Playoff puzzle

There was some angst in Yankeeland after the team failed to close out the Angels in game 5. However the Yankees would appear to still be in pretty good shape returning home up 3 games to 2 in the best of 7 American League Championship Series (ALCS).

This suggests the following puzzle. Suppose the Yankees will win each game with probability p (independent of the results of the other games). Then in a best of 7 playoff how large does p have to be for the Yankees to be worse off leading 3 to 2 than they were at the beginning before any games were played.

Blogger problem

Blogger was having having problems last night making it impossible to view some blogs including mine. Things seem to be fixed.

This seems like an opportunity to solict feedback. Anything you all would like to see more of? Less of?

Photovoltaic cell color

A silly controversy has arisen concerning the color of photovoltaic solar panels. Apparently a new book "SuperFreakonomics" contains the following (quoted here):

As an example he points to solar power. “The problem with solar cells is that they’re black, because they are designed to absorb light from the sun. But only about 12 percent gets turned into electricity, and the rest is reradiated as heat — which contributes to global warming.

Yglesias (among others) jumps on this statement (here and here) posting a photo of solar panels that appear to be dark blue and claiming:

... Still, it is worth dwelling a moment on the fact that their critique of photovoltaic literally rests on the idea that PV cells are black whereas in reality they’re usually blue:

First their critique depends on solar cells being dark (low albedo) not black. Perhaps they should have said "dark" instead of "black" but this is not a serious error. Especially since, Yglesias to the contrary, many cells are black. It is hard to judge color from photos because the cells are often reflecting the blue sky. See for instance this photo where the cells appear to be blue except at the upper right where they appear to be brown because they are reflecting brown branches instead of blue sky.

Anyway the critique is because solar cells are dark they may absorb more sunlight than whatever background they are replacing thus heating the earth. This can occur whether the cells are black or dark blue in appearance. However this effect is not important. Coal power plants also generate considerable waste heat as their thermal efficiency is only about 33%. It is doubtful that solar cells produce more excess heating per unit of electricity generated than the waste heat from coal power plants. And in any case the global warming concern with coal power plants is not their waste heat (which is not significant globally compared to solar heating) but the much greater long term heating effect from the CO2 emitted when coal is burned.

Does this mean photovoltaic solar cells make sense? Not really, they are inferior to wind turbines which also don't emit CO2 and are much cheaper .

Arcady Road

I went walking in Kitchawan Preserve again on Monday. This time I explored the western portion of the Preserve. One trail terminates at Arcady Road. It looks like it would be easy to add a few parking spaces there but this has not been done.

Arcady Road used to connect Old Kitchawan Road to Croton Dam Road but a portion was damaged by Hurricane Floyd in 1999 and never repaired. The damaged portion has now been officially abandoned (pdf file see resolution 180). I walked down the road towards the closed portion. Auto traffic is blocked just past a driveway but you can walk a bit further until a chain link fence blocks the road.

I took the picture through the fence. It shows part of the road washed away.

Sunset years

I recently turned 55. Trying to look at the bright side this makes me eligible for more senior discounts . It also provides an excuse to post the picture which I took this July when I was in Denver. It is looking across Smith Lake in Washington Park .

Mathematics and CDOs

This mathematics paper (with this FAQ ) has attracted some attention from bloggers. Briefly the paper starts with a model in which sellers construct collateralized debt obligations (or CDOs) from many different asset types (and with each asset type appearing in many different CDOs). If the seller knows some of the asset types are lemons (eg are worse risks than they appear) then the seller can create lemon CDOs by assigning them more than their fair share of the lemon asset types. The paper claims to show (using the conjectured intractability of the densest subgraph problem) that this nonrandom assignment is much easier for the seller to do than for the buyer to detect.

I have no reason to doubt the mathematics in this paper but I do doubt its real world significance. The larger risk with such CDOs from the buyer's point of view is that the CDOs will be overpriced across the board not that they will purchase CDOs from a malevolently constructed fraction of lemons. This is what went wrong with the mortgage backed CDOs whose loss of value contributed so much to the recent crisis. The pricing models for these CDOs overvalued them by incorporating a number of overly optimistic assumptions. When this became apparent their prices collapsed. As far as I know the scenario in paper is purely hypothetical.

I don't see much point in worrying about hypothetical problems before fixing readily apparent real problems. And I don't think this particular hypothetical problem would actually be all that difficult to solve. It seems to me that it should be possible to devise a transparent verifiable randomization procedure if that should be felt to be important.

My opinion is this problem will prove to be largely moot going forward. These CDO products grew explosively because they could be sold for more than they were worth. Presumably potential buyers have wised up and this will no longer be possible. In which case I don't think these products have much reason for existing and will largely disappear.

Dreams from My Father

After reading Polanski's autobiography I moved on to Barack Obama's 1995 autobiography "Dreams from My Father". This is a strange book. It is a bit hard to understand why anyone at the time would have thought publishing 442 pages of self-absorbed rambling reflections on family and racial identity by the youthful Obama was a good idea. But of course, in a development which should hearten parents of underachieving children everywhere, the conflicted aimless Obama of this book somehow went on to be elected President.

This book doesn't shed much light on how he did it. The Obama of this book is plagued by self doubts, too willing and able to pick holes in his preferred self image. He wants to be an authentic American black but knows that his mother was white and that he was raised by whites. He wants to be proud of his African blood but is all too aware of all of Africa's failures. The resulting lack of direction and self-confidence would seem to be a big handicap for a politician. Perhaps Obama's later book "The Audacity of Hope" (which I have not read) explains how he resolved his issues and became an effective politician but this book doesn't offer many clues. And the narrow focus makes it hard to get a clear picture of Obama as a whole.

I found the book readable and sporadically interesting. However it is also quite lengthy and seemed cliched at times. It is mostly of interest because Obama went on to be elected President. So unless you are a politics addict or relate to Obama's identity issues I would not recommend this book.