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So it's your position in space (3 numbers), your orientation (another 3 number vector), except instead of 6 numbers it can be reduced to 4? Stargate was wrong?

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Encoding your whole orientation would require 3 numbers. You are restricted only to the horizon, so one number is enough.

Orientation is only two numbers, since a unit vector does the job? So, three numbers in total?

That's why it doesn't encode free orientation.

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