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Betty Shannon, Unsung Mathematical Genius (scientificamerican.com)
196 points by breck on July 26, 2017 | hide | past | favorite | 47 comments


Thanks for sharing this article...not familiar with Betty Shannon, but her husband, Claude Shannon was really a genius...His paper "A Mathematical Theory of Communication" is one of the most elegant papers that I have read...

http://math.harvard.edu/~ctm/home/text/others/shannon/entrop...

Sigh...the one hundred years before 1990 was really a period of giants, with Claude Shannon, Kurt Gödel, Alan Turing, John von Neumann, Emmy Noether, David Hilbert -- as well as Albert Einstein, Paul Dirac, Louis de Broglie and the other quantum guys...

I have to admit it was those guys that inspired me to try to pursue a career in academia...but after I grew up, I found they were all dead -- or it might be the other way around...and many academic papers these days are filled with words that do not resonant, and with bloated references that do not shine -- some even marked with the acceptance rate of its publication to show off their elitism...

Seems that the age when a 25-page PhD thesis, containing only 2 references, could still be well accepted is fading further and further away...

( https://rbsc.princeton.edu/sites/default/files/Non-Cooperati... )


> Sigh...the one hundred years before 1990 was really a period of giants, with Claude Shannon, Kurt Gödel, Alan Turing, John von Neumann, Emmy Noether, David Hilbert -- as well as Albert Einstein, Paul Dirac, Louis de Broglie and the other quantum guys...

Most of giants of that period are giants in hindsight. We can see the results of their work and how those results still hold up today. I imagine those in 2117 will have their giants between 1990 and 2090 just like we do today.


Yes, but because human knowledge is so much greater than it was 100 years ago, a given lifetime of work is able to push knowledge forward less. Yes, we still have CRISPRs and other titanic discoveries, but even those are collaborations. There is no more room for an Isaac Newton who basically invents three different scientific fields.


A field depends on the body of work that comes afterwards. At the time of its invention, it's just a paper. I could imagine several people in computing alone that might end up inventing three different fields.

Remember that at one point, "computer science" was considered a subfield of "electrical engineering", and both of them have their roots in Claude Shannon's masters thesis. That's because after he published his result and it became widely known, thousands of others piled into those fields to study the consequences of digital circuits. Similarly, I'd bet that in a hundred years "computer science" isn't one field, it's at least half a dozen, and people will be studying the subfields of version control, distributed systems, CRDTs, neural nets, computer graphics, data storage, compression, information retrieval, and others. Actually, that isn't a hundred years, that's today.


When Isaac Newton was old, he used to give his visitors a lock of his hair in a small gold case, because he knew, and they knew, that they would be museum pieces one day. He was right, I saw one of them in a museum. I don't think any living scientist could confidently do that today.


> I could imagine several people in computing alone that might end up inventing three different fields.

I'm curious, who would those be?


Newtonian physics, Gravitational theory and Differential calculus.


At the time it was all just "natural philosophy."


Stephen Wolfram might disagree.


I think he might, but that's more because he has a very high opinion of himself.


I would have said Hawking or Knuth. Wolfram his personality (ego) always did bother me though.


Which of Shannon, Godel, Turing, von Neumann, Noether, Hilbert, Einstein, Dirac, or de Broglie are you implying were not regarded as giants in their own times?


I wasn't clear. I read 'scientific giant' as a 'scientific giant to general society' (those who start touching pop culture/media) as opposed to giant only in their field. For example, Shannon and Turing became giants to general society later on. Very few during their time knew the world of today that Shannon and Turing were creating. Shannon and Turing are only recently being recognized (hollywood films and biographies) in general society because we all now undoubtedly live in their world. And that is arguably why we're now learning about Betty Shannon.


Maybe you missed reading the article under discussion?

> His name has faded in our era, but in mid-20th century America, Claude Elwood Shannon of Bell Telephone Laboratories was a bona fide scientific star. In 1954, for example, Fortune featured Shannon in a list of the nation’s 20 most important scientists, alongside future Nobel Laureates Richard Feynman and James Watson, among others. Shannon also made the pages of Time and Life magazines, appeared on national television, and even earned a spread in Vogue, complete with a photo shoot by the renowned Henri Cartier-Bresson.


Being recognized within your field and the field itself being widely recognized are two different things. It takes a while for the public at large to recognize the importance of their contributions.


hopefully that would be the case...or perhaps my world view is a bit too pessimistic, but I feel that these days there are just too many different goals -- and many of them are mutually exclusive -- are amalgamated in academia...

I have seen quite a few cases where people with PhD degree in physics or mathematics went to Wall Street and became traders there and totally gave up their original pursuit of physics or mathematics...

also it is not a small number of people who would choose to pursue an academic career not because their research interests them but because it brings them fame and admiration, as well as stability in life -- as once they obtain their tenure, they would go start companies and pursue profits, instead of discovery...

I am not saying that there are not many people still hold their academic ideals pure and high...It is just that in this era when academic positions are highly respected, admired and well-paid, it might give people the incentive to pursue such a career not for its original purpose but for something else....And one of the very reasons why these days academic positions are highly respected, admired and well-paid was because those scientific and engineering giants in those old days had made really prominent and conspicuous contributions that made this world a significantly better place than it was a century ago -- and if we trace further to the reason why they chose science and engineering as their career in the first place and then made great contributions afterwards, it seems that in many cases it was not because science and engineering could bring them material profits, but rather they were genuinely interested and intrigued; and it was extremely fun to them...

But of course, it is a very difficult to say whether there is such a general decline in our pursuit for knowledge in general (such measurement is hard!)...not to mention the complexity in the essence behind some of the declining factors and drives...

Nevertheless, I wish that at the time when I am old and feeble, as I look back at those days in our time, I could say to myself, just as Odysseus might have said to himself, that I have lived in an age of many great ideals and many great heroes...Yet still, I feel that we should be warned that after the heroic Mycenaean period[1] ended, what immediately followed was several hundreds of years of darkness in the ancient Greek civilization[2]...

Note:

[1] https://en.wikipedia.org/wiki/Mycenaean_Greece

[2] https://en.wikipedia.org/wiki/Greek_Dark_Ages


And because of those already in it, those oddballs who might value the ideal academy rarely get hired. The metrics are different: fund raising ability, collaboration, paper publishing, etc. It's just a regular self-promoting job now.

On the other hand, the world is such that you don't need credentials to do truly independent work. You do need time and a way of supporting yourself, but at least you have means to be heard.


  > And because of those already in it, those 
  > oddballs who might value the ideal academy
  > rarely get hired. The metrics are different:
  > fund raising ability, collaboration, paper 
  > publishing, etc. It's just a regular 
  > self-promoting job now.
This is sadly true in many cases...and those oddballs, due to their eccentric nature and their inclination to avoid office politics, would hardly have the strength to fight this systematic encouragement for various digressions...

  > On the other hand, the world is such that 
  > you don't need credentials to do truly 
  > independent work. You do need time and a 
  > way of supporting yourself, but at least you 
  > have means to be heard.
Yes, I agree. But in C.Shannon's words, there is an issue of signal-to-noise ratio...sometimes, we have to rely on fortune to let some truly informative voice be picked up...


Hell, Shannon's masters thesis [1] is probably the most important masters thesis ever written and it cites six references.

[1] https://dspace.mit.edu/bitstream/handle/1721.1/11173/3454142...


Everyone remembers the first person to break the 4 minute mile "barrier". I bet only a fraction of those people know who the current world record holder is for the mile and what his time is (even though he would have left Roger Bannister trailing distantly in his dust).

Roger Bannister, Einstein, Turing et al were all giants but they are are well know because they were first and made giant strides in specific fields. People are no less clever or gifted today, but it is much harder to make breakthroughs when so much is already understood and achieved. In almost all fields it is currently incremental improvements.


hopefully, after many years, when we look back with our hindsight, we would find that we have been steadily moving forward...


> Thanks for sharing this article...not familiar with Betty Shannon, but her husband, Claude Shannon was really a genius...

There's no question about your characterisation, but he's hardly 'unsung'. I know you meant no ill (and voting isn't your fault), but it's a shame for an article about Betty to have its top comment be almost exclusively about her husband.


next time in such occasions, I will try to write "Betty's husband", instead of "Claude Shannon", to show my respect for her...( BTW, did Melania's husband tweet anything interesting lately? )

But, may Betty rest in peace...(she passed away this past May)...


...which begs the question, who are the giants of today? Why are we not hearing about them? Why are they not as "well-known" today as these men and women were?

One reason, as it appears to me, is that we are more in the age of the tech entrepreneur (primarily due to the Internet) as opposed to the late 19th/early 20th century which was the age of the inventor, the scientist.

Research and inventions are a much higher barrier to entry and a much longer cycle of work. Starting a startup is the easier route to name, fame, and riches today.

Sadly, I'm not sure it's for the better either.


Also the way people received information was different. The development of the information age. Newsreels. Learning how to appeal to a lot of people with new media.

I try to imagine how Einstein got famous. Even now hardly anybody, relatively speaking, understands that stuff. A good story, I guess: a lowly patent clerk changes our conception of space and time. Also entwined in the war - opposition to Germany, pro Zionism, the bomb - patriotism and propaganda. Our hero.

Feynman has a story that sells. Plays bongo drums, picks locks in a top-secret environment. Excellent at explaining things.

Nowadays, who invented CRISPR? They were Chinese. Is that a good story to tell? Maybe not to a western audience. Fusion, worked on by many many people, might be solved by AI. Will the AI become famous? Maybe the giants now are corporations: Facebook, Google, Apple, Microsoft.


> ..which begs the question, who are the giants of today? Why are we not hearing about them? Why are they not as "well-known" today as these men and women were?

It seems that one implicit assumption made in your question is that there exists such "giant" today...

Well, then that would depend on how you define "giant"...If we consider Isaac Newton as a giant, then perhaps one good description that illustrates his distinction is these two lines written by Alexander Pope:

  NATURE and Nature’s Laws lay hid in Night:
  God said, “Let Newton be!” and all was light.
In any age, inside any social structure that is not largely uniform, there are always "well-known" men or women -- that's a characteristic of human's social cognition capability...

Due to my ignorance, I don't think that in our time I could identify any living person who has advanced our knowledge as significant as Isaac Newton or other of those "giants" ( -- I just borrowed this term from Newton in my initial post...) -- I am not commenting on the aspect of human well-being, and I am only ranting about our knowledge...but as I am too ignorant, perhaps only with hindsight I could see better...

But still unless proved otherwise, there is a possibility there isn't (or won't be) any living giant in our time...This happened a few times in human history. For instance, 3000 years ago, after Mycenaean civilization ended, the Greek civilization seems to be moving into a state of falling back (which was a period that we refer as Greek Dark Ages): the practice of writing had ceased (i.e. linear B system), and even been forgotten in many places; their buildings were modest, and decorative art unimpressive -- even their favorite pottery was generally painted with less complex patterns ( -- perhaps it's not avant garde intentionally, as in our modern taste) ...bards and poets after the this dark period would only remember the heroes and giants in the Trojan war which happened in the Mycenaean age that preceded the dark age...

Nevertheless, the Greek Dark Age would eventually end, like all other historical periods...but I just feel sad for those people living in the dark days, although they might very likely not share this similar empathy for themselves (or they might factually have lived a very happy life)...


Conversely, mythologizing/lionizing mathematicians like that is one of the more annoying habits our field has, and I'm glad it's dying out. There are people doing fantastically innovative work that's outside of the mathematical mainstream. It took the Oxford quantum computing group years until categorical quantum mechanics taken seriously, because it was so different than what the "great mathematicians" before them had done.


Quite true...and I think my point largely concurs with yours, in that it is the scholastic content, instead of the administrative formalities, that should be valued...

I am not complaining about the giants are dead; I am complaining that the spirit of pursuing something truly great in academia seems to be fading out -- but of course, different people are most likely to see the world differently. Perhaps you still can enjoy that great atmosphere of pursuing truth rather than profits, which I feel really really glad to see and it helps me to restore some faith...It is just that perhaps these days I have seen a lot of dark lunatic side of academia that makes me feel pessimistic...


I'd like to tie your comment to an article that was linked to here the other day. It was to a paper by the economist Paul Romer on `mathiness'[0]. It is interesting to me that the standard bearers for progress and achievement (you and others select) are either mathematicians and/or physicists. Why physicists over any other natural scientist? Perhaps because physics is math-heavy and reliant on mathematical domain models to an extent that other fields and disciplines are not.

Let us review the fields of human exploration you have omitted. Art including music and literature, the social sciences, the life and medical sciences, economic and political theory, legal theory, the geo-sciences, … do I need to go on?

What makes math and physics so special? And before you dismiss my comments, I say this as somebody who has studied the history of mathematics and has read books on likes of Erdös and Ramanujan. (For instance, I would place Brouwer ahead of Hilbert, and I wonder how one can speak of Turing and Gödel but not of Church and Russell.) As for the physicists you mention, two of them were involved in the project that created the most devastating weapons ever used by man against man, weapons that hang over humanity to this day. That is some legacy.

Where has this math and physics devotion gotten us to? Collectively I mean. Where has it gotten us to collectively? I have come to believe that our entire culture is so much poorer because of it. Indeed the mindset is so pervasive that it has taken me me entire life to diagnose it in myself.

Did not know about about the age of the 25-page PhD thesis containing only 2 references (a slight exaggeration?) though. That is indeed a loss.

[0] https://paulromer.net/mathiness/


A field you yourself have omitted is philosophy. Not that I can blame you -- it's seen as inaccessible and/or without progress, and/or subsumed into other fields.

There's two things you mentioned I want to touch/speculate on. The first is the idea that there's a loss or shame in the dearth of new papers with few references. I think this is a function of the growth of disciplines: as the network adds neighbouring nodes, it becomes increasingly important to make your usage of terms and suppositions continuous with the rest of the relevant field. This way you avoid saying something important only to talk 'past' the readers. Where it does become a problem is in 'referentialism': the notion that what is being pulled out from a concept can only be described in the original terminology or via quotations. It's a serious problem in the humanities, but not exclusive to it. Ideas really are multiply realizable -- that's the beauty and creativity of analogies. I have a pet theory that this is a tension implicit in paradigm shifts, but one that isn't focused on enough in the process of academic 'meta-cognition'. My guess is that when it comes to 'standing on the shoulders of giants', it's all too tempting to marvel at the giants themselves than look to the expanded horizon. Perhaps that relates to the other posters' point about the Mycenaean age.

When it comes to Romer's paper, though I haven't yet read it all, I think there's an analogy in 'compsci-ness'. I suspect his observations work just as well with other epistemological (knowledge-kind) combinations and their tensions. It seems that what both highly abstracted fields do so well is further what we can do with the perceived objects and kinds in the world and how they relate. This kind of advancement seems it should improve our critical methods, and how we pin down the qualitative questions -- but it seems we are hard-coded to prioritise arrangement, not inspection. Perhaps it's that there is just too much for the potential Socrates archetypes to effectively 'Socratise', or perhaps they've been swallowed by Python.


Wasn't there a US university that shut down its philosophy department in recent times? Can there be any surer sign of mathiness than that?

'referentialism' is a problem but at least we have digital tools to help us now. I suppose we're in a more honest situation now than in the past. But it is indeed a problem. Why? Because now we'll be ranked by our citation scores.

> I suspect his observations work just as well with other epistemological (knowledge-kind) combinations and their tensions.

Yes, jargon-heavy humanities papers work in the same vein as math-heavy economics (for example) papers. They are both, ultimately, bullshit.


Good point re: citation scores. I like to imagine that people who think critically about data and measurement a lot don't take such things at face value. But maybe not.

Univ of St Thomas Houston & Univ of Zagreb seem to be 'reviewing' their Philosophy depts (though both cases have their nuances). Middlesex University (middle-of-the-pack Uni in UK) already closed theirs. Only couple mins of searching, I guess there's more. It's almost definitely mathiness from those who hold the purse strings. I think it's regrettable we have degrees for every job under the sun, it makes cross-pollination that much more difficult. Maybe something to do with the rise in total sum of bullshit.

It might be because I like to get an overview of things and read around, or because I find it difficult to commit attention for very long... But it seems to me like there's plenty of room for exactly the kind of thinking philosophical training is great for: fruitful interdisciplinary stuff between the humanities and sciences. Instead we seem to be getting profit-motivated consumption of the former by the latter, and filling the space with bachelors that stand in for what once was training in the workplace.


> I'd like to tie your comment to an article that was linked to here the other day. It was to a paper by the economist Paul Romer on `mathiness'[0]. It is interesting to me that the standard bearers for progress and achievement (you and others select) are either mathematicians and/or physicists. Why physicists over any other natural scientist? Perhaps because physics is math-heavy and reliant on mathematical domain models to an extent that other fields and disciplines are not.

Sorry...no offense to other fields...actually, I myself really don't think there is a definite separation in many fields that are administratively regarded as different...I personally feel that essentially they are all languages, using their different description systems to rationally describe the world as it is observed by them and then to make predictions...

most of my study background has been in computer science -- although I really do not think there are much difference that makes it so distinguishable from math or physics...and actually, sometimes I could not tell the difference between math and physics...I feel they are merely terms (or identifiers) used to refer certain things; and as I already mentioned that quite often we do not need to manually put boundaries on those certain things, the differentiability of the different terms then does not really matter here...

and if you like, we could call it study (or X) in general,or any other name would do, as long as it does not generate too much ambiguity...

> I would place Brouwer ahead of Hilbert, and I wonder how one can speak of Turing and Gödel but not of Church and Russell.

Yes, I was thinking of Church and Russell (and I really enjoy his non-math writing too) while I was writing those words...but then I felt that I would have to trace back to Georg Cantor -- and then I realized that I just need a few examples to make my points, instead of enumerating all the smart guys that I heard about (and many I even haven't heard about due to my insularity as human)...so I have to find a place to take a break...

> Did not know about about the age of the 25-page PhD thesis containing only 2 references (a slight exaggeration?) though. That is indeed a loss.

I did not know that either...I was looking for a 3-page PhD thesis, but did not find one (-- and also did not want to spend too much time on that)...then I came across John Nash's thesis -- so the act of ranting and complaining turned out to be a good learning experience as well...


I think the frequenters to HN are going to be predominantly comp-sci in background, but I have seen posts from persons with expertise in practically all knowledge domains.

My thinking about academia is that tools and methods should be taught independently of fields and disciplines. You should be able to study tools and methods to the best of your ability and you shouldn't be able to fail them. Certain skills precede certain others but you can keep leveling up so to speak for as long as you are able. This means that math and logic and programming and methodologies get taught to everyone and you're encouraged to push yourself as far as you can go with them.

This is an attempt to get rid of mathiness. If it's seen as a path anyone can journey along for as long as they want then we de-mythologize it.

We have to build a third culture. One that subsumes the arts/humanities and sciences. One that neither valorizes math and the hard sciences nor literature and its handmaidens.

Thinking about abstraction leads to the lambda calculus in the hands of Church and to abstract expressionism in the hands of Kandinsky.

What am I trying to say here? I guess it is, why do I have to go to Scientific American if I want to read about Betty Shannon but I have to read the Times Literary Supplement for the low down on Deleuze and Guattari?

Agh, maybe what I'm saying I'm not able to yet articulate. Hope this doesn't come across as pretentious waffle.


> I think the frequenters to HN are going to be predominantly comp-sci in background, but I have seen posts from persons with expertise in practically all knowledge domains.

Yes, I also have a similar feeling, although I don't have much data to back up this assumption -- but I think the name of the site, "hacker news", has certain appealing to people with that background, although these days the general semantics of the word "hacker" has been a bit different than it was in different time periods in the past [1]...

[1] http://www.newyorker.com/tech/elements/a-short-history-of-ha...

> My thinking about academia is that tools and methods should be taught independently of fields and disciplines. You should be able to study tools and methods to the best of your ability and you shouldn't be able to fail them. Certain skills precede certain others but you can keep leveling up so to speak for as long as you are able. This means that math and logic and programming and methodologies get taught to everyone and you're encouraged to push yourself as far as you can go with them.

I think quite a few other educators (i.e. Richard Levin and Cardinal Newman) also hold similar ideas about the purpose of college education (especially liberal education)... and in Levin's own words, "the purpose of liberal education is to develop the capacity for independent thought rather than to acquire specific or 'useful' knowledge"...

Nevertheless, in practice, regardless how you can make abstractions out of it, you have to use certain knowledge from specific domains as instances and examples for such teaching....and at the end of the day, it is always the practical skills thus acquired that would give any concrete meaning to those reasoning methods and tools...

> This is an attempt to get rid of mathiness. If it's seen as a path anyone can journey along for as long as they want then we de-mythologize it.

I always feel that one nice feature about mathematics that other disciplines -- if we really could separate mathematics from them -- do not necessarily possess is its convenience in measurement...I feel that the essence of measurement, be it scalar based or non-scalar based, is differentiation (and sometimes we could enforce certain types of ordering over this differentiation)...and hence it could be nicely used in various fields of study -- after all, the core of any study is often to differentiate and to categorize a certain set of objects...

> We have to build a third culture. One that subsumes the arts/humanities and sciences. One that neither valorizes math and the hard sciences nor literature and its handmaidens. Thinking about abstraction leads to the lambda calculus in the hands of Church and to abstract expressionism in the hands of Kandinsky. What am I trying to say here? I guess it is, why do I have to go to Scientific American if I want to read about Betty Shannon but I have to read the Times Literary Supplement for the low down on Deleuze and Guattari?

Well, I guess that's a problem of personal preference...although I myself have nothing against arts or humanities. But, for instance, what senses one can make out by teaching drawing for a kid who cannot see and does not have the willing to do that kind of expression? This example might be a bit extreme, but the point is that there is a whole spectrum with all kinds of nuances and individual differences over the set of the entire human race...

But I agree that we could have this "third culture" to give those students who would love to immerse themselves into such knowledge an opportunity to develop in those aspects...

And as a matter of fact, one of the practical goals that many liberal arts colleges in the United States ( -- I am sure many other parts of the world have also been doing similarly...) is to encourage students to develop in all kinds of areas they would enjoy. For instance, one of the students I know graduated with three bachelor degrees, one in music and one in computer science ( -- I don't remember the last one)....

> Agh, maybe what I'm saying I'm not able to yet articulate. Hope this doesn't come across as pretentious waffle.

I think you have articulated it quite well...and I myself personally enjoy this type of learning too :)


I read Mathematical Theory of Communication at a dear professor's request. It blew me completely away, if only because it was so simple (elegant?) and easy to follow, but ground breaking. Spent a semester debating switching from cs to pure mathematics because of that paper. Kind of wish I had.

Shannon died in 2001 in a nursing home from Alzheimer disease. Knowing that fills me with such a deep sadness, and a dash of complete panic at the reminder that shit just ain't fair.

Fuck Alzheimers.


> Even Shannon’s passions for investing and studying the stock market started with Betty. She became intrigued by the market and filled the home library with books on investment strategies and economics

Nowadays for many people it would be her browser's bookmarks and history getting filled with links to investment and economics sites and articles, rather than the home library getting filled with books.

I wonder if that makes it less common for one's interests to spread to others in the house?

With books, they get left around in living areas, ready to easily enthrall others who pick them up out of idle curiosity. When put away they are probably in bookshelves shared with others.

With bookmarked links there would be less opportunity to stumble across someone else's bookmarks. Everyone's bookmark list is on their own account, or even their own device.


I doubt it's much different. Sure, the content itself is more invisible, but social dynamics are probably a more important factor to spread. I know if I notice my wife engrossed in something on her phone or computer, I'm gonna ask her what she's found just out of sheer curiosity, and that's if she doesn't bring it up first. Conversely, if I'm fascinated by something, I'm gonna tell my wife (even if she doesn't care, much to her chagrin), and I'm gonna tell 'errbody who I think might have even a passing interest. Maybe we are unique in this regard, but I suspect not, given the success of everything from StumbleUpon to Delicious to Facebook...humans are just wired to share with each other.


* reads wiki, dissapointed

anyway, favorite quote

They would work side by side. Betty looked up references, took down Claude’s thoughts and, importantly, edited his written work. She offered her improvements and added historical references. As Betty put it, “Some of his early papers and even later papers are in my handwriting...and not in his, which confused people at first.” And not just his papers: Betty was a full partner in the gadgeteering, too. In fact, it was Betty—not Claude—who completed the wiring for Theseus the mouse.


The title and general coverage is actually pretty insulting to Betty Shannon, and suggests that we're scraping the bottom of the women in STEM barrel pretty hard, aren't we?


""[Shannon] didn't have much patience with people who weren't as smart as he was." It is telling that Shannon's few friends were themselves some of the era's greatest intellects: Alan Turing, John Pierce, Barney Oliver, Vannevar Bush."

Did Shannon ever meet von Neumann?


Yes, they were at IAS at the same time, along with Weyl, Einstein, and Godel. I think he met the latter two a few times but did not work with them. He did discuss ideas with Weyl and von Neumann, though.


quite likely...or at least they had communicated with each other...

It was von Neumann who suggested Shannon to use "entropy" as the word for the measurement of information...

http://spectrum.ieee.org/computing/software/claude-shannon-t...


For more on Shannon, "A Mind at Play: How Claude Shannon Invented the Information Age" is a recent book by the same authors (which I very much enjoyed).


They also did a very thorough AMA on reddit recently: https://www.reddit.com/r/IAmA/comments/6pa11p/we_spent_5_yea...


Indeed, very good book.


I'm really enjoying the new biography of Shannon this article is based on. (The authors were kind enough to send me a promo copy.)

It's amazing that such a central and fascinating figure hasn't had a book-length biography before now.




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