Wednesday, December 18, 2013

The Universe's Batting Average

People love simple numbers that serve as a measure of someone's level of success. When you are a high school student and you start worrying about getting into college, the first thing you find out is that colleges are primarily interested in two numbers: your SAT score and your GPA number. In the world of baseball, the all-important numbers are batting average (an indication of hitting skill) and ERA (an indication of pitching skill).

But is there any way to “scale up” this concept of “one number as a measure of success” concept? Can we compute a single number that we might call America's batting average? Or can we compute a single number that we might call Earth's batting average? I have no ideas on how someone might compute either of these. But I do have some ideas on how we might compute the universe's batting average.

My general strategy for computing the universe's batting average is as follows:
1. We identify some highly desirable physical occurrence, outcome, or characteristic, with great significance to life in the universe.
2. We calculate in what percentage of the cases that highly desirable occurrence or outcome happens.
3. We scale that percentage to get a statistic similar to the batting average (a number such as .500).
Let's look at three different ways in which we can apply this strategy.

Relevant Fraction #1: The Percentage of Galaxies That are Spiral Galaxies or Irregular Galaxies

Galaxies are collections of millions or billions of stars. There are three main types of galaxies: spiral galaxies, irregular galaxies, and elliptical galaxies.

Types of galaxies (Credit: NASA)

Elliptical galaxies can be considered rather inferior for two reasons. For one thing, most elliptical galaxies have relatively little free-floating gas and dust, and are apparently not forming new stars. This means that the very old stars that make up elliptical galaxies may not have enough of the heavy elements needed for life. It is believed that the amount of heavy elements in a galaxy is proportional to how many generations of stars there have been in that galaxy.

Also, from a purely esthetic standpoint, elliptical galaxies are lacking. Elliptical galaxies are just boring blobs that aren't nearly as beautiful as spiral galaxies.

Irregular galaxies and spiral galaxies do have lots of dust and gas, and do form new stars. So from the standpoint of life, we can regard both spiral galaxies and irregular galaxies as being more of a “sign of success” than elliptical galaxies.

The internet has differing estimates of the percentage of galaxies that are elliptical, spiral, or irregular. I will take this NASA web page as authoritative, and it says, “Like more than two thirds of the known galaxies, the Milky Way has a spiral shape.” Other sources say that 70% of the galaxies near our galaxy are spiral galaxies. We can therefore estimate that the total percentage of galaxies that are spiral or irregular (not elliptical) is about 70%. This gives us our first batting average for the universe.

Cosmic Batting Average Number 1: .700

This percentage is actually one of the most important success indicators of the universe. There are quite a few reasons why slightly different cosmic parameters (or slightly different laws of nature) would have resulted in either zero galaxies in the universe or a very low fraction of life-favorable galaxies.

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Relevant Fraction #2: The Percentage of Stars That Have Planets

Another important fraction-type indicator of the degree of success of a universe is the percentage of stars that have planets. Of course, it wouldn't do any good to have a beautiful spiral galaxy if there weren't any planets revolving around the stars in that galaxy (or at least the only good of such a galaxy would be the esthetic good its beauty would provide to observers in other galaxies).

Before it developed problems with its gyroscopes, the Kepler Space Telescope did years of observations that allow us to estimate the percentage of stars having planets. There is also a technique called microlensing that astronomers have used to detect planets revolving around other stars. One recent scientific paper by a large team of scientists stated: "We conclude that stars are orbited by planets as a rule, rather than the exception." Based on that study we can estimate that at least 60% of stars have planets, which gives us the following batting average:

Cosmic Batting Average Number 2: .600

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Relevant Fraction #3: The Percentage of Natural Elements That are Non-Radioactive

Another very important fraction-type quality indicator of the universe is the percentage of elements that are non-radioactive. If a large majority of the elements were to be radioactive, it would be incredibly difficult to have much of a life living in our universe. You might live for a short time, but all that radioactivity would quickly give you cancer, so you wouldn't live for long.

Since you know that most people older than ten do not have cancer, you can guess what the answer is here. The percentage of naturally occurring radioactive elements is only about 20%. There are some 98 naturally occurring elements (or 92, according to other estimates). Some 80 of these elements are not radioactive. (In any case in which an element has a stable isotope and a rare but radioactive isotope -- for example, carbon—I am counting that as a non-radioactive element.)

Since there are about 98 naturally occurring elements, and about 80 naturally occurring non-radioactive elements, the percentage of non-radioactive elements is roughly 80%. This gives us our final batting average:

Cosmic Batting Average Number 3: .800

I may note that we should not at all take for granted that we live in a universe with relatively little radioactivity. You could modify the universe's fundamental constants just a little, and we would not be so lucky. A decrease of only about 20% in the strong nuclear force would cause almost all elements to be radioactive. If that were the case, you would probably not reach the age of 20 without dying of cancer.

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Conclusion

If we add up these three numbers and divide by three, we get an average number of .700. So that is our final estimated batting average of the universe: .700.  As batting averages go, that is very good (much better than Ty Cobb's lifetime average).

There are two other important fractions that would be nice to learn to make a more definitive calculation of the universe's batting average. The first fraction is the approximate percentage of Earth-sized planets (in the habitable zone of a star) where life appears. The second fraction is the approximate percentage of life-bearing planets on which intelligence evolves. Both of these fractions have a great importance when considering the overall “degree of success” that the universe has. Unfortunately, we currently do not know what either of these fractions are. They could have any value between .000000001 and .999.

We might one day have a basis for estimating these fractions, particularly if we ever achieve radio contact with extraterrestrial civilizations. But for now the value of these fractions is completely unknown. So it will be a good long time before we can make a more definitive calculation of the batting average of the universe. All that can be said for now is that the preliminary indications are that the universe's batting average is very high.