Is there a method in mnemonics to quickly find out the number of objects in, for example, a heap of tooth picks.
There is this scene in the movie Rain Man, where the autistic protagonist can tell the number of toothpicks at a glance. Is something similar possible for "normal" people with the right kind of training or technique?
The act of perceiving quantity without actually counting is known as subitizing, and it's something we can all do up to quantities of about 4 (i.e. you can tell how many fingers someone is holding up without counting them, right?).
This open access article seems to review the idea quite nicely (although I've only skimmed it), including reference to so called "savants". There's also this paper, claiming that transcranial magnetic stimulation can temporarily induce subitizing abilities for larger numbers in participants, though personally I'm dubious.
Finally, to the best of my knowledge, the original, and definitive account of this ability (on which the scene in Rain Man was apparently based; Kim Peek, the inspiration for most of the film, apparently didn't couldn't, or didn't subitize like this) was by Oliver Sachs, in this wonderful book, but basically summarized in this article. If you really are interested, I can't recommend the book strongly enough, it's the reason I did psychology in the first place. It should probably be noted that I've heard criticisms of Sachs' account of the Twins somewhere, but I can't currently find a reference for them, so I don't think it's universally accepted that anyone can actually do this in reality.
No. This amazing ability is not well explained nowadays and it is a characteristic of individuals usually called the idiot savants. Most of them suffer from autism. One of the explanations is about their extreme attention and memory to details.
This is typical of a group of people that have what is properly known as savant syndrome. It is not limited to autistic people, although it is most prevalent among them. People that display these abilities are usually elevated on the autism scale, and have had some sort of traumatic brain injury or neurodevelopmental disorders.
Unfortunately, the methods by which they appear and function are not understood, although several theories (usually regarding the lower functions of the brain, inaccessible to normal conscious control) have tried to explain it.
The term "idiot savant" was originally used starting in the late 1800s, but isn't used now because not all savants fit the definition of idiot (severe mental retardation). While most savants are limited in scope of ability (i.e. one or two abilities), there have been some with multiple. The character in Rain Man is based on one, Kim Peek.
As far as mnemonics go, there have been many methods developed for being able to do things quickly (such as reading or memorizing items), but none have been able to approach the speed and completeness of a savant's ability.
