they take up the question of what would happen if one assembled a planet-sized sphere of moles (or comparable small rodents). It’s pretty awful:

The outer surface of the planet radiates heat into space and freezes. Because the moles form a literal fur coat, when frozen it insulates the interior of the planet and slows the loss of heat to space. However, the flow of heat in the liquid interior is dominated by convection. Plumes of hot meat and bubbles of trapped gases like methane—along with the air from the lungs of the deceased moles—periodically rise through the mole crust and erupt volcanically from the surface, a geyser of death blasting mole bodies free of the planet.

The blog has only been going a month or so; the previous posts (on Star Wars, SATs, and baseball) are also interesting.

Reading Rosenberg (with Feser)

July 13, 2012

A few years ago Alex Rosenberg, a professor of philosophy at Duke, published a short article online called “The Disenchanted Naturalist’s Guide to Reality”. I remember that it attracted a fair bit of attention at the time, for it set forth, briefly, the melancholy implications of philosophical naturalism (or ‘materialism’, or ‘scientism’): namely, that morality is unfounded, purpose illusory, freedom fictional, God non-existent, and even conscious experience a kind of elaborate deception. Rosenberg commented that though the premises of naturalism are widely held, the implications are, more often than not, ignored or denied, and that sooner or later that has to change.

Then last year he published The Atheist’s Guide to Reality, which presents the same argument in more elaborate and detailed form. It too has received a lot of attention — even being named “Worst Book of 2011″ by Leon Wieseltier at The New Republic, who evidently took offense at the book’s conclusions.

The problem is that, given its premises, those conclusions actually do follow. The book thus provides us with a welcome opportunity to critically examine the premises of naturalism (and, despite the title of the book, it really is naturalism, rather than atheism per se, that is the problem, even if, in practice, the two tend to go together in our culture). This is just what Edward Feser has done over at his blog, in an ambitious ten-part series of posts. He critiques Rosenberg’s argument for scientism, his framing of the relationship between Darwinism and theism, his (“nice”) moral nihilism, his denial of free will, his denial of the intentionality of thought, and much else besides. Feser typically argues that the radical (and sometimes incoherent) conclusions that Rosenberg believes follow from “the facts” are actually thoroughly entangled with the metaphysical commitments of naturalism (and particularly with the view of the natural world as a kind of machine), and do not follow if those commitments are suspended. In so doing, he has done us a good service. It makes for fascinating reading too.

Feser collected links to the whole series on one page, which makes it easy for me to recommend the whole project.

Higgs week

July 6, 2012

It has been a busy week, but I cannot let it pass without saying a brief word about the Higgs boson discovery at CERN. This is something that everyone has been expecting since the lab was upgraded to higher energies a few years ago. In other words, it is not a surprise — and, in fact, from a certain point of view it would have been more exciting if they had not found it. I will even admit that I was feeling a little blasé as the rumours of the discovery began to circulate in recent months.

That changed, however, when I saw this:

The bit above the dashed line is what the fuss is all about. (Source: CERN)

It is real!

The official scientific paper describing the findings has not been published yet, but CERN is reporting the discovery of a boson (a particle with integer spin) with a mass of about 126 GeV (as in the figure above). The mass is roughly equivalent to that of an iodine atom, making the Higgs boson the second heaviest known elementary particle (after the top quark).

The extent to which the properties of this new particle match those predicted by our theory will take time to sort out. Measuring the spin will be an obvious first step, if it hasn’t been done already. Its couplings to the other particles will have to be measured. In other words, a lot of work will be done to check whether this Higgs boson is the one we expected to find.

Time to shelve this away?

Many physicists are hoping that it is not. The cost to build and run these collider experiments is so enormous that if the current facilities at CERN find the Standard Model Higgs boson, and nothing else, there is considerable worry — well-founded worry, in my opinion — that the era of collider physics, which has taught us so much, will be over. The political will to build another, bigger, more expensive experiment will not exist.

If, on the other hand, there is something odd about this Higgs boson, or if CERN finds something else — something unexpected — in the next few years, then our theory will need revision, and more experimental studies will be needed to sort things out. That is an argument to keep going.

Despite those worries, this is a time for celebration. I think especially of the thousands of people who have worked so hard, for so long, to get to this point. The complexity and scale of these experiments beggars description; they are truly amazing feats of design and engineering, and those responsible for them can be justly proud at a time like this. All that work, and we reap the harvest.


This video gives an accessible but informative introduction to the Higgs boson. It takes a minute or so to really get going, and it looks better when viewed at full-screen.

When I consider the heavens…

May 2, 2012

Our good friend, Adam Hincks, S.J., has an article in the Jesuit weekly America in which he reflects on the relationship between contemporary cosmology and Christian faith:

Through much of Western history, it was thought that the motions of the heavens were regular and unchanging. The Christian notion that the cosmos had a beginning in time had to be accepted as an article of faith. With the advent of the Big Bang theory, it might seem that science corroborates revelation, but it is not that simple.

The article is temporarily available to non-subscribers. Read the whole thing.

(Hat-tip: Ibo et Non Redibo)

Burtt: Foundations of Modern Science

April 25, 2012

The Metaphysical Foundations of Modern Science
E.A. Burtt
(Dover, 2003) [1932]
352 p.

That man is the product of causes which had no prevision of the end they were achieving; that his origin, his growth, his hopes and fears, his loves and his beliefs, are but the outcome of accidental collocations of atoms; that no fire, no heroism, no intensity of thought and feeling, can preserve an individual life beyond the grave; that all the labours of the ages, all the devotion, all the inspiration, all the noonday brightness of human genius, are destined to extinction in the vast death of the solar system, and that the whole temple of Man’s achievement must inevitably be buried beneath the debris of a universe in ruins — all these things, if not quite beyond dispute, are yet so nearly certain, that no philosophy which rejects them can hope to stand. Only within the scaffolding of these truths, only on the firm foundation of unyielding despair, can the soul’s habitation henceforth be safely built.

– Bertrand Russell, Mysticism and Logic

I begin with this quotation because it gives us a vivid portrait of the predicament into which the metaphysics of modern science has led us. We have arrived at a picture of the world, and an understanding of our own place within it, which is, in a great many respects, hostile not only to the conception of human nature that reigned prior to the modern period, but, one is tempted to say, to even the most basic notion of man as a rational and moral creature. This situation, which I in certain moods can see only as an impasse, has come about in part because we have adopted a particular view of the natural world. It is the burden of E.A. Burtt’s classic book on the philosophy of science to outline this view, and to describe the historical circumstances in which it developed.

It developed out of something, and it is worth trying to sketch the basic contours of what preceded it. For late medieval man, nature was qualitative and inherently intelligible. Things has natures which were in principle knowable, and the whole natural order, though not itself intelligent, was nonetheless teeming with teleological relations. The texture of the world was thick: objects presented themselves to the understanding as unities, rich with colour and sound, and the beauty they conveyed to the mind was a modest but real intimation of a deeper, more permanent order. If man was considered to be, in some sense, above nature, this did not prevent his being at home in the world, for it was a world in which the human experience of will and desire, or the love of beauty, or the longing for knowledge was perfectly intelligible.

The birth of modern science did away with this view of things, perhaps with good intentions, sometimes with good reasons, and unquestionably with great success. Eventually it bequeathed us a world in which we appear as aliens, a world devoid of purposes, stripped of meaning, colourless and silent, comprised solely of bodies moving in space and time in a manner described by mathematical relations. We see the world as a massive machine, functioning according to fixed principles, best understood by examining its basic parts, and wholly governed by temporal (or, in Aristotelian terms, efficient) causation. Paradoxically, given the concomitant massive increase in our capacity to manipulate the natural world to serve our ends, the very framework whereby the world might be intelligible to us has been dismantled; we are reduced to speculation and inference based on neural signals produced by particles impinging on our sensory organs. The realm of qualities, purposes, and meaning, which can scarcely be entirely dispensed with, but which can find no place in the world so conceived, has been confined to scattered, and increasingly mysterious, things called ‘minds’. And now, with the turning of the wheel, the attempt is made to close the circle: to absorb even minds, hitherto the shelter for all those aspects of reality not compatible with the mechanistic, mathematical framework, into the framework itself. Our situation is, to say the very, very least, dramatic.

A thorough rehearsal of the historical development of the modern view would be a book-length project — indeed, it would be this very book — but I can sketch the main trajectory. Generally speaking, there are two important streams of thought to consider: the mathematical and the empirical. Both had roots in the medieval period. Though largely independent as they developed, they both informed the thought of Isaac Newton, who formulated an influential fusion of the two.

The revival of interest in Pythagorean thought was an important factor. Pythagoras had famously claimed that the world was made of “number”, and though the meaning of this claim was perhaps somewhat mysterious, it exerted a certain fascination. Late medieval astronomers showed a particular interest, and for intelligible reasons. It is easy to see, for example, how the sciences of astronomy and geometry, a physical science and a mathematical one, were considered closely related. In fact, Burtt argues that in the minds of at least some astronomers, astronomy just was geometry: astronomers studied the geometry of the heavens. To such men, it was natural, and even tempting, to believe that what was true in geometry was also true, in some sense, in the heavens. Thus when Copernicus proposed his heliocentric theory of the cosmos, the fact that it was mathematically simpler than the prevailing Ptolomeic model was interesting, and suggested to some, if not in Copernicus’ generation then certainly in the succeeding ones, that its mathematical simplicity was itself providing physical insight into the actual structure of the cosmos.

Johannes Kepler made a more radical claim: he argued that the mathematical order discernible in nature was itself the cause of the observed facts about the world. The real world was, in his mind, just the mathematical harmony discoverable in it. The strangeness of this idea ought to impress us: it was not that the world exhibited certain regularities such that aspects of it could be modelled using mathematical concepts exhibiting those same regularities — what we might call an instrumental use of mathematics — but rather that a mathematical description penetrated to the core of being, yielding a foundational understanding of the natural world. This essentialist view of mathematics was to prove very influential. An epistemological consequence followed: genuine knowledge of the world amounted to knowledge of its mathematical structure; mathematics provided not just a description of the natural world, but an explanation of it.

Kepler’s ideas influenced Galileo, who also believed that mathematical order implied necessity in nature. Galileo’s special contributions were, first, to explicitly abandon final causality as a principle of explanation in the physical sciences, and, second, to clarify the distinction, still hazy for Kepler, between the emerging concepts of primary and secondary qualities. The idea that final causality should be given up in favour of efficient causality had medieval precendent (in the thought of John Buridan, for instance), but until Galileo’s time it had not gained much traction. No doubt the waning influence of Aristotle was part of the reason why the time was ripe, and it is likely that the appeal of mathematical physics was another factor: it is more difficult (though not obviously impossible) for final causes to be given a mathematical formalism. To those seeking to construct a mathematical description of nature, therefore, and especially to those who believed that nature was intrinsically mathematical, final causes could have no appeal and provide no insight. The interesting question for these men was no longer ‘why’, but only ‘how’. The world so conceived was mechanical in substance: it consisted of bodies moving in space and time according to fixed mathematical relations. (Indeed, space and time now began to acquire status as fundamental metaphysical notions, which they certainly had not had in Aristotelian thought.) It is crucial to notice, in this context, that it was the method, inspired by a particular view of the natural world, that disposed with final causes, rather than, say, a particular discovery about the world.

The distinction between primary and secondary qualities was motivated — and, arguably, created — by the adoption of the mathematical concept of nature as well. Primary qualities are those features of an object that truly inhere in it, which cannot be separated from it. Secondary qualities, on the other hand, though we commonly ascribe them to objects, do not truly belong to them. For an Aristotelian, for instance, the redness of a red ball may be accidental, but it is still truly a property of the red ball that it is red, whereas for the early moderns like Galileo the ball only seems red, but it is not actually so; its redness is a secondary quality ascribed to the ball on the basis of certain peculiarities of the human senses; its redness exists only in the mind. The distinction between primary and secondary qualities arose for early modern scientists because they were committed to a mathematical view of nature, yet certain features of the natural world were not amenable to mathematical treatment. Those aspects of the world which could be treated mathematically — size, shape, position, motion, magnitude — were called “primary” and were considered real properties of objects, whereas those aspects which resisted mathematical treatment — colour, sound, smell, not to mention more intangible qualities like beauty or goodness — were called “secondary” and were relocated from objects to minds. Thus, on this view, objects in the external world possess only primary qualities, and second qualities are confined to mental life. Indeed, “man is hardly more than a bundle of secondary qualities”. Burtt comments on this state of affairs:

Observe that the stage is fully set for the Cartesian dualism on the one side the primary, the mathematical realm; on the other the realm of man. And the premium of importance and value as well as of independent existence all goes with the former. Man begins to appear for the first time in the history of thought as an irrelevant spectator and insignificant effect of the great mathematical system which is the substance of reality.

The mention of Descartes is natural enough at this juncture, but before continuing that line of clear and distinct thought it is worthwhile to pause a moment to reflect on the motives and the evidence for the mechanistic, mathematical view of the world. If Burtt is correct, this conception of the world is by no means a discovery of the sciences, but rather a methodological stipulation. What evidence is there for it? The question is more difficult to answer than one might expect. The incredible success that the sciences have enjoyed in describing a vast range of physical phenomena strongly suggests that there is something right about the general view, for under its guidance we seem to have gained real insight into the physical world. Moreover, we know that the atomic hypothesis is broadly correct: there really are particles moving around in space and time. But this is not really contested; the question is not whether this view is correct, so far as it goes, but whether it provides an exhaustive description. Is there nothing more to the world than these particles? The fact that the investigations of the sciences have never discovered anything which could not be fit into the mathematical framework, while sometimes cited as evidence for the truth of the framework, is nothing of the sort. Methodological limitations are being conflated with ontological ones. Is it, after all, a coincidence that the world as conceived by the mathematical physicist answers so perfectly to his needs?

Returning to Descartes, it is clear that his division of the world into res extensa and res cogitans was a natural development of the distinction between primary and secondary qualities: primary qualities belonged to the former and secondary qualities to the latter. Descartes, too, was convinced from an early age that mathematics was the key to genuine knowledge; his entire philosophical project was constructed on that assumption. Even more than some of the other early modern natural philosophers, Descartes was attracted by the idea that nature was not just mathematical, but geometrical. He resisted the idea that motion could be reduced to mathematical formulae only by attributing to bodies non-geometric qualities (such as mass); his famous vortex theory was a remarkable, though unsuccessful, attempt to produce a geometric theory of gravity. With Descartes the idea that nature is purely mathematical becomes tautological, for he defined the world external to the mind as consisting only of extended objects possessing primary qualities, with everything else pushed into the subjective realm of mind. In consequence, the mental realm was, for him, not a possible object of scientific study, for it consisted precisely of those qualities, attributes, and powers which eluded scientific methods.

Not everyone, however, was content with a sharp distinction between the physical and mental. Hobbes attacked Cartesian dualism, and made an attempt to subsume everything, including mind, into the res extensa. He was not successful, but his following has waxed greatly in the meantime. The question of whether that project can possibly succeed is an exceedingly interesting one that can, however, not deter us now. Instead, I simply note that, whether on the Cartesian or the Hobbesian side, many of the basic concepts were shared: efficient causality, mathematical description, bodies in motion, reductionism, and mechanism. The formulation of the metaphysics of modern science was substantially complete.

We have yet, however, to take account of the second principal stream of thought that informed the Newtonian synthesis: the empirical tradition. The principal figure here is Robert Boyle. Empiricists were, in general, less radical than their counterparts in the mathematical tradition. They resisted the push to reductionism, making productive use of concepts such as heat, weight, hardness, brittleness, etc. which could not obviously be ascribed to individual atoms. Boyle had moderate views: he valued qualitative descriptions, maintained the reality of secondary qualities, and was willing to entertain the existence of final causes. He also took a modest view of human knowledge, being suspicious of grand explanatory systems and thinking it often necessary to be satisfied with probable explanations rather than certainties. Paradoxically, it was he who began to point out certain skeptical consequences of the ideas propounded by those intent on obtaining genuine and certain (that is, mathematical) knowledge: if the picture of the world as conceived by Galileo and Descartes was correct, if the soul knows the world only through the effects of bodies impinging upon the senses, and if the world is not intrinsically ordered toward intelligibility, skeptical consequences follow. I will return to this point below. We should also note, however, that despite some differences, Boyle also accepted many of the new assumptions of natural philosophy. His view of man was largely Cartesian: “engines endowed with wills”.

In Isaac Newton these two traditions found a common advocate and were, to a large degree, integrated with one another. Newton’s basic method was, first, to work from observation and experiment to principles (in keeping with the empirical tradition), and then from principles to other phenomena (as in the mathematical tradition). Experiments were always involved at both the beginning and the end of an investigation, and the physical principles were always expressed mathematically. His synthesis has proved remarkably robust. Burtt notes, “Newton enjoys the remarkable distinction of having become an authority paralleled only by Aristotle to an age characterized through and through by rebellion against authority”. Though some of his scientific ideas have been superseded, his basic approach to scientific studies and the metaphysical system within which it was expressed remain dominant today.

Naturally, the emergence of the modern metaphysics of nature had an effect on theology. The relationship of God and the world has always been an important theological question, and it could not but be touched by a revolution in our views of nature. The repercussions within theological circles were sometimes comical — or would have been, had so much not been at stake. Henry More, for instance, gave this list of attributes: “one, simple, immobile, eternal, perfect, independent, existing by itself, subsisting through itself, incorruptible, necessary, immense, uncreated, uncircumscribed, incomprehensible, omnipresent, incorporeal, permeating and embracing all things, essential being, actual being, pure actuality” — as attributes of space! Space, he argued, was “divine presence”; even God, being real, was thought to be a res estensa! Malebranche too said something similar. Robert Boyle, as before, was more moderate in his views, but was nonetheless clearly under the influence of the mechanical worldview. He stressed, very wisely, that God was known naturally and normally through the world’s regularity, not through irregularities (that is, miracles); in his view, God maintained the “general concourse” of the universe as an harmonious whole. His view of God tended toward the Deist; he described God, using a phrase that was to have an unfortunate legacy, as the artificer of “a rare clock”. This general view he bequeathed also to Newton, who made a hash of it: he thought of God as providentially intervening in the world to “repair” it when necessary. For instance, he believed that God needed to intervene to keep the stars (which would tend to collapse together under the influence of universal gravitation) apart from one another. Burtt dryly notes that “to stake the present existence and activity of God on imperfections in the cosmic engine was to court rapid disaster for theology”. As time passed, under pressure from thinkers like Hume and Kant, the need for (and the knowability of) this God became more doubtful. The general story is familiar enough, but it is worth contrasting the God so conceived with the conception of God that was compatible with medieval metaphysics: in the medieval view, God had no purpose, but was the ultimate object of purpose, the final end of everything; natural processes were thus themselves examples of his providential action. In the modern view, he was demoted to custodial duties, his actions confined to the service of a greater end: the order and mathematical harmony of the universe.

God, however, has not been the only victim of skepticism in the light of modern metaphysics. I noted earlier the paradox that a view born principally of a desire for genuine and sure knowledge of the natural world should itself produce skepticism about that same knowledge, yet it is quite true. A universe consisting merely of atoms moving in space inclines one more or less strongly toward nominalism — that is, to the view that the world is not inherently intelligible, our concepts being merely conventions that do not correspond to real things. Moreover, the ascent of atheism itself intensified skepticism, for if the world is not underwritten by an intelligence, what reason have we to suppose it can be grasped by our intellects? “It was by no means an accident,” writes Burtt, “that Hume and Kant, the first pair who really banished God from metaphysical philosophy, likewise destroyed by a sceptical critique the current overweening faith in the metaphysical competence of reason. They perceived that the Newtonian world without God must be a world in which the reach and certainty of knowledge is decidedly and closely limited, if indeed the very existence of knowledge at all is possible.” And, in a kind of reductio ad absurdam of the mechanistic metaphysics, the effort to extend it into the mental realm results, as it apparently must according to the terms available, in the obliteration of specifically mental life itself and those things belonging to it, such as the very concept of knowledge. It is the ultimate apotheosis of skepticism. But that is a topic for another time.

At the end of this long analysis, I suppose the question hanging in the air is: if not this, then what? How should I know? I am as beholden to the modern assumptions as much as anyone — and, as a physicist, I am perhaps beholden more than most. Yet I can see the problems clearly enough, and I can see, too, that the positive arguments in favour of the currently dominant view are surprisingly weak. It seems likely to me that we are guilty of allowing our method to dictate our ontology, which is a clear fallacy.

Yet it is far from clear how best to respond to the situation. One possible step would be to reappraise the rejection of final causality. The sciences have in any case never been entirely consistent in rejecting them: biologists in particular find it hard to resist making teleological claims when they discuss their subject, and there may be resources within physics as well for a restoration of final causes (I am thinking of teleological interpretations of the action principle in both classical and quantum mechanics). It is sometimes thought that final causes, having to do with goal-directedness and purpose, require the existence of a presiding or immanent intelligence or will, which requirement seems to imply either personification of nature or theism, but actually this is not true; Aristotelian final causes imply neither. Second, we may reconsider our commitment to reductionism: even if it is true (as it is) that the world is comprised of particles in motion, is it really true that an understanding of the properties of those particles is, in principle, sufficient to understand everything else? Are the physical properties of ink molecules on a sheet of paper really enough to account for the meaning the written word conveys? It seems obvious that a bridge is out somewhere. A richer metaphysics could provide room, once again, for serious and honest engagement with non-mathematical aspects of reality. But I am a feeble philosopher, and such things are far beyond my competence.

In the meantime we are left with a view which, though having been wonderfully successful in certain respects, ultimately has no place in it for you and me: rational beings who think about things from a first-person perspective and act in the world out of our own freedom. As such, the battle is joined.

Applied physics

April 18, 2012

A friend sends a story about a professor who used physics to get out of paying a traffic ticket.

The paper outlining his argument is available here. I like the abstract (“The paper was awarded a special prize of $400 that the author did not have to pay to the state of California.”), and the paper itself (pdf) is a fun read. The physics involved is not beyond a high-school level.


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