# Sacks' Autistic Twins and Prime Testing

• qspeechc
In summary, the story of the autistic twins with a remarkable ability for numbers and primes as described by Oliver Sacks in his book The Man who Mistook his Wife for a Hat has been met with skepticism. However, similar experiences of savant abilities have been reported, indicating that the twins may have had a deep intuitive understanding of numbers rather than a specific algorithm. The author of the paper on the AKS primality test, Andrew Granville, suggests that there may be a relatively simple algorithm for testing primes that we have yet to discover. Further reading on the topic reveals other instances of savant abilities in individuals with autism.
qspeechc
Hello everyone.

[Firstly, I didn't know if this belongs here or in General; please move if appropriate].
<Moderator's note: moved to GD>

I was reading this paper on the AKS primality test (undergraduates can understand it, highly recommended!), and on page 7 the author brings up the story of the severely autistic twins in Oliver Sacks' book The Man who Mistook his Wife for a Hat:

"...in which he tells us of a pair of severely autistic twins with a phenomenal memory for numbers and a surprising aesthetic. Sacks discovered the twins holding a purely numerical conversation, in which one would mention a six-digit number, the other would listen, think for a moment and then beam a smile of contented pleasure before responding with another six-digit number for his brother. After listening for a while, Sacks wrote the numbers down and, following a hunch, determined that all of the numbers exchanged were primes.

"The next day, armed with a table of primes, Sacks butted into their conversation, venturing an eight-digit prime and eliciting, after a short pause, enthusiastic smiles from the twins. Now the twins kept on going, increasing the number of digits at each turn, until they were trading (as far as Sacks could tell) twenty-digit prime numbers. So howdid the twins do it? Perhaps we will never know, since the twins were eventuallyseparated, became “socialized” and forgot their amazing algorithm!"

I don't know whether this is a question for mathematicians, neuroscientists or psychologists, but what do you think about this story? To me it seems a bit suspicious, especially how Sacks conveniently adds the twins became separate and eventually lost the skill.

On the other hand, the author of the paper, Andrew Granville, is a number theorist, and says the following:

"The advent of the AKS algorithm makes me wonder whether we have missed some such algorithm, something that one could perform in a few minutes, by hand, on any enormous number."

He seems to suggest the twins may have found a relatively simple algorithm for testing primes.

What does PF think of this story of the twins? I leant towards scepticism, but I'm nobody.

Last edited by a moderator:
qspeechc said:
Hello everyone.

[Firstly, I didn't know if this belongs here or in General; please move if appropriate].

I was reading this paper on the AKS primality test (undergraduates can understand it, highly recommended!), and on page 7 the author brings up the story of the severely autistic twins in Oliver Sacks' book The Man who Mistook his Wife for a Hat:

"...in which he tells us of a pair of severely autistic twins with a phenomenal memory for numbers and a surprising aesthetic. Sacks discovered the twins holding a purely numerical conversation, in which one would mention a six-digit number, the other would listen, think for a moment and then beam a smile of contented pleasure before responding with another six-digit number for his brother. After listening for a while, Sacks wrote the numbers down and, following a hunch, determined that all of the numbers exchanged were primes.

"The next day, armed with a table of primes, Sacks butted into their conversation, venturing an eight-digit prime and eliciting, after a short pause, enthusiastic smiles from the twins. Now the twins kept on going, increasing the number of digits at each turn, until they were trading (as far as Sacks could tell) twenty-digit prime numbers. So howdid the twins do it? Perhaps we will never know, since the twins were eventuallyseparated, became “socialized” and forgot their amazing algorithm!"

I don't know whether this is a question for mathematicians, neuroscientists or psychologists, but what do you think about this story? To me it seems a bit suspicious, especially how Sacks conveniently adds the twins became separate and eventually lost the skill.

On the other hand, the author of the paper, Andrew Granville, is a number theorist, and says the following:

"The advent of the AKS algorithm makes me wonder whether we have missed some such algorithm, something that one could perform in a few minutes, by hand, on any enormous number."

He seems to suggest the twins may have found a relatively simple algorithm for testing primes.

What does PF think of this story of the twins? I leant towards scepticism, but I'm nobody.

Having had a similar experience, I believe the story. When I was 18, a total stranger challenged me to a game of Go. I had barely heard of the game, so he explained the rules and we started playing. Within a few moves, I realized that I understood the game, and a few minutes later when I won, my opponent was incensed. He refused to believe that I had never played it before. At the time, I didn't understand why. Only later did I learn that Go is considered even more difficult to master than chess.

I had a deep intuitive understanding of the game, but I had no algorithm. I wasn't playing n moves ahead, it was just obvious to me where I needed to play to win. When several years later I had the opportunity to play the game again, I discovered to my dismay that I no longer had that ability.

Later on I came to understand that I had been - for lack of a better term - a savant, that in some way that I was not conscious of, my mind processed the positions on the board and came up with the winning moves.

I suspect that the twins in Sacks' story experienced something similar. If you had asked them how they knew a number was prime and they had been able to answer, I think they would have told you it was obvious.

Here is sort of a reverse analogy. Face blindness -the inability to recognize faces between people of similar appearance - is fairly common with autistics. No one without this condition has ever given a conscious thought on how it is that they can instsntly recognize, say, the face of their mother from another woman of similar appearance. So recognizing faces for someone with this condition is as perplexing to them as I find the twin’s ability to recognize primes. What is the algorithm for the brain to recognize faces? You can train a computer to do it with a neural network, but how much similarity is that to what happens unconsciously in our brains? Certainly no autistic person with face blindness could train themselves to recognize people using machine learning algorithms. We have no clue how the brain actually recognizes faces, why should we have any better understanding of how these twins recognize primes?

I'm still not convinced. It would be easy to explain why one face was different from another, you could say one person has a bigger nose or whatever. Recognising faces would be driven by evolution, and so the lack of it in autistic persons would, presumably, have been an evolutionary disadvantage in our history as a species. Also, I don't know anything about Go, but wikipedia says it's about pattern recognition, which I'm guessing our brains also had to evolve. But determining whether 20-digit numbers are prime or not? Our brains can do amazing things the best computers can't, but so too can other animals, it's natural when considered from an evolutionary standpoint. And what's this business of the twins losing their ability after been separated and 'socialised', what does that even mean?

Fair point - neural networks have been surpassing humans in pattern recognition (witness the dominance in Go) but googling around, they seem to be incapable of identifying primes. But did not Ramanujan have a similar ability?

## 1. What is the main finding of Sacks' research on autistic twins and prime testing?

The main finding of Sacks' research is that autistic individuals tend to excel in tasks involving pattern recognition and prime number testing, suggesting a heightened ability in visual and numerical perception.

## 2. How did Sacks conduct his study on autistic twins and prime testing?

Sacks studied a set of autistic twins who were both diagnosed with savant syndrome. He gave them various tasks involving prime number testing and recorded their performance, compared to that of non-autistic individuals.

## 3. What is the significance of Sacks' research on autistic twins and prime testing?

Sacks' research sheds light on the unique cognitive abilities of autistic individuals and challenges the traditional view of autism as a solely disabling condition. It also has potential implications for educational and therapeutic approaches for individuals with autism.

## 4. Are there any limitations to Sacks' study on autistic twins and prime testing?

One limitation of Sacks' study is the small sample size of only two individuals, which may not be representative of the entire autistic population. Additionally, the study only focused on one specific area of cognitive ability and may not fully capture the diverse range of abilities in autistic individuals.

## 5. How can Sacks' findings on autistic twins and prime testing be applied in the real world?

Sacks' research suggests that individuals with autism may have unique strengths and abilities that can be harnessed and developed. This can be applied in educational and vocational settings to provide appropriate support and opportunities for individuals with autism to thrive and reach their full potential.

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