The Fourth Dimension by Cliff Pickover

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Have you ever considered how a four-dimensional being would appear to you if it suddenly came into your room?

I think they would resemble flesh-colored balloons constantly changing in size. We would see disconnected blobs of flesh, some attached to claws, teeth, lips, eyes, or hair. Let me tell you why.

Think of it this way. Consider a two-dimensional world resembling a sheet of paper. How would you appear to the inhabitants of such a world if you tried to interact with with them? The 2-D creatures would only see cross-sections of you as you intersected their universe. Your finger would look like a flat disc that grew in size as you pushed it through their world. Your five fingers might looked like five separate circles. They would just see irregular shapes with skin boundaries as you entered their world. Similarly, a hyperbeing who lived in the fourth dimension would have a cross-section in our space that looked liked a bunch of skin blobs.

A 4-D being would be a god to us. It would see everything in our world. It could even look inside your stomach and remove your breakfast without cutting through your skin, just like you could remove a dot inside a circle by moving it up into the third dimension, perpendicular to the circle, without breaking the circle.

A hyperbeing can effortlessly remove things before your very eyes, giving you the impression that the objects simply disappeared. The hyperbeing can also see inside any 3-D object or life form, and if necessary remove anything from inside. The being can look inside our intestines, or remove a tumor from our brain without ever cutting through the skin. A pair of gloves can be easily transformed into two left or two right gloves. And 3-D knots fall apart in the hands of a hyperbeing, much as a 2-D knot (a loop of string lying on a plane) can easily be undone by a 3-D being simply by lifting the end of the loop up into the third dimension.

What Do You Think?

Find out all about the fourth dimension in my book Surfing Through Hyperspace: Understanding Higher Universes in Six Easy Lessons (Oxford University Press).

Click here for more information on this book. In the book, I answer such questions as:

1. What would a being who could move in the fourth spatial dimension look like to us? Would these beings have teeth? If these beings evolved just like us, how would they look to us? Would they have internal organs like our own?

2. Would the beings look liked bags of skin or be more exotic?

3. What are the chances that we could learn to communicate at all with a 4-D extraterrestrial?

4. As a consequence of their access to a fourth dimension, what powers would seemingly amazing powers would they have? What would their sex acts be like? How might they think and act? How might we search for them?

5. If we encountered them, we would find they can perform levitation, bloodless surgery, disappear in front of our eyes, walk through walls. Nothing would be hidden from them, no matter how hard we tried to hide. Certainly if such a being was observed in biblical times, He would be considered a God with many characteristics of omniscience, omnipresence, omnipotence. How would an encounter today affect our world and religion? What is the religious significance?

6. Could God be a four-dimensional being?

7. Would we be able to hear the speech of a 4-D being inches away in the fourth dimension? How would sound work? What would the being sound like using 4-D vocal cords? What happens to photons in four dimesions? For example, how do 4-D beings see? We don't seem to be "losing" photons into the fourth dimension, so I'm not clear how 4-D creatures would use them to see us or themselves...

Some Random Thoughts

Is it hard to imagine a universe with four dimensions in which we are constrained to 3 dimensions? Could there be some mechanism constraining us -- such as being stuck to a surface via adsorption? If we were stuck to some surface in this manner, then the way free 4-D beings could interact with us would be constrained by that surface.

In our 3-D world, evolutionary mechanisms made us evolve into tubes. The earliest multi-celled sea creatures were tubes that could pump water through and pick up nutrients from the water as it went by. As life evolved, the primary structural differences involved the complexity of organs attached to the tube. We are still just tubes, but we carry a lot of that ancient sea around with us in the "inside" of a bag.

In higher dimensions, the fraction of volume near the surface of a baglike form increases dramatically compared to 3-D forms. Heat dissipation and movement of nutrients and oxygen (most of the blood vessels uniformly distributed through the bag will be close to the surface too) may be strongly affected by the proximity of the volume to surface. How would this affect the evolution of life? Would primitive 4-D beings may evolve so that they digest on the outer surface, with other organs, like brains and hearts not involved with nutrient an oxygen acquisition, deep inside? The outer surface would be digestive and pulmonary, and contain sense organs and orifices for excretion and sex. Is this tendency more likely as the dimension of the space increased?

Here is why the volume of a 4-D animal is more concentrated near the surface than 3-D animal volumes. Consider a D-dimensional sphere. The volume is

V(R) = S(D)*R**D / D.

where S is the solid angle in dimension D, and R the radius.

If you compare two spheres of radius 1 and 1 - a, where a is very small, the difference is

(V(1) - V(1 - a)) / V(1) = 1 - (1 - a)**D.

This is essentially the fraction of the volume within 1-a of the surface. Particularly, if you have a 10-dimensional sphere, then about 40% of the volume is within 0.05 R of the surface (a = 0.05). In a 4 dimensional sphere, about 34% of the volume is within 0.1R of the surface. In a 3D sphere, this is 27%. For that D=10 sphere, the fraction within 0.1R is 65%.

Here are some of my own images dealing with higher dimensions and spatial warps. Enjoy.

Klein Bottle
Banchoff Klein Bottle
Black Hole Embedding Diagram Showing Space Warpage
Gravitational Ripples Produced by Two Black Holes
Quantum Foam Embedding Diagram
Worm Hole Embedding Diagram

Explore the fourth dimension on your iPad or iPhone! Visit FourDimensionalApp for a cool iPad app for manipulating 4-D objects.

Return to Cliff Pickover's home page which includes the Wishing Project cataloging wishes from various cultures, computer art, educational puzzles, fractals, virtual caverns, JAVA/VRML, alien creatures, black hole artwork, and animations.