The Magic Square Trick

[Brown]

In this thread, I offered to explain the magic square trick (performed at TAM3 and repeated at TAM4) to anyone interested in learning it. I am re-posting the offer here.

The trick can be useful as an educational tool, or can be used to make people think you are a mathematical genius.

Some would say that it is not a "magic trick," although you can find some magic books that discuss it. Few professional magicians perform it. In fact, I've only seen one professional magician perform it, Harry Lorayne, and he treats it as a mental exercise rather than as magic.

 

[firecoins]

Jamy Ian Swiss does one on stage. A retired math professpr and part time magician Jack Diamiond does it in his act.

 

[Azrael 5]

Derren Brown did one on his tour a couple of years ago and also Marc Salem performs one.

 

[mroek]

Is this the trick where you have a 4x4 square grid that is filled (by the performer) with numbers that will sum up (in all directions) to a total that is given by a spectator beforehand?

 

[Bob Klase]

Besides Darren Brown and Marc Salem I've seen several professional magicians use it. Paul Daniels performed it years ago on his TV show. I know 2 pros in my area that use it regularly.

I've use a routine published by Lee Jacobs combining it with the out-to-lunch principle to create a square almost instantly (or at least 'magically fast').

Few professional magicians perform it.

Is that a reason to explain it? I could look through 5-600 magic books I have and find several thousand tricks that few professional magicians perform.

 

[Brown]

Is this the trick where you have a 4x4 square grid that is filled (by the performer) with numbers that will sum up (in all directions) to a total that is given by a spectator beforehand?

Basically, yeah.

Besides Darren Brown and Marc Salem I've seen several professional magicians use it. Paul Daniels performed it years ago on his TV show. I know 2 pros in my area that use it regularly.

I've use a routine published by Lee Jacobs combining it with the out-to-lunch principle to create a square almost instantly (or at least 'magically fast').



Is that a reason to explain it? I could look through 5-600 magic books I have and find several thousand tricks that few professional magicians perform.

Well, I make mention of this one because, unlike many other "magic tricks," this one has a pronounced educational value. The subject came up in connection with student education, and my feeling was that a teacher can make a stronger point by performing the trick himself/herself than by showing a video of someone else doing it (especially a video that, as has been pointed out, includes an error by the performer!).

A sixth-grade math substitute, Mr. Schlachtenhaufen, introduced me to magic squares as a mathematical recreation. One of my high school teachers, Mr. Zimmerman, taught me more advanced magic square construction, not as magic, but as a mathematical curiosity. He also described a clever "magic square generator" devised by one of his students that, as far as I know, has not been published. (This is NOT the up-over-down generator that can generate magic squares for an odd square.)

In other words, the subject of magic squares is not exclusively within the realm of magical performance. In light of my own personal experience as a student, I can say that there is educational value in magic square construction. I expect that some will take issue with this stance, but there it is. Also, I will not divulge any techniques in the forum, but will describe them only upon request. And furthermore, there are certain PERSONAL techniques (e.g., shortcuts, mnemonics) that I will keep to myself. Chances are that while these techniques work for me, they may not work for anyone else.

 

[Mercutio]

I don't think it gives anything away to say that the magic square demo would be a fantastic way to talk about "degrees of freedom" in a statistics class.

Any ability to also win bar bets would be just gravy...

 

[Brown]

One of the best uses of a magic square is to demonstrate a property of non-transitivity. This is an extremely counterintuitive concept, especially for adults, but a magic square is a good way to make the principle easy to grasp.

This non-transitivity concept could be the basis for a sucker bet, but that's true of a lot of mathematical or logical principles, especially the counterintuitive ones.

 

[Bob Klase]

In other words, the subject of magic squares is not exclusively within the realm of magical performance.

That's true. And I really don't have a problem with explaining it as a educational tool. But for tricks where education is a valid reason I don't think it makes a difference if it's being used by professionals or not.

For the most common magic square used by magicians, I changed the the math slightly to make it easier for me to remember the sequence. If you're interested I'll give you the change.

 

[Brown]

That's true. And I really don't have a problem with explaining it as a educational tool. But for tricks where education is a valid reason I don't think it makes a difference if it's being used by professionals or not.

For the most common magic square used by magicians, I changed the the math slightly to make it easier for me to remember the sequence. If you're interested I'll give you the change.

In the version I find easiest, I subtract 20 on the fly for a first-row entry and apply the mnemonic "Voted to knockdown my pooch, dazzler."

This remark will, I hope, mean absolutely nothing to anyone unfamiliar with the stunt or number mnemonics. But somehow I think you might know what I'm talking about...?

One of my high school teachers had an unusual method of presenting the 4-by-4 magic square. He would have the numbers arranged on cubes, and he would manipulate the cubes to create one magic square after another in rapid succession. I can see how combining this manipulation with the stunt might have some entertainment value as well as educational value.

 

[Bob Klase]

In the version I find easiest, I subtract 20 on the fly for a first-row entry and apply the mnemonic "Voted to knockdown my pooch, dazzler."

I subtract 21, then add 1 each time going counter-clockwise. No mnemonics.

 

[Checkmite]

The "inside joke" of magic is that you're doing something that it seems one would require a supernatural power to do - bending objects with your "mind", for instance, or teleportation, or telepathy.

I know this trick is called a "magic square", but that's really a misnomer, because the "act" here isn't that you possess supernatural powers, but rather that you're some sort of mathematical genius. Thus, I'm not sure it can even fairly be called a "magic trick", despite its use by the occasional magician. So, I don't think I would object to this trick being "exposed" so to speak.

 

[firecoins]

The "inside joke" of magic is that you're doing something that it seems one would require a supernatural power to do - bending objects with your "mind", for instance, or teleportation, or telepathy.

I know this trick is called a "magic square", but that's really a misnomer, because the "act" here isn't that you possess supernatural powers, but rather that you're some sort of mathematical genius. Thus, I'm not sure it can even fairly be called a "magic trick", despite its use by the occasional magician. So, I don't think I would object to this trick being "exposed" so to speak.

yes it can be considered a magic trick. Alot of math and science can be posaitioned as some sort of super feat. If you take credit for something impossible from super memory to super mental powers, you can call it a trick.

Exposing this trick does no harm in my opinion.

 

[Azrael 5]

It's a magic trick if you "dont know" the person's freely chosen number until after you have finished the square!

 

[Bob Klase]

It's a magic trick if you "dont know" the person's freely chosen number until after you have finished the square!

And there are at least a few magicians do the square like that. Alain Nu for one (myself for another).

 

[Checkmite]

Ah, well then, it's gravy - as long as we don't go and reveal how you figure out the spec's number...

 

[Bob Klase]

Ah, well then, it's gravy - as long as we don't go and reveal how you figure out the spec's number...

Well, it's magic of course.

 

[Garrette]

Well, it's magic of course.

Really?

I usually just have a cell phone connection to Sylvia Browne at all times. She whispers the number when I need it.

It's 85% to 87% accurate. Except when it's 100% accurate. Of course, we have to take into account those times when it's completely inaccurate.

All of which assumes the spectator is standing somewhere near water.

 

[glennwestmore]

Blog on magic squares

You can find out more about background history on Magic Squares in art, science and culture on Glenn Westmore's blog.