Here is the key passage, but the whole thing is eminently worth reading:
What actually happened in the 80s, however, was that central banks — most famously the Fed, but also the Thatcherite Bank of England and others — drastically tightened monetary policy to bring inflation down. And inflation did indeed come down — eventually. But along the way there were deep recessions and soaring unemployment, which went on much longer than you could justify with any plausible story about the monetary shock being unanticipated.
This was very much a vindication of more or less Keynesian views about the economy, and the 80s were in fact marked by the New Keynesian comeback.
Image source: “5 Dangerous Things You Should Let Your Kids Do”
Models in which human beings are always maximizing their utility perfectly are the simplest kinds of models. But it is hard to maintain that children are always maximizing their own utility perfectly. In a discrete-time model, it is easy to have an initial period in which someone is not nonrational, followed by later periods of full rationality. But In continuous time, there are likely to be an in-between period in which some types of decisions are close to full rationality, while other decisions are far from fully rational in advancing self-interest. (For example, this post on the Edutopia blog talks about the “hyperrational adolescent brain,” but is about anything but.)
In On Liberty, Chapter IV, “Of the Limits to the Authority of Society over the Individual” paragraph 4, John Stuart Mill has to face the lack of full-scale rationality on the part of children, using the phrase “self-regarding virtues” to talk about the kind of rationality that allows one to advance one’s own interest. He writes:
I am the last person to undervalue the self-regarding virtues; they are only second in importance, if even second, to the social. It is equally the business of education to cultivate both. But even education works by conviction and persuasion as well as by compulsion, and it is by the former only that, when the period of education is past, the self-regarding virtues should be inculcated. Human beings owe to each other help to distinguish the better from the worse, and encouragement to choose the former and avoid the latter. They should be for ever stimulating each other to increased exercise of their higher faculties, and increased direction of their feelings and aims towards wise instead of foolish, elevating instead of degrading, objects and contemplations. But neither one person, nor any number of persons, is warranted in saying to another human creature of ripe years, that he shall not do with his life for his own benefit what he chooses to do with it.
Notice that in American custom, we tend to add to the kind of deference John is recommending for another adult’s decisions in regard to that adult’s own life, a deference for a parent’s decisions in regard to that parent’s own children. But the logic is unavoidably weaker for deference to parent’s decisions about their own children than it is for an adult’s decisions regarding his or her own life.
One interesting area where our culture is shifting in regard to parent’s decisions about their own children is in our attitudes towards spanking. When I was a child, we children took the possibility of spanking (including many elaborated threats of spanking) and sometimes the reality of being spanked for granted. Not long into my experience as a father myself, I realized that social tolerance of spanking was waning. And nowadays, parents who spank their children often have a niggling, if perhaps exaggerated, fear that child-welfare arms of the government (“Social Services”) will punish them.
John Stuart Mill allows for the possibility that compulsion might be necessary in bringing up children. And I find it hard to rule out the possibility that there may be situations in which some form of corporal punishment for a child may be the best available option. But compulsion (of which corporal punishment is only one type) should only be used when absolutely necessary, since it tends to have unwanted side effects. For example, in "John Stuart Mill Argues Against Punishing or Stigmatizing, but For Advising and Preaching to People Who Engage in Self-Destructive Behaviors," I wrote
…punishing and stigmatizing may often be ineffective because the elements of a riven psyche one wants to encourage may have trouble seeing a punisher or stigmatizer as friendly.
Maryam MIrzakhani, First Women to Win the Fields Medal
Going beyond the usual news articles such as these two,
Quanta magazine gives a more in-depth treatment of the the work of the first woman to win a Fields Medal, which is aptly described as the Nobel Prize of mathematics:
I know about this article thanks to 's Facebook post on my wall. Mary points out that Maryam describes herself as pursuing what I have called “slow-cooked math” (most recently in my Quartz column "How to turn every child into a ‘math person’"):
Mirzakhani likes to describe herself as slow. Unlike some mathematicians who solve problems with quicksilver brilliance, she gravitates toward deep problems that she can chew on for years. ‘Months or years later, you see very different aspects’ of a problem, she said. There are problems she has been thinking about for more than a decade. ‘And still there’s not much I can do about them,’ she said.
Mirzakhani doesn’t feel intimidated by mathematicians who knock down one problem after another. ‘I don’t get easily disappointed,’ she said. ‘I’m quite confident, in some sense.
Her slow and steady approach also applies to other areas of her life.”
The J Curve
Reblogged from econlolcats:
Things are gonna get better.
Miles: I have a few thoughts about the J-curve in International Finance. The idea is that the medium-run supply and demand elasticities with respect to the exchange rate are higher than the short-run elasticities. So in an era of deprecations within a fixed-exchange-rate regime, that would mean that the quantities of exports and imports would at first respond less than the prices, but later on the quantities would move more, so the value of net exports would go down right after the depreciation, but later go up.
Here is my question. Think of a flexible-exchange-rate regime in which capital flows are determined by what people want to do with their portfolios, as I describe in my post "International Finance." Then, if the domestic central bank cuts interest rates and people want to shift toward foreign assets, that intentional capital outflow plus any unintentional capital flow plus any other flows of funds across borders that are not associated with the purchase of goods and services internationally (such as remittances) has to equal net exports. There might be a short time when unintentional capital flows cancel out some of the intentional flows, but it seems to me that in a flexible-exchange-rate regime, pretty soon net exports have to match those intentional capital flows. So the prediction would be that the low short-run elasticities of imports and exports would show up in a bigger movement in the exchange rate in the short run than in the medium run. Of course there are some risky arbitrage possibilities with that kind of movement. But do we see such a quickly-reverting pattern for exchange rates anyway? It certainly seems like exchange rates move an awful lot in the short run.
An interesting case is when the short-run price elasticity of net exports is less than one. (Note how different that is from gross exports or gross imports having an price elasticity less than one.) If depreciation means less of the local currency gets spent on net exports, then net exports can’t equilibrate with a fixed level of capital outflow. What I think would have to happen in the short run is that the initial capital outflow causes a drastic enough decline in the value of the domestic currency that the financial market rethinks the initial intentional capital outflow. That is, someone needs to see the domestic currency as so cheap they want to move their portfolio into it. It may take a very large depreciation before that is the case. Does that story make sense?
Here is a link to my 52d column on Quartz, “How to turn every child into a ‘math person.’”
In the companion post below, I have collected a few memories, ideas and suggestions that had to be cut out of the Quartz column to make the column flow well. I added some headings to make it clear where each bit fits in:
I spent at least as much time on math when I wasn’t supposed to be doing math as when I was: The teacher might have been talking about social studies, but I was finding the prime factorizations of all the numbers from 1 to 400 by writing “2 ×” for every other number “3 ×” for every third number, “5 ×” for every fifth number, etc.—and then repeating that process for every other even number, every third multiple of 3, every fifth multiple of 5, and so on). The prime factorizations I learned from that satisfyingly tedious task I distracted myself with in elementary school came in handy when I took my SAT’s. And to this day, the way I get a hotel room number firmly into my memory is by doing its prime factorization.
Nothing seemed like a failure: At one point I knew just enough algebra to know that doing the same thing to both side of an equation left it a true equation. So for a long time, I transformed equations endlessly with no idea at all of where I was trying to go with those equations. Later on, when I actually had a purpose in mind for what I wanted to accomplish with a bit of algebra, I was able to draw on all of that experience just wandering around in algebra-land. And because I knew what it was like to do math without having any particular objective, I was able to appreciate how important it was keep the objective clearly in mind when there was an objective.
Proofs on other topics to get kids ready for proofs in Geometry class: Many kids who do well with arithmetic and algebra have trouble with geometry class in middle school or high school. It is often very hard to understand the idea of a proof when can’t see any reason to doubt the proposition to be proved in the first place. It is much better to get kids used to the idea of a proof earlier on in a context where the proof tells them something that doesn’t seem obvious. My favorite is the proof that there are an infinite number of primes. (There is a whole page of Youtube videos to choose from on this.) And a lot of kids wonder if imaginary numbers are numbers at all. The proof that complex numbers with an imaginary components obey all the rules of arithmetic and algebra and therefore can be treated as legitimate numbers not only answers a question kids really have, but uses concepts from “The New Math” that confused many kids in the 1960’s in a way that is obviously useful.
Math resources I found useful:
Resources to check out that might be good but that I don’t have any experience with:
Note: if you want to advertise your tool or method for math instruction here, I encourage you to advertise it in a comment that you post in the comment box below. When I moderate the comments, I will approve comments that advertise tools or methods for math instruction like that unless I have reason to believe there is something wrong with that tool or method.