Electric Geometry

Walking in downtown Toronto yesterday I spotted a police camera hanging on a street corner. They're very easy to spot. I’ve seen them before, and thought about them before, but never considered them in this way . . .

Electricity has brought us post-Euclidean geometry.

Definitions, please . . . 

Euclidean Geometry = 

The ‘standard’ geometry which has been kicking around since Greek mathematician Euclid (who’d have guessed...) developed it. 

Based on a series of simple definitions such as ‘Two parallel lines will never cross,’ he develops the rest of his geometry with postulates, corollaries, definitions and other excitement, all stemming from these definitions in a logical manner only a computer or a savant can really enjoy.

Ultimately, Euclidean geometry—for one reason or another—is what we consider intuitive. It deals well with middle-sized objects at medium distances, and lays the scaffolding for Newton’s universe.

Enter Einstein, enter electricity, enter McLuhan, and goodbye Euclid.

Panopticon = 

A proposed prison design by Jeremy Bentham, late 18th century.

Basic idea is a prison designed in a circle where every cell faces inward. The diameter of the circle might be 30 metres across. All of this middle area is empty, except for a guard tower in
the centre, equipped with shutters. It’s like a bicycle wheel on its side, where the spokes are the lines of sight from guard tower to cell (and vice versa).

The inmates are well aware of the tower’s presence, but due to the shutters they can never see if a guard is watching them, or even on duty. The sense of surveillance is swallowed by the inmates. 

The cameras in major cities form a modern panopticon. That’s why there are signs alerting people of the camera’s presence, and why the cameras themselves are large and extremely visible. 

Consider how small a camera can be, say on your cell phone. Now remember you’re dealing with a police force, who has access to close to the cutting edge of surveillance technology. You know that if their priority was watching you, they could hide cameras anywhere and your every step would be monitored.

But who would watch the feeds from all these cameras? They’d be useless unless your city’s police hired hundreds or thousands of new employees. Not to mention all the extra cops as well, who would have to be dispatched to deal with every single infraction.

Instead, the idea is to make a giant, visible camera that—more than anything else—makes you aware you’re being watched. So nobody has to watch the feeds. For all you know, there aren’t even cameras in those boxes. The end result (hopefully): less crime.

Now for some geometry . . . 

Bentham’s Panopticon was a circle. 

Euclid, Book I, Def. 15 & 16 (paraphrased): A circle is a 2-dimensional shape. Every line drawn from its centre to its perimeter will be equal in length (aka, ‘radius’).

Of course, in a pre-electric world surveillance required a line of sight. 

Review of light: Light travels quickly. Light travels in straight lines. You can’t see around corners, over hills, or through other objects. That’s why Bentham’s Panopticon (Pan=all / Optic=sight) works. Euclid’s straight lines from the centre to the perimeter, or the perimeter to the centre (as it works in practice) are lines of surveillance.

Thank you Euclid.

Enter electricity. All bets are off.

Review of electricity: Electricity travels quickly. Electricity does not necessarily travel in straight lines. You can not only see around corners and over hills, but even the entire planet from distant satellites.

Goodbye line-of-sight, goodbye circle.

In a modern, electrified city, the panopticon is now distributed throughout. This gives a hint as to the direction of modern geometry. In some way, Euclid’s circle is still involved. Look back at the definition and see that ‘every line drawn from its centre to its perimeter will be equal in length. If we measure length in time, there’s no difference between a camera capturing something 12 metres or 12 thousand kilometres away. The hub to where these feeds all return is the ‘centre of the circle’.

But this is some rickety wheel. Good luck driving your wagon on it. One of the perimeter points is down the block, the other is on the other side of the city, and the hub doesn’t even have to be in the physical centre. Luckily, we’re not merchants selling beans at market. Those wagons—which previously connected us to others—use Euclidean wheels, and our new wagons (hint: the thing you’re using to read this) can use the post-Euclidean geometry I’m describing. 

What does this post-Euclidean circle look like?

I’m sorry, friend, but your question is misguided. If I could easily show you, then I’d be using Euclidean geometry. 

But this much we can say. The two shapes share an essential feature. Something which made a circle what it was—having equal lines from centre to perimeter is preserved in our electric circle. 

Make sense? I didn’t think so.

Here’s what keeps me up at night. Sometimes I think that as confusing as this geometry is to us, Euclid’s geometry may have been to people in his own time. It shows how differently we experience the world. That’s right, friends. People haven’t always thought of circles and cubes in the same ways we do. 

Having electricity helps us understand old geometry in a way nobody else could have ever. But because we understand it, it’s no longer so relevant.

Such is the price of knowledge.

Read on...

 Euclid’s Elements: http://aleph0.clarku.edu/~djoyce/java/elements/toc.html