Where in the article did you read anything suggesting that "They took the distance to the border (white matter) of all the points in a region."? I read the article, but didn't find anything like that.
You quoted it (I guess besides white matter it could also be just to the pia):
>"for each gray matter voxel we computed the distance to the closest non-gray matter voxel."
I do admit that whatever they did is difficult to follow without seeing images of the transform etc (and figure 1 does not help), but the idea they are somehow measuring density seems impossible to me.
Within a given region, if there is more gray matter, and it is more clumped together, then the distance to nearest non-gray matter will be larger on average. This is what the authors call thickness.
The gray/white/pial matter is not randomly distributed in the tissue so that there would be more or less clumping of gray matter.
I thought maybe you had some expertise regarding how they processed the data that could somehow make this (extremely strange thing) happen, but you have not demonstrated it. I guess I do not know for sure what they did without seeing the code, but if that is what they measured it is the most bizarre thing I have heard of when it comes to analyzing MRI data.
No one in this thread, or in the article, has claimed that gray matter is randomly distributed.
Regarding your comment about how incompetent I am, and how extremely strange this MRI analysis is:
Measuring cortical thickness by MRI is a standard technique in neuroanatomy since 15 years ago. And really, a quick search of the literature would have shown you this. But I suppose that's too much to ask.
>"No one in this thread, or in the article, has claimed that gray matter is randomly distributed."
I simply cannot imagine what you think is going on in order for them to be looking at "clumping" of gray matter as a proxy for density of the tissue via MRI and calling this "thickness".
>"Regarding your comment about how incompetent I am, and how extremely strange this MRI analysis is"
I thought perhaps you knew some technical detail about their analysis pipeline, but you still haven't mentioned anything technical... so I just don't have any idea what you are thinking.
>"Measuring cortical thickness by MRI is a standard technique in neuroanatomy since 15 years ago."
Sure, here is the first article I found regarding "cortical thickness":
Like I already told you, in order to fix your ignorance of how researchers use jargon, you can go through the literature. I'm sorry, but I'm not here to teach you these things, and it's not really my concern whether you're informed or not. I can recommend using Google Scholar as a starting point if you'd actually (surprisingly) be interested in educating yourself.