Neologista

Science Fiction Prototyping

pontiff — Wed, 18 Nov 2009 12:04:53 +0000

Science Fiction Prototyping

Last Friday I went to at talk by Brian David Johnson from Intel. That sentence sounds like any other that an academic could write--always with the going to seminars we acahacks are. That is until you hear that Brian David Johnson is a "consumer experience architect" in the Digital Home - User Experience Group at Intel. Okay that is a bit odd for a typical seminar speaker, but still lies in the "reasonable" range. And then you find out the title of his talks is "Brain Machines: Robots, Free Will and Fictional Prototyping as a Tool for AI Design" and you say, whah? Which is exactly what a group of about forty of us said upon hearing about this seminar, and is exactly why we showed up to hear the talk!

In his day job BDJ (sorry with a name that long, it gets turned into a TLA) is involved in television. That sounds kind of odd, but a company like Intel, which is constantly looking 5 to 10 years out in designing its new chips, has to be ready to supply the computing power in the proper form that is going to be relevant to the future of the company. Thus it would make sense that Intel should care about where technology is going, and why it is going that way. In particular this involves a lot of trying to understand how we incorporate technology into our lives. So yeah, dude's got a cool job where he gets to think about where technology is going and how consumers use technology. But that's not really what the talk was about.

What the talk was really about was an intriguing idea: is it possible to use science fiction to aid in creation of commercial products and research opportunities? Now that's a crazy idea. Here is a chunk of an abstract on the subject:

How can science fiction help prototype emerging science theory and experimentation? Expanding on the framework of consumer experience architecture, this talk explores how a fictional story, based specifically on current works of scientific research, can lead to the expansion and further experimentation of a dramatic new approach to artificial intelligence and domestic robots.

On a first reflection you could color me skeptic on this idea. I mean, sure, many scientists were influenced by reading science fiction at a young age (one need look no further than this to explain the many amusing personality traits of your scientist friends.) And yeah, sure, there are cases in which science fiction presages technical breakthroughs (step forth Greg Egan, and accept an award for a novel about quantum computers speeding up calculations in 1992!) Indeed, the hard nosed scientist in me (and probably the scientists in many who listened to the talk), says, this is kind of crazy, how could writing a science fiction story help in advancing science or technology?

And then, of course, the literature major in me kicks in (yeehaw!), and I think about why I like fiction. The best fiction in some manner transports your thought process into a new setting. A story can test what it would feel like if the world worked in a certain way, and, if it is good fiction, does so in a way that connects with your model of the world. This is true not just of science fiction, which tends to a cartoonish technologically heavy version of projection, but of all sorts of other fiction, where the new space explored tends to involve such things as love, hate, death, and the long list of subjects that lie at the heart of our lives. And thus, I would say, the idea that stories can help shape your research isn't all that crazy: the creative act of telling a story shares many similarities with the creative act of developing a new research idea or inventing a new technology. In particular I would point out that in both processes you need to make sure that you maintain a connection to reality in your speculation (for stories your must connect with a reader and in science you must not go against the constraints of what experiments have taught you.)

Indeed in reflecting more about this, I thought, "welI I know at least one researcher who I secretly suspect actually operates this way!" And then I realized, that, oops I know another, albeit less successful dude: The Equilibrium Theory of Games and The Library of Laplace are two short blog stories I wrote which, in some ways, are science fiction prototypes for research projects. Indeed the later is related to ideas I have explicitly tried to work on for years, but have never achieved any success in hashing this into a "real" research result. So I am not a successful science fiction prototyper, but at least I've experienced this idea up close.

Which brings me to the final point: should we be doing science fiction prototyping? Can taking current research and attempting to project it onto stories help us understand the next step in research? Can find we new technologies by writing "Do iPhones Dream of Electric People?" Well, I don't think we can answer that until we give it a try, and I'm particularly intrigued by the idea because thinking of good new creative ideas is extraordinarily difficult (at least for me!) And, of course, as an occupation, science fiction prototyper sounds like an awesome job. So if there is any company out there interested in hiring a science fiction prototyper, please consider my application submitted.

pontiff Wed, 11/18/2009 - 07:04

Tags

Neologista

Off The Deep End

Read You Tweed

Science

Storytime

Technology

Categories

Free Thought

Doesn't SF give a feel for how tech would be used. Think of Blade Runner Decades ago using a zoom in/zoom out for playing around with video. Play with Google Maps pictures and we are right there. (Absent the infinite sharpness) Think of Shockwave Rider by John Brunner with its worms and security attacks. All from the '70's.

I am not sure that anything would not have been done, but it doesn't hurt to have something concrete like that in mind when you are designing something. That I think is where it helps. to give an idea of what it would be like personally. If you were using that tech, what would it feel like.

Yes, there are hits in the record. Adding to Markk's list:

Star Trek (original) gave us 3 1/2 inch floppy disks and flip-phones. But only as use-cases. But it did not (yet) give us talking computers that explode when presented with Godelian assertions of the form "this is not a true statement". There was no 'science' in the SF of Star Trek, but there were enough monkeys pounding the keys to get some things close enough to reality that later its fans were able to make them for real.

Then there were A. C. Clarke's stories about geo-centric communications satellites (IIRC, based on a non-fiction paper he wrote around 1945). But in this case there was some science: the orbital math was right, just no then extant way to get the satellites up there. And then again, he was not alone, the idea was already "in the air" and had been since at least 1925.

But there is lately somewhat of a confirmation bias about the success stories from SF. They are not as numerous as is wanted to be believed. Even the big hits - Star Trek, Blade Runner, etc - have mostly unreal ideas.

But I will take issue on one little point: you must have had a very narrow exposure to SF to make the statements "science fiction, which tends to a cartoonish technologically heavy version of projection" and "other fiction, where the new space explored tends to involve such things as love, hate, death, and the long list of subjects that lie at the heart of our lives". Yes, Sturgeon's Law (90% of everything is crap) holds in SF as much as anywhere else, including mainstream fiction, but that last 10% does indeed exist. Sorry you missed out. Try Ursula K. LeGuin's books, or more recently Judy Czernada. The best SF stories are just like the best mainstream stories, but with the twist that the conundrums faced by the protagonists have a speculative basis in as-yet unrealized science, and where that science has at most one speculation but the rest is based on known results. It does exist, it is tougher to write because of the tech constraints. And it may also be that the writers and audience for SF are tending into ASD a little, rendering our inner experience of SF somewhat different to that of a normal.

To finish, I think the idea of SF Prototyping could be better expressed in the form of presenting use cases of an idea in the context of a fiction story in which the technology plays a role. I think it might be mostly fruitless to mine SF for tech ideas since there is no search algorithm by which to recognize the ones with real value as distinct from all the rest of the flights of pure fancy. Start with the idea and candy-wrap it, don't start with the candy-wrapping and hope there's a useful kernel inside.

Hey I did say "tend"!!!

Yeaaaah. If somebody at intel had had that kind of predictive power (5 to 10 years!), they (the giant that they are) would easily have beaten the iPod and the Kindle the tivo and what have you to the market.

I'm not so sure Greg Egan wants an award for Quarantine.

I thought Quarantine was an utterly hilarious satire of the Copenhagen Interpretation, in the vein of Stanislaw Lem's more fantastical excursions.

So I looked online, and found that everyone seemed think it was supposed to be a serious take on the implications of quantum theory.

Then I thought, "How can such brilliantly conceived and executed comedy be sailing over everyone's head?"

So I looked at page that Blake links above.

Then I thought, "Crap."

(Thus I am now trapped in a coherent superposition of mental states, my two different selves now respectively believing and dismissing the notion that Rucker wrote Postsingular as a systematic p*ss-take on every one of the tropes of its genre, with a shout out to P.Z. Myers squid fetish thrown in for good measure.)

My only criticism is that authors can have considerable biases.

I like Larry Niven, and he was noted to be a Misogynist and Human Supremacist. So alot of his books are outdated.

See James Blish, "The Science in Science Fiction." Collected in The Tale That Wags The God. The science is perhaps dated (rather space-opera-ish as I recall), but the thinking is perhaps still of value.

@Koray -- "If somebody at intel had had that kind of predictive power (5 to 10 years!), they (the giant that they are) would easily have beaten the iPod and the Kindle the tivo and what have you to the market."

Koray - not fair! Intel has been a commercial superstar. Remember the BUNCH (Burroughs, Univac, Sperry, NCR, Honeywell, Apollo, Sun, Altair, Imsai, etc etc...) You are picking a select number of successes -- but ignoring the many more failures. (Tivo is a cool technology, but a commercial disaster. Kindle may/may not be a BetaMax). Only the Ipod stands out. And here the statistic is cool:

Since 12/31/82 (first year that apple went public):

Apple's compound annual rate of return: 16.22%
Intel's compound annual rate of return: 16.12%

Dave: I volunteer for your prototype team. I'll do the financial projections...so long as I get to play with the toys!

Rocky

Well, the government has reached out to science fiction writers before to help goose their thinking about the future, so I don't see why other sectors couldn't give it a shot.

U.S. Mission for Sci-Fi Writers: Imagine That, Novelists Plot the Future Of Homeland Security

By David Montgomery
Washington Post Staff Writer
Friday, May 22, 2009

The line between what's real and what's not is thin and shifting, and the U.S. Department of Homeland Security has decided to explore both sides. Boldly going where few government bureaucracies have gone before, the agency is enlisting the expertise of science fiction writers.

--SNIP--

I find that a lot of Robert Heinlein's books, though they are often quite fantastical when alien life is brought into the equation, are very firmly based in real math and physics. His books helped spur the hippie movement as well as NASA's MMUs, among many other things. He also had quite workable ideas relating to space suits, artificial gravity, long distance space travel, and mechanized suits, which are all just starting to be looked at in more than a theoretical sense.

(1) I coauthored, for pay, a decade ago, a book on how Science Fiction has influenced actual business. This was to have been published by the #1 Business book publisher in the USA, who listed it in their catalog. The coauthor went nuts, after our Caltech co-alum Dave Brin helpfully suggested that the guy should have a written contract with me, money stopped, book never appeared, though about 1/2 completed, long story.

(2) One of my mentors, Dr. Herman Kahn (ex-Caltech PhD postdoc, head of RAND, founder of Hudson Institute, highest score seen before or since on standard U.S. Milkitary IQ test) explicitly used Science Fiction in a big way in his monumental book The Year 2000: A Framework for Speculation on the Next Thirty-Three Years, (ISBN 9780025604407): Herman Kahn, Anthony J. Wiener. He had a full-time employee who did little but read Science Fiction magazines and classify the ideas therein, Patrick Gunkel, with whom I've talked f2f.
http://ideonomy.mit.edu/

(3) I do a lot of refereed paper publishing and international conference speaking with a Full Professor of International Business and Economics, who also publishes Science Fiction.

Any questions?

That's a very small word for someone in a hurry. OK, got me.

@Gary Ha, no I deserve it. Also I knew I was provoking people when I wrote that sentence :)

@Dave - One of my marginal ASD issues is not knowing when my leg is being yanked. Sometimes funny, sometimes sad.

That said, it's a blast to have lived through those old sf fantasies and lasted long enough to see the beginning of the hockey stick their realizations is evoking. One's sense of time passing at my advancing age is not only flashing by - a month is a much smaller percentage of my lifetime now - but also the accelerating pace of change in the environment in which I live and work just makes a year seem so much further in the dim past. Sort of an analog of the expanding Universe in the context of subjective time.

Rocky,

The products I mentioned are brain dead straightforward ideas (mp3 players, e-book readers were already in the market BEFORE these products). Predictions accurate enough for 5-10 years ahead would let you see the real deals coming, let alone these pesky derivatives.

Intel indeed has been a commercial superstar. Not because of their vision. And not without evil.

About 1999 or 2000, I was contracted by the European Space Agency to research and write two articles for a series that looked to science fiction for ideas on the future of space exploration. My two topics were propulsion techniques and colonization techniques.

That was a really fun project (and they paid really well too).

The .pdf is here: http://www.esa.int/esapub/br/br176/br176.pdf

The backache is a pain or stiffness of the back. Pain in the inferior or average part is commonest to feel the back. In article findrxonline indicated The backaches are more common during the adolescence, but also the people of legal age suffer and who appear and disappear during periods of time.
The backaches can be caused by a pull in some of the 200 muscles of the back that allow us to maintain to us raised. The pull takes place when raising very heavy objects, when raising something from an uncomfortable position or when doing too much effort with muscles of the back. Most of the backaches the twist of a ligament or muscle can be caused by tension or.
The backache can be associated with:
â¢ Stiffness, creeps, loss of mobility in an arm or a leg
â¢ Pain Chest or difficulty to breathe
â¢ Increase of the intensity of the pain, although this with medicines
â¢ Difficulty to walk or to maintain the balance.

The best SF stories are just like the best mainstream stories, but with the twist that the conundrums faced by the protagonists have a speculative basis in as-yet unrealized science, and where that science has at most one speculation but the rest is based on known results.

Haha great story! Thanks for sharing and keep up the good work with the blog!

I do remember hearing on the history channel or something that the IBM guy who came up with cordless phones got a phone call during a Star Trek episode and would have to miss a portion of it and thus inspired him.

Humor as a Guide to Research

pontiff — Mon, 13 Jul 2009 11:48:46 +0000

Humor as a Guide to Research

Over at the optimizer's blog, quantum computing's younger clown discusses some pointers for giving funny talks. I can still vividly remember the joke I told in my very first scientific talk. I spent the summer of 1995 in Boston at the Smithsonian Astrophysical Observatory (photo of us interns) working on disproving a theory about the diffuse interstellar absorption bands by calculating various two photon cross sections in H₂ and H₂⁺ (which was rather challenging considering I'd only taken one quarter of intro to quantum mechanics at the time!) At the end of the summer all the interns gave talks about their work. I was last to go. In my talk, I drew (transparencies, you know) a cartoon of "photon man" (wavy line stick figure) who explained the difference between two photon absorption and absorbing two photons. No one reacted to these cartoons during the talk. But at the end of the talk, one of the other interns, trying to be cute asked me "So, what does photon man think about all of this?" I paused. Thought for a second. And replied "He was very enlightened by the whole thing!" The simultaneous groan emitted by the audience (who had sat through 8 straight talks) was, I must say, awesome. I have a vivid memory of my adviser in the back of the room giving a hearty actual laugh! And I have been hooked on trying to insert at least one bad joke in every talk I have given ever since.

Since I enjoy humor in talks, lately I've been wondering if there isn't an easier way to make funnier talks. The optimizers list is a good start, but I'm lazy. Which led me to the idea: maybe I can make funnier talks by simply basing my research on things that are inherently funny? I mean, you try taking How a Clebsch-Gordan Transform Helps to Solve the Heisenberg Hidden Subgroup Problem and making a funny talk! On the other hand it is, without a question, nearly impossible to give a talk about Time Travel without (purposefully or not) uttering really awesome (and well timed) jokes.

Actually I have a history for thinking that humor might be a decent indicator of good research or at least good problem solving (and not just a source of funny talks.) While a graduate student at Berkeley I participated in a San Francisco version of The Game (Fobik: there is a clue on these pages.) Basically this was a multihour (read: all night) puzzle hunt spread around the San Francisco bay area. The basic idea was that at each location there was a puzzle of some sort that you had to solve which would tell you the next location in the game. Imagine hundreds of geeks (including a world puzzle champion who was in my class at Caltech, #yeahrightlikeweweregoingtowin) piled into vans and cars racing from location to location, piling out of the car only to then sit around trying to solve a hard puzzle of some sort. Good stuff.

What does this have to do with humor and research? Well during this game I noticed something kind of interesting. Inevitably we would initially start working on the puzzle and someone would say something completely ridiculous. Like "I bet this puzzle is using flag semaphore!" Invariably, we would all laugh...yeah, right, like they would use semaphore in a puzzle involving chess. Then we would work for a while on the puzzle until someone had the audacity to think, "hey maybe it really does use semaphore." And lo and behold, yeah that was the key to cracking the puzzle. This didn't just happen once during "the game" but happened repeatedly (and not surprisingly as we got more tired, things got funnier, and we began to realize that the crazy funny idea we had right off the bat wasn't something to laugh at, but was something to actually try!) Every time I'm trying to solve a problem these days, I often think, "what would be a funny solution?"

But I wonder if this solution method ("solution by LOL?" "SoLOLution?") can't be extended to a method for theory research. Think about a subject area and then think of the funniest result you could derive in this area. "Wouldn't it be funny if..." And then instead of just laughing at the conjecture, maybe you should actually check and see if your humor is actually well tuned to the universe. I mean, if god is a comedian (see Voltaire), then wouldn't he have a special spot in his heart for funny research? The optimizer, in a previous blog post, has discussed sidesplitting proofs. So at least we know that in computer science the universe appears to favor humor. But what about in other fields? Economics (okay, maybe the whole thing is a joke?), physics (maybe the universe really is made up of spherical cows), mathematics (there is nothing funny about starting a paper with "Let x be..."), or biology (I mean molecular biologists already overuse the word "assay." Face it, that's a funny word to a ten year old boy.) Maybe the reason scientists are so dull is that they we have gotten away from the ultimate hilarity of the world (okay the conjecture that the universe is ultimately simply a joke isn't very funny, especially if you are Rosencrantz (but not, strangely, if you are Guildenstern.))

So today, instead of finishing the paper I should be working on, maybe I'll go browse the web for really bad jokes, apply them to quantum computing, and see what happens. Jokes involving superposition, entanglement and cats don't seem to get many laughs. But maybe I can find something funny about the Hidden Subpoop Problem?

pontiff Mon, 07/13/2009 - 07:48

Tags

Computer Science

Funny Ha Ha

Go Ahead, Waste Your Time

Self: Meet Center. Center: Meet Self.

Categories

Free Thought

Do you have any examples? Results that are funny and also important. Closed timelike curves are funny, but not very important. Is factoring funny?

188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059 LOL!

Cartoons can illustrate concepts and be funny at the same time.
Here's one take on the, uh, logical issues about the future of sex!:
http://xkcd.com/468/.
It's cute, but also gets people thinking about the paradoxes of set theory!

PS: I wonder if anyone can make a cartoon illustrating how "decoherence" somehow prevents macroscopic superpositions from persisting - that might or might not make up for the essential fallacy IMHO of comparing descriptions of ensembles (e.g., with varying phases between different instances within a run) to the status of superpositions in a given instance. If someone can illustrate that, maybe I'd be more sympathetic!

antidecostructionist

"humor might be a decent indicator of good research or at least good problem solving". As far as correlations go, OK, there are some good creative Scientists out there who are good at humor, who are the life and soul of the party, but consider the person who has none of the instant creativity that's needed for humor, or for whatever reason doesn't run well with the crowd, but who is willing to plod along for a few decades of hard work. Zero social credit. Doesn't get a tenure track job because their job talk wasn't as amusing as the one after, or because they didn't get to the job talk stage. How many of the instant fun people are also capable of the twenty year slog without getting distracted? Answer might be 80%, I have no data, but it's the nature of false negatives and false positives on the tails that missing one Einstein is sometimes extremely costly. Having an outright joker who gives superficially interesting talks as a point person for Science can also be a problem!!!!!!!!

Sorry the above isn't funny, although on a generous view I may have applied rule #5, and I belatedly stuck in rule #10 gratuitously. Applying rule #1, it might be a little harsh not to mention that you and Scott seem to me to be bloggers of substance. By the way, rule #4, I haven't got a PhD, so nothing I write here makes any sense (rule #16, probably).

Rule #11!!!!! and #10!!!!!!

Okay I didn't know the number would run off the side of the page. That really is funny. Anyone want to try to factor it? There is an easy method for doing this, I guarantee!

Peter: I guess what I'm interested in here is less the social aspect of humor and more about whether one can use humor as a personal guide to interesting new research. In other words, humor strikes me as a part of my and other psyche that we don't acknowledge as influencing our science. But might this cause us to miss important ideas?

There is, in fact, a serious point to be made about how funny the universe seems. And I do admit that it very often seems quite funny to me. Remember that "funny" had to evolve in humans. Perhaps "funny" is the reward system that our brain evolved for learning some new unexpected and useful insight about the natural world and our human counterparts.

Dan Dennett gives a great (and quite funny) explanation:

http://www.ted.com/talks/lang/eng/dan_dennett_cute_sexy_sweet_funny.html

The complacency of academic assumptions, perhaps? It's funny how long it takes for assumptions that seem natural from within a field to be picked apart from within, when almost everyone outside the field can see almost in a few moments that it's somehow narrow-minded, but can't take the ten or twenty years needed lovingly to understand the problem enough to find a creative and constructive way forward from where the field has come to. Sometimes a field produces fine fruit for a few decades, then atrophies, sadly. The action moves elsewhere, with many not quite knowing how it happened, nor why there's bitterness in the aftermath. Physicists don't like to think about the SSC.

Humor is often irony or satire, but it's painful when one is the target, as Science as of now often seems to be, especially when it's without quite understanding the joke. There is, as well, a hint of tragedy in self-regard, with possibilities for endings that are not so happy.

But you wanted to laugh at a few jokes. I saw a few weeks ago (or is it months?) that you have entered existential waters, which is a place where light relief is very welcome, and a wild critique may best be thought laughable.

The link offered by Geoffrey (which for me didn't work, but http://www.ted.com/talks/dan_dennett_cute_sexy_sweet_funny.html did -- I thought it rather good, with thanks) offers a cute summary (I offer something different from Geoffrey's summary) for my thesis: funny is to ensure that we find "debugging" (Dennett's word) a joyful task, something worth doing because it gets our pleasure centers to encourage us to do something that may intrinsically be rather painful. It's to encourage us to cross valleys, to adopt Lee Smolin's vocabulary. If the universe is funny, it's perhaps not just us, but it's not funny to be on a mountaintop with nowhere to go but down.

39807508642406493739712550055038649119906436234252
6708406385189575946388957261768583317
*
47277214610743530253622307197304822463291469530209
7116459852171130520711256363590397527
!

LOL!!!

@jon: And all without a quantum computer! Totally LOL.

Take the TV show "Big Bang Theory" - that's full of geeky humor!

State of the ?

pontiff — Sun, 01 Feb 2009 15:53:14 +0000

State of the ?

Amusing line from a New York Times article this morning:

"Are you aware under what conditions I worked in 1996?" he said by telephone from Mexico. "It's only because of my lawsuit that you or anybody else can pick up a tape. In those days, I could not leave the archives with that material. I used state-of-the-lost-art equipment. I brought in a team of court reporters to help me with the first drafts.

State-of-the-lost-art? He used a telephonoscope?

pontiff Sun, 02/01/2009 - 10:53

Tags

Funny Ha Ha

Neologista

State-of-the-lost-art? He used a telephonoscope?

Yes. In those days, we used to shake iron filings on audio tapes, and look at the pattern under an optical microscope, by candle-light.

Under the supervision of detective, Lord D'Arcy [Randall Garrett's Too Many Magicians], we succeeded in solving murder mysteries in an alternative reality. Shredded documents were restored by a combination of the proper spell, and rotating the mass of shredded paper in a drum cranked by interns so that when, randomsly, two shreds touched along edges formerly joined, they became magically rejoined, and so [Smoluchowski coagulation equation omitted here for brevity; integrodifferential equation introduced by Marian Smoluchowski in a seminal 1916 publication] coagulated to fully restored (and un-redacted) documents.

Brains, Brains, Brains, Brains

pontiff — Fri, 30 Jan 2009 11:49:18 +0000

Brains, Brains, Brains, Brains

Like many an arrogant kid before me, when I graduate from high school in my podunk hometown (no, it wasn't marshy, and I say podunk with all the warm feelings of a idyllic childhood), I was filled with confidence that I was one of the smartest people I knew. Oh, I'd never say it, and yes I knew I was good mostly at only one small thing, mathematics, but I'm pretty certain looking back that I was a pretty confident ass. As you can well imagine, then, transitioning from my high school to Caltech, an institution filled with near-perfect-SAT-scoring students, Nobel laureate faculty members, and a wide range of just frickin' brilliant people, resulted in a large dislocation in my perspective concerning my own capabilities. But over time, I began to realize that, while I wasn't the sharpest cookie in the cookie jar, every once in a very rare while I could do something worthy of interest to my fellow genii in grooming (mostly jokes, mad rantings, or random acts of bizarreness, if you must know.) Thus I came to the perspective that there was no such thing as a universal genius, that possibly, just possibly, there are people who are good at differing things---little genii of their own domains. It's often disheartening to sit in a room with a large number of brilliant people, until I remind myself of this fact. And Monday, while doing exactly this form of sitting, I began to ponder the different ways in which these people have their own styles of brilliance. Or, in short, I made a list.

Dave's horribly biased and totally incomplete list of the different facets of genius among the theorists he knows (just to cut out the comment before it happens, of course these are not mutually exclusive):

The Human Calculators (aka the Problem Solvers) When we all think of the stereotypical brilliant person, the picture most of us have in our head is someone from this category. These are the people who, if you give a hard problem, will be able to out problem-solve, out calculate, out prove everyone else around them. The legends about this group tend to involve feats of amazing mathematical prowess: proving an unsolved problem posed as a homework problem by an evil professor, inverting matrices in their head, or summing infinite series without batting an eyelash. The great thing about these people is that they have a great chance of solving any problem you give them. The hard thing must be that no one wants to talk to them about the problem they are working on...do that and the person might just jump the gun on you and solve the problem before you.
The Random Generators These are the people who generate ideas at a mile a minute. They sometimes have only a cursory understanding of details, and rely heavily on a "feeling" for the direction they are taking. They're the ones you'll see spending more time around the coffee table, spinning a yarn, or debating some off topic idea about a new iPhone application. Sometimes you'll see them say things out of the blue that amaze even themselves. As scientists we often give lip service to being creative, but truly pushing on the boundaries of the box isn't, I think, really recognized as a form of brilliance unless it is repeated more than a few times ("he was just lucky!" if you have only one interesting idea.) The great thing about these people is that they are a constant fount of inspiration. The hard thing about them is that they are a constant fount.
The Field Jumpers Detailed domain knowledge is often of little use in its original field, but can vastly impact seemingly unrelated fields. There are people who have not just mastered a tool, but have the flexibility of mind to apply it outside of where it was original designed to apply. We often say that people coming across the disciplinary divide have a "fresh perspective", but more often than not what they really have is a perspective shaped by their prior field. A strong marker for a field jumper is a history of changing fields: this characteristic is thus often latent until the day after tenure. The great thing about field jumpers is that they stir the pot. The dangerous thing is that when moving into a new field, they don't often do adequate background to understand what has been done and not done before (Physicists are notorious field jumpers in this respect.)
The Connectors (aka the Encyclopedia Connectica) A joke I used to tell: You can tell you're a theorist if someone describes jail to you (room, board, quiet) and you ask "Do they give me a pen and paper?" While there is no doubt that quiet contemplation aids the intellectual digestion of most theorists, sometimes its possible that you just don't have the mind (brains or frame of) to solve the problem you are working on. This is where the connectors come in. These are the renaissance scientists who have a vast encyclopedic knowledge of who did what when and, even better, when you talk to them about your problem can (a) understand your problem and (b) point you to the person or research that might best help you solve your problem. Now, you say, where is the genius in being able to point someone in the right direction? Well if it was so easy, why couldn't you just do it on your own. The encyclopedic keepers of our intellectual history, combined with the exceedingly efficient search engine known as "talking to them" (eat your heart out Google) is, to me, a true form of brilliance. The great thing about connectors is that you can talk to them about anything and they will often lead you into an entirely new direction or connect you to someone you'd never meet otherwise. The dangerous thing is that they might connect someone to you!
The Communicators The most ridiculed of the forms of genius, the communicator is able to take the results of deep science and turn them into something comprehensible. Don't think this is true genius? You obviously haven't read enough seminal papers lately---not that I'm a literature snob or anything, but complete sentence would be nice. The amazing thing about a communicator is that they can bridge the most difficult subject by illustrations that remain true to the spirit of the problem. Having currently been bashing my head up against writing book chapters, I can attest to the genius it takes to synthesize and coherently link together a body of knowledge in order to produce, for example, a textbook. Have you ever picked up a paper which upon reading the paper brushed aside hours you spent frustratingly trying to read written by experts in the field? That's the work of a communicator. Communicators filter and shape the language and form we have for our deepest results. On the other hand, their propaganda can fossilize the view of a particular field.
The Refactoratti So you've worked on your problem and solved it. You're exhausted from the focus you've had on simply getting to the end of the problem, but really happy to start talking with people about what you've done. If you happen, after doing this, to encounter one of the refactoratti, you might even be lucky enough to understand what you've just done. The refactoratti are able to see through your result and understand it for what it truly adds to our knowledge. These are the deep people we all seek out to discuss our results. I suspect that they have very coherent pictures of all of their knowledge in their head, and can thus more easily see how what you've done is innovative. They are usually the opposite of scatterbrained. Refactoratti are awesome for their reflected light. They are also dangerous, of course, because the reflected light might be that someone has already done what you just did!

One reason I find this interesting to think about has to do with the two talks and many blog posts written by Michael Nielsen on the general theme of open science. A point which Michael discusses is that the lack of openness in science (including mechanism for reward in such systems) is bad for many reasons, including the fact that one can be toiling away at a problem which could be easily solved by some other expert (or this is my interpretation of one of Michael's points.) An important piece to the puzzle of why their is reluctance to push into open science is, in my mind, that we often don't properly reward people for their contributions. We don't view the careful crafting of a paper as a skill worthy of major attribution nor of being the person who connected the two groups who were able to put their heads together to solve the problem. Because we view our work as PROBLEM...SOLUTION, and not as the more complex craft required to push science forward, we tend to think about science as a task of "me, solve problem, reward." But it shouldn't be this way, and we should recognize the manifold nature of genius in pushing science forward. With this, I think, comes a better ability to understand how to bring science out into the open. Or at least that's my optimistic hope sitting in a room surrounded by Human Calculators, Field Jumpers, and Refactoratti.

pontiff Fri, 01/30/2009 - 06:49

Tags

Extralusionary Intelligence

Your post reminded me of John Huchra's 7-dimensional classification of researchers in his essay, "On Being an Astronomer". An excerpt:

"Once upon a time in graduate school we had an astronomy department retreat for the faculty, postdocs, and students. It rained. Almost by definition, we ended up in a deep philosophical discussion concerning careers, and what made a successful scientist. We decided in the end that an individualâs success in the game could be predicted by their characteristics in a seven-vector space. Each vector measured a critical personal characteristic or set of characteristics such as intelligence, taste and luck, and the ability to tell oneâs story (public relations). The vectors and their ââunitââ vectors, the people against which one was measured in astronomy in those days, were:

Raw Intelligence S. Chandrasekhar
Knowledge A. Sandage
Public Relations C. Sagan
Creativity J. Ostriker
Taste W. Sargent
Effectiveness J. Gunn
Competence M. Schmidt
(Here, Iâve changed a few names to protect the innocent.)

"Each unit vector represented someone who was without equal at the time (1974 or so), for example Chandrasekhar was the smartest person in astronomy any of us had come across, and similarly, Allan Sandage represented the unit vector of knowledge (which is not the same as intelligence, although he is a damn smart cookie!). Some vectors are worth more than others, for example taste and creativity are probably more important than knowledge. Looking back on this Iâve come to realize that being nearly a unit vector in any one of the important characteristics almost guarantees you a tenured job, two are good for membership in the National Academy, and three put you in contention for the Nobel Prize."

It looks like there's some overlap with your classification scheme: Human Calculators -> Raw Intelligence, Random Generators -> Creativity, Connectors -> Knowledge, Communicators -> Public Relations.

you're an idiot for even posting such a list.

Zombie: "Mmmm, brains, mmmm."

Thanks for the opinion, though, it's highly valued. Even better is you ability to post like an anonymous coward. Where did you learn that trick?

It was enormously valuable for my academic and personal development to transition from the famous Stuyvesant High School in New York City (which today would be called a Math, Science, Engineering Magnet School) to the even more famous Caltech. Where I discovered that I was...

*** shock! ***

... below average.

You find that you're not on the Fast Track of genius when someone who came from the same high school at the same year to the same Caltech ends up a Provost and Vice President, and an overlapping classmate wins a Nobel prise for work done in his first year of Grad School.

If I may address your phenomenological classification:

(1) The Human Calculators: I've even had one as a student. One exam question involved multiplying a pair of 4x4 matrices (with few if any zero elements). He wrote down the correct answer with no derivation (and this was a no-calculator exam). When I accused him of cheating, and cheating stupidly by not using scratch paper, he insisted that he'd done it in his head. So I gave him another pair of 4x4 matrices. he stared into space for no more than 4 seconds and wrote down the correct product. Ever since then,I've openly accused students of cheating if I've caught them red-handed (crib sheet, copying from adjacent student, or texting/web tools mid-exam).

(2) The Random Generators: as I've recounted before, I asked Linus Pauling what was his secret for this. He nailed it, although it took me decades before I realized that he was imparting wisdom rather than sound bites: (a) learn how to have many many ideas; (b) learn how to be excellent at telling the good ones from the bad one.

(3) The Field Jumpers: Part of Caltech's place in history is the number of distinguished Physicists there who jumped to found modern Molecular Biology. Of course, even Nobel Laureates who fieldjump get accused of being crackpots.

(4) The Connectors: This is a niche that my collaborators praise. Well, at age 57, having been reading and writing copiously and promiscuously in a dozen fields, I'd better be useful this way, or else I've wasted half my life.

(5) The Communicators: Well, you and I both have double B.S. degrees from caltech, with one each being English Literature, so we are hardly objective. They laughed at Carl Sagan, and blackballed him from the National Academy of Sciences. They laughed at Brian Greene and Lisa Randall (to pick two students from literally the same class at Stuyvesant) for their best sellers. They laughed at Isaac Asimov, but gave him a PhD anyway. They laughed at Feynman for his pranks and for playing the bongo drums. Of course, they also laughed at Bozo the Clown.

(6) The Refactoratti: If anyone knew how to train people for this role, that country would take over the world. We have no idea. It's a kind of 2nd order genius.

You don't think that this is an orthonormal basis for the 6-space of Scientists, do you?

Excellent post. I can definitely relate to moment of discovering that, intellectually, your perception of yourself is perhaps somewhat inflated. I still hold onto my perception of myself as genius, if only because it keeps me motivated. I don't think it's productive to continually remind oneself how average one is.

I'm pretty sure there's a place in one of the Feynman books where they talk about people hiding their work from him, in fear that he would just spout out the answer to something they'd been working on for six months. Sure, it seems antithetical to the goals of science, but science is a human endeavour, done by humans, and so it's more than understandable, I think. I'm not sure what I would do if I were in that position...

Nice essay. Pay no attention to the zombie.

I like your closing paragraph. I just wish people would take your sentiments seriously. Perhaps, in an odd way, it points to another type of genius I might call "mass genius." That is, the collective small steps of many, many people over time that, individually, might not be considered genius, but when taken as a whole most certainly is.

Zombie is correct by his manner of thinking, rather than a troll. If you'd like, I can defend him right down to "logic is broken without assumptions," but there's no point in that.

What I'm curious about is this: Is the typo in this essay intentional or not?

Email me for sure if it is, if you want if it's not: Email deleted by Dave Bacon 5/11/09

Dave, You forgot to include my category, slacker:)

Jeff

Sorry for the double-post, all. If I could edit/delete my previous comment, I would.

@Jonathan: Your summation about Refactoratti might be true, but we can't have everyone be a pure Refactoratti. They'd just refactor all over themselves and cause our extinction. Also, I'm pretty sure the answer to your question is "no." David might be an idiot, but he's not that much of an idiot.

This list is a little (actually, very, but it doesn't damage its readability too much for me because I'm currently part of academia) academia-biased.

Also, Refactoratti are only useful in research, or if you want to refine your mode of thinking. In any other case, they're annoying. Really annoying. In fact, people are likely to think they're annoying simply for the sake of being annoying.

Aren't you worried that people will now slot themselves into one of these narrow classifications... pretty much making it unbearable to practice science?

K.B.: from the post "just to cut out the comment before it happens, of course these are not mutually exclusive"

Luke: from the post "Dave's horribly biased and totally incomplete list of the different facets of genius among the theorists he knows"

I strongly disagree that Refactoratti are annoying.

Anyone who's read Darwin should not be too quick to say that primary sources are difficult to read.

On the other hand, Darwin worked with his idea for many years before publishing it. Which leads me to another point:

Ideas, like cross-species pathogens, usually need to evolve before they will be highly contagious. An idea may be correct, but formulated in a way that's not very useful to others. (The medium is the message?) Or it may be partially correct. Or it may be an offshoot of the idea that's actually the most useful.

The refactoratti and the communicators appear to provide major value by evolving ideas to make them more generally useful (contagious).

(The rest of this post owes its inspiration to discussions with Jonathan Vos Post.)

Swinging the pendulum back from the idea-evolvers, through the idea-originators, we come to the crackpots. These are people whose work has poor grounding in science, but who have made an observation that's interesting enough so that an idea starts trying to spread itself through them.

Many crackpots, of course, produce work with no broader value. But some manage to find things that are genuinely interesting - though we can't know it till later, after their ideas have evolved to become more transmissible (and usually more correct).

Mesmerism was a crackpot idea - surely as flaky, in its initial form, as (e.g.) Reich's "orgone energy." But Mesmer managed to transmit his idea, which evolved into hypnotism.

I suspect that homeopathy has enriched our study of placebos.

On JVP's mailing list is a person who believes that electricity has little or nothing to do with electrons. It's worth noting that in the original (Catt) version of the theory, electrons don't even exist. The idea is evolving visibly.

So, if they can find a refactoratti who will listen and be inspired without catching the disease, this line of thought might - I say might - lead to, say, a new formulation of existing electromagnetic equations, which might be useful. Or their mental model of electricity might inspire an experimentalist to develop a new class of device. There's even the faint possibility that, like Mesmer, they've noticed something that's actually interesting in its own right.

Perhaps a crackpot is merely an extreme form of field jumper. But in another sense, the process that they (occasionaly) spark provides an unusually accessible illustration of a part of the scientific process: interesting wrong ideas developing into useful correct ideas. Since crackpots, almost by definition, don't refine their ideas to be palatable to science, we can study the evolution of their ideas in a way that we can't study the evolution of ideas within a single great brain like Darwin's.

How about "The De-constructors"? Is there not a certain genius attached to being able to quickly and correctly identify the flaw in an experiment or a line of theoretical reasoning?

"I have no great quickness of apprehension or wit which is so remarkable in some clever men..."
[from autobiography of Charles Darwin]

I thank Chris Phoenix for increasing the fitness of the ideas in that discussion of the ecological value of people labeled as crackpots.

Intellectual Selection
By DEBBY APPLEGATE
Published: January 29, 2009

âTrying to write intellectual history is like trying to nail jelly to a wall,â the historian William Hesseltine once observed. Standing hammer in hand, there are three obvious ways to grasp hold of this slippery subject. The first is to focus on the thinkers or, to continue the craftsman metaphor, the producers of the ideas. The second method is to concentrate on the genetic development of the ideas themselves, or the product. The third is to focus on the consumers; that is, to trace the transmission and interpretations of these ideas among the wider population."

"In 'Banquet at Delmonicoâs: Great Minds, the Gilded Age, and the Triumph of Evolution in America,' Barry Werth seeks to show how the concept of evolution evolved in the decades after the Civil War, to become a dominant lens through which Americans viewed their rapidly changing world. A slippery subject, indeed. But Werth, the author of 'The Scarlet Professor' and several other books, takes firm hold by keeping a tight, almost cinematic, focus on the intellectual producers â the fossil-hunters, biologists, preachers, economists, historians, industrialists, politicians and editors â 'who accepted the overall truth of gradual development as a principle of biological descent, but disagreed sharply among themselves on Âother essential questions, and on the deeper implications for society, and for God.'"
[truncated]

It wasn't my intention to claim that your classifications were mutually exclusive (or that you believed them to be). It just seems to be the case (at Caltech too) that people really like to think of themselves as belonging to some category or niche in terms of their intelligence.

Seeing a published list of such categories on this blog... I feared too many would be pushed over the edge.

I found myself at the end of the list! The Refactoratti. Cool name.

ANY time I come across a posting on Caltech I can't help but smile, regardless of what is going on in my life.

As a mom of 2 sons, one who attended Caltech(even going back for more 'punishment' as a grad student)and the other MIT, people always asked me which school I preferred-like I was the little genius who got admitted. As if....

Truth be told, I always had a soft spot for Caltech. I admired their quirky stabs at fun, loved the nurturing they gave their students, and looked forward to hearing about their next prank.

But most of all I liked what it gave my son - a sense of perspective, where one can be brilliant in high school, yet be humbled by ALL the genius floating around campus. I liked their collaborated efforts, as they all (except for the true geniuses!)labored into the night to complete a seemingly impossible problem set. Caltech taught team work, and that one should never say never.

MIT, the jewel that it is, is a little less personal, and the geniuses tend to work more on their own. But if it's intimacy that you crave on your , Caltech is the place to be.It is an oasis on the crazy, left coast.

Either way, I ADORE Techers!
Thanks for a delightful read.

benjamin franklin nicely encompasses all catagories.

Gosh, I can add two more classes:

Team-Builders: Von Neumann, Oppenheimer, Ramo, Wooldridge, Poincare, Thorne, Venter (to name just a few). Even Isaac Newton ... whose team at the Royal Mint accomplished the useful purpose of making Isaac Newton exceedingly wealthy! :)

Political Radicals: Priestly, Grothendieck, Leibniz, Galois (and many others)

I really like this list. Thanks.

Jeff: "slackers" probably hits too close to home :)

K.B.: Definitely everyone likes to have their own view of where they fit. I oscillate between whether this is important (understand yourself!) or limiting (by confining yourself to what you view are your own limits.)

I realized you forgot a pair of categories (I guess they might be super-categories that encompass several of the above). David Galenson, an economist at U. of Chicago, studied geniuses and concluded there were generally two broad categories: those who peaked in their relative youth and those who reached their pinnacle later in life - sometimes much later. This was not always simply associated with the type of field a particular genius was in (e.g. historians often complete their seminal work later in their careers). Here's a link to an article about him and his work.

I'm not a scientist by any means - just a retired software geek. At the tender age of 19 I was mentored by a great Communicator who was able to express very complex math to me in terms that made sense to me. What a gift he had and what a gift he gave me. Over my career I've encountered a few in your other categories, too. It's an interesting and insightful list that's inspired me to think back about some of the exceptional folks I've encountered over the years.

Thanks Mary. Everyone should click on Mary Foxworthy's link to see her lifestyle choice: the sailing life :)

Ian: so there are no mid-career geniuses? Doh.

I really like this post, I know people who fit perfectly into each type. I was a human calculator when I was younger, now I am a random generator and yes like you said I am a constant fount, I have trouble keeping my mouth shut.

Ah, the life of an oblivious white male. Of course, my experience was the opposite. Quite convinced that, despite my outstanding abilities in my small high school group, I would be confronted at university with crowds of superior minds. Alas, this was not to pass.

Putting people in certain categories sure is fun. It is also stupid and limits your perception of them.

There are 10 types of people who put other people in categories...

(1) The Human Calculators: they have memorized the Caltech/JPL phonebook and can tell you in 1.3 seconds in which category to place any name you read them from said phonebook.

(2) The Random Generators: they can create a new category at the drop of a hat. If they are about to become parents, they make a first-draft list of 1,001 possible names for the child, and hand that to their spouse/significant other.

(3) The Field Jumpers: if you tell them into which categories you have placed a number of Physicists that you know, they will do the same for a list of molecular biologists.

(4) The Connectors: you give them your list of categories, and they give you a stack of papers on Theory of Mind, Psychometrics, and tell a funny story about why the Navy administers the tests to people on NSF grants about to winter over at Antarctica;

(5) The Communicators: you give them your list of categories, and the next thing you know, they're explaining it on The Tonight Show.

(6) The Refactoratti: you give them your list of categories, and they organize a seminar on Epistemology and Ontology.

(7) The De-constructors: they ask "if someone categorizes all the people who DON'T categorize themselves, does that person categorize themself?"

(8) The Team-Builders: they arrange a lunch with you, a biographer from the History Department, and a gal from HR to draft the university standards for categorization;

(9) The Political Radicals: First they say: "I am not a number. I am a human being," and then they explain why categorizing people is a relic of the white establishment phallocracy which must be destroyed for the good of the ecosystem.

(10) Slackers: you try to give them your list of categories, and they say: "Dude, can't you just Twitter that to me?"

What about humor? I realize you guys are talking about what we might call "scientific brilliance" but the truly funny people in the world are, well, geniuses in their own way. Sort of hyper-refactorrati. Think of George Carlin: a superb communicator, for one, and possessing a remarkable ability to cut through B.S. and put things into context, and rate them in terms of value, usefulness, etc. I doubt he could do quantum mechanics, but I'd bet he could listen to you explain your work and give you a unique and original perspective on its place in the Big Scheme of Things.

There's actually a common theme to all of these categories. Does anyone else see what the theme is? No, not the science as profession part.

These are all symptoms or secondary effects of mild to moderate ADD and ADHD. So ADD is a disease, is it?

ADD/ADHD is to creativity what sickle-cell is to malaria resistance.

The Magicians:
Those who see something, that everyone is doing in a standard way, in a completely new and highly fruitful way; who create theories out of pure imagination that now one else would even have looked for; who are truly, really, amazingly original.

Everyone else is no genius--they merely have talent. Genius is a term used too often---the are very few geniuses.

Exanples: Heisenberg and Matrix Mechanics;
Von Neumann and the C^{\star} approach to QM, Faraday and Flux Tubes, Morse and Morse Theory, Einstein and General Relativity,
Nash and Isometric Embedding, Gromov and
Symplectic Topology, Feynman and Path Integrals/Wiener and Wiener Measure.

The inhumanly clever: Example, Ramnujuan.

A Ramanujuan amusement, what is the sum of
sqrt{1+sqrt{2 +sqrt{3.... ?

Hint: The solution is very short using freshman calculus.

Have fun!!

Eric the Red: From the post "just to cut out the comment before it happens, of course these are not mutually exclusive"

Mark: Very funny.

Penny: Of course we can quibble over the meaning of genius, but limiting it to five people seems to small to me. (Just kidding.) But of course I have a broader definition of genius: geniuses are people who do things that I can't, cause I'm no genius.

Ian: so there are no mid-career geniuses? Doh.

Have no fear Dave. There's still time.

Generalizations of penny's question:

Weisstein, Eric W. "Nested Radical." From MathWorld--A Wolfram Web Resource.

Also, sequence A072449 of the Online Encyclopedia of Integer Sequences:

A072449 Decimal expansion of the limit of the nested radical sqrt(1 + sqrt(2 + sqrt(3 + sqrt(4 + ... )))).

1, 7, 5, 7, 9, 3, 2, 7, 5, 6, 6, 1, 8, 0, 0, 4, 5, 3, 2, 7, 0, 8, 8, 1, 9, 6, 3, 8, 2, 1, 8, 1, 3, 8, 5, 2, 7, 6, 5, 3, 1, 9, 9, 9, 2, 2, 1, 4, 6, 8, 3, 7, 7, 0, 4, 3, 1, 0, 1, 3, 5, 5, 0, 0, 3, 8, 5, 1, 1, 0, 2, 3, 2, 6, 7, 4, 4, 4, 6, 7, 5, 7, 5, 7, 2, 3, 4, 4, 5, 5, 4, 0, 0, 0, 2, 5, 9, 4, 5, 2, 9, 7, 0, 9, 3 (

COMMENT

Herschfeld calls this the Kasner number, after Edward Kasner. - Charles R Greathouse IV, Dec 30 2008

No closed-form expression is known for this constant.

"It was discovered by T. Vijayaraghavan that the infinite radical sqrt( a_1 + sqrt( a_2 + sqrt ( a_3 + sqrt( a_4 + ..., where a_n >= 0, will converge to a limit if and only if the limit of (log a_n)/2^n exists" - Clawson, p. 229. Obviously if a_n = n, the limit of (log a_n) / 2^n as n -> infinity is 0.

The continued fraction is 1, 1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...

REFERENCES

Calvin C. Clawson, "Mathematical Mysteries, the beauty and magic of numbers," Perseus Books, Cambridge, Mass., 1996, pages 142 & 229.

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.2.1.

Aaron Herschfeld, "On Infinite Radicals", American Mathematical Monthly 42:7 (1935), pp. 419-429.

David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, London, England, 1997, page 30.

Stephen Wolfram, "A New Kind Of Science," Wolfram Media, 2002, page 915.

LINKS

Eric Weisstein's World of Mathematics, Nested Radical

Eric Weisstein's World of Mathematics, Nested Radical Constant

EXAMPLE

Sqrt(1 + sqrt(2 + sqrt(3 + sqrt(4 + ... =~ 1.757932756618004532708819638218138527653...

MATHEMATICA
RealDigits[ Fold[ Sqrt[ #1 + #2] &, 0, Reverse[ Range[100]]], 10, 111][[1]] A New Kind Of Science
PROGRAM

(PARI) (gives at least 180 correct digits) s=200; for(n=1, 199, t=200-n+sqrt(s); s=t); sqrt(s)

CROSSREFS

Cf. A072450.

AUTHOR

Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 01 2002

See also:
A099874 Decimal expansion of a nested radical: CubeRoot(1 + CubeRoot(2 + CubeRoot(3 + CubeRoot(4 + ...

A099876 Decimal expansion of a nested radical: sqrt(1! + sqrt(2! + sqrt(3! + ...

A099877 Decimal expansion of Nested radical: Sqrt(1^2 + CubeRoot(2^3 + 4thRoot(3^4 + 5thRoot(4^5 + ...

A099878 Decimal expansion of a nested radical: Sqrt(1 + CubeRoot(2 + 4thRoot(3 + 5thRoot(4 + ...

And, finally, with me playing the role of The Connector:

A105546 Decimal expansion of prime nested radical.

2, 1, 0, 3, 5, 9, 7, 4, 9, 6, 3, 3, 9, 8, 9, 7, 2, 6, 2, 6, 1, 9, 9, 3, 9, 6, 4, 9, 6, 8, 5, 3, 2, 5, 4, 4, 4, 0, 4, 2, 1, 6, 2, 2, 8, 8, 2, 4, 0, 0, 1, 3, 8, 7, 2, 9, 8, 6, 8, 7, 2, 8, 4, 5, 6, 3, 8, 8, 5, 1, 7, 0, 8, 4, 8, 3, 7, 3, 6, 2, 3, 2, 1, 8, 4, 6, 6, 9, 7, 4, 7, 6, 3, 3, 5, 5, 2, 1, 9, 4, 4, 9, 4, 0, 9

COMMENT

A105547 is the continued fraction representation of this prime nested radical. A105548 is the similar semiprime nested radical. A105548 is the Fibonacci nested radical. Sqrt(1 + Sqrt(2 + Sqrt(3 + Sqrt(4 + ... = ~ 1.75793275661800... "It was discovered by T. Vijayaraghavan that the infinite radical, sqrt( a_1 + sqrt( a_2 + sqrt ( a_3 + sqrt( a_4 + ... where a_n => 0, will converge to a limit if and only if the limit of (ln a_n)/2^n exists." [Clawson, 229; cf. A072449]. We know the asymptotic limit of primes and hence that the Prime Nested Radical converges.

REFERENCES
Borwein, J. M. and de Barra, G., Nested Radicals, Amer. Math. Monthly 98, 735-739, 1991.

Calvin C. Clawson, "Mathematical Mysteries, the beauty and magic of numbers," Perseus Books, Cambridge, Mass., 1996, pages 142 and 229.

S. R. Finch, Analysis of a Radical Expansion, Section 1.2.1 in Mathematical Constants. Cambridge, England: Cambridge University Press, p. 8, 2003.

LINKS

Eric Weisstein's World of Mathematics, Nested Radical Constant.

FORMULA
Sqrt(2 + Sqrt(3 + Sqrt(5 + Sqrt(7 + Sqrt(11 + ... + Sqrt(Prime(n))))).

EXAMPLE
2.10359749633989726261993964968532544404216228824001387298687284563...

MATHEMATICA
RealDigits[ Fold[ Sqrt[ #1 + #2] &, 0, Reverse[ Prime[ Range[ 80]]]], 10, 111][[1]] (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 31 2005)

CROSSREFS

Cf. A000040, A072449.

AUTHOR

Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 12 2005

penny:

Interesting problem! It's closely related to an easier one in which you compute sqrt(x + sqrt(x + sqrt(x + ...))), for any x. To solve this one, write S = sqrt(x + sqrt(x + sqrt(x + ...))), and note that S^2 = x + S. This is a quadratic equation that can be solved for S!

Jonathan,
I always enjoy your interesting posts.
Ramanujuan gave a solution to the problem that I posed. It is a reduction formula for a certain integral. That he found it is--to me--an indication of his almost superhuman intellect.

Zach,
Note that the problem you pose, when x=1 gives rise to the golden mean.

Speaking of "Facets of Genius" -- here is a link to the audio podcast of a recent symposium on this topic:

http://guides.lib.fsu.edu/aecontent.php?pid=99561&sid=747385

A Curmudgeon's and Improv's Guide to Outliers: Introduction

pontiff — Mon, 29 Dec 2008 16:15:21 +0000

A Curmudgeon's and Improv's Guide to Outliers: Introduction

So I picked up Malcolm Gladwell's newest book Outliers: The Story of Success the other day, as I'm sure many of you will be doing on your next trip to the airport (where stands of Gladwell's hardcover book, marked down thirty percent, block your every exit through the already cramped airport bookstores.) Gladwell's books are fun, but I find myself often disagreeing with his analysis, so I thought it would be entertaining to take my time reading his latest and jot down my thoughts as I progress. Well "entertaining" in that "holy shit dude you are pedantic" sort of way. Note that I really do like Gladwell's books, and indeed for me, reading with critical eyes is exactly the reason I like his books. Ah, the life of a curmudgeonly pedant, revealed before your eyes, here on these there intertubes!

To balance things out, I've also included some thoughts from the improv part of my brain: the part that takes ideas at more than face value and tries to run with them.

SPOILER ALERT: Dude, I can't talk about the book without giving away what the book is about, so if you don't want the book's main ideas to be spoiled, don't continue reading.

IDIOT ALERT: I'm in no way qualified in most of the fields Gladwell will touch on, so please, a grain of salt, before you start complaining about my ignorance. Yes I'm an idiot, please tell me why!

Outliers: Introduction

Don't have a heart attack: just move and integrate into Roseto???

Gladwell begins Outliers with an introduction describing the work of physician Stewart Wolf and John Bruhn on the town of Roseto, Pennsylvania (for the story as told by these authors see The Power of Clan: The Influence of Human Relationships on Heart Disease.) Roseto is a town which consisted largely of an close knit group of Italian immigrants who, during the 1950s and 60s exhibited a remarkable lack of cardiovascular disease (more specifically heart attacks.) The conclusion of Bruhn and Wolf was, after examining many different factors (hereditary, diet, exercise, and geography) which might cause this effect, that none of the normal factors could explain Roseto's good health, and that the only way to explain the effects in Roseto was that the Rosetians had good health because of the community they lived in. In particular Bruhn and Wolf noted that the community was very close knit and had a very strong family (three generations under one roof) and civil structures. Further studies (The Roseto effect: a 50-year comparison of mortality rates by B Egolf, J Lasker, S Wolf and L Potvin (1992)) evidence that as the community began to lose its strong social structure, the health of the inhabitants decreased. This effect, that community could lead to better health, has been termed by some the Roseto effect. This isn't a view which one hears too often, and indeed Gladwell tells us that Wolf and Bruhn had some work to do: "Wolf and Bruhn had to convince the medical establishment to think about health and heart attacks in an entirely new way: they had to get them to realize that they wouldn't be able to understand why someone was healthy if all they did was think about an individual's personal choices or actions in isolation."

So this, then, is where Gladwell begins his book: describing a town which was an outlier in terms of medical health, and describing how an unusual hypothesis, that community mattered, was largely responsible for this effect. And this, says Gladwell, is what he wants to do, but instead of explaining outliers in medical health, he wants to do this for success.

Curmudgeonly pedant's view: First of all, like most stories Gladwell chooses to focus on, this one is compelling upon first reading. And I'm inclined to give great artistic license to the introductory chapter (a philosonomicon, if you will) where a tone and main thesis are to be hinted at, but not defended in great detail. But that's no fun! Let the pedanting begin!

One issue that most bothers me when reading Gladwell is exactly the thing that makes him most enjoyable to read: argument by reference to research without the details of the research. So let's think a bit about the story being told. A physician finds a small town with a low rate of heart disease that also has a tight knit community. Surrounding areas with similar environmental hazards don't show these low levels of heart disease. Should I be surprised? Well, if you examine the relevant data you find that Rosero had about half the age adjusted mortality rate as that of neighboring Bangor. A closer look at that paper, it shows that this data it gives 95 percent confidence levels for the ratio of age adjusted mortality rates of Roseto and the nearby Bangor. For heart attacks in three decades the data shows that the ratio is statistically significantly at this level.

But this is where my ears perk up a little, not enough to really make me question the Roseto effect, but enough to put me in a bit of a ~~fowl~~ foul statistical mood. How many cities are there in the United States (somewhere in the neighborhood of 20000. How many of these are smaller than 10000 people? Well as of 1998 the number of towns in population great than 10000 was 2500. So even working backwards to the relevant time periods of the study one would guess that there is somewhere in the neighborhood of 10000 small towns which might potentially be a candidate for a study such as the one performed in Roseto. If we assume that age adjusted mortality rates for heart disease are normally distributed among cities, we thus might expect somewhere around 250 towns with abnormally low ratios like that of Roseto to Bangor (that's just a rough guestimate given the 5 percent significance, working with one side of the distribution, this means the number is perhaps a bit too high.) Of course the beauty of the story is that Roseto is a small town with a unique community culture, and putting a guess on how rare this occurs, is a hard task to put a number on. But if this number is anything like one in a hundred then I would be surprised if a place like Roseto doesn't exist, just in the United States.

Of course what is even more interesting is that the effect persists over three decades. It's a bit unclear to me what time period one should take for this effect. For example if we assume that these should be thought of as three separate instances of the Roseto effect, then the above statistical observation about the rarity of such deviations isn't as strong. My guess, however, would be that the effect should be binned approximately on a generational time scale, which is around 25 years in the United States.

This is, of course, not to say that I don't buy the overarching hypothesis of Wolf and Bruhn. But the work of just Roseto is not enough to convince me. So has there been other studies that take a larger approach to how community can effect community in the way Wolf and Bruhn hypothesize? Well as I said in the introduction, I'm not at all qualified to answer this, but a little searching did produce some interesting results. In particular I certainly learned a lot from reading Social capital and health promotion: a review by Penelope Hawe and Alan Shiell (2000). That paper has a ton of great references, but let me just quote from the conclusion:

We have suggested that the science of social capital, by which we mean its empirical capacity to explain health patterning, is relatively weak at present. The
concept is too broad relative to more precise, alternative constructs.
...
Progress will only be made, however, with cross-disciplinary literature reviews and more rigour in the translation from theory to measurement

Which is, to me at least, a nice way of saying there could be something here but we're not quite convinced yet. Note that this is fairly far from Gladwell's interpretation which is that this is well established, and by caveat, important.

And here, at the word "important", we get into a question of quantification of the size of the effect. Because the study of Wolf and Bruhn is limited to one city we can't get an idea for how large of an effect this is in comparison to the other effects listed by Gladwell. An effect can be unexplained by correlations with other factors, but still be small in size. And this, it would seem to me is an essential point to Gladwell's argument. Gladwell says

Living a long life, the conventional wisdom at the time said, depended to a great extent on who we were-that is on our genes. It depended on decisions we made-on what we chose to eat, and how much we chose to exercise, and how effectively we were treated by the medical system. No one was used to thinking about health in terms of community

But from my cursory understanding of the Roseto work, it isn't at all clear that one can draw a conclusion as to the relative size of any community effect versus all of the other factors, like genetics, diet, etc that are listed. For example, I've seen references (here's one) to studies where dietary changes account for a drop in death rate by heart disease of around twenty percent. What, if any, is the size of the Roseto effect compared to these factors? If one is going to "explain" how to live a healthy lifestyle and one leaves out the effects of diet, genetic, income, and exercise, would that be a good explanation? Somehow I'm a bit skeptical.

Improv's view: If a curmudgeon looks all ideas dead in the eye and says "I am skeptical", an improv's job is to take the ideas presented, not disagree with them, and then run with where ever they might lead.

And now, your highness, we will discuss the location of your hidden rebel base...

Take the Roseto effect, then, and multiply it a millionfold. What if, all of your health, were dependent exclusively on social structure of the community you belong to? I think what I'd like to know about such a society was how it dealt with rebels. You think you've got it bad, young rebellious high schooler, just imagine if your rebellion caused your friends to die! Get your ear pierced, give your dad a heart attack (okay, well, this one may hit too close to reality.) This reminds me a bit of these lines from ~~Roger Waters~~ Pink Floyd's "The Final Cut":

Tell me true, Tell me why, was Jesus crucified?

Was it for this that daddy died?

Was it you, was me, did I watch to much T.V.?

Is that a hint of accusation in your eye?

Of course, watching too much T.V. is exactly the kind of activity that does sort of kill you, since it tends to lead to an unhealthy lifestyle, but what if it wasn't this effect, but the fact that you were alone watching television instead of being out on the streets talking with your neighbors that killed you? I'm guessing that the pull of American Idol on the world would be a lot less powerful in such a universe, but then again, the power of Simon and Paula is pretty damn strong.

pontiff Mon, 12/29/2008 - 11:15

Tags

Extralusionary Intelligence

Categories

Enjoy the rest of the book, you'll have plenty of opportunities to write columns like this. Gladwell is an odd author to me. I have never been more frustrated in reading about things that are interesting, well written, by an intellectual, where there are so many slightly wrong steps and lack of context that I cannot actually believe the conclusions. I don't really want to, but I see so many errors of not considering alternatives in his works that I get disgusted over time. He cites tons of research and makes it sound like a done deal, and tells so many interesting facts, like about people holding warm cups for a second making them more agreeable, yet then makes arguments that fail to show the real significance of things.

Huh. You made me think: I belong to a group that has a very tight-knit community and also a greater-than-average lifespan (Mormons). However, as far as I know (I haven't done any research on this) the lifespan increase can be tied to the healthy behavior which is reinforced by belonging to the community (no smoking, drinking, drugs, etc.) - so I am willing to believe that tight communities foster healthy behaviors, and probably make people happier which also increases lifespan, but you'd have to do more work to convince me that the community itself did something directly.

charlene: In the case of Roseto, it appears that the community had just as many bad habits as other similar communities: lots of smoking, cooking with lard, etc.

From one pedant to another: a fowl statistical mood? :)

Yeah, the kid of statistical mood that you find at Kentucky Fried Chicken! Thanks, fixed.

Computer Science "Futures"

pontiff — Mon, 14 Jul 2008 11:37:20 +0000

Computer Science "Futures"

Ed Lazowska has penned an article over at the CCC blog about the state of computer science enrollments which is well worth reading.

My favorite part of the post is where Ed points out that the "news" reported in the "news" is not really "news":

The Taulbee Survey "headline" this year was (roughly) "computer science bachelors degrees drop again." In my view, this is not news -- it was entirely predictable from the legitimate headline four years ago: (roughly) "freshman interest and new enrollments drop again." The actual news right now in the CRA data is that freshman interest and new enrollments seem to be stabilizing and turning the corner -- starting to trend upward. "Degrees granted" is a lagging indicator -- it lags freshman interest by 4 years. The fact that the number of bachelors degrees granted this past year decreased is not news -- anyone could have looked at the freshman interest data from 4 years ago and told you it was going to happen.

Classic. I wonder if we are supposed to call events like this "olds" instead of "news?"

Anyway, Ed points to some interesting effects in Ph.D. data which are clearly a consequence of the dot-com bust. As a graduate student in the Bay Area during the dot com explosion (I left right as the bubble burst), I can tell you that it was very hard to convince many graduate students to stay away from the dot com's and finish their Ph.D.'s (okay, well I was a physics Ph.D., but even us physics Ph.D.'s sometimes can see opportunities when they are flashing "GREEN, GREEN, GREEN!" in front of us.) And, truth be told, in spite of the ominous economic times we currently live in, I really do get the same vibe of excitement that permeated the dot com boom from listening to all of the interesting startups going on in the Seattle area (John Cook's venture blog is a good source for this.) But, of course, I also know that the hype of the dot-com hasn't get escaped from people like me who see all sorts of exciting new opportunities, to the mainstream. Which makes me think that now is an excellent time to be venturing forth into new computing technologies. Of course, this prediction is something totally different from "news" and "olds", which some will call baloney, but which maybe we should call "futures?"

pontiff Mon, 07/14/2008 - 07:37

Tags

Computer Science

Neologista

Categories

Free Thought

"the dot-com bust."

That really was just a downturn on over-priced stock because so many of these VC funded start-ups thought future market value could rely solely on (ironically) market capitalization rather than earnings. That's why many wanted replace P/E and other earnings measurements with things like price per sales or even price per projected revenue (ha ha!).

But the demand for the Internet (and, thus, all the computer science and programming behind it) and its services did not go down, it went up. It even has a bigger market today because of the increase in broadband users. It was just certain unsustainable business models that busted. I can't see how there will not be more growth in demand for programmers over time (and, thus, the need for hardcore computer science as well).

Don't listen to the "news" (or the "olds" as you so eloquently label it!), there are still tons of Computer Science students out there- myself being one of them.

Part of the issue is probably that a lot of us have shifted to online colleges and universities for our degrees- we're busy people- and degrees aren't cheap. In this economy, I don't see how any could work and study at the same time (for me it's just not financially possible...).

The News Media probably doesn't use all-encompassing statistics, which perhaps don't even exist at this early point in what I'd call the distance learning explosion (let's hope it doesn't bust before I finish up my MSCS at American Sentinel!) and so the numbers look deflated.

As usual, the "news" is lagging behind the times, telling a story full of half truths, without doing any actual investigation of their own!

Rock on Dave!

Word of the Day

pontiff — Thu, 17 Apr 2008 09:11:08 +0000

Word of the Day

A word I accidentally mumbled in class: "crudimentary." I think it means both rudimentary and crude. Anyway, I like it, and am going to try to start weaseling it into as many talks as I possibly can. Speaking of which, here are slides for a guest lecture I gave to the local alternative models of computing class at UW.

pontiff Thu, 04/17/2008 - 05:11

Tags

Neologista

Self: Meet Center. Center: Meet Self.

Categories

Free Thought

Good one!
With a little modification, we have "crudumentary" - a documentary that is crud.
Expelled, perhaps?

I can imagine T. Bruce McNeely's suggestion leading to this one-line review:

"The crudumentary 'Expelled' is craptacular!"