More intuitive spacetime interval

Space is Euclidean.  Spacetime is hyperbolic.  Why?  Because time is imaginary.

From the Wikipedia article on the spacetime interval:

There are two sign conventions in use in the relativity literature:

${\displaystyle {�}^2=(��{)}^2-{�}^2-{�}^2-{�}^2}$

and

${\displaystyle {�}^2=-(��{)}^2+{�}^2+{�}^2+{�}^2}$

Let us take the second convention and rewrite it to a more standard hyperbolic form:

    s2 = x2 + y2 + z2 – (ct)2

But, since time is imaginary, we can rewrite this to the Euclidean (Pythagorean theorem) form:  
    s2 = x2 + y2 + z2 + (cti)2

The result is the same.  The addition of i (the imaginary number, square root of -1), when squared, reverses the sign of the time component.  But this formulation shows exactly what is going on in this distance equation.  The Pythagorean theorem holds in space as well as spacetime, but spacetime is hyperbolic because time is imaginary.

There are no inconsistencies, there are no contradictions.  Every concept is simple, even if the math is complex.  It even helps show that time is at 90 degrees to every space dimension, because the imaginary number line lies at 90 degrees to the real number line.

QED