[MV=PY]

"Can anyone explain to me how there can be a non-integer number of dimensions?"

Google "fractals."

How long, exactly, is a shoreline?

[disndat]

Twice as long as a byline.

A longshoreman told me it was so.

[who_would_fardels_bear]

With fractals, mathematicians seem to have come up with an idea that allows them to assign a more meaningful number to some physical phenomenon such as the total length of a coastline.

However it doesn't constitute something like a partial dimension in an orthogonal direction like the full x, y, and z dimensions of 3-space.

This seems like a similar case to what happens with infinite sums and String Theory:

Mathematically you can arrange for 1 + 2 + 3 + 4 + ... = -1/12

Physically you can use that "equality" to determine the number of curved dimensions in String Theory.

Because the crazy math seems to have an analog in crazy physics then somehow they both must be right.

So because some fun math with fractals can be analogized with the dense plasma soon after the Big Bang we can supposedly talk about fractional dimensions without giggling.

Two insanities don't constitute sanity. This seems like another case of "Just shut up and do the math," i.e. physics isn't telling us what there is out there in the real world, it is merely telling us what math equations we can write out to predict what mathematical values we will see when we conduct certain experiments.

[Pecos]

Obviously, the shoreline is just long enough to reach from port to port, after which it becomes a collection of piers, before turning into shoreline again.

[Yes, I do understand fractals.]