Randall Niles uses the famous illustration of a two-dimensional world to show the power of one extra dimension .

As a young child, Michio Kaku spent hours watching carp at the Japanese Tea Garden in San Francisco. He imagined the pond as an entire, two-dimensional universe, where the carp could only swim forwards and backwards, left and right. The concept of up, beyond the lily pads, was totally alien to them. Michio wondered, What if I could reach down and grab a carp and lift him up into my universe? What a wondrous story the carp would tell the others! He would babble on about new laws of physics and unbelieveable creatures that move without fins and breathe without gills. However, without such a visit to the third dimension, how could a thinking carp know anything about the unseen world above? One day it rained, and Michio saw the drops form ripples on the surface of the pond. Then he understood. The carp could see the rippling shadows. The third dimension was invisible to them, but vibrations in this dimension were clearly visible. The ripples might even be felt by the carp, who would invent scientific concepts such as light and gravity to help describe the unseen force. Of course, the other carp in the pond would laugh at the notion, since carp know theres no force at all, just the rippling of the water. Today, Michio Kaku believes we are the carp swimming in our tiny pond, blissfully unaware of invisible …