It is better to be vaguely right than exactly wrong.
- Carveth Read

When I first learned double-entry accounting, I was struck by how elegant some of the constructs were. There is a joy in knowing exactly where each number was supposed to go over the profit cycle of a business, when it bought assets and amortized fixed costs and generated a clear and continuous indication of profitability by using accounting as a type of low-pass filter smoothing out the cash flow.

I later realized accounting in reality doesn't work nearly so neatly. It isn't so much that the accounting constructs themselves are flawed - it's more that when interpretation is needed it's common to find the convention of conservatism being applied, and as such a precise but inaccurate answer being the standard.

This is due to the fact that the numbers that appear in accounting are more used for managerial oversight by owners, and not as quantitative thinking tools in their own right.

The statistics and biology used in clinical trials seem to fall in this category as well. Statistics is scientific accounting, and the audience in that case is the FDA.

The risk control applied in banks is another example. There statistics feed directly into accounting, and again are done in ways that are more precise than accurate.

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Most of the numbers that appear in our daily lives are there for their ability to be objective. As such, the techniques which produce those numbers have been tweaked to be as precise and ungameable as practical. That precision often comes at the cost of accuracy and space for intelligent judgment.

In the early 90s, when you wanted to drive from point A to point B you would consult a map and try to find the fastest route by tracing the route from local roads at A to highways and then back to local roads at B. If you went off your planned route along the way, you would stop to figure out where you were (maybe at a gas station) and then replan your route.

In the mid-90s, mapquest became available, and you could get directions online and print them. You'd run into a problem if you got too lost, as you would drive off the map you printed and not be able to see where you were.

Nowadays, you have a GPS unit that you enter the destination into, and no matter where you drive it would point to the destination. If there were a traffic jam along the freeway, I would often drive onto local roads in the general direction, ignoring the GPS for a little while to avoid the jam. I would then start following the GPS instructions after a bit.

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Using printed online directions is less reliable than using a GPS, and also less reliable than using a paper map. This was because when you use printed directions, you are reduced to following a set of instructions which have a very rigid dependence on each other. If any earlier step is followed wrongly, the later step would be wrong too. There is a sensitivity to detail which amplifies little mistakes and makes them big.

Result-orientation is the state of mind where you keep your attention on the result that you are trying to attain. The GPS is always considering where you are and where you want to be, and the route it formulates is based on parts that all look the same in that way. If the original assumptions were correct, and both the roads and the driving were ideal, then it isn't so different from following a fixed set of directions.

The differences appear when there are slight mistakes in the plan.
You have to break out of fixed instructions to account for mistakes (well, a smart person would try to salvage as much of the instructions as they can by trying to get back on the route). The GPS has actions at every point flowing from goal of getting to the destination, and so the overall activity becomes more robust, because mistakes or changes to details can be accounted for naturally as part of the same machinery.

In a changing world, a big part of learning "how" is learning "why". It is sometimes important to break the goal into sub-goals, and only then generate actions from those sub-goals, as opposed to generating a long list of actions from the goal directly.

If you are reading this post, you are likely reading it on a computer. The computer responds to your typing and clicking and allows you to find information which exists somewhere far away. Some of that information was sent specifically to you (e.g., your email), and some of that information was available to anyone who knew where to look (e.g., this blog post). Here the computer is a communication tool, and gets information from other people to you.

While typing an email, maybe you have spell-correct on - every word that you type is checked in the dictionary, and when it doesn't appear in the dictionary the word is highlighted and suggestions for the correct spelling appear. The computer isn't doing anything you didn't know how to do - you might not know how to spell every word, but with enough time you could have looked up every word in the dictionary - it's impractical but not impossible.

If you couldn't find your word in the dictionary however, how would you have tried to discover the right spelling? The way the computer does it is to compare your word against all the words in the dictionary and then display the words that are most similar. The number that is used for describing similarity (the Levenshtein disctance) is calculated in a very clever way, and so the computer can do this quite fast. This part takes many more steps than just trying to find every word in the dictionary, and is quite impossible to do by hand.

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When it comes to physical work, the difference between describing how to do something and actually doing it is quite obvious. Imagining in my head how I would carry an empty bucket down the stairs and carry back a bucket full of water takes no effort and no time, while actually doing it would cause me much physical strain and about 20 minutes.

Mental work is the same. If I gave you two 10-digit numbers, I'm pretty sure you would know how to multiply them using just a piece of paper. Again, there is a distinction between knowing how to do it and actually doing it. I can be pretty confident of multiplying two numbers together with a piece of paper even though I don't yet know what the answer is.

We have a name for the symbolic work that is done when we know how to get an answer and are merely following those steps and actually finding out what the answer is. We call it computation, and it is what your computer does well.

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A manager's job includes knowing how to instruct and delegate. A manager uses his time efficiently by teaching an employee how to do something and being able to do something else while the employee is doing the thing.

Computers have made this type of work more common for non-managers - if you can describe precisely all the simple steps that need to be done then you can save time as you will only have to spend time describing new tasks while the computer handles all the repetition.

Related reading: School for quants