Although the six dimensional space-time invariant interval represents space and time, we do not observe it as 6D. Instead, we observe space and time as 4D in one of two ways.

The full 6D space-time interval expressed in spatial units is:

*s² = Δ***r***² – c²Δ***t***² = **Δr _{1}² + Δr_{2}² + Δr_{3}² – c²Δt_{1}² – c²Δt_{2}² – c²Δt_{3}²*,

which can also be expressed in temporal units as:

*s²/c² = Δ***r***²/c² – Δ***t***² = **Δr _{1}²/c² + Δr_{2}²/c² + Δr_{3}²/c² – Δt_{1}² – Δt_{2}² – Δt_{3}²*.

As we’ve noted *here*, the space and time vectors are the displacement (**r**) and the distimement (**t**).

In practice this interval compresses into either 3D space + 1D time:

*s² = Δ***r***² – c²Δ***t***² = **Δr _{1}² + Δr_{2}² + Δr_{3}² – c²Δ*

**t**

*²*,

or 1D space + 3D time:

*s² = Δ***r***² – c²Δ***t***² = **Δ***r***² – c²Δt _{1}² – c²Δt_{2}² – c²Δt_{3}²*.

This is the pattern we’ve learned over and over: there are two ways to observe the world.

One remarkable thing about this is that *time is a vector*, even if only its magnitude is used (which is the effect of squaring it). Thus to be precise we should define velocity in terms of vectors:

**v** = *Δ***r** / |*Δ***t**|.

Celerity should be defined similarly:

**u** = *Δ***t** / |*Δ***r**|.

Why can’t we observe all 6D of space-time at once? One reason is our need to form ratios of space and time, which requires that we “scalarize” either space or time for the denominator. Another reason is our inability to visualize six dimensions together. Perhaps we could visualize 2D space + 2D time; that would be new.