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Exploring the Idea Space Efficiently

22 Post author: Elithrion 08 April 2012 04:28AM

Simon is writing a calculus textbook. Since there are a lot of textbooks on the market, he wants to make his distinctive by including a lot of original examples. To do this, he decides to first check what sorts of examples are in some of the other books, and then make sure to avoid those. Unfortunately, after skimming through several other books, he finds himself completely unable to think of original examples—his mind keeps returning to the examples he's just read instead of coming up with new ones.

What he's experiencing here is another aspect of priming or anchoring. The way it appears to happen in my brain is that it decides to anchor on the examples it's already seen and explore the idea-space from there, moving from an idea only to ideas that are closely related to it (similarly to a depth-first search)

At first, this search strategy might not seem so bad—in fact, it's ideal if there is one best solution and the closer you get to it the better. For example, if you were shooting arrows at a target, all you'd need to consider is how close to the center you can hit. Where we run into problems, however, is trying to come up with multiple solutions (such as multiple examples of the applications of calculus), or trying to come up with the best solution when there are many plausible solutions. In these cases, our brain's default search algorithm will often grab the first idea it can think of and try to refine it, even if what we really need is a completely different idea.

Of course, the brain is not so stupid that it will choose the first idea it has and refine it forever. Even in the ancestral environment, we would have run into problems where depth-first search is not very effective. Rather than spending time on refining your skills at chipping flint to make tools, for example, you may have been better served by learning to pick a better type of flint to work with before even starting. In modern times, however, these problems have grown more challenging and more numerous. I'm sure all of us have had the experience of working on some problem for a long time, refining our solution, maybe even trying to make the problem fit the solution we came up with out of frustration, only to give up, come back later, and then suddenly have a completely different and obvious solution come to mind. While part of this is probably due to some peripheral processes in our brain analysing the problem while our conscious thoughts were not focused on it, I think the key component is that by leaving the problem alone we "forgot" our first solution and were free to look for a better one.

Similarly, it is possible that if Simon stops trying to come up with examples whenever he remembers the examples he's seen before, and only returns to the task when his mind is relatively blank, he might be able to produce something original. Even if he does that, unfortunately, he might still find himself coming up with only one example at a time, and then being stuck thinking only of examples that are somehow similar to it. Either way, having to pause for several hours every time he finds himself primed to think of something is far from ideal, and there are better solutions.

 

The fundamental thing you should do when approaching a difficult, but tractable1, problem is to avoid proposing a solution immediately. The moment you propose a solution, your brain will be primed to to try to refine it or to look for similar solutions, even when it might be much more efficient to further analyse the problem or to look for other, radically different, solutions. Even when you have thoroughly understood the problem, however, you should still wait before proposing a solution, unless the problem is fairly easy and one solution is all you need.

What I would recommend that you do before that is come up with a map of the idea-space, describing where the possible solutions might be found. For instance, before looking at a single example of calculus, Simon might have written down a list of idea areas to explore: "jobs, personal life, the natural world, engineering, other". He would then take the first broad category, "jobs" and expand it into a longer list, perhaps "agriculture, teaching, customer service, manufacturing, research, IT, other". With this longer list, he can then focus on each area in turn and either expand it further if it seems especially rife with examples, or come up with an example from the area directly. Once the area is depleted, which he might decide is the case if it takes him longer than one minute to come up with an example, he would move on to the next area.

There are two main advantages to this approach. The examples Simon finds should be fairly representative of all the examples he can think of, since he started with a map of all such examples, and, better yet, he should be able to find examples much faster because he knows to stop looking in one small area when it becomes depleted.

The same approach is also useful when you're trying to come up with the single best solution. For example, if you're trying to come up with a way to deal with climate change, you might write down "reduce carbon emissions, engineer the climate to be better, adapt to climate change, other" and move on from exploring one option to the next when the option runs into significant difficulties. Note, however, that in this case it is important to arrange your options in order of how likely you think you are to find your best solution within each of them to make sure you explore the most solution-rich areas first.

In general, there are three main things2 to keep in mind when creating a map of your idea-space:

  • Don't get overly specific with the initial areas, since you will refine them when you're expanding them.
  • Try to include all the areas that might contain a solution and none that do not.
  • Try to pick areas so each of them is equally likely to contain a solution (or order the areas by the number of solutions and move on more quickly from solution-poor areas).

For instance, when Simon came up with his list of areas for calculus examples, he correctly did not include "philosophy" in the list, since it contains much fewer examples than any of the other areas.

 

In sum, when dealing with a challenging problem or coming with a lot of examples: don't jump to a solution, instead carefully consider the problem, come up with a map of areas of ideas where solutions might be found, and search the map until you get the solution you're looking for. If you use this approach, solutions should come to you faster, be needlessly complex less often, and be a lot more correct than the ones from your brain's naïve search algorithm.

 

Footnotes

1: It's important to note that if the problem is not tractable for you, in the sense that you can't tell if you're getting closer to a solution or not, these recommendations won't do much. For example, if I asked you "What is the next number in the sequence 14, 15, 16, 17, 21, 23, 30, 33?" it will help only slightly to hold off on coming up with solutions, and your best bet might be to start doing a depth-first search (as long as you keep in mind that you should not look for overly complicated solutions).

2: This is somewhat similar to Vladimir_Nesov's post recommending that we consider representative data sets (in particular the three mistakes he lists, which are well worth reading).

Comments (26)

Comment author: Kaj_Sotala 08 April 2012 07:16:13AM 25 points [-]

I am not familiar with the neuroscience of what's going on, but a plausible story is that the areas of the brain corresponding to the examples he's just seen are activated.

This made me cringe. "I don't know the relevant science, but instead of looking it up, let me speculate anyway." To be fair, a lot of posts on LW probably do this, but few state it so explicitly. I'm only singling you out because you were so upright about it, which isn't how it should work. So I'm not downvoting you because of that.

The advice given at the end of this post seemed plausible to me, but the initial speculation about how the brain works seemed speculative and unsupported, and didn't really add anything to the post itself. I think the post could be improved by deleting everything between the initial paragraph and the one that starts "The fundamental thing you should do..."

Comment author: Elithrion 08 April 2012 02:30:15PM *  5 points [-]

Unfortunately, I think some of that section is needed to explain what is the nature of the problem that's being addressed (i.e. brain tending to do depth-first search). That said, the two sentences about a likely neuroscience story probably should go. I was actually pretty tempted to take them out when posting but somehow talked myself out of it. I'll go do that now. Hopefully it's not considered bad form to edit without leaving a note?

Thanks for the helpful comment, by the way.

Comment author: ciphergoth 08 April 2012 09:34:26AM 6 points [-]
Comment author: pjeby 13 April 2012 04:04:59AM 6 points [-]

What I would recommend that you do before that is come up with a map of the idea-space, describing where the possible solutions might be found

There is a formal technique for doing this, developed by Edward DeBono, and called a "concept fan". I did a quick web search but didn't find anything that actually explained the technique - everything I found on the web has a very shallow description that mostly misses the point of the technique, i.e., its systematic nature.

In a concept fan, you separate ideas from intentions, so that you see an idea like "carbon credits" as an idea for the intention of "reduce carbon use", which in turn is intended to "have less carbon in the atmosphere. You can then intentionally ask, "what are other ways to reduce carbon use?" or, "what are other ways to end up with less carbon in the atmosphere?", and so on.

(The technique is described in more detail in DeBono's book, "Serious Creativity"... a book which has as its main premise that creativity is something that can and should be approached systematically. Even when randomness is used (e.g. random words as provocations), they're recommended for use in a systematic way, for the specific purpose of keeping brains from going in circles over already-known territory, rather than as a source of mysterious inspiration.)

Comment author: John_Maxwell_IV 18 April 2012 11:23:33PM 0 points [-]
Comment author: AstraSequi 08 April 2012 07:04:55AM *  4 points [-]

I would add that we should remember that proposing "categories in which solutions might fall" might itself be subject to priming/anchoring within category-space. =)

So for example, we could consider systematized ways to map the idea-space - I imagine that certain categories could be easily missed, and/or are very likely to show up for specific classes of problems.

Comment author: Elithrion 08 April 2012 02:22:18PM 1 point [-]

I'm sure it is! In fact, when writing the "jobs, personal life, the natural world, engineering, other" list, I noted that "jobs" and "personal life" have a sort of opposite category connection for me, as does "the natural world" and "engineering" (i.e. human inventions), so I definitely primed myself to come up with areas that are somewhat related.

Fortunately, it's less of a problem for really broad categories, since there are just so much fewer of them, so you should end up accidentally too focused or missing stuff less often. Not so fortunately, I'm not sure how to fix the problem, short of maybe having a giant list pre-written and picking up all that apply, or something laborious like that.

Comment author: bogdanb 09 April 2012 12:15:43PM *  1 point [-]

I noted that "jobs" and "personal life" have a sort of opposite category connection for me, as does ...

You know, you might be up to something here. At least in the “find examples of” category, having a list of opposite concepts, picking a few pairs at random and trying to find examples associated with each member of each pair should do quite well to force your brain to detach from whatever it’s primed on. (Since, being opposites, examples of one would usually not apply to the other.)

I’m primed to this idea so maybe my brain is just making this up, but this seems to be what’s going on in your climate change example, too, there’s a fix the cause/fix the effect dichotomy there (stop change/adapt to change, fix the input (emissions) / fix the input processor (climate)).

We might be able to find a list of dichotomies that are helpful for general problem solving. A larger list of essentially random opposites would be nicer, but I suspect most would not work for a particular problem. Though we could just try using an antonym dictionary and see what happens.

Comment author: AstraSequi 08 April 2012 08:32:54PM *  1 point [-]

Yeah, that's what I was thinking of when I suggested that it might be done systematically. I hope that a pre-written list wouldn't be necessary though, since I think such a list would also cause priming unless it were completely exhaustive.

Also, a separate idea I just thought of - although making a list as you suggest is a big step forward in generating ideas, I would speculate that every idea is still primed in some way, even if only by your previous thoughts. (For example, if I forget a thought that I wanted to consider more, often thinking about what I was thinking about right before will let me produce that thought again, even though the previous thoughts were ostensibly unrelated. Similarly, a category like "jobs" will tend to elicit different initial thoughts in different people, which would then prime their next thoughts, etc.) So I'm suggesting that making a list could perhaps be interpreted as "preparing many unrelated ways of priming yourself beforehand so that when you exhaust one search you can re-prime yourself from another starting point." And then you would cover a much larger region of idea-space as a result - although I'm not sure how this different interpretation might help in the search for more ideas.

Comment author: tgb 09 April 2012 12:30:06PM 3 points [-]

I nominate this skill as something which is both worth practicing at the Center for Modern Rationality and is specific enough to do so.

Comment author: sketerpot 10 April 2012 07:20:39AM *  2 points [-]

Interesting concept! Come to think of it, I've found myself doing something similar to this, for pretty much the same reasons you decribed: I'll think of a solution, and then say "okay, cool solution -- now drop it from your mind, think about the problem again, and then come up with a different solution." Repeat a few times, then judge the solutions you've come up with. Here's how it might work for Simon, looking for examples for his calculus textbook:

  1. Simon thinks of engineering, then agriculture, then irrigation, then comes up with a cool example involving marginal increases in crop yield from money spent on irrigation. He makes a note of it, then carefully stops thinking about it.

  2. Simon thinks of something not engineering. Whenever he starts thinking of engineering, he stops thinking of engineering and instead thinks of something else. Specifically, he thinks of biology, then evolution, then comes up with an example involving peppered moths and changing allele frequencies caused by changing probabilities of being eaten by a predator before reproducing, coming from changes in the soot concentration in England during the Industrial Revolution.

  3. Simon mentally blacklists engineering and biology, and decides to derive some basic equations for the motion of an object under continuous acceleration, like a perfectly spherical cow shot out of a cannon. Everybody loves those examples, right? I know I did.

In other words, as an alternative to doing breadth-first or simple depth-first search, you can do depth-first search while marking recently-explored areas of the idea space as off-limits since you've thought about them recently. (This sounds similar to Tabu search, if you enjoy over-stretching metaphors as much as I do.)

The thing I like most about this method is that it's really easy to remember to do -- I just need a reflex that says "now clear your head and think of a different solution" to make my saving roll against tunnel vision. I'm not sure I would have the willpower to start listing possible areas in idea-space before exploring any of them, at least not on a regular basis.

(By the way, whatever method ends up working best, avoiding tunnel vision is a really important skill. Using the method I just described, I managed to save myself several days of work about a week ago. That's pretty high payoff for such a simple habit of thought!)

Comment author: Elithrion 10 April 2012 07:41:18PM 1 point [-]

That approach definitely does seem neater as a habit to adopt. The only problem is that it seems more mentally challenging--it may be harder to tell your brain to avoid an area and come up with a new one after it's already focused on it (this may be true for some problems more than others).

Comment author: shminux 08 April 2012 08:33:08PM 2 points [-]

This is a decent recapitulation of what has been discussed here to no end, what is missing is how to recover from the situation. Once you realize that you have been primed and anchored, what do you do to recover? (I have some ideas, but will refrain from proposing them just yet.)

Comment author: Michaelos 10 April 2012 02:19:32PM 0 points [-]

Personal anecdote: describes me, may not be at all like everyone else:

Write down answers to the existing refining/priming until you can't think of any more and you feel a slight bit of mental exhaustion. This allows you to feel confident that you aren't going to waste any of the effort you started doing when you accidentally entered refine mode. Save your writings. It doesn't have to be finished or grammatical, and you don't have to post it, but you sort of give your brain the mental signal "I've saved your work on this refining this topic and will be able to use it later."

Do something unrelated which refreshes you mentally. and allows you to refocus your thoughts.

Start a new from the problem, attempting to think wide again. Do not look at the old document.

The futile part for me is attempting to think "Bad brain! Stop that! Get out of refine mode at once and back into wide mode!" That just wastes time. where I counter with "These ideas are relevant and I refuse to forget about them until you acknowledge them!" It's better to simply do a speedy "Refine draft" of what you have been primed and anchored to, and then start again.

Actually, now that I've laid out HOW I do this, I now have a desire to actually time myself to see how fast it is. I mean, it feels like the best solution in my head... but it should at least be theoretically testable. I would imagine there would be a lot of confounding factors.

Comment author: Swimmer963 08 April 2012 05:09:42AM 2 points [-]

Excellent post!

For instance, before looking at a single example of calculus, Simon might have written down a list of idea areas to explore: "jobs, personal life, the natural world, engineering, other". He would then take the first broad category, "jobs" and expand it into a longer list, perhaps "agriculture, teaching, customer service, manufacturing, research, IT, other". With this longer list, he can then focus on each area in turn and either expand it further if it seems especially rife with examples, or come up with an example from the area directly.

I am going to start searching for any opportunity I can find to use this method, because I'm really curious to see how well it works.

Comment author: Elithrion 08 April 2012 02:16:02PM 3 points [-]

I used it to come up with twenty examples of regression to the mean error in the real world. Unfortunately, I'm not sure how long that's supposed to take, so all I can say for sure is that my examples were nice and diverse, and that the method is neither terrible nor magic. It took me around three hours to come up with the twenty, although had I been someone less subject to akrasia it might have been considerably faster. Also on the benefits side, I never felt really "stuck", which was nice.

Comment author: handoflixue 09 April 2012 07:58:07PM 1 point [-]

Hmmm, interesting. It seems like the trick is to just take "Be Specific" and reverse it - go up the abstraction ladder until you reach a more general area, one which is small enough to easily jot down a lot of general categories. Then take each of those and be more specific.

Basically, you're stuck in one "branch" of the "abstract tree", and if you just climb back to the root of the tree, you can then explore other branches. (I'm a programmer, so my trees are naturally upside down. For everyone else, apologies for the mixed directional metaphor :))

Comment author: MaoShan 09 April 2012 02:51:18AM 1 point [-]

It looks like the only reason Simon might stand a chance of success is because he is in StorySpace; he can start off with a broad search base because his narrator is leading him in the right direction. If I did the same thing, my research on calculus would turn into a manual on guinea-pig nutritional tips or something. The probability of a breakthrough from that direction is extremely improbable, which is why one would benefit from just a little bit of priming.

Comment author: Elithrion 09 April 2012 03:20:02AM 1 point [-]

Could you explain what you mean? As far as I can tell, the method I propose would actually be pretty effective for generating a bunch of reasonable examples (as indeed, I have used it for doing so). Maybe I was unclear somewhere...

Comment author: MaoShan 10 April 2012 02:03:26AM 0 points [-]

I don't doubt that your actual results have been effective, but I think that you're underestimating the subtlety of priming--in your examples, it reads less like conquering the priming effects and more like just failing to mention them. Due to positive association, there are going to be paths that your mind takes, regardless of whether it chooses to inform you of that.

On the other hand, as you have pointed out, priming is useful. As you become more expert at recognizing and counteracting it, how will you know when to stop?

Comment author: maia 12 April 2012 06:15:40PM 0 points [-]

This is an interesting suggestion on how to be more creative in approaching a problem.

My hunch is that you could do scholarship and learn a lot more about creativity, however. For instance, did you know that being in a room with the color green makes people generate more creative ideas? (Source: 59 Seconds.) That's just a tidbit; there may be a lot more out there that's already known!

Comment author: Jello_Raptor 11 April 2012 11:52:55AM 0 points [-]

Off Topic

 What is the next number in the sequence 14, 15, 16, 17, 21, 23, 30, 33?

damn that 30, i can't think of any valid hypothesis that includes that.

Comment author: timtyler 11 April 2012 04:14:41PM 0 points [-]

Did you Google it? Google seems to have the sequence. It suggests that one possible answer is 120!

Comment author: Jello_Raptor 11 April 2012 06:44:04PM 0 points [-]

Nah, where's the fun in that? ;)

Comment author: Elithrion 11 April 2012 05:27:32PM 0 points [-]

Huh, 120 is correct! I didn't realise it was googleable. I guess I should have actually checked that and picked a different similar sequence (like umm 30, 33, 36, 39, 41, 45, 50, 55, 63, 113 a lot of these seem to be googleable now and this one is arguably harder)--woops.

Comment author: army1987 11 April 2012 05:49:21PM *  0 points [-]

It hadn't occurred to me to google for it. But now I remember about the OEIS. (“svsgrra va onfr svsgrra zvahf a”? I would never have thought of that myself!)

(Edited to rot-13 spoiler -- sorry if anybody read it first.)