Still thinking of easier way to explain.
We all understand the best contrast for a black and white negative is half the contrast of reality.
Well, it's closer to 5/8 but easier to imagine half. We want a relatively low contrast negative to print on relatively high contrast paper.
That's the gist of it.
Going back to half. If you develop to half contrast of reality, then giving four times the exposure gives two times the density.
Now the pictures we take tend to have a good portion of their image detail in the straight-line portion of the film's "characteristic curve".
A picture taken with four times the exposure will have all the same relationships between light and dark, they will just be further up the straight line.
If we look at the negatives on a light table and block half the light from under the negative that received proper exposure, it should match a negative next to it that had four times the exposure on the same light table with all the light from the light table coming through.
That's where the 0.30 Neutral Density filter comes in. It blocks half the light.
0.40 Neutral Density filter, we've concluded with a little discussion, blocks the amount of light that would make the two negatives look the same at a higher contrast closer to ASA parameters.
Sound easier to grasp?