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Cheating on a string theory exam
21–30 of 76 posts
Re: Cheating on a string theory exam
#22Earlier quoted context omitted.
Using this on only 3 questions, you get 2/3 success rate: 000,001,010,100,000 -> buddy signals 0, I write 000 111,110,101,011,111 -> buddy signals 1, I write 111 with 7 bit you definitely win 14 questions from 21
You can get at least 17 by using the 1 bit to express preference for just the first 12 questions, and the remaining 11 bits the answers to the last 11 questions exactly. I've been trying to think if there's a clever scheme to spread the knowledge around to beat 17 with statistical tricks. (As a fun aside: 17/23 is about 73%, which typically gets you a C -- so you'd pass the exam.)
I wrote a simple program to test all possible majority-of-group breakdowns for generic number of questions and bitlengths, and found that the optimal result in all cases for this class was to use all but one bit for individual questions and then use that one bit for majority of the rest.
You can probably get better bit usage by doing some sort of more complex error code correction scheme--imagine having overlapping groups that you know majority vote on. It's been a decade since I've touched that stuff, so I don't know any concrete numbers here.
Re: Cheating on a string theory exam
#23Pick 5400 23-bit vectors (the answers you will write) and your friend picks the one that minimizes its Hamming distance to the true answer. 5400*23 + 5400*23*22/2 so answering 21 questions with certainty is impossible. (Pick the true answers so as to maximize the Hamming distance between it and whatever answer you decide to write, regardless of the scheme used.) And there is a size 4096 [1] see n = 23, R = 3 here htt…
Correct! You're the second person to find the answer (the first was not on HN).
Now for the extra credit part: What's the connection between this solution and string theory?
Re: Cheating on a string theory exam
#24I like the double entendre in the title.
Re: Cheating on a string theory exam
#25Pick 5400 23-bit vectors (the answers you will write) and your friend picks the one that minimizes its Hamming distance to the true answer. 5400*23 + 5400*23*22/2 so answering 21 questions with certainty is impossible. (Pick the true answers so as to maximize the Hamming distance between it and whatever answer you decide to write, regardless of the scheme used.) And there is a size 4096 [1] see n = 23, R = 3 here htt…
You didn't answer the extra credit, how this relates to quantum physics. I'd love to know that.
Re: Cheating on a string theory exam
#26Pick 5400 23-bit vectors (the answers you will write) and your friend picks the one that minimizes its Hamming distance to the true answer. 5400*23 + 5400*23*22/2 so answering 21 questions with certainty is impossible. (Pick the true answers so as to maximize the Hamming distance between it and whatever answer you decide to write, regardless of the scheme used.) And there is a size 4096 [1] see n = 23, R = 3 here htt…
Correct! You're the second person to find the answer (the first was not on HN). Now for the extra credit part: What's the connection between this solution and string theory?
This was a neat brain-teaser (I took an information theory class years ago so it was a nice refresh), but the answer ended up being a lot less interesting than I had hoped :P
Re: Cheating on a string theory exam
#27Pick 5400 23-bit vectors (the answers you will write) and your friend picks the one that minimizes its Hamming distance to the true answer. 5400*23 + 5400*23*22/2 so answering 21 questions with certainty is impossible. (Pick the true answers so as to maximize the Hamming distance between it and whatever answer you decide to write, regardless of the scheme used.) And there is a size 4096 [1] see n = 23, R = 3 here htt…
Correct! You're the second person to find the answer (the first was not on HN). Now for the extra credit part: What's the connection between this solution and string theory?
Sadly, I can only give the Google answer to this one:
> Working on a branch of physics called supersymmetry, Dr. James Gates Jr., discovered what he describes as the presence of what appear to resemble a form of computer code, called error correcting codes, embedded within, or resulting from, the equations of supersymmetry that describe fundamental particles.
Re: Cheating on a string theory exam
#28Earlier quoted context omitted.
Correct! You're the second person to find the answer (the first was not on HN). Now for the extra credit part: What's the connection between this solution and string theory?
This was a neat brain-teaser (I took an information theory class years ago so it was a nice refresh), but the answer ended up being a lot less interesting than I had hoped :P
I said it was cute, not that it was interesting. :-)
(And while asrp's answer is correct, it would have been nice if he had stated what the code is rather than merely citing the fact that it exists.)
Re: Cheating on a string theory exam
#29TIL about Golay codes; interesting read, thanks!
Re: Cheating on a string theory exam
#30Pick 5400 23-bit vectors (the answers you will write) and your friend picks the one that minimizes its Hamming distance to the true answer. 5400*23 + 5400*23*22/2 so answering 21 questions with certainty is impossible. (Pick the true answers so as to maximize the Hamming distance between it and whatever answer you decide to write, regardless of the scheme used.) And there is a size 4096 [1] see n = 23, R = 3 here htt…
If someone could ELI5 this, that'd be great!