is rescued by clearly defining what we are talking about and sticking to that definition thoughout the discussion.
Now, the concept of dimension
requires that we have a particular space
If we involve time
in a discussion about points in space
we are mentally constructing a spacetime
, which is a type of four-dimensional space
. "Instanton"s, which physicists
s, are 0-dimensional points in that space.
So what about a "point" that "exists through time"? Well, we have to define "existence through time". Now, our own stream of consciousness
gives us a convenient way to order
three-dimensional slices of our spacetime. We identify events from one slice with events from the slices that come before or after it.
In our minds, we are imposing an equivalence relation
on our abstract spacetime. What we think of as a "point through time" is really one of the equivalence class
es, turned into a space by our ordering.
We can talk about the spacetime itself, in which case each event is a 0-dimensional object and each "point through time" is a one-dimensional
We can talk about a single slice through spacetime, in which case events are still 0-dimensional points, but "time" and thus "existence through time" has no meaning.
We can discuss an identification space
constructed from all of the "points through time", which revert to being our familiar 0-dimensional objects. But then, events are not elements of that space and cannot enter the discussion.
Of course, we could confuse our models with each other, and come up with a "dimension" for an event in our identification space. Unfortunately, if we do that, we stretch our definition of "space", upon which we have relied up to this point, into something we can't rely upon. So there isn't really such a thing as a "-1 dimension", since we don't have a model containing an object that might possess such a thing.