Æsthetic or Anæsthetic ?

One doesn't normally pair these two words, one normally thought of in terms of art and the other in the world of medicine, but why not? They are after all from the same Greek roots.

Æsthetics is a branch of philosophy dealing with the nature of beauty art, and taste, and with the creation and appreciation of beauty.¹

An Anæsthetic is used to temporarily reduce or take away sensation, usually so that otherwise painful procedures or surgery can be performed.²

By the rules of semantics, those two words should be opposites. But like so much of what passes for art in the later half of the Twentieth Century, much music neither qualifies as beauty nor reducing sensation (at least not on the ears). Perhaps the real desensitization is that of compassion of some for their fellow man? And perhaps that goes hand-in-hand with cacaphony and antisocial lyrics and the general absence of beauty.

¹ Definition 1 of aesthetics from the "Merriam-Webster Dictionary" Online.
² Definition from the NetDoctor.com website.