If someone were to grab the right and left hand sides of this picture and pull, notice how the image distorts from its original state.
Now, let's squash the poor fish.
Keep in mind that we do not want to tear this image, we just want to distort it. One could easily argue, and be correct that the images above are different in many ways, but the fact remains that they still are fish!
An entire branch of mathematics is
devoted to the ideas mentioned above, and is called Topology. Topology
deals with the ways that surfaces can be twisted, bent, pulled, or otherwise
deformed from one shape to another. A topologist is interested
in the properties that remain unchanged after all these transformations
have taken place.