Mar 5 2017

You Don’t Have to be a Mathematician (to be British)

But the age of chivalry is gone. That of sophisters, economists, and calculators has succeeded. –Edmund Burke

Lewis Carroll, a.k.a. Charles Dodgson, (1832-1898) is perhaps England’s best known mathematician. But many British writers were not so inclined. Consider a passage about C. S. Lewis (1899-1963) in Philip and Carol Zaleski’s The Fellowship: the Literary Lives of the Inklings (2015):

The Latin and Greek portions of Responsions presented no problem, but Lewis failed the section on mathematics. He had a terrible head for numbers and was unable to handle even the simplest arithmetical problems—counting change was a daily ordeal—much less algebra, a prominent part of the exam. Algebra is defined by the OED as “a calculus of symbols,” and Lewis’s failure to master it is worth bearing in mind, in light of his later controversial forays into the application of logic to metaphysics and theology. Nonetheless, he was accepted into University College and returned to Oxford on April 26, 1917, enrolling as an undergraduate on April 29.[1]

Compare philosopher and Prime Minister Arthur Balfour (1848-1930):

I wish I were a mathematician. There is in the history of the mathematical sciences, as in their substance, something that strangely stirs the imagination even of the most ignorant. Its younger sister, Logic, is as abstract, and its claims are yet wider. But it has never shaken itself free from a certain pretentious futility: it always seems to be telling us, in language quite unnecessarily technical, what we understood much better before it was explained. It never helps to discover, though it may guarantee discovery; it never persuades, though it may show that persuasion has been legitimate; it never aids the work of thought, it only acts as its auditor and accountant-general. I am not referring, of course, to what I see described in recent works as “modern scientific logic.” Of this I do not presume to speak. Still less am I refer ring to so-called Inductive Logic. Of this it is scarce worth while to speak.1 I refer to their more famous predecessor, the formal logic of the schools [i.e. of John Stuart Mill].[2]

Compare Balfour’s colleague Winston Churchill (1874-1965):

All my life from time to time I have had to get up disagreeable subjects at short notice, but I consider my triumph, moral and technical, was in learning Mathematics in six months. At the first of these three ordeals I got no more than 500 marks out of 2,500 for Mathematics. At the second I got nearly 2,000. I owe this achievement not only to my own back-to-the-wall resolution for which no credit is too great but to the very kindly interest taken in my case by a much respected Harrow master, Mr. C. H. P. Mayo. He convinced me that Mathematics was not a hopeless bog of nonsense, and that there were meanings and rhythms behind the comical hieroglyphics j and that I was not incapable of catching glimpses of some of these. Of course what I call Mathematics is only what the Civil Service Commissioners expected you to know to pass a very rudimentary examination.

I had a feeling once about Mathematics, that I saw it all Depth beyond depth was revealed to me the Byss and the Abyss. I saw, as one might see the transit of Venus or even the Lord Mayor’s Show, a quantity passing through infinity and changing its sign from plus to minus. I saw exactly how it happened and why the tergiversation was inevitable: and how the one step involved all the others. It was like politics. But it was after dinner and. I let it go![3]

Finally, there’s G. K. Chesterton (1874-1936):

A great deal is said in these days about the value or valuelessness of logic. In the main, indeed, logic is not a productive tool so much as a weapon of defence. A man building up an intellectual system has to build like Nehemiah, with the sword in one hand and the trowel in the other. The imagination, the constructive quality, is the trowel, and argument is the sword. A wide experience of actual intellectual affairs will lead most people to the conclusion that logic is mainly valuable as a weapon wherewith to exterminate logicians. [4]

NOTES

[1] Zaleski and Zaleski. The Fellowship: the Literary Lives of the Inklings 75.

[2] Balfour, Theism and Humanism: Being the Gifford Lectures 176.

[3] Churchill, My Early Life: a Roving Commission. NY: Charles Scribner’s Sons. 1930. Ch. III.

[4] Chesterton, Twelve Types. 1906. “Thomas Carlyle” p. 125.


Dec 21 2016

Did Arthur Balfour Predict Facebook a Century Ago?

porticos in Bologna, Italia

Did Arthur Balfour Predict Facebook a Century Ago?

Did Arthur James Balfour (1848-1930), the former Prime Minister of Great Britain, and twice the giver of the Gifford Lectures,  stumble upon the idea behind Facebook–that it can collect data on people and try to predict their behavior–nearly a century before its advent?

The region where these uncompromising doctrines show to least advantage is human character. I do not propose to discuss causation and free will; but I may with advantage say something on a less hackneyed theme, namely, negligibility and foreknowledge. The thesis I desire to maintain is that, in dealing with a human character, full foreknowledge is theoretically impossible, even though free will be wholly absent, and the succession of psychic states be completely determined. Practically impossible we know it to be. But most determinists would hold that this impossibility is due partly to our ignorance and partly to our incapacity. We know too little either of the general laws of mind, or of individual character, or of surrounding circumstances, to make accurate forecasts; and, even if we possessed the requisite information, we could not use it, owing to the irremediable weakness of our powers of calculation. It is this contention that I wish to traverse. I hold that, had we the supernatural powers of Laplace’s calculator, armed with a knowledge of the human heart which supernatural powers of observation could alone supply, we should still fail, because we are face to face with that which is inherently incalculable.

The contrary opinion is due, I think, to an imperfect comprehension of the doctrines I have touched on in this lecture. All human foreknowledge depends on detecting old sequences in a new context. The context, of course, is always new. There is never full or complete repetition. But, unless there be partial repetitions embedded in the universal flux, prescience is impossible. This is the doctrine of “negligibility.”

Now consider two illustrative examples. First, imagine yourself standing on the edge of a valley down which a landslip has just let loose the waters of some great reservoir in the hills. The catastrophe is sudden in its onset, brief in its duration, wildly irregular in its character. Even the most tumultuous cataract retains a certain steadiness of outline: and few sights are more impressive than the stationary waves in a great rapid. But there is here no trace of order imposed on disorder, fixity on motion. The rushing wall of water, spouting into foam over every obstacle it encounters, the tossing flood that follows furiously behind, seem in their brief violence to present the very ideal of incalculable confusion. But we know it is not so. In the presence of such a spectacle our calculator would not feel a moment’s embarrassment. He could forecast without difficulty the whole scene down to its minutest eddy; the motions of each drop obey laws with which he was perfectly familiar; and the total effect, catastrophic though it be, is but the sum of all these component examples of natural uniformity.

Turn now and contemplate a calmer scene. Consider the commonplace life of a commonplace man as it develops in the untroubled prosperity of a steady business and a quiet home. Such a career seems as orderly and uniform as the flood I have been describing is terrible and strange. Surely no supernatural calculator is required to cast the horoscope of its hero: for he does, and leaves undone, the same actions, he thinks and leaves unthought the same ideas, as thousands of his contemporaries; and, so far as outward appearance goes, he is an indistinguishable member of an undistinguished crowd.

Yet, in spite of this, we know him to be unique. There never has been before, nor will there ever be again, another individual exactly like him. A similar statement, it may be urged, can be made about our catastrophic flood. Though this has plenty of parallels, none of them, strictly speaking, are exact. Where, then, lies the distinction on which I am trying to insist? Let me endeavour to mark the contrast.

If the material world be conceived as a mechanical system, the flood in my illustration may be regarded as a piece arbitrarily cut out of it at the whim of the spectator. It possesses no natural unity; and, like the whole of which it is a fraction, the moving particles which compose it do each obey laws which are (we assume) perfectly well known, and have been endlessly exemplified. Its behaviour is the sum of the behaviour of these several parts; and it is by estimating their movements that our imaginary calculator can prophesy its course with absolute exactness. He is never perplexed by the problem of negligibility; for negligibility in such a case can be accurately measured, and our calculator possesses all the data required for its measurement. In short, the principle of regularity may here be applied in its most uncompromising form; it requires no qualification, nor can it be pressed too boldly or too far.

–Balfour, Arthur James. Theism and HumanismBeing the Gifford Lectures. NY: Doran. 1915. p.  207–11.


Nov 4 2016

The Theory of the Theory is Still a Theory

Texas wildflowers

The Theory of the Theory is Still a Theory

Writing about Freud and his loss of influence, Samuel Moyn at The Nation observes:

This skepticism toward the overarching theories of the 19th and 20th centuries has come to incarnate something of the spirit of our age and it is another reason why the prominence of psychoanalysis has declined.

But does Moyn not realize that this statement is itself a “overarching” theory? Or as A. J. Balfour put it:

If a proposition announcing obligation requires proof at all, one term of that proof must always be a proposition announcing obligation which itself requires no proof…. If we have a moral system at all there must be contained in it at least one ethical proposition of which no proof can be given or required….”[1]

Compare Leo Strauss:

All studies in social science presuppose that its devotees can tell human beings from other beings; this most fundamental knowledge was not acquired by them in classrooms; and this knowledge is not transformed by social science into scientific knowledge, but retains its initial status without any modification throughout. If this pre-scientific knowledge is not knowledge, all scientific studies which stand or fall with it, lack the character of knowledge….[2]

And Cicero:

For nothing can be reduced into a science unless he who understands the matters of which he would form a science has previously gained such knowledge as to enable him to constitute a science out of subjects in which there has never yet been in science.[3]

NOTES

wood-h-small

[1] Quoted from Pratt, James Bissett. “The Ethics of St. Augustine.” International Journal of Ethics. Vol. 13. No. 2. (January 1903.) 222–35 at 232.

[2] Strauss, Leo. “What is Political Philosophy?” Journal of Politics. Vol. 19. No. 3. (August 1957.) 343–68 at 352.

[3] Cicero, Marcus De oratore. Translated by E. W. Sutton. Cambridge, MA: Harvard UP. 1967. I, 41, p. 55; I, 50, pp. 66–67.