Somewhat of a cryptic title, but I'm sure that many of you will already know where this post is heading...

Many of us here perform or know how to perform a classic 4 x 4 magic square, and my guess is that the majority of us perform exactly the same one (if the title of this post looks familiar then we're on the same page here...). I first learnt this from The Magic Book, though I wouldn't be surprised if this is considerably older (...anyone who knows an older source for this 'type' of square, I'd be interested to hear from you).

In recent years there have been several marketed magic square routines which offer a new slant on the classic in which the magician just stands there and fills in a square with a spectators chosen number. Two recent ones are Luis de Matos' The Magic Square, and Richard Wiseman's The Grid. Something that I found extraordinary when watching the advertisements for both these routines is that they make use of the exact same square we've all been doing for so long. Now, neither routine claims to have come up with a completely new concept, and both of them promise that no calculation is involved (so that the basic arithmetic that is needed to do the routine the classical way is no longer necessary). So I am not condemning the routines for regurgitating the old...

What I am surprised about is that people (De Matos, Wiseman, myself, and almost surely many others) don't make any conscious effort to hide the fact that we're using the same method. I remember a conversation I had with my maths teacher when I was around 11 years old about how I do this magic square but then I cannot repeat the effect. The next day, he came in and had a piece of paper on which he'd written down the 'method' for 12 more squares which were all dissimilar, which could be used for the effect. At the time I was amazed and assumed this was quite a complicated thing to have done. Now that I am older, and a better mathematician, I realize that in fact it is really quite easy to come up with new squares. So why do none of us do it?

Even if its just for advertising purposes... I went into watching the video for The Grid really intrigued. As soon as I saw the finished square I realised that instead of purchasing the effect I could spend some time and backtrack through the working and arrive at a similar result (whether this is ethical or not is for another post... I hasten to add that I have not actually done this, however). Now, if Richard had used a different square (but with the same principle) then this would not have been recognizable to all the magicians watching the advert... and I'm pretty certain this would boost the sales considerably!

The fact is that this, and de Matos', and almost all other magic square routines, are intended for a lay audience. From that point of view it doesn't matter which square you choose (assuming that your audience don't make a habit of returning to your show / watching other performers do magic squares); however, I'd have thought that given that it is the magicians who are purchasing the product, one would want to try to fool them before purchasing.

Both de Matos' and Wiseman's routines appear to have positive reviews, and I do not want this to turn into a debate about those particular routines (they were just the catalyst for the post). What I'm really interested in is why none of us bother to change up the square... It is almost as though we keep it the same as a acknowledging nod to any other mathematical magicians who might be watching, as a sign of solidarity!

Owen

An interesting post Owen. I can see the advantages of using a different square when performing for magicians and the mathematically sophisticated.

There are restrictions on what magic squares will work for many effects. Most effects are based on one of the "most-perfect" (pandiagonal) 4 x 4 squares because these give many more ways of producing the total than a square that simply works on the rows, columns, diagonals and corners.

Interestingly, there are only THREE basic most-perfect 4x4 magic squares, of which Harry Lorayne's is one of them (and certainly the most popular among magicians). The other two are the ancient Jaina Square and a (shuffled) version of the well-known Durer Square of 1514.

Each of these three squares can itself generate 128 variations by wrapping, rotation and mirroring. It would certainly be easy (and more deceptive) to use one of these variations, rather than always start the square with the same number in the top-left corner.

I have much more information on magic squares in my ebook "Mostly Perfect", where I also suggest mixing up the square in performance by mirroring or rotation.

You can download a FREE EXTRACT of Mostly Perfect from Lybrary.

http://www.lybrary.com/mostly-perfect-p-124662.html

Mike

Hi Mike.

You make a great point about the pandiagonals! I had neglected to mention this since I personally never point them out when I perform the magic square (personal taste, but I feel that the message is understood once one has done rows, columns and diagonals), and had promptly forgotten that the square in question has this property. However, many do like to draw attention to them and so as you point out, the possible squares that can be used is hugely depleted... justifying the use of the 'standard' square.

Thanks for the post.

Owen

I had exactly the same reaction on seeing the ad.

I think for lay audiences it's worth it to give up some features of a magic square in return for others--e.g. the corner squares give the birthdate of the participant, even though the pandiagonals and some 2x2 squares may not work out.

Or you could base the effect on one of the other most-perfect 4x4 squares (Jaina or shuffled Durer). These are practically unknown by magicians.

That would allow you to use the pandiagonals, 2x2 and other patterns.

Mike

In truth, the methodology of magic squares for mystery entertainment purposes has advanced far beyond what was possible with the method used by most entertainers.

I have published extensive material on the magic square over the years (beginning with "Flash Squared" in 2002. My most recent contribution is "On the Square", a new (and greatly simplified) approach for building magic squares in real time.

There are lots of reviews on the above-linked two pages (and for all my material), so you can get a good sense of what's available.

I favour writing the square with sequential numbers (with at most one extra jump at one point) since that makes it look beautifully homogeneous and different each time even though the numbers are always written in the same order.

/Tomas