[Williams]

It seems to me that in "reality" numbers are not "real" and it's facinating the savant in this case "sees" the numbers as shapes, and then "sees" the resulting shape after the numbers are manipulated. I can visualize that if the example is "1+1" but obviously most of us can't visualize it with large numbers and complex math. But if the math is representative of "something" then he obviously can visualize a representation other than numbers. But can we understand how one number appears as a motion, the other as a thunderbolt, and his mind turns them into a third shape which is the correct answer?

One big question is, if he sees shapes instead of numbers, how does he convert his images into a precise number?

Just as a suggestion, it's possible that his higher understanding is an elaborate mental "trick" which only he can perform. He spent an enormous amount of time in life counting everything, for example the leaves on trees. He would count every pebble on the beach. Perhaps his mind then created visual representations of every number value he counted. His mind then has the capability of revisualizing these represenrtations and performing correct math with them. His mind retains the precise number count associated with each. In essence, he ends up visualizing many many units whereas I believe the average person cannot visualize more than 11 distinct objects at a given time.

He still would have an extraordinary capability for a human being, but it wouldn't exactly be a window into another view of reality.

[snarks_when_bored]

If you can't get hold of Luria's book (see the link to a description in post #21 above), definitely go ahead and read this Borges short story, which is online:

"Funes, the Memorious"

It won't take you long to read it. It gives one a sense of what it might be like to have a truly imagistic memory (although so overwhelmingly comprehensive was the memory of Funes, that it made it difficult for him to do anything at all, even calculate).