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Comment by Jun8 | Hacker News Reader

Naming time the "fourth dimension" is a misnomer, it's not a dimension in the usual sense of the. Hence the spacetime of relativity, formulated in Minkowski space, is different than standard 4-ED Euclidean space (see http://en.wikipedia.org/wiki/Minkowski_space).

As Einstein says, "Make things as simple as possible, but not any simpler." The time as fourth dimension thing, I think, is an example of a wrong analogy pushed to make it easy for people to understand what in effect is quite hard to grasp.

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I always understood a dimension as "a variable that you can change to avoid occupying the spot." In 3d space, two objects cannot be in the same spot so either their x,y, or z coordinate must be different. If I add time as a fourth dimension then two objects can be at the same x,y and z, but not at the same time. You are right that time is a special dimension, but there are many things it has in common with the 3 spacial dimensions as well, my example being one.

I've always heard dimensions being referred to as "timelike" or "spacelike", similar in vein (though not in concept) to the difference between "flat" and "rolled up" dimensions.

You're right, in an intuitive sense. In math, especially dealing with weird stuff like extra dimensions, intuition may break down, though. For example, in the 4D Minkowski space you can have a unit sphere with a radius of -1! One has to understand what is meant when we say that "time is a special dimension". otherwise teh analogies we draw may fail. The Wikipedia article I linked explains these in a simple way.

They said "4th dimension", not "4th Euclidean dimension" so I don't see that there was anything incorrect there.

While you're right that it's not a dimension in the sense that most people are used to, I think that it appropriately conveys the fact that time and space are intertwined. When you start traveling very quickly your sense of distance and time change in a way that is exactly proportional to each other. The fact that space and time need to be treated as a single entity was in fact one of the key conceptual advances that Einstein made.

-1 (if I in fact had the points to do it), for assuming that changing the metric space obviates calling a dimension a dimension.

Of course it doesn't :-) However, I wonder how many people reading this article in the Guardian know about different metric spaces. Hawking's presumed audience here is "laymen".

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