# Power and difficulty

A specific bias that Lesswrongers may often [get from fiction](/lw/k9/the_logical_fallacy_of_generalization_from/)^\[1\]^ is the idea that power is proportional to difficulty. The more power something gives you, the harder it should be to get, right?

A mediocre student becomes a powerful mage through her terrible self-sacrifice and years of studying obscure scrolls. Even within the spells she can cast, the truly world-altering ones are those that demand the most laborious preparation, the most precise gestures, and the longest and most incomprehensible stream of syllables. A monk makes an arduous journey to ancient temples and learns secret techniques of spiritual oneness and/or martial asskickery, which require great dedication and self-knowledge. Otherwise, it would be cheating. The whole process of leveling up, of adding ever-increasing modifiers to die rolls, is based on the premise that power comes to those who do difficult things. And it's failsafe - no matter what you put your skill points in, you become better at something. It's a [training montage](http://tvtropes.org/pmwiki/pmwiki.php/Main/TrainingMontage), or a [Hero's journey](http://tvtropes.org/pmwiki/pmwiki.php/Main/TheHerosJourney). As with other fictional evidence, these are not "just stories" -- they are powerful cultural narratives. This kind of narrative shapes moral choices^\[2\]^ and [identity](http://en.wikipedia.org/wiki/Narrative_identity). So where do we see this reflected in less obviously fictional contexts?

There's the rags-to-riches story -- the immigrant who came with nothing, but by dint of hard work, now owns a business. University engineering programs are notoriously tough, because you are gaining the ability to do a lot of things (and for signalling reasons). A writer got to where she is today because she wrote and revised and submitted and revised draft after draft after draft.

In every case, there is assumed to be a direct causal link between difficulty and power. Here, these are loosely defined. Roughly, "power" means "ability to have your way", and "difficulty" is "amount of work & sacrifice required." These can be translated into units of social influence - a.k.a money -- and investment, a.k.a. time, or money. In many cases, power is set by supply and demand -- nobody needs a wizard if they can all cast their own spells, and a doctor can command much higher prices if they're the only one in town. The power of royalty or other birthright follows a similar pattern - it's not "difficult", but it is scarce -- only a very few people have it, and it's close to impossible for others to get it.

Each individual gets to choose what difficult things they will try to do. Some will have longer or shorter payoffs, but each choice will have some return. And since power (partly) depends on everybody else's choices, neoclassical economics says that individuals' choices collectively determine a single market rate for the return on difficulty. So anything you do that's difficult should have the same payoff.

Anything equally difficult should have equal payoff. Apparently. Clearly, this is not the world we live in. Admittedly, there were some pretty questionable assumptions along the way, but it's almost-kind-of-reasonable to conclude that, if you just generalize from the fictional evidence. (Consider RPGs: They're designed to be balanced. Leveling up any class will get you to advance in power at a more-or-less equal rate.)

So how does reality differ from this fictional evidence? One direction is trivial: it's easy to find examples where what's difficult is not particularly powerful.

Writing a book is hard, and has a respectable payoff (depending on the quality of the book, publicity, etc.). Writing a book without using the letter "e", where the main character speaks only in palindromes, while typing in the dark with only your toes on a computer that's rigged to randomly switch letters around is much much more difficult, but other than perhaps gathering a small but freakishly devoted fanbase, it does not bring any more power/influence than writing any other book. It may be a sign that you are capable of more difficult things, and somebody may notice this and give you power, but this is indirect and unreliable. Similarly, writing a game in machine code or as a set of instructions for a Turing machine is certainly difficult, but also pretty dumb, and has no significant payoff beyond writing the game in a higher-level language. \[Edit - thanks to TsviBT: This is assuming there already is a compiler and relevant modules. If you are first to create all of these, there might be quite a lot of benefit.\]

On the other hand, some things are powerful, but not particularly difficult. On a purely physical level, this includes operating heavy machinery, or piloting drones. (I'm sure it's not easy, but the power output is immense). Conceptually, I think calculus comes in this category. It can provide a lot of insight into a lot of disparate phenomena (producing utility and its bastard cousin, money), but is not too much work to learn.

As instrumental rationalists, this is the territory we want to be in. We want to beat the market rate for turning effort into influence. So how do we do this?

This is a big, difficult question. I think it's a useful way to frame many of the goals of instrumental rationality. What major should I study? Is this relationship worthwhile? (Note: This may, if poorly applied, turn you into a terrible person. Don't apply it poorly.) What should I do in my spare time?

These questions are tough. But the examples of powerful-but-easy stuff suggest a useful principle: make use of what already exists. Calculus is powerful, but was only easy to learn because I'd already been learning math for a decade. Bulldozers are powerful, and the effort to get this power is minimal if all you have to do is climb in and drive. It's not so worthwhile, though, if you have to derive a design from first principles, mine the ore, invent metallurgy, make all the parts, and secure an oil supply first.

Similarly, if you're already a writer, writing a new book may gain you more influence than learning plumbing. And so on. This begins to suggest that we should not be too hasty to [judge past investments as sunk costs](/lw/9si/is_sunk_cost_fallacy_a_fallacy/). Your starting point matters in trying to find the closest available power boost. And as with any messy real-world problem, luck plays a major role, too.

Of course, there will always be some correlation between power and difficulty -- it's not that the classical economic view is wrong, there's just other factors at play. But to gain influence, you should in general be prepared to do difficult things. However, they should not be arbitrary difficult things -- they should be in areas you have specifically identified as having potential.

To make this more concrete, think of Methods!Harry. He strategically invests a lot of effort, usually at pretty good ratios -- the Gringotts money pump scheme, the True Patronus, his mixing of magic and science, and Partial Transfiguration.  Now that's some good fictional evidence.

  

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\[1\] Any kind of fiction, but particularly fantasy, sci-fi, and neoclassical economics. All works of elegant beauty, with a more-or-less tenuous relationship to real life.

\[2\] Dehghani, M., Sachdeva, S., Ekhtiari, H., Gentner, D., Forbus, F. "The role of Cultural Narratives in Moral Decision Making." Proceedings of the 31th Annual Conference of the Cognitive Science Society. 2009.