# How are autistic savants able to perform certain mathematical computations so quickly?

• How do autistic savants (or other people with these abilities) compute equations like $81^{100}$ in 2.5 minutes?
• Which algorithms do they use? Is it an efficient one, or do they just have a lot of memory?
• Can non-autistic savants use these algorithms to solve equations just as quickly?
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Not $81^{100}$ but have a look at Arthur Benjamin does "Mathemagic" in TED where he tries to show his thought processes. – lhf Jun 26 '12 at 1:06
Due to the number $81^{100}$ involved, I think he's referring question: Mathematical Discoveries that were made or supported by Savants – draks ... Jun 26 '12 at 10:12
Related question about child prodigies and math. – Josh Gitlin Jun 26 '12 at 11:49

Savants apparently don't compute consciously; from what I've seen, they see numbers as shapes. When savants multiply numbers together, they see two shapes. The image starts to change and evolve, and a third shape emerges. That's the answer.

Humans can have synesthesia. It is a process in the brain which can associate numbers or names to certain shapes. For example, consider the two shapes:

Tests like this demonstrate that people do not attach sounds to visual shapes arbitrarily. Which shape would you call "Bouba" and which "Kiki"? I would call the one on the left "kiki" and the one on the right "Bouba".

You can see this interesting video on the wonderful savant Daniel Tammet. Start from 32:16 if you want to see how a neurology team administered various tests to him to make sure he's not using some techniques. See also how he uses "Kiki-Bouba"-like shapes to do complex computations at 40:35.

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can you present reference on the statement that savant-like capabilities are always associated to synesthesia? Tammet is an example, not necessarily a rule – glS Jan 1 '15 at 0:31

How one performs quick mental calculations through tricks and shortcuts can easily be looked up on the internet. How some Savant's do it cannot because we don't know. There is some argument that some do those same tricks but others seem not to do so.

Consider that a substantial amount of computational power goes into immediately recognizing that your friend is deeply unhappy when you first see them but puts on a brave face for you and is avoiding talking about something deeply troubling them. You see that immediately while the typical savant sees nothing, or confusion. That same Savant can do amazing mathematical, or spatial computations with tremendous facility. So, perhaps the reason we don't understand it is because it's actually a different kind of a mind.

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