Like Whitman’s spider, here we cast a filament between a few reads, prompted by “Number”.
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Somewhat in keeping with recent posts, I found Tobias Dantzig’s “Number” (fourth edition – 1953) an interesting tale of the evolution of the number concept that calls attention to things we so completely take for granted today, such as positional numeration (“The struggle between the Abacists, who defended old traditions, and the Algorists, who advocated the reform, lasted from the eleventh century to the fifteenth century and went through all the usual stages of obscurantism and reaction.”). Much of the book is fascinating, such as the following excerpts of possible interest to our readers.
(The human computer is quite different from that there laptop,)
The advantages of the base two are economy of symbols and tremendous simplicity in operations. It must be remembered that every system requires that tables of addition and multiplication be committed to memory. For the binary system these reduce to 1 + 1 = 10 and 1 X 1 = 1; whereas for the decimal, each table has 100 entries. Yet this advantage is more than offset by lack of compactness: thus the decimal number 4096 = 2^12 would be expressed in the binary system by 1,000,000,000,000.
(On the term cipher and the spread of the concept of zero,)
[...]In the English language the word cifra has become cipher and has retained its original meaning of zero.
The attitude of the common people toward this new numeration is reflected in the fact that soon after its introduction into Europe, the word cifra was used as a secret sign; but this connotation was altogether lost in the succeeding centuries. The verb decipher remains as a monument of these early days.
(Think infinite and calculus,)
The conflict between discrete and continuous is not a mere product of school dialectics: it may be traced to the very origin of thought, for it is but the reflection of the ever present discord between this conception of time as a stream and the discontinuous character of experience. For, in the ultimate analysis, our number concept rests on counting, i.e., on enumerating the discrete, discontinuous, interrupted, while our time intuition paints all phenomena as flowing. To reduce physical phenomena to number without destroying its streamlike character – such is the Herculean task of the mathematical physicist; and, in a broad sense, geometry too should be viewed as but a branch of physics.
(And here we take a trip…)
The latter brings to mind Virginia Woolf’s “Mrs. Dalloway” (1925),
All the same that one day should follow another; Wednesday, Thursday, Friday, Saturday; that one should wake up in the morning; see the sky; walk in the park; meet Hugh Whitbread; then suddenly in came Peter; then these roses; it was enough. After that, how unbelievable death was! – that it must end; and no one in the whole world would know how she had loved it all; how, every instant …
Of course, I note the following congruence between “Spent” and “Mrs. Dalloway”…
From Geoffrey Miller’s “Spent” (2009),
[...]Almost every dog breed has some idiosyncratic high-maintenance feature that makes it an effective means for displaying conscientiousness, and all require regular feeding, watering, walking, vet care, and diligent physical restraint by leashes and fences. Hence the social and sexual popularity of single people who can be seen walking dogs that are conspicuously well fed, well-groomed, well trained, nonneurotic, and nondead.[...]
From Woolf’s “Mrs. Dalloway”,
Then Clarrisa, still with an air of being offended with them all, got up, made some excuse, and went off, alone. As she opened the door, in came that great shaggy dog which ran after sheep. She flung herself upon him, went into raptures. It was as if she said to Peter – it was all aimed at him, he knew – “I know you thought me absurd about that woman just now; but see how extraordinarily sympathetic I am; see how I love my Rob!”
Now, Elena Ferrante’s “Days of Abandonment” is stylistically reminiscent of Woolf’s “Mrs. Dalloway”. As Septimus (and Clarissa) verge on dissolution in “Mrs. Dalloway,” Olga in “Days of Abandonment” gives us a view into the mind of someone on the brink of insanity.
From “Days of Abandonment” (2005 english translation),
[...]I tried again to open the door. I couldn’t do it. I leaned over, I examined the key closely. Finding the imprint of the old gestures was a mistake. I had to disengage them. Under the stupefied gaze of Ilaria, I brought my mouth to the key, tasted it with my lips, smelled the odor of plastic and metal. Then I grabbed it solidly between my teeth and tried to make it turn. I did it with a sudden jerk, as if I wished to surprise the object, impose a new statute, a different dispensation. Now we’ll see who wins, I thought, while a pasty, salty taste invaded my mouth. But I produced no effect, except the impression that, because the rotating movement of my teeth on the key wasn’t working, it was finding an outlet in my face, tearing it like a can opener, and my teeth were moving, were being unhinged from the foundation of my face, taking with them the nasal septum, an eye brow, an eye, and revealing the viscid interior of my head.
(Anon, through sane eyes, we find “The key turned in the lock simply.”)
Notable is the portrayal of insanity as a representation of the world constructed by a person’s mind that skews too far from the necessities of the reality around them, a representation incoherently blurred by memories and imaginations and hallucinations, a representation that makes their ability to survive, reproduce, function out there in the world quite difficult. (One could think of the economic bubble that recently occurred as insanity.)
Which somehow made me think, if people’s representations of the world could be assigned some sort of numerical metric and be plotted over the number of people with that representation, should we visualize a bell curve of a normal distribution? Ah, but, bell curves bring to mind means. Aristotle spoke of means; to that end, from “The Ethics of Aristotle” (1953 English translation),
In anything continuous and divisible it is possible to take the half, or more than the half, or less than the half. Now these parts may be larger, smaller, and equal either in relation to the thing divided or in relation to us. [...] The man who knows his business avoids both too much and too little. It is the mean he seeks and adopts – not the mean of the thing but the relative mean.
Of course, Aristotle makes me think of Greek philosophers. Coming back to “Number”, Dantzig quotes Philolaus, a Pythagorean, as saying,
All things which can be known have number; for it is not possible that without number anything can be either conceived or known.
Alas for the Pythagoreans, the irrationals revealed by the Pythagorean Theorem! Hippasus drowned! Dancing round the ruler and compass, what was it Eliot said in “The Hollow Men”,
Between the idea
And the reality
Between the motion
And the act
Falls the Shadow
Moving us toward where we parted, William Blake in “Augeries of Innocence” now pops into mind,
To see a World in a grain of sand,
And Heaven in a wild flower,
Hold Infinity in the palm of your hand,
And Eternity in an hour.
Perhaps, as Wordsworth once wrote, “the world is too much with us”; but then we have these sublime writers, poets, mathematicians! Alas, the act is up; the thread must be caught; summer’s grand finale is at the door. So, we end with the close of Dantzig’s “Number”,
In this, then, modern science differs from its classical predecessor; it has recognized the anthropomorphic origin and nature of human knowledge. Be it determinism or rationality, empiricism or the mathematical method, it has recognized that man is the measure of all things, and that there is no other measure.
It’s turtles all the way down, dear reader, turtles all the way down! 