SpaceTimeLand

What is reality? Is the physical reality we see around us all there is?

Most scientists insist that there is nothing but the physical, material universe. They reject any talk of a reality that can’t be measured empirically with scientific instruments. If it can’t be measured, it doesn’t exist.

Lately it has become popular in science to talk of a multi-dimensional reality beyond the four-dimensional universe (space plus time) we’re all familiar with. For example, string theory, a branch of physics, posits ten or eleven dimensions of spacetime (or twenty-six or…). The books I’ve read about string theory (The Hidden Reality and Hyperspace) explain that the reason we can’t perceive these other dimensions of reality is because they are really really small—the theory says these other dimensions must be “curled up” into some tiny space smaller than our measuring devices can detect. (See this Nova article or this short essay by the author of Hyperspace, Dr. Michio Kaku)

People who are spiritually inclined talk about angels or higher beings that exist on another plane of existence. Others talk about higher levels or dimensions of consciousness. There seems to be a common attitude among spiritual seekers that the physical reality we live in is an illusion or dream, and that the spiritual realm or higher dimensions are reality.

I think these views about reality are mistaken, and there’s a fabulous allegory called Flatland: A Romance of Many Dimensions that explains why I believe this. Flatland, by Edwin Abbott, is a short novel published in 1884. Mr. Abbott provides a very useful way to imagine how other dimensions can exist by creating a two-dimensional society called “Flatland.” [Read the full book online, see Carl Sagan discuss it.]

The creatures in Flatland live only in two dimensions of space, like the surface of a piece of paper. Their entire universe is in that flat surface. Flatlanders are two-dimensional shapes: circles, squares, triangles, etc. One of the Flatlanders travels to a new world where there is only one dimension—all the creatures are straight lines—and he sees how these Linelanders can’t comprehend him because they only see a one-dimensional “slice” of his shape. They see his movements as magic. This experience allows Flatlander to see that a great mystery in his own life can be explained by the addition of a third dimension to space. Flatlander has met a SpaceTimeLander (my name for the creature), a three-dimensional person, who performs what appear—to Flatlander—to be miracles.

In order to understand Flatland, it might be helpful to do a little experimenting. First, let’s get comfortable with what life as a two-dimensional creature would be like. In the photos below, the square of cardboard is Flatland, and the triangle and circle are Flatland residents.

The first issue to grasp is that Flatlanders can’t see their two-dimensional shape. Circle does not see Triangle’s shape the way we do. The Flatlanders’ view of life is completely from within the flat plane, they see each other only as lines of varying length, with subtle shadings that they learn to interpret to get some sense of the two-dimensional shape. In the same way we don’t see another person’s body in three dimensions. We see two-dimensional surfaces and intuit the rest. We can’t see a three-dimensional object fully and all at once, in the sense we see a circle fully and all at once.

In the next photo you can see the view a Flatlander would have. Circle and Triangle are side by side. Can you tell which is which?

Because the Flatlanders are flat, they are completely flush with the two-dimensional plane of their world. They wouldn’t stick up into the air, which is the third dimension, at all, but for the purposes of demonstration we need to have a little dimension for us to see what’s going on.

Here’s the top view, without having rearranged the shapes:

If you look again at the Flatland view, you can see that with practice you’d be able to intuit differences in shapes by the way light fell on their lines. A Flatlander would have some concept that the circle and triangle were different, but their perception of their “actual” shapes would be limited.

Here’s a photo of Triangle in a cage. From the Flatlander’s perspective, there’s no way out, because in the flat plane all sides are enclosed:

But from a SpaceTimeLander’s perspective it’s easy to break Triangle out of the cage: we just lift him out. But—from Circle’s perspective, when a SpaceTimeLander lifted Triangle up out of the cage, Triangle would disappear for a time, then magically reappear the moment he re-entered the flat plane.

Imagine doing surgery on our Flatlanders. Say that that raspberry is causing Circle trouble. A 3D SpaceTimeLander would be able to reach into Circle and operate on the raspberry or even remove it without cutting into the “outside skin” of her 2D body (the line of the circle) because he’d be entering from the third dimension.

There are quite a few unanswered questions in physics. For example, there is the puzzling finding that subatomic particles, once separated, are still somehow linked. This is called “quantum entanglement.” In addition, experiments seem to show that subatomic particles blink in and out of physical existence. There are still no explanations of these phenomena within our 4D reality.

We can use Flatland to visualize an answer to these questions. First, cut a piece of plastic out of a milk jug or the top of a container, any shape you like. Fill a bowl halfway with water, and drop the plastic on the water so it floats. The plastic is your Flatlander, and the surface of the water is Flatland.

Now stick your thumb and finger into the water, separated by a couple of inches. 

Move your thumb and finger together, then apart. Imagine what Flatlander would think about the movement: “There are two lines (because all he can perceive is the cross-section of your thumb and finger that are in his flat plane) moving in a coordinated fashion even though there is no apparent connection between them.” If he’s scientific he’ll try and come up with a theory; a causal link to explain the coordination.

Now point your index finger and dip it repeatedly into the water, lifting it out of the water each time. What would Flatlander make of this? “A line magically appears and disappears.”

Try a third trick: stick your first and second fingers into the water joined together, now move them apart to form an inverted V. Flatlander will think, “a line has split into two separate lines that are moving apart and yet are still somehow communicating.”

What you can see from this experiment is that the world of three-dimensional space would not be perceivable to Flatlander, even though he is living within it. But, unlike what string theory proposes, the third dimension of space is not “curled up” in some tiny space. It is as full and complete as the two dimensions a Flatlander can experience.

Also, unlike what some spiritual people believe, the fact of the third dimension does not in any way invalidate the reality of the two dimensions of Flatland; it’s not an illusion. What’s revealed is that the two-dimensional world is just a limited perspective of reality.

In the novel, Flatlander can’t see the third-dimension because his world-view, which insists there are only two dimensions, screens it out of his consciousness. When he is somehow opened up to the existence of the third-dimension, then it is there to experience just as big and full as the two dimensions he had known before. 

I believe it is possible that other dimensions are around us right now, as full and big as the four that we know. Some scientists don’t seem to realize that sometimes when you can’t measure something, it’s not that it doesn’t exist or that it is really really small, sometimes it means that you are asking the wrong questions or using the wrong equipment.

Maybe we’re only seeing a tiny part of the whole picture. Imagine our four-dimensional physical reality as a slice of the full, complete reality, like an MRI slice is a two-dimensional image of a three-dimensional brain.

When you’re only seeing a limited part of reality you will draw incorrect conclusions and will be confused about what you’re seeing. But it doesn’t mean what you’re seeing isn’t real.

There are lots of examples of how a limited understanding of physical reality led scientists to some strange conclusions. One of my favorites is the Ptolemaic theory of planetary motion. Ptolemy lived in about 140 AD. At that time everyone “knew” that the earth was stationary at the center of the universe and everything revolved around us. In addition, Plato had asserted that the celestial bodies moved in perfect circles; this was also “reality.” But there was a problem—the stars moved in stately circles but the planets (“planet” means wanderer in Greek) traveled all over the sky. So Ptolemy came up with a theory that explained the seeming anomaly: the planets moved in circles within circles. (Watch an animation of this theory.) For 1500 years this theory was accepted as truth because it could predict a planet’s future position very precisely. As new observations were made that seemed to call the theory into question, astronomers simply added more circles to the planets’ path. Then Copernicus had the insight that the earth revolved around the Sun and the whole theory was thrown out.

The Copernican Revolution can be thought of as a movement into a higher-dimensional reality. When humans believed Earth was the center of the universe, they perceived everything in the sky as decoration on a circular dome overhead. There was no dimension to it; it was flat. (See this illustration) What Copernicus did was open up a third-dimension in the sky.  All of a sudden the sky wasn’t a comfortable ceiling overhead, but a disconcerting open space through which we were moving. No wonder people of the time found it disturbing, and the Catholic Church rejected it as heresy.

What Flatland allows us to see is that, if it is true we are only seeing a four-dimensional slice of a larger reality, we will misinterpret objects and events. Unfortunately, our minds may never be able to perceive this larger reality directly, because we have been evolved to think in a four-dimensional world (see Language is a Window into Human Nature).

Maybe the higher dimension that spiritual people talk about isn’t some place foreign to the physical world; maybe it’s here and now surrounding us if we just had the eyes to see. That multi-dimensional reality includes our 4-dimensional realm. That means the physical realm is not an illusion, it is real; it’s just a limited part of the whole.