Hack Away at the Edges

See also: Challeng­ing the Difficult and Tips and Tricks for An­swer­ing Hard Ques­tions.

From Michael Niel­sen’s Rein­vent­ing Dis­cov­ery:

In Jan­uary 2009, [math­e­mat­i­cian Tim] Gow­ers de­cided to use his blog to run a very un­usual so­cial ex­per­i­ment. He picked out an im­por­tant and difficult un­solved math­e­mat­i­cal prob­lem, a prob­lem he said he’d “love to solve.” But in­stead of at­tack­ing the prob­lem on his own, or with a few close col­leagues, he de­cided to at­tack the prob­lem com­pletely in the open, us­ing his blog to post ideas and par­tial progress. What’s more, he is­sued an open in­vi­ta­tion ask­ing other peo­ple to help out. Any­one could fol­low along and, if they had an idea, ex­plain it in the com­ments sec­tion of the blog. Gow­ers hoped that many minds would be more pow­er­ful than one, that they would stim­u­late each other with differ­ent ex­per­tise and per­spec­tives, and col­lec­tively make easy work of his hard math­e­mat­i­cal prob­lem. He dubbed the ex­per­i­ment the Poly­math Pro­ject.

The Poly­math Pro­ject got off to a slow start. Seven hours af­ter Gow­ers opened up his blog for math­e­mat­i­cal dis­cus­sion, not a sin­gle per­son had com­mented. Then a math­e­mat­i­cian named Jozsef Soly­mosi from the Univer­sity of Bri­tish Columbia posted a com­ment sug­gest­ing a vari­a­tion on Gow­ers’s prob­lem, a vari­a­tion which was eas­ier, but which Soly­mosi thought might throw light on the origi­nal prob­lem. Fif­teen min­utes later, an Ari­zona high-school teacher named Ja­son Dyer chimed in with a thought of his own. And just three min­utes af­ter that, UCLA math­e­mat­i­cian Ter­ence Tao—like Gow­ers, a Fields medal­ist—added a com­ment. The com­ments erupted: over the next 37 days, 27 peo­ple wrote 800 math­e­mat­i­cal com­ments, con­tain­ing more than 170,000 words. Read­ing through the com­ments you see ideas pro­posed, re­fined, and dis­carded, all with in­cred­ible speed. You see top math­e­mat­i­ci­ans mak­ing mis­takes, go­ing down wrong paths, get­ting their hands dirty fol­low­ing up the most mun­dane of de­tails, re­lentlessly pur­su­ing a solu­tion. And through all the false starts and wrong turns, you see a grad­ual dawn­ing of in­sight. Gow­ers de­scribed the Poly­math pro­cess as be­ing “to nor­mal re­search as driv­ing is to push­ing a car.” Just 37 days af­ter the pro­ject be­gan Gow­ers an­nounced that he was con­fi­dent the poly­maths had solved not just his origi­nal prob­lem, but a harder prob­lem that in­cluded the origi­nal as a spe­cial case.

This epi­sode is a micro­cosm of how in­tel­lec­tual progress hap­pens.

Hu­man­ity’s in­tel­lec­tual his­tory is not the story of a Few Great Men who had a burst of in­sight, cried “Eureka!” and jumped 10 paces ahead of ev­ery­one else. More of­ten, an in­tel­lec­tual break­through is the story of dozens of peo­ple build­ing on the ideas of oth­ers be­fore them, mak­ing wrong turns, propos­ing and dis­card­ing ideas, com­bin­ing in­sights from mul­ti­ple sub­fields, slam­ming into brick walls and get­ting back up again. Very slowly, the space around the solu­tion is crowded in by dozens of in­ves­ti­ga­tors un­til fi­nally one of them hits the pay­load.

The prob­lem you’re try­ing to solve may look im­pos­si­ble. It may look like a wrong ques­tion, and you don’t know what the right ques­tion to ask is. The prob­lem may have stymied in­ves­ti­ga­tors for decades, or cen­turies.

If so, take heart: we’ve been in your situ­a­tion many times be­fore. Al­most ev­ery prob­lem we’ve ever solved was once phrased as a wrong ques­tion, and looked im­pos­si­ble. Re­mem­ber the per­sis­tence re­quired for sci­ence; what “thou­sands of dis­in­ter­ested moral lives of men lie buried in its mere foun­da­tions; what pa­tience and post­pone­ment… are wrought into its very stones and mor­tar.”

“Ge­nius is 1 per­cent in­spira­tion, 99 per­cent per­spira­tion,” said Thomas Edi­son, and he should’ve known: It took him hun­dreds of tweaks to get his in­can­des­cent light bulb to work well, and he was already build­ing on the work of 22 ear­lier in­ven­tors of in­can­des­cent lights.

Pick any piece of progress you think of as a “sud­den break­through,” read a his­tory book about just that one break­through, and you will find that the break­through was the re­sult of messy progress like the Poly­math Pro­ject, but slower: mul­ti­ple in­ves­ti­ga­tors, wrong turns, ideas pro­posed and com­bined and dis­carded, the space around the fi­nal break­through slowly en­croached upon from many an­gles.

Con­sider what I said ear­lier about the prob­lem of Friendly AI:

I doubt the prob­lem will be solved by get­ting smart peo­ple to sit in silence and think real hard about de­ci­sion the­ory and metaethics. If the prob­lem can be solved, it will be solved by dozens or hun­dreds of peo­ple hack­ing away at the tractable edges of Friendly AI sub­prob­lems, draw­ing novel con­nec­tions, inch­ing to­ward new in­sights, draw­ing from oth­ers’ knowl­edge and in­tu­itions, and do­ing lots of te­dious, bor­ing work.

...This isn’t the only way to solve hard prob­lems, but when prob­lems are suffi­ciently hard, then hack­ing away at their edges may be just about all you can do. And as you do, you start to see where the prob­lem is more and less tractable. Your in­tu­itions about how to solve the prob­lem be­come more and more in­formed by reg­u­lar en­coun­ters with it from all an­gles. You learn things from one do­main that end up helping in a differ­ent do­main. And, inch by inch, you make progress.

So: Are you fac­ing an im­pos­si­ble prob­lem? Don’t let that stop you, if the prob­lem is im­por­tant enough. Hack away at the edges. Look to similar prob­lems in other fields for in­sight. Poke here and there and ev­ery­where, and put ex­tra pres­sure where the prob­lem seems to give a lit­tle. Ask for help. Try differ­ent tools. Don’t give up; keep hack­ing away at the edges.

One day you may hit the pay­load.