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A Note on Direction


A ship in motion has a “heading”.

Thus a ship proceeding on a compass heading of 90° (due East) has the same orientation as another ship proceeding on a heading of 270° (due West) , but its motion (a translation) is in the opposite sense.

  • The two ships' courses are parallel, and
  • their orientations are identical, but
  • their translations are opposed

Direction and Sense, though nearly always conflated (as they are in the notion of “heading” and in the definition of a vector*), are not the same thing.

The ships, for example, could change the senses of their translations without altering their directions (they could go astern if going ahead, or go ahead if going astern), and their directions (by rotation) without altering the senses of their translations (they could steer to port or starboard, whether going ahead or astern).


When speaking of direction, a geometer should not speak of a heading, because it is not a heading; it is an orientation. A geometer should, as well, not speak of reversal as, “change of direction”, because it is not such a change; it is change of sense.

Then, when a bud's form alters with it's planet's lunar alignment, it changes with direction, but not with sense, or with distance, the planetary properties that concern that bud seem properly geometric (that is, having only to do with elementary incidence), and not—possibly against expectation—algebraic (or physical, at least in the generally received meaning of that word).

    * A vector is said to have “magnitude and direction”. It is more properly and completely described as having magnitude, direction and sense, or as having magnitude and heading.  

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