Mathematics books

My friend Vineet visited the US last week and I had a very enjoyable discussion with him. Vineet has a great interest in all things mathematical. So, not surprisingly, one of the interesting things we talked about was an old blog post of his that listed a series of great books on mathematics. You can go to the post to check out all his recommendations, but here I'm going to highlight three of them. Vineet recommended the first two for my kids:

• Sideways Arithmetic from Wayside School by Louis Sacher.
  Louis Sacher is the author of the very popular Wayside School series; our kids have loved these books. This Sideways Arithmetic book consists of "50 mindboggling math puzzles". For example, the first puzzle in the books is: elf + elf = fool. The problem in this case is to identify the number that each letter stands for.
• The Number Devil by Hans Magnus Enzensberger.
  This book looked even more interesting. It's about a young boy who visits a "...bizarre magical land of number tricks with the number devil as his host." And in this land, kids are introduced to all kinds of mathematical concepts including prime numbers ("prima donnas"), irrational numbers ("unreasonable"), and roots ("rutabagas"). Sounds fun and educational!
  

And for older kids (or adults like me!), he recommended "What is Mathematics?" by Richard Courant (after whom NYU's Courant Institute is named) et al. This was a book originally published in 1941, and recently revised in 1996! Any book in print since 1941 has to be a classic. This isn't a book about mathematics (in the sense that it isn't about the philosophy of mathematics or about meta-mathematics). Rather, it provides an elementary approach to the ideas and methods of mathematics. Albert Einstein apparently said of this book "A lucid representation of the fundamental concepts and methods of the whole field of mathematics...Easily understandable"!

I think I'm going to get all three books (for my kids and for me!) and check them out.

David Swensen on investing

Stock markets all over the world are in free fall. With the demise of Bear Stearns, the sub-prime crisis is only appearing to get worse. Oil prices are going through the roof, and even food prices are surging. How should we react to all this? Specifically, how should we change our investment portfolio?

The answer, says, David Swensen is "do nothing"! David Swensen has run the hugely successful Yale endowment fund since 1988. He was interviewed by the NY Times about a month ago. His basic advice is:

Don’t try anything fancy. Stick to a simple diversified portfolio, keep your costs down and rebalance periodically to keep your asset allocations in line with your long-term goals.
...
For most people, he recommends a very basic approach: use index funds, exchange-traded funds and other low-cost instruments, and stick to your long-term asset allocation — even when the markets are in tumult.

And that's exactly what I'm doing, following the ETF portfolio I've written about in the past. I have no idea when the markets are going to turn around. And that's exactly the point: if I was to drastically change my asset allocation to react to current events, I'd have to figure out when to get back to this strategy (presumably when the markets start to recover). Which means I'd have to be right twice to make this strategy work---once to know when to sell (I'm already late on this) and then to know when to buy back into the market (I'm sure I'd be late for that too). Much simpler to leave well alone, and incur no trading or tax costs.

What strategy are you using?

My God, it's full of stars!

Arthur C. Clarke died early today in Sri Lanka. The NY Times has a very good obituary. Growing up, I was a great fan of Clarke's writing. His most famous work, 2001: A Space Odessey, is of course a classic book and movie (Stanley Kubrick co-wrote the movie). I must be the only person in the world who's read the book but not seen the movie! It turns out that Clarke wrote the book after he co-wrote the movie with Kubrick (based on Clarke's original ideas). He felt compelled to write the book because he disagreed with Kubrick's "...obscurism and mysticism..." in the movie (see here for a discussion). So the movie and the book disagree in exactly those areas where Clarke disagreed with Kubrick. In fact, Dave Bowman's famous line in the book as he enters the monolith ("My God, it's full of stars") does not appear in the movie!

While 2001 was an amazing book, he had other equally amazing books. I remember being particularly enthralled by Rendezvous with Rama, a fascinating story of an encounter with a huge, cylindrical alien craft that comes swooping into the solar system. And then, of course, there's his frightening classic Childhood's End, featuring aliens who look like devils. Clarke gave me a lot of joy with these and other books. I hope he finds that where he's gone now is full of stars!

Sudhir Venkatesh on the Colbert Report

I've written previously about Sudhir Venkatesh and his series on watching The Wire with thugs. Venkatesh recently appeared on the Colbert Report. Check out his short 5 minute appearance:



(Thanks to the folks over at Freakonomics for the pointer.)

On a related note, Ashish had pointed out in the comments to my previous note that Venkatesh has also done research on the economics of street prostitution. Not surprisingly then, Venkatesh has some interesting comments on the the recent events involving Eliot Spitzer.

AWOL

It's been about 3 weeks since I last posted a entry. It's not that there haven't been things to write about---there were lots of interesting things going on. But I just got really busy with one thing and another (conference reviewing, taxes, actual work, being sick, ...!). Hopefully things are getting better now.

Sub-prime mortgage mess explained

You're all no doubt familiar with the sub-prime mortgage disaster that has wreaked havoc on the stock market. But do you really understand what this mess is all about? If you don't, here's something to help you. There's a slide show making the rounds that uses cartoons to do a great job of explaining the mess (original author unknown)! I found it in a recent post by Roger Ehrenberg. Here it is for your viewing pleasure:

Download explanation_of_sub_prime_issue.pps

Solar panels for the home

The San Jose Mercury News recently reported that Severin Borenstein, a business school professor at UC Berkeley and the Director of the UC Energy Institute, says that:

Installing solar panels on homes is an economic "loser" with the costs far outweighing the financial benefit ...
...
The technology, using photovoltaic panels to generate electricity, is not economically competitive with fossil fuels and costs more than other renewable fuels

The solar industry, naturally, disagrees with Borenstein's conclusions. But I have to say that, based on the little research I've done, I have not been convinced about the financial utility of installing solar panels. In my mind, the primary benefit of installing solar panels appears to be the good feeling one gets from doing something about climate change. Borenstein explicitly notes that

...he didn't take into account the feel-good benefit or societal value of installing a solar system on your roof.

But is there a different way to get these benefits without incurring the financial costs of installing solar panels? I think there is.

Some utilities allow you to opt for "green energy" alternatives; for a small premium one can buy energy from renewable sources. For example, Palo Alto Green is a program that allows you to buy your electricity from renewable sources for a premium of only 1.5 cents per kWh. Currently, 97.5% of the this renewable energy is from wind and the remaining 2.5% from solar. (Of course, the actual energy delivered to your home isn't guaranteed to be from a renewable source, but the utility promises to buy the right amount of electricity from renewable sources based on the usage by subscribers to this program.)

We've been subscribers to this program for some time now. And based on Borenstein's analysis, I don't think I'm going to rush in to install solar panels on our roof. Rather, I'll let the utilities install large solar farms or other renewable energy sources, and get the "good feeling" by supporting their efforts. Presumably, the utilities will ensure that these renewable sources are cost effective.