The Magic Square Trick

Brown · 14th January 2007, 08:25 PM

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 · 14th January 2007, 11:42 PM

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

Azrael 5 · 15th January 2007, 05:41 AM

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

mroek · 15th January 2007, 06:43 AM

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 · 15th January 2007, 07:56 AM

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').

Originally Posted by Brown

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 · 15th January 2007, 10:35 AM

Originally Posted by 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?

Basically, yeah.

Originally Posted by 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').

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 · 15th January 2007, 10:53 AM

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 · 15th January 2007, 05:16 PM

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 · 15th January 2007, 06:14 PM

Originally Posted by Brown

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 · 16th January 2007, 12:24 PM

Originally Posted by Bob Klase

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 · 16th January 2007, 01:44 PM

Originally Posted by Brown

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 · 16th January 2007, 05:47 PM

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 · 16th January 2007, 06:06 PM

Originally Posted by Joshua Korosi

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 · 16th January 2007, 06:17 PM

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

Bob Klase · 16th January 2007, 10:08 PM

Originally Posted by Azrael 5

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 · 17th January 2007, 05:29 PM

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 · 17th January 2007, 10:27 PM

Originally Posted by Joshua Korosi

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 · 18th January 2007, 05:40 AM

Originally Posted by Bob Klase

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.

14th January 2007, 08:25 PM	#1
Brown Philosopher Join Date: Aug 2001 Location: Twin Cities, Canada Posts: 9,117	The Magic Square Trick 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.
	__________________ Klaatu: I'm impatient with stupidity. My people have learned to live without it. Mr. Harley: I'm afraid my people haven't. I am very sorry. I wish it were otherwise. -- The Day The Earth Stood Still, screenplay by Edmund H. North "Don't you get me wrong. I only want to know." -- Judas in Jesus Christ Superstar, lyrics by Tim Rice

14th January 2007, 11:42 PM	#2
firecoins Illuminator Join Date: Sep 2006 Location: Nyack, NY Posts: 3,065	Jamy Ian Swiss does one on stage. A retired math professpr and part time magician Jack Diamiond does it in his act.
	__________________ NY Paramedic, skeptic, 9/11/01 Reality-ist. I am both right wing nut and left wing lunatic. Deal with it.

15th January 2007, 05:41 AM	#3
Azrael 5 Illuminator Join Date: Sep 2003 Location: Yorkshire,Uk Posts: 4,219	Derren Brown did one on his tour a couple of years ago and also Marc Salem performs one.
	__________________ "I achieve these results through a mixture of magic,misdirection,suggestion and showmanship"-Derren Brown Photography here

15th January 2007, 06:43 AM	#4
mroek Critical Thinker Join Date: Mar 2004 Posts: 379	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?
mroek Critical Thinker Join Date: Mar 2004 Posts: 379

15th January 2007, 10:35 AM	#6
Brown Philosopher Join Date: Aug 2001 Location: Twin Cities, Canada Posts: 9,117	Originally Posted by 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? Basically, yeah. Originally Posted by 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'). 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.
	__________________ Klaatu: I'm impatient with stupidity. My people have learned to live without it. Mr. Harley: I'm afraid my people haven't. I am very sorry. I wish it were otherwise. -- The Day The Earth Stood Still, screenplay by Edmund H. North "Don't you get me wrong. I only want to know." -- Judas in Jesus Christ Superstar, lyrics by Tim Rice

15th January 2007, 07:56 AM	#5
Bob Klase Master Poster Join Date: Mar 2002 Location: Largo, FL Posts: 2,445	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'). Originally Posted by Brown 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.

15th January 2007, 10:53 AM	#7
Mercutio Shakespeare's Sock Puppet Join Date: Mar 2003 Location: Live Free Or Die Posts: 16,329	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...
	__________________ "But to see her was to love her Love but her, and love forever."

15th January 2007, 05:16 PM	#8
Brown Philosopher Join Date: Aug 2001 Location: Twin Cities, Canada Posts: 9,117	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.
	__________________ Klaatu: I'm impatient with stupidity. My people have learned to live without it. Mr. Harley: I'm afraid my people haven't. I am very sorry. I wish it were otherwise. -- The Day The Earth Stood Still, screenplay by Edmund H. North "Don't you get me wrong. I only want to know." -- Judas in Jesus Christ Superstar, lyrics by Tim Rice

15th January 2007, 06:14 PM	#9
Bob Klase Master Poster Join Date: Mar 2002 Location: Largo, FL Posts: 2,445	Originally Posted by Brown 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.

16th January 2007, 12:24 PM	#10
Brown Philosopher Join Date: Aug 2001 Location: Twin Cities, Canada Posts: 9,117	Originally Posted by Bob Klase 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.
	__________________ Klaatu: I'm impatient with stupidity. My people have learned to live without it. Mr. Harley: I'm afraid my people haven't. I am very sorry. I wish it were otherwise. -- The Day The Earth Stood Still, screenplay by Edmund H. North "Don't you get me wrong. I only want to know." -- Judas in Jesus Christ Superstar, lyrics by Tim Rice

16th January 2007, 01:44 PM	#11
Bob Klase Master Poster Join Date: Mar 2002 Location: Largo, FL Posts: 2,445	Originally Posted by Brown 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.

16th January 2007, 05:47 PM	#12
Checkmite Skepticifimisticalationist Join Date: Jun 2002 Location: Third in line Posts: 8,649	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.
	__________________ Nuclear energy is GREEN energy.

16th January 2007, 06:06 PM	#13
firecoins Illuminator Join Date: Sep 2006 Location: Nyack, NY Posts: 3,065	Originally Posted by Joshua Korosi 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.
	__________________ NY Paramedic, skeptic, 9/11/01 Reality-ist. I am both right wing nut and left wing lunatic. Deal with it.

16th January 2007, 06:17 PM	#14
Azrael 5 Illuminator Join Date: Sep 2003 Location: Yorkshire,Uk Posts: 4,219	It's a magic trick if you "dont know" the person's freely chosen number until after you have finished the square!
	__________________ "I achieve these results through a mixture of magic,misdirection,suggestion and showmanship"-Derren Brown Photography here

16th January 2007, 10:08 PM	#15
Bob Klase Master Poster Join Date: Mar 2002 Location: Largo, FL Posts: 2,445	Originally Posted by Azrael 5 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).

17th January 2007, 05:29 PM	#16
Checkmite Skepticifimisticalationist Join Date: Jun 2002 Location: Third in line Posts: 8,649	Ah, well then, it's gravy - as long as we don't go and reveal how you figure out the spec's number...
	__________________ Nuclear energy is GREEN energy.

17th January 2007, 10:27 PM	#17
Bob Klase Master Poster Join Date: Mar 2002 Location: Largo, FL Posts: 2,445	Originally Posted by Joshua Korosi 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.

18th January 2007, 05:40 AM	#18
Garrette Philosopher Join Date: Aug 2001 Posts: 7,964	Originally Posted by Bob Klase 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.
Garrette Philosopher Join Date: Aug 2001 Posts: 7,964	__________________ My kids still love me.