Smart shows have smart writers, and none are smarter than the writers of Futurama.  We’ve seen a number of clever math references in Futurama and the Simpsons.  Now a fully fledged theorem is written up on screen.

If I had a TV show that’s exactly what I would do.  As it is I just post on Math Factor.

The theorem is by staffer and Math PhD Ken Keeler.  In the show Harlem Globetrotter, and all-round genius, Sweet Clyde comes up with a theorem to solve an apparantly intractible problem.

To quote Professor Farsnworth ‘Who says pure maths isn’t useful in the real world!’

Professor Farnsworth invents a mind-switching machine.  A lot of plot later nine people have their minds in the wrong bodies.  Unfortunatley the machine has a limitation, it cannot process the same two bodies twice.

There seems to be no way out until Clyde and EthanTate enter.  Clyde comes up with ‘Sweet Clyde’s Inversion Theorem’ and saves the day.

He shows that however many people there are, and however mixed up their minds, it is always possible to get every mind back in the right body as long as you have two extra bodies to help, and you know your maths!

This is the mess they are in:

Fry’s mind is in Zoidberg’s body

Professor’s mind is in Bender’s body

Bucket’s mind is in Amy’s body

Leela’s mind is in Professor’s body

Emporer’s mind is in Bucket’s body

Hermies’ mind is in Leela’s body

Zoidberg’s body is in Fry’s body

Bender’s mind is in Emperor’s body

Amy’s mind is in Hermies’ body

Take a moment to solve this yourselves.  Remember you need to get each mind back in the right body by repeatedly switching the minds of two bodies.  No switch can be repeated.  You cannot switch two of the original nine bodies because we have lost track and assume those combinations have already been used.  So every switch must involve Clyde and/or Ethan.  

Read on for the solution.

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Trauma at home; my wife has just lost one of her golden earnings.  Fortunately I know someone who will sell me a bunch of similar earrings, for a price!

I know that one of his earrings is fake, but that’s okay because I can work out which one, replace my wife’s earring and still make a profit. 

I will have to bring out my earring weighing machine, the Radar Love, which lets me compare two groups of earrings and tells me whether one group is heavier or lighter than the other, or whether they are the same wieght.  This is the only clue I will get.

The Radar Love only has three charges.  At most how many earrings can I have bought and still be confident that I will find the fake?

Can you find a general formula for a given number of charges?

“There is a crack in everything, that’s how the light gets in” Leonard Cohen, ‘Anthem’

It is the things that don’t make sense that teach us the most.  

If you want to learn something new, start with something you don’t understand, something which doesn’t make sense.

However much you know there will always be chinks in your knowledge, chinks of light that may lead you to somewhere beautiful.

Consider this:

On a Sunday afternoon your prison guard tells you that he will conduct a surprise inspection at 10am over the next seven days.

You work out that he can’t wait until next Sunday, because then it wouldn’t be a surprise. 

So, could he do it on Saturday?

On which days would the inspection be a genuine surprise?

There is no consensus on this, which is why I describe it as a chink of light, a way to get at something deeper.  But what do you think?

In this special segment, John H. Conway reminisces on his long friendship and collaboration with Martin Gardner. 

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Martin Gardner died this week.

One of his books is on my coffee table.  This is not a coincidence, there is always one of his books on my coffee table.

Many of my puzzles have come from these books.

I know him as the greatest collator and populiser of math puzzles, but of course his talents went far beyond this.

Rather than try to do my own second-rate obituary I will just point you at some links.

Scientific American, for whom he wrote for 25 years.  http://www.scientificamerican.com/report.cfm?id=Martin%20Gardner,%201914-2010

Make your own Martin Gardner Flexagons here, http://www.youtube.com/watch?v=4DETMhTC0H0.

The Daily Telegraph on his deconstruction of Lewis Carroll’s Alice books, http://www.telegraph.co.uk/news/obituaries/culture-obituaries/books-obituaries/7765184/Martin-Gardner.html

He wrote over 70 books.  Nothing I can say can begin to encompass his long and amazing life.  He is someone you need to discover for yourself.

He is already missed.

Greg Chaitin, author most recently of MetaMath!,  discusses the ubiquity of undecidability: incredibly all kinds of mathematical and physical systems exhibit utterly unpredictable, baffling behavior– and it’s possible to prove we can never fully understand why!

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Stephen Wolfram, creator of Mathematica and author of A New Kind of Science, discusses the Principle of Computational Equivalence and why even simple systems can give rise to irreducibly complex behavior. 

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Quick interviews with folks here at the Gathering For Gardner, including Stephen Wolfram, Will Shortz,  Dale Seymour, John Conway and many others. 

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We’re at The Gathering For Gardner, G4G9, and catch up with Ed Pegg of mathpuzzle.com and numerous other exploits; Ed gives us three quick puzzles to chew on– answers at his website. 

@MathFactor is tweeting pictures and more, and more short podcasts from the festivities!

(And Jeff didn’t make it! Rats!)

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You and other party-goers are lead to different places in a wood blind-folded.  You’re instructed to remove your blindfold at the sound of a horn and read a letter you’ve been provided.  When the bell sounds, you remove the blindfold and the letter reads thus:

You’ll notice around you that there are lengths of rope tied between hundreds of trees around you.  You may notice that any tree with any rope tied to it has exactly two ends tied to it, each stretching to a different tree.  In fact, these hundreds of treees form a giant concave polygon.  Some of you are inside that polyon and others are outside.  To win the game, you must be the first to reach the clubhouse at the top of the hill (which is outside of the polygon!) and report correctly whether you were initially inside the polygon or outside of it.  You can pass under the ropes, but please don’t change them in any way.  Good luck!

What strategy might you employ to determine your status and require as little time as possible to get back to the clubhouse?