Arcadia Discussion Zone

Mariano Tomatis simply got it wrong about the Knight's Tour and the decipherment of the Large Parchment - neither Philippe de Cherisey or Pierre Plantard ever mentioned Euler in any of their writings, documents or correspondence - and when Plantard mentions the Knight's Tour technique relating to the decoding of the Large Parchment in one of the issues of 'Vaincre, he gives a version that is different to Euler's - in that it worked in reverse-order, mirror-fashion, to Euler's technique. Had Plantard used Euler's version then he would have copied Euler's technique and not a reversed-order version of it. It cannot even be argued that what Plantard copied in the issue of Vaincre was "suggested" by Euler since we do not know what source Plantard used.

The simple fact is that Mariano Tomatis announced what he thought was a "brilliant discovery" in relation to the Knight's Tour and the Large Parchment and then someone provided Plantard's authentic reference found in an issue of Vaincre showing that it was not copied from Euler, and that Tomatis made a mistake.

In fact, I have just received a note from someone giving me a clue as to what Plantard's source was relating to the Knights' Tour of the chessboard, and if it turns out positive then Euler definitely becomes a red herring.

Hello All,

For those with an interest in mathematics there are are a very large number of potential solutions to the 'knight's tour.'
26,534,728,821,064 to be exact.

For the basics see Wikipedia. For more in depth information, with external reference, see Wolfram's Math Word: http://mathworld.wolfram.com/KnightsTour.html

If anyone has an interest in reading Euler's original paper on the tour let me know. I can provide copies on request.

Best,

A. Nesos

Available here:
http://math.dartmouth.edu/~euler/docs/originals/E309.pdf


I never wrote that Euler was the source of Plantard. Euler's path is closed and it can be reversed and broken everywhere. For this reason, it was copied in many many other books about mathematical games. Who knows from which book Plantard got it? I don't.


Totally wrong. Reading Euler's complete paper, he suggested to reverse and break elsewhere his closed path. And this rule is present in many other books about mathematical games. Who knows from which book Plantard got it? I don't.


Being 26,534,728,821,064 the different potential knight's tour, the probability of using BY CHANCE the same closed path by Euler (as Plantard did) is 1 out of 26,534,728,821,064. I cannot believe that he invented it. He obviously took it from any book which originated from the old Euler source. Who knows from which book Plantard got it? I don't.


I never announced any brilliant discovery. I just quoted the oldest closed path identical to the one used by Plantard appeared in print.

From a mathematical point of view, they are absolutely the same.
If you have any doubt, just ask to any topology expert. It is a problem of Closed (or Cyclic) Graphs (a very simple one, because from each vertex there are just two connections).

CYCLIC TOUR BY EULER:


SAME CYCLIC TOUR USED BY AUTHOR OF PARCHMENT (just rotated):

Hello Tomatis,

Thanks for the interesting and clarifying reply. I agree entirely with each of your points and never concluded that you were claiming a 'great discovery.' Thanks also for the link to the Euler paper. You have an engineering background, no?

Kind Regards,
A. Nesos

Yes
Thank you, A.N.!

Then omit Euler's name and his Paper from your article.



Then omit Euler's name and his Paper from your article.



It did not originate from "the old Euler source" since Plantard's Tour is a reverse-version of Euler's Tour.



It is not identical. Plantard's Knights Tour is reversed version of Euler's technique.



That's right, they are mirror-image reflections, showing that Plantard did not copy Euler. And the technique Plantard used he obviously got from a source different to Euler.

You keep mentioning that Euler and Plantard Knights Tours are "the same". Look at the Knights' Tour in Putnam and Wood's book - there is a Third variation. So we have now three versions in existence. Putnam and Wood did not get their information from Euler.[/quote]

That's right - the Knights' Tour given by Plantard in "Vaincre" is different to Euler's technique. The move may be the same, but the starting and finishing position of the Knight chess piece differs. You need to have a mirror to look at Plantard's Knights' Tour to claim it is identical to Euler's.

" "

This only sentence is enough to discredit all your speech.
It is up to anyone to ask a topologist expert if they are the same. They are. I will not spend any additional word to confirm what is obvious for any expert.
But I stress the fact that being 26,534,728,821,064 the different potential knight's tour, the probability of using BY CHANCE the same closed path by Euler (as Plantard did) is 1 out of 26,534,728,821,064.

WE ALL KNOW THAT.
THERE IS NO REASON TO RAISE THAT FACT.

Mariano Tomatis does not want to discuss the variations - whereby the Knight Chess Piece starts from a different position and finishes in a different position on the chessboard.

Variation 1 - Found in Putnam and Wood's Book. The authors did not know Euler.

Variation 2 - Found in Vaincre 3, September 1989. Plantard never mentioned Euler.

Variation 3 - Found in Euler, "Solution d’une question curieuse qui ne paroit soumise à aucune analyse" (1766).

At least we agree on something: Plantard is a variation of Euler's path. It would have been really stupid for him to use the same starting position!

That's why he did exactly what Euler suggested on the same paper.

Variation by rotating the chessboard:


Variation by inversion of direction:


Variation by changing starting position:


These rules are so obvious that now they are present in any modern books about mathematical games. Who knows from which book Plantard got it? I don't. I just located the oldest closed path from which Plantard's tour was generated: the one by Euler. It would be really interesting to find an older author of the same closed path (or of one of its variations).

I never wrote that Plantard read Euler's text: it is an information which is absolutely useless which cannot be demonstered, being the same rules and the same path in tons of other more recent books.

Everything is available here:
http://www.renneslechateau.it/rennes-le-chateau.php?sezione=studi&id=greatparchment
See footnote #6.

Not from Euler.

Interestingly, the earliest known examples of a cryptotour (which is what this is) were published in a French magazine in the mid 1800s ( http://faculty.olin.edu/~sadams/DM/ktpaper.pdf page 8 ), right in the time of Sauniere.

And you opened a thread just to write such a dogmatic sentence you can't prove?!

In 1880 Italian "Scapigliatura" (the artistic movement which developed in Italy after the period known as Risorgimento) printed a booklet titled "La farfalla" (The butterfly) with a closed knight's tour as solution of a word puzzle. You can find here the "rebus" and its solution:
http://www.renneslechateau.it/indagini/articoli/5x260.pdf
It was published by me on Indagini su Rennes-le-Château 5 (2006), p.260.

The information relating to Euler should be consigned to a footnote, because it is only of marginal interest to the subject matter of the Large Parchment and which Knights Tour is used to decrypt the hidden message.

Mariano Tomatis is very good at putting the most important and most relevant information into footnotes, and the most useless and boring rubbish into the main text of his articles.

I totally agree!!!

Then the reference to Euler should be relegated to a footnote.

Be serious, please. All Rennes-le-Château history should be relegated to a footnote in the History of the Mankind.

The reference to Euler is only of marginal interest to the article about the Large Parchment.

In many fields and contexts, such as historical writing, it is almost always advisable to use primary sources if possible.
It is irrelevant the DIRECT (primary or secondary) source of Plantard's Knight's Tour. It is relevant the oldest identical cyclic Tour in print. Euler's work is the primary source. That's why I quoted him in a paper about Knight's Tours. It is quite obvious.

I know very well why you'd like to relegate it to a footnote: you are worried by the opportunity I give to some hypotetical silly person who could write that Euler's tour proves that Abbé Bigou was the author of the parchment. I think that it would be absolutely silly, but I will not manipulate facts by hiding them (as you suggest) just because you are afraid of silly scholars.

It is not identical.
It is a reverse-version.

Plantard never mentioned Euler.

And here is the Primary Source for the Knight's Tour on the chessboard in relation to the Large Parchment: "Vaincre" Nr 3, September 1989. As mentioned by Pierre Plantard.

You cannot distinguish between primary and secondary sources. I quoted both.