Does Einstein's theory of gravity say anything about the direction of space Why is every representation of Einstein's theory of gravity depicted like this:

and not like this:

And many other ways it can be depicted. They suggest that the fabric of space-time is a flat plane
There are numerous ways to try to explain space-time by analogy, and the flat plane is one of them. Another is the inflating balloon. The are all only analogies. Either of your pictures above is equally valid, however the one &quot;the right way up&quot; is simpler to understand.
For humans, who can easily conceive of 3 dimensional space, an example that works in 3D is essential. If you have ever tried to visualise more than 3 space dimensions, you'll find it very tricky.