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Google researcher, long out of math, cracks devilish problem about sets

quantamagazine.org

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Re: Google researcher, long out of math, cracks devilish problem about sets

#2

Post by acctant »

> He also worked with a textbook by his side so he could look up formulas he’d forgotten. “You’d think someone who comes up with a great result shouldn’t have to consult Chapter 2 of Elements of Information Theory, but I did,” Gilmer said.

Always enjoy seeing this sentiment reaffirmed. Funny that Gilmer states it in a somewhat self surprised tone.

Rings of the Einstein quote:

“[I do not] carry such information in my mind since it is readily available in books. He also said, “…The value of a … education is not the learning of many facts but the training of the mind to think.”

Re: Google researcher, long out of math, cracks devilish problem about sets

#3

Post by [deleted] »

acctant wrote: post #2

> He also worked with a textbook by his side so he could look up formulas he’d forgotten. “You’d think someone who comes up with a great result shouldn’t have to consult Chapter 2 of Elements of Information Theory, but I did,” Gilmer said. Always enjoy seeing this sentiment reaffirmed. Funny that Gilmer states it in a somewhat self surprised tone. Rings of the Einstein quote: “[I do not] carry such information in my…

[deleted]

Re: Google researcher, long out of math, cracks devilish problem about sets

#6

Post by mandmandam »

acctant wrote: post #2

> He also worked with a textbook by his side so he could look up formulas he’d forgotten. “You’d think someone who comes up with a great result shouldn’t have to consult Chapter 2 of Elements of Information Theory, but I did,” Gilmer said. Always enjoy seeing this sentiment reaffirmed. Funny that Gilmer states it in a somewhat self surprised tone. Rings of the Einstein quote: “[I do not] carry such information in my…

The vast majority of academic "achievement" measures are centered on tests which entirely disallow looking things up.

Especially in poorer public schools, learning is modeled as recitation. It's awfully sad. Most students are lucky if they get one or two teachers that break that mold.

Re: Google researcher, long out of math, cracks devilish problem about sets

#7

Post by jobs_throwaway »

acctant wrote: post #2

> He also worked with a textbook by his side so he could look up formulas he’d forgotten. “You’d think someone who comes up with a great result shouldn’t have to consult Chapter 2 of Elements of Information Theory, but I did,” Gilmer said. Always enjoy seeing this sentiment reaffirmed. Funny that Gilmer states it in a somewhat self surprised tone. Rings of the Einstein quote: “[I do not] carry such information in my…

"The value of a … education is not the learning of many facts but the training of the mind to think."

While anyone with a (good) STEM education knows this to be obviously true, its frightening how many people go through 16+ years of formal schooling where they mostly do rote memorization and regurgitation.

Re: Google researcher, long out of math, cracks devilish problem about sets

#9

Post by rkp8000 »

Always cool to see unexpected applications of information theory, especially outside of probabilistic contexts.

A related toy example that comes to mind is the puzzle where you're given 12 metal balls and told that one of them is either heavier or lighter than the rest. You're then given a balance/scale and instructed to figure out which ball is different and whether it is heavier or lighter using the balance a maximum of three times to weigh different combinations of balls.

Part of the reason this is solvable is because there are 12x2=24 different possibilities (or log2(24) = 4.58 bits) for the ball ID/weight and 27=3x3x3 possible outcomes (or log2(27) = 4.75 bits) for the weighing process (left heavier, right heavier, or equal in each use). Thus, there's a chance the weighing sequence could convey the ball ID/weight. If there were 14 balls, however, then you would require log(28) = 4.81 bits of information to specify the ball ID/weight, so the puzzle would be unsolvable, since there wouldn't be enough information available in the weighing sequence to specify the ball ID/weight.

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