Perhaps, when one is using a microscope, viewing single-celled organisms, he takes note of the "cell membrane" that each one has. This "outer skin" protects the cell from other cells in this flat, 2-dimensional environment. How "protected", though, would the cell be, from the person viewing, who has access to the sum total of everything inside the "outer skin" - the cell fully unaware of being observed?

The book Flatland deals with little sentient beings - "Flatlanders" - who live in such a "tabletop-like" world. Such a universe would be limited entirely to a mere length and width. What would life in such a world be like? You'll find that no Flatlander possesses a full digestive tract - it would split him into two pieces! In another very similar book, The Planiverse, we find 2-dimensional creatures who cannot 'walk past' another creature they happen to encounter - one must literally "climb over" the other to get to the other side!

Even so, such a creature, like the single-celled organism under the microscope, is limited totally to its 'tabletop', unaware of the space that lies above the tabletop - (the space from which we observe the creature): the 3rd dimension. Could such creatures comprehend the 3rd dimension? Would they require our help? Or could they actually do it 'on their own'? And if they could comprehend the 3rd dimension without our help, just how did they go about 'understanding' something that they can neither sense, nor prove?

-- Introduction continued --

"Thinking 4-d" cannot prove the existence of a fourth spatial dimension, in that the world we experience does not provide the sensory information necessary to do so. Yet all concepts presented in "Thinking 4-d" are spatial. "Thinking 4-d", furthermore, does not claim to present an exact replica of the fourth dimension and its properties, but is merely a system that aids one in understanding the fourth dimension by studying the 3 dimensions that are part of our everyday lives.

What do you think of Thinking 4-D? Do not hesitate to e-mail me at my ALL NEW e-mail account: jsfsite@yahoo.com. Your input will shape the future of Thinking 4-D!