Claude Shannon: How a Genius Thinks, Works, and Lives(medium.com)
medium.com
Claude Shannon: How a Genius Thinks, Works, and Lives
https://medium.com/the-mission/10-000-hours-with-claude-shannon-12-lessons-on-life-and-learning-from-a-genius-e8b9297bee8f
108 comments
I went to school with his grandson - incredibly, ridiculously, intelligent guy, who was the only person three years ahead at the school - I and one other were two ahead, and a dozen or so were a year ahead.
That said, I always felt for the chap, as socially inept didn't begin to cover it (as someone who graduated school two years early I can say with surety that it wasn't solely the temporal displacement that fettered his sociality - it was definitely a factor for us all, but he couldn't/wouldn't communicate even with other maths geeks), and I could only see him pursuing a career in academia - which he is.
I also felt for him as as a mathematically brilliant Shannon expectations couldn't have been higher - I was going to cap this off by saying I'm sure he'll do great things, but instead, I'll say I hope he has a happy life.
That said, I always felt for the chap, as socially inept didn't begin to cover it (as someone who graduated school two years early I can say with surety that it wasn't solely the temporal displacement that fettered his sociality - it was definitely a factor for us all, but he couldn't/wouldn't communicate even with other maths geeks), and I could only see him pursuing a career in academia - which he is.
I also felt for him as as a mathematically brilliant Shannon expectations couldn't have been higher - I was going to cap this off by saying I'm sure he'll do great things, but instead, I'll say I hope he has a happy life.
Wow... what school is this, where everyone is years ahead?
King's Canterbury. Out of 700 pupils, there were about 20 one or more years ahead - I was skipped a few years when I was six, at a previous school, so just continued from there - similar for him, I believe. No idea how it is there now, I left 15 years ago.
I had the advantage of having always been tall for my age, so mostly hid the fact that I was young - Alex, however, was a fairly small chap and I think suffered for it.
Fond memories of celebrating my 18th at university, and the college bar being like "lol what, we've been serving you for a year".
I had the advantage of having always been tall for my age, so mostly hid the fact that I was young - Alex, however, was a fairly small chap and I think suffered for it.
Fond memories of celebrating my 18th at university, and the college bar being like "lol what, we've been serving you for a year".
Hasn't that school been running for over 1400 years?
Are the gifted students all in the same class?
No, and oddly, kids who were years ahead weren't necessarily viewed as being gifted - just ahead. The scholars were the gifted (grafters, bluntly, rather than gifted) ones, and wore special gowns and got discounted fees.
Rather than having a number of classes for each year, they operated a set system for each subject, so if you were great at maths and sucked at Latin, you could be in the top set for maths and bottom set for Latin.
Rather than having a number of classes for each year, they operated a set system for each subject, so if you were great at maths and sucked at Latin, you could be in the top set for maths and bottom set for Latin.
So the Shannon family moved to UK?
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As a psychology enthusiast (and soon to be student), I'm quite annoyed with our fascination with "geniuses".
It seems obvious that people who are very famous in their field became "very intelligent" because of a combination of hard work and genetics. But it's as if these books capitalize on the faint hope of being a repressed genius of some sort. I highly doubt Einstein or Shannon (as the article implies) ever saw themselves as more than passionate. And the ego required to want to find your inner genius goes contrary to the enormous humility they seemed to display.
That aside, these books and articles all make the same mistake of studying a single person after the fact. It's similar to mimicking Steve Jobs: That's not how he became Steve Jobs. We literally cannot know how much luck was involved in his (or Einstein's) success. Might as well study the lives of lottery winners.
So if not that, how can we maximize our potential and generally better ourselves intellectually? Simply by referring to the very vast fields of learning, motivation and general cognitive science.
But "learn the science" doesn't have quite the same ring to it as "how to be Einstein", now does it?
It seems obvious that people who are very famous in their field became "very intelligent" because of a combination of hard work and genetics. But it's as if these books capitalize on the faint hope of being a repressed genius of some sort. I highly doubt Einstein or Shannon (as the article implies) ever saw themselves as more than passionate. And the ego required to want to find your inner genius goes contrary to the enormous humility they seemed to display.
That aside, these books and articles all make the same mistake of studying a single person after the fact. It's similar to mimicking Steve Jobs: That's not how he became Steve Jobs. We literally cannot know how much luck was involved in his (or Einstein's) success. Might as well study the lives of lottery winners.
So if not that, how can we maximize our potential and generally better ourselves intellectually? Simply by referring to the very vast fields of learning, motivation and general cognitive science.
But "learn the science" doesn't have quite the same ring to it as "how to be Einstein", now does it?
This is speaking about a life a lot of us wish we had. That we are special, that people will see us as special, that money and awards pile up so much we can't be bothered to accept them, while feeling free to do whatever we find intellectually interesting.
I find no value in the hero worship myself. I find the notion of getting all excited because (name of person) said something kind of offensive.
Hard work and genetics aren't nearly enough. Saying "luck" doesn't even describe it either.
We often ignore the social element - the people that helped along the way, the parents that supported them dropping out of college, the professor or teacher that took a particular interest in them. When we do talk about it, it seems the usual message is "they were kind of an asshole"(e.g. Jobs).
We ignore the emotional element even more. I don't mean "they failed 3 times but their 4th startup was amazing, keep trying!". I mean the headspace that lets them do that. The little thing that lets Woz show his computer to Jobs and not just say "oh, it's a stupid little toy, meh". There are tons of setbacks in life for everyone, and it's not fair to say "well, they kept trying!" Things made that possible.
As you said, motivation is supremely important. If you get rewarded and acknowledged for playing with things, then you will. If you're struggling to find your identity and your parents want you to get a "real job", well...
I find no value in the hero worship myself. I find the notion of getting all excited because (name of person) said something kind of offensive.
Hard work and genetics aren't nearly enough. Saying "luck" doesn't even describe it either.
We often ignore the social element - the people that helped along the way, the parents that supported them dropping out of college, the professor or teacher that took a particular interest in them. When we do talk about it, it seems the usual message is "they were kind of an asshole"(e.g. Jobs).
We ignore the emotional element even more. I don't mean "they failed 3 times but their 4th startup was amazing, keep trying!". I mean the headspace that lets them do that. The little thing that lets Woz show his computer to Jobs and not just say "oh, it's a stupid little toy, meh". There are tons of setbacks in life for everyone, and it's not fair to say "well, they kept trying!" Things made that possible.
As you said, motivation is supremely important. If you get rewarded and acknowledged for playing with things, then you will. If you're struggling to find your identity and your parents want you to get a "real job", well...
To be blunt, most "genius worship" is just another way for someone to feel like they're better than you. Genius lay in the eye of the beholder - one person's unsung genius toiling in obscurity is another person's fool following their folly.
Geniuses may have additional creative, productive, or other cognitive capacities, but they are still humans. Indeed, having greater capacity means geniuses can waste far more time than an average person can access.
Geniuses may have additional creative, productive, or other cognitive capacities, but they are still humans. Indeed, having greater capacity means geniuses can waste far more time than an average person can access.
I like your comment about the eye of beholder. It captures the obstacle I find when trying to form a complete argument why, say, studying chess is a pursuit inferior to studying information theory.
Adjusting it closer to your comment, can we say that a chess genius is better than an information theory genius? Counter arguments would question the way I'm using "better".
Adjusting it closer to your comment, can we say that a chess genius is better than an information theory genius? Counter arguments would question the way I'm using "better".
Disclaimer: Was a Psych student. Now a programmer. :)
I have to agree that the word "genius" is just too loaded and misleading. There are many ways an individual can excel and many ways they fail to; most people are a mixed bag.
Shannon was gifted with a powerful curiosity and love of discovery, something not shared by all (and I'm not making a value judgment here at all; simply stating a fact). He never chose to have those motivations, so he should not be overly credited with the consequence of having them.
I have to agree that the word "genius" is just too loaded and misleading. There are many ways an individual can excel and many ways they fail to; most people are a mixed bag.
Shannon was gifted with a powerful curiosity and love of discovery, something not shared by all (and I'm not making a value judgment here at all; simply stating a fact). He never chose to have those motivations, so he should not be overly credited with the consequence of having them.
You might be interested in Walter Isaacson's The Innovators because it tries to show how collaboration rather than individual genius is at the heart of innovation. Isaacson writes about these ideas rather explicitly.
Maybe the genius is just that curious personality who never fit it and refuses to give in to society? That person would certainly have a sense of both their intelligence and creativity (and contrast it to most people's) and of how society treats them like complete blabbering fools on a hill.
This is the same underdog story every geek romanticizes for that never quite seems to match the biography of most known geniuses. Known geniuses seem to figure out how to fit into society and make it work for them.
It could easily be argued that known geniuses are known because they, for some reason, managed to fit in well enough, and not that they managed to fit in because they were geniuses.
There are known and measurable negative social effects that is strongly affecting people with high intelligence as measured by standard tests. Some fraction of highly intelligent people will certainly also be highly socially skilled - as skills really don't appear to be exclusive, a few will have an exceptionally strong drive to succeed, and some fraction will be in the right place at the right time. It is likely that those we know of have some measure of either, of those characteristics, and that the others simply never rose from obscurity however talanted they might have been. There are exceptions, as there is to all generalisations.
There are known and measurable negative social effects that is strongly affecting people with high intelligence as measured by standard tests. Some fraction of highly intelligent people will certainly also be highly socially skilled - as skills really don't appear to be exclusive, a few will have an exceptionally strong drive to succeed, and some fraction will be in the right place at the right time. It is likely that those we know of have some measure of either, of those characteristics, and that the others simply never rose from obscurity however talanted they might have been. There are exceptions, as there is to all generalisations.
I remember reading in Nikolai Tesla's biography how he didn't fit in the "way of Americans" feeling alienated and how his "correspondence" with women in USA felt odd.
It's not always about fitting into broader society. Tesla fit into a small niche of people who were into the same things. That's very similar to Shannon's story.
It's not always about fitting into broader society. Tesla fit into a small niche of people who were into the same things. That's very similar to Shannon's story.
I think there are two parts to the general idea of genius.
One part is the claim that some people are fundamentally more intelligent than others. I agree that this is good to discard.
But another part is that some people can make quantum advances in a given field. I think that is worth considering. It seems reasonable to think that some advances in a field are incremental and require simple effort and that other advances involves a jump - either digging very deeply into a still unsolved problem or taking insights from entirely different fields. Here, the term "genius" is good. Not implying an average person can't achieve a "genius insight" but that such insight may require reflection, a willingness to go down possibly blind allies, a willingness to take a different point of view from a different field, a willingness to challenge consensus views within one's own field and so-forth.
And this is also to say that "following your genius" may indeed be a great gamble. Combining a variety of seeming deep relations may result in something great or it may just result in a large project that falls apart on close inspection.
And here, one might say taste and temperament enter into what could be a genius approach (or oppositely, could be a disaster).
One part is the claim that some people are fundamentally more intelligent than others. I agree that this is good to discard.
But another part is that some people can make quantum advances in a given field. I think that is worth considering. It seems reasonable to think that some advances in a field are incremental and require simple effort and that other advances involves a jump - either digging very deeply into a still unsolved problem or taking insights from entirely different fields. Here, the term "genius" is good. Not implying an average person can't achieve a "genius insight" but that such insight may require reflection, a willingness to go down possibly blind allies, a willingness to take a different point of view from a different field, a willingness to challenge consensus views within one's own field and so-forth.
And this is also to say that "following your genius" may indeed be a great gamble. Combining a variety of seeming deep relations may result in something great or it may just result in a large project that falls apart on close inspection.
And here, one might say taste and temperament enter into what could be a genius approach (or oppositely, could be a disaster).
Could you recommend some research papers on learning, motivation and general cognitive science?
Relevant xkcd: https://xkcd.com/896/ (on becoming the next Marie Curie):
"But you don't become great by trying to be great. You become great by wanting to do something, and then doing it so hard that you become great in the process."
"But you don't become great by trying to be great. You become great by wanting to do something, and then doing it so hard that you become great in the process."
I highly doubt Einstein or Shannon (as the article implies) ever saw themselves as more than passionate.
They may have kept it to themselves, but they were certainly aware of their status.
Who are we to say what the author should or shouldn't study? Why is studying a genius a bad thing? (And they are geniuses, if it's possible to compare one person to another at all.)
You've made some good points about how someone becomes a genius: it's mostly luck, especially in genetics and upbringing. But there's no reason that studying this is inherently useless.
They may have kept it to themselves, but they were certainly aware of their status.
Who are we to say what the author should or shouldn't study? Why is studying a genius a bad thing? (And they are geniuses, if it's possible to compare one person to another at all.)
You've made some good points about how someone becomes a genius: it's mostly luck, especially in genetics and upbringing. But there's no reason that studying this is inherently useless.
This topic runs close to home for me in a a couple of ways. First, my research is broadly in the area - not geniuses, but individual differences. Second, as a scientist, in professional capacity I've come into personal contact with a couple of giants in the field who have been called geniuses, some who most people here would recognize, others who might be less well-known.
I've grown very disillusioned with the term "genius." Part of this has become because of how painfully obvious randomness plays in all of this, from a scientific perspective - not all, but a lot of it. Another part of it, though, is from seeing how social factors shape our labeling of geniuses from others, and the consequences that has. Maybe they're the same thing, but to me they're a bit different, in that you can ask "why is this high-ability person the way they are" but you can also ask "how is that this high-ability person becomes singled out"?
It's not so much that those labeled geniuses haven't made contributions. But in the couple of cases I'm aware of, it's almost as if there's a cult of personality surrounding them, that amplifies the apparent importance of what they did, far beyond the person's actual contributions. So that their mistakes, and the sometimes serious consequences of those mistakes are conveniently forgotten; also forgotten are others in the field who contributed the same ideas or findings, but at the wrong time or in the wrong outlet. There's dynamic patterns, too, in that the person who proposes the same things, but to the wrong audience or at the wrong time is literally discouraged and punished, and the other is encouraged and rewarded. Is a framework that includes the concept of genius even accurate then?
I think one needs to take very seriously in life whether or not they believe in a just world and why.
I've grown very disillusioned with the term "genius." Part of this has become because of how painfully obvious randomness plays in all of this, from a scientific perspective - not all, but a lot of it. Another part of it, though, is from seeing how social factors shape our labeling of geniuses from others, and the consequences that has. Maybe they're the same thing, but to me they're a bit different, in that you can ask "why is this high-ability person the way they are" but you can also ask "how is that this high-ability person becomes singled out"?
It's not so much that those labeled geniuses haven't made contributions. But in the couple of cases I'm aware of, it's almost as if there's a cult of personality surrounding them, that amplifies the apparent importance of what they did, far beyond the person's actual contributions. So that their mistakes, and the sometimes serious consequences of those mistakes are conveniently forgotten; also forgotten are others in the field who contributed the same ideas or findings, but at the wrong time or in the wrong outlet. There's dynamic patterns, too, in that the person who proposes the same things, but to the wrong audience or at the wrong time is literally discouraged and punished, and the other is encouraged and rewarded. Is a framework that includes the concept of genius even accurate then?
I think one needs to take very seriously in life whether or not they believe in a just world and why.
I agree with your sentiment, however I would extend it beyond genius to success in general; and our tendency to conflate the two makes it substantially harder to study either, I think.
Fair enough regarding the status.
> Who are we to say what the author should or shouldn't study? Why is studying a genius a bad thing?
The authors can do whatever they want with their time. But people who buy books and read articles on geniuses would be better served buying and reading science-based books on intelligence. They mostly have all the same advice without the fluff of big names. Also they are actually empirical science, which can't always be said about studies on "famous" people (which to me seem more akin to profiling).
That's not to say you can't enjoy a good biography. But titles like these and what they imply just rub me the wrong way. We're not Einsteins, we'll never be geniuses, and that's fine.
> Who are we to say what the author should or shouldn't study? Why is studying a genius a bad thing?
The authors can do whatever they want with their time. But people who buy books and read articles on geniuses would be better served buying and reading science-based books on intelligence. They mostly have all the same advice without the fluff of big names. Also they are actually empirical science, which can't always be said about studies on "famous" people (which to me seem more akin to profiling).
That's not to say you can't enjoy a good biography. But titles like these and what they imply just rub me the wrong way. We're not Einsteins, we'll never be geniuses, and that's fine.
I concur. As a teacher and mentor to students, I find that assigning the label of "genius" to anyone famous for their accomplishments can have a negative affect on young learner's goals. They often think "oh, they're just a genius, that's how they've accomplished X". I try and dispel this, giving them examples of how most "geniuses" just worked really hard on one thing, and that if they focus and work hard on the one thing they are passionate about they will find that someday they may be referred to as a "genius".
Yes. They worked to get to the limits of their abilities, and that's how they accomplished so much. Without that work, their potential would have been wasted.
Everyone's limits are at a different location for different tasks, and they can be pushed to some extent, but not indefinitely. (If nothing else, people eventually die.) Finding how far your limits in a useful or fun area can be pushed is a worthwhile task as well, and progress is measured by change relative to your past, not someone else's.
So we sit between two tragedies:
On the one hand, we have people who believe genius is magic, and unapproachable, who never work to find what their level is, and never work to push it out.
On the other, we have people who think any level can be attained through hard work, who work themselves into burnout or worse trying to reach goals their lives aren't long enough to attain, and who never appreciate the progress they have made.
Everyone's limits are at a different location for different tasks, and they can be pushed to some extent, but not indefinitely. (If nothing else, people eventually die.) Finding how far your limits in a useful or fun area can be pushed is a worthwhile task as well, and progress is measured by change relative to your past, not someone else's.
So we sit between two tragedies:
On the one hand, we have people who believe genius is magic, and unapproachable, who never work to find what their level is, and never work to push it out.
On the other, we have people who think any level can be attained through hard work, who work themselves into burnout or worse trying to reach goals their lives aren't long enough to attain, and who never appreciate the progress they have made.
> But people who buy books and read articles on geniuses would be better served buying and reading science-based books on intelligence.
I'd say they'd be even better served buying and reading actual science books. Suddenly they could realize they're smarter than they thought.
I'd say they'd be even better served buying and reading actual science books. Suddenly they could realize they're smarter than they thought.
Perhaps, but not necessarily. Sadly I've found most people have reasonable innate intelligence but were never taught logic. They were never given the subtle tools need to even figure out basic problems on a logical basis, instead relying on intuition and some basic pattern recognition. Dealing with vast logical abstractions, even if put in layman's terms, simply overwhelms them.
You first have to teach them analysis, how to break things down and recombine them. A good example here is teaching beginning computer science students how to divide a large, complicated task into a long list of small tasks. Or teaching derivations in basic physics. It's something that's not really formally taught outside of the sciences, and that's a shame.
You first have to teach them analysis, how to break things down and recombine them. A good example here is teaching beginning computer science students how to divide a large, complicated task into a long list of small tasks. Or teaching derivations in basic physics. It's something that's not really formally taught outside of the sciences, and that's a shame.
Any books to get improve my logic muscle?
There are plenty of good books on Mathematical logic and set theory, but they're pretty dense, dry and tend to lack context.
Honestly I'd recommend the more complex puzzle games. Top recommendation there would probably be SpaceChem: https://www.gog.com/game/spacechem
Solutions to each problem are readily available on youtube, and while it starts off extremely basic the mid and upper level puzzles force you to break things down into distinct parts and have them work together. Best part is there's theoretically thousands of solutions to every puzzle, so even if you crack and look one up, you can then challenge yourself to make a better solution in some way. In fact the game shows you metrics at the end of each puzzle, showing how your solution compared to other players in terms of time, number of parts used, etc.
It's also a lot more entertaining than a textbook as has a pretty awesome soundtrack. :)
Honestly I'd recommend the more complex puzzle games. Top recommendation there would probably be SpaceChem: https://www.gog.com/game/spacechem
Solutions to each problem are readily available on youtube, and while it starts off extremely basic the mid and upper level puzzles force you to break things down into distinct parts and have them work together. Best part is there's theoretically thousands of solutions to every puzzle, so even if you crack and look one up, you can then challenge yourself to make a better solution in some way. In fact the game shows you metrics at the end of each puzzle, showing how your solution compared to other players in terms of time, number of parts used, etc.
It's also a lot more entertaining than a textbook as has a pretty awesome soundtrack. :)
But nonetheless, this is exactly the kind of thing that will open the door for me! Thanks.
I'd still be interested if you had any books to recommend.
If the books are dense and dry then how we teach them about logic.
Bump, I'm curious about this aswell.
I really hope Chandrasekhar realized he was a genius. Anything less would be tragic.
If I hold this hope for someone who is a genius but sadly not a household name, I should probably hope the same for people who happened to become famous as well.
If I hold this hope for someone who is a genius but sadly not a household name, I should probably hope the same for people who happened to become famous as well.
People never really do accept the notion that success, genius, wealth, etc are not so easy to replicate. Meanwhile people selling these books have actually figured out a way to replicate the wealth aspect, hence the existence of a self help industry. It's not much different from people here goggling at Thiel or Musk.
Hindsight is a bitch, and our heuristics tend to fail in the face of it.
Hindsight is a bitch, and our heuristics tend to fail in the face of it.
Interestingly, I just listened to a decent podcast with Ed Thorp (an interesting man in his own right) who briefly talked about his work with Shannon.
https://www.bloomberg.com/news/audio/2017-07-14/ed-thorp-the...
https://www.bloomberg.com/news/audio/2017-07-14/ed-thorp-the...
Was curious enough about the thesis paper, I went searching for it.
http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425...
http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425...
Vint Cerf's article on Claude Shannon: http://www.nature.com/nature/journal/v547/n7662/full/547159a...
>But if his tendency to follow his curiosity wherever it led sometimes rendered him less productive, he also had the patience to keep coming back to his best ideas, over the course of years.
[snip]
>“He never argued his ideas. If people didn’t believe in them, he ignored those people.”
I think there's a connection here which reveals a common misconception about intellectual creation, namely that scientific theories are born in a legalistic fashion by criticism, argument and debate. In reality the role of criticism is to defend against ideas we don't like. Ideas we do like are shielded from explicit criticism, for instance by ignoring critics, and allowed to grow in our brains over time. It's a pleasure to return to such ideas again and again, while they remain interesting, so 'patience' isn't required either.
[snip]
>“He never argued his ideas. If people didn’t believe in them, he ignored those people.”
I think there's a connection here which reveals a common misconception about intellectual creation, namely that scientific theories are born in a legalistic fashion by criticism, argument and debate. In reality the role of criticism is to defend against ideas we don't like. Ideas we do like are shielded from explicit criticism, for instance by ignoring critics, and allowed to grow in our brains over time. It's a pleasure to return to such ideas again and again, while they remain interesting, so 'patience' isn't required either.
> "Letters he didn’t want to respond to went into a bin labeled “Letters I’ve Procrastinated On For Too Long.” ... Inbox zero, be damned."
moving things to folders is... the definition of "inbox zero"?
moving things to folders is... the definition of "inbox zero"?
My thought exactly. The authors seem to have gotten it completely backwards.
If you have no intention of actually doing anything about them, then yes.
Boy is this article filled with unwarranted hyperbole. And Tim Ferris, really?
Substance is overwhelmingly like a self-improvement article, cherrypicking details to support whatever point the author stands to posit.
Substance is overwhelmingly like a self-improvement article, cherrypicking details to support whatever point the author stands to posit.
>Substance is overwhelmingly like a self-improvement article
Because many believe that if they just work or behave like a genius or successful entrepreneur they will be one as well. It's the mental equivalent of a trendy diet. It's not that there's not some interesting habits in the article, but people will focus on the easy bits and start riding unicycles, not reading their emails and leaving checks uncashed.
Like diets, people want to hear things like: Eat a lemon with every meal and only poop on Thursdays. Allowing yourself to be mentored is hard, if it doesn't come natural to you. Being patient and keep working on problem for years on end is equally hard. It's not bad advise, it's just really hard to implement.
Because many believe that if they just work or behave like a genius or successful entrepreneur they will be one as well. It's the mental equivalent of a trendy diet. It's not that there's not some interesting habits in the article, but people will focus on the easy bits and start riding unicycles, not reading their emails and leaving checks uncashed.
Like diets, people want to hear things like: Eat a lemon with every meal and only poop on Thursdays. Allowing yourself to be mentored is hard, if it doesn't come natural to you. Being patient and keep working on problem for years on end is equally hard. It's not bad advise, it's just really hard to implement.
I bet there would be many more geniuses with ubi
Quite possibly. From what it sounds like, Shannon's job with Bell Labs was kinda his form of UBI. They didn't really make him "work"; they just kinda gave him money, and told him to do what he felt like. That lead to a bunch of impressive things, given the resources he had access to.
Granted, a lot of that came after some of his groundbreaking work on information theory, which is what earned him his fame.
Granted, a lot of that came after some of his groundbreaking work on information theory, which is what earned him his fame.
If there were many more geniuses wouldn't all them considered normal? Geniuses are only geniuses because they have been perceived to operate several standard deviation above the average level of achievements. It's too bad that humans usually value themselves in relative to people near them. Like top students at bottom ranked schools probably feel really proud and happy on a day to day basis, but bottom students from top schools are often depressed and occasionally commit suicide. Even the top student at bottom schools feel depressed that they couldn't get into a better school out of college, when in reality most people in the world didn't have opportunities to go to college.
> During World War II, those friends included Alan Turing, with whom Shannon struck up a lively intellectual exchange during Turing’s fact-finding trip to study American cryptography on behalf of the British government.
This little tidbit has always fascinated me from a What-If perspective, because of course because of the War and secrecy, Turing and Shannon did not discuss cryptography, the Bombe (Turing's Enigma-cracking machine) or the Colossus (arguably the first electronic computer, except its very existence remained a secret until the 1970s).
How would've things gone had they been able to talk freely?
This little tidbit has always fascinated me from a What-If perspective, because of course because of the War and secrecy, Turing and Shannon did not discuss cryptography, the Bombe (Turing's Enigma-cracking machine) or the Colossus (arguably the first electronic computer, except its very existence remained a secret until the 1970s).
How would've things gone had they been able to talk freely?
There seems to be a lot of parallels in how Shannon lived and how Feynman lived. Obviously, Feynman was more gregarious, but they both found inspiration and solace in curious play. I think more than curiosity, which most people have, they both showed a profound disinterest in hiding their interests or fear of looking dumb.
That might be the biggest difference between smart guys who work jobs and geniuses who pave new paths. It is both sad and empowering because it means we simply get in our own way when we try to be "serious adults".
That might be the biggest difference between smart guys who work jobs and geniuses who pave new paths. It is both sad and empowering because it means we simply get in our own way when we try to be "serious adults".
I've seen 3 Claude Shannon articles on HN in the past 2 weeks. What's the occasion?
There's a new biography on him, A Mind at Play
https://www.amazon.com/Mind-Play-Shannon-Invented-Informatio...
https://www.amazon.com/Mind-Play-Shannon-Invented-Informatio...
Honestly it is hard for me to regard as very credible an author who openly admits not knowing who shannon was before starting this book..
We all start from zero. If a person can't be knowledgeable after a bit of rigor, then no one can be trusted in any subject and we can see how everything will become "fake news" and "alterntative facts"
I suppose. Another part of this I try to read science writers who have a bit of a stem background, like the very good http://www.ericaklarreich.com/
I find people with no stem background, even when they mean very well and work hard, just miss a lot when doing writing of this sort. They simply do not and in a real sense cannot understand the process of creating new scientific knowledge. Their impressions are merely metaphorical and not direct. Having the words 'genius' in the title...ugh. I suppose I am maybe not the target audience for this though.
I find people with no stem background, even when they mean very well and work hard, just miss a lot when doing writing of this sort. They simply do not and in a real sense cannot understand the process of creating new scientific knowledge. Their impressions are merely metaphorical and not direct. Having the words 'genius' in the title...ugh. I suppose I am maybe not the target audience for this though.
Well, I find it very motivational.
You lost me at "10'000 hours".
One thing that occurred to me is that if Einstein or Shannon hadn't discovered their respective theories, someone else would have. It probably wouldn't have taken very long, either.
I'm not sure what to do with this information, but it seems true.
I'm not sure what to do with this information, but it seems true.
The same is true of most (all?) scientific discoveries. A good evidence for it the fact that most important breakthroughs were made independently, within the space of months or years, by two or more people/teams that didn't collaborate with each other.
My takeaway is that science is very incremental, and discoveries depend on what the state of scientific knowledge is at any given time, and not on particular smart individuals.
I also believe the same applies to social progress - e.g. if Martin Luther died as a child, someone else would start the Reformation; if Marx and Lenin decided to pursue art instead of economics/politics, someone else would invent communism anyway, etc.
My takeaway is that science is very incremental, and discoveries depend on what the state of scientific knowledge is at any given time, and not on particular smart individuals.
I also believe the same applies to social progress - e.g. if Martin Luther died as a child, someone else would start the Reformation; if Marx and Lenin decided to pursue art instead of economics/politics, someone else would invent communism anyway, etc.
Someone mentioned this earlier - "The Innovators" by Walter Isaacson is pretty much this thesis exactly. Progress comes from building on previous work, usually collaboratively.
Now, I think it's fair to say that there are "geniuses" and it's perhaps a little uncharitable to claim that we shouldn't look up to them at all - but there is certainly more than one dimension to progress.
Now, I think it's fair to say that there are "geniuses" and it's perhaps a little uncharitable to claim that we shouldn't look up to them at all - but there is certainly more than one dimension to progress.
Its very tempting to believe that because most of math/science (e.g.) is incremental, that all math is incremental. Once in a long while I stumble onto something really new, a theorem or a proof which simply has no precedent. These things make you go "wow how did someone think of that?" - and it is the ability to do that which distinguishes a genius from a regular and competent mathematician.
It's very easy to dismiss all ideas as being incremental, but I think there exist real, rare sparks of genius which leapfrog the field forward, and these sparks of genius only get deeper and more mysterious the more you think of it. My only reaction to these ideas is a certain sense of awe.
It's very easy to dismiss all ideas as being incremental, but I think there exist real, rare sparks of genius which leapfrog the field forward, and these sparks of genius only get deeper and more mysterious the more you think of it. My only reaction to these ideas is a certain sense of awe.
Incremental, or low cost/risk? A more general concept. Because sometimes what seems non-incremental, is just a change in economics.
At a history of biology colloquium, a sociology of science person, was trying to fit a narrative of new perspectives unlocking previously unconsidered questions. And the pushback was, no, the dominant effect was the cost of various tools dropping by multiple orders of magnitude. Which changed previously intractably (and thus uninteresting) questions, into potentially fruitful ones (worth pursuing).
One of the many problems with patents, is non-obviousness being incorrectly assumed time-invariant. Granting multi-decade monopolies for "you did it this year, that's cute - everyone else was waiting until next year, when it would be easy", which doesn't promote the progress of science and useful arts.
At a history of biology colloquium, a sociology of science person, was trying to fit a narrative of new perspectives unlocking previously unconsidered questions. And the pushback was, no, the dominant effect was the cost of various tools dropping by multiple orders of magnitude. Which changed previously intractably (and thus uninteresting) questions, into potentially fruitful ones (worth pursuing).
One of the many problems with patents, is non-obviousness being incorrectly assumed time-invariant. Granting multi-decade monopolies for "you did it this year, that's cute - everyone else was waiting until next year, when it would be easy", which doesn't promote the progress of science and useful arts.
Although it's true that there are many examples of multiple independent discoveries (supporting the zeitgeist theory of invention), this does not fully explain the nature of discovery and invention.
Consider that many of the examples, when examined carefully, fail to maintain the independence constraint. If the inventors were not in communication with each other but were consulting the same sources, or studying the same past failures (which was often) the case for independence becomes weaker. Nonetheless, one can still make the argument that since all the pieces were in place, that the inventor was less important. Three things stick a wrench in this: people who were truly ahead of their time, when there are many qualified yet with only a few succeeding and when there are outstandingly prolific individuals.
1) A notable example of someone ahead of their time is Hermann Grassmann, who toiled for many years in relative obscurity, quietly nursing a zoo of groundbreaking ideas. Gregor Mendel is another example. His discoveries took 30 more years to be independently rediscovered by 3 different individuals when the time was more ripe.
2) At each point in time, one can argue that many individuals met the criteria, from an intellectual and knowledge standpoint, to produce an invention yet only a handful do. There were plenty of people just as or even more intelligent than Einstein. Some even got very close to making the breakthroughs he did but none ever quite did. It seems genius individuals are able to grasp enough of a space to take steps that are locally suboptimal but end up escaping local optima for far better optima. There's a great deal of chance to this and it's not an issue of just out of the box thinking and high IQ (but sadly for the rest of us, it's likely still an innate quality).
3) It's difficult to look at the works of Gauss and Euler and not think there was something special about them. Genius individuals tend not to be one hit wonders and usually have something of an outsized effect on their field. While it's true that there is a rich get richer effect, the ability of geniuses to generate novel ideas and fields of investigation slightly outpaces their peers. And when advantages multiply, which is likely the case for productivity, these unique individuals end up dominating.
In the language of machine learning, geniuses seem able to sample more widely and are better at learning to learn. Even though it's likely that they're only a bit better at those things and they don't think qualitatively differently than the average person, it still ends up making a large amount of difference.
All in all, 2) impacts 3) which makes it so multiple independent discoveries can more readily occur. This doesn't mean the importance of environment can be discounted. Genius only appears under conditions of stability and sharing, the availability of gifted mentors and a rich set of freely shared and interacting ideas.
Consider that many of the examples, when examined carefully, fail to maintain the independence constraint. If the inventors were not in communication with each other but were consulting the same sources, or studying the same past failures (which was often) the case for independence becomes weaker. Nonetheless, one can still make the argument that since all the pieces were in place, that the inventor was less important. Three things stick a wrench in this: people who were truly ahead of their time, when there are many qualified yet with only a few succeeding and when there are outstandingly prolific individuals.
1) A notable example of someone ahead of their time is Hermann Grassmann, who toiled for many years in relative obscurity, quietly nursing a zoo of groundbreaking ideas. Gregor Mendel is another example. His discoveries took 30 more years to be independently rediscovered by 3 different individuals when the time was more ripe.
2) At each point in time, one can argue that many individuals met the criteria, from an intellectual and knowledge standpoint, to produce an invention yet only a handful do. There were plenty of people just as or even more intelligent than Einstein. Some even got very close to making the breakthroughs he did but none ever quite did. It seems genius individuals are able to grasp enough of a space to take steps that are locally suboptimal but end up escaping local optima for far better optima. There's a great deal of chance to this and it's not an issue of just out of the box thinking and high IQ (but sadly for the rest of us, it's likely still an innate quality).
3) It's difficult to look at the works of Gauss and Euler and not think there was something special about them. Genius individuals tend not to be one hit wonders and usually have something of an outsized effect on their field. While it's true that there is a rich get richer effect, the ability of geniuses to generate novel ideas and fields of investigation slightly outpaces their peers. And when advantages multiply, which is likely the case for productivity, these unique individuals end up dominating.
In the language of machine learning, geniuses seem able to sample more widely and are better at learning to learn. Even though it's likely that they're only a bit better at those things and they don't think qualitatively differently than the average person, it still ends up making a large amount of difference.
All in all, 2) impacts 3) which makes it so multiple independent discoveries can more readily occur. This doesn't mean the importance of environment can be discounted. Genius only appears under conditions of stability and sharing, the availability of gifted mentors and a rich set of freely shared and interacting ideas.
This sort of determinism seems wrong. It implies that if you had a Monte Carlo simulation engine of the universe and ran it 1,000 times beginning at the 20th century through today, you would expect those iterations to look a lot like our world. Only with some of the names and people being different, but fundamentally, everything else would still have happened.
That seems unlikely, no?
That seems unlikely, no?
Yeah, sort of. I'd say it's quite likely.
The thing about how engineering and the markets work - they are attracted towards local optimas. So I'd expect each iteration to e.g. have cars that are more-less like we know. I'd expect it to have soft drinks; maybe not Coca Cola, but something very similar and recognizable to us, etc.
The thing about how engineering and the markets work - they are attracted towards local optimas. So I'd expect each iteration to e.g. have cars that are more-less like we know. I'd expect it to have soft drinks; maybe not Coca Cola, but something very similar and recognizable to us, etc.
The thing about Einstein, at least, is that he formulated a precise, compact framework that expressed a variety of results that had arrived already in his time.
Without Einstein (and maybe Shannon and other geniuses), all of the results might still be here but might be summarized in a much more difficult and confusing fashion. Perhaps someone later would discover the compact formulation but quite possibly would not be able get it accepted due to the more verbose and confusing formulations already being established.
Maybe not exactly equivalent but some claim that using a constant tau, equal to 2 times pi, would simplify a lot of math - of course good luck changing that now.
See: https://www.scientificamerican.com/article/let-s-use-tau-it-...
Without Einstein (and maybe Shannon and other geniuses), all of the results might still be here but might be summarized in a much more difficult and confusing fashion. Perhaps someone later would discover the compact formulation but quite possibly would not be able get it accepted due to the more verbose and confusing formulations already being established.
Maybe not exactly equivalent but some claim that using a constant tau, equal to 2 times pi, would simplify a lot of math - of course good luck changing that now.
See: https://www.scientificamerican.com/article/let-s-use-tau-it-...
> Einstein ... formulated a precise, compact framework that expressed a variety of results that had arrived already in his time
Einstein had an especially productive 1905, publishing three groundbreaking papers among others [1].
His paper on Special Relativity certainly consolidated the work of Poincaré, Lorentz, Minkowski and others, much as you say.
His paper on the photoelectric effect, while building on Planck's work, outright contradicted the earlier work of Maxwell and was a crucial contribution to quantum mechanics.
His paper on Brownian motion, on the other hand, built on very little earlier work and provided the first work offering a method to count molecules; moreover, the paper was the foundation for Perrin's demonstration of the physicality of Dalton's atomic theory.
Each of these three papers had enormous immediate impact, and we still use much of the mathematical forms he introduced in each.
Einstein did not stop with these 1905 papers.
> be summarized in a much more difficult and confusing fashion
Einstein certainly proposed a number of write-downs that were neither easy nor unconfusing. General Relativity (GR) is perhaps a good example of one of those in a theory that has proven to be highly successful. Solving the field equations of GR requires solving a system of ten nonlinear partial differential equations (which in itself would exceptionally difficult even before confronting the explosion into the thousands of elliptical, hyperbolic and undefined terms in the PDEs' couplings in general coordinates). Indeed, we're still confused about how one can decide whether a given solution to the field equations is unphysical and derivative questions like whether a physically plausible solution to the field equations can always be studied using the initial value formulation or something similar.
The mathematical structure of GR is complete and self-consistent, and the notation Einstein developed was extremely concise, but it would be wrong to think that the tersest notation (omitting indices and constant factors) G = T makes GR only as complex as tersest notation (omitting constant factors and in coordinates in which momentum vanishes[2]) E = m of Special Relativity.
---
[1] In 1905 he published more than twenty other papers too, several of which are only "lesser" in that they do not figure in the minds of non-specialists.
[2] People tend to underestimate the complexity of Special Relativity; with suitable choices of coordinates one can use it extremely liberally in flat spacetime, including where acceleration is non-negligible (i.e., where there is obviously non-uniform motion in the systems under study). It's only the presence of real gravity that wrecks the globality of Special Relativity; but even where there is real gravity -- which is never exactly uniform or linear -- Special Relativity is still valid locally).
Einstein had an especially productive 1905, publishing three groundbreaking papers among others [1].
His paper on Special Relativity certainly consolidated the work of Poincaré, Lorentz, Minkowski and others, much as you say.
His paper on the photoelectric effect, while building on Planck's work, outright contradicted the earlier work of Maxwell and was a crucial contribution to quantum mechanics.
His paper on Brownian motion, on the other hand, built on very little earlier work and provided the first work offering a method to count molecules; moreover, the paper was the foundation for Perrin's demonstration of the physicality of Dalton's atomic theory.
Each of these three papers had enormous immediate impact, and we still use much of the mathematical forms he introduced in each.
Einstein did not stop with these 1905 papers.
> be summarized in a much more difficult and confusing fashion
Einstein certainly proposed a number of write-downs that were neither easy nor unconfusing. General Relativity (GR) is perhaps a good example of one of those in a theory that has proven to be highly successful. Solving the field equations of GR requires solving a system of ten nonlinear partial differential equations (which in itself would exceptionally difficult even before confronting the explosion into the thousands of elliptical, hyperbolic and undefined terms in the PDEs' couplings in general coordinates). Indeed, we're still confused about how one can decide whether a given solution to the field equations is unphysical and derivative questions like whether a physically plausible solution to the field equations can always be studied using the initial value formulation or something similar.
The mathematical structure of GR is complete and self-consistent, and the notation Einstein developed was extremely concise, but it would be wrong to think that the tersest notation (omitting indices and constant factors) G = T makes GR only as complex as tersest notation (omitting constant factors and in coordinates in which momentum vanishes[2]) E = m of Special Relativity.
---
[1] In 1905 he published more than twenty other papers too, several of which are only "lesser" in that they do not figure in the minds of non-specialists.
[2] People tend to underestimate the complexity of Special Relativity; with suitable choices of coordinates one can use it extremely liberally in flat spacetime, including where acceleration is non-negligible (i.e., where there is obviously non-uniform motion in the systems under study). It's only the presence of real gravity that wrecks the globality of Special Relativity; but even where there is real gravity -- which is never exactly uniform or linear -- Special Relativity is still valid locally).
Could be, at the same time I would argue that those who had disproportional impact almost by definition thought very differently from others (defying convention is tough: imagine what is must feel like to question the multi century reign of Newton as a lowly patent clerk).
Very few minds have done the work to come within reach of the conclusions that these guys have been able to draw. From there I suppose it ought to be possible to approximate the likelihood of a Eureka moment probabilistically.
I'd be interested whether future scientific progress is so complex that it cannot be attributed to a single mind (some indicators are rising numbers of contributors for influential papers).
Very few minds have done the work to come within reach of the conclusions that these guys have been able to draw. From there I suppose it ought to be possible to approximate the likelihood of a Eureka moment probabilistically.
I'd be interested whether future scientific progress is so complex that it cannot be attributed to a single mind (some indicators are rising numbers of contributors for influential papers).
I think this is precisely what 'sillysaurus3 is arguing against. Studying relativity a bit closer in its historical context shows that most relevant groundwork for the theory was already laid down by other scientists. Einstein might have been the first to connect those dots and publish, but I seriously doubt that he was magically smarter than all the other interested people. That is, if he didn't do it, someone else would, probably at most few years later.
He wrote three groundbreaking papers in 1905; Special Relativity was just one of them. He continued writing groundbreaking papers for decades after that. Even his unsuccessful investigations produced interesting insights.
Sure, "someone else" may have eventually written down much of the content of any one of these three papers, but probably not all three and not all in the same year.
Notably, he could have won the Nobel prize for any of those important 1905 papers (and did so for the photoelectric effect, rather than Special Relativity). In the same year he also had more than twenty other papers published, several of which were intersting, and all of which are eclipsed by the famous one on relativity.
In objectively quantifiable terms, the count, rate, and accuracy of his published papers over the years is simply exceptional.
A bit more detail here: https://news.ycombinator.com/item?id=14823796
Sure, "someone else" may have eventually written down much of the content of any one of these three papers, but probably not all three and not all in the same year.
Notably, he could have won the Nobel prize for any of those important 1905 papers (and did so for the photoelectric effect, rather than Special Relativity). In the same year he also had more than twenty other papers published, several of which were intersting, and all of which are eclipsed by the famous one on relativity.
In objectively quantifiable terms, the count, rate, and accuracy of his published papers over the years is simply exceptional.
A bit more detail here: https://news.ycombinator.com/item?id=14823796
I was hoping someone would mention Newton. I think if we measure Genius by (time of discovery before that discovery would have happened without the individual), Newton would rank as the greatest Genius in human history.
Most apparent with Darwin's theory of natural selection: He had to rush to publish because someone else had stumbled upon the same thing while he was still analyzing his data and compiling it together.
Is that true? That's very interesting. The common story is that he had to rush to publish it because he was worried about his health.
Yes, GP is correct: https://en.wikipedia.org/wiki/Alfred_Russel_Wallace#Natural_.... Where is that story common, I've never heard it.
From Darwin himself: https://archive.org/stream/originofspecies00darwuoft/origino...
My work is now (1859) nearly finished; but as it will take me many more years to complete it, and as my health is far from strong, I have been urged to publish this Abstract.
I remembered this quote, yet failed to recall the very next sentence:
I have more especially been induced to do this, as Mr. Wallace, who is now studying the natural history of the Malay archipelago, has arrived at almost exactly the same general conclusions that I have on the origin of species.
Whoops. That's some impressive integrity!
My work is now (1859) nearly finished; but as it will take me many more years to complete it, and as my health is far from strong, I have been urged to publish this Abstract.
I remembered this quote, yet failed to recall the very next sentence:
I have more especially been induced to do this, as Mr. Wallace, who is now studying the natural history of the Malay archipelago, has arrived at almost exactly the same general conclusions that I have on the origin of species.
Whoops. That's some impressive integrity!
Yes it is true. Alfred Russel Wallace was on the other side of the world doing his own independent work and looked to Darwin for advice about his own theories. ARW is a bit of an unsung hero with regard to what he contributed to this part of Biology (at least to those that are not deeply involved in Biology).
https://en.wikipedia.org/wiki/Charles_Darwin#Publication_of_...
https://en.wikipedia.org/wiki/Charles_Darwin#Publication_of_...
It steam engines when it's steam engine time, and I guess it theory-of-relativities when it's theory-of-relativity time.
It's still pretty remarkable that Einstein/Shannon were the ones to discover their respective theories though. Can you imagine what it must have been like for them? I've always envied genius. Genius always know exactly what it's supposed to do and just does. Recently I'm wondering whether I'm truly cut out for my chosen field (programming).
It's still pretty remarkable that Einstein/Shannon were the ones to discover their respective theories though. Can you imagine what it must have been like for them? I've always envied genius. Genius always know exactly what it's supposed to do and just does. Recently I'm wondering whether I'm truly cut out for my chosen field (programming).
If Einstein or Shannon hadn't discovered their respective theories, they would have discovered something else.
Not sure what that does for you, but it also seems true.
Not sure what that does for you, but it also seems true.
if Einstein or Shannon hadn't discovered their respective theories, someone else would have
Maybe
It probably wouldn't have taken very long, either. It actually could take decades, centuries, millenia. Think of all the discoveries lost to antiquity that had to be rediscovered. Think of Eulers findings that would take decades for some othe mathematician to figure out afresh
It probably wouldn't have taken very long, either. It actually could take decades, centuries, millenia. Think of all the discoveries lost to antiquity that had to be rediscovered. Think of Eulers findings that would take decades for some othe mathematician to figure out afresh
Well, Fermat's last theorem is one such example. How long did it take to rediscover a proof?
I believe the consensus among mathematicians is that Fermat either didn't have a proof or had an incorrect proof.
Any statement of the modern proof would require hundreds of pages and results not available to Fermat. So it's likely Wiles didn't rediscover the proof but simply discovered it.
Any statement of the modern proof would require hundreds of pages and results not available to Fermat. So it's likely Wiles didn't rediscover the proof but simply discovered it.
What makes you think so?
Throughout history, many ideas have been discovered independently at the same time. Newton/Leibniz is the most famous example.
There are so many people looking over so much of the idea landscape that this seems like the norm rather than the exception. And if it's the norm, that means for any given groundbreaking idea there are likely a few people within a few years of discovering it.
It's impossible to know for sure, but it has interesting implications if it's true. For example, publishing first is more important than being correct in every detail.
There are so many people looking over so much of the idea landscape that this seems like the norm rather than the exception. And if it's the norm, that means for any given groundbreaking idea there are likely a few people within a few years of discovering it.
It's impossible to know for sure, but it has interesting implications if it's true. For example, publishing first is more important than being correct in every detail.
I meant specifically for Einstein and Shannon. I’m not so sure anyone was right on the heels of Einstein, and at least physics seems to be full of discoveries that nobody even anticipated.
Lorentz and Minkowski were developing special relativity at the same time as Einstein (albeit in a mathematical context). And Hilbert arguably produced general relativity prior to Einstein as well.
> but it seems true.
It's definitely true. Here's a proof (?):
1) The universe has a static (if high) and objective number of rational facts that can be stated about it.
2) Anyone can discover these facts via accident, intuition, trial-and-error, experimentation or direct observation.
3) We have a smallish but more or less constant percentage of people who are obsessed with discovering these various facts as their life's work and who are gradually teasing out these facts from the mountain of mystery that lies before us.
4) Therefore, if Shannon hadn't discovered some of these facts, eventually someone else would have.
It's definitely true. Here's a proof (?):
1) The universe has a static (if high) and objective number of rational facts that can be stated about it.
2) Anyone can discover these facts via accident, intuition, trial-and-error, experimentation or direct observation.
3) We have a smallish but more or less constant percentage of people who are obsessed with discovering these various facts as their life's work and who are gradually teasing out these facts from the mountain of mystery that lies before us.
4) Therefore, if Shannon hadn't discovered some of these facts, eventually someone else would have.
I would contest step 1.
If we assume that rational means "true", then it is clearly false:
If statements A and B are true, then the statement "A and B" is true. In fact, if the statement A is true, then "A and A" is true, so if there is at least one true statement, there are infinitely many.
If by "rational" you mean "true and meaningful", well, then we have to define meaningful.
The strongest definition of meaningful that I can muster is "contains information that cannot be logically deduced from previously known rational statements". But then by Godel incompleteness (assuming that we accept arithmetic as rational), there will always be a (true) statement we can make that is independent of our previous statements.
So while I think the discovery was more or less inevitable, there's certainly a flaw in your proof!
If we assume that rational means "true", then it is clearly false:
If statements A and B are true, then the statement "A and B" is true. In fact, if the statement A is true, then "A and A" is true, so if there is at least one true statement, there are infinitely many.
If by "rational" you mean "true and meaningful", well, then we have to define meaningful.
The strongest definition of meaningful that I can muster is "contains information that cannot be logically deduced from previously known rational statements". But then by Godel incompleteness (assuming that we accept arithmetic as rational), there will always be a (true) statement we can make that is independent of our previous statements.
So while I think the discovery was more or less inevitable, there's certainly a flaw in your proof!
"A and A" is not a meaningful statement, though; it's a tautology, no? if you exclude those, what do you have?
It's not a tautology, because its truth relies on the truth of A. A true tautology would be something like "A or not A".
However, I address your concerns in the second part of my comment, as "A and A" is derivable from "A", and so is excluded.
However, I address your concerns in the second part of my comment, as "A and A" is derivable from "A", and so is excluded.
5) Where 'eventually' means months to years at most. Not sure about Shannon, but to the extent I'm familiar with discoveries in physics, they're usually pretty incremental - at some point the state of the field becomes ripe for a breakthrough, and the first person to connect the dots is the one that gets credited as genius, even though their direct contribution is pretty small.
Everyone stands on the shoulders of giants, where that giant is composed of everyone who stood on the shoulders of the previous giants, ad recursionum
Someone discovering something or inventing something is a rare event. I believe its the confluence of hard-work, timing, luck, good health, inspiration from peers' work, etc. Its even more unlikely that TWO people would be in that exact same situation. Maybe they're 'destined' to be the person whose name gets mentioned in the textbooks.
I read The Idea Factory, about Bell Labs, and they had a few sections on Shannon. Honestly, from what I read, it sounds like the guy didn't want to work, or have a job. And the Fates were kind, and dropped him into a situation where not only was he able to make that a reality, but he was able to provide several meaningful contributions to the fields of programming and information theory while doing so. He was able to not have to "work", and get to be part of some pretty amazing stuff.
>he was able to provide several meaningful contributions
Don't you think that's severely downplaying his role?
He invented the field of information theory, not just made several contributions. He founded digital circuit design. The entire concept of being able to use electrical circuits to implement boolean logic, and proving you can use those circuits to solve any problem that boolean logic can. He also came up with sampling theory, bringing communications into the digital world (as well as signal processing).
And then sure, he made several (extremely important) contributions to the field of cryptography
> get to be part of some pretty amazing stuff.
He WAS a lot of that pretty amazing stuff.
Don't you think that's severely downplaying his role?
He invented the field of information theory, not just made several contributions. He founded digital circuit design. The entire concept of being able to use electrical circuits to implement boolean logic, and proving you can use those circuits to solve any problem that boolean logic can. He also came up with sampling theory, bringing communications into the digital world (as well as signal processing).
And then sure, he made several (extremely important) contributions to the field of cryptography
> get to be part of some pretty amazing stuff.
He WAS a lot of that pretty amazing stuff.
Maybe I did downplay a bit. But the key takeway was, he was involved with all of that, not because he was assigned to it, but because it was interesting to him, and he wanted to do something with it. His work with digital circuit design arose out of him playing with making maze solving robots.
He, of all people, clearly embodied the idea of, "Get a job you love and you'll never work a day in your life." Of course, it doesn't help that he had an extremely tolerant employer, one who realized that letting him do things like play with the robots, would lead to such breakthroughs.
He, of all people, clearly embodied the idea of, "Get a job you love and you'll never work a day in your life." Of course, it doesn't help that he had an extremely tolerant employer, one who realized that letting him do things like play with the robots, would lead to such breakthroughs.
asdfologist(2)
I collected photos of the gadgets he built to play games (now in the MIT Museum) and put them on this list in boargamegeek[4].
[1] https://www2.bc.edu/arthur-lewbel/Shannon.html
[2] https://www2.bc.edu/arthur-lewbel/toys1.jpg
[3] https://www2.bc.edu/arthur-lewbel/toys2.jpg
[4] https://boardgamegeek.com/geeklist/143233/claude-shannon-man...