- #1

qspeechc

- 844

- 15

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

"...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.

Further reading

[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.

Further reading

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