The distribution of random points on the sphere, that is uniform over its surface has the interesting property that each of its coordinates taken alone is uniform over [-1,1]. Of course, because of the symmetry of the sphere, this is then true for any axis we can orient. Can we make a distribution with this property is R^2, or in general R^n?

Recently I've developed some noticeable tinnitus. I'm pretty sure I've always had some but recently it's gotten way worse. There's not really any proven effective treatment as far as I'm aware.

The issue is that tinnitus isn't the direct result of problems with the ear, it's a central nervous system disorder.

As in, in some fraction of people with hearing loss (I was in concert band for 12 years), two changes in auditory cortex occur: too many neurons get assigned to a single area of the frequency spectrum, and the overall level of circuit inhibition decreases.

It's actually somewhat similar to epilepsy.

Regarding issue (1) there's decent evidence that hearing a given pitch causes more neurons to become responsive to that pitch, giving rise to "notched sound therapy" in which a person listens to sounds/noise/music with the tinnitus frequency cut out, in order to nudge neurons that are receptive to the tinnitus frequency away from that cluster which has formed.

Tonight I'm going out on a limb and trying to listen to a slowly sweeping tone (pure sine wave going from 2500 Hz to 15000 Hz and back over the course of a couple minutes). My idea for this is mainly that I want to have the opposite effect of noise: to try my best to narrow the receptive fields of the neurons.

but that's not the best that can be done... I think it would be more ideal for the pitch to jump around discretely and randomly. And to have the ability to focus on specific pitches while excluding others.

Tinnitus sounds awful. (Pun not originally intended.) Hope you find a solution!

Merry 20's everyone! :D