Posts tagged columns
Posts tagged columns
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.
The idea for this column emerged during my trip to Rome, when I talked to Luigi Guiso about the economic and political situation in Italy. I wanted to thank him for all of his insights. Don’t construe that as his endorsement of my proposal, though!
Here is a link to my 49th column on Quartz, “Cheer Modi On: Why you really want India to join the US and China as a superpower.” I kept my working title as the title of this companion post, since it better reflects the content of the column.
Important Note: Thirumaran makes the case in these storified tweets that Narendra Modi has been given a bad rap for his performance during the Gujarat riots in 2002. What I say in my column about that incident is based entirely on the Wall Street Journal article "Why Narendra Modi Was Banned From the U.S." I would be glad to hear reactions to Thirumaran’s additional perspective.
Populations of the Most Populous Nations. I found the population figures in Wikipedia’s “World population” for the most populous countries very interesting.
United States: 318,201,000
I hadn’t realized that the US was the third most populous nation. All of Europe, including 110,000,000 in the European part of Russia, is only listed at 742,000,000. The reason it makes sense to focus on population figures is that catch-up economic growth up to the cutting-edge level of income per capita is much easier than the economic goal of the US of pushing income per capita to levels the world has never seen before for any large nation.
I was clued into India being headed for beating out China in overall population by Thomas Piketty’s Capital in the 21st Century. It is a fat enough book that I am only partway through. And I am glad I am reading it on a Kindle.
Here is a link to my 48th column on Quartz “The Man in the Tank: It’s Time to Honor the Unsung Hero of Tiananmen Square.” In addition to my editor, Mitra Kalita, I want to thank my father, Edward Kimball, for excellent editorial suggestions in putting together this column.
The Tiananmen Square Massacre is an event well-deserving in its infamy of a two-day memorial. Tomorrow’s post will also remember.
I have two related columns not directly linked in this piece: “Monetary Policy and Financial Stability" and my discussion of Janet Yellen’s views: "Janet Yellen is Hardly a Dove: She Knows the US Economy Needs Some Unemployment.”
What I say in the column about how a low elasticity of intertemporal substitution affects how the Fed should respond to risk premia is informed by the discussion I gave of a paper of Mike Woodford and Vasco Curdia at a Bank of Japan conference (which I mentioned and linked to here.) Claudia Sahm, Matthew Shapiro and I are working on literature review of empirical work on the elasticity of intertemporal substitution for our paper on that topic. I will have more to say on that in the future.
Update: I wrote this column (which is about much more than Jeremy Stein himself) just in time. On April 3, 2014, Jeremy Stein announced he was resigning from the Fed. But we might see him again in the future in high government office.
Here is a link to my 46th column on Quartz, “One of the biggest threats to America’s future has the easiest fix,” coauthored with Noah Smith. I talked about some of the issues of capital budgeting addressed in this column a while back in my post "What to Do When the World Desperately Wants to Lend Us Money" and Noah has talked about the importance of infrastructure investment a great deal on his blog Noahpinion.
Other Threats to America’s Future: Our editor wanted to title the column “The biggest threat to America’s future has the easiest fix.” I objected that I didn’t think it was the very biggest threat to America’s future. I worry about nuclear proliferation. Short of that, I believe the biggest threat to America’s future is letting China surpass America in total GDP and ultimately military might by not opening our doors wider to immigration—a threat I discuss in my column "Benjamin Franklin’s Strategy to Make the US a Superpower Worked Once, Why Not Try It Again?"
Technical Afterword to the Column (Please Read Column First):
There is a very interesting feature to our proposed capital budgeting system that we should highlight. How can the capital budget ever be negative? The capital budget plus the non-capital budget must add up to the total budget. So for a given total budget, a negative capital budget makes the non-capital budget bigger. What is going on is this: regular maintenance is like a quasi-entitlement within the non-capital budget. In any given year, regular maintenance as a component of the non-capital budget is fixed in advance and can’t be altered by the legislature. The only way it changes is that it is gradually reduced if the quantity of capital to be maintained gets lower, or gradually increased if the amount of capital to be maintained gets bigger.
In this lack of discretion about regular maintenance as a component of the non-capital budget, there is no real tying of the hands of the legislature: they could always choose to have a very negative capital budget, which would increase the non-capital budget enough to cover that maintenance. So if the legislature as a whole acted like a fully rational actor, this principle is not a constraint at all. But as political economy, it makes a difference, and a good one. The legislature can increase the non-capital budget and reduce the capital budget. But what the legislature can’t do is get more funds for other things by letting capital decay without it showing up in the accounting as an increase in the regular budget and reduction in the capital budget.
I briefly considered titling this post “The 2014 State of the Union Hints at Shifts in the Overton Window.” I say a bit about the “Overton window” in my post "The Overton Window." In brief, the “Overton window” is the set of “respectable” policies that are discussed by actual politicians and those closely associated with them.
This is a followup to my Christmas column "That baby born in Bethlehem should inspire society to keep redeeming itself."
I am not making a narrowly legal argument in "The case for gay marriage is made in the freedom of religion." It as addressed at least as much to current and future voters and legislators as to lawyers crafting arguments for judges.