Twenty-four years younger than Shakespeare, Thomas Hobbes, in “Leviathan,” alluded, in his discussion of the origins of religion, to this “stuff” of dreams: “And that the soul of man, was of the same substance, with that which appeareth in a dream, to one that sleepth; or in looking-glass, to one that is awake; which, men not knowing that such apparitions are nothing else but creatures of the fancy, think them to be real, and external substances….”
Thus Hobbes suggests that the “stuff” of dreams are “apparitions” and “creatures of the fancy” and that people mistake such fleeting imaginary phenomena with real, actually existing external things. At the same time, one may interpret Shakespeare’s remarks to imply the claim that “we” or “life” consist of that same fleeting “stuff” as Dreams. Thus the objects we perceive in waking life are no different than the apparitions we experience in the dreams of night. (I am reminded of all the popular ballads and folk songs centered around the line, “life is but a dream.”)
We may read the poetic assertion of an identity between “life” and “dream” as rather a metaphor, suggesting perhaps some poignant similarities between two mental states; the “waking” state and the “dreaming” or “sleeping” state. For we normally know the difference between “life” or the “awake” state and dreaming, but at the same time we may appreciate the poetic sentiment expressed by Shakespeare or in popular music.
In order to investigate further how the “stuff” of dreams may be analogous to the “stuff” of (waking) life, I propose to focus on the nature of conscious human perception and in particular on the way in which ordinary perceptual illusions arise in everyday life. I take a definition of perceptual illusion (and much inspiration) from A. D. Smith’s fine text, “The Problem of Perception.” Therein Smith states the following: “The term ‘illusion’ is to be understood as applying to any perceptual situation in which a physical object is actually perceived, but in which that object perceptually appears other than it really is, for whatever reason.” The term “hallucination” is similar to “illusion” except that in hallucinatory states, there is no “that object” appearing other than it really is. In such situations a subject seems to perceive a normal physical object, but no such object exists at all.
In order to “put some meat” on these definitions, let us look at some examples of well-known and extensively discussed perceptual illusions. One example, pertaining to the sense of vision, and which has been around for a few thousand years, is called, “The Bent Stick in the Water.” In this situation you take a more or less straight stick or long piece of wood thin enough to wrap you hand around it, and place the stick upright into some shallow water, as along the bay or lagoon. Hold on to the stick so you may feel the contact of the stick with the sea bottom. Now, depending on the lighting conditions, you may want to tilt the stick a bit, so that it slants into the water. Now, as you look down at the water and the stick, you will clearly see a sharply bent stick in the water. This clearly meets the definition of a perceptual illusion in the sense I am using the term. You know “really” and objectivity that the stick is not bent, that it didn’t suddenly get bent as you placed part of the stick in the water. Nevertheless, the stick appears as being bent, and this “bentness” is a feature in your visual field that does not belong to real stick.
Yet you may object to calling such phenomena “illusions” insofar as they have an objective physical bases. They do depend on human perceptual consciousness. They would show up on pictures taken with a suitable camera and are perfectly explainable and predictable using the relevant laws of physics, optics, and mathematics. Besides the normal physical objects we seem to encounter in our everyday experience, like tables, chairs, cars, trees, etc., there are also in our conception of reality what Smith calls “physical phenomena.” These may be short-lived events that fall short of the full three-dimensional substantiality and sharply defined boundaries we attribute to normal physical objects. This includes items such as clouds, reflections in water or the atmosphere, mirror images, shadows, etc., that lie, so to speak, on the edges of reality but nevertheless are phenomena of the physical world.
Yet there are other illusionary situations that have no independent physical basis and depend solely on the physiology or psychology of the perceiving mind-brain of the perceiver. Smith calls these “subjective illusions” and we will provide some very interesting examples of such in due order or subsequent articles. But first I want to take a brief glance at other perceptual delights that may be experienced in our untutored extrusions along the island’s shores.
The constant play of light, atmosphere, and water seems a visual treat, at least for me, as I roam the island’s shoreline. Sunrise and sunset are the best shoes in town. One phenomenon I’ve noticed, beautiful yet bewildering, occurs when you look over the sea toward the setting sun. You see a kind of golden path of light reflecting on the surface of the waters, reflecting from beneath the sun to you. Then, as you along the shore, the path follows your eye. The strange thing, if there are other people on the shore, you don’t see any path of light going toward them. Yet each of the others have the same experience as you. The other person sees the path of light going toward him or her, and none coming toward any others. How can this be? Is the path of light really there? Will it show up on a camera? Or is it a common everyday hallucination in regard to our unique relationship to that ancient God, the Sun? Here is a general phenomenon, which may apply to any perceiver, and which at the same time, unique, private, and subjective to at any one unique person. Some phenomena we call “universal” an others, “particular.” But his phenomenon of the golden path across the waters mysteriously straddles both categories at once. I’ve only heard talk about this sort of phenomenon by Kepler when talking about a public painting of a figure whose eyes seemed to follow uniquely any individual who gazed at them. My poetic take on this event is that each of has a unique, private, subjective path in life — one that only you may live, even though we live in a common world under a common sun, and the threads of life are woven mysteriously by the golden light of the sun especially for you.
Puzzle
The sequence: (7/9) x (26/28) x (63/65) x … is called an “Infinite Product.” Each faction in parentheses is called a “term” and “x” stands for multiplication. The nth term of the sequence is found by using the formula ((n + 1)^3 – 1)/((n+1)^3 + 1), starting with n = 1 for the first term. This infinite product converges onto a number that is a simple proper fraction (one digit numerator and denominator). Can you find that number?
Answer to last week’s puzzle
X = ( 1 +/- sqrt 5 )/2 and Y = ( 1 -/+ sqrt 5)/2 ( Note: “sqrt 5” means “the square root of 5.) Then it follows that 1/X + 1/Y = -1, and X^3 + Y^3 = 4. Q. E. D.
