I was digging through some old files the other day and unearthed this short story I wrote back in 2001 and (after cleaning it up a bit) thought I'd share it here. If you like reading absurd short story fiction with a mathematical slant, read on. If you have any comments or constructive criticism feel free to leave a comment.
My dear reader, have I ever told you of Dr. Farklebends? If I had, you would have certainly remembered, as he had the most peculiar belief that the set of natural numbers had a finite cardinality! It was Hobbes, my classmate and pal at university, who had informed me of this particular professor's odd conviction. "Hobbes," I had asked, "how could a learned man hold such a silly belief?"
Hobbes had responded to my query in very hushed tones. "Dr. Farklebends," he had started, "puts a great deal of faith in empirical data. His contention, you see, is that since infinity cannot be empirically conceptualized, it does not exist." Hobbes leaned in closer and spoke in an even quieter voice. "The implications of this assertion are illogical - Dr. Farklebends adamantly believes that there is an upper bound to the set of natural numbers!"
"An upper bound!?" I had exclaimed in disbelief. As an avid student of mathematics, such a preposterous notion was beyond my comprehension. Here was Hobbes, my bestest friend in all of school, telling me the seemingly impossible - that one of the professors at our renowned college firmly believed that there was some "greatest" integer, some integer for after which no greater integer existed. The concept of such a number was most amusing to me, and to Hobbes as well, for he had a coy smile on his usually stolid face. "Pray tell, dear Hobbs, what number does Dr. Farklebends believe to be this 'upper bound?'"
"You give Dr. Farklebends too little credit, my dear friend. If our respected professor were to name a number as the upper bound then he could instantly be disproven by someone who took the time to add one to that upper bound. No, our esteemed Dr. Farklebends is much wiser than that, much wiser. He is the first to admits that he does not know the upper bound of the set of natural numbers." It was at this point that Hobbes, with that coy smile still lingering on his cherub face, leaned back in his chair and paused, waiting for my comment.
I responded thusly: "Does he not see the absurdity of his claim? By his own words, he cannot name an upper bound because he knows that someone can name a number greater. How, then, can there be an upper bound?"
Of course, Hobbes agreed with my conclusion and over the course of the next several days we gaily joked about this odd professor and his illogical beliefs. Admittedly, I was a trifle embarrassed for both my beloved college and poor Dr. Farklebends. I ask you this, dear reader, what could be worse for a professor than for a couple of youthful students to speak of him and his work in such jovial and irreverent terms? After some time our interest toward the matter subsided and I had forgot about Dr. Farklebends.
And this would be the end of my story, dear reader, if it weren't for a most unexpected incident that occurred several weeks later. It was the middle of the week, bright and sunny outside, and I, your apt pupil, was strolling through the college commons on my way to an afternoon lecture when I happened to stumble upon a rather gaunt man standing alone while nervously scribbling down notes on a small pad of paper in hand. This man appeared to be quite frail. His suit, which would hardly fit most healthy men, looked to be two sizes too big for his sickly frame. His disheveled hair was balding and gray, his glasses were smudged and nearly falling from the tip of his bony nose. The only part of this ghastly fellow that seemed well were his eyes. They were large and bright, paying great attention to those notes he was furiously recording.
Having left a few minutes early for my afternoon class, I decided to stop and observe this interesting specimen before my eyes. The notebook held firmly in his hands seemed to be far too small for all practical purposes. This creature filled the pages at an amazing rate, flipping to the next one every few moments. With each new page this possessed man continued his scribblings with the same frantic pace. After a few minutes of observation I decided that I must find out what, exactly, this tortured soul was so furiously recording. I approached the specimen slowly, cautiously, so as not to startle him.
"Excuse me," I said slowly and evenly. The man did not immediately look up. Instead, his scribbling slowed, just a bit at first, and then more so. And soon, he stopped altogether and then, at that point, raised his head, his bright eyes full of passion and life meeting mine, which, I must admit, must have looked pretty timid and confused.
"Yes?" There was a bit of contempt in that voice that seemed to say, "Who are you, lad, and why have you interrupted my work?"
"Yes," I said, regaining my composure. "Sir, I couldn't help but notice you so intently writing in your notebook there that I just had to take a moment to ask, with all due respect, Sir, what it is that you are recording."
"Oh?" asked the man, his voice alive and without any of the bite it had possessed upon our first exchange. And his eyes! Already full of vitalizing energy, they seemed to glow even brighter at my inquiry. "Yes, that, my work! I am working on a very important mathematics problem, a most acutely interesting one with unforeseeable applications and consequences!"
Before I could offer thanks for his response and excuse myself so as not to be late for lecture, the man continued. "Yes, yes, it is quite an important little problem. Are you familiar with mathematics?" I nodded. "Let me ask you this, then. Pray tell, what is the greatest number that exists?"
It was at this exact moment, my dear reader, that I realized that this squirrel of a man was no one other than the infamous Dr. Farklebends! This revelation had stunned me into abrupt silence, and I failed to answer the doctor's question with anything more than an agape mouth.
"I take your lack of a response is because you don't think that there is any sort of upper bound?" Still a bit startled I did not attempt to respond verbally, as I feared my tongue would fail me. Again, I nodded. "Ah, but why? Why do you think there is no such 'greatest number' out there, one that has no number great than it? You are a student of mathematics, explain your reasoning."
I swallowed hard and decided to respond as graciously, yet as accurately, as possible. "Dear Sir," I began, "it can be shown by a proof of contradiction that there is no greatest number." I paused to give the doctor an opportunity to interject; Dr. Farklebends' intense eyes widened, encouraging me to continue. "For instance, assume that there is some greatest number, call it x. But if x is the greatest number than x + 1 must be less than x, which is illogical. Hence, there can be no x such that it is greater than all other numbers."
A great smile that matched the intensity his bright eyes appeared on the doctor's face. "Ah, yes, that is what everyone concludes, my son, but who is to say it is true? Where are the hard facts, the empirical data to support it?"
Forgetting that I was speaking to a professor, I responded, perhaps a bit too curtly, "And where is your empirical data, Sir? Can you give some number that is, indeed, greater than all other numbers?"
Dr. Farklebends' smile widened, his eyes grew brighter. "Ah, yes," he said slowly, "that is a very good point. And that, my son, is what I am working on here!" At this point he held up his dog-eared notebook. "You see, I am working to find that 'greatest number,' and working very hard, indeed!"
"Working to find the greatest number? How, what formulae are you using? What mathematical techniques?" I asked breathlessly.
Dr. Farklebends continued his incessant grinning. When I had first observed him scratching down notes his face, save for his eyes, had appeared downtrodden and most sickly. But now, my dear reader, his face was alive as if my questioning and rejuvenated his ailing body. "I am using the most basic mathematical techniques. The most simple and fundamental formulae." With this, an elated and proud Dr. Farklebends handed me his prized possession - his worn notebook. I took it from his frail hands timidly and with great care, as if it were a religious relic or ancient artifact that might crumble at my touch. For you see, dear reader, I could sense that to this scrawny man these tattered pages were his most valuable possession.
I turned my attention to the notebook, opening it to the first page. To my great astonishment I saw the following markings:
0
0+1 = 1
1+1 = 2
2+1 = 3
3+1 = 4
In disbelief, I flipped the worn page, and quickly scanned the next.
5+1 = 6
6+1 = 7
7+1 = 8
8+1 = 9
9+1 = 10
I looked up at the doctor in bewilderment. In telling you this tale now, how I wish I had a mirror that afternoon, for I am certain the look on my face must have been most amusing, an absurd mix of utter shock and confusion. Yet Dr. Farklebends only widened his already unnaturally wide smile. His eyes only grew brighter and more intense. I had to look back down at the notebook to avoid those eyes and that smile. I started blindly flipping through the pages.
3243246+1 = 3243247
3243247+1 = 3243248
3243248+1 = 3243249
3243249+1 = 3243250
3243250+1 = 3243251
I turned to another random page, further in the notebook:
2346234384+1 = 2346234385
2346234385+1 = 2346234386
2346234386+1 = 2346234387
2346234387+1 = 2346234388
2346234388+1 = 2346234389
I looked back up at the doctor in disbelief. He inquired softly, "Do you see now?" I just stared back at the doctor, unable to even grunt. "I am going to find the greatest number, my son, through empirical means! Yes? When I reach that illustrious number to which I cannot add one to anymore, then, young man, THEN I will have found that obscure number!"
I quietly handed the professor back his worn notebook. Dr. Farklebends' smile did not diminish as he took the book back from my hands, nor did his eyes lose any of their fiery energy as I turned and continued to my afternoon lecture (which, I'll have you know, I was most embarrassed to have arrived five minutes late). As I made my way across the commons, my body limp and my eyes tired from this most perplexing encounter, I turned back for one last look at the tortured Dr. Farklebends. There he stood where I had left him, his notebook back open, his eyes electric, his hand furiously continuing its interrupted work.