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Introduction - a little geometry

In the comfortable Euclidean geometry seen on billions of video displays two parallel straight lines can be described as

ax + by + c1 = 0 and ax + by + c2 = 0

and the distance between the two lines can be calculated as

|c1 - c2 | / √ (a2 + b2)

In the comfortable Euclidean geometry seen on billions of video displays two parallel straight lines can be described as

ax + by + c1 = 0 and ax + by + c2 = 0

and the distance between the two lines can be calculated as

|c1 - c2 | / √ (a2 + b2)

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In an infinite Euclidean geometry two straight lines are either parallel or they eventually intersect. It has always been simple to draw crisp horizontal and vertical lines. As pixels have gotten more numerous and smaller, and as screen real estate has increased it has gotten somewhat easier for viewers to visually distinguish that a programmer really meant to depict a straight line. It has also become less difficult to determine if lines are truly parallel or merely quasi-parallel, meaning that their intersection is well beyond the visible area.

In many non-Euclidean geometries lines become geodesics, and these can either intersect; be parallel (so they intersect at infinity); or be ultra-parallel (do not intersect event at infinity).

As program construction shifts away from simple linear models using one thread on one core it is useful to keep non-Euclidean geometries in mind as the programmer navigates among different execution acceleration strategies. Similarly, as national strategies shift from what is best for one's tribe to how an entire economic ecology interacts, more is expected of political leaders. Astute readers will discern that

Black Swan events like major earthquakes are thankfully rare, and are, despite our efforts, very difficult to predict. Nevertheless, leaders must at least plan for them.

In many non-Euclidean geometries lines become geodesics, and these can either intersect; be parallel (so they intersect at infinity); or be ultra-parallel (do not intersect event at infinity).

As program construction shifts away from simple linear models using one thread on one core it is useful to keep non-Euclidean geometries in mind as the programmer navigates among different execution acceleration strategies. Similarly, as national strategies shift from what is best for one's tribe to how an entire economic ecology interacts, more is expected of political leaders. Astute readers will discern that

Black Swan events like major earthquakes are thankfully rare, and are, despite our efforts, very difficult to predict. Nevertheless, leaders must at least plan for them.