Category: Statistics
Stunning gun statistics
The following statistics come from an article in the Minnesota Post:
680 Americans were killed accidentally with guns each year between 2003 and 2007.
46 Americans committed suicide with guns each day between 2003 and 2007
Two-thirds of all murders between 2003 and 2007 involved guns. The average number of Americans shot and killed daily during those years was 33.Children in the U.S. get murdered with guns at a rate that is 13 times higher than that of other developed nations.
Carbon-14 Itself Argues for an Old Earth
I was reading The Cosmic Story of Carbon-14 and had a thought involving the Abundance of the Elements and isotopes. We now know how the elements formed, and have measured their relative abundances for a while and across the universe. The theory of how they form matches every measurement. Basically, Hydrogen and traces of Helium have been around for over a dozen billion years. Heavier elements form when the mass attraction of enough hydrogen squishes a star’s core to fuse together helium and some lithium, a star is born.
All the rest form from the extreme compression and sudden release of supernovas. All that hydrogen and helium (basically protons and neutrons as there are no attached electrons at those pressures) are squeezed to dissolve into a quark soup then expanded and quick-frozen before they can push themselves apart. What is expected from this is an asymptotic curve of element abundances with hydrogen at the high end, and slight peaks forming at iron, xenon, and lead (particularly stable elements).
This is what is measured in our solar system:
Don’t let the zig-zag pattern confuse you. Odd numbered elements are harder to hold together than even ones; each pair of protons needs a pair of neutrons to let them stick together. But odd numbered ones have that odd pair of singles; they are just less likely to form.
But how does Carbon-14 fit in? What really freezes out from the splash of quark soup is not so much elements as isotopes. Every possible isotope forms in its proportional place along the curve. Then the unstable ones follow a decay chain until either they reach a stable element, or we measure them somewhere along the way. Uranium, for example, has 3 isotopes that last long enough to have hung around the 5 billion years or so for us to measure them. Technetium, on the other hand, is only found today as a decay byproduct from other elements.
So back to carbon. The three most common isotopes of carbon weigh 12, 13, and 14 atomic units (aka fermion masses: neutrons or protons). C-12 is most of it, C-13 is 1.1%, and C-14 is about 1/1,000,000,000,000 part of it. Carbon 13 is an odd-numbered isotope, and therefore intrinsically rare. Carbon-14 has a half life of 5,730 years. So if it were created in the expected normal proportion to carbon-12 billions of years ago, we would expect to not see any left. Where it all comes from is recent nuclear collisions between protons (cosmic rays) and nitrogen in the upper atmosphere. (More details here).
We see the amount of carbon-14 that we’d expect for a regular continuous influx of cosmic rays that we do measure. But if all the elements had been made 10,000 years ago, we’d expect about C-14 to be about 1/4 of the total carbon, not the mere 1/1012 of it that we know is produced by cosmic ray collisions.
It turns out that comparing the abundance of isotopes of any element indicates the age of the planet to be between 4,000,000,000 and 5,000,000,000 years.
But what (I can predict this argument) if God created the elements with the isotope distributions intentionally skewed to just look like everything is that old? The old God-is-a-liar and created the young world old to eventually test faith of careful observers argument. I counter this with:
Given God and the Devil, which one has the power to put consistent evidence in every crevice of this and other planets and throughout the universe for every method of observation in every discipline for all interested observers of any faith,
and which one might inspire a few men men to write and edit a book and spread its message eagerly that can be interpreted to contradict that massive universe of evidence?
The real risk of an American dying in a terrorist attack
Comedy Central’s Indecision presents some rather unsurprising statistics that need to be read by every member of Congress. What is an American’s likelihood of dying from a terrorist attack?
According to government statistics, roughly as many Americans are killed annually by unstable furniture and falling televisions as are killed in terrorist attacks.
What else is more dangerous than a terrorist attack?
16 oz. sodas, inconvenience of going through TSA security at an airport (which discourages many people from flying, causing them to die on the highways), use of your bathroom, texting, autoerotic asphyxia, alcohol and tobacco, weather, suicide, hospital infections and doctor errors and stress.
One more thing: What is the risk of an American dying in a terrorist attack? Ronald Bailey of Reason suggests a very liberal estimate (an estimate assuming death to be more likely) would be 1 in 1.7 million, and he offers these additional statistics:
Taking these figures into account, a rough calculation suggests that in the last five years, your chances of being killed by a terrorist are about one in 20 million. This compares annual risk of dying in a car accident of 1 in 19,000; drowning in a bathtub at 1 in 800,000; dying in a building fire at 1 in 99,000; or being struck by lightning at 1 in 5,500,000. In other words, in the last five years you were four times more likely to be struck by lightning than killed by a terrorist.
This same article indicates that the U.S. spends $400 million dollars per life saved in antiterrorism security measures (cost$1 Trillion since 2001), but this number doesn’t include military expenses by the United States. It’s also important to keep in mind that the U.S. spends more on maintaining a military than the rest of the world combined.
Perhaps if Americans weren’t so afflicted with innumeracy, we could accept the true (miniscule) risk of dying from a terrorist act, and focus on preventing much more likely forms of death. Perhaps we could spend a significant chunk of that “anti-terrorism” money to combat innumeracy.
Al Qaeda injures or kills 1.2 million Americans every year
Ooops. What I meant to say was that because Americans choose to text or talk while driving, Americans cause 1.2 million traffic accidents per year. Many of these accidents cause serious injuries and deaths. As the linked article states, many of these tragedies are caused by people who are yapping or texting while on-the-job for an American business.
I’m waiting to hear our politicians announce a war on cell phone use while driving–an all-out war employing check points, high tech surveillance and violations of fundamental civil liberties.
This war won’t happen, though, because these injuries, like 99% of the problems America currently faces (these things include wildly out-0f-control obesity, repealing Glass-Steagall and gutting the First Amendment) are self-inflicted. Further, our calculus for deciding public policy is mostly geared to finding an other to blame. In America, a tragedy caused by someone deemed to be an outsider is 1,000 times more “serious” than a tragedy caused by an American. The needless injuries and deaths due to cell phone use constitute Exhibit A.
The size of many things, large and small
I’ve seen similar websites allowing you to compare tiny and large things of the world, but this is a new one called “The Scale of the Universe.” I spent ten minutes enjoying the comparison, then decided to share the link to the site.
Here’s one thing that I noticed for the first time: The distance from the Earth to the Moon is 250,000 miles. If you traveled that long distance, starting from the surface of the sun, traveling toward the center of the sun, you’d be only 1/3 of the way through the sun.
The facts regarding unintended pregnancy
Guttmacher Institute has released a Fact Sheet on unintended pregnancies in the United States. Here’s what I learned:
Most American families want two children.
About half (49%) of the 6.7 million pregnancies in the United States each year (3.2 million) are unintended.
By age 45, more than half of all American women will have experienced an unintended pregnancy, and three in 10 will have had an abortion.
Unintended pregnancy rates are highest among poor and low-income women, women aged 18–24, cohabiting women and minority women. In 2006, black women had the highest unintended pregnancy rate of any racial or ethnic groups.
In 2006, 43% of unintended pregnancies ended in abortion and 48% ended in birth.
Compared with higher-income women, poor and low-income women are less likely to end an unintended pregnancy by abortion.
In 2006, two-thirds (64%) of the 1.6 million births resulting from unintended pregnancies were paid for by public insurance programs, primarily Medicaid.
Total public expenditures for births resulting from unintended pregnancies nationwide were estimated to be $11.1 billion in 2006.
Two-thirds of U.S. women at risk for unintended pregnancy use contraception consistently and correctly throughout the course of any given year; these women account for only 5% of all unintended pregnancies. In contrast, the 19% of women at risk who use contraception inconsistently or incorrectly account for 43% of all unintended pregnancies. The 16% of women at risk who do not practice contraception at all for a month or more during the year account for 52% of all unintended pregnancies.
Without publicly funded family planning services, the number of unintended pregnancies and abortions occurring in the United States would be nearly two-thirds higher among women overall and among teens; the number of unintended pregnancies among poor women would nearly double.
What is randomness?
Radiolab’s show on “Stochasticity” offers entertaining examples to explain the concept of randomness. The story starts with the example of a 10 year old girl named “Laura Buxton” who released a balloon with a message: “Return this balloon to Laura Buxton.” The girl who received the balloon when it came down many miles away was another 10 year old girl named “Laura Buxton.” There were many other coincidences between the two Laura Buxtons.
Contrary to the assumptions of most people, randomness involves results that look like patterns. What about getting seven heads in a row? If you were only flipping the coin seven times, this can happen only one time out of 100, but if you get seven heads in a row somewhere in the process of flipping a coin 100 times, you can expect this to happen one time out of six, not improbable.
Another example is the case of Evelyn Adams, who one the lottery twice in two consecutive years. If you look only at whether this will happen twice with the purchase of two tickets, it would only happen once in 17 trillion times. If you consider the entire universe of people who buy lottery tickets, the question becomes “what are the odds that somebody somewhere will win the lottery twice?” The answer to that question is that it would be surprising if that didn’t happen repeatedly, and it has happened repeatedly (listen to minute 17 of the show).
The lesson? (at minute 19) “If you don’t see past yourself [to look at the big picture], you become prey to superstition.”
In the case of the Laura Buxtons, the story becomes much more interesting when we focus only on the similarities of the two girls and downplay the many many things they don’t have in common. But of course, listing their dissimilarities would not have been a good story, yet we prefer to believe in “magic” (see min 20).
See also, this post on patternicity.
Extremely long odds say that you should not exist.
For me to exist, my mother and father had to meet each other, which is a rather unlikely thing to have occurred in the scheme of things. Even assuming that they met, they would also need to mate at just the right time, and then the right sperm (out of hundreds of millions in each ejaculation) had to fertilize the right egg (or which there were many thousands of candidate eggs). But the same thing had to happen to each of their parents, and their parents, and so on. How many sets of parents did this need to happen to? Quite a few–consider my earlier post, “Ancestors Along the highway.” Before all of those parents came onto the scene, the right non-human ancestors had to meet and mate, and before them . . . [skipping way back] the right sponges had to have offspring, and the fungi before them. Had any of these organisms been eaten as prey prior to having offspring, I wouldn’t be here. If any of them had succumbed to disease prior to having offspring, I wouldn’t be here. If any of them had broken a leg or gotten lost in the forest, they might not have gotten around to mating on that critically important date and time (from my perspective). The adventures of Marty McFly (“Back to the Future”) barely scrape the surface.
The seemingly impossible hurdles faced by each of us are addressed by a well-constructed website, “What are the Odds,” which stirs quite a bit of eye-popping mathematics into the description. Wait until you get to the bottom of the page to read about the trillion-sided dice.
Actually, “What are the Odds” overstates the odds that you or I would exist, because there’s far more to being “you” than your biological substrate. If you were raised in a war-torn region rather than a suburban American school, you would be a very different version of you. And ask yourself whether you would be you even if a few of your closest, most influential friends or acquaintances weren’t around to influence you. Or what if you hadn’t happened to read some of the ideas that most influenced you, or if even one or two of those important character-building events that defined you (joyous or tragic or in between) hadn’t occurred?
Thus, it’s almost impossible that you should be here reading this post. Then again, you are here, because all of the antecedent events necessary to make you actually did occur.
I don’t know what lesson one is supposed to draw from this idea that it is essentially impossible that you should be here. Perhaps it’s merely an excuse for a healthy dose of humility. It also seems to me that working through this thought experiment is good for one’s mental health, at least once in a while. I consider it an existential vitamin that I should take periodically.
The wrong type of math
In this three-minute talk, Mathemagician Art Benjamin urges that we change our emphasis when we teach our children math. I couldn’t agree with him more.
It saddens me to consider the immense amount of self-inflicted damage that Americans could have avoided, if only they were more savvy regarding probability and statistics. For example, very few Americans die of “terrorism,” whereas the lives of millions of Americans are severely damaged or destroyed every year by crappy schools, lack of health care (including the failure to obtain colonoscopies), wars begun on the basis of lies, various risky behaviors and many other problems almost too many to mention, all of which leave the actual danger of “terrorism” in the dust. Yet Americans spend a massively lop-sided portion of their tax-dollars each year preventing “terrorism.” Each of the serious causes of death we face would be much more preventable if only Americans had a better grasp of statistics and probability. With better training in statistics and probabilities, Americans could better understand the risks that they faced and the probabilities of success of various proposed “solutions.” With better training, as Art Benjamin suggests, we would be better able to order our national priorities to better prevent the things that are most likely to harm us.
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