[Absence and presence] are exceedingly important. They have to do with mathematics also with some of the greatest emotions— [as in] 'Absence makes the heart grow fonder' and 'Presence of Mind.' Absence and presence are very much and constantly in all the arts and sciences. Occasionally the two things meet—the scientific way and also the artistic way.To illustrate, Mr. Siegel presented a person in history, he said he imagined very few people had ever heard of—Constantine Francois Comte de Volney, whose years are 1757 to 1820. "Volney has affected me for a long time," said Mr. Siegel. He was one of the earliest travelers to the East. He knew Arabic and wished to observe what the East was like. "Volney did it so well" Mr. Siegel noted, "Napoleon used his observations when he invaded Egypt.
He read about contemplating the ruins of Palmyra from Volney's book The Ruins; or Meditation on the Revolutions of Empires and the Law of Nature, translated by Joel Barlow. "The idea of going back to the past is here" said Mr. Siegel,"associated with something scholarly. This passage has affected me for years; it is pretty exact but also one of the most emotionally fraught passages in French Prose. If given a certain structure it is poetic." Volney writes:
"The sun had sunk below the horizon: a red border of light still marked his track behind the distant mountains of Syria; the full orbed moon was rising in the east, on a blue ground, over the plains of the Euphrates; the sky was clear, the air calm and serene; ...The aspect of a great city deserted, the memory of the times past compared with its present state, all elevated my mind to high contemplations. I sat on the shaft of a column, my elbow reposing on my knee, and head reclining on my hand, my eyes fixed, sometimes on the desert, sometimes on the ruins, and fell into a profound reverie."And of the Reverie Volney writes:
"And now behold what remains of this powerful city: a miserable skeleton! What of its vast domination: a doubtful and obscure remembrance! To the noisy concourse which thronged under these porticoes, succeeds the solitude of death. The silence of the grave is substituted for the busy hum of public places; the affluence of a commercial city is changed into wretched poverty; the palaces of Kings have become a den of wild beasts; flocks repose in the area of temples, and savage reptiles inhabit the sanctuary of the gods. Ah! how has so much glory been eclipsed? How have so many labors been annihilated? Do thus perish then the works of men — thus vanish empires and nations?""This has something which is tinglingly, poignantly, emotional as anything" commented Mr. Siegel "how it once was — how different from long ago. To say it is concerned with the procedure of science and mathematics can be illustrated quite indefinitely.”
Mr. Siegel commented that Volney "is poetic here but his knowledge of poetry as such is lacking. There is one semi-colon after another, or comma. He doesn't see certain statements should be by themselves and have periods." And Mr. Siegel showed how the arts and sciences meet in a surprising way when he said:
"Style is just as scientific as geometry. Geometry is always concerned with curves and angles, curves and straight lines and style is too. In style we have the angular and the cut short and then the gliding."Then to show absence and presence differently, Mr. Siegel read Volney’s portrait of a camel, made famous by the 19th Century Critic, Sainte-Beuve. Noted Mr. Siegel, "The camel is here seen as the one animal which man could not live without in Arabia or Asia Minor." Translating from the French, Mr. Siegel read the following of Volney quoted from Causeries du lundi of Sainte-Beuve, February 14, 1853. It reads in part:
"...the desert would become uninhabitable and it would be necessary to leave it if nature had not attached to it an animal of a temperament so strong and also frugal with the ungrateful and sterile soil, if she had not placed here the camel. No animal presents an analogy so marked and so exclusive to its climate.... Wanting that the camel live in a land where it would find but a little nourishment, nature had economized the matter in all its construction. She did not give it the plenitude of forms neither of the cow, nor of the horse, nor of the elephant; but limiting itself to a small head without ears, on top of a long neck without flesh. She has taken off its legs and its thighs all useless muscle to the movement of them.... She fortified it with a strong jaw in order to chew the harshest foods but for fear that it would eat too much made its stomach small and obliged it to ruminate....The camel alone serves all the needs of his master. Its milk nourishes the Arab family in the diverse forms of curdled milk, of cheese, and butter. Often one eats its flesh. Shoes are made and saddles from his skin. Clothes and tents are made from his hide. Heavy burdens are transported by means of the camel...Such is the importance of the camel for the desert which if one leaves it out, one will subtract or take away all the population of which it is the unique pivot."Commented Mr. Siegel "The camel is presented as if God or evolution were just working to have certain areas of Asia inhabited. If the camel were absent other things wouldn't be present.” I was affected to hear about the camel and to see how the opposites of presence and absence are in his very structure and show his value. Of Volney's writing here, he explained:
"The description of the camel is careful enough and emotional enough to be a dual presentation of art and science. Volney is a mixture of scientific explorer and letting emotion go as much as emotion can go."Next, Mr. Siegel read from a book he had used in Elementary School published in 1909 by Ginn & Co., and part of a series which he said are the most famous textbooks of their kind in America: Wentworth's Complete Arithmetic. He said, "It was this very book. Arithmetic that you didn't write down I just loved. " Ms. Reiss commented later in the class, "One got a sense of Mr. Siegel himself, developing, as he was in the midst of Elementary school, this beautiful way of seeing the world which made for Aesthetic Realism. He wanted to like the world.”
Commenting first on an illustration of a girl and a boy with a string across a pit, he said, "There is a quality of things present and absent." And under the heading "Rectangular Solids" he read this:
"These children are measuring an excavation, and find it to be 6 ft. 2 in. wide, 8 ft. 4 in. long, and 4 ft. 3 in. deep. Assuming it to be practically rectangular, how many cubic feet of earth have been removed?"Said Mr. Siegel "You get the feeling cubic feet are present and absent. All mathematics," he continued "is a study in presence and absence." And he showed that these opposites are in reality as such: “A pore, a hole, a pocket, a vacancy is a oneness of presence and Absence.”
Then Mr. Siegel went on to more complicated problems. He said, "I know I loved some of these questions years ago. This is one of them":
"If the greatest known depth of the Atlantic Ocean is 27,366 feet, and Mt. Washington is 6,279 feet high, how high does Mt. Washington stand above the bottom of the Atlantic at its greatest known depth?"Mr. Siegel went through the calculations saying, "You add 27,366 to 6,279. It is 33,645 feet above the bottom of the Atlantic. The idea of a mountain and the bottom of an ocean is already taking."
Under the chapter heading "Common Fractions," Mr. Siegel read a problem, which he said "gives one a scientific sensation and also an aesthetic, sensation." And he added, "I must say, I worked it out.”
"A boy lost 1/4 of his kite string in a tree, 1/3 in some wires, and 1/5 in a hedge. What part of the string was left?""Here the common denominator has to be 60" Mr. Siegel explained. "There would be 47/60ths lost, 13/60ths left. To feel 13/60ths of some string has been saved—it is exact and also right in the midst of reality."
What Mr. Siegel said next, points to the understanding of self he came to through his seeing that the structure of all reality is an aesthetic oneness of opposites. “I asked in lessons,” he commented, "what is the common denominator with people. What do people who are different have in common?" And in a discussion, which followed this talk, an elementary school teacher said that through what she has learned from Aesthetic Realism she is able when teaching math to her class, comprised of students who are Hispanic, African-American, Asian, and white, to show how "Equivalent fractions" are both the same and different as people are. For instance: "2/4ths, 1/2 and 8/16ths all look different but they have the same value. I’ve asked “Does that show that the persons sitting next to you, though they may look different, may be more like you, have more in common with you than you may see at first?"
In the Wentworth there is a definition of a circle. "We have the definitions of what can happen to space," Mr. Siegel said. And he read this: "A plane figure bounded by a curved line all points of which are equally distant from a point within is called a circle." "You get a sense that the world makes sense at last. Things have happened but that center from which all points in the circumference are equally distant will always be the same. People don't answer letters, there could be fires--it is the same." Mr. Siegel used so many more examples of problems about pickles and olives and firkins of butter and rolls of matting, all having within them scientific principles while also making for new and surprising emotion about the world. He said, "Whatever can cause emotion is very close to art."
About the last example I'll read, Mr. Siegel said "This... problem is one of the most beautiful I can think of—it makes you concentrate exactly and makes you see reality in such a way.” Under the chapter heading "Problems of the Farm" he read:
"Taking the annual rainfall of Indiana as 41.5 in., what will be the weight of water that will fall on 1 sq. ft. of land per year? on 1 sq. rd.? on 1 Acre?""The idea of rain falling in Indiana on a sq. ft. for a whole year is exceedingly engaging," Mr. Siegel noted. And he continued, “It is well to feel we're thinking of possibilities of quantity, possibilities of life, and at the same time we are thinking of beauty.”