I believe Euclid lived on a flat earth.

The debate of how the world was and looked was long and varied but, my favorite conception of these times is that the earth was a large air bubble half filled with dirt. Not unreasonable given the available information.

It was Euclid who gave us our present and ubiquitous design grid. After examining geometry’s clouds of random weightless, dimensionless points Euclid reasoned it useful to arrange this ethereal population into something an army commander might relate to; rows, columns and finally blocks of straight lines. Neat and logical. Had Euclid more information available at the time he might have chosen differently. It turns out there are no straight lines in the universe and thus infinite planes and flat planets are impossible. Oh well.

Teaching Dilation Strategy to others I have observed an almost universal inclination to refer to dilations as grids. The difference between dilations and grids is important enough to labour a bit. Most certainly dilation strategies are not grid strategies and function more like a “warp engine” than specific increments of divided space extended out on a flat table. Increments, right angles and flatness are not prerequisites but, dilations can when needed supply grids of any desired metric or granule units of any size. Dilation strategy then doesn’t bother to impose organization on space, but rather assumes any given space to be a perfectly acceptable, self organizing, space to design in. Any given space can be self incremented by dilation. The difference then, rather than making designs fit a particular grid, grids, when you want them, are derived for a particular design space.

Dilation strategy doesn’t replace grids but, rather includes them in a different conception of design space and like Euclid’s design space dilation strategy is simple, neat and logical, but far more flexibly inclusive.

Mark Boulton has made some good work on grids avaiable at his site.

Had Euclid spent more time in the Scythian men’s “tent” he may have discovered an arrangement of imaginary points that accorded better with how the universe actually works, saving artists and designers 2000 plus years of monkeying with only partially adequate systems. With a slightly more “laid back” approach he would have deduced the geometry of gravitational fields that eventually upset ” Euclidian Geometry.”

Though, to be fair to Euclid, it was Pythagorus who earlier developed the habit of thinking in grid squares glued on to the outside of things.

1. ) Euclid knew that every triangle, square, rectangle, circle or regular polygon has a center. ( center of gravity )

2. ) Euclid knew: If A. and B. be any two given points, there is one point C. who’s distance from A. and B. is equal. ( i.e. we can divide any line in half. )

3. ) We all know we can divide half a line in half again and again forever. ( or until we hit one of those little points again.)

4 . ) Where ever two lines cross they meet at a point.

Happily, this is all the geometry an artist or designer needs to be a master of any given design space.

This is where we depart from grids for a while. Don’t worry they aren’t lost or anything, but next time we meet them they will have graduated from obedience school.

Time Dilation

We need to go back to 350 BC or so, for a few minutes. Euclid of Alexandria is sitting in his room scribbling up the Elements and we stop in to drop off a diagram. Euclid would likely glance at our diagram for several seconds and ask us to leave, because, he has a whole library of things on his mind and like any designer with cash in the bank, is pretty much a full on workaholic. You see, a dilation diagram doesn’t exactly leap out at you the way a box of Tide does. It doesn’t scream Eureka! In fact, it sort of looks like a spider web with nothing in it. Empty. At first glance, it appears to be the sort of thing a Roman might roll up and use to set fire to something.

Euclid would have and did, like everyone else, fail to notice a very functional constellation of properties.

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