Ice Cream Cone Universe

First, watch this Science Asylum video.

Each dimension is at a right angle to all others, by definition.  Up and down, forward and back, left and right.  These are the three dimensions of space.  Space, as nearly our best measurements can tell, is flat, or circular, or spherical in 3 dimensions.  That means the Pythagorean theorem holds.  A² + B² = C². 

Spacetime, on the other hand, is curved, as our best measurements have shown.  This is because time is hyperbolic.   A² - B² = C².

Circles are where a plane cuts through a cone horizontally.  They are also where a sphere resting inside the cone touches the cone.  Hyperbolas are where a plane cuts the cone vertically.  Vertical is at right angles to horizontal.  (Please note that the diagram below, stolen shamelessly from the internet, has an error.  A parabola is not a vertical slice.  Rather, it is a diagonal slice that exceeds the critical angle, and so isn't an ellipse.  A hyperbola isn't a "deep vertical" slice, whatever that may mean.  It's simply vertical.  Words have meanings.)

And thus, time is at 90 degrees to space.  

When using matrices to formulate spacetime, the three space dimensions are always written with a negative sign.  This is because space goes both ways.  Negative times negative is positive.  The time dimension is always written as a positive number, because time only and always goes forward.  positive times positive is still positive, and there is no way to make it become negative.

The angle of the cone represents the speed of light, the speed of causality.

We live in a sphere resting in a cone.  Our universe, in a very fundamental way, resembles an ice cream cone that never, ever drips down the sides.