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A Mathematical Theory of Communication (1948) [pdf]
- igg 6y agoThe article was renamed "The Mathematical Theory of Communication" in the 1949 book of the same name, a small but significant title change after realizing the generality of this work.
- qppo 6y agoThe forward is also essential reading, even for those uninterested in the math. It's one of the best descriptions of a field of science I've ever read.
- dredmorbius 6y agoWhat was the original title?
- igg 6y agoA Mathematical Theory of Communication
- dredmorbius 6y agoSo "A" was changed to "The"?
- apetresc 6y agoExactly.
- smitty1e 6y agoShannon's work has had vast influence. Here is a great, short overview of the topic => https://youtu.be/_PG-jJKB_do https://youtu.be/_PG-jJKB_do There is no entropy regarding question of whether the Jade is an attractive presenter.
- markus92 6y agoWhat I think is telling, is how easy to read Shannon’s paper is. Even today it is used pretty much as is at many EE colleges to teach communication theory. Another cool fact: Shannon’s master thesis is most likely the most influential one of all time: in it, he linked Boolean algebra to electrical circuits with switches, essentially inventing digital circuit theory.
- danharaj 6y agoBTW here's the paper by Hartley cited on the first page it is also very readable and insightful. I found it helped clarify some of the subtler points in Shannon's paper to read it as well. http://keszei.chem.elte.hu/entropia/Hartley1928text.pdf http://keszei.chem.elte.hu/entropia/Hartley1928text.pdf
- dredmorbius 6y agoA well-deserved perennial. Some prior discussions: 2016, 53 comments: https://news.ycombinator.com/item?id=12079826 https://news.ycombinator.com/item?id=12079826 2017, 11 comments: https://news.ycombinator.com/item?id=15095393 https://news.ycombinator.com/item?id=15095393
- vga805 6y agoI just recently finished the biography of Shannon called "A Mind at Play." It was quite a joy and I highly recommend to anyone interested in these sorts of bios.
- dbcurtis 6y agoConcur. That is a good read.
- dredmorbius 6y agoRecommended on an earlier thread: From Aristotle to John Searle and Back Again: Formal Causes, Teleology, and Computation in Nature" by E. Feser. https://muse.jhu.edu/article/618359 https://muse.jhu.edu/article/618359 http://www.netherhallhouse.org.uk/wp-content/uploads/2018/03/formal_causes.pdf http://www.netherhallhouse.org.uk/wp-content/uploads/2018/03... Source: https://news.ycombinator.com/item?id=12080670 https://news.ycombinator.com/item?id=12080670
- abetusk 6y agoAnyone have good recommendations on LDPC or Turbo Code theory?
- dbcurtis 6y agoDavid MacKay did some good stuff, and source code is available: http://www.inference.org.uk/mackay/CodesFiles.html http://www.inference.org.uk/mackay/CodesFiles.html I find MacKay's explanations very clear. Sadly, he passed away far too young.
- dbcurtis 6y ago> The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning ... I never fail to suppress a chuckle when I read that.
- enriquto 6y agoThe crucial point is the word "selected". As in "selected from a pre-agreed set of possible messages".
- sl8r 6y agoIf you're interested in this, check out Cover's Information Theory textbook — the rabbit hole goes much deeper. One of the most interesting examples, is that when you're betting on a random event, Shannon entropy tells you how much to bet & how quickly you can compound your wealth. Cover covers (heh) this, and the original paper is Kelly: http://www.herrold.com/brokerage/kelly.pdf http://www.herrold.com/brokerage/kelly.pdf
- PaulRobinson 6y agoKelly's paper (based on this paper by Shannon), is responsible for fundamentally reshaping equity, commodity and even sports betting markets. I highly recommend William Poundstone's book, "Fortune's Formula" as a biography of those ideas - it's almost as good as any Michael Lewis book on the subject would be.
- auntienomen 6y agoI think this gets posted on Hacker News once or twice a year. It's a pleasure every time.
- dr_dshiv 6y agoThere seems to be a great, unresolved difference of opinion about whether information entropy and thermodynamic entropy are commensurable. In trying to connect Shannon entropy to thermodynamic entropy, I always get stuck on the fact that you need to have a defined alphabet or symbol set.
- Q_is_4_Quantum 6y agoIt seemed clear to me at the time when I read (a few of - but especially https://bayes.wustl.edu/etj/articles/theory.1.pdf https://bayes.wustl.edu/etj/articles/theory.1.pdf) ET Jaynes' papers on classical thermodynamics that they were commensurable. I'm mildly surprised there is some question about that!
- wrnr 6y agovs an arbitrary defined number of dimensions? Their are more exotic mechanisms to define entropy: https://en.wikipedia.org/wiki/Parastatistics https://en.wikipedia.org/wiki/Parastatistics
- dr_dshiv 6y agoIn a thermodynamic sense, information input (say, of photons) is generally going to increase the entropy of a receiving system. Only certain kinds of information can reduce the entropy of the receiving system. Too much information (i.e., too many photons) can literally burn your eyes. I don't see how to square those manifest physical effects with the immateriality of Shannon information entropy.
- wrnr 6y agoIs this not the problem of Maxwell's Daemon, if an intelligent agent observes and interferes with a particle system to reduce the system's entropy then overall entropy is still increasing because the agents needs to store and calculate information in some physical medium, be it brain matter of silicon.
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- noema 6y agoProbably one of the dozen or so most important publications of the twentieth century. Ironically though it would be Norbert Wiener's interpretation of information (exactly Shannon's times minus one) that would cement itself in the popular lexicon due to it being far more intuitive. Where Wiener posits information as negative-entropy (or "order"), Shannon interprets it as representing a degree of freedom, or uncertainty. The problem with Wiener's is that the underlying epistemology carries a subjective bent, where information is equivocal to "meaning" or semantic content. Shannon's, meanwhile is ultimately superior as an objective metric, though far less intuitive (under his interpretation, a random string is technically the most information-saturated construct possible, because it possesses the highest degrees of freedom).
- ssivark 6y agoBut isn't the information gained from a message necessarily subjective? It depends on just on this message, but from the distribution from which this message was drawn, and more appropriately, the distribution anticipated by the observer will determine the value (information content) of the message. That is exactly how it becomes useful in practice. This "surprisal" can be parametrized by relative entropy (Kullback-Liebler divergence), which reduces to the Shannon entropy formula only when the observer has the correct anticipated distribution.
- noema 6y agoI think there is a distinction to be made between information in the ontological sense and information in the pragmatic sense. The former does not have any purchase on "meaning" or "use", only a metric of informational entropy or degrees of freedom, irrespective of observation. However, the sense in which you speak of information is the pragmatic dimension, where an observer receives a datum of semantic content against a given backdrop of pre-established "meaning". This sense is problematic as an objective metric.
- GoatOfAplomb 6y agoI'm trying to find a quote I read about this paper once. To paraphrase, not only did this paper create a new field of academic inquiry, it answered most of that new field's interesting questions, too.