RIP Martin Gardner

More than any classroom teacher I ever had, Martin Gardner shaped my mathematical interests. "For 35 years, he wrote Scientific American's Mathematical Games column, educating and entertaining minds and launching the careers of generations of mathematicians"

I learned that he died on Tuesday. Only two days before, I stood in the front yard of my Mother's home in Fort Worth and told Alex, my sister's grandson, aged 12, that if he wanted to nurture his curiosity for math and science he should find anything in the library by Martin Gardner and read it every year for the next ten years of his life, and each year, I promised, he would find something new in the reading.

I can not do justice to the life of a man who was the mathematical Pied-Piper of mathematics for a generation of us; so here is link to the article in Scientific American.

The rumors of my death have been greatly exaggerated?

After several inquiries, I thought I should admit that I am alive and well, but not finding much time to blog. I am attending to my beautiful sweetheart while she has a minor surgery and along the way trying to teach my two AP classes some extended "after the exam" topics from five time zones away.... go ahead, try to get up and teach at 3am.... I am not at my best at that time...and I really need to have them see my hands wave....

My stats kids are doing some stuff on game theory, and the calc kids are exploring Topology...

Doing all this over a well-secured but not always compliant military connection has required extreme patience on the part of my students, my very capable substitute teacher, and occasionally even I have had to monitor my temper bursts...
I promise to roar back soon and blast away with my trivia/mathematica...

In the meantime, if you haven't seen Dan Meyer's talk on Ted.... check it out...he is one of my favorite bloggers, and the video will show why...

A Guest Blog (Rant?) from Dave Renfro

I mention Dave a lot here because his regular supply of interesting journal articles from today back 200+ years has been a major source of my continuing education in the last few years... Dave sent me a copy of a recent set of remarks he had written about recent posts related to Pi day. Actually Dave calls it a "rant" but we should all keep in mind that he is NOT referring to MY pi-day post (That's right, isn't it Dave.....DAVE? Talk to me Dave?)
Anyway, here is Dave's guest post, and I greatly appreciate him letting me be the on-line voice for his ideas this time.
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I've mostly tried to not read anything about pi day, but in two cases I failed, with predictable results.
In the March 8-12 issue of "The Chronicle of Higher Education" there is an article about pi day titled "A Small Number With a Big Following". At one point in the article I saw the following comment:

"pi--so tiny (it's closer to three than four) yet random and infinite (as far as anyone knows)."

A question immediately occurred to me. Given the readership audience, which consists mostly of academic Ph.D.'s, why say something as meaningless and silly as this?

"random" -- What does that mean? I guess when computers calculate the digits of pi they're just randomly guessing what the digits are and then someone comes along and checks (how, nobody knows) to see if the digits are correct. Also, there are plenty of clearly non-random-looking sequences of arithmetic operations that generate pi, such as 4 - 4/3 +
4/5 - 4/7 + 4/9 - ... Unlike the CHE writer, some of us don't think the only way to represent a real number is by (integer) + a/10 + b/100 + c/1000 + ...

"infinite" -- If they mean the decimal expansion is infinite, then so too is the expansion of 1/3, the expansion of 1/7, etc. Maybe they mean that pi can't be described in a computable way, like Chaitin's constant "omega", except everyone knows pi is computable in very simple ways (as far as computability theory measures of complexity go), or do they?
Perhaps not everyone can type "pi" into Google and skim the pi Wikipedia page (the top hit when I tried this).

I think I know what they wanted to say, which was that no one knows whether, for each n, all possible n-digit strings appear in the decimal expansion with the same limiting frequency, although all computer explorations into the digits of pi seem to suggest this. Of course, they might want to express it a little less mathematical than this, but still
get the point across. As for saying "infinite", that's silly and a waste of words. Besides, it's automatic if you say something along the lines of what I just said, not to mention that everyone learns in 10th grade geometry (probably in 7th or 8th grade math books by now) that pi is irrational. Personally, I think knowing pi is irrational and what that means regarding decimal expansions is at least equivalent to knowing some of the literary references and schools of thought that get mentioned in their other articles without batting an eye. But you see, it's O-K in educated circles to say "economic determinism", but you don't ever want to say "irrational number".
The other article I saw showed up on March 12 at the CNN internet news
page:
http://www.cnn.com/2010/TECH/03/12/pi.day.math/index.html
The article is titled "On Pi Day, one number 'reeks of mystery'", and surprisingly it seems to be pitched at a higher mathematical level (probably 8th or 9th grade) than the Chronicle of Higher Education article (about 6th or 7th grade). Here is an excerpt from the CNN article:

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Mathematicians know that pi is irrational -- it cannot be represented as one number divided by another -- and transcendental, meaning it is not algebraic. That means, theoretically, that its digits will continue on indefinitely without ending in repetition -- in other words, the digits won't suddenly continue infinitely as 5s after 3 trillion digits (Pi's digits were calculated out to a record 2.7 trillion places in December
by French computer scientist Fabrice Bellard).

That also means, mathematicians theorize, that any string of numbers you can imagine is somewhere in pi -- for instance, look for your birthday. Coincidentally, "360," the number of degrees in a circle, occurs at digits 358 to 360. (Pat here..how cool, I did not know that... I know that it's a coincidence, but I love it)

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Right off the bat, in the first sentence, we have something any good middle school student would question -- isn't pi equal to pi divided by 1, and hence pi can be represented as "one number divided by another"? O-K, so the editor was asleep on that part. Let's continue. What's with this "theoretically" part? The digits of any irrational number (it's
worded as if you need to know that pi is both irrational and transcendental to conclude this, which is also an editorial oversight)continue indefinitely without being periodic, period. Then, in the next paragraph, we have another editorial flop. It's written as if the fact that pi is an irrational number (and maybe also the fact that pi is a transcendental number, an ambiguity we're left to figure out on our own)might mean that pi contains every finite string of digits, which of course isn't true -- plenty of irrational (and even transcendental)numbers have this property and plenty don't. Mathematicians theorize that pi might have this property, and even the much stronger limiting frequency property of these digit strings that I mentioned earlier, but to say that mathematicians theorize this on the basis of pi being irrational is extremely misleading. I think the author just wanted to write "This also means" because it sounded like a good transitional phrase, without worrying about what the phrase actually meant, and apparently the editor didn't worry about what it actually meant either.

And finally, what's up with saying "transcendental" means "not algebraic"? Does the author really think anyone who doesn't know what a transcendental number is will be helped by saying this is a number that isn't algebraic? I found this especially puzzling in view of the fact that in practically every single news article I've ever come across in which the term "light year" is used, the author seems compelled to state that a light year is the distance that light travels in 1 year (and then the author usually gives the equivalent in miles), and yet here "algebraic number" is thrown in without comment. I'd be willing to bet almost anything that far more people know what a light year is than what an algebraic number is. If I were editing the article I would have suggested saying something like
"although mathematicians have known that pi is irrational since the late 1700s, and transcendental--a certain extreme way that a number can be irrational--since the late 1800s, to this day no one knows . . ."There's no need in an article like this to define transcendental, but one should probably use the word since it's so well connected with pi
that it would seem strange to knowledgeable readers to not use the word.
If all this careful language analysis sounds unfair, ask yourself if being this sloppy with language usage would be accepted in an article about a bank robber (oops, I mean an alleged bank robber) or in an article about world affairs. No, it wouldn't. But it's O-K in math for some reason, and why this is allowed without much criticism is rather curious for a society that is so science-math-technology based.
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I hope I got all that right, and if not, it was almost certainly my cutting and pasting that created the problem. Thanks Dave, for bringing a little class to my blog... (hey, since I wrote part of this, does this qualify as co-publishing??? I'm ready to stretch the rules where needed...)

And Dave, If you ever have something else to share with my (somewhat limited) audience, I would love to host you again.

Good Sense

from Hit & Run by Katherine Mangu-Ward... just talked to my stats kids about this a couple of days ago....
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A great post from Robert Wright at the New York Times about why the disproportionate attention paid to Toyota recalls is worrisome and innumerate:

if you drive one of the Toyotas recalled for acceleration problems and don’t bother to comply with the recall, your chances of being involved in a fatal accident over the next two years because of the unfixed problem are a bit worse than one in a million—2.8 in a million, to be more exact. Meanwhile, your chances of being killed in a car accident during the next two years just by virtue of being an American are one in 5,244.

So driving one of these suspect Toyotas raises your chances of dying in a car crash over the next two years from .01907 percent (that’s 19 one-thousandths of 1 percent, when rounded off) to .01935 percent (also 19 one-thousandths of one percent). I can live with those odds....

But it worries me that this Toyota thing worries us so much. We live in a world where responding irrationally to risk (say, the risk of a terrorist attack) can lead us to make mistakes (say, invading Iraq). So the Toyota story is a kind of test of our terrorism-fighting capacity—our ability to keep our wits about us when things seem spooky.

Passing the test depends on lots of things. It depends on politicians resisting the temptation to score cheap points via the exploitation of irrational fear. It depends on journalists doing the same. And it depends on Americans in general keeping cool, notwithstanding the likely failure of many politicians and journalists to do their part.

If you're curious about how he did the math, go here and scroll down. If you want to see a bunch of commenters miss the point, keep scrolling on that same page.