# Daggers, Swords, and Maps

Imagine you're a trader in medieval Europe, looking for a way to defend yourself. You can choose among three weapons.

First, there's the dagger. You stick it in your pocket, and when you see someone dangerous on the street, you whip it out, stab them, and run away. Maybe you also learn to block the most common sword attacks. It's convenient, quick, and easy to use.

Second, there's the sword. You carry around your sword and spend a lot of time practicing with it. You easily defeat dagger-holders. You learn when to parry, when to riposte, etc. There are people who spend their whole life mastering the sword; it has hundreds of advanced techniques, complex and interesting metagame, etc.

Finally, there's the map. You look at a map of this afternoon's meeting place, and decide to approach from the plain, where you can be sure of not getting ambushed. You hire two swordsmen to patrol the adjacent forest. Then you show up to the meeting empty handed.

What's the best choice for a medieval trader? Probably a combination of the dagger and the map. Learn to use the map, so you can do a good job directing swordsmen you hire. Then practice a bit with the dagger, so you can defend yourself in the moments before your hired hands rush over. Don't waste your time with the sword; even if you spend a hundred hours practicing, you'll never compete with a professional. And you're not trying to be a swordsman. You're a trader.

Past medieval defense, lots of skills break down roughly into daggers, swords, and maps. There's a simple and light hack for the easy cases (the dagger). There's a deep and complex set of techniques that people spend their lives mastering (the sword). And there's a way to externalize the problem (the map).

For logo design, the dagger is knowing how to use the paint bucket tool to fill in a stock image you found online. The sword is designing a logo and using Illustrator to make it. The map is learning to use Fiverr to contract a professional designer.

For multiplication, the dagger is knowing your 12s tables. The sword is being able to do out 3x3 multiplication by hand. The map is being fast with a calculator.

For integration, the dagger is being able to do easy u-substitution in your head. The sword is stuff from the Integration Bee: trig replacement, weird change of variables, double integration by parts, etc. The map is offloading it onto Mathematica.

All three cases admit practice. For the dagger, you can drill to get fast intuition for mental integration problems. For the sword, you can do textbook problems that require 3-5 minutes to think out. For the map, you can spend time learning how to use Mathematica.

In school, you spend the vast majority of your time practicing with the sword. Thinking back to how I learned integration, for instance, we had lots of tests where we were given an hour to do fifteen medium-difficulty problems. But we were never asked to do 100 easy problems in five minutes (the dagger), or to solve an extremely difficult integral with Mathematica (the map).

Ideally, I think you would practice integration in the exact opposite way. Spend some hours drilling the dagger cases, so you don't have to think about them when they come up in practice. Spend some hours learning the map, so you can deal with hard integrals you encounter in the world. But don't spend any time practicing the sword case. Leave that to the professionals.

I'm not saying that you should ignore the sword case for absolutely everything. In fact, the reason I advocate ignoring it for almost everything is so that you can pour your discretionary time into truly mastering the sword case for something important.

In other words, rather than being a mediocre swordsman across the board, accept the dagger and the map for almost everything and then become a world class swordsman where it counts.