Helical Flight Logic

Regarding the recent midair collision between a commercial 737 and a Legacy executive jet over Brazil... It struck me that a simple change would greatly reduce the incidence of such events. The 737 was traveling eastbound at 37,000 feet; with modern avionics and GPS, this altitude is maintained almost exactly. (Next time you're on a plane with live flight statistics, note that the altitude is almost always an exact multiple of 1000 feet.) The Legacy was traveling westbound, and theoretically should have been flying at an even-numbered altitude; e.g., 36,000 or 38,000 feet. But transcripts show that it was nevertheless cleared for 37,000 feet, inadvertently putting it on a collision course with the 737 jet.

The quantization of altitude into units of 1000 effectively reduces the usable airspace from 3D to 2D, dramatically increasing the probability of collisions. But there is an easy way to not only reduce the random probability of collision (by allowing the full 3D space to be used), but indeed to lower the risk even further. Consider:

Planes traveling east (0 degrees) should fly at XX,000 feet.
Planes traveling north (90 degrees) should fly at XX,250 feet.
Planes traveling west (180 degrees) should fly at XX,500 feet.
Planes traveling south (270 degrees) shoud fly at XX,750 feet.

Furthermore, this system can be made continuous: planes traveling northeast should fly at XX,125 feet, and so on. It creates a continuous helical pattern, in which aircraft at similar altitudes will always be traveling in similar directions, thus dramatically reducing the chances of collision during the long stretches of flights where altitudes are maintained.

Update: Here's a detailed mathematical analysis of this idea.