by Jean-Pierre Messager, 08/24/2005. (french version here)
One of the many blunders of Igor and Grichka Bogdanoff's book Avant le Big Bang is the assertion, written twice in the very first chapter that "phi, the golden ratio, is transcendental". It is only one (quite elementary though) in many, many others. No one, except Igor and Grichka, never insisted much on this issue (there are more interesting blunders in their work - for the "Bogdanov supposed hoax affair" - about physics and intermediate math). Anyway, They first tried to justifiate technically this assertion, but they got completely lost in the details of Liouville work or in basics of algebraic geometry and wrote even bigger stupidities then. At the end, they explained, on a french speaking forum first (in a forwarded e-mail from Igor Bogdanov by a 'fan' first, then by Igor Bogdanov - as the nickname 'Anonymus' - himself), then everywhere, that this was the editor fault (which is Grasset), "quote has been deleted around the word 'transcendental'".
(Note : a transcendental number is, by definition, a number which is not a solution to a polynomial equation with integer coefficients. Phi, the golden ratio, by definition, is the greatest solution of the equation X^2-X-1 = 0, which is... a polynomial equation with only integer coefficients.)
Here are the interesting parts of Igor & Grichka official justification :
Dans les premières épreuves de notre livre (cf. copie ci-jointe des épreuves: http://igor.bogdanov.free.fr/EPREUVE.jpg , et http://igor.bogdanov.free.fr/epreuve-detail.jpg) le petit paragraphe consacré, en note, au nombre d'or était différent de celui qui apparait dans le livre. Voici ce que nous avions écrit page 22 des épreuves du 26 mars 2004 :Later on the same forum, Igor Bogdanov wrote :
Et si vous calculez, sur une courbe logarithmique transcendante appelée 'spirale d'or', le rapport entre deux nombres successifs de cette suite, vous obtiendrez un nombre 'transcendant' (qui comme le nombre pi n'a pas de fin et que les mathématiciens du XVIIe siècle ont appelé « nombre d'or ».)
Chacun peut comparer avec la page 22 de cette épreuve que nous avons mise en ligne : le mot « transcendant » apparaît bien entre guillemets.
Dans les épreuves de l'ouvrage, nous avions donc (i) placé la phrase `sur une courbe logarithmique transcendante appelée `spirale d'or'' et (ii) écrit le mot transcendant (nombre `transcendant') entre guillemets, pour spécifier (dans un sens non strict) son lien avec la fonction transcendante engendrant la spirale d'or (et de manière implicite son lien avec le mot infini de Fibonacci). En tout état de cause, les guillemets placés à `transcendant' étaient destinés à lui attribuer un sens `grand public'. Dans le premier tirage, la phrase `sur une courbe logarithmique transcendante appelée `spirale d'or a été jugée trop technique par l'éditeur et a donc été supprimée.
Finalement, suite à la normalisation du traitement de texte, les guillemets n'avaient pas subsisté mais ont été rétablis depuis. Il faut donc lire: 'un nombre `transcendant' (qui comme le nombre pi n'a pas de fin..)'. Muni de guillemets, le mot transcendant ne prête absolument pas à confusion (et renvoie implicitement aux propriétés du mot de Fibonacci).
En ce qui concerne la « transcendance » du nombre d'or, j'ai indiqué le lien qui renvoie aux épreuves du livre où le mot « transcendant » apparaît entre guillemets. Le sens que nous avions donné, dans cette note en bas de page, au mot « transcendant » (la courbe transcendante, etc) est clair.
[...] Il en va de même pour les autres « erreurs » relevées par YBM.
which is, roughly translated :
In the first preprints of our book (here are scans : http://igor.bogdanov.free.fr/EPREUVE.jpg and http://igor.bogdanov.free.fr/epreuve-detail.jpg) the small paragraph, a footnote, about the golden ratio was different to what appears in the book. Here is what we wrote on page 22 of the preprint on Mars 26, 2004 :
If you compute, on a transcendental logarithmic curve called 'golden spiral', the ratio between two successives numbers of this sequence [The Fibonacci sequence], you'll get a "transcendental" number (which, as well as pi has no end) called the "golden ratio" by XVII century mathematicians
Anyone can compare this with the page 22 on this preprint we've made available on line : the word "transcendantal" appears clearly between quotes.
In these preprints, we had written (i) the sentence "on a logarithmic transcendental curve called 'golden spiral'" and wrote the word transcendental ('transcendental' number) between quotes, to specify (in a non-strict sense) its link with the transcendental function generating the golden spiral (and, in an implicit manner, the link with the word infinite from Fibonnacci). As a matter of fact, the quotes around 'transcendental' was there to give this word a more 'popular' meaning. At the first print the sentence "on a logarithmic trenscendant curve called 'golden spiral'" has been considered too technical by the editor and has been deleted.
Finaly, because of the normalization of the text processor, the quotes didn't subsist, but has been restablished then. You should so read "a 'transcendental' number (which, like the number pi has no end...) With such quote, the word transcendental leaves absolutely no confusion (and is a implicit reference to Fibonacci's word).
About the « transcendentality » of the golden ratio, I gave the link to the preprints of the book where the word "transcendental" appears between quotes. The meanning we gave, in this footnote, to the word "transcendental" (the transcendantal curve, etc.) is clear.
The same applies to others "mistakes" pointed out by YBM.
The undoubtfull proof being these images (stored locally and annotated) : a so-called scan of a preprint page from the editor and a a more detailled view of the text.
Clearly quotes are surrounding the word transcendental. As far as I am concerned that doesn't change much. But anyway, why not.
But let's wait a minute, there is something strange on the spacing of the two lines involved... And, even stranger, if you have a look at Igor Bogdanoff web site listing (as of 08/19/2005, but it didn't change within almost a year) you would notice another file : Epreuve.psd (shift click to save, it is unlikely your brower will display it), an Adobe Photoshop file!
Important : this file is stored locally as a exact binary copy of the original, here are checksums in order to authentify it :
md5sum = 074ff20771ce30bcc07d22f2e66baefa
sha1sum = 6827c81603054331fc8363ddd7ce43a961ef1c4e
I started from this file (since it have the better resolution), and did some checking of spaces comparing with a scan of the first printed edition of the book (lightgrey is Bogdanov's scan, black is from the printed book) :
(click on the image to see a full sized version)
Spaces are all wrong! There are two obvious problems :
Another curiosity, is that the "trans-" chunk is slightly outside of the paragraph box, as it would have been moved by hand.
But I noticed something even more puzzling : the 't' after the french opening quote had some problem, it has been partially erased by a white square (such as the one you have when copy/pasting a character as a bitmap with Photoshop). I did look at the jpeg files Igor and Grichka uploaded again, curiously, there, the 't' was complete. So I opened the photoshop file again and then realized I had (un)fortunately disabled one of the layer of the document. This layer kept a trace of Igor's editing of the bitmap file : replacing a partially erased 't' with a real one and moving a bit another part of the sentence to give room to the closing french quote. Here is the layer which kept track of the moves of two bitmap blocs (the void part of the layer being filled in green) :
If you do have Photoshop you can check this easily. If you haven't you can use the great free software tool The Gimp, as I did. With this beautiful piece of software I designed a small gif animation where you could see alternatively the state of the footnote, with and without this interesting layer visible :
(click on the image to see a full sized version)
The wrong spacing and the image processing recorded in this layer prove that the final so-called "scan of a preprint" (including a timestamp supposed to be a evidence) is nothing but a fake designed with Photoshop by copying the selections of two french quotes taken elsewhere on the page (ironicaly, probably around « nombre d'or ») and pasting them around the cut word "trans-cendant", chunks of text had to be moved slightly in order to make room for the quotes and a 't' had then be copied to hide the pasting of the opening quote. Another interesting detail : the image editing timestamp, recorded by Photoshop inside the file itself (28 of september 2004) is quite posterious to the first printing of the sold book (june 2004).
At this point what can we say? That the Bogdanov's brothers are liars? Yes. They are fraudsters? Yes. They even falsified their own text in order to escape critics? Yes. That they are incredibily unskilled, even in fraud? Yes.
And we can say that because we have an electronic, authentified, proof of it.
By the way, I can now assume, as Igor insisted, that the same applies to the others Bogdanov's blunders : They could only respond to them by falsifications and lies, what they did for the ones they answered.
N.B. As of 15 of september 2005, Igor Bogdanov has removed on his site all related files. The URLs and file contents has been authenticated and stored by a bailif on the 25 of august 2005. The certificate of the depository could be obtained, on well-founded demand, at firstname.lastname@example.org.
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