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One time several years ago in graduate school, I simply could not remember the word "syrup", so I called it "pancake gravy". That title was already taken(!), so I added "cane" because when I was a child in the Panhandle of Florida (aka Lower Alabama), my family grew sugar cane and made our own cane syrup.

Monday, April 14, 2014

Billion Dollar Brackets and Fine Tuning

Backgammon PrecisionDice

For this year's NCAA Men's Basketball Tournament, Warren Buffet offered to pay $1 billion to anyone who could correctly predict the outcome of every game.  Unsurprisingly, no one won.  Many stories and commentaries have cited numbers about just how improbable it is to pick every game correctly.  What none of these stories and commentaries seem to have noticed is that the question is meaningless.

The usual comparison is with a lottery.  Lotteries are run so that every possible combination of numbers is equally likely, which means that no one strategy is any better than another.  Choosing "1 2 3 4 5" for Powerball works just as well as "2 3 5 7 11" (the first 5 primes) or "8 15 16 23 42" (from the Lost sequence) or any other sequence of 5 natural numbers less than 60.  (Don't play any of those sequences, though.  Because there is a "reason" for each of them, several other people are probably already playing them, which means that even if you won the prize, it is much more likely that you'd have to split the winnings!)

Most estimates of the "odds" of getting all the games right in a bracket challenge probably assume that the odds getting each individual game right are 50/50.  Since there are 32+16+8+4+2+1 = 63 games in a bracket (not counting the play-in games), this would make the odds of a random bracket winning 1 in 263, or 1 in 9.223 x 1018.  However, no 16 seed has ever beaten a 1 seed in the NCAA basketball tournament, but 93.75% of brackets chosen completely at random will have at least one 16 seed beat a 1 seed.  Clearly, there are better strategies for filling out a bracket than just flipping a coin.

So what is the best strategy for filling out a bracket?  No one knows!  My strategy is to choose the winner of each matchup so that the odds of the team with the lower seed winning are (15 + difference in seed numbers)/30; that way, the odds of a 1 seed beating a 16 seed are 100% but the odds of one 1 seed beating another 1 seed (in the Final Four or Championship Game) would be 50%.  This assumes that the people on the committee that sets the seeding really know what they are doing, which is debatable -- but what isn't debatable is that they know more about college basketball than I do.

Of course, there is a lot more information available -- the outcomes of games through the season and the order in which they came, the stats for individual players, the general strategies of the coaches, and the announced injury situations.  No one really knows how to put all this together!  Then there is information which is not publicly available (exactly how the players feel, physically and emotionally) and there are unpredictable things that will happen over the course of the tournament.

In the case of Powerball, any strategy is the ideal strategy, but in the case of a basketbal bracket, the ideal strategy is unknown.  If the strategy is unknown, how can we know how likely it is to win?

At any rate, let me pretend that someone who really knows basketball can choose the 1 vs 16 matchups correctly 100% of the time and the other ones 70% of the time.  His odds of getting all 63 games right are 0.759, or 1 in 1.378 x 109.  Probably no one is really that good, and he would still face long odds, but he is a billion times more likely to fill out his bracket correctly than the crude estimate had indicated!

Let's go a little further.  Suppose someone is a super-genius at college basketball and can pick games correctly 99% of the time (and I'll give him the 1 vs 16 matchups for free).  Someone like that would already have his own billion dollars, but he's going to play anyhow.  His odds of filling out the whole bracket correctly are 0.9959, or 55.27%.  To me, that is the best measure of just how hard this is!

Unfortunately, it's not hard to find people quoting probabilities as though they were meaningful when they really are not.  What are the odds that your marriage will end in divorce?  Sorry, national stats are really useless in this case, because you are not a typical person.  No one is.  Your background and personality (and that of your spouse) are unique, and they have everything to do with whether you two will decide to remain together.

One particularly frustrating (to me) use of bad statistics comes in the fine-tuning argument for a Creator.  This is based on the fact that there are 25 free parameters in the Standard Model; these are physical constants with values that can only be determined by experiments, not on the basis of some principle we know.  In several cases, a change of a few percent to one of these parameters might have caused the Big Bang to collapse on itself again, or for stellar nucleosynthesis to create a world in which no atoms are more complex than hydrogen or in which all stars are neutron stars.  In such a universe life as we know it would be impossible.  What are the odds that this happened by chance?

Once again, we do not have enough information to answer the question, and it is dishonest to pretend we do.  Since these are "free parameters", we obviously need additional information to determine their values -- but we also need additional information to know anything about the distribution from which they might be randomly chosen.

Dice (typical role playing game dice)  

Think of it this way:  Maybe the universe is the way it is because, Einstein notwithstanding, God did throw dice to determine the answer to the Ultimate Question of Life, the Universe, and Everything, and 42 was the number that came up.  We can further specify that all the dice were fair and identical, and that the most likely value for the throw was 63.  What are the odds that 42 came up?  The number will depend on whether it was 6 20-sided dice (6 x 10.5 = 63) or 18 6-sided dice (18 x 3.5 = 63).  Even in this simple example, if we do not know what kind of dice were used, we cannot answer the quesion.

Saturday, April 12, 2014

Marriage and Materialism

It has recently occurred to me that one of the main reasons that "gay marriage" has garnered so much public support is the widespread acceptance of materialism.  Before I go any farther with this, though, let me get a few things out of the way.
  • When I say materialism, I do not mean consumerism.
  • I find materialism entirely unconvincing, in part because only a spirit can be convinced or deceived.  To claim that we are bodies deceived into thinking that we have minds has always struck me as the most complete nonsense; it would make more sense to think we are souls deceived into thinking we have bodies, though I don't agree with that, either.  The point of this post is not the strengths and weaknesses of materialism, though, so I will leave it at that.
  • Acceptance of "gay marriage" is not determined by whether or not materialism is embraced.  The Soviets were materialists, but they remained basically sexually conservative.  Many Protestant clergy accept "gay marriage", but they presumably reject materialism. 
Anim engrenages droits

A good argument could be made that Americans (and Europeans) are, if anything, more superstitious now than at any time in the recent past, and that might seem to be at odds with them increasingly embracing materialism.  Not really, at least in this case.

Take, for instance, the fascination with "paranormal investigations". Even though they use the word "spirit", they have a very corporeal idea of what a spirit is:  they use conservation of energy to "explain" survival of the soul after death, they use conservation of energy; they look for them using electromagnetic field detectors; they try to explain why some places are haunted in terms of their vague understanding of the electrical properties of quartz and water.  They try to explain ghosts as phenomena of natural science, even though their "science" is merely pseudoscience.

Likewise, zombies and vampires are wildly popular, but they are almost always shown as people who didn't really die (though it may have looked like they did), but rather sufferers of some viral infection.  Science fiction/fantasy is not much better -- that genre consistently misreads "Any sufficiently advanced technology is indistinguishable from magic" to mean "Anything we can imagine magic might do can be done by a sufficiently advanced technology," and they proceed to make a weird mishmash of superstition and pseudoscience that fails to make any sense.  For example, in the Star Trek universe all humans are apparently atheists -- at least that was the story while Gene Roddenberry was still alive -- but (to name a few) the "prophets" or "wormhole aliens" from Deep Space Nine were functionally gods, as were the members of the Q Continuum.  At least they were more powerful than most or all of the Greek and Norse gods.  These beings may involve exotic materials, maybe materials that involve other dimensions (a la string theory), but it is always stated or assumed that material explanations (of some sort) are entirely sufficient.

In contrast, consider the objects of mathematics:  numbers, geometric shapes, etc.  Although we may have 1 apple, 2 apples, 3 apples, or whatever, certainly the numbers 1, 2, 3, ... do not exist physically, yet it is hard to shake the feeling that they somehow have an existence independent of us and that we discover them rather than invent them.  Not everyone agrees on this point; some think that mathematics does not describe a kind of non-physical reality, but that it only tells us something about how the way the human mind works.  To me, at least, that is very unconvincing; surely a civilization of intelligent aliens would know about the natural numbers (and all the integers, and the rational numbers, and the real numbers, ...) and Euclidean geometry (and hyperbolic geometry, and spherical geometry, ...).  The aliens would know that the ratio of the circumference of a Euclidean circle to its diameter is a constant, and that the value of that constant is an irrational number that is approximately 3.14159265.

It should be pointed out that just because we know the integers and the operations of addition, subtraction, multiplication, and division does not know that we know everything there is to know about them, nor does it mean that we cannot make wrong guesses about them.  Gödel's incompleteness theorems show that there are truths about the integers which we cannot prove axiomatically.  It is not yet known whether or not the Twin Primes Conjecture is true, though significant progress has been made on that question recently.  The Polya Conjecture has been shown to be wrong, as has the Mertens Conjecture.  The key thing is that if a conjecture can be proved to be true, like Fermat's Last Theorem was, then it is true everywhere, at every time, and for everyone; if it is proved to be false, it is false everywhere, at every time, and for everyone.

Those who claim that the Natural Law exists (I am one of them) insist that the Natural Law is something similar:  like mathematics, it exists independently of human opinion or knowledge.  In some ways, medicine might be an even closer analogy, because medicine is about humans (as the Natural Law is), is more contentious, and rarely if ever has the full rigor of mathematics (what does?).  Yet again, truth is not just a matter of opinion.  Even when it was believed that tobacco could cure cancer, it was still a health hazard.

It is silly to insist that serious materialists would be unable to use adjectives or verbs, but materialist philosophy taken seriously will impact how language is understood -- particularly the subjunctive mood.  "People should not smoke tobacco" would have to mean something like "Smoking tobacco leads to health problems, which most people and societies wish to avoid."  Even that formulation is a bit iffy, since "smoking tobacco" is an abstraction, and "people" and "societies" are universals.  A materialist might still be willing to use them (it is hardly possible not to), but he would consider the universals to be merely nominal -- just a name we impose for convenience, not a reality in itself -- that comes in handy for fuzzy thinking.

I think no reasonable person could insist that this is always wrong.  For example, it has become clear that there is no sharp distinction between a comet and an asteroid, or between an asteroid and a planet, or between a planet and a brown dwarf, or between a brown dwarf and a star.  It is very useful to have such words to narrow down what we are talking about, but no matter how we define these categories, there will be objects (not necessarily in our own solar system) that straddle the boundaries.  These words are names that we impose on nature, not ideas that we discover in nature.

Likewise, it would not be reasonable to insist that there is a universal ideal of American football that is discovered.  At any given time, there are several different sets of rules for American football -- at the high school level, the college level, and the NFL, for example -- and the details of the rules change from year to year.  It is probably a safe bet that no other society within the observable universe plays football with exactly the same rules set by the NCAA for the 2013 season.

My contention is that a materialist worldview has been widely absorbed by the public.  This would explain why some people clearly have so much trouble understanding that there are some parts of reality the government cannot change by passing a law or issuing a ruling from the bench.  The government can pass a law making it illegal to smoke tobacco, but if the government passes a law that the smoking of tobacco cures cancer, that law will have no effect.  In 1897, a bill was proposed in Indiana to establish by legislation based on a claim by Edwin Goodwin that he had discovered a way to square the circle (a known impossibility); the bill would also have had the effect of establishing one (or more!) different values of π from the one established by mathematics.  The bill did not pass, but even if it had, it would have changed nothing; as it is, it only made Indiana the butt of jokes.

The real disagreement, then, is over whether marriage is something with a fixed substance, or not; is it something like football, where we can change the rules as we please, or is it something like math, where we can't?   If many people today believe that all universals are merely nominal and that all laws -- of math and physics as well as the Congress -- express only the culture currently in power, it will be nearly impossible for them to understand, let alone persuade, supporters of traditional marriage -- and vice versa.

Every Child a Wanted Child?

Someone in Pakistan thought that was a good idea.

Monday, April 7, 2014

Proverbs 26: the Internet Chapter

Seriously, just read through it and think about what you have read in comments on blogs and news articles recently.  "Answer not a fool according to his folly, lest thou be made like him."  That's one for me; I am too often "made like him."  "As he that taketh a dog by the ears, so is he that passeth by in anger, and meddleth with another man's quarrel." We call these "trolls" today.

Sunday, March 9, 2014

A Century Later

Kaiser Wilhelm I

One hundred years ago, World War I started.  No one really wanted it to start, but all the key players in Europe had bound themselves up in such a way that they could see no way to avoid war without losing face.  The sad truth is that politicians, then and now, would rather see a disastrous war that kills millions than "lose face" by admitting they were doing something stupid.

Then and now:  because it's happening again.  When politicians compare Putin to Hitler, what does that do?  Well, do you negotiate with Hitler?  Heck no -- no one wants to be compared to Neville Chamberlain.  Do you defeat him and allow a negotiated surrender?  Apparently not:  the demand for unconditional surrenders extended World War II and cost many lives, but it was thought to be necessary.  

But how do you persuade a nuclear superpower to surrender unconditionally?  You don't.  Let's be clear on a couple of points here:
  1. Russia is a nuclear superpower.  They may have fewer nukes than in the past, but it's easily enough to cause several hundred million deaths.  If they wanted to, they could destroy the United States (at the obvious cost of being destroyed themselves).  The people who survived would no longer be "the United States".   Ditto for the European Union.  A superpower is defined not in terms of what it can create, but what it can destroy.  Superpowers can only be pushed around so much.
  2. We (the US, the West, whatever) did not "win" the Cold War, except in the all-important sense of surviving the Cold War.  Of course, in that sense, the Russians won, too.  It is true that the Soviet Union did not survive the end of the Cold War, but Ronald Reagan did not bring down the Soviet Union.  The Russian people brought down the Soviet Union.  If we keep getting this wrong, we will keep screwing up our policies in that part of the world.
If we are prepared to act like adults for a while -- what now?  What is needed is a compromise that gives everyone what they insist on and respects the realities of the situation.  I have two suggestions in mind.
  1. Russia leases the Crimea from Ukraine for 100 years.  The US leases Guantanamo Bay from Cuba, even though relations between the two countries have been terrible for decades.  Hong Kong was leased to the UK from China even during the Cold War.  The main advantage of this solution is that it acknowledges that Crimea is in principle a part of Ukraine (to soothe their pride) while also acknowledging Russian control.  Also, instead of a costly war, at least Ukraine would get something for the loss of control of Crimea.  This is my preferred option.
  2. Russia buys the Crimea outright, the way the US bought (for example) Alaska and the Louisiana Purchase.  Arriving at a fair price would be challenging, to say the least, but again Crimea gets something in return, as opposed to the huge losses that could be expected in a war.

Thursday, March 6, 2014

The Problem with News

Photo by Stefano Corso via Wikimedia Commons.

When it comes to factual data that is easily understood and of little long-term consequence, the synoptic news media can probably be trusted.  If they say that the current temperature of Buffalo, NY is 21 degrees Fahrenheit, or that last night Chicago beat Indianapolis 109-87, they're probably right.

When it comes to editorials and opinions, they are usually wrong and always untrustworthy.

The hard part comes with the in-between stories:  stories that are supposed to deal with facts, but facts that are not easily confirmed; stories that can take on a whole different appearance depending on what is reported and what is buried or on the precise choice of words; stories in which we are "supposed" to see that there are "good guys" and "bad guys", possibly due to the political, cultural, or geographic bias of the news organization, possibly just because such stories attract more eyes and ears.  In these in-between situations we may be getting "nothing but the truth" without getting "the truth, the whole truth", but more often we will have a few lies, mistakes, and insinuations mixed in even with the few limited truths we are given.

This comes up in situations like Syria and the Ukraine.

In the case of Syria, the narrative from most of the media is that Assad is a monster; the narrative from many Catholic and Orthodox sources is that the rebels are Muslim fanatics who murder Christians and desecrate churches.  The odds are that both are true as far as they go.  So what should "we", meaning the US, do?  Honestly, this is the kind of fight we should stay out of.  I slightly prefer the devil I know to the devil I don't know, but that doesn't mean I think we should help Assad.  Whoever wins will be morally problematic, and whoever wins will be in power only for a few years, eventually to be replaced by people who hate them.  There is NO SUCH THING as a long term in situations like this.  We're best off keeping everyone at arms length and not identifying with anyone.

In the case of the Ukraine, depending on who is telling the story it appears to be parallel to one of four precedents.

  1. The US invasion of Panama under Operation Just Cause.  The US had several reasons for this, but the nominal one was to defend US personnel in the Canal Zone.  At least the US did not annex Panama.
  2. The US annexation of Hawaii. It's hard to see this as really justified, and the US did seize the territory on the excuse of protecting Americans in Hawaii.  But at least the annexation stopped there, and over the long haul this has probably worked out to the advantage of the Hawaiians. 
  3. The German annexation of the Sudetenland. The "reason" for this was to protect ethnic Germans living in Czechoslovakia.  However, the annexations did not stop there.  Also, the annexation was not to everyone's advantage early on and ultimately was to absolutely no one's advantage.
  4. The German annexation of Poland, northern France, etc.  There was little attempt to present an excuse; Germany wanted the land and was able to take it, period.
The synoptic media make this sound like the annexation of the Sudetenland; Russian statements make it sound like Operation Just Cause; and American politicians make it sound like it might be most like the German annexation of Poland.  My guess is it's closest to the US annexation of Hawaii, but under the circumstances, it's just a guess.  It's based in part on the fact that although I am not quite sure what to think of Putin and contemporary Russia, I am very sure what I think about Barack Hussein Obama and the European Union.

Sunday, March 2, 2014

Once a German Professor, Always a German Professor


I am a great admirer of Pope Emeritus Benedict XVI, as I have been since I was first introduced to his writings in the late 1990's when I began to learn about the Catholic Faith.  He is obviously a man of great learning and wisdom.  However, like all of us, Benedict has been shaped by his experiences, and reading his writings it is often obvious that he was once a German professor.  

Often this shows in his selection and presentation of material.  One problem faced by a scrupulous  academic is that what he wishes to be both accurate and very precise.  All too often, this approach backfires.  Care for precision can sound like doubt, and the delay in coming to the point can be extremely frustrating.  Of course, this sounds familiar to those who know some German, in which language the meaning of a sentence is often impossible to guess until the last word.  More seriously, though, the bulky verbiage can be confusing to those not used to it, and especially to those (in the secular media, for example) who do not believe the fine distinctions represent important differences.

Another noteworthy characteristic of the German language is that it uses long words where English would use phrases.  The main practical difference is that we would tend to vary the phrase more than a German would find synonyms for the long word.  Also, these words tend to be logical to the point of being very funny.  For instance, in English we have a "wrist", but in German the same joint is called a Handgelenk (= "Hand Joint").  In English, we have a "glove", but in German gloves are called a Handshuh (= "Hand Shoe").

All these things stand out clearly to me as slowly work my way through the last encyclical that Benedict wrote alone -- Caritas in Veritate, or Charity in Truth.  The subtitle of this encyclical is On Integral Human Development in Charity and Truth, and the phrase "integral human development" occurs 21 times within the body of the text.  I'm not sure, but I suspect that the phrase works much better in his native German than it does in English.  Regardless, this and certain other stylistic elements have made this encyclical unduly difficult to work through.  Isn't there a better English expression for the same concept?

I think there is; I suggest the word "flourishing".  Flourishing has the connotation of robust, energetic, holistic growth -- growth for both the individual and the society, growth that encompasses the spiritual, physical, moral, cultural, and economic spheres.  This is the main gist of what Benedict was trying to say:  laws and policies must be designed to promote the flourishing of all affected parties, while in the process never doing evil that good may result.

This explains why so many Catholics saw this as an attack on Capitalism.  Even at its best, Capitalism has as its goal the prosperity of each participant, each looking out for himself, ideally while never doing evil that good may result.  If society as a whole also prospers, or if other affected parties prosper, it is a happy coincidence.  The same can be said of the other aspects of flourishing -- the moral and spiritual dimensions, for example.  Capitalism has, of course, provided greater material prosperity, though very unequally.  A quick glance at the headlines clearly indicates that it does not lead to great advances in the cultural, spiritual, or moral spheres.

It's a sad thing that I have to point out that this is by no means an endorsement of Socialism.  Nearly a quarter century after the end of the Cold War, many people are still stuck in the idea that there are only two possibilities:  unrestricted Capitalism or Socialism/Communism.  No; but trusting to dumb luck is not wise, and we can set the bar higher than the egocentric pusuit of material prosperity.