Tricks using a De Bruijn cycle?

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Postby Bob Cunningham » 11/28/10 01:27 AM

A coworker pointed me to a recent improvement in digital compression which the researcher said was based on a synergy of two magic tricks.

One of the effects was based on a binary De Bruijn cycle. (think of a memorized deck where you have arranged the colors so that each possible combination of red & black for six cards appears no more than once). If you have the deck memorized, then someone can remove six cards, tell you the colors, you would be able to tell them the suit and value.

A mathematician in Chile combined De Bruijn cycle with another mathmagic principle to improve compression ratios over current standards (i.e. Make your mp3 files, or .zip files, smaller than they are now)

If you are interested, the article can be found here: http://www.technologyreview.com/blog/arxiv/

The reason I am posting this is I would like to know if there are any other effects using a De Bruijn cycle? If you know of any could you post the effect and where I can find it?

Thanks,

Bob
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Postby Max Maven » 11/28/10 02:21 AM

There have been quite a few tricks in print using the de Bruijn cycle. (Not always binary, and not always in six-unit groups.)

The earliest to explore this was probably Charles Jordan, about ninety years ago. Others who have generated ideas include Persi Diaconis, Karl Fulves, Alex Elmsley and Leo Boudreau.

Another name for this type of composition is Grey Code, and it is with that title that most magic references can be found.
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Postby Paul Gordon » 11/28/10 02:59 AM

If I recall correctly, Justin Branch wrote a small ms on it in the early/mid 80's. Paul Gordon
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Postby Bob Cunningham » 11/28/10 03:20 AM

Thanks Max!

The breadth of your knowledge is always impressive.

"Another name for this type of composition is Grey Code,"

That's interesting; In digital communications, Grey code is a binary variant that only allows one bit to change between adjacent numbers for the purpose of reducing the impact of an error. For example, a nibble representing a decimal 7 is 0111 in binary. If a system measuring the intensity of some event were to confuse a reading of 7 for 8 the binary representation becomes 1000 - this changes all four bits. In grey code, a decimal 7 is 0100 and an 8 is 1100. Between the two adjacent values only a single bit changes.

The functions of Grey code and a de Bruijn cycle are similar, but would be distinguished from each other in data communications.

I appreciate you pointing me in the right direction. I have some books by Fulves and Elmsley in my library, so i will start looking there. If any specific routine, or book, or anything else comes to mind on this subject I'd be grateful for your insights.

Thanks again,

Bob
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Postby Bob Cunningham » 11/28/10 03:26 AM

Thanks Paul!

If you happen to think of the name of that pamphlet, I might be able to find someone who would be willing sell an old copy.

Thanks again!
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Postby Joe Mckay » 11/28/10 08:53 AM

Firsty - I would recomend the three Leo Boudreau books in this area. They are 'out of print' but are available as ebooks from lybrary.com - Leo's work in this area is fantastic.

Also - Alex Elmsley has some nice ideas using this principle in the second volume of his collected works.

And here is a link to an interesting papaer by Persi Diaconis and Ron Graham which teaches some ideas. It is very maths-intensive so you may understand it better than me...

PERSI DIACONIS/RON GRAHAM

One last thing. Persi Diaconis and Ron Graham are also working on a book called 'From Magic To Mathematics - And Back' which should feature alot of work to do with GRAY CODES as well...

All the best,

Joe
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Postby Denis Behr » 11/28/10 09:44 AM

There's manuscript by Reinhard Mller from his Escorial series from 1989 that is worth looking for if you are interested in this topic. It discusses and collects what has been published until then.

Some sources are listed here: Gray Code

Also make sure to have a look at T.A. Waters' Mind, Myth & Magick, starting on page 405.

(I put together an application of my own as the last trick in Handcrafted Card Magic)
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Postby Bob Cunningham » 11/28/10 11:40 AM

Joe & Denis,

Thank you very much!

These are great references. I have some, others are relatively easy to obtain. I am looking forward to a lot of fun studying!

Thanks again,

Bob
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Postby Joe Mckay » 11/28/10 07:26 PM

Denis? I saw Earl Keyser mentioned as part of the listing of GRAY CODES effects on your database. Do you know who Earl Keyser is? A part of me wonders if it might be one of the various pseudonymns for Persi Diaconis? Or maybe a pseudonym for Karl Fulves?

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Postby Raj Madhok » 11/28/10 10:22 PM

Earl Keyser is a retired computer teacher who now lives in Iowa. He was active on the Magic Castle scene years ago and put several items in print over the years. He is also one of the original members of the Minnesota MindPsi mentalism group.
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Postby Bill Mullins » 11/29/10 01:48 AM

While the color can be spelled "gray" or "grey", "Gray code" is named after Frank Gray, and should not be spelled "Grey code".
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Postby Denis Behr » 11/29/10 04:49 AM

Joe, Raj answered that one, thanks!

By the way, Earl Keyser also published the edge-writing idea as in "Unshuffled", see Last Item Here. The Genii reference (Vol.37/11) predates it by about a month, but according to Fulves (page 202) it's Fulves fault because he sat on the contribution for some time.
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Postby Philippe Billot » 12/03/10 05:11 AM

Regarding the Grey Code, effects in Encyclopedia of Card Tricks (1937) like Perfect Card Divination By Howard Albright (page 241) and The Buddha Whispers By Joe Ovette (page 388) are applications of this principe?

Thanks in advance.

PS: can we name the Grey Code a binary code?
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Postby Dick Christian » 12/03/10 10:52 AM

There are also several book tests by Bob Hummer and Al Mann that use the Gray Code principle.
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Postby Bill Mullins » 12/04/10 12:35 AM

Philippe Billot said: ""can we name the Grey Code a binary code?"

Not really -- there are Gray codes for base 3 and other alphabets. See Martin Gardner's essay "The Binary Gray Code" in his collection of essays from Scientific American Knotted Doughnuts and Other Mathematical Entertainments
.
And again, it's "Gray Code," not "Grey Code".
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Postby Philippe Billot » 12/04/10 06:42 AM

Thank you Bill.

I get the essay and learn that the name derives from Frank Gray, a research physicist at the Bell Telephone laboratories who died in 1969.
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Postby Doug Dyment » 12/11/10 02:02 AM

You can find material based on de Bruijn sequences in two of my books: Stimulacra and Tricyclic.
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Postby Doug Dyment » 12/11/10 03:47 AM

Gray codes and de Bruijn sequences are related notions, but they are not the same thing, and have different mathematical constructions.

It's true, though, that some sequences satisfy both sets of properties, and can correctly be given both labels.
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Postby Joe Mckay » 12/15/10 06:28 PM

If Paul Gordon is reading this - any chance you could (or anyone else?) pass along the title for the Justin Branch manuscript on GRAY CODES? I have checked GOOGLE and ASK ALEXANDER and had no luck so far...

Thanks!

Joe
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Postby Richard Forster » 12/26/10 04:13 AM

See also the Card Colm for December 2008 entitled What's Black and Red and Red All Over? This is part of a column published by the MAA (Mathematical Association of America) on mathematically based magic.
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