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Maths Magic at Mile End

Renowned mathematicians brought maths magic to QMUL in a series of shows, exploring the maths behind card tricks and the magic in mental maths.

  • School/Institute/Department: School of Mathematical Sciences, CS4FN
  • Subjects: Maths, Computer Science, Magic
  • Audience: KS5, 16, 17, 18, general public, undergraduates

Magic comes to Mile End with renowned mathamagicians Dr Brent Morris, Dr Arthur Benjamin and Dr Colm Mulcahy. Three seminars exploring the maths behind card tricks and the magic in mental maths were held at QM, featuring Queen Mary's very own maths geniuses Matt Parker and Peter McOwan. 

If you'd like to bring a little magic into your own life, you can watch the videos on our YouTube channel, or see the trailers below. Videos are also available on iTunesU - just search 'Magic at Mile End'.

Review of Dr. Arthur Benjamin's show

Dr Arthur Benjamin astounded an audience of hundreds with amazing feats of mental maths, baffling the audience and his willing volunteers with his ability to read their minds, outperform calculators and guess their day of birth.

Ask a normal person to multiply to one-digit numbers together in their head, and most will be able to do it without any trouble. Give then two larger numbers - say two three digit numbers - and they will be reaching for paper and pencil. But Dr Arthur Benjamin can multiply two digits together in his head even when they have 5 digits. Dr. Benjamin treated the audience to a mathemagical display by challenging 5 audience members with calculators to a maths-off, to see who could compute faster (clue: it wasn't the calculator).

Next up, Dr. Benjamin picked one of the four digit numbers he had just calculated and asked the calculator-wielding volunteers to pick any three digit number and multiply the two numbers together. When each volunteer read out all but one digit their number (in any order), he was able to work out the omitted digit.

Finally, he let the calculators and their owners take a rest and got down to the tricky business of working out the day of someone's birth when given their birthdate. Dr. Benjamin was capable of working out what day any date would fall upon, even as far as 3000 years into the future!

After baffling and amazing the audience, Matt Parker led a question and answer session where Dr. Benjamin explained the maths behind his mental magic.He revealed some of his tricks: from using a letter code to remember numbers (which allows him to remember dozens of digits of pi), to a clever trick involving the letter nine. The audience were left equipped with all of the tools to replicate the tricks themselves - with a lot of patience and practice!

Review of math magic show featuring Dr. Brent Morris

The combined lecture and magic show Magic Tricks, Card Shuffling & Dynamic Computer Memories took place on the 20th of February 2013.  It was organised by the Centre for Public Engagement at Queen Mary University of London

By Dr. Søren Riis

Dr. Brent Morris is famous among magicians as well as mathematicians for having written a PhD thesis on… card shuffling!  As a mathematician and former member of the Danish Magical circle, I had been looking forward to this talk in eager anticipation, and I was not disappointed.
The talk was an excellent combination of magic, good showmanship, slight of hand, and mathematics of the slight of mind variety - in equal measure.

As a young child Brent watched Buffalo Bob produce a dove pan of popcorn on the Howdy Doody Show, and this inspired him to become a magician. Then later as a math student he wrote a project on card shuffles, which his advisor recommended him to publish. This was followed by another project on card shuffling that also got published.  These papers were the foundation of Brent’s PhD thesis (1974) on card shuffling

A layperson might find it strange that it is possible to say anything interesting about card shuffles. However, following Dr. Morris’s pioneering work multiple papers and more than a handful of PhD theses have been written on the topic.

Dr. Morris’s research mainly considers the perfect faro shuffle. To do a perfect faro shuffle with an ordinary deck of cards the magician must be able to split the deck into equal halves of 26 cards, and then push them together so as to make them perfectly interwoven. Each such shuffle can be varied by either doing an in-shuffle or an out-shuffle, depending of whether the top card goes second or remains on top after the shuffle.  Dr. Morris demonstrated this shuffle during his show.  

To do a perfect faro shuffle requires a sleight of hand. And to understand the theory of the perfect faro shuffle requires a sleight of mind.  In the talk Morris only scratched the surface of his work, and for readers who are interested in more detail I strongly recommend his book with the title Magic tricks, card shuffling, and dynamic computer memories

Hardline mathematicians might enjoy the article: the mathematics of perfect shuffles, by Diaconis, Graham, and Kantor published in Advances in Applied Mathematics (1983) 4 (2): 175–196. The article links the perfect in- and out-shuffles to deep topics involving intriguing mathematical structures such as the Weyl groups and the Mathieu group M12.

During his show, Dr. Morris showed us a card trick he invented based on his results on card shuffling.

Here goes;

A (seemingly) shuffled deck of cards was placed on the table. Dr. Morris told the audience he would make exactly 6 shuffles and bring a randomly selected card to a randomly selected position. To demonstrate this, a spectator was asked to call out ANY card. In the actual performance, the king of diamonds was selected. Then another spectator was asked to call out ANY number from 1-52. In the actual performance, the number 42 was selected. After some calculations Dr. Morris was ready to make his 6 shuffles.

After the shuffles, 42 cards were carefully counted down from the top of the deck. Lo and behold, card number 42 was indeed The King of Diamonds!

People were amazed, and Dr. Morris got a well-deserved round of applause.  Of course, every one who had followed Dr. Morris’s explanations understood what had happened. However, what followed next showed that Dr. Morris is not just a mathematician with a sleight of hand, but a real magician!

After, the applause had died out Dr. Morris showed that all the remaining cards in the deck were:

…. suspense…

in complete deck order, i.e. Ace to King in each suit !!!!

This was of course a real kicker!

Not surprisingly some spectators were bowled over, and were genuinely puzzled how this last feat was possible. But as Dr. Morris explained, this secret is protected by the Magician’s Oath:

The secret of an Illusion should never be revealed – unless to a student of magic who also takes this Oath.

However, let me reveal  (as Dr. Morris did in his show) that the deck contained an extra joker and that any one who had read (and understood) Dr. Morris’s book should be able to understand how the full effect is achieved. The book by Morris also explains why the effect cannot possibly work with a deck of 52 cards.

Dr. Morris finished his talk by giving an example of how ideas from card shuffling can be used in computer memory design

Magic and Science

In 1973 British author, inventor and futurist, Arthur C Clarke famously wrote: Any sufficiently advanced technology is indistinguishable from magic.

From this quote it is not surprising that cutting edge technology and science often have the flavour of magic.
Vice-Principal for public engagement Professor Peter McOwan (who is a keen amateur magician himself) is actively drawing on this link between technology and magic in teaching as well as in research.  Together with Professor Paul Curzon (also at Queen Mary) they have published a number of booklets as well as outreach materials on Magic of computer science. In recent years scientists have been increasingly interested in understanding illusion and magic.

As a surprise, the event featured a short presentation by Dr Andy Bushby from the School of Engineering and Materials Science at Queen Mary. Card magicians have noticed that certain sleights are almost impossible to do with a deck of brand new cards, but are easier to do after the cards have been “warmed up” with a few shuffles.  To investigate this scientifically, Dr. Bushby had used electronic microscope and other material science tools to compare decks of cards where the card had been put under various strains and bends, with a deck of cards shuffled by the master Dr. Morris himself. Dr. Bushby explained how the cards had been affected by the shuffling and suggested ways that this research could be taken forward.

Reception and magic jam session

At the reception that followed, it became clear that there were a number of magicians in the audience. There were, for example, two excellent card magicians from the magic society at UCL. Dr. Morris’s talk was in being recorded, but at some stage he asked that the cameras were turned off so he could properly share a few secrets with the magicians present. After this, the reception fast developed into a magic jam session with some excellent mind-blowing card magic.  

All in all, it was a highly enjoyable event, which put me in mind of Einstein’s quote: Reality is merely an illusion, albeit a very persistent one.

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