The optimal number of things to think about

I think our minds (brains, whatever) are like a multi-product firm. We have to decide how many things to think about — how many different products to produce. We don't think about just one thing all the time; but we don't think about an infinite number of things either. There must be fixed costs of thinking about each thing, so initially increasing returns, otherwise we would think a little bit about everything. But eventually, as we think more and more about one particular thing, we run into diminishing returns. So we think about more than one thing. Each topic of thought has a U-shaped average cost curve, or inverse-U-shaped average product curve.

In any particular second, true, we are perhaps thinking about only one thing. But over the course of a day, or week, we think about several things. It's like a multi-product firm that does batch-processing, not continuous processing. The other things we are working on are at the back of our minds, like semi-finished goods.

But unlike the multi-product firm, we have a fixed quantity of resources, or hours of thought. We can't just hire more, in the way that a firm can hire more labour. So we face a trade-off between the extensive margin (thinking about more things) and the intensive margin (thinking more about each thing).

At the optimum point on the trade-off the marginal benefit at the extensive margin equals the marginal benefit at the intensive margin. Both margins have diminishing returns: at the intensive margin the more time you spend thinking about one thing, the less the benefit of an extra minute spent thinking about it; and at the extensive margin, you start with the most important (productive) topics, and the more topics you think about the less important is the next topic in line.

Given diminishing returns at both the extensive and intensive margin, if your total time available for thinking were to decrease, you would move along both margins: you would think about fewer topics; and also spend less time thinking about each one. Just like a Ricardian model of land use, where a fall in population means less land is farmed, and the land that is still farmed has fewer workers per acre.

It's just the same if, instead of having less total time to think, you face an increased demand for topics to think about. The new topics both displace some original topics, and displace some of the time you spend thinking about each topic you do continue to think about.

All this is just to say that I have been (acting) associate dean again since July 1st, so I'm now having to think about things I didn't have to think about before, when I was on sabbatical. So fewer blog posts, and less time spent thinking about each one.

People like Tyler Cowen and Brad DeLong really impress me. Not so much on the quality of their thoughts (though that is very good), but on the sheer number of things they can think about at that quality. I think they must have very small fixed costs of thinking about things. My fixed costs are much higher.

I wonder if the financial crisis was caused by most economists having high fixed costs of thinking about things?

7 comments

  1. DW's avatar

    Nick,
    Why not just blog about some of the things you’re called upon to think about as associate dean?

  2. Andrew F's avatar
    Andrew F · · Reply

    You might be interested in the computer science equivalent of prioritization of processes on a processor when doing concurrent processing. Switching between processes (called context switching) is very costly in time, as it involves saving the state of the processor to memory, loading the next process, etc. And in the case of using disk memory, which is very slow, it’s akin to working on a project, with all your papers spread out on your desk. Before you finish, you need to work on another project, so you gather the papers into a folder and put them into your filing cabinet. Only, your filing cabinet is on the other side of the continent–from where you will need to retrieve the files before you can resume. And yet, the illusion of parallelism that is achieved through concurrency is worth this overhead.
    This overhead reduces the amount of time the processor can spend thinking in aggregate, but increases the amount of things it can be thinking about ‘at once’. But the more things want it to think about at simultaneously/in a given time frame, the less actual thinking it can accomplish.

  3. Nick Rowe's avatar

    DW: Hmmm. I might just do that, and see if there’s any interest. Some of it actually has economic application. Like the violation of Walras’ Law in the Barro-Grossman repressed inflation regime, when we had an excess demand for seats in courses back a few years ago. (A student might only want one more course, but would register an excess demand for 5 courses, trying 4 more when he couldn’t get into the first one). But some of it’s a bit too confidential/sensitive.

  4. Nick Rowe's avatar

    Andrew: I hadn’t thought of switching costs (from one topic to another). I had been thinking about fixed costs of just getting started on thinking about a topic. If timing doesn’t matter, you would never switch; you would always finish one batch of thought before starting on the next, to avoid any switching costs. But then the phone rings, someone comes by your office, or there’s a meeting. So timing matters, and so those switching costs matter. You are right. Good model. One more thing to think about.

  5. Andrew F's avatar
    Andrew F · · Reply

    But there are times when it is a waste to continue thinking on a topic at that given time. Maybe you are waiting for more information, etc. Processes will tell the kernel (the boss process that hands out the resources) that it’s done what it can for now, and rather than tie up the processor. This is done when it is passively waiting for an event, such as input (a mouse click, or a disk access, etc.) to occur.

  6. Thomas De Long's avatar
    Thomas De Long · · Reply

    I suppose a think-tank would be like an open system, where different units are given topics to work through, hopefully each performing their assigned thought process the most efficiently. Then, if one were to add another person to the mix, it would be like opening trade with another country, and topics might rearrange appropriately. Would there be a period of decreased output while tasks are redistributed? Or would the process be gradual(perhaps waiting for resolutions to the current problems before transferring similar problems to the new guy, similar to contracts running their course before getting outsourced)?

  7. Too Much Fed's avatar
    Too Much Fed · · Reply

    From a macroeconomic point of view, I would suggest focusing on too much cheap labor, too much cheap debt, asset prices being too high, too much wealth/income inequality, and a “fungible” money supply that is skewed towards too much debt.

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