Whether to delegate

You shouldn’t necessarily do things that you’re good at. In economics, this idea is known as comparative advantage. Delegating may free up your time to do something more profitable. It might be to a country’s advantage to import something that they could produce cheaper domestically. Importing one thing might free up resources to export another thing that’s more valuable.

Comparative advantage is often illustrated by a hypothetical lawyer and an assistant. A lawyer who can type very quickly is still better off hiring someone else to do the typing because he can make much more per hour practicing law. If he could type twice as fast as an assistant, and he could earn more than twice as much practicing law as it costs to hire an assistant, he makes money by delegating.

This illustration makes sense at one level, but it also sounds a little quaint. In fact lawyers do quite a bit of typing. That’s explained by another economic idea: transaction costs. It costs time to recruit and hire an assistant. And once you have an assistant, it takes time to explain what you want done, time to wait for the work to come back, time to review the work, etc.

Highly paid executives type their own emails, at least some of the time, because it’s not worth the transaction costs to have someone else do it. But for a larger task, say typing up hundreds of handwritten pages, it’s worth paying the transaction costs to get someone else to do the typing.

Most advice on delegation is simplistic. It ignores transaction costs, and has a naive view of opportunity costs. It says that if you make $50 an hour, you should delegate anything you can hire done for $40 an hour since the opportunity cost of doing the $40 an hour task rather than delegating it is $10 an hour. But things are more subtle than that.

Opportunity costs only apply if you’re turning down an opportunity. If you stop doing $50 an hour work to do $40 an hour work, then you’re losing $10 an hour compared to what you could earn (ignoring the transaction costs of delegating). But if you don’t have $50 an hour work to do, if you’re otherwise idle, then delegating $40 an hour work is costing you $40 an hour, not saving you $10 per hour.

People are not machines. If you have an idle machine, give it work to do. And if two machines could do the same work, use the one that can do the work the cheapest. But people are more complicated. We like some kinds of work better than others, we learn, and we need time to rest.

Suppose you enjoy doing work that you could delegate for $40 an hour. You find it refreshing. There’s no opportunity cost in doing it yourself if the time to do it comes out of time you would have spent on a hobby.

Suppose you don’t enjoy doing work that you could delegate, but there’s something you could learn from doing it. In that case, there may be an opportunity benefit as well as an opportunity cost: learning something new may create opportunities in the future.

The previous two paragraphs account for enjoyment and learning, but not rest. If you don’t have $50 an hour work to do, doing $40 an hour work is only one alternative. Another alternative is to do nothing, which is very valuable in ways that are hard to quantify. And even work you enjoy may take energy away from other work.

Managing energy is more important than managing time. Energy is what gets things done, and time is only a crude surrogate for energy. Instead of only looking at what you could earn per hour versus what you could hire someone else for per hour, consider the energy it would take you to do something versus the energy it would free to delegate it.

If something saps your energy and puts you in a bad mood, delegate it even if you have to pay someone more to do it than it would cost you do to yourself. And if something gives you energy, maybe you should do it yourself even if someone else could do it cheaper.

Finally, note that energy isn’t the same as pleasure, though they often go hand in hand. Some activities are enjoyable but draining, and some are not enjoyable but invigorating. For example, I enjoy teaching, but it takes a lot out of me. And most people don’t enjoy exercise that much even though it gives them energy.

Hum-drum fairy tales

The subtitle of That Hideous Strength is “A Modern Fairy-Tale for Grown-Ups.” C. S. Lewis explains in the preface why the book begins with mundane scenes even though he calls it a fairy tale.

If you ask why—intending to write about magicians, devils, pantomime animals, and planetary angels—I nevertheless begin with such hum-drum scenes and persons, I reply that I am following the traditional fairy-tale. We do not always notice its method, because the cottages, castles, woodcutters, and petty kings with which a fairy-tale opens have become for us as remote as the witches and ogres to which it proceeds. But they were not remote at all to the men who made and first enjoyed the stories.

Some fields produce more false results than others

John Ioannidis stirred up a healthy debate when he published Why Most Published Research Findings Are False. Unfortunately, most of the discussion has been over whether the word “most” is correct, i.e. whether the proportion of false results is more or less than 50 percent. At least there is more awareness that some published results are false and that it would be good to have some estimate of the proportion.

However, a more fundamental point has been lost. At the core of Ioannidis’ paper is the assertion that the proportion of true hypotheses under investigation matters. In terms of Bayes’ theorem, the posterior probability of a result being correct depends on the prior probability of the result being correct. This prior probability is vitally important, and it varies from field to field.

In a field where it is hard to come up with good hypotheses to investigate, most researchers will be testing false hypotheses, and most of their positive results will be coincidences. In another field where people have a good idea what ought to be true before doing an experiment, most researchers will be testing true hypotheses and most positive results will be correct.

For example, it’s very difficult to come up with a better cancer treatment. Drugs that kill cancer in a petri dish or in animal models usually don’t work in humans. One reason is that these drugs may cause too much collateral damage to healthy tissue. Another reason is that treating human tumors is more complex than treating artificially induced tumors in lab animals. Of all cancer treatments that appear to be an improvement in early trials, very few end up receiving regulatory approval and changing clinical practice.

A greater proportion of physics hypotheses are correct because physics has powerful theories to guide the selection of experiments. Experimental physics often succeeds because it has good support from theoretical physics. Cancer research is more empirical because there is little reliable predictive theory. This means that a published result in physics is more likely to be true than a published result in oncology.

Whether “most” published results are false depends on context. The proportion of false results varies across fields. It is high in some areas and low in others.

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New blog: Symbolism

I’ve started a new blog called Symbolism. Each post will take a symbol and say a few words about it.

So far I’ve written about the equal sign, the chi-rho, and the long S.

I’ve also started a Twitter account to go with the new blog, @DailySymbol.

[Update: The Twitter account @DailySymbol is still online but I no longer post there. The posts from the Symbolism blog have been archived here (mathematical posts) and here (non-mathematical).]

A strange mixture of luxury and squalor

The second chapter of Out of the Silent Planet opens by describing a room as “a strange mixture of luxury and squalor.” It gives examples such as the room as having fine armchairs but no carpets or curtains, strewn with debris. The room has “empty champagne-bottles” and “teacups a quarter full of tea and cigarette-ends.” The room belongs to a scientist and an investor who have the resources to live in beauty and comfort, but instead have a few luxurious items in a pigsty. The scene is a metaphor for science and business detached from humane uses, one of the themes of the book.

Beavers and category theorists

From Moonshine Beyond the Monster:

Much as beavers, who as a species hate the sound of running water, plaster a creek with mud and sticks until alas that cursed tinkle stops, so do category theorists derive elaborate and obscure definitions in an attempt to capture a concept that to most of us seemed perfectly clear before they got to it. But at least sometimes this works admirably …

Rational cosines

When does a rational portion of a circle have a rational cosine?

If r is a rational number, cos(2πr) rational if and only if the denominator of r is 1, 2, 3, 4, or 6.

This means that the special values of cosine you learn in a trig class, with a simple argument and simple value, are the only ones possible. (Here simple argument means an angle with an integer number of degrees and simple value means a rational number.) And if you see a result such as cos(π/7) = 837/929, you know it can’t be exactly correct, though in this case it’s very close.

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Techniques, discoveries, and ideas

“Progress in science depends on new techniques, new discoveries, and new ideas, probably in that order.” — Sidney Brenner

I’m not sure whether I agree with Brenner’s quote, but I find it interesting. You could argue that techniques are most important because they have the most leverage. A new technique may lead to many new discoveries and new ideas.

Micro-consulting and mentoring

Sometimes a quick answer to a question is priceless. It can even be valuable to know that you could get a quick answer to a question, even if you never ask. For example, if your company is considering doing something new, knowing that there’s someone to help could make the difference in the decision to go forward.

Next year I’ll be offering this sort of micro-consulting and mentoring. For a monthly retainer, I will be available to answer questions and give advice. This would be for questions I could answer on the spot or with minimal research; anything more involved would have to be a separate consulting project. You would be guaranteed my availability for a certain amount of time per month and a quick turn-round on correspondence. (My response might be “I don’t know,” but I’d get back to you promptly.)

I’ve done some of this kind of consulting, and clients have found it very valuable. I’d like to do more of this next year as a way to fill some of the interstitial time between larger projects. I also expect it will lead to larger projects, e.g. “We like your idea of what we should do. Could you do it for us?”

If this sounds interesting to you, please contact me.

Heisenberg, Gödel, and Chomsky walk into a bar …

Seth Godin tells the following joke in The Icarus Deception:

Heisenberg looks around the bar and says, “Because there are three of us and because this is a bar, it must be a joke. But the question remains, is it funny or not?”

And Gödel thinks for a moment and says, “Well, because we’re inside the joke, we can’t tell whether it is funny. We’d have to be outside looking at it.”

And Chomsky looks at both of them and says, “Of course it’s funny. You’re just telling it wrong.”

Related: A priest, a Levite, and a Samaritan walk into a bar …

Visualizing Galois groups of quadratics

Yesterday Jack Kennedy told me about a graph he’d made as part of a project he’s working on and I asked if I could post it here.

The Galois group of a quadratic polynomial x2 + bx + c is either A2 or S2. If b2 – 4c is a perfect square, the polynomial has rational roots and the Galois group is the trivial group A2. Otherwise there are distinct irrational roots and the Galois group is the two-element group S2.

As b and c range over integers, color a pixel yellow if the group is A2 and black otherwise. This produces the image below.

Note that what appear to be the crossed lines y = ±x intersecting at 0 are actually the lines y = ±(x+1) intersecting at (-1,0).

You can find a larger image here. View the page source to see the JavaScript that produced the image. The page is calculating and setting the value of one million pixels, and yet the time to render the page isn’t even noticeable.

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