There are definitely cases where there is little hope of proving “100% intended performance”. For example, RSA only works as intended if factoring is hard. Most computer scientists strongly believe this is true, but this is not likely to be proven any time soon.
sludgepuddle
Karma: 82
Low dose ketamine has been shown to promote synaptogenesis in the prefrontal cortex. (in rats) Link to abstract
It is currently being investigated as a potential antidepressant in humans, but based on anecdotal evidence, it seems likely that it’s also a nootropic.
Alexander Grothendieck used the analogy of opening a nut to illuminate two different styles of doing mathematics. One way is to strike the nut repeatedly with a hammer and chisel.
I can illustrate the second approach with the same image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible through weeks and months—when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado!
I am extremely poor at visualization, can’t even picture a line or a circle (I just tried it) and I don’t remember images from my dreams. Strangely, when I was a child, I was sometimes able to visualize, but only with extreme effort. More recently, I have experienced what I would call “brain movies”, involuntary realistic visualizations, under the influence of opiates.
It seems I am fundamentally capable of visual thinking, but my brain is just not in the habit, though I wouldn’t mind being able to summon the ability. It sounds kinda cool.