Thanks, that makes sense given your assumptions and results.

You think it is likely/possible that a nuclear war kills almost everyone in the US and Europe. Since you estimate the chance of this happening to 1 in 6, are you moving to South America or Australia for a year or two? 

With the right prompt, I get the following results for a few examples I tried (first attempts, no cherry-picking).

Input: ( ) ( ( ) )

Output: Balanced

Input: ( ) ( ( )

Output: Unbalanced

Input: ) (

Output: Unbalanced

Input: ( ) ( ) ( )

Output: Balanced

So it is definitely able to learn balancing a small number of parentheses.

The number 0.0000000000000000000000000001 does not tell me much. Numbers in high dimensions are tricky. For example, the volume of a unit sphere decays exponentially with dimension. A unit sphere in dimension 24 has very little volume.

Agreed. The diagram strongly suggests that they do sum to one, so this geometrical method is more confusing than helpful.

Are these misconceptions really common? I thought Kahneman was pretty clear on this in Thinking, Fast and Slow.

It is not a good proxy. Deepmind is a small team and there are many more teams within Alphabet doing machine learning. Remember that the market cap of Goog is $500 billion. (Although if one wants to invest in AI in general I think it is a cheap stock)

I'm convinced that humans must spike their blood sugar and/or pump their body full of stimulants such as caffeine in order to get past the natural tendency to find it unbearably dull to memorize words and syntax by rote and lifeless connection with the structures in their native language.

Just a comment: This is certainly not true for every human. Some people really enjoy that.

I actually think it would work pretty well. The banned user sees all of their contributions and any IP used by the banned user also sees their contributions. All other users and IPs do not see it.