I just caught a snippet of the little boy’s conversation as he excitedly told the librarian, “It is going to last forever, like 140 million bazillion years.” Ah, yes, I do recall that troublesome challenge of turning the philosophic concept of forever into a concrete number. In my grade school days, we would said “infinity plus one.” Ricocheting comments like “can so,” “can not” could be promptly ended by saying, “can so, infinity plus one.” Somehow using math seemed so concrete and definitive compared to saying “forever” or even “forever and a day,” and the phrase had such a specific context that no one ever thought of saying “infinity plus two.” However, I certainly never pondered the deeper implications of infinity or forever, or its mirror image, zero, the null and void.
The early 1960s was a troublesome time to think about forever. We would sit in church and recite, “as it was in the beginning, now is and ever shall be, world without end,” smugly confident in the permanence of this world and our dominance. But then the next day we would have bomb drills at school. The siren went off and we immediately scurried
beneath our desks and put our head between our knees and our hands over our heads. Some of the luckier classes would crouch in a windowless hallway which seemed more secure than our flimsy wooden desks. Regardless, as a fourth grader I intuitively knew that nothing could save us from the bomb. We were all doomed – no world without end for us, we were headed for the void.
Meanwhile our next door neighbors were busy building a bomb shelter in their basement. For reasons I never completely understood, we had a prickly relationship with the Cartons – even our dogs snarled at each other across the property line. Therefore, it was something of a surprise when the Cartons invited us to bunk in with them in the event of a nuclear attack. Perhaps Mrs. Carton was just trying to be neighborly as a payback for all the block parties my mother worked so hard at. Perhaps she wanted to create an invitation-only scenario to avoid the anticipated chaos that would descend on her bomb shelter door, like the last helicopter out of Saigon. Regardless, my mother politely declined the offer saying, “I’d rather be dead than live in a world like that.” I tried to put thoughts of my impending nullness aside. Instead I wondered whether the world my mother was referring to was the thought of sharing cramped quarters with the Cartons, or the broader context of post apocalyptic devastation. But the fragility of a world with an end was troubling.
“Mom, what will I feel like when I die?” I asked.
My mother was not a deep thinker, and tended to push difficult questions aside, but she was infinitely clever and said, “Well, remember what you felt like the entire time before you were born, well I think that you will feel the same way the entire time after you die. It is the now that is important.”
This simple philosophy seemed to settle the issue for a while and the collision between infinity, forever and reality did not come up again until high school. My sophomore year I had reveled in geometry where I found security in the unassailable truths in proofs of geometric figures – side/angle/side, angle/side/angle, side/side/side. You were given point A and point B and the challenge was figuring out how to get from one finite point to another. But the destination, not the journey, was the final truth. English was another story. I struggled with our English teacher who aggressively challenged us to interpret the William Carlos Williams poem the Red Wheelbarrow.
so much depends
upon
barrow
glazed with rain
water
beside the white
chickens.
The teacher said, “Do you think that the three points of the wheelbarrow represent the father, the son and the holy ghost? What about the chickens, are they a symbol of man’s dominance, while the rain represents man’s impotence? Why do you suppose the wheelbarrow is red as opposed to some other color?”
“Good lord, I thought, “You’ve got to be kidding. This is just a farm scene, and the wheelbarrow is red only because the farmer had extra paint after he fixed up his barn. Why can’t a wheelbarrow be just a wheelbarrow?”
The truth was that since there was no one correct interpretation I really didn’t care about any interpretation. In English, there was only point A and an infinite number of ways of getting to no particular destination original site. I was so happy to rush off to my math class.
Unfortunately the safe haven of geometry segued to calculus and math started to have symbols. We were formally introduced to irrational numbers, like π (pi), the ratio between a diameter and a circumference. For practical purposes pi was 3.14, but in reality the ratio went on to infinity. Clever classmates would get up and recite pi to ten or twelve digits, and
I suppose that you could earn some cachet by claiming that you were the only person on earth who knew the final digit of pi, but the pressing question from the calculus teacher was “How could pi be a real number if it cannot have a defined value. Can infinity be real? Is there any such thing as forever?” I trembled – math had just gotten messy and philosophical and was veering off into the uncomfortable vagueness of the red wheelbarrow. The teacher then wrote the irrational number 0.99999 stretching out ad infinitum. He said, “let x equal .99999 and let 10x equal 9.999999, and when you subtract the first equation from the second the infinite string of .9999’s will cancel each other out, leaving you with 9x=9 or x=1:”
10x = 9.9999999
x = 0.9999999
9x = 9 and then x=1
“Now, students here is the paradox, you can see that x equals both 0.9999 and 1, proving that at some infinite point the fraction will become one.” In that moment I realized that there could be no such thing as infinity, forever or eternity and that the world must have an end. It is just that we cannot know when the end is, when that last 9 will flip over like a odometer and trigger a mass conversion to the number 1.
The teacher then went on to explain that if we believed in infinity, we would not be able to sit down. The surprising but seemingly logical line of reasoning was that before we could sit all the way down we would first need to sit half way down, and then a quarter of the way and an eighth of the way with smaller and small fractions extending on to infinity. Our ass could hover ever closer to the seat as we continued to halve the distance, but if infinity existed the fractions would keep getting smaller and we would never get there. As I sat there in calculus, I also realized that I should not be able to get up, but the bell rang and I stood in total defiance of infinity.
The sitting and standing example was actually a good example of the opposite of infinity, i.e. infinitesimal, the smallest number possible. At some point there must be a fraction so small that it becomes zero. But we have rejected that scenario, since no one wants to admit that there are hopeless situations. There is a funny line in the movie “Dumb and Dumber” where the clueless doofus Jim Carey character is trying to wrangle a date with the attractive Lauren Holly. She says that there is no chance that she would date him, and he replies “really there is no chance?” To throw him a bone she replies, “yes maybe one in a million.” He beams ecstatically and says, “Well there is hope,” and we all laugh at his delusional optimism. But his odds are a lot better than anyone who buys a lottery ticket. As the pot grows bigger and bigger, more and more people rush out to buy a ticket even as the odds approach zero that any one individual will win. But there it is in the paper the next day, some lucky bastard defying infinity by sitting in the lap of untold luxury. You can’t deny hope if someone has got to win.
Calculus was the end of my math career. It lost its appeal as it became more philosophical than practical and symbols exceeded numbers. As I progressed through college I assiduously avoided any English courses and focused on the comforting facts of science. The last course I took in college was the required course English 101 where I got randomly assigned to a poetry interpretation class with a bunch of eager freshman.
I panicked, “it’s going to be that damn red wheelbarrow again with a bunch of chickens in the rain. Unless I can figure out what it means I might never graduate.”
But then I realized that even though there was a definite appeal to knowing when I was absolutely right, the impossibility of being totally wrong was also pretty attractive. There are infinity plus one possible interpretations why chickens in the rain are important; I took a personal one, ran with it and aced the class.
Forty years later, I still look to numbers for their concrete value as I have pursued a career in medicine, and I still avoid the collision of math and philosophy – after all if two wrongs cannot make a right, how can the multiplication of two negative numbers be positive? The threat of nuclear war has been assimilated into the deep background of daily life, and the new owners of the Carton’s house turned the bomb shelter into a very snappy wine cellar. Point A is receding into the distance, but I don’t spend any time dwelling on the where, when and how of point B and beyond, and appreciate that it is the big uncertain mess in the middle that makes life interesting. Our son Ned told me about his 19 hour journey in a hot, dusty, overcrowded train in India. A Muslim man asked him where he was going after he died, at which point Ned said, “Well I’m willing to be surprised.” My mother, who is now beyond point B enjoying the hereafter, must be smiling at her grandson’s here and now response.
The missing words in the following poem are anagrams (like spot, stop, post) and the number of dashes indicated the number of letters. One of the words will rhyme with either the previous or following line. Your job is to solve the missing words based on the context of the poem. Scroll down for the answers.
Math and geometry were my favorite subjects when I was just a youth,
I thought, “numbers — —- the universe” and provide us with the truth.
But in calculus, mathematical concepts of infinity began to appear,
And when added to philosophy suddenly things became ——-
Infinity must have a beginning and an end, a paradox that is hard to comprehend
Unless of course a ——- attack brings these thoughts to an apocalyptic end.
So don’t get — —– worrying about the heretofore and the hereafter,
Just hope that the uncertainty of surprise brings you love and laughter.
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Answers: can rule, unclear, nuclear, an ulcer
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