Category Math

Is ISIS’s popularity low? Hard to Tell

The Washington Post reported on a Pew survey of countries with a significant Muslim population, asking whether people there have a positive or negative view of ISIS:

FT_15.11.17_isis_views
Pew survey of countries with a significant Muslim population, spring 2015.

As the graph shows, in every country, ISIS is unpopular, by huge margins (and I find it interesting that according to the same survey, attitudes vary more from country to country and between religions; but I’m not sure that’s important right now).

But there’s low, and then there’s low. I wouldn’t drink water that was “only” 1% arsenic (the EPA limit is a million times smaller than that), and if there were “only” a 1% chance of crashing every time I got on the Beltway, I’d likely be dead within a year. So there’s small and then there’s small.

If the KKK enjoyed the same level of popularity in Alabama as ISIS does in Turkey, above, it wouldn’t be reported as “KKK only has minority support”. It would be reported as “One in 13 Alabamans still supports KKK”.

So I’d like to see some figures for comparison: how popular is ISIS compared to, say, the Lord’s Resistance Army, or Nazis, or the Tutsi army? Maybe they have comparable levels of popularity, and the double-digit favorability numbers are statistical artifacts. And in fact, it seems that the fact that its popularity varies more from country to country, than from religion to religion within the same country, points at this explanation.

But my fear is that ISIS really does enjoy insufficiently-low popularity.

Catholic Church 99 44/100% Pure

BillDo has a post in which he plays down the Catholic priesthood’s image problem:

Catholic League president Bill Donohue comments on the findings of the 2011 Annual Report on priestly sexual abuse that was released by the bishops’ conference; the survey was done by a Georgetown institute:

The headlines should read, “Abuse Problem Near Zero Among Priests,” but that is not what is being reported.

According to the 2011 Official Catholic Directory, there are 40,271 priests in the U.S. The report says there were 23 credible accusations of the sexual abuse of a minor made against priests for incidences last year. Of that number, 9 were deemed credible by law enforcement. Which means that 99.98% of priests nationwide had no such accusation made against them last year. Nowhere is this being reported.

If that’s his standard of purity, then I’m sure Bill would have no problem drinking a glass of 99.98% water and only 0.02% urine, right?

The thing is that very few men in general are child abusers. The question (or one question) is, does the Catholic clergy contain more child abusers than the population at large?

I wasn’t able to quickly find child-abuse statistics for the United States, but I did find the FBI’s Uniform Crime Reporting statistics for violent crime in 2010, which shows an aggregate of 27.8 forcible rapes per 100,000 victims. The FBI defines “forcible rape” as:

The carnal knowledge of a female forcibly and against her will. Rapes by force and attempts or assaults to rape, regardless of the age of the victim, are included. Statutory offenses (no force used—victim under age of consent) are excluded.

So the numbers are not directly comparable: the report Donohue is quoting concerns itself only with sexual abuse of minors, while the FBI’s number covers all rape. The FBI’s 2010 number excludes sexual abuse of males, while BillDo emphasizes that in the report he’s quoting, “almost all the offenses involve homosexuality“. And BillDo calculates the rate per offender while the FBI counts the rate per victim, which means that BillDo’s number tends to undercount priests who abused multiple victims, compared to what the FBI counts.

Having said that, BillDo’s figure of 9 credible accusations and 40,271 priests works out to 22.3 per 100,000, compared to the FBI’s 27.8 per 100,000. So the number of pedophile priests seems to be in the same ballpark as the number of rapists in the US as a whole. That seems pretty bad, especially for a group that presents itself as the guardians of morality.

BillDo also ignores, as usual, that the Catholic church’s problem is not so much one of having rapists in its ranks — any large organization is bound to have some — but of covering up its members’ crimes. The abuse itself can be blamed on individual priests, sure. But the coverup is a problem for the organization.

What’s Three Orders of Magnitude Among Friends?

(Alternate title: “Numbers Mean Things”.)

The increasingly-irrelevant Uncommon Descent blag had a post today, commenting on an article in Science News.

Right now, UD’s post is entitled “Timing of human use of fire pushed back by 300,000 years”, but when it showed up in my RSS reader, it was “Timing of human use of fire pushed back by 300 million years“. This mistake survives in the post’s URL:
http://www.uncommondescent.com/human-evolution/timing-of-human-use-of-fire-pushed-back-by-300-million-years/

From skimming the Science News article, it looks as though a new study found evidence of fire being used one million years ago, pushing back the earliest-known use of fire by 300,000 years. So presumably the previous record-holder was 700,000 years ago.

The author at Uncommon Descent reported the 300,000-year difference as “300 million years”. But hey, what’s a factor of 1000 between friends?

To illustrate, imagine a student in school in 2012, writing a report about, say, e-commerce. At first, she dates the origin of e-commerce to 1994, when Amazon.com was founded. But upon further investigation, she finds an example of a company selling stuff on the Internet in 1987 and revises her report to say that e-commerce is 25 years old, not 18. That’s about the magnitude of what the scientists found.

Now, along comes UD and reports this as “Origin of e-commerce pushed back to 22,000 BC.” That’s the size of their mistake.

It’s easy to make fun of primitive people whose counting system goes “one, two, three, many”. But the truth is, we all do this to some extent. Imagine a newspaper headline that says, “Federal budget increases by $600 billion, including $300 million increase in NASA funding.” Did you think, “holy cow! NASA got half of that extra money!”? If so, I’m talking to you: you’re not counting “one, two, three, many”, but you are counting “ten, hundred, thousand, illion”.

At any rate, I still question the numeracy of whoever wrote that UD headline. If you’re going to spell out “million” in letters, it should trigger a reality-check mechanism in your brain that makes you ask, “Wait a sec. 300 million years ago. That’s the age of dinosaurs or earlier.”

Numbers Mean Things

So I saw this headline in The Washington Post:

UN envoy says $5 billion malaria fight has saved several thousand lives in recent years

My first thought was, “$5 billion divided by, let’s say 5000 people, that comes out to a million bucks per person saved. A noble result, to be sure, but isn’t there a more cost-effective way of achieving the same result?”

Then I read the first paragraph:

UNITED NATIONS — The U.N. chief’s envoy for malaria says a $5 billion campaign has saved several hundred thousand lives in recent years, keeping international efforts on track to virtually end deaths from the mosquito-borne disease by 2015.

(emphasis added) and now the cost per person drops two orders of magnitude, from $1 million to $10,000. Much more reasonable (though it’d still be nice if it were even cheaper).

But I suspect that either the reporter, or someone at AP or WaPo decided that the word “hundred” didn’t change the meaning enough to make it worth taking up valuable headline space. I’m sorry, but it does.

Then again, what’s two orders of magnitude among friends?

(Cross-posted at UMDSI.)

Answer to the Saturday Puzzle

On Saturday, I gave the following puzzle:

Can you make the following equation correct by moving just one number?:

45 – 46 = 1

Answer below the jump. Read More

Saturday Puzzle

I love Richard Wiseman’s Friday Puzzles. So as a tribute of sorts to this one, here’s one of my own:

Can you make the following equation correct by moving just one number?:

45 – 46 = 1

I’ll post the answer on Monday.

Fact-Checking the BillDo

Recently, BillDo farted the following onto the intertubes:

Moreover, Jenkins wrote that “Out of 100,000 priests active in the U.S. in this half-century, a cadre of just 149 individuals—one priest out of every 750—accounted for over a quarter of all allegations of clergy abuse.” In other words, almost all priests have never had anything to do with sexual molestation.

(italics in the original).

Just for comparison, the Wikipedia page for Crime in Detroit, Michigan, says that the murder rate there was 40.1 per 100,000 people in 2009.

Assuming that each murder was committed by a different person, this means that about one Detroiter out of every 2500 accounted for all of the murder in 2009. In other words, almost all Detroiters are not murderers.

So by BillDo’s reasoning, Detroit does not have a murder problem. Good to know. Presumably if I gave him a glass of water with only one part of arsenic in 750, he’d drink it.

Snakes on A Euclidian Plane

Via A., here’s a cool video about doodling in math class, that somehow keeps circling back to knot theory:

[youtube http://www.youtube.com/watch?v=heKK95DAKms&fs=1&hl=en_US]

This should be required viewing for anyone who doesn’t see what the appeal of math is, or who thinks math is only about numbers and formulas.

My favorite line is the one about the two snakes who can’t talk to each other because one only speaks parseltongue, and the other only Python.

What Good Is Math?

I think most people, if you asked them, would say that teaching math in school is a good thing. If you ask why, the usual answer is something like, it allows you to figure out how much carpet and wallpaper you need to buy to redecorate your living room, to determine whether the 12-can pack of ravioli at Costco is cheaper than what you can find at Safeway, and so forth.

But that’s all elementary and High School level stuff: arithmetic, geometry, a dash of algebra. I’ve rarely used trigonometry after college, and I know one person who used calculus in quilting. I think it’s safe to say that most people never use calculus, differential equations, prepositional logic, etc. after college. But I still say there’s value in studying math beyond the practical.

Let me ask a contrasting question: why should kids play sports in school? Only a tiny minority of them will make a living playing or coaching sports, and less than half will even play on the office softball team or the like.

The answer I get most often is that sports teach teamwork: how to subsume your immediate desires for the greater good, make sure you do your part and trust your teammates to do theirs, and communicate effectively to make sure you’re not working at cross-purposes. You learn to win graciously and learn from your failures.

In other words, it’s not so much that playing sports develops muscle tone and general fitness. But rather, it’s an indirect way of teaching other skills like cooperation. They may not be taught explicitly, and there are other ways of teaching them, but this works.

The same thing, I think, applies to math. A few years after learning it, you probably won’t be able to prove that there is an infinite number of primes, or how to integrate a function. But that’s okay, because math teaches skills other than the purely pragmatic.

Proving theorems, for instance, forces you to distinguish between what you think is true, and what you can demonstrate; what looks right, and what is right. Geometry teachers always admonish students not to reason from the diagram because concrete examples are often misleading: just because line AB is perpendicular to line CD in this drawing doesn’t mean that that’s always the case. The point is to figure out what’s universally true, not just what’s true about this particular instance.

These are skills that apply to non-mathematical professions: judges and lawyers often deal with people who have clearly done something wrong, and need to distinguish between “I know that ain’t right” and whether the action in question is legal or not. Police officers likewise need to know the difference between “I know Jimmy’s been selling crack to students” and “I can prove to a jury that Jimmy’s been selling crack”. Programmers will find that they write code that works in situations that they didn’t imagine, because it’s a truism that end users will do weird things with your software that you never dreamed of. Financiers should be able to put together a portfolio that can survive unexpected catastrophic changes in the market. (And as much as it pains me to defend the Bush administration, Donald Rumsfeld was quite right in distinguishing between “known unknowns” and “unknown unknowns”, and trying to plan for both.)

Or take the discussion about defining information in the “I Get Email” thread; specifically, the exchange between Tom and Troublesome Frog on whether all living beings contain information. It seems that Tom doesn’t quite get the difference between ∀ x ∀ y p (no matter how you define information, all living beings contain information) and ∃ x ∀ y p (we can come up with a definition of “information” such that all living beings contain information).

Math is very big on abstraction. This starts in algebra, which is all about figuring things out about things that you know you don’t know much about. And it just gets more abstract from there. The first time you demonstrate that there is no solution for some equation, or better yet, that there can be no proof of a given proposition, can be quite a thrill.

And abstract thought is one of those things we humans are good at. It’s what allows us to formulate moral rules that apply to everyone, and see things like “the market” instead of a bunch of people trading stuff. It seems that we ought to learn to do it well.

One of my favorite types of SAT question is the one that presents a math problem, and one of the possible answers is “not enough information to solve the problem”. The lesson here isn’t just “know your limitations”. It also shows that just because something looks solvable doesn’t mean that it is; that just because something is printed in an official-looking book doesn’t make it kosher. And also, the sooner you figure out that a problem has no solution, the less time you’ll waste looking for one.

Finally, one thing that everyone should get out of any math class is that you can figure stuff out on your own, without looking the answers up in the back of the book. Yes, the same is true of science and other classes, but math is one of those branches where you don’t need fancy equipment to work on a problem and figure out the solution.

One problem I see is that a lot of people seem to think that knowledge is something that is handed down from on high, rather than something that can be created. This seems to be at the root of the claim that evolution is just another religion: “I have my priests who tell me that God created humans, and you have your priests who tell you humans evolved. The only difference between creation and evolution is which team you’re on.” There’s no arguing with someone who simply repeats what they were taught; but if you’re in an argument with someone who thinks that mere mortals can work out answers on their own, you might get somewhere. And that’s something we could use more of.

Genetics and Collectible Card Games

Let’s say I’ve started collecting cards, like Magic: the Gathering, or baseball cards. Yesterday, I bought a pack of 100 random cards. Today, I bought another pack of 100 random cards. 5 of them were duplicates of cards that I already had from yesterday.

Question: how many distinct cards are there in the game? I.e., if you wanted to collect the whole set of cards published by the game company, how big an album would you need? Read More