## Happy Birthday to The Science Guy Tuesday, Sep 10 2013

On 10 July 1917, Donald Herbert Kemske (later known as Donald Jeffry Herbert) was born in Waconia, Minnesota. Back when university educations were a bit more about education and a bit less about establishing vocation, Donald studied general science and English at La Crosse State Normal College (which is now the University of Wisconsin-La Crosse). But Donald liked drama, and he became an actor. When World War II broke out, Donald joined the US Air Force, flying over 50 missions as a bomber pilot.

After the war, Donald began to act in children’s programs at a radio station in Chicago. Perhaps it was because of his love of children’s education, perhaps it was the sudden visibility of the power of science, as evidenced by the nuclear bomb, or perhaps something else – but Donald had an idea for a tv show based around general science experiments. And so Watch Mr. Wizard was born on 3 March 1951 on NBC. (When I think about it, I’m surprised at how early this was in the life of television programming). Each week, a young boy or a girl would join Mr. Wizard (played by Donald) on a live tv show, where they would be shown interesting and easily-reproducible science experiments.

Watch Mr. Wizard was the first such tv program, and one might argue that its effects are still felt today. A total of 547 episodes of Watch Mr. Wizard aired. By 1956, over 5000 local Mr. Wizard science clubs had been started around the country; by 1965, when the show was cancelled by NBC, there were more than 50000. In fact, my parents have told me of Mr. Wizard and his fascinating programs. Such was the love and reach of Mr. Wizard that on the first Late Night Show with David Letterman, the guests were Bill Murray, Steve Fessler, and Mr. Wizard. He’s also mentioned in the song Walkin’ On the Sun by Smash Mouth. Were it possible for me to credit the many scientists that certainly owe their

I mention this because the legacy of Mr. Wizard was passed down. Don Herbert passed away on June 12, 2007. In an obituary published a few days later, Bill Nye writes that “Herbert’s techniques and performances helped create the United States’ first generation of homegrown rocket scientists just in time to respond to Sputnik. He sent us to the moon. He changed the world.” Reading the obituary, you cannot help but think that Bill Nye was also inspired to start his show by Mr. Wizard.

In fact, 20 years ago today, on 10 September 1993, the first episode of Bill Nye the Science Guy aired on PBS. It’s much more likely that readers of this blog have heard of Bill Nye; even though production of the show halted in 1998, PBS still airs reruns, and it’s commonly used in schools (did you know it won an incredible 19 Emmys?). I, for one, loved Bill Nye the Science Guy, and I still follow him to this day. I think it is impossible to narrow down the source of my initial interest in science, but I can certainly say that Bill Nye furthered my interest in science and experiments. He made science seem cool and powerful. To be clear, I know science is still cool and powerful, but I’m not so sure that’s the popular opinion. (As an aside: I also think math would really benefit from having our own Bill Nye).

## Dancing ones PhD Saturday, Aug 11 2012

In my dealings with the internet this week, I am reminded of a quote by William Arthur Ward, the professional inspirator:

We can throw stones, complain about them, stumble on them, climb over them, or build with them.

In particular, I have been notified by two different math-related things. Firstly, most importantly and more interestingly, my friend Diana Davis created a video entry for the “Dance your PhD” contest. It’s about Cutting Sequences on the Double Pentagon, and you can (and should) look at it on vimeo. It may even be the first math dance-your-PhD entry! You might even notice that I’m in the video, and am even waving madly (I had thought it surreptitious at the time) around 3:35.

That’s the positive one, the “Building with the Internet,” a creative use of the now-common-commodity. After the fold is the travesty.

## Not so Nobel today Monday, Nov 28 2011

When I was in high school, a good friend of mine wrote a haiku that ended up being published in the Atlanta Journal Constitution. It goes something like this

Turkeys flee in fright
Have a happy Thanksgiving
Bye-bye Indians

I remember it to this day. And the AJC thought it fit to publish – which is pleasant.

I also wanted to note that Thanksgiving is not only a welcome vacation and a promise of delicious food. It’s also the time for the Ig Nobel awards. Such notable (real) studies include No evidence of contagious yawning in the red-footed tortoise!

The math award this year was not as exciting as the others, in my opinion. It went to a series of people who predicted the world would end… and were wrong (it would seem). This is supposed to teach people to be careful about making mathematical assumptions and calculations.

In fact, I find it particularly uninspired.  Nonetheless, it is very entertaining, and I highly recommend it.

## Giving Journals Saturday, Jul 23 2011

Firstly, I wanted to note that keeping a frequently-updated blog is hard. It has its own set of challenges that need to be overcome. Bit by bit.

But today, I talk about a sort of funny experience. Suppose for a moment that you had acquired a set of low-level math journals throughout the undergrad days, journals like the College Mathematics Journal, Mathematics Magazine, etc. Presuming that you didn’t want to keep them in graduate school (I don’t – they’re heavy and I have online access), what would you do with them?

## Back and Forum-ing: Beating a dead horse Friday, Jul 1 2011

I’m back! Croatia, Greece, Turkey… all behind me. In the meantime, I’ve fallen even more in love with math.stackexchange and have ended up as a temporary moderator for philsophy.stackexchange (check them out). To announce my return, a little fun:

#### from Loers Hey everyone thanx for the amazing effort that u provide us with , over here . just gotta a simple questions why cannot we differentiate |x|when x = 0 ? or let’s say |x+2| when x = -2 this is really annoying me I cannot see a proper reason for it thanx again

We strive to develop our humor. The Chaz (quite the internet sensation, if you haven’t run across him) writes: (more…)

## The Collatz Conjecture – recent development? Monday, Jun 6 2011

On his site, John D. Cook recently proliferated a paper by Gerhard Opfer that claimed to solve the Collatz Conjecture. The Collatz Conjecture is simple to state:

Collatz (or the 3n + 1 conjecture):
Starting at any number do the following: if n is even, divide by 2; if n is odd, multiply by 3 and add 1.
The conjecture states that no matter what positive integer you start at, you will end up at 1 (the so-called 1-4-2 loop).

At first, I had high hopes for the paper. It seems relatively well-written and was submitted to the Mathematics of Computation, a very respectable journal. I even sent out a brief email about the paper. But the paper is flawed. The problem, I think, can be succinctly summarized by the following: he relies on the assumption that starting with any number $n_0$, one will eventually hit a number that is less than $n_0$. When stated like this, it seems obvious that there is a problem, but he only relied on that one number (rather than the apparent infinite descent that could follow). The exact problem occurs with his ‘annihilation argument’ on page 11 of the pdf above. He more or less states that one can start at 1 and reach every number by doing a sort of reverse Collatz function (he’s actually a bit wittier than that), but does not prove it.

More commentary can be found on reddit, reddit again, and on math.SE (a question protected by Qiaocho Yuan – go him).

I use this as an intro to a sort of joke that goes around mathematician’s circles. A while back, Sean Carroll wrote up ‘The Alternative-Science Respectability Checklist,’ and it’s awesome. Find it here. It turns out that Scott Aaronson wrote up a similar article, inspired by Sean Carroll, that is titled “Ten Signs a Claimed Mathematical Breakthrough is Wrong.”

His inspiration was the time-old problem that simply stated problems encourage generations up people to attack them, and frequently to think that they have made progress. So he asks :

Suppose someone sends you a complicated solution to a famous decades-old math problem, like P vs. NP. How can you decide, in ten minutes or less, whether the solution is worth reading?

And thus his 10 signs were created. I happen to have heard a few people say that this most recent paper on the Collatz Conjecture only failed three: #6 (The paper jumps into technicalities without presenting a new idea), #8 (The paper wastes lots of space on standard material), and #10 (The techniques just seem too wimpy for the problem at hand). {though perhaps #8 is debateable – some say it’s related to a different convention of writing papers, but I don’t know about any of that}

In my experience, I rely mostly on #1 (it’s not written in $\TeX$), #4 (it conflicts with some impossibility result), and #7 (it doesn’t build on any previous work). But both of these articles are very funny, though not exactly precise nor entirely true.

## Daily Math in Zagreb Tuesday, May 24 2011

So I’m in Zagreb now, and naturally this means that I’ve not updated this blog in a while. But this is not to say that I haven’t been doing math! In fact, I’ve been doing lots, even little things to impress the girl. ‘Math to i-impress the g-girl?’ you might stutter, a little insalubriously. Yes! Math to impress the girl!

She is working on finishing her last undergrad thesis right now, which is what brings us to Croatia (she works, I play – the basis for a strong relationship, I think… but I’m on my way to becoming a mathematician, which isn’t really so different to play). After a few ‘average’ days of thesis writing, she has one above and beyond successful day. This is good, because she is very happy on successful days and gets dissatisfied if she has a bad writing day. So what does a knowledgeable and thoughtful mathematician do? It’s time for a mathematical interlude –

#### Gambling and Regression to the Mean

There is a very well-known fallacy known as the Gambler’s Fallacy, which is best explained through examples. This is the part of our intuition that sees a Roulette table spin red 10 times in a row and thinks, ‘I bet it will spin black now, to ‘catch up.’ ‘ Or someone tosses heads 10 times in a row, and we might start to bet that it’s more likely than before to toss tails now. Of course, this is fallacious thinking – neither roulette nor coins has any memory. They don’t ‘remember’ that they’re on some sort of streak, and they have the same odds from one toss to another (which we assume to be even – conceivably the coin is double-sided, or the Roulette wheel is flat and needs air, or something).

The facts that flipping a coin always has about even odds and that the odds of Roulette being equally against the gambler are what allow casinos to expect to make money. It also distinguishes them from games with ‘memory,’ such as blackjack (I happen to think that Bringing Down the House is a fun read). But that’s another story.

But the related concept of ‘Regression to the Mean’ holds more truth – this says that the means of various sets of outcomes should eventually approximate the expected mean (perhaps called the ‘actual mean’ – flipping a coin should have about half heads and half tails, for instance). So if someone flips a coin 20 times and gets heads all 20 times, we would expect them to get fewer than 20 heads in the next 20 throws, Note, I didn’t say that tails are more likely than heads!

#### Back to the Girl

So how does this relate? I anticipated that the next day of writing would not be as good as the previous, and that she might accordingly be a bit disappointed with herself for it. And, the next day – she was! But alas, I came prepared with sour cherry juice (if you’ve never had it, you’re missing out), and we picked up some strawberries. Every day is better if it includes sour cherry juice and strawberries.

## An even later pi day post Thursday, Apr 7 2011

In my post dedicated to pi day, I happened to refer to a musical interpretation of pi. This video (while still viewable from the link I gave) has been forced off of YouTube due to a copyright claim. The video includes an interpretation by Michael Blake, a funny and avid YouTube artist. The copyright claim comes from Lars Erickson – he apparently says that he created a musical creation of pi first (and… I guess therefore no others are allowed…). In other words, it seems very peculiar.

I like Vi Hart’s treatment of the copyright claim. For completeness, here is Blake’s response.

## A Bag’s Journey in Search of its Owner Tuesday, Mar 29 2011

This is the story of a bag,
who lost its owner and trav’led the whole world!
And though it left with lots o’ tags attached,
She absolutely lost it, when she flied.

How many days would it be?
She arrived with hope, but found only tears.
The bag just disappeared,
so she flew in without any gear.
But she gets a call the next morning,
“Where are you, your bag is right here!”
Thousands of miles afar.
When she looks in the mirror so how does she choose?
The same clothes worn day after day.
When travelling homeward bound,
her bag seems never to be found.

This is the story of a bag,
who lost its owner and trav’led the whole world!
And though it left with lots o’ tags attached,
She absolutely lost it, when she flied.

[loosely to “Story of a Girl”]

This is one of those strange stories – girl gets ready for flight from Atlanta to New York to Prague, girl ends up going Atlanta to Norfolk to New York to Prague, but bag ends up going Atlanta to New York to Atlanta to New York to Prague to New York to Atlanta to a warehouse to Atlanta to New York to Prague to Krakow… you know, the typical story. To be fair, the flight change through Norfolk as opposed to a direct to New York was last minute, and it makes sense for the bag to have been detained in New York. Perhaps it would make it on a later flight to Prague – such is life.

But nothing so simple occurred. The bag makes it to Prague, and when the girl notes that the bag should be sent to her home, one might expect the story to end. Instead, the bag ends up back in New York, then back in Atlanta. Of course, girl doesn’t know this – it’s all a big mystery (as she borrows friends’ clothing, of course). Fortunately, a Delta worker named Carl (I think) finds this bag and its tag in this warehouse, looks it up and calls girl. Girl asks for it to be shipped to her – no problem, he says. Carl is very good at his job, I think, and I commend him. Unfortunately, the bag gets to Prague again and somehow whatever instructions were once somehow connected to the bag are lost. So now someone at Prague calls up girl – what do you want to do with this bag? So the bag goes to Krakow, but that’s okay. That’s where the girl found the bag.

A very logical route, one might say.

## Mathematical ‘Urban Legends’ Sunday, Mar 27 2011

One particular topic at mathoverflow.net has accumulated a large series of incredible stories. While many of them might not be true, they are fantastic. So I thought I would share some of them.

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