Linear Gamma

katheo

I've been reading about raw capture and linear gamma vs. gamma corrected (adobe white paper). I get stuck on understanding why the linear distribution gradient looks the way that it does at the bottom of page 2. The Linear Distribution visually looks like a nonlinear gradient and the Gamma Corrected Distribution looks more linear (I realize that this is why we apply a gamma!). But, why does the Linear Distribution look that way in the first place?

Here is my logic....
I'm imagining the CCD array as an array of light 'buckets'. If you turn the Linear Distribution gradient on it's side with the white on the top, each light bucket would be like a graduated cylinder used for liquids. Some buckets are completely filled with photons (we call this level 4,096). Some are half-filled (we call this level 2,048). And so, on... Why is a half-filled bucket so pale? Where would middle gray appear in the Linear Distribution gradient as a percentile (12-18%?)?

I have a feeling that this has something to do about reflected light and logarithms but I am confused. I thought that the logarithms stemmed from perceptual issues and not actual light quantities (linear raw capture).

Can anyone help me understand this topic?

Thanks!