Could A Real-life Version of "Rain Man" Count 246 Toothpicks At A Glance

A Real Life Rainman

In the 1987 movie “Rain Man,” a waitress in a diner brings a box of toothpicks to the table and accidentally spills them on the floor. Raymond Babbit, a savant played by Dustin Hoffman, studies them on the floor and instantly calculates the number: “246 toothpicks.”

Dustin Hoffman (L) as Rain Man, inspired by Kim Peeks (R) 

His cocksure, manipulative brother Charlie (played by Tom Cruise) asks the waitress how many toothpicks the box holds. When she tells him 250, Charlie—skeptical of his brother's quirky certainty—says a bit triumphantly, “Pretty close, Ray.”

But as he walks away, the waitress calls after him, “There's four left in the box.” [Psychiatric News, March 5, 2010].

Is such a feat within the capacity of the human mind? The Rain Man scene is fictitious but was inspired by a real-life person, Kim Peek, a savant with unimaginable mental abilities despite his measured IQ of 87. The ability to know the numerical quantity of a collection of objects without counting them is called subitizing. Most humans do not need to count 4 objects on display, they instantly know the quantity at a glance. Beyond 4 objects, the frequency of errors increases rapidly. Humans solved this deficiency by enumerating (counting) which has no limit but requires time and attention roughly proportionate to the number of objects.

Subitizing is not confined to humans. For example, bees don't enumerate but do subitize quantities up to 3 or 4 as demonstrated by navigating a simple maze by following the one unique path marked by the same number of objects as that posted at the entrance of the maze (article).

Some savants are able to spontaneously estimate the number of objects in a large group but even Kim Peek could not reliably estimate 246 toothpicks scattered on the floor. Autistic savant twins, John and Michael" saw a box of matches spill on the floor and simultaneously said "one hundred eleven" followed by "thirty-seven". When the matches were counted, there were exactly 111 scattered about (I suspect this event inspired the toothpick scene in Rain Man). When asked about 37, they smiled and said in unison "37, 37, 37, 111". They "saw" that 111 could be factored into three groups of 37.

The ability to factor numbers was even more evident in a game they were observed playing as adults. One day the twins were taking turns calling out numbers and smiling. "All the numbers, the six-figure numbers, which the twins had exchanged, were primes - i.e., numbers that could be evenly divided by no other whole number than itself or one. Had they somehow seen or possessed such a book as mine - or were they, in some unimaginable way, themselves 'seeing' primes, in somewhat the same way as they had 'seen' 111-ness or triple 37-ness? Certainly, they could not be calculating them - they could calculate nothing." (excerpt from Chapter 23 of Oliver Sacks' The Man Who Mistook His Wife For a Hat). 

The twins were finding very large prime numbers without the aid of books or calculating devices. The game the twins were playing escalated to 12 digit numbers. There is no known way to find prime numbers using any simple mental rule.

One hypothesis is that the twins (and other savants) naturally access lower level unprocessed information in the brain. That is, they are directly aware of details without being encumbered by the higher-level assembly of information into meaningful patterns and recognizable memories. In the case of the twins, the number 111 might have been immediately "seen" and then automatically decomposed into its factors (37). A non-savant would have immediately engaged higher-level mental processing that would visually separate the matches into groups of, say 5, to eventually arrive at 111 by counting the recognizable clusters of 5 and adding the remainder 1. In essence, savants may bypass the time consuming and energy-demanding process of looking for patterns that are consistent with their past experiences. This hypothesis is consistent with studies of brain injuries that induce savant-like characteristics in previously normal persons.

Postscript on Kim Peek

Kim Peek, unlike the twins, was not autistic. In general, not all autistic people are savants and savants are not all autistic. Most (but not all) individuals with autism spectrum disorder (ASD) have similar characteristics: difficulty with social interactions, obsessive repetitive behaviors, language impairment, and hypersensitivity to sensory stimuli. 

Kim lacked most of these traits. Kim's unique mental abilities were attributed to the lack of a corpus callosum, the part of the brain that transmits information between its right and left hemispheres. This explains how Kim was able to read two pages simultaneously, one with his right eye and one with his left eye.

Kim was intimately familiar with musical compositions and Shakespeare's plays. "He had memorized so many Shakespearean plays and musical compositions and was such a stickler for accuracy, his father said, that they had to stop attending performances because he would stand up and correct the actors or the musicians. He'd stand up and say: 'Wait a minute! The trombone is two notes off,' ..." A fascinating article about Kim's abilities can be found here; a summary is posted below.

• Not only could he read at 18 months of age, but he could also read two pages at once; one with his left eye and the other with his right eye. He retained this ability for life retaining 98% of the contents of over 12,000 books. 
• He memorized maps and encyclopedias. He could give driving directions within and between all major cities in the United States. 
• He memorized all zip codes and area codes in the United States and could recite which were served by what television stations. 
• He could identify most classical music compositions and knew the date the music was written and could recite details about the composer's life. He had equally detailed knowledge in a long list of other areas such as history, sports, literature, movies, etc.