Desargue’s Theorem

Desargue's TheoremThe extensions of a triangle’s sides meet the extensions of its shadow’s sides along a single straight line… It always feels like a miracle when it works.
The Shadow Club, Roberto Casati, 2003; p. 186

This drawing illustrates Desargue’s Theorem, invented four centuries ago to help artists. The theorem shows how to construct shadows of solid objects. The blue triangle is the shadow of the red triangle. Light rays are shown in yellow.

Desargue’s Theorem is a technique of perspective drawing used by artists to visualize solid objects on a flat surface.  Perspective drawing projects 3D onto 2D.

Like Desargue four centuries ago, we also face the challenge of projecting higher dimensions onto fewer dimensions – new thoughts onto old. When Einstein published Special Relativity in 1905, Minkowski showed that it meant time was a fourth dimension, intimately connected to our three dimensional world. Our world changed from Space and Time to Space-Time. Physicists have added more dimensions since then – up to 11 now, per latest developments in String Theory.

But that’s just physical space. Today, in social networking space, we talk of "six degrees of connection" between any one person on the planet and any other.

We routinely communicate, daily, with friends and friends of friends by cell phone, texting, email, Facebook, and Twitter. Phones aka mobile devices will soon outpace computers as the one device that everyone has and uses to connect to everyone else.

Today we design and purchase products housed within Digital Virtual Environments such as Second Life, where we have additional projected existences as avatars residing in a cloud computing cyber dimension existing solely on computer servers.

It’s complex but we seem to be keeping up with it. We keep our brains flexible, our minds open, and an eye on practicality.

Alice laughed. "There’s no use trying," she said, "one can’t believe impossible things."  "I daresay you haven’t had much practice," said the Queen. "When I was your age, I always did it for half-an-hour a day." Through the Looking Glass by Lewis Carroll


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