Have you ever considered how a four-dimensional being wouldappear to you if it suddenly came into your room?I think they would resemble flesh-colored balloons constantlychanging in size. We would see disconnected blobs of flesh, some attached toclaws, teeth, lips, eyes, or hair.Let me tell you why.
Think of it this way. Consider a two-dimensional world resemblinga sheet of paper. How would you appear to the inhabitants of such aworld if you tried to interact with with them? The 2-D creatureswould only see cross-sections of you as you intersected theiruniverse. Your finger would look like a flat disc that grew in sizeas you pushed it through their world. Your five fingers might lookedlike five separate circles. They would just see irregular shapes withskin boundaries as you entered their world. Similarly, a hyperbeingwho lived in the fourth dimension would have a cross-section in ourspace that looked liked a bunch of skin blobs.
A 4-D being would be a god to us. It would see everything in ourworld. It could even look inside your stomach and remove yourbreakfast without cutting through your skin, just like you couldremove 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. Thehyperbeing can also see inside any 3-D object or life form, and ifnecessary remove anything from inside. The being can look inside ourintestines, or remove a tumor from our brain without ever cuttingthrough the skin. A pair of gloves can be easily transformed into twoleft or two right gloves. And 3-D knots fall apart in the hands of ahyperbeing, much as a 2-D knot (a loop of string lying on a plane) caneasily be undone by a 3-D being simply by lifting the end of the loopup into the third dimension.
What Do You Think?
Find out all about the fourth dimension in my bookSurfing Through Hyperspace:Understanding Higher Universes in Six Easy Lessons (OxfordUniversity Press).Click herefor 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 dimensionlook like to us? Would these beings have teeth? If these beingsevolved just like us, how would they look to us? Would they haveinternal 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 allwith a 4-D extraterrestrial?
4. As a consequence of their access to a fourth dimension, whatpowers would seemingly amazing powers would they have? What wouldtheir sex acts be like? How might they think and act? How might wesearch 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 tohide. Certainly if such a being was observed in biblical times, Hewould be considered a God with many characteristics of omniscience,omnipresence, omnipotence. How would an encounter today affect ourworld 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? Wedon'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 orthemselves...
Some Random Thoughts
Is it hard to imagine a universe with four dimensionsin which we are constrained to 3 dimensions? Could there be somemechanism constraining us -- such as being stuck to a surface viaadsorption? If we were stuck to some surface in this manner, thenthe way free 4-D beings could interact with us would be constrained bythat surface.In our 3-D world, evolutionary mechanisms made us evolve intotubes. The earliest multi-celled sea creatures were tubes that couldpump water through and pick up nutrients from the water as it went by.As life evolved, the primary structural differences involved thecomplexity 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 abaglike form increases dramatically compared to 3-D forms. Heatdissipation and movement of nutrients and oxygen (most of the bloodvessels uniformly distributed through the bag will be close to thesurface too) may be strongly affected by the proximity of the volumeto surface. How would this affect theevolution of life?Would primitive 4-D beings may evolve so that they digest onthe outer surface, with other organs, like brains and hearts notinvolved with nutrient an oxygen acquisition, deep inside? Theouter surface would be digestive and pulmonary, and contain senseorgans and orifices for excretion and sex. Is this tendency morelikely as the dimension of the space increased?
Here is why the volume of a 4-D animal is more concentrated near thesurface than 3-D animal volumes. Consider a D-dimensionalsphere. 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 verysmall, 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 thesurface. Particularly, if you have a 10-dimensional sphere, thenabout 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 ofthe surface. In a 3D sphere, this is 27%. For that D=10 sphere, thefraction within 0.1R is 65%.
Klein Bottle
Banchoff Klein Bottle
BlackHole 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 iPadapp for manipulating 4-D objects.
Return to Cliff Pickover's home page which includes the Wishing Projectcataloging wishes from various cultures,computer art, educational puzzles,fractals, virtual caverns, JAVA/VRML, alien creatures, black holeartwork, and animations.