Claude Shannon: How a Genius Thinks, Works, and Lives

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".

> 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.

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.

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.

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".

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.

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.

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.

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.

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.

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.

That seems unlikely, no?

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!

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.

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[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).

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.