>It looks like the inside of the pan has the same fins, which makes sense otherwise they'd have uneven thicknesses. That would be a serious cleaning issue.
Doesn't look like that at all to me; in fact I think if the inside was finned it would be an immediate no-go for most, for the very reason you've stated.
Given that the company goes to enormous lengths to never show or talk about the inside of the pan, I have to assume this is the Achilles heal. If the fins aren't replicated on the inside, then some areas will be mm from the flame, other areas cms (which, as an aside, means an enormous amount of material per pan) -- aluminum is a decent heat conductor, but that would still be a very bad recipe for cookware.
In addition they would be ridiculously expensive to manufacture if the fins were only on the outside. Normally cookware is made on a lathe (http://youtu.be/8uuFWzkRcAg?t=1m12s) or a press from sheet metal. So, if you have areas that are thicker than others you'd need to use an entirely different method of manufacturing them... like casting or welding on the "fins" after the rest of the pot/pan was shaped.
That reminds me of the guy who tried to protect his fingers from the pedestal grinder by using the sleeve of his hoodie instead of walking 20 feet to the tool room to get some gloves. His sleeve got caught at torn completely off. Fortunately he wasn't hurt and banned from the metal shop.
Might be wrong, but I suspect they don't show the inside because it looks like a normal saucepan and it's the futuristic exterior that likely gets them sales. Just can't see how a saucepan with those fins inside would be at all useful, whether they're far more efficient or not. Couldn't stir a sauce or easily cook pasta, etc?
Doesn't look like that at all to me; in fact I think if the inside was finned it would be an immediate no-go for most, for the very reason you've stated.