Trigonometry.

“The study of angles and of the angular relationships of planar and three-dimensional figures ... .” Mathworld.

“ … sure wish folks could ever, ever understand that we ALL could learn so much from someone like Trig — I know he needs me, but I need him even more ... the world needs more "Trigs", not fewer.” Sarah Palin. 3 July, 2009 [Emphasis added].

So there’s trigonometry and trig functions (above, left), and then there’s Trig, the little boy with Down’s Syndrome. Ubiquitous math phobia notwithstanding, most would agree that the first two are useful. What about 21^st chromosome trisomics? At least among their mothers, the majority view is thumbs down; most are aborted. That’s what makes Palin’s observation so remarkable and, to this author, himself the parent of a special needs child, so very genuine. Her critics, most of them not having had the experience, can hardly be expected to appreciate the plusses. What they do understand, albeit in many cases but vaguely, is that caring for a “special needs” child is difficult, time consuming and expensive.

It's also parenting for life. In the usual sense, most of these children do not grow up; conventionally, they do not fledge. Their bodies mature, of course – often abnormally and typically with a raft of attendant medical issues, the treatment of which is complicated by the underlying disorder. But intellectually, emotionally and behaviorally, they remain forever young. What waits after Mom and Dad is not the independence of adulthood, with its sundry trials and triumphs, but an existence at best sheltered, more often, neglectful, at worst, abusive. Indeed, when I first saw Sarah, having just delivered the best speech of the political season and holding her son, I could only wonder if she had any real idea as to what she was in for.

That uncertainty was set to rest by the remark quoted above. Like other parents who put their developmentally disabled child first and let the rest sort itself out, Sarah Palin understands that children like Trig bring purpose to life in ways that are both unique and uniquely fulfilling. Like Sarah, my son needs me, even as I need him. But unlike Sarah, no “rendezvous with destiny” looms in my future. You think the Palinophobes [emphasis on the second syllable] don’t sense that such an encounter awaits in hers? Of course, they do. It is the taproot of their rage; the prospect that appalls. Sarah will fight and triumph, God willing, for her son, and, in that victory, secure the future for us all.

Some say that the time evolution of complex systems is marked by unexpected twists and turns; others that the Lord works in ways mysterious. Take your pick. Trig is Sarah’s bow of burning gold; her arrows and her spear; her chariot of fire. With apologies to the spirit of Wm. Blake for changes (square brackets) to the original:

"[She] will not cease from Mental Fight,

Nor shall [her] Sword sleep in [her] hand:

Till we have built Jerusalem,

In [this, our great] & pleasant Land."

Surprisingly, there’s a path that leads from trig, the branch of mathematics, to Trig, the child. Along the way, there are stops at demography, mathematical optimization and medical ethics. Having followed it, we may better understand the tumult of August, 2009. [To be continued].

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"When People Stop Believing in God, ...

Ecopsychology, a new online journal, has just issued a Call for Papers.

According to their website, "This quarterly Journal examines the psychological, spiritual, and therapeutic aspects of human-nature relationships, concern about environmental issues, and responsibility for protecting natural places and other species."

The blurb continues —

"Ecopsychology places psychology and mental health disciplines in an ecological context and recognizes the links between human health, culture, and the health of the planet. With its groundbreaking and diverse collaboration of psychotherapists, social science researchers and contributors from other environmental-related fields, Ecopsychology is the only peer-reviewed journal of its kind."[Emphasis added]

"Timely and provocative topics include:

• The role of connection to nature in healthy development and self identity
• Emotional and psychological factors that drive environmental issues
• Ecotherapy and the use of wilderness for health and healing
• Coping with anxiety or grief about environmental destruction
• Effective ways to motivate sustainable behaviors
• Spiritual and cultural practices that support a healthy environment"

One could use this offal as a springboard for discussion — the rise of neo-paganism; G. K. Chesterton's remark alluded to in our title; the eclipse of reason in a technological society; the evolutionary basis of group-think; ... . Another day.

[Tip of the hat to CCNET.]
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On Exactitude in Science.

Whereas the simplest climate models reduce earth's energy budget to a single differential equation, the current infatuation of climate modelers is enormously complicated simulations with thousands of equations running on the world's fastest computers — see, for example, McGuffie, K. and A. Henderson-Sellers. 2005. A Climate Modeling Primer. J. Wiley, NY. Such productions are beyond the reach of conventional dynamical systems theory — which is to say that they replace a system we don't understand with models we can't understand — at least not mathematically.

Regarding the utility of proliferating detail in scientific hypotheses, the Argentinian writer J. L. Borges (left), had something important to say. And he said it in a single paragraph decades before science in simulo, as they like to call it, was even a momentary synaptic fluctuation in some computer programmer's misguided mind. Given the failure of contemporary models to iterate to the data, to say nothing of the mischief consequent to unthinking acceptance of their predictions, Borges' essay merits consideration. Here is what he wrote:

On Exactitude in Science.
(Hurley, H. 1998. Jorge Luis Borges, Collected Fictions. Penguin Books. NY)

".... In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast Map was Useless, and not without some Pitilessness was it, that they delivered it up to the Inclemencies of Sun and Winters. In the Deserts of the West, still today, there are Tattered Ruins of that Map, inhabited by Animals and Beggars; in all the Land there is no other Relic of the Disciplines of Geography.

Suárez Miranda, Viajes de Varones Prudentes, Libro IV, Cap. XLV, Lérida, 1658." [attribution fictitious]

Point, Set, Match.

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Triumph of the Slow Variables or 'Rat in a Box.'

More than one conservative commentator has suggested that President Obama’s (BHO's) redistributive agenda equates to European-style socialism. Sadly, there are other, more troubling possibilities. We discuss one of them and introduce a concept from mathematics that bears on how we reached this awful state of affairs. Like Tinky Winky, we save the rest for later.

Socialism.

1. Whatever one thinks of the merits of state ownership, income redistribution, etc., it is important to distinguish democratic socialism from Marxist-Leninism. The former can be voted out; the latter, not.


2. The available evidence suggests that BHO is a people's republic sort of guy. The academic-activist culture from which he emerged is rife with sympathy for countries and revolutionary movements that practice or promote dictatorship of the proletariat. BHO’s “odd” associations, his long-standing working relationships with Ayres, Wright, Khalidi, etc., his recent appointments, Holdren, Singer, etc. — all are explained. Pares cum paribus facilime congregantur, loosely, “birds of a feather flock together.”


3. Likewise explained are BHO’s radical inclinations, his sympathies, disparate reactions to Iran and El Salvador, not least of all, his vocabulary.


4. "Change we can believe in" arguably equals revolution, at the ballot box, thus far, but revolution nonetheless. BHO’s foreign policy positions are best understood as adjunctive to the same. They amount, above all else, to disengagement from the external world, much as the Soviet Union disengaged after the Bolshevik revolution. Overseeing a revolution consumes time, energy and money, in which circumstance, foreign entanglements are distracting.


5. The exception is when foreign policy can be used to support “transformative” initiatives at home. Keeping the army (sharp tip of the spear) elsewhere occupied (Afghanistan) is an obvious example. Appealing to particular constituencies in an ethnically diverse society is another.


6. BHO's proposed national service corps, a "community organization" armed and empowered by law, can only be comprehended as the iron hand beneath the glove.

Separation of Time Scales.

One approach to studying the behavior of complex systems is called "separation of time scales." Here, one sorts variables according to their rates of change. More precisely, one distinguishes "fast" variables from "slow." When this is possible, one can eliminate the fast variables, thereby simplifying the analysis — see, for example, Lin and Segel (1988). In short, it's the slow variables that call the shots," even when it's the rapidly fluctuating fast variables that catch one's attention.

Rat in a Box.

Now suppose we are performing an experiment and that the slow variables are experimental conditions we can control. For concreteness, imagine measuring the metabolic rate of a rat in a chamber, the temperature of which can be varied. Further suppose that we turn the knob slowly and that, after each twist, wait a while for the animal's physiology to adjust before taking data. Over a wide range of temperatures, the so-called "thermo-neutral region" (flat portion of the graph), there is little or no change in metabolism — the animal regulates its body temperature by constricting or dilating its peripheral blood vessels, thereby reducing or increasing heat loss to the environment. But reduce the external temperature below a certain point, and metabolic rate goes up — the animal shivers. Likewise, if the temperature is set too high, metabolic rate also increases — the animal pants. In both instances, passive temperature regulation is replaced by active, energy expenditure kicks in, and metabolic rate increases. Too hot or too cold, of course, and the animal cannot adjust; it dies (dashed lines in the figure).

Triumph of the Slow Variables.
BHO's election to the Presidency is a triumph of the slow variables — 40⁺ years of "progressive" policy innovations having eaten away, bit by incremental bit, at the country's shared presumptions, at the institutions that translate these presumptions into policy, at the professions that transmit the presumptions from one generation to the next. This is especially the case in education. That is what Annenberg / Ayres is all about, although it is worth noting that social engineering has become part and parcel of all manner of programs, some of them, for example, the awarding of National Science Foundation research grants (go here), quite far afield. In the case of complex systems generally, as in that of the unfortunate lab rat, the effects of such change can be abrupt and catastrophic. Sadly, we are the rat in the box. And we have just been pushed outside the thermo-neutral region.

SPQR.
Yes. The slow variables have triumphed. Preserving our democracy is now going to take considerably more effort than going down to the polls a couple of times a year. Lest we shrink from the task, remember this: the letters SPQR (Senate and People of Rome) continued to adorn the legions' standards long after Caesar was murdered in the forum, and the Senate, to convene. But the Roman republic was dead, having been replaced by the panoply of emperors, some good, some bad, who counted themselves as gods. Let not future historians write that these were the final days of its American counterpart.

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