Most of us think of consciousness as a kind of division between several states. We can be awake, unconscious, or maybe somewhat drowsy on the boundary between the two, and occasionally interact with our out-of-reach “subconscious” without realizing it. But is there more to the concept? In his book “The Tides of Mind”, Yale computer scientist & cognitive researcher David Gelernter makes the case that consciousness is more of a continuum: at any given moment, you are at some point on a spectrum ranging from pure thinking to pure feeling. You move up and down the spectrum depending on how focused and logical your thoughts are and how connected with the outside world. At the bottom, you retreat inward into your mind, and fall asleep.
So, what does this have to do with mathematics? Gelernter points out a famous quote by physicist Eugene Wigner about John Von Neumann, who is widely acknowledged as one of the greatest mathematicians of the 20th century: “Whenever I talked with Von Neumann, I always had the impression that only he was fully awake”. Now of course, we need to take Gelernter’s use of this quote with a grain of salt, since Wigner was probably speaking in a colloquial sense and not aware of this modern theory. But he does point out that in this spectrum theory, logical thinking and reasoning is at the very top, indeed the most ‘awake’ portion of that spectrum. And this might also explain why mathematics tends to be more challenging to the average person than many other human pursuits: it requires that you keep focused attention, avoiding any temptation towards reminiscence, daydreaming, or emotion. And if you fall asleep, you probably won’t get any math done.
Of course, there are certain other types of genius that can occur when someone has exceptional abilities farther down the spectrum. Gelernter also points out the example of Napolean, who was skilled at stirring the emotions of his followers, and could draw vast quantities of past military experiences from his memory to guide his plans and policies. As a young officer Napoleon is said to have claimed, “I do a thousand projects every night as I fall asleep”. In other words, in his semi-conscious state near the bottom of the spectrum, he could easily retrieve various scenarios from his memory, varying them and playing with them creatively to discover different ways the next day’s battle might play out.
The position of emotions and memories in this theory is also somewhat strange. Gelernter writes, “Emotion grows increasingly prominent as reflective thinking fades and the brightness of memories grows— and by not creating memories, we unmake our experience as it happens”. In other words, what others might call the subconscious is simply your internal array of memories; rather than having a separate subconscious mind, the illusion of a subconscious is just what results when you are low on the spectrum and increasingly drawing from your memories instead of logically observing the outside world. Emotions are our internal summaries of the flavor of a set of memories, which become increasingly prominent as we are lower on the spectrum.
One interesting consequence of this theory, in Gelernter’s view, is that “computationalism”, the idea that the human mind might be equivalent to some advanced computer, is fundamentally wrong. Due to our reliance on the capabilities of the mind to analyze memories in an unfocused way and generate emotions, no computer could replicate this state of being. I may not be doing the theory justice, but I don’t find this argument very convincing. Ironically, it might be said that he’s assuming a computer model of a human mind is restricted to a “Von Neumann architecture”, the type of computers that most of us have today, and which seem to directly implement the logical, mathematical thought that occurs at the top of our spectrum. But there are many alternative types of computers that have been theorized. In fact, currently there is explosive growth happening in “neural network” computers, inspired by the design of a human brain. While I would tend to agree with Gelernter that the spectrum of consciousness would be very hard to model in a Von Neumann architecture, I would still bet that some brain-like computing device will one day be able to do everything a human brain can do. On the other hand, that might just be a daydream resulting from my down-spectrum lack of logical thinking at the moment.
And this has been your math mutation for today.