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Nir Dahan Inner circle Munich, Germany 1390 Posts |
Hi all,
Another interesting topic is how many times math principles in the magic literature are published under a wrong name. Here are two famous examples: "Gray code" effects- these are actually called De Bruijn sequences - published wrongly in many mentalism books. The "second" and "third" Gilbreath principles - actually there is only one and the others are generalizations of it. nir |
ddyment Inner circle Gibsons, BC, Canada 2499 Posts |
It's probably worth noting that although these terms refer to different things (and that Frank Gray's name is often used erroneously in place of N.G. de Bruijn's), the concepts are closely related. Further, the common de Bruijn cycle for n=2 actually generates a Gray code ordering, so in this case either description could be used to discuss the ensuing sequence.
Note, incidentally, that the "G" should be capitalized in Gray code, and the "d" should not in de Bruijn. ... Doug (who is striving for accuracy while trying not to be pedantic)
The Deceptionary :: Elegant, Literate, Contemporary Mentalism ... and More :: (order "Calculated Thoughts" from Vanishing Inc.)
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Nir Dahan Inner circle Munich, Germany 1390 Posts |
Doug,
Gray code is a counting system in which the next number in turn changes by one "bit" only, de Bruijn sequence is just what it is - a sequence/chain/string - one long number which in turn we select a portion out of. Moreover de Bruijn codes are not restricted to binary representations. Nir One more thing for those who are a little more interested and want to explore a bit this site is recommended: http://www.theory.cs.uvic.ca/~cos/gen/neck.html |
ddyment Inner circle Gibsons, BC, Canada 2499 Posts |
Nir...
You don't need to explain math to me; I'm familiar with the terminology. Contrary to your assertion, however, a Gray code is not "a counting system", but simply an ordering of all n-bit binary values such that consecutive numbers differ in precisely one bit position. On the other hand, a de Bruijn sequence of length 2^r is a string of 2^r symbols, such that every substring of r symbols appears precisely once (including wrap arounds). I'm sure that most Magic Café readers have little or no interest in the details of this; my point was simply that it is perfectly correct to refer to a de Bruin sequence of length 2^2 as a Gray code, since its substrings -- taken in order -- are exactly that. Thus your broad claim (that this is an example of a "misnamed math principle") is incorrect in this instance. ... Doug
The Deceptionary :: Elegant, Literate, Contemporary Mentalism ... and More :: (order "Calculated Thoughts" from Vanishing Inc.)
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Nir Dahan Inner circle Munich, Germany 1390 Posts |
Doug,
I didn't mean to offend you, and sorry if it came out like that. I do think that some of the members of the Café are interested in those things, and that is why I am happy that we have a new area to discuss those things. As for Gray code (with a capital G): 1) Just because the length 4 de Bruijn sequence generates Gray code symbols (of length 2) Doesn't mean ALL do (and they don't). That is just a private case. TA Waters makes the mistake in his book MMM, and calls his de Bruijn sequence a Gray code. 2) a finite set that has some sort of order (also infinite but that is for another time) can be associated with an arbitrary numbering system. Therefore we can "count" with a Gray code the same way we "count" with the ordinary binary system - the word "count" is used here to indicate that the order(!) is important. (This has many uses in digital design) The reason I posted it was that in my everyday job I am an electrical engineer. I am handling Gray codes on a daily basis. I found the use of the name "Gray code" inappropriate when talking about de Bruijn sequences - that's all. Nir p.s. not all de Bruijn sequences need to be of a power-of-2 length. e.g. 010 with the symbols 01, 10, 00 |
Bill Hallahan Inner circle New Hampshire 3222 Posts |
Nir,
Good point about de Bruin sequences being called Gray codes in some books about mentalism. It might be worth notifying the authors. You mentioned the “MMM” book. I wonder what other books about mentalism you were referring to? Although I am an electrical engineer, I was taught the formal mathematical definition of a Gray code. It is: "An encoding of numbers so that adjacent numbers have a single digit differing by 1." I have seen other mathematics texts word this differently, something like: “An ordering of numbers such that adjacent numbers have a single digit differing by 1." Note that these definitions do not require that the numbers are binary numbers! Binary Gray codes are a special case, albeit the only case I have ever encountered in use. You can easily find definitions that state that Gray code numbers must be binary numbers. However, these are generally from engineering sources, not mathematics sources. As I am sure you have noted, most engineering textbooks avoid rigor in mathematics. The mathematical treatment of the Dirac Delta function in most engineering textbooks is one example of this. Also, on a formal mathematics exam, if you called a Gray code a counting system, your answer would be marked as incorrect, even if you specified all other required properties of a Gray code, although of course Gray codes can be used for counting. Mathematicians require minimalist and precise definitions. Incidentally, the first person known to use a Gray code was Emile Baudot in 1878. Frank Gray, a researcher at Bell Laboratories, patented the Gray code in 1953. I don’t know whether he patented the general case, or a specific Gray code, but all Gray codes are now named after him. The issue of there being only one Gilbreath principle is mentioned at: http://www.themagiccafe.com/forums/viewt......forum=37
Humans make life so interesting. Do you know that in a universe so full of wonders, they have managed to create boredom. Quite astonishing.
- The character of ‘Death’ in the movie "Hogswatch" |
Nir Dahan Inner circle Munich, Germany 1390 Posts |
Bill,
First please understand that English is not my native language and regarding the "counting" term - I said in the post above that the term "count" is used to specify ordering (which is important here) anyway maybe we go down to too little details NOW. As for the Dirac delta function I do not know any effects using it.. although maybe checking the shock (impulse) response for some mental effects (electrical engineers will understand this lame joke.) As for the other books I saw it in - I think in one of the Center Tear issues it was mentioned as a Gray code as well, and many times here. That actually made me post a question on the Café one time if anybody really knows any effects with Gray codes. Nir |
magiczak Regular user Granada Hills, CA 159 Posts |
What are some of the applications of these principles?
**Zak**
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Slim King Eternal Order Orlando 18012 Posts |
Yea! What he said! Are there some applications that could be used with my "Over The Phone" fetish? I slept through my high school years, so this is kind of new to me. But I'm willing to learn.
Thanks Dave Maybe a source for some effects that utilize this priciple would be good. One or both...since I'm kind of confused at the moment.
THE MAN THE SKEPTICS REFUSE TO TEST FOR ONE MILLION DOLLARS.. The Worlds Foremost Authority on Houdini's Life after Death.....
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acmp Elite user Nottinghamshire 466 Posts |
I don't have much what you're talking about, but it is interesting!
A practical example would be nice.
acmp<><
"Well if I had one wish in this god forsaken world, kids It'd be that your mistakes would be your own" |
magiczak Regular user Granada Hills, CA 159 Posts |
I second that
**Zak**
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Papa Legba Special user home-an unremarkable spiral arm of an insignificant galaxy 750 Posts |
An old thread I know, but I wanted to chip in.
Nir Dahan said that there is only one Gilbreath principle, there is no 'second' and 'third'. Well for non mathematicians aren't they just convenient names? Isn't 'Gilbreath's second principle' better (more convenient) than 'THE First generalisation of Gilbreath's Principle'? Just a thought.
Use the FORCE Luke.
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