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ai;dr 5 months ago

said “groks the world”; didn’t read

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Tiny Books Fit in One Hand. Will They Change the Way We Read? 8 years ago

“A print-book!” It was hard to tell whether Dors was shocked or amused. “That’s from the Stone Age.”

“It’s certainly pre-Empire,” said Seldon, “but not entirely so. Have you ever seen a print-book?”

“Considering that I’m a historian? Of course, Hari.”

“Ah, but like this one?”

He handed over the Book and Dors, smiling, opened it–then turned to another page–then flipped the pages. “Its blank,” she said.

“It appears to be blank. The Mycogenians are stubbornly primitivistic, but not entirely so. They will keep to the essence of the primitive, but have no objection to using modern technology to modify it for convenience’s sake. Who knows?”

“Maybe so, Hari, but I don’t understand what you’re saying.”

“The pages aren’t blank, they’re covered with microprint. Here, give it back. If I press this little nubbin on the inner edge of the cover–Look!”

The page to which the book lay open was suddenly covered with lines of print that rolled slowly upward.

Seldon said, “You can adjust the rate of upward movement to match your reading speed by slightly twisting the nubbin one way or the other. When the lines of print reach their upward limit when you reach the bottom line, that is–they snap downward and turn off. You turn to the next page and continue.”

“Where does the energy come from that does all this?”

“It has an enclosed microfusion battery that lasts the life of the book.”

“Then when it runs down–”

“You discard the book, which you may be required to do even before it runs down, given wear and tear, and get another copy. You never replace the battery.”

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Jane Street Puzzles 8 years ago
   n=1, A=2:
   h    b   #tri  #non-congruent tri
   1    4   b-1   roundup(#tri/2)
   2    2   b-1   roundup(#tri/2)

   .
   .
   .
   
   n=4, A=16:
   h    b      #tri  #non-congruent tri
   1    2A/h   b-1   roundup(#tri/2)
   2    2A/h   b-1   roundup(#tri/2)
   4    ...    ...
   8    ...
   16   ...          ...
summing up #non-congruent tris for each n I see
   n  tri
   1  3
   2  7
   3  15
   4  31
so I think that answer may be 2^(n+1) - 1.

Could be wrong because I forgot what congruent really means.

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Why Throwing 92 Heads in a Row is not Surprising [pdf] 9 years ago

If we are flipping a fair coin, the "surprise" we have at the result of any individual flip should be the same for all individual flips. Therefore, the entropy of the event, call it "A", of 92 fair coin tosses each resulting in heads is the same as the entropy of any other 92 fair coin tosses, "B". The sum of the individual event entropys must be the same so entropy(A) = entropy(B).

If you are talking about information theory entropy and saying a message of a billion bits composed of all "ones" has lower entropy than a "random" billion bit message, then sure. This is like saying we can compress the billion bits of ones and send less bits but the same amount of information. But I don't think this is synonymous with the above. It would be like saying for event A, each proceeding individual event has less entropy than the previous -- we aren't dealing with a fair coin anymore.

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How to Read Mathematics 9 years ago

I believe sci-hub has been taken down, at least temporarily. The .cc and .bz domains weren't working for me. I think it's possible to setup custom DNS servers on your machine and access that way, but I haven't played around with it.

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