Relativity in Ten Minutes (more or less) By the homeless science writer, Chongo
Imagine slowly passing a simple, solid, three-dimensional object through the surface of a pool of perfectly still water. Keep in mind that the surface is the boundary between the air and the water, and so does not include the water of the pool itself or the air above the water. An oblong, American-style football serves this purpose well. As the football passes through the plane of the surface of the pool it would intersect this two-dimensional surface first as a point, then as the changing contour of a football, and finally as a point again as it finished, leaving the surface unrifled, flat, and still, just as it was before the football began entering.

Let us imagine further, that the surface of the pool represents a two-dimensional perspective of observation. The changing outline of the object, the football, as it passes through the surface, is how the three-dimensional object is perceived from a two-dimensional perspective. From a two-dimensional perspective, it is impossible to ‘perceive’ a three-dimensional object in its entirety. The two-dimensional perspective allows only two-dimensional cross-sections of the three-dimensional solid object (the football). So, no matter how many dimensions an object might have, from a two-dimensional perspective, no more than two dimensions can ever be perceived, in any given moment, directly.

What does a shape passing through the surface of a pool of water have to do with explaining a more correct and fundamental way to look at motion? How can this image lead us to a simpler way to explain the relativity of the measures of space and the measures of time? We can answer this question by imagining passing a much more complex shape through this same surface; a single object that would intersect the surface at many points simultaneously, thus creating many different, individual cross-sections at the same time, instead of just a single one as the football would. A classic, outdoor television antenna, it being a complex lattice of rods, would serve this purpose well. I t is a complicated three-dimensional shape that would intersect the surface at many individual and distinct places; all of them small in area, like points.

We can imagine passing the complex shape of a classic outdoor television antenna through this surface straight down, perpendicular to the surface, and equally important, at a steady, uniform rate of motion. We will orient the antenna in such a way that no rod will be perpendicular to the direction in which it is introduced to the surface. Passing it in such an orientation prevents any rod from being parallel to the intersecting surface, and thus excludes any rod from intersecting this perceiving surface in more than a single “point” (meaning discrete region). From the point of view of this perceiving surface, the “points’ of intersection would change their position, as the object passed through, either approaching or receding from one another. The sharper the angle of the intersecting rod with respect to the surface of the pool, the faster its intersections would change position.

The changing positions of these points on the surface could easily be mistaken for something other than the changing contours of an antenna. They could easily be mistaken for something else because they would look exactly like something else to any two-dimensional creatures inhabiting the two-dimensional surface of the pool. They would be convinced, and quite reasonably so, that what they were perceiving was the ‘motion’ of discrete and individual points moving across their two-dimensional surface, it being their version of “space”.

From our perspective we imagine the antenna dropping as a whole, with the points of intersection changing. We imagine the rods as rods, in their entirety. But we must realize that the number of dimensions to one’s perspective is the limit on the number of dimensions that one can perceive. Accordingly, for two-dimensional beings the moving intersections of the antenna on the surface would be perceived as “bounded’ points in two dimensions only, NOT in the three dimensions that the antenna would really have. We can use this picture of an antenna passing through the surface of a pool for explaining relativity in a very simple and very understandable geometric way.

When we imagine passing the television antenna through the surface of the pool, we might assume that it is the antenna that moves, while the water and its surface remain fixed. However, from the perspective of the television antenna, it can consider itself to be perfectly at rest (just as we do while we’re reading, yet still moving with the motion of our planet, solar system, and galaxy through space). Let us assume such a state of affairs; that it is not the television antenna moving, but rather the level of the pool that rises, so that instead of dropping the antenna into the water, we simply hold it in place, letting the water, and its surface, do the rising, again at a steady and unchanging rate.

Early two-dimensional physicists among the two-dimensional creatures inhabiting the surface of the pond would realize that any clock always ran at the very same pace, anywhere on their surface, and that this meant that they could specify time as being the same everywhere. They would therefore logically conclude that their entire surface was always rising, anywhere and everywhere, at the same steady rate (speed), regardless of one’s position on it. They would specify “speed’ according to the relationship between the rate with which the surface was rising and surface distances. Consequently, they would treat rising as a dimension. They would treat it as such because they would, in their mathematical models, associate the line defining the dimension of time as being parallel to an observer at rest on a rising surface. Considered in such a way, time would seem perfectly perpendicular to the two-dimensional “flat’ surface of their pool. Two-dimensional physicists would utilize time in this way, as a convenience, just as our early three-dimensional physicists did.

Just like the first three-dimensional physicists, their two-dimensional equivalents would initially believe time was something completely independent of, and clearly distinguishable from “space”, which would be their surface. Such a thing would be clearly obvious, because they would believe that no one could intuitively “reason’ motion itself being an actual physical dimension, inseparable from space, any more than one could reasonably consider time as being a physically real part of the geometry of their universe. They’d have reasoned most incorrectly; time (according to relativity’s impeccable description of nature) is identical to space.

Because their surface would be, just like our three-dimensional space is, always rising at the same rate, regardless of one’s position on it, two-dimensional physicists would have no basis for believing that this would not also be true regardless of one’s motion upon it as well. They would so presume because motion in their realm would be confined to such slow speeds that they would never observe anything moving fast enough to suggest otherwise. Under closer examination however, they would realize that this could not possibly be true because they would notice repeatedly that their speed of light was, just as it is in our universe, a constant and finite speed everywhere, even on things in motion. This is not necessarily what they might imagine happening, since the speed of such motion should, intuitively, be expected to add to or subtract from the speed of the emitted light, along the direction of motion., yet it would not (as it doesn’t in ours)

Intuitively we know, just like the two-dimensional creatures on our rising surface would surely know as well, that by pushing something it goes faster. So naturally, if light travels at a particular speed, and whatever it is that is creating the light is pushed to make it move faster, then, intuitively, the light should go faster in that direction. Likewise, in the direction opposite to the motion, light should correspondingly slow down, its speed reduced, or “canceled’, by the motion. Conversely, moving the observer with respect to the light should have the same effect, too, since that is what happens when we push anything else. Anything except light, that is; for light doesn’t change; in both directions of motion as well as in any other direction, its speed always measures the same. Only the measuring of wavelengths can change with motion, as in the red shifting of rapidly receding stars and the blue shifting of rapidly approaching stars.

You can neither speed up light nor slow it down using motion, no matter how much or fast you push it or pull it. Early two-dimensional physicists would be most perplexed by this fact, and they would lack a logical explanation of how this could be, unless there were a very astute and insightful physicist among them, so astute and insightful that he or she recognized just what the speed of light being constant really meant, and so was able to explain why this speed could NEVER be changed by “moving” it (or by moving anyone observing it, either).

By explaining why and how the speed of light never changed, this exceptionally astute and insightful physicist would recognize many things, all of them as a result of realizing just one thing, which is that his or her surface was NOT the sole and only surface, but rather, just one among many other surfaces in his or her universe, all “tilted” uniquely with respect to each and every other surface, each corresponding to a unique motion in this universe. That is to say, that the surface of anything moving would “tilt” into the future in one direction for a surface considering itself not moving, and tilt into the past in the opposite direction for that surface not moving. Such a physicist would have discovered an extremely significant quality of their world. That quality, to be precise, would be the inseparability (i.e. relativity) of time and space with respect to motion. That physicist would have recognized exactly what the great, three-dimensional physicist of our own universe, Albert Einstein, recognized over a century ago.

This remarkable two-dimensional physicist would have discovered the Theory of Special Relativity. With Special Relativity this physicist, or any other, could describe just how another surface tilted, changing when and where events occurred, as a consequence of uniform motion on their or any other observer’s surface-motion that does not change speed or direction. To be precise, Special Relativity explains just how anything and everything in the universe can be both at rest and moving, with respect to anything and everything else in it, at the same time.

That is not all. Most amazingly, a universe of tilting surfaces leads to the most accurate description of gravity ever conceived, as the next edition’s science article will explain. Yes, the speed of light never changing would lead to a description of gravity that has endured for nearly a hundred years, and that is responsible for, among other things, the original television and all successful space exploration.

© 2007, C. Tucker (Chongo). All rights reserved.
(Excerpted from RELATIVITY IN HALF AN HOUR, by Chongo in collaboration with Jose. To see all the books that Chongo has written on the physical theory of nature, go to, which is a web site dedicated to educating those who have the least opportunity for learning the scientific foundations that describe nature accurately. Chongonation provides books that allow such opportunity, in lay terms, without any math. Simply click on either “Nature’ or “Products & Prices’ to see just how many books are available.)