Figure 1.1   The Map of Physics – Image by Dominic Walliman


Direction (or orientation) is a component of space.  No one seems to disagree with this arrangement.  There doesn’t seem to be any authoritative source on whether direction is a property, quality, quantity, attribute, parameter, constant, or whatever.  Some experts claim that it’s a thing that isn’t a thing.  Additional perspective about this thing can be realized through the use of this geometric approach. It doesn’t appear to change anything that is already known regarding Euclidean 3-space, except for around the extremely remote edges where we get very near to the chasm of ignorance.

It may seem that some of the ideas have been overblown, or overthought, or over-complicated, in some misguided attempt to exaggerate the significance of the concepts.  Some experts have claimed that the approach is either too trivial or too tedious to try and understand.  Sadly, at the time of this publication there doesn’t seem to be anyone outside our group that takes this material seriously.

All we can ask of the skeptics is that they do the math.   The implications of the math itself are what are being discussed here.  The math is mostly trigonometry and algebra,  and although the underpinnings are fairly straightforward, the insights that are gained can be extremely subtle and at the same time extremely significant.