Two Dimensional Gravity

The April Scientific American has an article on two-dimensional gravity, "Quantum Gravity in Flatland."  It shows how you can simulate gravity to some extent in two dimensions by changing the topology of the two dimensions. 

For me, the main interest is in seeing how an n-1 environment can help us understand an environment with n dimensions.  We think that we live in an environment of three spacial dimensions, plus time.  What if we live in an environment of more dimensions, which we cannot sense.  We have five senses: sight, touch, hearing, smell, and taste.  Most of what we know about our universe comes from just two of those, sight and touch.  Microscopes, telescopes, machines and tools help us extend these senses to very large and very small things, but we are still basically depending on sight and touch.  What if the things we sense are only part of the universe; they might be just part of, or effects of, things which we cannot sense directly. 

That is what is interesting to me about two-dimensional simulations of a three dimensional world.  Suppose you lived in a two dimensional world where you could only see the flat shadows of three-dimensional objects.  As the sun rose and set, shadows would go from being infinitely long to small, and back to being infinitely long again.  What could you figure out about the object; would you think it changed size or shape, when only the light source was moving? 

Or what if there is some other dimension, like time, that is not a physical dimension.  Could we even conceive of what it is?  Basically what makes a dimension is our ability to measure it.  We measure time with clock.  Einstein found that the measurable dimensions are not absolute, but vary relative to each other.  Could it be that we are looking at the moving "shadows" and that there is something out there that is constant? 

String Theory

The reports of neutrinos moving faster than the speed of light and the entanglement of electrons lead to the possibility of additional dimensions. Extra dimensions could also help explain the possibility of dark matter and dark energy, which seem to be necessary to explain the makeup of the universe, although there is no physical evidence of them.  One response to this possibility is string theory. 

To see the possibility of additional dimensions, think about trying to figure out our three dimensional universe by looking at two dimensional shadows.  By looking only at the shadows, it would be very difficult to figure out exactly what the three dimensional shadows casting the shadows looked like.  A sphere, for example would cast a circular shadow, but so would a cylinder, if it was held the right way.  An egg could cast a circular shadow or an oblong shadow, and so on. 

For string theory, consider drawing a line on a sheet of paper.  If you look at the edge of the paper, you would only see a dot, where the line started, but if you could look down on the paper, you might see an infinitely long line, if the paper was infinitely long.  Or, you could draw a line that started at one point on the edge of the paper, then then went in crazy curves all over the paper, before coming back to the edge.  If you looked only at the edge, you would see only two points, one where the line started and one where it ended.  You would think these were separate points, but in fact they would be part of the same line.  This concept could explain the idea of entanglement, which says that if you know the state of one electron in a pair, you instantly know the state of the other.  In the line case, you would think you are looking at two separate points, but in fact you are looking at two ends of the same line.  Therefore, if one point was blue, for example, you would know that the other point would also be blue, because they are part of the same line.  But from looking only at the two points on the edge of the paper, it would be impossible to know what the line did between those two points, whether it went in a relatively smooth curve from one to the other, or went for miles and miles in all sorts of crazy curlicues between the two points. 

NYT Likes Carmelo Anthony

The New York Times ran a complementary article about Denver's Carmelo Anthony today. He is apparently one of the stars in a documentary of one of the first professional black basketball teams.

NY Times Math Blog

Finally a blog that it makes sense to list in the Colorado Athenian: a New York Times blog on math.

Rein in Goldman

One problem with Goldman Sach's huge earnings is that it shows that they are taking too many risks. The various articles about it say that they continue to take huge risks, although they are clearly winning. The WSJ said that they had reduced their leverage, but they still made too much money to be trading conservatively. It illustrates the need for stronger regulation. Goldman can't control itself. Arguably its traders are smart enough to beat the market on a regular basis, but unfortunately for our financial security if Goldman can trade wildly, so can everyone else, which includes whoever will replace Lehman, Merrill Lynch, etc. Goldman is still doing what Wall Street firms were doing a year ago when they almost destroyed the global financial system. They shouldn't be allowed to continue to do that. Government has to cut back their margins, leverage, portfolio size, something, so that they are not too big to fail, and also not big enough to destroy the world.

Another problem, illustrated particularly well by Matt Taibbi in Rolling Stone, is that while playing the market has been good for Goldman, it has not been good for America. He says Goldman is responsible for many of the recent financial bubbles, including the oil bubble that ran gas over $4 per gallon last year.

An additional problem is the excessive compensation. It's not good to have such huge differences in wealth. It makes America look and act like a banana republic. The rich guys -- capital -- control everything, including the government, while the poor guys -- labor -- suffer for the mistakes of the rich guys, e.g., in almost destroying the global financial system. Maybe it should be okay for individuals to trade like Goldman does with their own money, but a bank should not be able to. That would somewhat limit the number of fantastically rich people. But also a more progressive income tax would cut down the gap. It looks to me like Reagan destroyed the wonderful America that existed for about 30 years after World War II when he significantly reduced taxes on the rich. Obama's election may show how uncomfortable a slight majority of Americans has become with this situation.

No Second Stimulus

The US faced a genuine crisis at the end of George Bush's term. It looked like the financial system could collapse. But Bernanke, Paulson and Geithner took some drastic action that prevented the economy from self-destructing. So, now we are just in a regular, cyclical recession. Let it go.

It's as if a huge fire threatened to destroy a city. They called out all the fire departments in the region, and the put the fire out. There's a lot of destruction, but the rest of the city is no longer going to be destroyed. The extra firemen can go home.

The bankers and economists who run the government thought they had eliminated the business cycle, but it turned out that their attempts only postponed booms and busts and thus made them worse when the next one came. The only Fed chief who has faced up to a recession is Paul Volker. Greenspan tried to get out of them painlessly and created more pain in the process. Bernanke hasn't been tested, yet. We don't know whether he has an exit strategy, and if he does, whether it will work. In any case, the exit should be painful to reduce the risk and depth of the next recession. Nobody wants to inflict pain. It doesn't seem fair that the middle and lower classes should pay for the recession created by the supposed barons of Wall Street, but that's the way it is. A few of them will suffer, but many, like the employees of Goldman Sachs, will continue to profit munificently.

Rather than a stimulus, the US needs more of a social welfare net, more unemployment benefits, more medical care for lower classes, something like they have in Europe. Tax breaks for small business are not the answer, no matter how loud the Republicans scream that they are. But neither are a lot of make-work jobs. We just need to care for those who need it while the economy recovers on a regular cycle. In the meantime, we need to hold down inflation and support the dollar with some fiscal and monetary discipline.

Foreclosure Ain't What It Used To Be

The WSJ ran on op-ed claiming that the problem with foreclosures is not so much sub-prime mortgages as it is no-money-down mortgages. The more I think about it, the more I agree. If you have no skin in the game, foreclosure is not so bad.

In the old days, you had to make a 20% down payment; you would probably have to save for years to get enough for the down payment. Then if you lived in the house for a while, you would make substantial progress paying off the mortgage. Your mortgage might be 50% or less of the value of your house. So, if you lost you job and lost your house, you lost a lot of savings. On a $200,000 house, you might lose $100,000 which would represent years and years of savings.

During the housing bubble you could buy a house for nothing down and perhaps get a mortgage that didn't even require you to make full interest payments, so that the principal owed would get bigger as you lived in the house. In addition, because of the income tax mortgage deduction, the government subsidized this arrangement. Because of the income tax deduction and the negative interest payments, you might actually be able to buy a house more cheaply than you could rent a comparable one. But because you have no skin in the game, it's really comparable to renting. You can walk away and lose no more than if you walked away from a rental unit.

Under these conditions, it makes sense to walk away from a house if the payments get to be too much, or if you think they are too high for the house in the current market. You might get a black mark on your credit history, but that's nothing compared to losing hundreds of thousands of dollars that you had saved over decades.

Now the government is trying to prevent foreclosures, based on the old notion of the hardship it caused, when today it causes much less hardship. Many of the people facing foreclosure have just been scamming the system, getting government subsidies for living in houses that they can't afford. Now the government is concerned that can't continue to live in these same houses and is coming up with new subsidies to keep them there. It is a strong disincentive to people who bought their houses the old-fashioned way.

In helping prevent foreclosures, the program should look at how much equity home owners have. If they have negative equity, it's probably more of an indication that they paid no money down and got concessionary interest rates, which means they probably don't deserve to be bailed out. They've just been renting. The government should not go to any great pains to bail them out. But if someone has a lot of equity and is going into foreclosure because he lost his job or had huge health expenses, then some help is merited.