Now that you’ve read my previous posts and have the 4-D thing working well, you’re ready to go for a few more dimensions. Consider the apple that struck Isaac Newton’s head. The event occurred in 1665, in England at 52°55´N by 0°38´E, roughly three feet above ground level. The apple, variety “Flower of Kent,” weighed about 8 ounces and was probably somewhat past fully ripened. Got that picture in your head? You’re doing great.
Now visualize the apple taking thirty seconds to move twenty feet diagonally upward, northward and eastward as it morphs to an underripe 4-ounce Damson plum.
The change you just imagined followed an eight-dimensional path: three dimensions of space, one of time, one of weight, one for degree of ripeness, and two category dimensions, species and variety.
Length in a given direction is only one kind of dimension, as Sir Isaac’s example demonstrates. A mathematician would say that a dimension is a set of values that can be traversed independently of any other set of values. A dimension can be confined to a limited range (360 degrees in a circle) or be infinite like … well, “infinitely far away.” A dimension might be continuous (think how loudness can vary smoothly from sleeping-baby hush to stadium ROAR and beyond) or be in discrete steps like the click-stops on a digital controller. The physicists are arguing now whether, at the smallest of scales, space itself is continuous or discrete.
Color vision’s a good example of dimensions in action. For most of us, our eyes have three types of cone cells, respectively optimized for red, green and blue light. We see a specific color as some mixture of the three and that’s how the screen you’re looking at now can fake 16 million colors using just three kinds of color-emitting elements (phosphor dots in old-style TVs, LEDs in most devices these days).
Where did that 16 million number come from? The signal-processing math is seriously techie, but at the bottom the technology uses 256 intensity levels of red, 256 levels of green and 256 levels of blue — each is a discrete dimension with a limited range. Together they define a 256x256x256-point cube. Any point in that cube represents a unique mix of primary colors. One of the colors in the little girl’s hat, for instance, is at the intersection of 249/256 red, 71/256 green, and 48/256 blue. The arithmetic tells us there are 16,777,216 points (possible mixed colors) in that cube.
Well, actually, there’s one more dimension to color vision because our eyes also have rod cells that simply sense light or darkness. Neither brown nor grey are in the spectrum that cones care about. A good printer uses four separate inks to produce browns and greys as mixtures of three dimensions of red-green-blue plus one of black.
So color is 3-dimensional, mostly. But that’s just the start of color vision because most of us have millions of cone cells in each eye. A mathematician would say that any scene you look at has that number of dimensions, because the intensity registered by one cone can vary in its range independently of all the other cones.
Ain’t it wonderful that you’re perfectly OK with living in a multi-million-dimensional world?
Next week – a word from the other side
~~ Rich Olcott