HR. CardColm

And on this Friday the 13th edition of Ozarks at Large, our resident math professor,

Chaim Goodman-Strauss, has walked under ladders, walked in front of a black cat,

and come to the Anthony and Susan Hoyt Newsreel.

Welcome.

It's Friday the 13th.

It is.

It's one of three this year.

Oh, that's right.

That's cool.

Are you a superstitious person?

I'm not going to tell you on the radio.

I would assume mathematician would not be superstitious.

Could you work with numbers and facts and absolutes?

I'm definitely suspicious of numbers.

I think most mathematicians are.

Most people sort of view numbers as sort of real things, but mathematicians kind of, you know,

it's just another one of those numbers.

Right, right.

But they do have a special resonance, definitely.

I mean, I think I'm interested in numbers like most mathematicians,

and they sort of have sort of magical powers, but I don't really know.

I couldn't help but notice that you brought a deck of cards with you today.

Oh, thank you for bringing that up.

I think people should dig up a deck of cards.

We have a very special guest.

We have a guest coming shortly.

Okay.

That'll be later in the program, so have a deck of cards.

Okay.

And we're also going to remind people right now about a sort of challenge.

That's right.

That we had several weeks ago, and our schedule's having a line.

We want to answer it today, but first let's refresh people what this challenge was.

Right.

So the basic version would be something like, there are blank twos in this sentence.

And to make that a correct sentence, you'd say there are two twos in this sentence.

And that's correct.

That's valid.

We could sort of make that a bit fancier.

We could say, let's make it more than one sentence.

Let's have a whole paragraph.

We could have, there are blank ones in this paragraph.

There are blank twos in this paragraph.

There are blank threes in this paragraph.

And there are blank fours in this paragraph.

Now, of course, one little side thing.

There are blank fours.

That means it sounds like you've got to have at least two.

But you could have.

Because it's plural.

But we're just skipping grammar.

Right.

We're not going to work.

So what we want to do is make this paragraph completely.

There are blank ones in this paragraph.

There are blank twos in this paragraph.

There are blank threes in this paragraph.

There are blank fours in this paragraph.

What's the combo there that you need to come up with to make it all work?

And there's actually a couple of possible answers.

Okay.

And we're going to hear about that and play with some playing cards in the second half hour of the show.

Awesome.

Okay.

Hopefully people have gotten their playing cards for our guest in a minute.

I'm back with Haim Goodman-Strauss, our resident math professor here.

Let's make this paragraph work.

So maybe we'll just say how to fill in the blanks and then we'll read it.

So one way to fill in the blanks would be three, one, three, one.

So if you said there are three ones in this paragraph, there's one two in this paragraph,

there are three threes in this paragraph, and there's one four in this paragraph.

Bingo.

And that would be a –

You'd have to write it down and check.

Right.

And you go back and you go, oh, okay.

And there's another solution, which is two, three.

Two, one.

Two ones, three twos.

Two threes, one four.

Right.

And there are no others.

Is there a pattern here that we're going with?

Well, it turns out that there is a pattern eventually.

So we could make these paragraphs longer.

There are so many ones, twos, threes, fours.

So many nines, tens, elevens.

And it turns out that there's – if we go to five, there's only one solution.

If we go to six, one – so blank ones, blank twos.

So there's no solution.

No solution.

But from then on, there actually is a solution that will always work or a pattern of solution.

And I guess we'll just put that on the website, mathfactor.uark.edu.

And there's another thing I'd like to touch on there as well about a way to solve these things rather efficiently.

Because I would solve these like I used to solve Sudoku puzzles where I'll try this and then I'll erase it and I'll try this.

I wasn't really – but you say there's a way to figure these out without having to do them randomly.

Well, actually, that's a real great way to do it is you fill it in sort of blindly and you'll get the wrong answer.

It will be wrong probably.

But then you sort of keep track of what it should – like so you fill it in wrong but there were some number of ones, some number of twos.

Write that down as your next solution.

OK.

And then do that over and over again and sometimes you'll actually converge to the right thing.

And now you – several weeks ago when we started talking about this, you said this relates to Alan Turing.

Whose centenary is 2012.

Yes.

He was born in 1912.

And he was the father of the modern computer among many other very notable achievements.

Helped defeat the –

Helped defeat the Nazis by decrypticizing the codes.

So this method of solving this thing is actually sort of tangentially related and I'll mention that on the website.

OK.

But the main thing here is that we have language talking about itself, which is really a powerful thing.

And now when you say language talking about itself –

Well, we just did that, didn't we?

Oh.

Weirdly.

Right.

But this sentence is false would be a classic example of that.

Because if this sentence is false, then it's true.

But if it's true, it's false.

So all kinds of trouble breaks loose.

And that turns out to be a wellspring of an enormous amount of mathematical and philosophical ideas.

So when you have numbers kind of talking about themselves?

Yeah, basically.

Like that.

Yeah.

A computer program has this dual nature.

It's a recipe for doing something.

But it's also itself data.

You can – for a really weird example, you might actually try opening the Microsoft Word program in Microsoft Word if you dare.

This is like –

Holding up two mirrors to each other or something?

Okay.

What happens when you do that?

I don't know.

You get a bunch of junk mainly.

But the main point is that a program is both data and a series of actions.

Right.

It's sort of data talking about itself and tremendously important and powerful perspective.

So with us is Colm McKay of Spelman College in Atlanta.

How are you doing?

Good, Hyman.

How's it going with you?

Pretty great.

And so among other things, among your many activities, you have a column on the MAA website at MAA.com.

Well, it's called Card Column, which is a pun on my name.

It's spelled C-A-R-D and C-O-L-M.

And every two months, I turn in a new piece, mostly original, mathematical principles and explorations using a deck of cards.

Awesome.

Well, we've got one right here.

So let's have a card trick right now.

You have a deck of cards handy?

I sure do.

I'd like you to shuffle the cards, please.

Okay.

And while you're shuffling, why don't you tell me what your favorite flavor of ice cream is?

I'll go for chocolate.

Chocolate.

Good choice.

So when you're finished shuffling, take off about a quarter of the deck.

Okay.

And we'll work with those.

You can ignore the rest of the cards after that.

Okay.

I've got about a quarter.

You've got about a quarter.

So mix them up again.

Make sure they're good and mixed.

And then peek at the bottom card, please, and tell me what the bottom card is.

I have the two of clubs.

Two of clubs.

Okay.

So what's going to happen is you're going to get three scoops and three toppings of delicious chocolate ice cream, but it's all low calorie.

So you do the scooping and the dropping for the toppings.

So here we go.

I want you to hold the cards in your hand, face down.

The bottom card is the one you know, the one you peeked at.

And now start dealing the cards to the table in a pile, one for each letter.

So C-H-O-C-O-L-A-T-E.

That uses up nine or ten of your cards.

You drop the remainder on top.

Okay.

C-H-O-C-O-L-A-T-E.

And then put the rest on top?

Drop the rest on top.

Got it.

So pick up the cards, and we're going to do this two more times.

Okay.

C-H-O-C-O-L-A-T-E.

The scoop is C-H-O-C-O-L-A-T-E.

And then you drop the remaining cards on top.

Okay.

So that's your second scoop, second topping.

Got that.

Then you go for the third one.

C-H-O-C-O-L-A-T-E.

Third scoop, third topping.

Got it.

Now, have you done magic before?

No.

Not a lot.

Well, let's see if you can do some now.

I'd like you to press down hard on the top card, please.

Okay.

And see if you can turn it into the Two of Clubs.

Why, it is.

That's amazing.

Well, now, what really happened there, of course, is that the bottom card at the outset

ended up being the top card.

And what's interesting is it doesn't really matter what ice cream flavor you spell out.

Uh-huh.

That's almost true.

There's a mathematical fact that is important.

You said chocolate, which I think has nine letters.

I said pick off a quarter of the deck, which is about 13 cards.

As long as the number of cards you're working with is between 9 and 18,

the original number of letters in the word spelled out, and twice that number, it's going to work.

Hmm.

So it's quite remarkable, because most people say strawberry, chocolate, or vanilla.

So you're almost always safe working with a quarter of the deck.

Uh-huh.

Yeah, I guess most people would say that, right.

I've noticed.

And so the bottom card will end up being the top.

And that's, you know, the magic trick is, of course, you peek at the bottom card without the other person knowing.

And then at the end, you say, turn it into, and you pick a card.

Okay.

Randomly out of the air that you name, which, of course, is the one you sneak to peek at earlier.

And it looks pretty amazing.

That is amazing.

So I guess, how does that work?

I guess maybe you can't explain that now.

Well, it works based on, one way to figure out what's going on is to actually take maybe all the cards of a particular suit, perhaps spades.

Take all the spades and order them from ace through king.

And maybe do it face up and watch what happens to all the cards.

There's some mathematics going on there in terms of how the cards get rearranged each time.

And what's interesting is that if you start with a little.

If you start with a little packet of range from an ace to a king, I had you do the dropping and dealing three times.

That brings the bottom card to the top.

If you repeat it another time, do it four times, the bottom card, the original bottom card goes back down to the bottom.

What's astonishing is that when you do it four times, everything is back to where it used to be.

The cards have been restored to their original order.

So in the language of mathematics, the operation of dropping, dealing and dropping has period four.

It's one of these things where if you do it four times, it's as if you hadn't done it at all.

That's very cool.

So we met recently in Atlanta for the Gathering for Gardner.

And I guess that's a really remarkable collection of people.

It certainly is.

It's been going for about 20 years.

It happens every two years.

This was the 10th one.

And it celebrates the astonishing legacy of Martin Gardner, the many things he was interested in.

Mathematics, magic, puzzles, games, logic, Lewis Carroll, all the many things that he wrote about for such an extraordinarily long period, an 80-year period.

And it brings together some very talented.

And it brings together some very talented and innovative people in the sciences and the arts.

And it's always an intellectual overload almost to go because it's three or four days of just mind-blowing stuff.

It absolutely is.

And among other things, you've started a Twitter feed.

That's right.

We launched something on the last day.

We wondered, you know, if Martin Gardner, in whose honor this conference is in part, were alive today.

He passed away just two years ago.

I asked myself the question, what would Martin Gardner do?

What would Martin Gardner tweet?

So if you have suggestions for what you think he would tweet, you can email them to what would Martin Gardner tweet, which is a Gmail account.

And the Twitter feed is just the initials for those words.

So it's WWMGT.

And we've been running that for a couple of weeks now.

Very amusing stuff.

And we would encourage people to follow it.

And I guess we note the passing of Tom Rogers, the great founder of the Gathering for Gardner.

That's correct.

And sadly, a couple of days ago, Tom Rogers.

He was of Atlanta, passed away.

He had been ill recently, but he worked very hard to make sure that the Tent Gathering was just as good, if not better, than all the ones that preceded it.

He was one of the people, along with Elwin Burlickamp and Mark Setter-Ducati, a mathematician and magician, respectively.

Tom was a puzzle collector who formed this concept, conceived of the Gathering for Gardner, in the early 1990s when Martin was still alive.

And in those days, it was a small meeting, basically for friends of his, but it has blossomed into something very international that draws people.

People from all over the planet, several hundred people.

Yeah, he's left really an incredible legacy.

Absolutely.

For which I know there's...

I'm very personally grateful, and I know many, many, many other people are as well.

One of the intellectual highlights of your life, if you can get to see the Gathering for Gardner, you'll meet some of the coolest people.

They'll come away really stimulated.

And it's not just the Gathering, because the Gathering happens every two years, and it is a conference that costs money to attend.

And it's not something to be taken lightly.

But every October, following Martin's...

own passing two years ago, Tom and some friends put together another concept, which I think is perhaps more brilliant, which is the Celebration of Mind.

And that's designed to happen around about October, which was Martin's birthday, but it's flexible.

And it's just a question of people getting together anywhere in the world.

And we've had events on all seven continents.

We're looking for somebody to host one of the North Pole.

We did get Antarctica this year, passed.

And we want to do this every October and have people just come together and share fun.

Recreational mathematics.

And there are a lot of puzzles in the spirit of Martin Gardner.

But it's not something organized.

It's something that you want to...

You might choose to organize yourself.

It could be just a few people meeting in a restaurant.

It could be a lecture on a campus.

It could be a meeting in a library, school.

There are a lot of fun, we've had two here.

And that's a Gather...

Where is the website for that?

Just, if you just search, Celebration of Mind.

And I guess as we go out, do you have a quick puzzle for us?

Well, it's funny, one of the last good puzzles that Tom Rogers shared with me a couple of months ago, I guess it was last year.

I don't think it was last year.

I guess it was leading up to the last celebration of mine, was this one.

And he found it very amusing because he said he found it very easy,

but he discovered that the more mathematical training people had, the harder they found it.

And I have found, in sharing with other people, that perhaps that's a very valid insight.

It's a very simple question.

It asks you to consider two triangles.

One of them has sides 5, 5, and 6.

Okay.

And the other triangle has sides 5, 5, and 8.

Oh, this is one of the things you tweeted from the gathering.

I think we tweeted that one.

The question, very simply, is which triangle has the greater area?

Can you say which triangle has the greater area?

5, 5, 6, and 5, 5, 8.

And I believe that puzzle comes to us from Dick Hess.

It's a very, very good puzzle.

Tom just thought it was so funny that the people with the more advanced math training got stuck on it.

Well, certainly.

There's sort of an intuitive answer, which must be the wrong one.

Well, thank you very much, Colin.

Enjoy.

And we'll see you in a couple of years.