The psychologist and the author met at the restaurant sitting in its lower portion. Think in terms of a cave.
The author was in better spirits. “Can you tell me, Jocelyn, is there something special about circles—I’m referring to our last meeting in which you claimed that hemineglect sufferers will draw a complete circle when asked to draw a clock?”
“Well, Marcia, I am not so fortunate as Euclid or Descartes to have spent years in studying the ins and outs of mathematical objects. The fact is, far from knowing what’s special about a circle, I have no idea what it is.”
“Surely you’re trifling with me Jocelyn. Weren’t you ever taught what they are in school?”
“Possibly, but I must have forgotten because now I’m ignorant of them. Maybe you can tell me what their proper definition is?”
“But there is no difficulty about it. Let us consider the point A; a circle is the set of points in the plane that are equidistant from A.”
“I seem to be in luck. I asked for one circle and find you have a whole swarm to offer. Seriously Marcia, suppose I asked you to define a cat, to tell me its essential nature, and you replied that cats are of many different kinds. How would you respond if I then asked: Is that what makes a cat a cat that there are many and various and that they differ from one another? Or would you agree that there is some other quality such as size or color in which they differ?”
“I should respond that while size and color differ from one cat to the next, neither of these defines the essential nature of cats.”
“But this is what I want you to tell me. What is the characteristic in respect of which they are all the same?”
“Well Jocelyn, as I am not an expert in the field of zoology, I have nothing to say at all except that in so far as cats are cats, they don’t differ from one another.”
“I presume you would agree that it is possible to determine the exact characteristic that distinguishes a cat from all other animals, say by using DNA?”
“No, I would not agree since each day brings us closer to the impossibility of even differentiating between the males and females of our own species.”
“Let us leave cats for now and try something quite general. Take café . . .” Plato’s wife appeared before the psychologist could complete her sentence. “Please help us, Jean, to discover the nature of Plato’s Cave. Would you say that it is a cave or a restaurant or a café?”
“Is that a serious question, Jocelyn or are you making fun of me?”
“Please Jean, we find ourselves in a quandary. If you will but enlighten us, then everything will be as it should be.”
“Good heavens. It’s a restaurant, not a cave and certainly not a café.”
“Why is that I wonder? It appears to be a cave.”
“We are a full service restaurant,” Plato’s wife insisted.
“So, if I understand you, you mean that since food is served here, this is a restaurant?”
“I agree, but when I went to Carlsbad Caverns, there was a restaurant inside the cave.”
“Permit me to interfere,” the author barged in. “Plato’s Cave is a restaurant with a cave inside it while Carlsbad is a cave with a restaurant inside it. I feel sure the distinction must be significant.”
“That’s no restaurant! It might be a cafeteria or such like but not a full service establishment like we have here. Plato’s is the real thing,” Plato’s wife asserted.
“So we may say in general that Plato’s Cave is a restaurant or restaurant?”
Plato’s wife shook her head: “Doltishness, sheer doltishness. That’s what my mother calls it when people talk nonsense. Will you be taking lunch with your questions?” she asked.
“Not doltish at all,” the psychologist continued, “If it is a restaurant, then there must be a list of restaurants of which Plato’s is but one. If, on the other hand, it is restaurant, then we must conclude that Plato’s is the idealized form, the cookie cutter to which all eating establishments aspire. It means quite simply that Plato’s Cave and restaurant are equivalent.”
“Yes that’s it. Will you order now?”
“Souvlaki,” the author responded.
“For me as well,” the psychologist agreed. “Before you bustle off, Jean, do me a small favor and tell me what a cat is.”
“Fluffy, sneaky creature, terribly intelligent and likes to hide a lot.” Before the psychologist could form a response, Plato’s wife had whisked away the menus and disappeared from the cave.
“I don’t know what we got out of all that,” the author commented. “If we were sitting in the template for all restaurants, would perfect food actually appeal to us mere mortals or would it taste like plastic or metal or even clay?”
“Up to your tricks, Jocelyn. Poor Jean is in a state.”
Unabashed by Plato’s sudden appearance, Jocelyn said: “I’m glad you’re here Plato because I have a question for you. Permit me to explain a little first. Marcia and I are trying to determine the essential nature of a cat. Could you help us?”
“A cat is a carnivorous mammal, a stealthy quadruped. Most in my experience are like my Socrates—conceited and self absorbed. Alcibiades, now there’s a fine hound for you—sincere and frank, dotes on Socrates. They even sleep together.”
“Your definition suffers from plurality, Plato. We’re looking for the essence of a cat, the characteristic that distinguishes it from all other animals.”
Plato shrugged. “Maybe there is no such thing with regards to cats or even dogs.”
“I’m not ready to accept that, but it does seem as if you are claiming the need for a checklist.”
“Hard to disagree with your conclusion, Jocelyn.”
“Humor me with your definition of a circle, if you don’t mind,” the author interjected.
Again Plato shrugged: “Its beginning and end are indistinguishable.”
“I can’t fault you there, but isn’t that equally true of all closed two dimensional figures, a square for instance begins in its ending. Do you agree?”
“Then what quality separates a circle from a square or even a rectangle?”
“I guess you’re saying that squares and rectangles are composed of multiple lines whereas a circle is composed of a single line?”
“Let’s try a bit of a thought experiment. Imagine a perfect square and proceed to snip off the corners in a regular fashion. What are we left with?”
“A stop sign.”
“From which point let us go forward with our snipping. Does this not give us a sixteen-sided figure?”
“Certainly,” Plato replied.
“Then according to you, the number of sides doubles each time?”
“And what if you were chained up in this cave with nothing to do except snip all day?”
“That is not reasonable,” Plato objected. “How would I eat?”
“Jean will take care of all your needs and of course you will be facing the back wall so that when the setting sun projects the fair city of Eugene through the pinhole, you will at least have some diversion. Please tell me, sir, the result of a lifetime of snipping.”
“I might have a circle.”
“It would look like a circle.”
“Do you agree that given infinite time and infinitely accurate scissors, you would eventually have a circle?”
“Oh I don’t know. I would have to say that it would merely be a figure of infinite sides. Nothing is quite as perfect as a circle except infinity.”
“So when you get to infinity, the circle will be complete?”
“By the very nature of infinity, you can never get there.”
“Let me remind you, Plato, this is a thought experiment. We can go anywhere in the mind including to infinity and back. Do you agree that once we reach infinity, the circle will be perfect?”
“Yes, I agree, but don’t be thinking I’ll let you chain me up,” on which statement, Plato made a getaway.
The author turned to the psychologist. “Where have we gotten ourselves now? These endeavors do not seem to have brought us any closer to the truth; in fact, I am more perplexed than when I started out this morning. If you will permit a metaphor since writers are fond of these devices, I shall compare you to the Gorgias butterfly. Its beauty draws us in, but should anyone come in contact with it, it numbs her, and that is the sort of thing you seem to be doing to me now. My lips, my tongue, my mind are all numb, and if you are planning to fling any postmodernistic fertilizer about the unfeasibility of discovering truth, don’t bother. I shall merely think you a complete idiot.”
“Compose yourself, Marcia; we’ve learned a great deal from Plato. In the first place, he has told us that circles exist only in the mind.”
“Everything exists in the mind, Jocelyn.”
“Ah, but whereas cats and dogs may be found in nature; that is to say, our knowledge of them is inspired by nature, circles and infinity are entirely human conceptions.”
“Is that your complete argument?”
“Yes, unless you can explain how it fails.”
“It does not answer the original question.”
“Why do hemispatial neglect patients draw a complete circle?”
“Did we not just prove that circles and cats are treated differently in the brain?”
“How so? Indulge me if you will; my brain is befuddled.”
“A circle is its own definition; a cat on the other hand, requires a checklist. The most likely interpretation is that these concepts are not handled by the same regions of the brain. From experimental data, we know that hemispatial neglect is associated with lesions cropping up in particular areas of the brain. The inferior parietal is particularly favored, but as I am not an expert in the field, you should consult the Venerable Ramachandran if you wish to know more.”
I stopped reading. “What do you think? Is it a fair representation of your conversation with Jocelyn?”
The author responded with soft laughter: “It’s uncomfortably accurate, but let us not dwell on that. I’m rather keen on having pancakes for breakfast. How about you, Bob?”
“Only if I can dissect them into an infinite number of pieces until they disappear into the void of my stomach.”
“Yeah, I have a void as well, but it’s somewhat more ill defined.”
“That’s no surprise,” I replied.
“Not a very nice thing to say.”
“Well, I just can’t seem to get my mind around what if anything we’ve learned from this whole exercise.”
“We now know more than we did about unilateral neglect. What’s more, we’ve been afforded a first hand view of three dimensional neglect.
“Seriously? Where was I when this was going down?”
“Clearly, Jocelyn has concluded that you are dangerously insane . . .”
“What makes you think that!”
“She made a call. The men-in-white are probably on their way as we speak. If you attempt to explain that Jocelyn suffers from massive unilateral neglect rendering her incapable of noticing the world you come from, Marcia, even though it’s right next door, they’ll indubitably include you into a straight jacket since the bulk of humanity suffers from the exact same neglect problem.”
“I don’t like the sound of that, not one little bit. Maybe you should just take me home, Bob.”
“You dealt the cards and now you’re going to have to play out the hand, Marcia.”