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Yesterday, I went hiking with friends who are all studying the same electronic engineering degree with me. During the hike, we talked about female classmates within our degree. Since there are only few female classmates within our degree, I only needed to use one or two sentence to describe that female classmates (such as the female classmates who has a fat boyfriend) and my friends could immediately know who I am talking about.

But I suddenly notice that this phenomenon go against the idea of Huffman Code. In Huffman code, we encode the rarest incident with the maximum number of bit, but for my case, I can describe the female classmates with very limited information, even though female classmates are rare occurrence in our class. Why is it the case?

Marcus Müller
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galoischan
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  • this is classical homework :) maybe without the slightly sexist aspects... anyway: Hm, selecting 1 of 10 female classmates has much lower entropy than selecting 1 of 100 male classmates. So, you've got your thinking (for some reason I really don't understand) upside down when it comes what is "rare". – Marcus Müller Dec 14 '21 at 23:24
  • To add to Marcus' comment: the probability of you guys talking about classmate $x$ is not uniformly $1/N$ for a class with $N$ students. – MBaz Dec 14 '21 at 23:31
  • I understand that everything make sense if we try to explain this phenomenon with entropy. But what if I insist that I want to use the concept of Huffman code to explain it? How can I apply the concept of Huffman code to this phenomenon? Or if we can't explain this phenomenon with Huffman code, can you point out what prevent us to apply the concept of Huffman code to this little story of mine? What is the difference between my "encoding" of female students and Huffman code? – galoischan Dec 15 '21 at 21:48

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In this case you have limited the context to females, so your "codes" are shorter because of the smaller overall vocabulary. To put it slightly differently: in that context the probability of the discussion object to be female is much higher than for males, thus shorter phrases.

blamocur
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