Imagine a sphere and a cube.

Scenario 1:

The sphere is heated slowly. The sphere changes temperature. Before heat is applied, it's cold and after it's heated, it becomes hot. How would Heraclitus have described this sphere-heating event? He would've said: the sphere changed from cold to hot. The intriguing aspect of this description is that Hercaltius' description can be rephrased as: The sphere was cold and (now, aftering heating it) the sphere is hot. Notice though that, Heraclitus, despite the fact that he claims the temperatures are different, he's talking about the same sphere.

In other words, the temperature has changed but the sphere is the same.

If so, Hercalitus is right - change occurs (temperatures are different); Parmenides is also right - no change occurs (the sphere is the same sphere). Both are right!

However, if one is to subscribe to the view that both Heraclitus and Parmenides can't be right we would necessarily have to create some form of heirarchy of properties such that an object's essence is defined in terms of one of the possibly many levels in it. For instance, I could say temperature is a secondary property and is of lesser significance than the shape which is a primary property. Thus, we could say that in this scenario there's no change as the sphere remained a sphere and temperature change is inconsequential. On this view Parmenides is right and Heraclitus is wrong.

On the other hand, if every property of an object is equally important, Heraclitus is right - change does occur.

However, Heraclitus faces a problem. As part of his theory that all things change, as can be discerned from his description, there has to be something that doesn't change. In the example above, "...something that doesn't change..." is the sphericity of the sphere. For Heraclitus, there must exist a continuity between two things A and B to make the assertion that A changed into B. What happens if the necessity for some kind of continuity is removed from the conditions that need to be met for change to have to occured. See scenario 2 vide infra.

Secnario 2:

Keep the sphere and the cube side by side. If continuity isn't necessary for change to have occurred, we're fully warranted to say the sphere has changed into a cube. The problem here is that the sphere is, after heating, hot but the cube, spared this mistreatment, is cold and then we would have to say that the same thing is both hot and cold, a contradiction.

Thus, Heraclitus must concede a continuity between something and that thing which it's changed into. What is continuity but just another name for no change?

Since Heraclitus continues to refer to the hot sphere as the same object as the cold sphere, that which doesn't change in the sphere, that which establishes the continuity, is part of the, or is the very quality that defines, the essence of the sphere and let's not forget that the temperature change did nothing to alter the object's essence for precisely the same reason.

In conclusion, Heraclitus is in a bind. He can't talk about change unless he believes/accepts that something doesn't change (the basis for the continuity); also since he refers to both that which was and that which what was becomes as the same thing, it must be that whatever the change that has occurred, it did nothing to alter the essence of that which underwent the change. Basically, Heraclitus, despite being right about change occurring, must agree to an heirarchy of properties, the highest level ones being those that become the basis of the continuity necessary for the concept of change but in doing that he's admitting that change in essences can't occur and that maybe exactly what Parmenides has in mind when he said, "change is impossible."