A (non)Definition of Depth

We’ve posted a number of reflections about the idea of “depth” in (especially) mathematics and related science (for the complete list of these, click here: http://worldofdrjustice.blogspot.com/search/label/depth ), without ever really defining the term.  And this, for a reason:

Two interrelated ideas that have been widely assumed to be unanalysable  are those of one scientific theory being deeper and more unified than another.

-- John Watkins, Science and Skepticism (1984), p. xiii

The idea of theoretical depth has considerable importance in Popper’s philosophy of science.  “If at all possible, we are after deep theories.”  But he was pessimistic about the possibility of any sharp characterisation of the idea.

-- John Watkins, Science and Skepticism (1984), p. 188

And that, not necessarily for any ‘deep’ reason -- not correlating intimately with the intricacies of physics, say -- but much as it is hard to characterize sharply such multifaceted (or blobby) concepts as beauty or game.    And here, I must sympathize with the archetypal philistine of a hundred New Yorker cartoons,  genially conceding, “I don’t know much about art, but I know what I like.”   A mathematician or physicist may not be able to define depth in a way that would satisfy the notoriously finicky tribe of philosophers:  but he knows it when he sees it.  And smiles.

So, sorry, no necessary-and-sufficient conditions, nor even a rough-and-ready dictionary definition;  but anyhow, an epigram:

Whewell’s requirment that a deep hypothesis, one that gets hold of nature’s ‘alphabet’ as he put it, must enable us ‘to explain … cases of a kind  different from those which we contemplated in the formation of our hypothesis.

-- John Watkins, Science and Skepticism (1984), p. 190

(A similar metaphor, more popular since Whewell’s day:  a good theory must “cut Nature at the joints”.)

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Hmm, now I’ve piqued my own curiosity.  How does a practicing lexicographer go about characterizing the term deep in the sense(s) of interest here?

Okay, for starter’s, a British one -- Collins English Dictionary (1979):

deep:  … (6) difficult to understand or penetrate; abstruse

(7)  learned or intellectually demanding: a deep discussion

Sense (6) is of no interest.  We went to some effort in this post (“A Dive to theDepths”) to distinguish depth from difficulty.  (For the list of posts re difficulty: http://worldofdrjustice.blogspot.com/search/label/difficulty .)   Sense (6) would be used by a lazy man, giving up -- “Too deep for me.”   Here he is not even using the word with its native literal resonance -- he could quite as well speak with poor Mr Tulliver, who often confessed that the world was “too many” for him.   Indeed, sense (6) might deserve one of those non-semantic/non-grammatical, sociolinguistic labels like “ -- Not in polite use”:  here,  “-- Not used in this sense by serious thinkers.”

Actually, by a twist of pragmatics, the phrase does get used by serious thinkers -- but typically as an ironic put-down.  Thus:

The towering 19^th-century mathematician Hamilton  labored hard on his “Law of Hodographic Isochronism”,

but when he sent it to John Herschel (whom Hankins calls “the best-known and best-regarded British scientist of his time” [p. 134]), he got the reply:  “You are fairly got out of my depth”.  (This was Herschel’s regular response when he did not have the time or inclination to follow Hamilton’s long analytical excursions.)

-- Thomas Hankins, Sir William Rowan Hamilton (1980), p.

And again, roughly a century later:  After presenting a rather absurd and convoluted, goalpost-moving series of proposals from Lakatos and Morrall:

I am out of my depth with a claim of this kind.

-- John Watkins, Science and Skepticism (1984), p. 334

Here he is being disengenuously self-deprecating;  and his reply is all the more biting.

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A more general thought, though, on depth versus difficulty.   I almost wrote that the latter was “much less interesting” -- though really, that depends on your day-job.  If you teach primary school, you need not (ex cathedra) worry your head one bit about depth in our sense;  whereas you must ever be alert to the perils of difficulty.  To epigrammatize into a dichotomy:  Depth (again, in our privileged sense) inheres in the subject itself;  Difficulty is relative to the practical limitations of some species (be it human, chimp, or the poor fly stuck in the fly-bottle) when grappling with the problems in that subject.   Since the philosophy of this blog is Platonist, we have little interest in the latter (no intellectual interest;  though some emotional interest, maudlin or morbid, as here).

From that perspective, sense (7) is also disappointing.   A subject itself (such as algebraic geometry or M-theory) cannot be called “learned” (i.e., learnèd):  that epithet might only be applied to whoever is gassing on about it.  “Intellectually demanding” could be applied either to a subject or a particular discussion or presentation thereof.  And that quality might be due to anything from the intellectual limitations of the audience (“The concept of evidence is too intellectually demanding for Trump voters”)  -- thus, back to sense (6) -- to an (overly) condensed presentation on the part of the lecturer, to actual depth inherent to the subject (and which would still be apparent to an angel, who understood the subject perfectly well).   Thus, neither sense goes far towards elucidating what mathematicians mean when they refer to a “deep result”.

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Curious now whether my old alma-mater Merriam-Webster  did any better, I looked it up in their Collegiate Dictionary (Eleventh Edition),  I found something quite different.

First, their treatment of the geospatial, ‘literal’ sense of the term, from which all others ultimately derive, is unexpectedly rich and reticulated (I almost wrote:  “deep”), containing sub-subsenses like

deep  1 b (1) : extending well inward from an outer surface <a ~ gash>

(That is the sort of distinction you come up with when you are working from a generous deskful of carefully chosen citation-slips, rather than copying other dictionaries  or pulling the definition out of your butt.)

But then things sort of fall apart.  The sense “difficult” is not treated as a top-level numbered sense, as in the Collins, but as a subsense of a sense not defined save as the sum of its (rather disparate) subsenses:

deep  3 a : difficult to penetrate or comprehend : recondite < ~ mathematical problems>

3 b : mysterious, obscure <a ~ dark secret >

3 c : grave in nature or effect <in  ~est disgrace>

3 d :  of penetrating intellect : wise <a ~ deep thinker >

along with several more lying well off our axis of interest.   And oddly, despite all the careful hair-splitting, nothing really corresponding to Collins’ (7).

Thus, we still have come no further towards our goal.

~

The subject of depth, unlike that of mathematics, or Christianity (or oahspe),  tends not to attract disquisitions of the “What  is ….?”  sort.   We tried our hand at one for math (here), basically coming up with little more than a florilegium of blind-men-and-the-elephant stabs at it, for the overly general definiendum mathematics itself;  more fruitful was the task of characterizing topics within mathematics, like affine connection or topology, since here (at least for the former example) the definer’s intention is more in the nature of targeted enlightenment  than an after-dinner speech :  the result was a nice bouquet of epigrams.

~

Back to Depth vs Difficulty.    

(1) A deep remark or insight  is associated, not with presenting difficulties (as in Collins sense (6) ), but -- quite the contrary -- with resolving them.

A humble but poignant case  has been recounted here (Induction/Recursion), where a problem that had seemed difficult (to New Jersey third-graders, back in the complacent days before the impact of Sputnik  had filtered down to elementary school) -- that of multiplying multi-digit numbers -- suddenly became transparent, under the impact of an insight which (relative to what we had learned so far, most of it from the Mickey Mouse Club) might qualify as (qualifiedly) deep. 

(2) Above, we made something akin to an actio/actum distinction between difficulty and depth (human activity vs. the subject itself);   yet now we may make an additional distinction, on the same -- human -- side of the Platonic/psychological divide.  You might call it horizontal/vertical,  syntagmatic/paradigmatic :  judging words (concepts) by the company they keep.

~

Let us recur to that subsense in Webster’s Colleagiate,  “3 b : mysterious, obscure”, and consider the idea of  deep as it appears in company with that of being hidden:

The mind is in a sad state, when Sleep, the all-involving, cannot confine her spectres within the dim region of her sway, but suffers them to break forth, affighting this actual life, with secrets that perchance belong to a deeper one.

-- Nathaniel Hawthorne, “The Birthmark”

(I.e., a deeper, hidden something, that somehow itself  amounts to a “life”.)

And from a mathematical physicist:

It is indeed true that we can prove, from this kind of Euclidean argument,  that squares, made up of right angles, actually do exist.  But there is a deep issue hiding here.

-- Roger Penrose,  The Road to Reality (2004), p. 28

Namely (tying in with cosmology):

His fourth postulate asserts the equality of all right angles.  … In effect, the fourth postulate is asserting the isotropy and homogeneity of space.

-- Roger Penrose,  The Road to Reality (2004), p. 29

~

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More on Measurement and Metrization

We earlier treated the matter of a metric on a topological space, in a series of essays beginning here:

The Urysohn Metrization Theorem:  for real this time

Now, as lagniappe, we offer a pair of Metrization Epigrams, which the budding mathematician, stuck for an opener with that leotard-clad vision at the espresso bar, can use for a pick-up line:

 A discrete space is like the autistic atomism of the Tractatus, or Leibnizian monads.

An indiscrete space is (as one writer charmingly put it), “really quite crowded:  each point is an accumulation point of every other set.”  (One pictures the Jellyby children in Bleak House, ever tripping over one another’s legs.)

(Believe me, chicks go wild over such things.  Or at least, if you are like most gangly Adam's-apple-challenged graduate-students in math, it’s your last best shot.)

~

It is by no means only topological spaces that one might wish to subject to a metric: all kinds of things, really:    Which species lie how close to which others (and different metrics -- phenotypic, cladistic, etc. -- yield different results);  which languages are neighbors in linguistic space (again there is a phenotypic/cladistic distinction:  descent vs. Sprachbund); which people have a natural affinity with which other (seating-plans at dinner-parties; blind dates; etc.)  And more generally, what is the curvature tensor of the noösphere?

As (from a philosopher of science):

One sometimes wants to say that a theory has much more testable content than some other statement:  for instance, the Newtonian theory has much more testable content than ‘The moon orbits the earth’.  But our apparatus, as it stands, does not entitle us to say this.  We have no metric for testable content.

--John Watkins, Science and Skepticism (1984), p.  185

Compare Keynes’ critique of relative subjective probabilities.

Here a noted philologian on the notion as applied to languages:

Was nun die Sache selbst anlangt, so meine ich  daß immer Sprache und Sprache, mögen sie auch noch so weit auseinander liegen, in wissenschaftlichem Sinn  enger zusammengehören  als Sprache und Literature, seien es auch die  desselben Volkes.

-- Hugo Schuchardt, “Über die Lautgesetze”  (1885), in Leo Spitzer, ed., Hugo Schuchardt-Brevier (1921; 2^nd edn. 1928), p. 85

And here, indeed, he polemicizes against the nominalist treatment or ‘indiscrete toplogy” of diachronic linguistics:

Ist es denn nun nicht an sich ganz gleichgültig, ob rom. andare von adnare oder addare oder ambulare oder einem keltischen Verbalstamm herkommt;  ob in diesem Dialecte  l zu r  und in jenem  r zu l  wird usw.?   Welchen Sinn haben alle die Tausende etymologischer und morphologischer Korrespondenzen, die Tausende von Lautgesetzen, solange sie isoliert bleiben, solange sie nicht in höhere Ordnungen aufgelöst werden?

-- Hugo Schuchardt, “Über die Lautgesetze”  (1885), in Leo Spitzer, ed., Hugo Schuchardt-Brevier (1921; 2^nd edn. 1928), p. 84

~

This metaphor of ‘metrization’, outside the exact sciences, is very loose, as it is not strictly needed -- for taxonomic purposes, a more approximate neighborhood-system will suffice (a “Uniformity”) so to speak -- and still less is to be obtained.

As, a pair of British linguists comments:

Once recent attempt by French researchers  has given us the term dialectometry, which describes a formula for indexing the dialect ‘distance’ of any two speakers in a survey.  So far, the utility of the index has not been demonstrated.

--J.K. Chambers & Peter Trudgill, Dialectology (1980), p. 112

This, in the synchronic arena, is reminiscent of the glottochronology of Morris Swadesh, who attempted a sort of carbon-dating of linguistic evolution, based on an assumed universal rate of lexical decay, in the absence of direct evidence.

[Update 17 January 2016]  Another cautionary tale about the fetishization of metrics:

TWO of our most vital industries, health care and education, have become increasingly subjected to metrics and measurements. Of course, we need to hold professionals accountable. But the focus on numbers has gone too far. We’re hitting the targets, but missing the point.

http://www.nytimes.com/2016/01/17/opinion/sunday/how-measurement-fails-doctors-and-teachers.html?ref=international

Philologisches:

Whether, in that opening paragraph, the author wrote “metrics and measurements” intending to refer to two distinct though related concepts, or whether it was just an idle bit of synonymic accumulation like “bequeath and bestow” for those who might be unfamiliar with the somewhat technical word metric, is there unclear.  But it does raise a linguistic point.

The word metric, and its close kin meter, metrical, metrization, derive from Greek.

Mensuration and commensurable  go back to Latin mensura.

Measure comes ultimately from that Latin word as well, but via the phonetics of medieval French.

The same Indo-European root  is said to lie at the base of all of them.

English, an etymological patchwork, has some tendency to layer its vocabulary by origin, Greek roots being reserved for the most technical, followed by Latin,  with the Saxon vocabulary as jack of all work.  In this, it contrasts with German:  to Graeco-English oxygen, hydrogen, nitrogen  correspond homely-sounding Germanic compounds Sauerstoff (‘sour-stuff’), Wasserstoff, Stickstoff.   And Freud’s German originals for the English ego and id, were nothing but nominalizations of the ordinary pronouncs, das Ich & das Es.

Roughly such tiering is at work in our Wortfeld of ‘measure’. 

Measure sounds reasonably English (though partly just because it chimes with pleasure and leisure, which are likewise French words in disguise), and is in everyday use for all purposes (though it also has technical specializations, as in mathematical measure theory).

Latinate mensuration (little used) is scarcely more than a stuffy synonym for ‘measuring’;  commensurate is literate and has everyday though businesslike uses (“a salary commensurate with the job responsibilities”); while commensurable is mostly technical, whether in its mathematical sense, or its more recent philosophic sense (“commensurable discourses”).

Metric is kind of a green-eyeshade/clipboard sort of word at best.  If becomes fully technical in mathematical uses like metric space and semi-metric,  finally soaring off into the intellectual empyrean with metrizable.

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Still wearing our lexicographer’s hat, here is an attestation for a word with which I had previously been unfamiliar, used by a philosopher of science.  After a rather confusing Gedankenexperiment judging the verifiability of a physical geometric hypothesis, involving all sorts of skulduggery with measuring rods, and “tampering with the semantic anchorage of the word congruent”  (that’ll get you two weeks in the clinky  without the option), and in which Albert Einstein (from beyond the grave) plays a role like that of Fantomas, battling the equally post-mortem shade of Pierre Duhem,  our professor writes:

The required resort to the introduction of a spatial dependence of the thermal coefficients  might well not be open to Einstein.  Hende, in order to retain Euclideanism, it would then be necessary to remetrize the space.  ….  Einstein’s geometric articulation of that thesis  does not leave room for saving it by resorting to a remetrization in the sense of making the length of the rod vary with position or irientation  even after it has been corrected for idiosyncratic distortions.  But why saddle the Duhemian thesis as such  with a restriction peculiar to Einstein’s particular version of it?  And thus why not allow Duhem to save his thesis by countenancing those alterations in the congruence definition which are remetrizations?

-- “The Falsifiability of Theories”, in: Adolf Grünbaum, Collected Works, vol. I (2013), p. 72-3

As indicated, I couldn’t really follow the dialectical taffy-pull in that conterfactual-strewn discussion, but simply the passage as though on one of those “citation slips” we used to rely on at Merriam-Webster.

~

Just happened upon a passage which we quoted earlier in another context (here):  a use, by a mathematician (or if you prefer, a logician) of the in-itself-not-expressly-mathematical term measurement,  not in a technical mathematical sense such as measure zero or measure theory,  but sliding mathwards towards concepts very far from any plain man’s conception of “measurement” (as: wholly non-numerical, non-quantitative   fundamental group):

Mathematics is, as it has always been, largely the science of measurement.  But “measurement” must here be understood as referring to more than the meter stick.  The genus of a topological figures measures one of its aspects;  objects of genus zero  are in a sense simpler than those of higher genus. 

There are many dimensions of measurement ….:  characteristic, transcendence degree, cardinality, fundamental group … Occasionally we are so successful in the science of measurement  that we can completely characterize an object … by giving, as it were, its latitude and longitude:  its measurements in the relevant dimensions.

-- Herbert Enderton, “Elements of Recursion Theory”, in:  Jon Barwise, ed. Handbook of Mathematical Logic (1977), p. 554

I originally cited that as a not-especially-successful attempt (in its first sentence) at a one-line characterization of What Mathematics Is.    Measurement, in the usual sense, is common to a great many studious activities, from chemistry to engineering to dressmaking.   He only manages, in what follows, to make that characterization  more or less work, by moving the goalposts  and re-defining measurement in his own Pickwickian sense.

Scattered Objects

There is no reason to boggle at water as a single though scattered object,  the aqueous part of the world.  Even the tightest object, short of an elementary particle, has scattered substructure  when the physical facts are in.

-- W.V.O. Quine, Word and Object (1960), p. 98

In support of this:

(1) “the aqueous part of the world”:  cf. “empty space”, an anything but simply-connected entity (object).

(2) “scattered substructure”:   Unsure quite what he meant by this -- quarks are substructure of hadrons, but were unknown -- nay, unhypothesized -- in 1960, the publication-date of Quine’s classic.   However, a “smeared-out” (not really ‘substructural’)  nature of something so tiny-tight as the electron (still regarded as truly elementary) was suggested already by the double-slit experiment.

For the full essay, to which this is a footnote:
 http://worldofdrjustice.blogspot.com/2011/09/on-what-there-is_28.html

Refutation vs. Disconfirmation

We continue our observations about Verification (essay here) and Modus Tollens (essay here).

It has been maintained that there is an important asymmetry between the verification and the refutation of a theory in empirical science.   Refutation has been said to be conclusive or decisive, while verification was claimed to be irremediably inconclusive. … The falsity of [the theory] is indeed deductively inferable by modus tollens.

-- “The Falsifiability of Theories”, in: Adolf Grünbaum, Collected Works, vol. I (2013), p. 62

That is basically because an empirical law is, in general, a universal: ∀x P(x).   Given any  ¬P(a), that is falsified.    Whereas successive confirming instances, while perhaps increasing one’s confidence in the hypothesized law, do not deductively entail it.   Nor need that fact be, in practical terms, a mere quibble, in cases of an infinite domain:  thus, a conjecture in number theory might be verified for all values of n up to a billion -- a trillion -- a googolplex -- yet still turn out to be false.  (Indeed, toy conjectures of this sort  are trivially easy to dream up.  E.g. “No integer is evenly divisible by a googolplex.”)   Taking confirming instances ‘too seriously’, is the Fallacy of Affirming the Consequent.

Grünbaum then, however, in a Duhemian vein, weighs in against such modus-tollentic tyranny, with the observation that, in empirical science, you are really assuming (ex hypothesi) not merely a theory, but (in unspoken conjunction therewith) various Auxiliary Assumptions:  and one or more of these, rather than your pet theory, might be the ones to suffer the fury of the tollendum.  Thus,  “Isolated component hypotheses of far-flung theoretical systems are not separately refutable but only contextually disconfirmable” (id., p. 63).

The same idea, more sociologically stated:

Typically  a theory is abandoned, not because of recalcitrant observations on their own, but because of these together with some, perhaps quite complex, reasoning from them:  in the extreme case, the observations may all be quite well known already, and all that is new  is the reasoning.

-- Michael Dummett, Truth and other enigmas (1978), p. 409

Compare:

… that falsity, not truth, is the primary notion.

-- Michael Dummett, Truth and other enigmas (1978), p. xl

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It is seldom that a theory is decisively k.o.’d by a Popperian uppercut to its predictive jaw.   Often the process happens slowly, like a river silting up;  there is no single Aha! moment (or rather, Oy veh! moment).   In science, as in life,  sometimes love grows old and love grows cold.  As, assessing a certain philosophical program:

The further one goes down the reformist path, the more implausible the consequences of one’s theory are likely to become, until  at some point  the implausibility of the consequences  comes to outweigh the initial attractiveness of the theory.

-- Scott Soames, Philosophical Analysis in the Twentieth Century (2003), vol. I, p. 299

That gradual, einsickernd, process of disenchantment, lacks the drama of Popperian refutation, or of Kuhnian paradigm-shift;  it is more reminiscent of the dissatisfying phenomenon (if it even is one) of truth decay.

~

The history of science -- though not the historiography of science -- is littered with once-flourishing theories that somehow just … faded, without necessarily ever having been decisively confronted or refuted.  It is no fun to research and write about these, since
(a) they are losers in the lottery (rightly or not), and scarcely known today (so that one’s potential readership is infinitessimal -- and indistinguishable from zero among working scientists); and
(b) there is seldom a clear-cut moral in the tale.

The occasions on which one does get an insight into some defunct theory  tend to be biographies of otherwise-great scientists -- e.g.  Theodore Porter’s fine account of the (as we now reckon him) statistician Karl Pearson, which must needs notice that hero’s period of infatuation with, mm, ahh, … ether squirts (pas devant les enfants!);  or Thomas Hankins‘s  of William Rowan Hamilton.  Or, sometimes, a historian of science rolls up his sleeve and deconstructs/resurrects  some particular thread of experiment.  As, Gerald Holton’s commendable study of “Subelectrons and Presuppositions”, involving the “classic” Millikan experiment, of which we all get a telescoped and sanitized version in high school physics.  The actual saga is more anfractuous, and less rich with easily digestible lessons.

[Millikan] found himself working with the wrong presupposition, but he knew how to rid himself of it eventually.  Millikan launched into that work with the same energy and obstinacy  as into his earlier work on the quantization of the charge of the electron, yet with the opposite assumption.

-- Gerald Holton, The scientific imagination (1978), p. 72

And re the related experiments of Felix Ehrenhaft:

There was never a direct laboratory disproof of Ehrenhaft’s claims.  … Lorentz … remark[ed]:  “The question cannot be said to be wholly elucidated.” In his review of the case, R. Bär noted …: “the experiments left, at the very least, an uncomforable feeling.”  Like most such controversies, this one also faded into obscurity, without anything as dramatic as a specific, generally agreed-upon falsification taking place at all.  Indeed, Ehrenhaft continue to publish on subelectrons into the 1940s, long after everyone else had lost interest in the matter.

-- Gerald Holton, The scientific imagination (1978), p. 79

And that, within (central, classical) physics.  The less rigorous (natural and social) sciences  are much pocked with such as well.

~

Science, not as logically implying some new phenomenon (such as the gravitational bending of light), but as suggesting likely places to look.   Thus:

The search, which has proved so successful, for chemical atoms  having specific nuclear and electronic constitutions, and for chemical molecules having specific atomic constitutions, has been stimulated by the previous construction of theories to explain the consitution of atoms or of molecules already known, theories which had, as it were, ‘gaps’ in them.

-- Richard Braithwaite, Scientific Explanation (1953), p. 70

And indeed, not only the existence of, say, atoms or isotopes with a given atomic weight and atomic number  are thus -- not exactly ‘predicted’ in the deductivist sense, but pointed to -- but additionally, we shall expect certain behaviors, or ranges of behaviors, based upon the place in the periodic table of that species (should it exist).

Thus, when the eka-aluminum that Mendeleev hypothesized  was eventually identified (by a Frenchman, who thus had naming-rights and called it gallium) and turned out to have behavioral values very close to those predicted,  while not proving the theory of atomic chemistry as it then stood, was still much more than just one more danged black raven.

[A footnote on another such predicted discovery, that nicely illustrates consilience in the sciences, combining both forefront atomic physics  and practical geology:

At the time Bohr was developing his theory, the element following lutecium was undiscovered.  But Bohr … asserted that, in this unknown element, the added electron would have to be placed in the level n = 5. This would imply that the unknown element would have an electronic configuration analogous to that of zirconium.  Inasmuch as elements that are chemically analogous  are usually found in the same minerals, Bohr claimed that the missing element should be sought in minerals containing zirconium.  It was indeed in such ores that the missing element, called hafnium [after the Latin name of Bohr’s hometown] was detected.

-- A. D’Abro, The Rise of the New Physics (1939),  p. 549.  ]

This “guiding-light” role of a theory, not being a formal entailment, is likewise not subject to modus tollens (though of course it might be abandoned in the face of an accumulation of recalcitrant instances):

Whereas discovery of observable properties which fill such gaps in a theory  is rightly thought to provide a weighty confirmation of the theory …  failure to discover such properties would not be regarded as weighing against the theory, except perhaps in very special cases.

-- Richard Braithwaite, Scientific Explanation (1953), p. 70

“Green Hat” monostich

~

~      ~

it smelled  as grass might smell   in fairy land

~       ~

~

"I say ... rather good, that."

[Source:  Michael Arlen, The Green Hat (1924); edited slightly  metri causâ]

Esse est percipi: the "collapse of the wave-function"

Distinguishing discontinuous state-reduction (which he dubs R) -- i.e., the “collapse of the wave-function” upon “observation”  -- from linear evolution as per the Schrödinger equation,   a mathematician remarks:

I do not mean to imply that the experimenter deliberately sets up a ‘measurement’ to achieve this.  … Nature herself is continually enacting R-process effects,  without any deliberate intentions on the part of an experimenter or any intervention by a ‘conscious observer’.

-- Roger Penrose,  The Road to Reality (2004), p. 593

Thus achieving the esse of percipi  ‘naturally’ (vacuously).

[For the full post  to which the above is a footnote, click here:

http://worldofdrjustice.blogspot.com/2013/09/esse-est-percipi-redivivus-ter.html  ]

Note:

D’Abro (in The Rise of the New Physics (1939)) writes  less dramatically  of an act of measurement against a given parameter as triggering “instantaneous condensation” from the previous diffuse cloud of potential values.

In Are Universes Thicker than Blackberries? (2003), p. 4, Martin Gardner, a staunch foe of Science Porn, gives an even less catastrophic-sounding synonym of “collapse of the wave-function”:  rotation of the state vector.   He goes on to polemicize (very readably) against the Many Worlds Interpretation, ultimately concluding that “As far as we can tell, universes are not as plentiful as even two blackberries.”

ISIL : the Prequel

To people ill-acquainted with history, the antics of ISIL (ISIS, Dâ`ish, the Islamic State) seem something utterly new under the sun.   But there are precedents.   (Here we speak only of their public theatrics.  Their actual theology, rather than really innovative, is second-hand Wabbabi Salafism.)

ISIL trademarks, with antecedents:

Destruction of antiquities:

Hitler retaliated for the raid on Lübeck, sending German bombers against British cities with medieval town centres.  The raids were known as Baedeker raids, after the German guide books.

-- Martin Gilbert, A History of the Twentieth Century, vol. II (1998), p. 438

More here.

Head-fetishism:

Aztec skull-racks.

The Huns, marking their advance  with mountains of skulls.

(H.G. Wells, on Hulagu:  “Pyramids of skulls were his particular architectural fancy;  after the storming of Ispahan, he made one of 70,000.” -- Outline of History.)

Mexican narcotraficantes, using severed heads as bowling-balls.

More here.

Morals police

We summarized the VICE News ride-along with ISIL’s al-Raqqa Hisbah (حسبة) here.   This kind of unit is not unique to ISIS -- AQAP now has one of the same name, and both are preceded by the dreaded Saudi muṭawwiʿūn (مطوعون)

There are precedents as well among American Puritans:

The state exists to punish vice, to spread “salutary terror” in the hearts of men.

-- Wilson McWilliams, The Idea of Fraternity in America (1973), p. 126

Bragging about it:

A historian quotes a memoir from Japanese-occupied Manchuria during WWII:

As part of their education, my mother and her classmates  had to watch newsreels of Japan’s progress in the war.  Far from being ashamed of their brutality, the Japanese vaunted it  as a way to inculcate fear.  The films showed Japanese soldiers cuting people in half, and prisoners tied to stakes being torn to pieces by dogs.  There were lingering close-ups of the victims’ terror-stricken eyes  as their attackers came at them.

The Japanese watched the eleven- and twelve-year-old schoolgirls  to make sure they did not shut their eyes, or try to stick a handkerchief in their mouths to stifle their screams.

-- Martin Gilbert, A History of the Twentieth Century, vol. II (1998), p. 443

Note that the point here  is not that the Japanese committed atrocities, but that (unlike, for instance, the Nazis, for the most part, or Stalin) they boasted about it, publicized it.

In the case of ISIL (we have argued), the beheadings are aimed at more (much more) than terrorizing the enemy:  they have a demonstration effect on their own ranks. 

Ditto for the Japanese;  re the year 1937 (when the Japs were already up & active, well before Pearl Harbor):

The Japanese company commander, Tominaga Shogo, later explained how, after decapitating a Chinese prisoner with his sword, “I felt something change inside me.  I don’t know how to describe it, but I gained strength somewhere in my gut.” 

-- Martin Gilbert, A History of the Twentieth Century, vol. II (1998), p.165

That wasn’t done to “inculcate fear”;  it may well have been done out of sight.  Psychologically, it is more comparable to cannibals eating the warriors they have slain, to incorporate the mojo.

These were not isolated, private acts.  From 1942:

On Singapore Island, 5,000 Chinese civilians  … were rounded up and … killed:  first their hands were tied behind their backs, and then their heads cut off with a sword.

-- Martin Gilbert, A History of the Twentieth Century, vol. II (1998), p. 165

That, note, is likewise ISIL’s favored posture for decapitation.

More here.

Triste bilan

Le SOHR a publié des chiffres concernant les décédés dans la guerre en Syria pendant 2015 :  55.000,  dont trente mille femmes  et quarante mille enfants.

Pour vous informer davantage dans ce sens, cliquez ici .

Pour l’ensemble de nos drolatiques soties  en matière de francophonie, ici.

http://www.theguardian.com/world/2015/nov/24/canada-exclusion-refugees-single-syrian-men-assad-isis