The boy is twenty years old, has slept for nearly five years, wakes up after a confirmed absence of cardiac electrical activity. Temporary hypersensitivity and demonstrated sensory defensiveness for twelve hours. Muscular atrophy. However, after this brief transitional dysfunction, he speaks without any indication of brain damage, and from a simple mathematics question, he intuits the conceptual paradox of infinity.
--Harold drinks his water in two swallows, then continues.
I asked Robbie to discuss the differences between the two simple mathematics problems: an addition problem and a multiplication problem. The question requires Robbie to describe the difference in function, and why--when applying the different functions to the same numbers--the functions lead to different results.
He told me his first inclination was to identify--correctly it would have seemed--the function as the essential difference. But then his mind grabbed on to the idea of the equal sign in each problem as the central issue. Of course he is correct: there is no equation without the equality demand. We all understand that both sides of an equation, by definition, are the same.
But Robbie made a critical, intuitive leap: he equated the mathematics problems with the Rorschach test associations. He intuited two concepts: all questions are equations; and all questions are formulated through desire--the most basic, relevant desire being the desire for a solution to a problem.
He proceeded to ask me what my associations were with the ink blot progression we had look at earlier in the morning. I told him I had made no conscious associations with the blots; my energy was focused on Robbie's reactions, rather than my own. He pressed me, wondering whether or not my thoughts should be the same as his. In essence, he wondered whether there was a function or property tied to himself, or instead tied to the picture. So, if "Robbie's Thoughts" equal "ink blot," and if "Harold's Thoughts" equal ink blot, then shouldn't "Robbie's Thoughts" equal "Harold's Thoughts?"
I had to offer him a tentative explanation of the Rorschach test--though I neglected to explain that I was testing him specifically to gauge his unresolved familial connections. Instead, I told him I was interested in how he thinks, rather than what he thinks.
By this point, he had cleverly manipulated me to a point in his logical argument where he could answer the mathematics problem to his own satisfaction, He told me that the question itself was irrelevant. He told me the questions were incomparably different.
I asked him, then, whether he identified any similarities at all between the two equations.
Here was his answer: of course! When you dissect each equation's identity into all of its fundamental components and elements, the pieces may be exactly the same--though the consciousness that breaks down the identity into pieces affects the sizes of those pieces. I initially assumed he had missed the point of equations here--the larger identity, the value of the equation, is not the essence of a mathematics problem; an equation is an attempt to identify the name and power of the tiniest piece of the larger identity and not the larger identity itself--to name those components and elements that seemed to have little or no value in Robbie's mind.
Regardless, Robbie believed that when you ask the question, any question, you are suddenly and arbitrarily setting boundaries around a random collection of elements, and you are asking for a name, for a value, for that plane of awareness. Each of the two equations represents an arbitrarily established identity--an identity unique from any other identity. Most significantly, he said that there was no possible way to find an objective similarity between these two identities (five and six, in this case).
The only way we give the question meaning is by allowing two subjective desires to converge at the same place, and same moment in time.
In Robbie's mind, my story problem sounded like this: a doctor has two mathematics problems set before a boy, laid out in two separate cards. One card contains an equation with an identity of five, and the other card contains an equation with an identity of six. The doctor then asks, "what is the difference between five and six?"--a pointless question, correct?
But in just the way that two different people respond differently to the same picture, when you have two people discussing the answer to the same question, suddenly you have meaning.
Although I doubt this was his intention, he might have said "there is no way for someone to objectively analyze the way another person relates to an ink blot." Only the picture itself is sterile enough to have an objective meaning.
And when the boy looked at the ink blots, he created a web strand of meaning, subjectively.
When I collected and reviewed his responses, I added a new web strand of meaning, subjectively.
Now that you are hearing and internally responding to this story, the web of subjective meaning has expanded in a way that surpasses simple, exponential expansion. The web has expanded infinitely.
Robbie said that this subjectivity was the answer to the mathematics question. He might as well have said this:
Subjectivity = Meaning
The way people think when they share those thoughts with other people--that is the only type of thought that has any lasting importance, that has any meaning. And Robbie's conception, this web of relevant, subjective thought which fluctuates forward and backward in time, throughout space, is nothing short of our understanding of infinity.
--The conference room hummed with the buzz of fluorescence, the tin clicking of ventilation, the murmurings of white coats reviewing what they had heard. Some expressed interest; others glanced at Harold with exasperation; most of the psychiatrists were bored.
One old man lounging by himself toward the back of the room called over the noise of discussion: "Your boy hasn't intuited the notion of infinity, you ninny!"
Explain yourself, Harold demanded.
"I'm sure you understand me, you silly fart. You're just like the rest of us, Harry, trying to make meaning. What your young prodigy has intuited is simply the difference between zero and error on any calculator. The former, the zero, is identity--paradoxically the theoretical foundation of knowable reality, the whole concept of identity and equation and causality. But the latter, the so-called "undefined" error, is an absurdity, Harold--not a concept of infinity. If you take any identity and divide by the principle of identity, if you divide by zero, you get the undefined absurdity."
What makes this different from infinity? Harold asked. If I have a box that holds ten normal building blocks, it will hold twenty half-size building blocks, and forty quarter-size building blocks. But when I use the principle of identity, this concept of zero--how many "zero" sized building blocks can I fit inside the box? An infinite number. And this value of infinity has no meaning without the relationship between two entities. We have blocks; we have a box. We have Robbie explaining infinity to me, and I am explaining it to you. This is Robbie's subjective web of meaning.
"Harold, you haven't done your math properly. Infinity has no identity. Fitting an infinite amount of blocks inside a box? Are you listening to yourself? If you fit an infinite number of blocks into a 'finite' box, and then immediately emptied the box, would you have zero blocks? Look at these equations:
Infinity - Infinity = ?
and
Infinity / Infinity = ?
and especially
Infinity / 0 = Infinity
"Infinity isn't an identity. You can't subtract infinity from itself; you can't divide in infinity by 'itself,' and this last equation, upon which you've championed your prodigy, is an absurdity. On the one hand, mathematics makes allowances for you to calculate such absurdities--but your results won't be real numbers. Your results will be various numbers.
"Therefore, Harold, your boy hasn't given you subjective access to infinity; instead, he's shown you that no one has any concrete identity at all!"
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