Mathematics and Morality

In our series of essays “Theologia Mathematica”,  we have focussed on philosophical and epistemic issues, very far from the sort of thing discussed in the pulpit of a Sunday.   We have striven both to enrich theism and to defend it against its intellectual detractors -- yet in this special vein of argument, do not aspire so high as Christianity, or indeed morality in general.  Nor have I, really, any insights to share upon this head:  in cases where I do make so bold as to venture onto the public square,  such political or ethical statements as I might hazard  make no claims at all upon any results from physics or from mathematics -- although, as with philosophers and theologians in all times, they are of course informed by logic.

Still, as the subject lies inevitably near at hand, it seems meet to at least put up a bulletin-board, on which we can post any quotes we may come across, which illustrate cross-fertility between the moral and the mathematical spheres.

~

Koestler, Sleepwalkers , I.2.ii, characterizing the philosophy of Pythagorus:

Numbers are eternal, while everything else is perishable … They permit mental operations of the most surprising and delightful knd, without reference to the coarse external world … -- which is how the divine mind must be supposed to operate.  The ecstatic contemplation of geometrical forms and mathematical laws  is therefore the most effective means of purging the soul of earthly passion, and the principal link between man and divinity.

Koestler, Sleepwalkers , I.2.iv [39]: “It is said that Pythagoras, like St Francis, preached to animals.”

~

John Henry Newman, Apologia pro Vita Sua (1864):

He who made us, has so willed, that in mathematics indeed we arrive at certitude by rigid demonstration, but  in religious inquiry  we arrive at certitude by accumulated probabilities.

I cite this simply as an amiable proof-text, while disagreeing with basically all of it.

Cardinal Newman

In mathematics, you approach certainty, over the centuries, by experiment, insight, and eventually a proof (or “rigid demonstration”) -- or perhaps a succession of improved proofs, as subtle flaws are found in the first one.

Arriving at -- again not really “certitude”, but what used to be known as moral certitude (“beyond a reasonable doubt”), by accumulated probabilities, strikes me as a nice thumbnail description of the process of science;  theology, not so much.  Theology additionally relies on Revelation -- or “intuition” -- that inward vision -- as it is mystically known in math.

~

For mathematics as the science of reckoning, Chesterton has little feeling;  but the more modern conception of math is the science of pattern, and Chesterton has strong intuitions about the spiritual content of shape.

G. K. Chesterton, Robert Louis Stevenson (1927):

Whether or no we see faces in the carpet, we ought to see a mind in the carpet; and in fact  there is a mind  in every scheme of ornament.  There is as emphatically a morality expressed in Babylonian architecture or Baroque architecture  as if it were plastered all over with Biblical texts.

~

The above concern a fancied moral tinge to mathematics itself.  Quite different is the relatively familiar thesis that moral reasoning can or does proceed more mathematico.  Thus Spinoza.  Or cf. David Hume, Enquiry Concerning the Principles of Morals (1751):  Whether something is to be considered a “crime … consists not in a particular fact … but it consists in certain moral relations, discovered by reason, in the same manner as we discover by reason  the truths of geometry or algebra.”

John Henry Newman, Apologia pro Vita Sua (1864) acknowledges that “every article of the Creed is beset with intellectual dificulties”, yet “ten thousand difficulties do not make one doubt; difficulty and doubt are incommensurate.”   And if you think he is here sidestepping the issue, he adds a telling analogy:

A man may be anoyed that he cannot work out a mathematical problem, of which the answer is or is not given to him, without doubting that it admits of an answer.

Steven Pinker, in The Blank Slate (2002), pp. 192-3, speaks respectfully if non-commitally about the Platonist viewpoint concerning numbers, and goes on to hypothesize that moral truths may have the same status -- “out there” to be discovered, and analogous from planet to planet.  “Our moral sense may have evolved to mesh with an intrinsic logic of ethics  rather than concocting it in our heads out of nothing.”

By the by:  Pinker's richly suggestive book, ranging afar across fields and meadows, adds  in passing  a suggestion of what we might term Aesthetic Realism:  "Even if an art form matured in the West, it may be  not an arbitrary practice  spread by a powerful navy  but a successful product that engages a universal human aesthetic."
Here he has left any area in which I have expertise, so no comment;  read his argument pp. 407-9.

Kahneman, Dyson; Freud and James; plus Pinker

Daniel Kahneman is an intellectual grey-eminence of the past several decades.  If you read at all, you have met some of his ideas (usually written in conjunction with his trusty sidekick Tversky) , though generally at second-hand.  Now he has written his own lengthy and systematic account of his research, aimed at a lay audience.

Most reviews of Daniel Kahneman’s new book (Thinking:  Fast and Slow) simply choose a few from his wealth of anecdotes  and recount them.  Not a bad plan -- they are all worth hearing.  By contrast, Freeman Dyson, in a typically canny offering in the current New York Review of Books, goes beyond the usual review, offering some trenchant personal experiences that illustrate the cognitive case being made, and -- quite surprisingly in the current climate -- puts in a word for Freud:  not the Freud of Die Traumdeutung or the cigars, but of the seminal Psychopathologie des Alltaglebens.   He concludes: “The insights of Kahneman and Freud  are complementary rather than contradictory.”

Noting that neither Sigmund Freud nor William James comes in for mention in Kahneman’s long book, Dyson also outlines the present relevance of this giant of psychology (and one of the heroes of this blog).

Make no mistake -- Kahneman, like Steven Pinker, is one of psychology’s good-guys, plumbing the richness of human experience  though coming to mostly dry and deflating conclusions.   Unlike the eliminative materialists (which includes many of the tribe of neuroscientists), they do not take mere mechanism as a posit, rather than as an occasional result.  James and Dyson, unlike most of their scientific colleagues then and now, have thought deeply about religion and take it quite seriously;  our family had the benefit of Dyson’s teaching at the Presbyterian Church in Princeton.   His invariably broad and thoughtful perspective is ever welcome.

~

In an earlier essay, we examined the politics and natural selection of sex as reflected in the writings of Steven Pinker.   There is a Kahnemanian cognitive dimension here as well, of which we now give an example.

Pinker wades patiently through the swamps of Political Correctness;  we salute his perseverence.   It really is remarkable, the sort of emotionally-founded cognitive distortions he must contend with.

Thus, consider this thought-experiment:  Imagine that some researchers published a study suggesting that the higher crime rate for American Blacks is a consequence of innate criminality.  They would of course be denounced by Blacks and their champions;  but would scarcely be denounced as blaming White crime victims.  So much is obvious.

Yet now put in different substitutions for x and y, and though the logical structure has not changed, the political picture has changed entirely.   The Blank Slate, p. 161:

Even heavier bipartisan fire has recently been aimed at Randy Thornhill and Craig Palmer  for suggesting in their book A Natural History of Rape  that rape is a consequence of men’s sexuality.  A spokesperson from the Feminist Majority Foundation called the book “scary” and “regressive” because it “almost validates the crime and blames the victim.”

By contrast,  men as such  did not object.  We’re used to it.

The average zealot would be quite incapable of perceiving the logical parallelism between the two accounts.
Similarly Pinker, op. cit., p. 372, re the "Laws of Behavior Genetics":  "It is because the laws run roughshod over the Blank Slate, and the Blank Slate is so entrenched,  that many intellectuals cannot comprehend an alternative to it, let alone argue about whether it is right or wrong."  A depressing, accurate, and important observation.

~

Here and elsewhere, Pinker counters the Noble-Savage ideology that whatever is found in nature must be good.  P. 164

It is inherent to our value system that the interests of women should not be subordinated to those of men, and that control over one’s body is a fundamental right  that trumps other people’s desires.  So rape is not tolerated, regardless of any possible connection to the nature of men’s sexuality.

So far, the standard viewpoint, sensibly put.  But then Pinker, whose logical scalpel is sharp, cuts down another level to make a quite interesting philosophical point:

Note how this calculus requires a “deterministic” and “essentialist” claim about human nature:  that women abhor being raped.  Without that claim  we would have no way to choose between trying to deter rape  and trying to socialize women to accept it, which would be perfectly compatible with the supposedly progressive doctrine that we are malleable raw material.

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For college psychology instructors:

Here is an experiment you can do with your class, if you don’t mind being denied tenure.

Divide your students randomly into two groups, and send them to separate rooms.  To the first group, present the sentence:

Men are hot;  women are cold.

(This is along the lines of such parlor-game titles as “Men are from Mars, Women are from Venus”.)

To the other group, present this sentence:

Women are hot;  men are cold.

Assignment:  Discuss.

Prediction:  Both groups will denounce their respective sentence as sexist and anti-woman.

[Postscript]  Chesterton anticipated this sally:

Re G.B. Shaw:

He has pleased all the bohemians  by suggesting that women are equal to men;  but he has infuriated them by suggesting that men are equal to women.

-- G.K. Chesterton, Heretics (1905)

~

Kahneman, as Dyson points out, avoids discussing religion; this is probably just as well.  Pinker -- whose range of interests is extraordinarily broad -- to his credit  does not avoid it;  indeed he quotes (pp. 186-7) from the magnificent 1996 address by Pope John Paul II on the subject of Natural Selection and the “ontological  discontinuity” (we have treated of this subject here);    but analytically, in this arena, he is not at his best.  On page 189  he dishes up an absurd false-dichotomy:

Who says the doctrine of the soul is more humane than the understanding of the mind as a physical organ?

Already so much has gone wrong.  We do not adhere to the doctrine of the soul (or of free will) because it is “humane”, but because it is true, and we experience it as such.   Nor does such a doctrine impede or even impinge upon the understanding of the brain as a physical organ.  As for the mind as a physical organ, um, did you really mean to write that?  Are we back with Descartes and his lodgement of the soul in the pituitary or the pineal gland or wherever the hell he placed it?

It gets worse.  The consequences of the “doctrine” of the soul (though, in our view, this is rather like speaking of the “doctrine” of the existence of the physical world)  is “letting people die of hepatitis  or be ravaged by Parkinson’s disease  when a cure may lie in research on stem cells…”  Indeed a cure might be thus expedited, or it might not;  the soul is nothing to the issue.   The moral quandary is rather to what extent society is willing to go, to benefit group A at the expense of group B.   Effective but morally debateable maneuvers include:  harvesting stem cells from embroyos;  harvesting embryos; harvesting aborted fetuses; harvesting fetuses not yet aborted but which, for a fittybone, the unwed mother would be happy to sell you.  Plus harvesting organs from dead adults; from living but brain-dead adults; from criminals; from political prisoners; from the luckless, kidnapped for this very purpose.  Perhaps less effective from a flinty Western medical perspective, but quite real and effective to its practitioners, is harvesting such organs as genitals from living children (our group B, here rather at a disadvantage) for use in sorcery to benefit group A (which in their own estimation, includes all the best people).  All these practices may be found in the world today, though generally not in places where the influence of the Holy Mother Church is at its strongest.   John draws the line at one place, Mary at another; and if you were to do a statistical study, it might well be that churchgoers, on average, place it somewhat more towards the less-interventionist end  than do vivisectionists, grave-robbers or eliminative materialists.   That would be sociologically rather interesting, if true;  Pinker has however made no logical point.   Nor does his heroically rising to the defense of helpless Alzheimer’s patients, who apparently are being abused by nuns when these are not otherwise engaged in cackling over the sufferings of Parkinsonians,  contradict anything a theist would say (apart perhaps from heretics like Christian Scientists):  “Sources of immense misery” (notice the purely emotion-evoking addition of the adjective) “such as Alzheimer’s disease … will be alleviated   not by treating thought and emotion of manifestations of an immaterial soul  but by treating them as manifestations of physiology and genetics.”   Amen; hear, hear;  we can all of us drink to that.  Pinker’s lance has pierced a straw-man.

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Pinker touches bottom with this assertion:  “The doctrine of a soul that outlives the body  is anything but righteous, because it necessarily devalues the lives we live on earth.”   (Compare:  "The doctrine that we should become adults  is offensive, as it devalues childhood.")
Leave aside that outsider’s-assessment-word “righteous”, analogous to the skewed perspective of the word “humane” above (We believe, or disbelieve, or simply hope, as the case may be, in eternal life, from conviction or revelation or even logic or what have you, but not because such a belief -- true or false -- seems “righteous”).  Notice, though, that qualifier “necessarily”, which changes the assertion from a sociological generalization or barroom opinion  into one of logico-philosophical apodixis.  Yet the only evidence he offers for this extraordinary doctrine  is the self-serving rationalizations (or irrationalizations) of maniacs who kill their kids, and the rants of al-Qaeda suicide-bombers.  (Page 189 -- look it up if you can’t believe your eyes.)

Good - Heavens!  For all we know, some serial killer has excused his crime-spree by an allusion to the Riemann Hypothesis;  the effect of such grotesques upon number theory  will rightly be nil.

Beyond the logical point, Pinker’s assertion is psychologically absurd.   It may well be the case (though God forbid), that those who hope they may one day rest in the bosom of Abraham  are destined to be cruelly disabused;  but their doctrine does tend rather to distinguish this view of life  from that of scorpions in a bottle.

For a glimpse at the value placed upon human life  among a proud, free people  unpolluted by Christian superstitions, click here, and here.
[update 8 May 2012] And now here:
http://latimesblogs.latimes.com/world_now/2012/05/south-koreans-confiscated-pills-human-remains.html
South Korean customs said it had confiscated more than 17,000 “health” capsules smuggled from China that contain human flesh, most likely extracted from aborted fetuses or stillborn babies.



(Note, though:  these are quibbles;  just a turf thang, folks.  Pinker's book overall is broad, sound, and beautifully written.)

(For more along these lines: )

http://www.linguasacrapublishing.com/justice.html

On Symbols

We spoke earlier of the relative adequacy, as a “symbol”, of the traditional OT picture of Jehovah,  to the uncountably infinite trans-reality of the Godhead Him-/It-/Blorg-/self.  This symbol is, literally, infinitely inadequate.  And yet adequate to our understanding, depending upon how high we have climbed on the ladder;  and crucially more adequate than certain alternatives, proposed by various paganisms and modern heresies.  Our purpose here is broadly  to defend the very idea of using symbols, and indeed the intellectual integrity of an admittedly threadbare image, simply by pointing out that such reduction to the palpable  is no mental vice unique to religion, but may be found even within -- nay, not science merely, to show that would be child's-play:  but even within that most abstract and impalpable exercise in mental extension, mathematics.

Consider, then, one of the simplest of mathematical objects:   the torus.  You have all seen this described as the “surface of a donut”.  Set aside the humbly sensuous coffee-dunking aspect of this:  the very essence of the image, be it of inner-tube or anchor-ring (the latter metaphor  was favored by our ancesters), is already a concession to our infirmity:  specifically, to our own creaturely incarnation in three spatial dimensions (this particular Sitz im Leben being of no mathematical significance whatsoever).  It is a symbol -- and quite an adequate one -- of the embedded torus:  but not (and this is crucial) of the torus as mathematicians now understand it, as conceived within itself:  but rather as embedded (with some bending) into the cramped space in which we dwell.   Beholding the donut, you think:  How curvaceous, surely more curvy than the surface of a tennis ball.  And yet, in its essence, it is not curved at all: Its intrinsic geometry is completely flat; and this “inner flatness” manifests itself  even in the embedded object, whose Euler characteristic turns out to be zero (as against 2 for the sphere).  (For a magisterial exposition of all this, see Jeffrey Weeks,  The Shape of Space.)   A more adequate symbol would be simply a rectangle with opposite edges identified -- or better yet, the toroidal covering-space which carpets R x  R with infinite replications of this patch-sample.  (Already how distantly we have left behind the donut !)   This symbol is still not the torus itself, as it thrones in Platonic heaven;  but it is a symbol which, unlike that of the donut, is wonderfully productive of new ideas.  As: Identify one pair of opposite edges as before, in parallel; but the other pair, anti-parallel, “with a twist”.  The result is a Klein bottle, not embeddable in three-space at all.  (Though four will suffice.)   Or, as:  Instead of parallel-identification of opposite edges of a square, perform an orientation-matching identification of opposite faces of a cube (thus resulting in a universe that is finite though Euclidean -- something they told me was impossible, when I was but a little boy in short-pants).   Or indeed (and now the usual geometrical torus of the nursery, seems as pale a reflection of the basic idea, as does that java-sodden donut of the former):  Consider any product (finite or infinite, countable or not) of R-mod-1 with itself -- a torus let loose from the leading-strings.
Similar such exercises result in surfaces we could never previously have imagined, as the very best scientists did not, but which, looked at correctly, become almost intuitive.  One of them might be the shape of the very space we live in.

It is, I suspect (speaking under correction), in part for such intellectual   reasons, that the Church Fathers, cognizant of the very partial truth of the God-the-Father Yahweh image, attempted to fill the picture out, with the doctrine of a Trinity (a blessed doctrine, it may be:  but arrived at, not handed to us on a platter in the Bible).  The symbol is not fruitful if you press it into fetishistic ends, snorfling up triads wherever they may be found; but it is an improvement on what went before.

A New (Non-)Proof of the Existence of God

Actually an old one, of eighteenth-century vintage.  Let D. E. Smith tell it (History of Mathematics, 1923, vol. I, p. 523):

Diderot had somewhat displeased the Czarina  by his antireligious views, and so she persuated Eurler to assiste her in suppressing him.

Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of God… Euler …said gravely, and in a tone of perfect conviction:

     Monsieur, (a + b^n)/n = x, donc Dieu existe; répondez !

Diderot, to whom algebra was Hebrew, was embarrassed and disconcerted, while peals of laughter arose on all sides …

For my own brilliant demonstration that modern syntactic theory implies the truth of the Nicene Creed, click here.

These are, of course, nonsense;  and are offered simply as counter-weights on the other side of the balance-pan, to equally ludicrous (though seriously meant) would-be scientific demonstrations of the opposite (chemicals go sploosh when you think of a tree, therefore we’re all just robots).

~

Denis Diderot, penning one of his zingers

Kripke offers a useful correction to the hoary anecdote:

In fairness to Diderot, it should be mentioned that the incident surely never took place as described.  In fact  Diderot was the author of several learned mathematical essays. 

If we do not take care, however, some of our philosophical discussions are in danger of coming to resemble the legendary confrontation.  I have seen cases where a very simple, almost mathematically trivial technical trick  has captured a philosopher’s imagination, and been used as if it were the key   that easily and mechanically unlocked  doors that were forever closed to ordinary philosophical investigation.

-- Saul Kripke, “Is There a Problem about Substitutional Quantification?”, in: Evans & McDowell, eds., Truth and Meaning (1976), p. 415.

Keynes makes the same point in some detail in his philosophically-attuned Treatise on Probability.

A Tragedy in the Annals of Particle Physics

“There’s a Boson here to see you, sir.”

“Eh?  Which Boson would that be.”

“The Higgs, sir.”
"Bother the Boson.  I'm busy."
"He says it's urgent, sir."

“Don’t know any Bosons by that name.  One of the Dorsetshire Boson-Bosons, perhaps? “

“I believe he said he was from Porlock, sir.”

“Well, throw him out.”

“Very good, sir.  Although we must bear in mind what the Bard said about time and the forelock --“

“Bugger the Bard.”

“Yes, sir.”

“Bugger him thoroughly.”

“I shall endeavor to do so, sir.  The poet Keats --“

“-- be buggered, Jeeves.  Can’t you see I’m otherwise engaged?  I’m trying to balance this egg on its end.  They say Columbus managed it, but I’m frankly finding it dashed difficult.  Beginning to expect the old Genoese might have used some sort of trick.”

“The nation of Genoa are proverbial for their craftiness, sir.  Quoth Petrach --“

“Bother Petrarch.  Tell the Boson to ring back later.”

“I shall do so sir.  Although -- in a case of this kind, working near the Planck scale, where every yoctosecond counts --“

“Eh?”

“-- we would do well to bear in mind the observation of the Swan of Avon, when he remarked that, if ‘twere done, when ‘tis done, ‘twere well it were done quickly.”

“Remind me to ask you someday what that might mean.  All right Jeeves, you win.  Show him in.”

“Very good, sir.”

But when Jeeves reached the foyer -- the Boson was gone !

Its decay products streaking across the cosmos in every direction.

And thus the chance of spotting that elusive particle was lost -- possibly for all time.

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[For further truelife tales from the annals of science, click
h e r e ... ]

Leading the Good Life

For all good men and true:  a suggested emploi du temps, pour la vie dévote.

(1) Dawn:  Rise with il frate sole.  Recite matins; Gregorian chants; break the fast on a radish, perhaps.

(2) Morning:  Intensive research into the Riemann Hypothesis (or any other deep idea of your own choosing).

(3)  Lunchtime:  Lunch, consisting of a carrot.  Silence should prevail at this meal, while the astonishing results of the morning’s labors are mulled-over and digested.

(4) Afternoon:  Labor in the vegetable garden.   And should Peter Rabbit come hopping, hopping, -- slipping and swiping a cabbage or two -- Ah, go easy with the rascal, he is God’s creature too.

(5) Supper:  The abbot reads from Scripture, while the brothers sup on beef and red wine.

[Note:  This is the regime for Sunday through Friday.  On Saturday night, we break out the abbey ale, dispensed in massive tankards.  Lusty songs are sung in Latin.  This too is the time for scrumptious strumpets to drop by:  for as C.S. Lewis puts it:  Sins of the flesh are bad;  but they are the least bad of all the sins.]

(6) Evening:  Free time.  Backgammon;  card games; quiet talk; prayer; crossword puzzles; detective stories (Murphy is particularly recommended); comparing notes on the morning's discoveries; and deeper researches  which we cannot begin to describe, since we do not understand them:  let us call them “pataphysical geometry”, simply to have a name.

(7)  Bedtime:  Kneeling, say your prayers;  then dream in the bosom of Abraham.

Gratias agimus tibi, domine ...

~

(For additional epiphany, click here: )

http://www.youtube.com/watch?v=FwzOXzZWUik

Physics/Math Smackdown

William James, The Will to Believe (1897), p. 52:

The physical order of nature, taken simply as science knows it, cannot be held to reveal any one harmonious spiritual intent.  It is mere weather.

But!but!  (you splutter).  Physics is the science of the very cosmos in which we live !

-- Which is to say:

Bertrand Russell, Introduction to Mathematical Philosophy (1919; 2^nd edn. 1920), p. 192:

this higgledy-piggledy job-lot of a world  in which chance has imprisoned us

            If you wish some glimmering of further insight into the – I won’t even say the Nature, for that is beyond us, but some sense of the Sitz im Leben of the Necessary Being, you’re better off checking out the action, not in physics (let alone chemistry let alone …), but in the arena of Necessary Truths:  and these are to be found in abundance in Mathematics.

            I’m not against researching the laws of physics and biology, as glimpsed (dimly) from our present perch in the universe:  given that we’re stuck here (like a turd in amber), it’s about the best we can do.  But viewed more broadly, as activities go, it’s rather parochial, like rooting for your local high school basketball team.  (But then – who else ya gonna root for?)

            And yet consider.  What is Doctor Ynxnkx there doing, in the pool of light in his study, on the planet Gronx in the galaxy Mnx, in a disjoint and parallel universe?  He is not thinking about basketball, because his species don’t have arms or legs; he is not thinking about the Unified Field Theory, because their particular cosmos doesn’t have gravity (just kidding about the planets and galaxies).  He’s thinking about – what else – about the Riemann Hypothesis, which is just as true or as false  and at all events as looming, in his reality as in ours.

Physics Strip-Tease

By now I’ve read a fairish number of general overviews of modern physics, written for the layman  by physicists of note (Arthur Eddington, George Gamow, Werner Heisenberg, Richard Feynman, Heinz Pagels,  J. C. Polkinhorne,  P. C. W. Davies, Steven Hawking, Steven Weinberg, Kip Thorne, Martin Rees, Paul Davies, Roger Penrose, Brian Greene,  …..), along with a smattering of actual textbooks;  and thus managed  with time  to acquire  a veneer of acquaintance  with things that, for the most part, I don’t truly understand.  This is not intended to be as shocking a confession as may sound:  Few of us really understand much of anything;  we just get by.  And many a physicst has ‘fessed up to not truly understanding quantum theory, though able to do the calculations well enough.  (For an emo outgushing  about the similar situation in mathematics  -- if anything more severe -- click here.)

There is a metaphor  beloved of analytic philosophers:  “Our spade is turned.”  Meaning, after immense intellectual labors  continuing those going back to Plato, we can finally dig no further into the ontological fundament.   Only,  for the layman, in contemporary physics, our spade gets turned rather early.   We seldom get past the state of gaping (by the reader) and hand-waving (by the author).

It’s not the expositor’s fault.  This stuff really is hard.  It’s not enough anymore even to be a professional physicist:  if you are not a string-theorist, you probably won’t understand string theory.

So there are two things the would-be popularizer (meaning this in a good sense -- haute vulgarisation) can do.

            (1)  Sink to “physics porn”:  enticingly fluttering colored veils, till the readers are panting (Time travel !  Parallel universes !!  Higgs effing boson !!!)  and have the illusion that they have learned something.   But they will never actually enter that dark portal …

            (2) Patiently, patiently  lay it all out. -- The most successful attempt in this vein is Richard Feynman’s concise but trenchant The Character of Physical Law.  More generous with the mathematics (though short on shareable physical insight) is the not-at-all concise (doubles as a doorstop  if you never make it through) and perhaps not maximally-modestly titled  The Road to Reality, by Roger Penrose.  And even here, at its least-good, this brick-of-a-book is essentially just more abundant and more elaborate mathematical window-dressing;  I must reluctantly concur with the stern but just review here.

There is so much to learn … but the head hurts so …  Sometimes I envy the hamsters … …. ………