Political Animal

The Riemann Hypothesis

THE RIEMANN HYPOTHESIS….A few weeks ago I blogged about a book I had just finished that told the story of a mathematical problem called the Riemann Hypothesis. Why, you might wonder, was I reading this book? Today I’ll tell you.

It goes back to this post from April, where I wrote offhandedly that “I imagine that lunch with John Derbyshire would be quite enjoyable if we stuck to discussions of mathematical puzzles and prime numbers.” This reminded me that Derb was writing a pop math book of some kind, so I searched for it and found out that it was a book about….the Riemann Hypothesis.

I was curious to see what kind of book he might write, so I went off to my local bookstore to buy a copy. It turned out that it hadn’t been released, but I did notice another book on the shelf about the Riemann Hypothesis by a guy named Karl Sabbagh. That seemed like a remarkable coincidence, so I bought that book instead.

Then, a couple of weeks ago, Derb’s book finally came out. I bought it and finished reading it a couple of days ago and it was pretty good. What was most interesting to me was that I had just finished two books on the same arcane subject, but there was almost nothing in common between them. Sabbagh’s book skipped lightly over the actual math and spent a lot of time on current efforts to solve the RH. Derb’s book concentrated on the history of efforts to solve the RH and went into the actual math much more deeply.

In the end, Derb’s book ? for me ? was much better. I like history and I like math, whereas the idiosyncracies of mathematical culture hold only a small attraction for me. If you’re the opposite, Sabbagh’s book is for you. And if you couldn’t care less about any of this stuff, then skip them both.

POSTSCRIPT: Actually, it turns out there’s also a third book published recently about the Riemann Hypothesis: The Music of the Primes, by Marcus du Sautoy. Three popular books on the Riemann Hypothesis within a month! This has got to be a monumental drag for the authors, who were each writing a book with a pretty small audience to begin with and now have to split their audience three ways.

Why did this happen? A few years ago a $1 million prize was offered for solutions to seven different problems, and the Riemann Hypothesis was one of them (and certainly the most famous of them). All three of these guys must have thought this was a good hook for a book (not to mention this guy, who wrote a book about all seven problems.) I guess it wasn’t quite as unique an idea as they thought.


TAXES….Taxes, taxes, taxes, how much is enough?

This post isn’t about persuading anybody about anything. I just want to present a few numbers to put the whole tax/budget debate into perspective.

The chart on the right shows total federal tax receipts. As you can see, they have been relatively steady for the past 50 years, averaging about 18% of GDP (yellow line). There’s also a pretty obvious dynamic at work: whenever taxes start to rise to around 20% of GDP, they get reduced. This happened most recently in 2001, and during the 2000 election there was a bipartisan consensus that taxes ought to be lowered. (Bush and Gore differed on the size and nature of the cuts, but both agreed that taxes should come down.)

But what about the future? It’s remarkable, really, that even with the growth of Social Security and Medicare over the past half century tax rates have stayed pretty stable. But it can’t last forever, and the best estimates of the Social Security trustees are that taxes have to increase by about 3% of GDP over the next three decades in order to fund Social Security at its present level (Figure II.D5 in this report). Medicare has similar problems, and the best estimate is that its cost will also grow by about 3% of GDP during the same period (Figure I.E2 in this report). That’s a total of 6%.

(Of course, it’s possible that Medicare as it currently exists will be gone by 2030 and America will have some kind of national health plan. I’m ignoring that possibility.)

So here’s the deal: if tax rates have averaged 18% of GDP, and we need to raise that by 6 points over the next few decades, that’s an increase of about one-third. In other words, a lot.

But ? if we’re running budget deficits of 3-4% of GDP into the far future, then in order to fund Social Security and Medicare and balance the budget, tax rates may need to rise by 9 or 10 points. That’s an increase of over 50%.

This is why deficits and current tax cuts matter. If we want to keep Social Security and Medicare around in their current form ? and I think a large majority of people do ? then taxes will have to rise by about 1% a year over the next 30 years. If Republicans keep cutting taxes and we end up having to fix a chronic deficit as well, then taxes have to go up nearly 2% a year instead. That’s a big difference.

Social Security and Medicare are expensive programs, and we should have a national debate about their future. The current round of tax cuts is part of that debate, but their impact is being obscured by tax cut zealots who are deliberately trying to create a crisis atmosphere in which it’s “obvious” that we can’t continue to fund these programs.

But we can. Repeal the Bush tax cuts and agree to a tax increase of 1% a year for the next 30 years and we can do it. If you don’t think that’s worth it, fine. Make your argument. But in any case, let’s argue honestly and may the best argument win.

UPDATE: From comments, I see that a couple of things are unclear. First, this chart does include payroll taxes, which have gone up fairly steadily for the past few decades. Second, the final year in the series is 2003. My charting software didn’t make that clear.