The main point is not quantity or speed—the main point is quality of thought.
Posts tagged with creativity
The spirit of mathematics is not captured by spending 3 hours solving 20 look-alike homework problems. Mathematics is thinking, comparing, analyzing, inventing, and understanding.
The main point is not quantity or speed—the main point is quality of thought.
The jazz educator David Baker had this to say about jazz improvisation:
You start out learning scales; modes; whole songs. You play along with your favourite records. Then you start breaking it down to pieces—licks, long bits of solos. Gradually as you get more and more mastery of your instrument and over yourself, your control becomes more and more atomic. At the level of full mastery you are feeling, and choosing, every note, every rest. Eventually it’s every fraction of a note, or fraction of a rest, that you’re playing. Actively.
You also want to extend your range. Your body has a wide range of expression at your command. It’s not just your instrument that can make sound. Clomps, stomps, screams, claps, yelps, lip trills, Brooklyn raspberries, exhaling, inhaling, crying out—all of these are tools at your disposal. You also want to become comfortable in every range of your instrument—even very very high, and very very low, have a purpose that in expressing some emotion you may want to utilise.
The bolded part especially rings true for me much more broadly than in music performance. Free will, I feel, can be exercised to varying degrees. If I check my email in the morning, go on Facebook, check my twitter notifications, whatever, I’m yielding up my free will. I’m passively responding to things that I put in front of myself. On better days, or at least the days when I assert more atomic control over my time and choices, I actively spend time in the moment and/or ask myself what I really want to be doing, rather than rolling the wheels through the ruts of habit or letting stimuli lead me to respond.
For me the question of free will isn’t about yes/no deductions—it’s about how much, today?
[I]t is … anachronistic to apply the term artist with its modern connotation to Leonardo [da Vinci]. Artists in the sense that we understand and use the word, meaning practitioner of fine art, didn’t exist in Leonardo’s time. It would be more appropriate to use the word artisan in its meaning of craftsman or skilled hand worker.
In the historical literature ∃ a perfectly good term to describe Leonardo and his ilk, Renaissance artist-engineer, whereby one can actually drop the term Renaissance as this profession already existed in the High Middle Ages before the Renaissance is considered to have begun.
[T]he artist-engineers were … regarded as menials. An artist-engineer was expected to be a practical mathematician, surveyor, architect, cartographer, landscape gardener, designer and constructor of scientific and technical instruments, designer of war engines and supervisor of their construction, designers of masks, pageants, parades and other public entertainments oh and an artist.
The … polymath … that everybody raves about when discussing Leonardo … actually … perfectly normal … any Renaissance artist-engineer—the only difference being that Leonardo was better at nearly all of them than most of his rivals.
As far as his dissections and anatomical drawings are concerned these belong to the standard training of a Renaissance artist-engineer—the major difference here being that Leonardo appears to have carried these exercises further than his contemporaries and his anatomical sketches have survived whereas those of the other Renaissance artists have not.
Having denied Leonardo the title of artist I think it is only fair to point out that it was the generation to which Leonardo belonged who were the first to become recognised as artists rather than craftsmen and in fact it has been claimed that Raphael was the first artist in the modern sense of the word….
[an exhibition on da Vinci] emphasises the few occasions where Leonardo drew something new or unexpected whilst ignoring the vast number of scientifically normal or often incorrect drawings, thereby creating the impression that his anatomical drawings were much more revolutionary than they in reality were. Also whilst the drawings published by Vesalius in his De fabrica in 1543, i.e. a couple of decades after Leonardo’s death, are possibly not quite as good artistically, as those done by Leonardo, they are medically much more advanced.
Several years ago I sat (after yoga class) with some Zaa Zen practitioners. As I understood the practice from doing it once, Zaa Zen basically consists of sitting in good posture, staring at a blank wall, and clearing your mind.
It wasn’t my favourite meditation I’ve ever tried. (So far my favourite was something that into the continuum introduced me to: Vipassana meditation. The way I did it was to sit outdoors in nice weather and listen to the sounds and stop thinking about my own anxiety or problems. Something much like the John Cage lecture that until a single soliton survives posted. Being aware of the world around you and “listening” or “taking in” rather than “forcing” or “pushing out”.)
But I definitely remember the conversation I had with one of the practitioners (Tony) afterwards. Tony was maybe 20 or 30 years older than me but I felt we instantly connected on some mental level. He told me he had been a failure at pretty much everything he had tried in life. How he was a black sheep of his family; how he tried to be a biologist; there were a few other things he tried and he hadn’t been very good at any of them. But in some sense it didn’t matter (remember, this is the wisdom of years talking. According to economic research people tend to mellow, their aspirations and hopes drop to a realistic level, and they become intimately familiar with the passing of time—whatever you optimise, whatever you read, however much you drink, whatever you earn, however you train, however many relationships you destroy—that passing of time always clicks, click, click, tick, steady.) and he could always come back to his practice. A different meaning of “return to the breath”.
Anyway, we were talking about various I guess spiritual things. More like a mixture of the mental-ethereal and the sense-grounded. He was telling me how Zaa Zen was so great and I would really like it and I should read this book and so on. You know how people always do that—they’ve read a book and then they say you would love it. Well, no, I think just you liked it and I have my own stack of stuff that’s my to-read list already. So normally I would just keep that kind of thought to myself but since Tony and I had an unusual level of honesty and directness for perfect strangers who just met, I brought up what I see as the circular-logic problem of picking up any book.
This is why, I said, I won’t read the book you’re telling me I will like so well. From my outsider’s perspective I don’t trust enough in the Zaa Zen idea. Not to say that it is some hokey New Age crystals or whatever, but I don’t sense—from standing on the threshold—that this is a house I want to get comfortable in.
(This is also why I started reading so much mathematics. From an outsiders’ perspective it seemed like “This is where the truth is. Following Wolsey’s idea, with a hungry reification of Plato’s philosopher-kings, if I put in only veracity and earnest labour, the result should be something good.)
Tony told me this attitude was actually quite Buddhistic or Zen of me. So I felt very proud that in avoiding looking at the Zaa Zen I had apparently picked up something of it—and it’s a nice geometric shape now that I reflect on it.
I had nothing but ideas.
O.K., they weren’t strictly mine, in the sense that these ideas were acquired, arranged, styled, photographed, published and distributed by entities bearing no relation to me whatsoever.
People think mathematicians are brilliant because they talk about things like C* algebras or B-splines or A-modules or D-branes or … really any combination of unexplained letter with abstract noun. (Extra points if the letter is Greek!)
But when I think of really genius ideas, I think of things like:
Let me go a little deeper into several of the brilliant things about modern toilets.
That’s leaving aside the efficient manufacture of commodes and the sewage system, which I’m sure are both marvels of their own. You think about something like New York City, it’s a human habitation of 6 million people, each taking maybe 5-10 dumps per week (well, in good times). That’s 30–60 million pieces of crap every week that nobody wants to see or smell ever again.
Imagine you just dug a hole in the side of a hill, Hobbit-style, in a natural clearing. Suppose, too, that you’re close enough to a lake or stream that you can get water to your house easily. (Or it rains enough and you bought some huge rainbarrels.) Then what the crap are you planning to do with all of the crap you generate?! That’s a conundrum for ya.
After talking to a number of PhD students, I’ve come to conclude two things. First, that many (especially in “genius disciplines” like maths or physics) are motivated by the goal of being the smartest human who ever lived—“the next Einstein”, or Feynman, or Grothendieck—not like the humans themselves, but rather like the symbols: revolutionary rarities who personally transformed some small corner of the world.
Second, I’m tentatively concluding that base hits are “actually the way forward”—that is, that home-run projects become magnum opi that never get finished because they’re not perfect, or the passionate ego-drive weakens, or the idea of expressing the ultimate moral worth of one’s psyche through academic paper-writing does not lead to successful ideas. Maybe the cure to cancer doesn’t come from a flash of insight but from a more mundane process of trying this, then that, then another thing. The dissertation that gets done comes from a concrete plan, consisting of steps, which lead to a sequence of words on a page.
The revolution, if it happens, is more likely to come from a sequence of papers which actually get written, than from an unhatched geniusling that doesn’t get written. And let’s face it: most of us aren’t geniuses, nor would we want to be, but we’re still interested in being productive.
In business one can think about base hits as well. My first business was a base hit. I didn’t sell for a jillion dollars, I just gave myself and some other people jobs for a number of years and didn’t fail. Which was my goal at the outset: not to be unprofitable. My plan was to copy an idea I had seen work somewhere else, make a few tweaks, and do it.
OK, so maybe it turned out to be more of a bunt and I should go for a double next time. But at least I wasn’t trying to dream up a revolutionary mobile app that will change the world, justifying paying $250k to various programmers as justified on a massively outsized conception of the “genius” of my “idea”, and ending up with something looking suspiciously like a mashup of Foursquare, Linkedin, OKCupid, and airplane reservations.
I definitely keep my left eye on acquisition prices as a way to gauge interesting spaces to enter—but I’m also thinking about what are the things I can accomplish, with the team I could reasonably assemble, the skills & knowledge I actually have, and the hours I’m actually going to want to work. What are the high-probability base hits I could string together to get from here to there?
(Just to give an example, I will not be founding the next Heroku. That got a nice bid, but the founders were engineers who knew a lot about hardware. That’s not me.)
Maybe Citadel wasn’t built from a “genius” signal using all the latest machine-learning hoopla, but from a smart (and obsessive) kid making trades he thought he could win on, and not making the other trades. And then building from there. Learning what’s a good opportunity, how long it takes to scope out a trade, how much research can reasonably be done in a month, and so on.
In short, maybe all of the “homeruns” I can think of, are actually just a sequence of small steps definitively forward.
In writing I find myself looking more and more for base hits as well. When I first started isomorphismes.tumblr.com, I had very, very high hopes for how awesome the material would be. (I won’t admit how high.) But now after posting 250 short bits of mathematics, I’m much more focussed on
I still think that after some unspecified amount of time, I may be able to string together a more magnum-opusy kind of work—once the pieces (short blog posts) are mostly there on the cutting-room floor. But that’s much more like stringing together a series of base hits than genius-ing out the heartbreaking work I would like to imagine I’ll create.
But what’s my rush? I’m accumulating tumblr followers every day, I’m plugging away at the craft, I’m putting out material. Looking back over a year of following that formula, I’ve put out a surprising amount of text and have a surprising number of subscribers. It’s kind of like the short-term/long-term fallacy working in reverse (working in my favour).
∫short term adds up to more than I thought it would.
Maybe Elliott Smith or Conor Oberst didn’t succeed because they were inspired geniuses who one night invented one of the best songs ever. But instead, first they learned to play the guitar, then they wrote one song when it occurred to them, then they wrote another. That’s the way Phillip Glass describes his own journey in the biopic about him.
Elon Musk and Larry Summers take a contrary perspective. @elonmusk says “I don’t know why all these entrepreneurs are trying to solve small problems”. Larry Summers says “It’s just as hard for an economist to think about important problems as about unimportant problems. The intellectual effort is the same, it’s just the output that’s better.”
Well, maybe they know better than I do. I still suspect in the day to day it’s about “What is the paper I can write, rather than the paper I’d like to be able to write” or “What are the practical steps I can take today to get closer to my business goal?” rather than “What do I wish for?”.
I can’t prove I’m right, this is just where my thoughts are at the moment. I think there’s a cult around genius and a cult around business superstars. Both of which do harm by increasing people’s appetites for success—feeding ambition, feeding vanity, feeding swagger, feeding overexuberance, feeding bad investments—above what’s reasonably achievable in a succession of 3,500 days.
Three and a half centuries before Christ, Plato outlined his conception of a great society in The Republic.
The important decisions are made by “philosopher-kings”—an overclass who arguably represent Plato’s idea of human perfection.
Although circles don’t actually exist, one can conceive of a circle and Plato thinks there’s something important about that.
Taking the reins back from Plato: what I’ve found in my life is that concepts I learn, feelings I feel, stories I hear, experiences I remember, newspaper crap or history books I read — all inputs expand my own private language. Almost like adding elements to a basis? Doug Hofstadter told a story that illustrates “personal metaphors” well.
As I learn more mathematics, I find my internal vocabulary expanding quite a lot — faster than through any other learning activity, and definitely faster than just-experiencing life passively. (“Personal” and “private”really are the right words for it; sharing these thoughts is really hard! Hence the writing.)
That’s background. Now, on to the topic of originality.
Question: Are there any truly new ideas? I sometimes sense that a few Big Ideas occur to many, many people, and that the history of philosophy is just an exercise in rehashing them through different filters. I got the same feeling reading A Canticle for Leibowitz, a work of speculative fiction that spans several millennia and displays what I felt was a 16-year-old history nerd’s overly simplistic view of the broad trends of history.
Is there any music that isn’t totally derivative of something else? Questions like that turn artists to LSD in search of originality.
I have a different suggestion: there are truly new ideas today, ideas that demonstrably could never have occurred to Plato, and they come from 20th-century mathematics. (I’m not saying there aren’t new ideas elsewhere—just that with the mathematical ideas it’s quite clear that nobody could have thought of them before.) So we of the 21st century essentially have a reserve of raw idea-ore which we can mine and smelt for use in some creative pursuit—even if it’s just thinking about life differently.
I’m sort of relying on the Edward Gorey theory of creativity here: that people don’t necessarily generate original ideas, but they can filter their sensory input, and refilter / resample their internal dynamics, and still make output that’s visibly different than everything else that’s come before.
Does a unique piece of music count as original, even if it’s just a convex combination of musics that previously existed? In the biopic about him, Philip Glass described his music as a fusion of East and West (like ragas and haute couture strict piano).
While science rightly uses empirical evidence (”facts”) as the ultimate arbiter of truth, those who experiment and analyse field data usually only credit or discredit ideas / frameworks that some theorist has previously invented.
Tagline. Science: We finally figured out that you could separate fact from superstition by a completely radical method: observation. You can try things, measure them, and see how they work!
Hence the name “theory-killers” for experimental physicists.
Where do these theories come from, though? My own experience and my observations of others lead me to believe that an economic theorist’s deep creative centre is informed, flavoured, shaped, and sullied by her own personal experiences, biases, stereotypes, and assumptions about what’s normal. If you talk to people who have deeply integrated into their psyche concepts like “opportunity cost”, “rationality”, “search”, “strategy”, “information”, “evolution”, “optimisation”, and so on, and you disagree with this statement, please tell me.
(For example: a professor of game theory told me that he cannot fathom the motivations of a suicide bomber. He can’t fathom them, so he can’t model them, so we have no theory to predict and curtail their bombing behaviour.
Example 2: Do you think Daniel Ellsberg started running psychological experiments at random until he stumbled upon his famous "Ellsberg Paradox"? No, he had the idea in his head that these two kinds of “uniform distribution” should be different—perhaps getting the idea from Keynes or Frank Knight—and then tested the idea.)
Since there’s a "lone genius" limit on novel* economic theories, a finite upper bound follows on how much fact-checking can improve a theory’s soul. Although one can certainly benefit from pulling on threads, reading monographs, looking at data tables and so on, ultimately I believe deep insights come from the same brain process that generates the fallacy of lack-of-imagination (argumentum ad ignorantiam). Just as people form judgments by the “Does this fit with what can I imagine” test, so too—says I—do economic theories rise from the same murky pit. Personal experiences where we’ve taken in reams of high-dimensional streaming data (like at work) feed this imaginative capacity, such that we can run and assess counterfactual dramas in our heads (sort of like a Monte Carlo). "What if the vendor had said this to my boss? Nah, she wouldn’t have reacted that way. Not like her." There are some biologists who say that our brains have an especial capability to think through such human dramas. (And in writing that sentence I used the same often fallacious imaginative faculty.) The imaginative faculty is abused by cheap stereotypes—
Ideas can be checked against experiences and personal symbols much more easily than against a tome of facts. Since theoretical creativity proceeds in inspirational flashes and needs to run verificational checks at the speed of imagination, only the checks that can be done very quickly influence the creative process.
* Of course most theories derive from the joining of ideas from the existing literature. But those aren’t “novel” ideas.
It’s my conviction, therefore, that theoretical economists would come up with better theories if they spent more time in “the real world” and less time thinking about isomorphisms.
The problem is more acute in economics than in physics, because economic theories are much harder to kill (so many alternative explanations / dismissals one can retreat to) — which shifts some of the burden of correctness to the theorists. If you know that
then you would be quite reasonable in polishing & perfecting a theory—working to cleanse yourself of biases and myopia, asking yourself if what you’re writing is really quite true, what are the underlying assumptions, and so on.
The problem is also more important for economic theorists to address because those who theorise about the human mind have, erm, direct access to the thing they’re theorising about.
The difficulty of killing an economic theory has been discussed much elsewhere:
and if you read the things I read, you’ve probably had similar thoughts as:
and many others. Point being, if you are educated on this stuff, then I’m sure you can see how the Slutzsky decomposition is a compelling advance in “research technology”, but can’t carry over as-is to the ultimate subject of interest, which is human behaviour and feelings.
Am I just carping? A bit, but I also can propose something like a solution. If those who give out grants for economic research could be convinced that
were important indicators of future relevancy and correctness of research—along with knowledge of a body of literature, knowledge of mathematical/statistical/experimental methods, consulting/political experience, and/or a Ph.D.—then up-and-coming economists would have the incentive to spend time in “the real world” and find out, in a personal way, what the people they theorise about go through.