Amazing Grace

Dear Everybody,

I was just listening to "Amazing Grace" on my Internet New Age radio station.

I think it is my favorite song, but I like it played on the bagpipes best.

Have a great day, don't forget to boogie, and have some fun.

Sincerely,

Lynn

Morning with Internet New Age

My insomnia had me wide awake at 4 AM. Shortly after I'd read some of the NYT online and drunk my first cup of coffee, I read this at I Cite.

I've lost a sense of why blog.

Perhaps it is a 'thinkers block.' This is rare for me. Usually, I have ideas. I know what I want to try to understand, try to think, try to say. Right now I just feel trapped, unclear, lost in a lack of understanding.

And, I feel guilty--for not responding, for not having ideas, not being able to contribute. And, I think, what's the point? Why bother? There is a world of thinking and speaking and discussing out there.

The city is still asleep, and I am trying to write something, anything, if only this blog.

The novel sits on the floor beside the desk. Tomorrow is the day I promised myself I would make the call on whether to send it out or not. I lack the courage to make the decision. I know the novel is not good enough, yet I don't want to admit that the time I spent writing it was in vain. I long to escape this seemingly trivial decision. Is that why I have an Internet New Age radio station playing on the laptop?

I have a new idea for a novel. That is the one I want to think about. I record my ideas, a nascent pastiche for a novel.

And my public blog? It's lately been even more trivial and banal than usual: sports, trivial math, a few memories, the stray thought, and a few failed attempts at seriousness, all of it silliness. Of course, I can sit in the local bar for several hours and listen to a huge cacophony of silliness either genuine or disingenuous, yet not think it time wasted.

"Ariel was glad he had written his poems." Wallace Stevens from Planet on the Table

"The trick is not minding that it hurts." Peter O'Toole from Lawrence of Arabia

I am a fool. My blog exposes me to the world.

Thanks, Senator

Senate Majority Leader Bill Frist has joined the ranks of those who support stem cell research.

Hook 'Em Hawkeyes!

The college football season is almost upon us. The University of Iowa Hawkeyes, America's Team, is highly ranked in all the preseason polls. And why not? They are custom made from head to toe.

So, take your Hawkeye gear out of the closet, and Hook 'Em Hawkeyes!

Mickey, Sports Betting, and Statistics

I know a guy, let's call him Mickey, from the local bar who likes to bet lots of money on baseball. We've had some interesting conversations about sports betting. Mickey thinks he has a system to win at baseball betting. I claim he doesn't.

The last time I saw him was about month ago. We were watching the ESPN Sunday night baseball game, a game on which he had bet $3,000. He was very worried because he was in hock to his bookie for $10,000 which was due the following day. Not a problem except he told me he did not have the money.

Mickey won his bet that night on the game, and we once again had our conversation about whether he had a winning system. His system was little more than betting on the team who had a hot winning streak. I tried to explain to him that he would sooner or later fall victim to the efficient market hypothesis.

The efficient market hypothesis was developed for the financial markets, but statisticians and economists have applied it to sports betting and researched the hypothesis across all sports. Basically, the efficient market hypothesis says that if you do not have insider information, then you cannot beat the average market return. If you want a higher return, then you have to take on higher risk in your investment portfolio. Developing these ideas have won several people the Nobel Prize for economics, so it should not be dismissed out of hand.

Of course, betting on the market to make better than average returns is worse than a 50-50 proposition since betting in the financial markets has transaction costs. Betting with a bookie has transaction costs too, for he charges you the juice on each winning bet. The reason why financial markets rise over time is because they are tied to overall economic growth. You should not expect to beat the long term growth though. That is why the buy and hold strategy with a mutual fund, whose portfolio matches the overall market, and whose transaction costs are minimal, is considered to be the best investment strategy.

I'm no statistician, but I like applying elementary statistics to various situations. My interest was rekindled when I started to use an Internet sports betting bookie several years ago. I decided to invest some time studying the latest statistical research on sports betting. All the studies show the efficient market hypothesis applies, or in the case of Steven Levitt's study, it can be worse.

I like to bet pro football, and I have enjoyed a lot of success for more than ten years. In fact, last year I got hot during the playoffs and won 8 out of 11 games. I have a good deal with my Internet bookie because if I deposit my money on a certain day and bet on a certain day, the bookie does not take any of my winnings with the juice. That means given the efficient market hypothesis, my betting is like betting on the flip of a fair coin. Winning 8 bets out of 11 during the football playoffs is not the work of a genius, but the luck of a guy betting on coin flips.

I'll never go back to making extravagant bets based on my feeling that I have a system.

I have not seen Mickey since that Sunday night. I have been afraid to ask about his whereabouts. I'm pretty sure I'll never convince him of the efficient market hypothesis. I like him, and wish I could.

Cubs Chances Update

The Mayan calendar.

The results of the latest 200 trial Monte Carlo simulation are in. The Cubs were successful 27 times. That's 1.35% for those of you without computers or calculators. This is a slight improvement over the previous week.

In their last ten real games, the Cubs won five out of ten. 59 games remain to their season.

Tick tock, tick tock, Cubs!

Battlestar Galactica

The new episodes of Battlestar Galactica started this month on the Sci Fi Channel. I am so glad. It continues to be one of the best shows on TV.

The gist of the story is that robots called Cylons are trying to kill off the human race. Some Cylons are duplicates of humans which causes a lot of trouble.

The remaining humans are trying to find the mythical planet Earth whose whereabouts have been lost in the mists of time. James Edward Olmos plays the Captain of the Battlestar and Mary McDonnall plays the President of the federation. They compete for control of the fleet and power.

Aboard the fleet is the universe's brainiest scientist. His mind is not right though. He sees a sexy blonde woman all the time who tells him what to do and claims to be in love with him. No one else sees her because she is a creature of his mind. This woman also makes appearances as a Cylon on other planets.

Lots of love stories, tense spaceship battles and chases, fast moving subplots, and other interesting characters make every episode fascinating.

I like stories about forgetting, memory, and the search for those things lost in the past, a search that may save the human race from total annihilation.

We are living through that story ourselves.

Cubs Win on a Honey of a Day

Jose Macias slides across home plate for the winning run in the bottom of the 9th. Cubs 4, D'backs 3.

I told you it was a honey of a day.

Honey of a Day

It is another honey of a day in Chicago, but warmer. I love summer. There is still lots of good baseball yet to be played, and I find my mind still works on some days. That's good enough for now.

Have a nice day everybody!

Cubs Chances Redux

Since I ran my Monte Carlo simulation last week on the Cubs chances of winning a Wild Card spot, the Cubs won 2 out of 3 from the Cards in St. Louis. They just beat the Giants 2 out of 3 at home.

However, I am still not enthused about the Cubs chances. The majority of their remaining games are against good teams including ten games against league leading St. Louis.

Of course, the ultimate World Series would be the White Sox vs. the Cubs. One of those teams getting there would be a miracle. The chances of both defy the imagination.

Spell Check

Do you find it odd that Blogger does not recognize the word "blog" in its spell check program?

Oops

I've been forgetting to post on my blog. I've been drifting and dreaming more than usual this past week. That is my only excuse.

P. S. I'm still on my exercise program and diet.

Cubs Chances

I know my readers, especially the baseball fans, have been anxiously awaiting the results of my Cubs Monte Carlo simulation. Here's the results.

I ran a 1,000 trial simulation of the Cubs remaining 67 games assuming their current winning percentage of .505 as the p value. In only 43 out of 1,000 trials did the Cubs manage to achieve a winning percentage .600 or above in the last 67 games. That equates to 88 wins for the season.

I figure 88 wins is the absolute minimum they need to get a Wild Card spot.

Things are looking pretty grim. It is going to take a miracle.

Baseball

The Cubs play the St. Louis Cardinals tonight. I remain a loyal Cub fan, but I fear that the Cards will pound the final nail into the coffin known as the Cubs 2005 baseball season. I inspected the standings a couple of days ago and the way I figured it was that the Cubs would need to play over .600 baseball for the rest of the season to have a shot at the Wild Card spot.

What is the probability that a team, who has played .500 baseball for almost 100 games, can play over .600 baseball in their remaining 60 plus games? I don't know, but I expect it is not good. Rather than taking pencil, paper, and the calculator in hand to work it out, I think I'll just run through a few Monte Carlo simulations on the computer to see what it shows.

The Red Sox are in town playing the White Sox (best record in baseball). The White Sox lost a 6-5 heartbreaker to the Red Sox last night. The White Sox committed an unaccustomed three errors during the game. The third error, a dropped foul ball by third baseman Joe Crede, led to a Manny Ramirez solo shot that won the game.

I have a ticket to tonight's Sox vs. Sox game.

Mathematics and Art

I once heard somebody say, I don't remember his name, that you can tell where a philosopher is coming from by what she says about mathematics. I think that is true.

The central question in the philosophy of mathematics is whether mathematics is discovered or whether it is created. I think it is created, but I think all of our higher studies are created. That includes science, art, philosophy, and religion. I don't mean to say they have nothing to do with the world, for each endeavor must mesh with the world at some points to make any sense.

Some people might find it strange to think of mathematics as akin to art. However, mathematics, once considered the ultimate test of reality, has gotten to the stage where most or at least much of it really does not have an application. That's not a bad thing. You never know when the creations of mathematicians might find an application in other studies.

Art has its practical uses, but when I stroll through the museum I do not ask what use it is. I feel the same about mathematics. I recall Pythagorus's proof that the square root of two is irrational, or Euclid's proof that there are infinitely many prime numbers, and I delight in their beauty rather than what earthly good I can use them for.

Whatever good things we may have accomplished as a species, we got there because of our imaginations and our delight in imagining.

What was it worth?

Since I started blogging last year, I have often wondered what it's worth. I certainly have not blown the doors off the blogging world.

However, I've met a few people I really like even if I may never meet them in person.

Some people say the age of letter writing is dead, but I wonder if blogging hasn't replaced letters in its own more public way.

P. S. I found another way to figure square roots manually, but we won't go into that now.

Square Root of Two

From Prime Obsession by John Derbyshire. Consider the sequence 1/1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, 577/408, 1393/985, 3363/2378, ....

Each term in the sequence gives a better approximation to the square root of two. The rule is add top and bottom to get new bottom, add top and twice bottom to get new top.

Homework assignment: prove the sequence converges to the square root of two.

Another cool way to get an approximate value for the square root of two is to enter 2 in your calculator and hit the square root key.

P. S. If Hoagie gives a correct proof, keep in mind he has a Ph.D. in statistics.

Stem Cell Research

Curtis at a-sdf and I have had some discussions, or disagreements, about stem cell research. He has been gracious and generous to me throughout the discussion, so I decided to answer his comment on my Why the garbage can? with another post. He comments:

It would seem that neither option is ethically sound for those who view human embryos as persons. Simply put, they shouldn't be thrown away. Having said that, this fact doesn't impact the research end of the question, because performing research that involves destroying the embryo is, ethically, the same thing. Thus allowing them to be destroyed in research is simply making it legal to throw the embryos away in a different fashion.

I think the ethical argument can be made on utilitarian grounds.

There are between 100,000 and 200,000 pre-embryonic cells abandoned in fertility clinics. Most donors for various reasons will not give them to people who are not the genetic parents. Few people want to adopt them. These frozen cells will die by natural degradation, equipment malfunction, or operator error. Fertilization clinics are under no compulsion to keep them alive even if they could.

These clusters of 100 undifferentiated cells, that is, no human anatomy, could be used for stem cell research. All current lines approved by President Bush have degraded to the point where they are useless for research.

I don't see a third option in the matter. The cells are going to die. Why not use them to heal the living?

I am sure we will continue to disagree, but I ain't throwin' the towel. I'll bet ten bucks to a donut he ain't either.

Square Roots

It was driving me crazy, but it isn't any longer. I went back to first principles and figured out how to calculate them.

Persistence

I finished writing my latest novel yesterday morning. I turned a first draft with the germ of a good idea into a novel sentimental, maudlin, and boring. This is the third time I have done it.

I consider it failure on a massive scale, for the opportunity cost for writing these novels is huge. I am reminded of some of my other failures.

I loved long distance running once. In 1982 I achieved personal records in all distances from 10K through half marathon. One of my goals in running was to run a marathon in under 3 hours. Each year I ran a marathon on a flat course the first weekend in November. 1982 was the year I felt I had my goal in reach. So, September and October I trained even harder than usual.

When race day came I changed my previous strategy of starting out slowly and running each successive 10K faster. I went out fast. My strategy was working fine until I hit the ‘wall’ at 20 miles, the first time it ever happened to me. My time was horrible.

The failure weighed heavily on me. I never ran another marathon nor seriously tried to improve my running. I eventually stopped running.

I have all these other ideas for books I’d like to write. My imagination seems on fire this morning with ideas. The question is whether I can afford another failure. I will put the question out of mind today and start writing another book. When August 1 rolls around, I’ll decide whether or not to send out my latest novel.

Persistence is a blessing and curse, for there is no finish line.

P. S. I exercised all seven days last week, and I only ate 3 meals out of 21 outside my diet. Where are they holding the 2104 Olympics?

Why the garbage can?

Stem cell research has spawned many subtle philosophical and theological arguments by those on both sides of the issue. What gets lost is what is being proposed by stem cell researchers and the bill passed by the House of Representatives. The proposal is to rescue abandoned cells in fertility clinics, cells that have gone unclaimed by their prospective mothers, cells destined to be thrown in the garbage.

The question that should be answered is why it is better to throw the cells in the garbage rather than give them to scientists for medical research.

The issue never gets addressed that way, nor arguments mashalled in defense of throwing cells in the garbage.

I am hard pressed to find any argument that would justify throwing fertilized cells in the garbage rather than using them for medical research.

2 A. M.

I could not sleep. I got out of bed. I sat down at the table with a math paper, pen, and paper. I worked my way through the details of proofs of several theorems that had been troubling me.

4 A. M. I was tired and pleased. I had just spent two hours lost in something beautiful. I fell asleep happy if only for a little while.

Hey, Doc, I don't feel so good.

I like engaging in thought experiments. Here's one I have been thinking about.

I believe it is certain that stem cell research will come to maturity and fruition. The potential to cure terrible diseases is too great, and the potential to make lots of money off the medicine is way too seductive.

Let's say it is 25 years hence, and that there are many medical treatments available that arose from stem cell research. How many people who oppose stem cell research today will refuse medical treatment in the future either for themselves or someone in their family when the medical treatment was made possible by stem cell research?

Here's my guess. None!

Blow Me Away

Thomas L. Friedman writes about a poverty of dignity and wealth in his recent NYT Op-Ed piece. His says it is time to face the fact that the world's suicide bombers are angry young Sunni males.

When you bracket the politics of suicide bombing, and set it aside, what you have left is a group of seriously troubled youths and a group of murderous old men frustrated by their inability to gain power via legitimate means.

All I see is a bunch of criminals who try to disguise their true motives behind politics and religion.

The Fat Old Pig

I realized Monday morning that I could no longer avoid it, diet and exercise that is. I have grown into a fat old pig.

So, I promptly started a modest exercise program, and what for me passes as a change in diet. The nice thing about the exercise is that I get the little buzz or high afterwards that I enjoyed when I was a devout 50 mile a week runner.

My goal, fit into the blue jeans I wore four years ago.

Of course, I still have to confront my whiskey, beer, and cigarette addictions. I think I'll quit smoking first and work on the beer and whiskey later.

"Rome was not burned in a day." Bo Hopkins in American Graffiti.

World Series of Poker 2005

Greg "Fossil Man" Raymer, last year's winner, heads into day four of the big one as the chip leader. Given over 2,500 entries last year and 5,619 entries this year, it would be amazing if he won again. The field is down to about 170 so he is definitely in the hunt.

Would two wins in a row make him one of the greatest players, or a guy who stood out in two thunderstorms and got struck by lightning both times?

Intellectual Curiosity

The picture is of the prime number counting function. It displays the values of the function up to 100. Note, the x and y axis have different scales. One can use the Sieve of Eratosthenes to verify it's accuracy.

Many of the most interesting and difficult problems of mathematics are spawned by the desire to find a function that estimates pi(x) to within square root accuracy. You don't have to be a mathematician to understand the problem, but you have to be one of the world's most talented mathematicians if you stand a ghost of a chance of solving it.

So, if you are not a brilliant mathematician, why care? Curiosity I suppose.

Summer

I like the warm weather, but I like the early morning light just as well. The city rests quietly for a few minutes.

The 7 Eleven across the street closed two weeks ago, so State Street stands even more alone and empty in the faint light before sunrise.

I can believe almost anything is possible at first light. Then the city wakes, dispelling the pretty notion.

More Distribution of Primes and RH References

Here are a few interesting articles on the Internet about the Riemann Hypothesis. They are written for the non mathematician, and give an excellent idea of what the problem is all about.

Marcus du Sautoy has written two articles for the online magazine +Plus: The prime number lottery and The music of the primes. Only very basic math is required to follow along.

Barry Mazur has posted lecture notes he gave on RH at the Clay Math Institute: Are there still unsolved problems with the numbers 1, 2, 3, 4, . . . ? The lectures notes are in PDF and the link I give takes you to a page where you can link to the PDF notes. There were slides that accompanied the lecture, but I have been unable to find them online. Even without the slides, his lecture gives you a very good idea of how RH fits with finding a good estimate to the prime number function. Once again, only basic math is required to read the article.

Happy Fourth of July

Have fun, and be careful with those M-80s and cherry bombs!

Little Green Notebook

I have this little green notebook that I use to record the odd theorem or calculation related to the Riemann Hypothesis. When I am sitting around, I can take out my little green notebook and play around with numbers and ideas. It’s my new toy, and I am having lots of fun with it. Some of the best toys are the cheapest.

Of course, the best place to start finding the interesting results related to RH is the Internet. You’ll find everything from excellent presentations designed for the interested layman to lecture notes for analytic number theory courses.

I also found an excellent textbook, The Prime Number Theorem by Graham Jameson. It is a model of clarity, presentation, and organization. That does not mean it is easy. The math behind PNT gets hairy in a hurry. But if you are willing to apply a little elbow grease, it is a good place to start given the requisite background in math.

I also recommend The Riemann Hypothesis by Karl Sabbagh, The Music of the Primes by Marcus du Sautoy, and Prime Obsession by John Derbyshire. All of them are written for the non mathematician, and are excellent reads about how high powered math is conducted, and the history of prime number math. Derbyshire’s book contains more math than the other two books, but he explains all the concepts he uses quite well. You can also skip the math that seems too difficult and still have a good read.

Keep on countin' and calculatin'.