[HN Gopher] Shannon Entropy Imposes Fundamental Limits on Commun...
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Shannon Entropy Imposes Fundamental Limits on Communication
Author : harscoat
Score : 19 points
Date : 2022-09-07 20:07 UTC (2 hours ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| _wldu wrote:
| One example I like to use (when talking about entropy):
|
| A four digit numeric PIN (that we know) has 0 bits of entropy.
| There is no uncertainty about what the PIN actually is. A
| randomly selected one (that we do not know) has just over 13
| bits.
|
| print(math.log(10)/math.log(2)*4)
|
| 13.28771237954945
|
| The more entropy, the more uncertain we are.
|
| However, humans are not random. We use the year we were born,
| some keyboard sequence or some other predictable number as our
| PIN. We don't know exactly how much entropy these PINS have
| (there is some degree of uncertainty), but we do know they are
| significantly less than 13 bits.
| acjohnson55 wrote:
| The information theory class I took in grad school was one of the
| most mindbending classes I've ever taken. It made doing gnarly
| math problems fun.
|
| Claude Shannon was a titan. He's also known for publishing what
| some call the most important masters thesis of all time,
| https://en.wikipedia.org/wiki/A_Symbolic_Analysis_of_Relay_a....
| bob1029 wrote:
| Information theory is so cool. I feel like having a solid grasp
| of the fundamentals is critical for achieving mastery in software
| development. Closely related would be digital signal processing
| and frequency domain techniques, both also extremely useful in
| many branches of software.
|
| The actual information content of a thing has always surprised
| me, especially when factoring in slightly imperfect (but
| passable) representations such as JPEG or MP3. To lose some
| information seems entirely acceptable in many cases.
| mpalmer wrote:
| Information theory is fascinating to anyone who likes the mathy
| underpinnings of seemingly non-mathy things, and it's
| _everywhere_. Cool stuff.
|
| Speaking of information and decompression, my brain initially
| interpreted the title as a breaking news headline about a female
| supervillain who's also a theory nerd.
|
| It was only the added context of the domain name that fixed the
| error.
| rkp8000 wrote:
| For anyone interested in these ideas, I'd highly recommend
| reading Shannon's original 1948 paper (linked in the article).
| While technical and precise it is actually quite digestible for
| someone with a bit of a quantitative background.
| ivan_ah wrote:
| link to paper abstract:
| https://ieeexplore.ieee.org/abstract/document/6773024
|
| direct link to PDF:
| https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=677...
| prophesi wrote:
| I'd also highly recommend watching The Bit Player documentary.
| Not as info-dense as an article or paper, but it's a fun ride.
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