Nature on El Naschie

Honestly I have a problem with journals published by a for-profit corporation to begin with unless it's something like "IBM Technical Notes" or something like that. I tend to think non-profit societies are the better place for journals, but I also think peer review in general is in a very slow decline, particularly with the advent of the arXiv. Some string theorists were supposedly publishing exclusively on the arXiv over a decade ago.

Perhaps this is a good place to mention that Springer deleted the arxiv references from a paper Sean and I recently published in ICALP. I corrected this on the proofs and they neither replied nor made the changes.

It made me realize that referencing journals at all is just a polite fiction that most of us subscribe to. Really we should only reference the arxiv, since that's what we actually read.

Aram,

Good grief. That's ridiculous. And unethical. I wonder if Springer is a member of "Committee on Publication Ethics"?

Oops - I spoke too soon. After I complained a third time, cc'ing a random senior editor, I got a reply saying that it was not their policy, but a technical error and that they'd be happy to print an erratum for our article.

Aram you should make them print the erratum. I mean sure you won't make any friends at Springer, but still that would be one awesome erraturm. One you could show the grandkids :)

http://elnaschiewatch.blogspot.com

just want to let you know about my blog

Der ZEIT Artikel über Hr. Mohammed S. El-Naschie, den gröÃten Physiker unserer Zeit wurde nun endlich entfernt. Es ist eine Schande wie die Neider Hr. El-Naschie immer wieder den Nobelpreis vorenthalten. Es muss mit seinem Einsatz für Israel zu tun haben oder damit, dass er Muslim oder Araber ist. Seine Theorien sind bahnbrechend und jeder der das nicht findet ist doof. Und wird verklagt. Die ZEIT hat jetzt eingesehen, wer hier den Längeren hat. Hr. El-Naschie lässt sich doch nicht von einer renommierten deutschen Wochenzeitung diktieren, was wahr ist und was nicht. Er ist der Erfinder unzähliger nach ihm benannter Theorien! Er hat in sich schon irgendwie immer recht! Und das kann er auch mit Geld und Einfluss gegenüber der ZEIT durchsetzen. Und Hr. El-Naschie hat als Leidtragender nun irgendwie im Nachhinein logischerweise auch das Recht, den Autoren Hr. Drösser mit Hitler zu vergleichen. Zum Beispiel hier in diesem Blog: http://www.sciam.com/article.cfm?id=the-self-organizing-quantum-universe
Wie auch immer. Das Gute hat gesiegt. Nieder mit der Wahrheit, der Pressefreiheit und dem LHC! Jeder der das anders sieht ist ein Nazi!
Es lebe das Selbstplagiat und der Wissenschaftsbetrug!

You are talking about John Baez and someone mentioned Mohamed El Naschie so let me tell you that. It is really more than depressing to see in which publicity and media society we are living. Some wrote a great deal and I am sure with good intention. Unfortunately whether they realize it or not, they relied entirely upon hearsay. I am afraid they are being used without their knowledge to publicize what a determined little clique want the world to believe. If you are interested in facts then here are the facts. Mohamed El Naschies work was plagiarized by a group who wrote a paper published about a year or so ago in Scientific American. The group leader is Dr. Renate Loll. She works with the Nobel laureate Gerard âtHooft in Utrecht. She is originally German and worked in Max Blanc Inst. near Berlin. She knows Prof. El Naschie very well. Many years ago El Naschie gave a lecture in her Max Blanc Inst. in Germany. That is the first connection. The second connection is that El Naschie is a very close personal and scientific friend of Gerard âtHooft. Without his knowledge many scientists, students and collaborators of El Naschie wrote angry letters and comments to Scientific American complaining about Loll. This was quite embarrassing for Renate Loll and many of her friends came to her rescue. It was also embarrassing for Nobel laureate Gerard âtHooft because Renate got 1.2 million Euro prize for this work in addition to a 2.4 million Euro grant research money for the Inst. of Gerard âtHooft. In a cloak and dagger action decision was taken to punish and discredit El Naschie. That is how the whole thing started. The one man internet army John Baez was called to direct the attacks and a meticulous plan was drawn involving Nature, the Inst. of Physics, UK and finally Die Zeit in Germany. All this failed to reach the ultimate goal and now they are baffled as to how El Naschie could sustain all these attacks and stay stedfast. If you check you will find that Die Zeit first modified their article, then withdrew it. In addition El Naschie won a case in Munich against Die Zeit and another case in Hamburg is about to be won. It is established beyond any doubt that Christoph Drosser, the journalist of Die Zeit was lying. He was lying to help his friend also a German named Quirin Schiermeier who works for Nature. Nature has realized that they have been conned. They withdrew their article from the internet. There is a case pending in the High Court in London. El Naschie is a victim of a colossal defamation campaign led by all the above. Now to the facts about him. He is a scientifically and financially totally independent person since he was 30. He is now 66 and has run the journal for two decades. He neither needs promotion, nor fame nor in fact money. He got his Diploma in structural engineering from the University of Hannover. He got his Ph.D. from University College London in 1974. He was a student of Lord Henry Chilver who was the science advisor of Margaret Thatcher. He was invited to join Cambridge. He never applied nor needed to apply for a job anywhere, including Cambridge. He has published about 900 papers and his average productivity dropped when he became the Editor in Chief of Chaos, Solitons & Fractals which he founded. Chaos, Solitons & Fractals is still being produced and carries the name of Mohamed El Naschie and his papers are still being published. Scientific questions of the merit of his work should be discussed in scientific papers, not on blogs devoted to gossip. None the less, here we are. We live in a world it seems controlled by gossip. I am in Google, thus I am. It is really sad, extremely sad and the most sad point about it is that the truth nowadays is a function of repetition and publicity. John Baez notorious article about El Naschie disappeared and so did all the other articles. However from this evil defamatory article, millions of other articles mushroomed and the truth is totally lost. Then a year or two later these gossips land on your desk and you try to rationalize the irrational but all that you have done was really planned for you to do without your knowledge. I hope these facts do not depress you as it does depress me and I hope you check everything for yourself. Do not jump into conclusions. Just remember what Hitlers propaganda minister said. When you make a lie, make it so big that most people will say it is impossible for it to be a lie. Mohamed El Naschie was a great guy for twenty years running the journal which he founded for all that time. All of a sudden, after the publication of Renate Lollâs paper, everything changed and John Baez and his Zoran Skoda, the self appointed guardian of science has nothing else to do lately except defame El Naschie, his collaborators and students.

Best regards,

The comment signed by Otto Rossler makes the point of the previous comment. It is not from Otto Rossler. The comment is from a well known internet criminal and a perverted insect called Jason. He runs a pornographical blog devoted to obscenity and defamation. All what is written in German is lies and it is not from Rossler. He simply hijacked the name of a well known chaos scientist, namely Otto E. Rossler. Do you now see the point. Lies, pornography, kidnapped identity and then you are talking about a Pontiff? My dears, good luck and chow.
The Real Pontiff

Mmmm, tasty sock puppets.

El Naschie sock puppet "The Real Pontiff" thinks or pretends to think I wrote the comment above signed "Otto Rössler". I didn't, and I don't know who did.

I did, of`course!

Nothing but sick creatures whether they are called Jason, John Baez or Jack the Ripper. The internet was a great invention. People like Dr. Baez and the truly sick Jason have turned it into a sewer. A man who spends his time on these things could not be a man and not even a virus.

"man who spends his time on these things could not be a man and not even a virus." as opposed to those who spend time commenting on the commentors? Begone trolleo!

I was discussing the disgraceful affair of Jan Hendrik Schone. My friend reminded me of the despicable media witch hunt which sometimes exceptionally good scientists are subjected to. False accusations in science are not uncommon. In fact most of the accusations of fraud in science turn out sooner or later to be tendacious or downright criminal. The false accusations against Mohamed El Naschie are very similar to those made against Thereza Imanisha-Kari who was a colleague of Nobel laureate David Baltimore. Mohamed El Naschie is a senior colleague of Nobel laureate Gerard tHooft. Not only that but he is a very close personal friend to the entire family. Therefore I find it extremely disheartening to see that the media on the internet is not rehabilitating Prof. El Naschie with the same enthusiasm with which they defamed him. For instance the famous mathematician John Baez from the Dept. of Math. Of Riverside University in California, USA owes El Naschie a big apology. I have just read an article by Baez praising the golden mean to the sky. A few months earlier he was calling anybody who deals with the golden mean like El Naschie a crackpot. Occasionally it is very easy to find out the truth about things even if one is not a specialist. The citation index of Mohamed El Naschie is in the order of 4,000. By contrast the citation index of this man who made it his business to defame Prof. El Naschie, a certain mathematician from Croatia with a remarkable name Zoran Skoda is only 10 or 12. Jealousy seems to be an affliction to which scientists and not only film stars are prone. I must say that Nature seems to be the exception. Despite the high profile and the high prestige of Nature as the leading scientific magazine in the world, they have withdrawn all their allegations and have conducted a thorough investigation to find out how they were wrongly led to write the defamatory article against El Naschie. There is no doubt that the damage done to molecular electronics by Schones deception is tremendous. However it is nothing compared to the damage wrongly caused to Imanisha-Kari and Mohamed El Naschie. I think Dr. Renate Loll from the Dept. of Physics University of Utrecht Holland also owes a big apology for the witch hunt El Naschie was subjected to. She more than anyone else knows the reason and the force behind it.

The Proprietor of this blog may like to have a look at Sarah Limbricks article dated 2 Nov 2009. It is clear from this article entitled Editor of Scientific journal sues Nature that El Naschie has taken serious legal steps against the subject matter of your blog. El Naschie has hired one of Englands leading libel experts and a well established firm Collyer Bristow of London. It will definitely be a long and costly legal battle. However it is now clear to any level headed person that El Naschie must have profound reasons to take this step in the High Court. I think it is the new culture of internet defamation which must be stopped. Without the internet the allegations made by N Category Cafe could not have been possible and consequently this entire regrettable affair.

Sarah Limbrick would surely be interested to know what the leading libel expert in England had to say about the Nature article complained of. He said he is in a state of disbelief that the worlds most respectable scientific journal Nature should publish an article which bears all the hallmarks of the tabloid press. Another interesting point is the conspiracy theory linking the plagiarism of El Naschies work published in Scientific American with the Nature article as well as a far worse article published in Die Zeit. Interestingly all of these three publications are owned by Macmillan. I understand from confidential sources that a mega surprise will be released at the trial engulfing highly reputed names some of whom are Nobel laureates. The site is http://www.pressgazette.co.uk/story.asp?sectioncode=1&storycode=44545&c….

Sehr geehrter Herr Blog-Intendant,
anscheinend machen Sie sich ernsthafte Gedanken über Islam und Wissenschaft. Ich nehme an, dass Sie nicht an einer Verleumdungskampagne teilnehmen wollen, denn dafür gibt es im Internet genügend Personen die ihr Leben damit vertrudeln andere Menschen aus Frust zu beschimpfen und ihnen alles Mögliche in die Schuhe schieben. Wenn ich in dieser Annahme richtig bin, dann möchten Sie sicherlich folgendes wissen.
1. John Baez ist kein ernsthafter Mathematiker und noch weniger Physiker. Er hat sich lediglich durch seine groÃe Klappe einen Namen gemacht.
2. Renate Loll hat viele Arbeiten veröffentlicht, die letzte in Scientific American, die nichts anderes sind als eine Reformulierung der Theorie von Mohamed El Naschie, Laurent Nottale und Garnet Ord. Dies ist eine wissenschaftliche Unehrlichkeit in gröÃtem MaÃe.

3. Als Rache an EL Naschie hat Loll die mit Baez sehr befreundet ist ihn beauftragt die Verleumdungskampagne zu inszenieren. Nature, Quirin Schiermeier und Christoph Drösser waren nur Werkzeuge von John Baez.
4. Rückenstärkung bekommt Professor Renate Loll von ihrem Chef dem Nobellaureat Geradus `t Hooft. SchlieÃlich wird das Preisegeld zusammen geteilt.
5. Geradus `t Hooft ist ein enger Freund und Kollege von El Naschie. Was für eine Freundschaft. Der Rest ist Schweigen.
6. Wenn Sie im Obergericht in London nachfragen, werden Sie wissen, dass El Naschie Nature, Quirin Schiermeier, DIE ZEIT und Scientific American vor den Kadi genommen hat. Das ist das erste Mal in der Geschichte der renommierten Zeitschrift Nature, dass sie vor Gericht stehen. Glauben Sie im Ernst, irgendein Professor wird diesen Schritt wagen wenn er im Unrecht wäre. Sie müssen auch wissen, das die gröÃte Anwaltskanzlei Londons Professor Mohamed El Naschie repräsentiert. Diese Kanzlei würde niemals jemanden gegen Nature repräsentieren wenn er im Unrecht wäre. Die haben einen Namen zu bewahren.
Das sind die Tatsachen und wenn Sie es unverändert in Ihrem Blog veröffentlichen dann helfen Sie dabei die Wahrheit ans Tageslicht zu bringen.

The time of Huxley and Darwin were the golden age of science. Now we have funding, American style. Once you have money playing such a fundamental role, as is the case in big science, then for better or worse, ethical standards change. You remember a theorem a day means promotion and pay. Mohamed El Naschie was of course quite naïve. He is an engineer. High energy physics is not his professional work. He practices it in a gentlemanly manor as a hobby. He was woken up in a bitter way. Unlike engineers prizes are the only way for theoretical physicists to come to big chunks of money. Do I need to say more? Good luck with your litigation. You will need all your savings, El Naschie that is, to pay your lawyers.

It is not just a matter of funding which is behind the defamatory article in Nature. I think prestigious prizes also play a fundamental role. I read that somewhere on the net but strangely it was removed. The prize in question seems to be the Nobel Prize. Some say that not even the devil could have thought of something as harmful to science as the Nobel Prize. They reckon it is not the prize money itself but the publicity which the Nobel Prize brings. In turn this is translated into money. Noting the recent discovery of the sleaze at the Ivy Leagues in the US I am not astonished that this cash is badly needed. If this is true for Harford why should it not be true for the Einstein Inst. in Berlin or the University of Utrecht in Holland. The names involved with Mohamed El Naschie are quite interesting. Somebody wrote yesterday that he would not be astonished if a best seller comes out of this horrific story in the next few years. It is alright for some. The same writer said try as hard as he can, he simply cannot fathom how the Editor in Chief of Nature could allow this tabloid piece to be published in his journal. He must have his reasons or he had a very deep snooze. He added that he may have had too much respect for Nature just as he used to have for the Nobel Committee. This implies that he has none any longer which is interesting. Finally the writer noted that Mohamed El Naschie had no vested interest and certainly no materialistic interest in publishing his papers because he was sufficiently rich and famous before turning to theoretical physics. The author of this remarkable comment closed by noting that any successful engineer who leaves engineering to be become a theoretical physicist should have his head checked. In other words, he doubts the sanity of theoretical physicists, Mohamed El Naschie included.

I am pleased that the truth has prevailed. Nature is now accused of trying to undermine Mohamed El Naschie deliberately. This accusation is not frivolous. How else can we explain the blind vicious attack by certain doubtful blogs on the golden mean work of El Naschie and how Quirin Schiermeier the journalist working for Nature utilized these vicious attacks to write a completely unacceptable article in Nature. Then came the heavenly justice when a German professor von Storch complained on his blog that the Nature article of Schiermeier deliberately misquoted him. He was gentle enough to say that the harm was not great. However in principle the harm could have been great. No one has the right to smear the reputation of anyone whether deliberately or recklessly due to irresponsible journalism. Now to the burning scientific question. How does the golden mean enter into quantum mechanics. The answer is as simple as it is ingenious. Mohamed El Naschie reformulates quantum mechanics in spacetime following the same concepts used by Richard Feynman as well the classical work of Einstein. Since the building blocks of spacetime are his elementary random Cantor sets and because these random Cantor sets possess the golden mean as a Hausdorff dimension, the golden mean slips into the fundaments of quantum mechanics. Nothing that quantum mechanics is the most fundamental theory upon which science is based, the golden mean could rightly be described as the basis of science. From this reasoning the ideas which Ed Nash expressed in his previous comment follows effortlessly.

Pardon me if repeating something above (I just don't have time) but wouldn't it be a good journal policy, to require even Editor's papers to be approved by referees as much as anyone else's?

Dave, what is very surprising is the fact that the so called El Naschie supporters all over the planet are finding blogs and spamming them with the same kind of comments.

http://jatkesha.wordpress.com/2008/11/14/el-naschie-revolution-in-hep/

Looks like there are a bunch of his supporters and they think he is being victimized for reasons I don't want to mention here.

I imagine the journal Bertrand, which only publishes papers not publishable in any journal. Does its editor in chief publish papers in Bertrand?

Natureâs Lawyer Taylor Wessing supposedly a reputable law firm is losing its marble. The reason is as childish and idiotic as one could possibly think. El Naschie is giving interviews in Arabic newspapers scorning Nature and its low standards. Quoting from the obscene site called Watching El Naschie day and night, they say he gave false information about the High Court Case El Naschie versus McMillan, Nature and Quirin Schermeier. El Naschie is supposed to have said he more or less he won the case and that Nature will pay him ten million pounds. I am not sure about the ten million pounds but I am sure that El Naschie has more or less won the case. Nature has no case whatsoever. Anyone familiar with British libel law knows that for sure. The third point is that Taylor Wessing is using all conceivable delay tactics. Complaining about interviews in Arabic newspapers must be an expression of Taylor Wessingâs desperate attempt to defend their client. They should know better. England is not the USA where noise and big words could score anything with the court. English judges are very cool. On the other hand, Taylor Wessing could not find a client who is more willing to pay than the rich McMillan. The lawyers of El Naschie are confident that they will win the case. Collyer Bristow are far more professional than Taylor Wessing. They have their client under control. They are calling the shots and setting out the tactics. By contrast Taylor Wessing are counting time sheets. I am ready to bet one to ten that Nature is going to lose this case no matter how well connected they think they are. Nature has been twisting things for too long and there is something like a backlash now particularly with regards to environmental issues. Quirin Schermeier lied and his colleague in Die Zeit Christoph Drosser, is on the records of the courts in Hamburg as a blatant liar. Wouldnât it be better for Nature to donate the money they are spending on a hopeless lawsuit to some charity or even to scientific research?

Natureâs Lawyer Taylor Wessing supposedly a reputable law firm is losing its marble. The reason is as childish and idiotic as one could possibly think. El Naschie is giving interviews in Arabic newspapers scorning Nature and its low standards. Quoting from the obscene site called Watching El Naschie day and night, they say he gave false information about the High Court Case El Naschie versus McMillan, Nature and Quirin Schermeier. El Naschie is supposed to have said he more or less he won the case and that Nature will pay him ten million pounds. I am not sure about the ten million pounds but I am sure that El Naschie has more or less won the case. Nature has no case whatsoever. Anyone familiar with British libel law knows that for sure. The third point is that Taylor Wessing is using all conceivable delay tactics. Complaining about interviews in Arabic newspapers must be an expression of Taylor Wessingâs desperate attempt to defend their client. They should know better. England is not the USA where noise and big words could score anything with the court. English judges are very cool. On the other hand, Taylor Wessing could not find a client who is more willing to pay than the rich McMillan. The lawyers of El Naschie are confident that they will win the case. Collyer Bristow are far more professional than Taylor Wessing. They have their client under control. They are calling the shots and setting out the tactics. By contrast Taylor Wessing are counting time sheets. I am ready to bet one to ten that Nature is going to lose this case no matter how well connected they think they are. Nature has been twisting things for too long and there is something like a backlash now particularly with regards to environmental issues. Quirin Schermeier lied and his colleague in Die Zeit Christoph Drosser, is on the records of the courts in Hamburg as a blatant liar. Wouldnât it be better for Nature to donate the money they are spending on a hopeless lawsuit to some charity or even to scientific research?

One has to be totally blinded by hatred not to acknowledge that the golden mean in quantum mechanics is the greatest surprise ever confirmed experimentally in the recent history of quantum mechanics. I for one was skeptical about El Naschieâs golden mean quantum mechanics. I was skeptical because I did not do the calculations for myself. I relied on hearsay and that there are many extravagant claims made in science based on the golden mean. That was my prejudice and my mistake. Doing the elementary calculation of the two slit experiment with quantum particles using El Naschieâs golden mean topological probability was a unique experience. See this confirm now in the laboratory is almost a divine experience. This is Paul Diracâs criteria of beauty taken to its ultimate. It is breathtaking to know that nature is that subtle and that beautiful. Even someone who is as down to earth as Gerard âtHooft must admit that El Naschieâs quantum golden field theory is breathtaking in its simplicity and aesthetics. Maybe I am being over the top for the moment but you do not get every day an exact irrational value such as the golden mean coming out of a laboratory testing a fundamental theory.

Sorry "Charles" you've stumbled on someone who actually knows what the experiment which revealed the "golden mean in quantum mechanics" is about. And it ain't got nothing to do with anything El Naschie has ever written as far as I can tell. It's certainly not "fundamental": it's a discovery about the perturbation of the critical point of a transverse Ising model where the particle spectrum is related to an E8 spectrum. It's very cool, and good solid research as opposed to, in my opinion, the garbage that is created by the love of your life.

Please, sockpuppets, if you're going to spam here, at least make them interesting and not just love letters to your leader.

Oh wow, reading these comments is almost as much fun as browsing vixra... Fruitloopery, sockpuppets *and* a complete inability to write in paragraphs! Surely it doesn't get any better than this.

Dear Dave Bacon, I do not doubt at all your expertise on the subject of Ising model. However this is a fundamental difference between the narrow view and the large picture. The Ising model is embedded in the larger picture. This is not a love letter to our leader. This is only an attempt to be fair and even handed, if you know what I mean. When you read the comments of leading scientists you will immediately realize that they are very excited about the larger picture. Charles merely points out that Mohamed El Naschie talked of the larger picture before anyone else. Prejudice creates selective reading. How else could I explain that you are forgetting the hundreds of thousands of comments coming from John Baez and his internet army as he calls it mocking El Naschie because of the golden mean. They totally overlooked that the golden mean is inert to E8. They also overlooked the necessity for an additional transfinite correction to E8 to fit completely into Hamiltonian dynamics. It is all explained in The theory of Cantorian spacetime and high energy particle physics (an informal review), Chaos, Solitons & Fractals, 41, 2009, p. 2635. Since you are so familiar with this subject then you should have stumbled on some very early papers by El Naschie in which he applies his theory of the golden mean E8 to polymers as well as the Ising model. I recall that El Naschie referred to Garnet Ord who dealt with similar models. I also recall something connected to knot theory. I meant no offense and I hope my remarks are useful. Thank you for your comments.

Open mind indeed. Of course you are welcome to your own opinion (especially here in the United States where we do not have onerous libel laws which are often used to suppress free speech.) My _opinion_ is that the stuff in that paper isn't even close to real science.

If you want we can play "explain that." I'll find something in the paper which is incorrect or blatant non-sense, and you explain it to me! It will be fun (by fun I mean a waste of my time.) Let's start with a simple one. In section 5.1 it is claimed that the mass of the charge pion is related to the mass of the electron via the elegant. M_pion= (2 alpha^(-1) -1 ) M_e. Of course this is numerology of the worst sort...the kind that is experimentally wrong:
M_pion = 139.57018(35) MeV
M_electron = 0.510998910(13) MeV
alpha^(-1) = 137.035999084(51) (or is it just 137 as is claimed in the text...either way it won't work.)
i.e. 2 alpha^(-1) -1 = 273.071998168
i.e. (2 alpha^(-1)-1)M_electron = 139.5394934
Which is....not correct up to experimental accuracy. Oops, my mind isn't open enough to accept results which are...um...experimentally ruled out.

Please Dave, you forget to add transinfinte correction and gravitational correction due condensation of gravitational instantons. I promise, if you have included these type of corrections you will, hopefully, get the correct result.
You should think in terms of the larger picture.

El naschie and his followers usually think in terms of this large picture. To grasp reality one should be immersed in this larger picture. As Huan (one of the greatest supporter of E-infinity theory).
You can check yours self a typical paper for Huan using E-infinity theory

Hierarchy of wool fibers and its interpretation using E-infinity theory
Chaos,Solitons and Fractals 41 (2009)1839 â1841
Ji-Huan He, Zhong-Fu Ren, Jie Fan, Lan Xu
Abstract
Why do wool fibers show excellent advantages in warmth-retaining and many other practical properties? The paper concludes that their hierarchical structure is the key. Using E-infinity theory, its Hausdorff dimension is estimated to be about 4.2325, very close to El Naschieâs E-infinity dimension, 4.2360, revealing an optimal structure for wool fibers.

The same article again with little modifications
Hierarchy of Wool Fibers and Fractal Dimensions
International Journal of Nonlinear Sciences and Numerical Simulation,9(3),293-296, 2008

http://works.bepress.com/cgi/viewcontent.cgi?article=1037&context=ji_hu…

Abstract
Wool fiber shows excellent advantages in warmth-retaining and many other practical properties possibly due to its hierarchical structure. Its fractal dimension of wool fiber is calculated which is very close to the
Golden Mean, 1.618. The present study might provide a new interpretation for the reason why wool fiber
has so many excellent properties.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

You can notice the confilict between the two abstracts, in the first fibre wool has dimension 4.2325 (which is greater than the embedding space) and in the second it is 1.618. I hope El naschie can explain these remarkable results.

Finally please don't lough, these results are very remarkable if you think in terms of larger picture.

The path toward the large picture is well trod by Sheep. That was what I was missing!

Now I know why that damned coupled rf-squid model doesn't match experiment... (smacks head)... we forgot to add the damned transinfinite correction again.

Come to think of it a lot of theoretical physics becomes pretty easy once you take the transinfinite correction into account.

First apply the transfinite correction, guys. Only if that doesn't work should you resort to the transinfinite correction.

The experimental discovery of the golden mean should come as no surprise to anyone who is familiar with the VAK. The VAK attractor of Kolomogorov is a conjecture made by the great French topologist Rene Thom. It is nothing more than applying KAM theorem to quantum mechanic. KAM theorem states that the most stable stationary states which are called periodic orbits correspond to the most irrational winding numbers. The most irrational number is the golden mean. Applied to quantum mechanics, this means that the most stable particle which can be observed experimentally will relate to the golden mean. That is all folks. You see we theoretical physicists have always a minimum of new ideas. Our ideas are always extremely simple. We tend to prefer making very difficult computations rather than strenuous thinking using new ideas. All what distinguishes Mohamed El Naschie from the rest of us is that he was less lazy with regards to new ideas and extremely lazy when it comes to strenuous computations. That is how he came to the VAK and he tried it out. The discovery of the golden mean in quantum mechanic in Helmholtz Centre must be a triumph for the VAK. It is not a triumph for Mohamed El Naschie because no one person has ever done anything on his own. It is always the collective effort of humanity. If Rene Thom would be alive today, he would have bagged a Nobel Prize in physics besides his field medal in mathematics. If you do not want to give Mohamed El Naschie a prize because he is a Muslim, I assure you many Christians, Jews as well as atheists worked on the VAK. I am sure you will find somebody suitable who is not offensive to the establishment to give a Nobel Prize to for solving the mystery of quantum mechanics.

"Applied to quantum mechanics, this means that the most stable particle which can be observed experimentally will relate to the golden mean."

Um, the particles in the experiment on E8 and the transverse Ising model are not exactly what I'd call "stable."

It must be fun to live in a metric space in which the distance between the work discussed in the above comment and a Nobel prize is considered short. We shall call it the "El Naschie metric"!

I have a theory that may or may not relate to the golden mean. Based on the grammatical and syntactic similarities of all of the pro-El Naschie commenters here, my theory is that they are all the same person posting under different names. I would speculate that in fact they are all El Nashie himself.

To test this hypothesis, I ran all the comments in question through a Helmholtz Centre VAK attractor-based sphygmanometer biased with a transinfinite correction and voila, a consistent theory of quantum gravity based on E8 symmetry popped out! Of course since I'm one quarter Scottish the Nobel committee will snub me.

"No one can take us out of the E-infinite paradise created for us by El naschie, I see it but I can't believe it"
Ping-Bong He

El naschie is a real spark in the human written history, he is startling . Al his predictions based on E-infinity theory are well verified. Among many and just to name:

1-The well experimentally verified results about fiber wool pioneered by Huan. Who showed that the Hausdorff dimension of fiber wool is to be about 4.2325, very close to El Naschieâs E-infinity dimension, 4.2360. According to Huan this reveals an optimal structure for wool fibers. This is an easy proved fact and it doesnât need high energy.

Hierarchy of wool fibers and its interpretation using E-infinity theory

Chaos, Solitons & Fractals, Volume 41, Issue 4, 30 August 2009, Pages 1839-1841

Ji-Huan He, Zhong-Fu Ren, Jie Fan, Lan Xu

2- A remarkable achievement of El naschie is his unique extra ordinary talent in revealing a deep connection between double slit experiment and particle physics. That is really a breakthrough in the field has never been acheived.

The two-slit experiment as the foundation of E-infinity of high energy physics

Chaos, Solitons & Fractals, Volume 25, Issue 3, August 2005, Pages 509-514

M.S. El Naschie

3- El naschie is gifted in doing simple calculations and getting non-perturbative results. While ordinary people can get results by using supper computer in a one year, El naschie get the same results straight forward by counting on his fingers without using computer at all. These are due his GOLDEN FINGERS.

On quarks confinement and asymptotic freedom

Chaos, Solitons & Fractals, Volume 37, Issue 5, September 2008, Pages 1289-1291

M.S. El Naschie

Quarks confinement

Chaos, Solitons & Fractals, Volume 37, Issue 1, July 2008, Pages 6-8

M.S. El Naschie

4- With a simple rope with knots El naschie could derive the spectrum of possible Elementary particles, and realy this is the discovery of the century.

Any one can just bring a rope with knots and could easily testify El naschieâs conjecture.

Fuzzy multi-instanton knots in the fabric of spaceâtime and Diracâs vacuum fluctuation

Chaos, Solitons & Fractals, Volume 38, Issue 5, December 2008, Pages 1260-1268

El naschie may be the greatest thinker in the history of mankind and his theory is the most important discovery since the invention of wheel. El naschie maybe the most remarkable event after cosmic big bang. His theory can describe every thing after big bang and Iâm sure El naschie will extend his theory to accommodate what has been before big bang. Please donât wonder it is an E-infinity theory that could deal with such a long history of time.

My Physics professor wife used a "supper computer" when she wrote:
"The Dinner-Time Machine", (short story) Space & Time #83, 1994.
CARMICHAEL, CHRISTINE (M.) PH.D. [Mrs. Jonathan V. Post]; also as Christine Post
* The Dinner-Time Machine, (short story) Space & Time #83 1994
* Major Weir's Bookcase, (novelette) Amazing Sep 1988
* My First Body, (short story) Space & Time #81 1993
* Periodic Table of Aliments (with Jonathan V. Post), (humor) Analog Oct 1992
* A Scorpion-Tailed Romance, (short story) Space & Time #82, 1993
* Twilight in the Western Isles, (short story) Amazing Sep 1989

To: Researchers working on El Naschie E-infinity Cantorian-fractal spacetime theory of quantum high energy physics.
Dear All,
Even the most gullible, unsuspecting and least inclined to a conspiracy theory must be asking themselves by now why all this viscous attack not only against E-infinity and fractal spacetime as a theory but far worse against Prof. Ji-Huan He, L. Marek-Crnjac, Prof. Mohamed El Naschie, Gerardo Iovane and in fact every single member of the E-infinity group. Who is behind all that? Who is behind El Naschie Watch and the daily hundreds of perverted viscous comments aimed at any and everybody who has anything good to say about us, particularly Prof. El Naschie and Prof. He? Is it the establishment and what kind of establishment is this which is scared to death from a couple of simple equations and the word fractal spacetime? If I did not know better I would think that a Cantor set is where the devil himself lives or it is a code name similar to D-day or Dessert Storm only directed towards theoretical physics. In what follows I would like to explain to you in some detail that we have achieved a great deal with our theory. The work of Goldfain, Mohamed El Naschie and before them Nottale and Ord and Richard Feynman were all not in vain. I would like to explain that we are on the verge of a great truth and paradigm shift in physics. Some unteachable elements of the establishment are resorting to methods far away from science which failed in the past to prevent the inevitable. Others more cunning are working hard to translate our terminology to another terminology. The famous plagiarism which took place in Scientific American is only one of the very early and visible examples of this cunningness which is in reality lack of scientific honor as aptly described by one of us in a letter to the people concerned.
Let me start by first counting the unshakable final results which we have achieved on a few points and then we will move from there to discuss the wider picture and the experimental facts which are coming in daily. In brief we found the following results which will endure any future discoveries and could be counted as the absolutely secured part of what we have done.
1.The geometry of micro spacetime is best described by a fractal. This is the result of the work of Garnet Ord and Laurent Nottale following the pioneering idea of Richard Feynman and his path integral method.
2.The building blocks of spacetime are elementary random Cantor sets. The Hausdorff dimension of these elementary random Cantor sets is the golden mean. By varying the resolution you can obtain everything you want from an infinite collection of these Cantor sets. This is the essence of the work of Mohamed El Naschie, L. Crnjac, Ji-Huan He and also G. Iovane.
3.The expectation value for the Hausdorff dimension is 4 plus the golden mean to the power of three. This is 4.23606799. The expectation value for the topological dimension is exactly 4. The formal dimensionality is however infinite. This will bring us nearer to the theory of multiverse as I will explain later.
4.The most fundamental symmetry groups are the exceptional Lie symmetry groups. These are 8 in all forming a family. The most important member of this family is E8. What is important however is that the sum over all exceptional Lie symmetry group leads to a probability measure which is consistent with the random Cantor sets and its golden mean dimension. The sum of the dimensions of all eight groups was shown by El Naschie to give a total dimension equal 4 ¬α Ì=548 where ¬α Ì = 137.
5.You can extend summing over exceptional Lie group to compact and non-compact exceptional Lie groups and find 17 of them. The sum of all dimensions was shown by El Naschie to be 5α Ì=685. This theory led to speculation about an even larger symmetry group, namely E12 which is more important than the recently discovered E10 and E11 but I will not consider this part of secured knowledge and I will stop here, mentioning only that Ray Munroe was the first to find E12 before El Naschie.
As for the experimental verification we now have a few extremely important ones:
1.Indication of a Cantorian spacetime and a fractal spacetime coming from an analysis of the cosmic rays and microwave background radiation. The expert on the first is Goldfain and on the second Mohamed El Naschie and you can consult their publications on this. However there are many results independent of our group confirming the same and it would be great if Goldfain could write a report for us all on this for internal use on our blog.
2.The discovery of E8 in nanostructures and the golden mean in quantum mechanics which was recently made public by the Helmholtz Center in Germany is the most definite result confirming Cantorian spacetime geometry experimentally. I say this is the tip of the iceberg. From now on you will see the golden mean mushrooming everywhere in quantum mechanics and high energy physics.
Under these circumstances many people became worried and anxious that a group like ours, not considered to be specialists in mathematical physics and high energy particle physics should have made such a major step forwards and been able to predict the masses of elementary particles and the value of fundamental constants with such precision and ease. The frustration is to a certain extent understandable and the reason is the following.
1.Garnet Ord and Nottale did not use set theory per se. Mohamed El Naschie was also not the first to propose set theory in quantum mechanics and high energy physics. The first impulse came from somewhere completely different. They came from David Finkelstein and Carl Friedrich von Weizsaker. The two great scientists were not interested in details. However Stanley Gudder in the USA and his school as well as Fay Dowker in England and her collaborators felt that partially ordered sets could solve the problem of quantum mechanics. They were rather near but not quite there because they had no simple way of performing real quantitative calculations. Far better suited to quantum mechanics are random Cantor sets. When you use them you have the golden mean. And when you use the golden mean then you have at your hand an unrivalled number system which can handle any complex computation with unheard of simplicity. This was Mohamed El Naschieâs good luck or misfortune. By pure accident or providence El Naschie stumbled on a basic problem in fundamental mathematics. Basing your number system on the irrational number and the irrational golden mean system you can see the world with new eyes with unheard of simplicity. The recent book by Alexey Stakhov published in World Scientific under the title The Mathematics of Harmony is a profound meditation on this theme. Chaos, Solitons & Fractals had the honor of publishing the larger part of Prof. Stakhovâs work. I think when certain elements in the establishment realize that we surpassed everybody else, they panicked.
2.When certain elements of the establishment panicked, they published the paper in Scientific American in 2008. To overcome the problem of not having the golden mean they used the most powerful existing new generation of computers and pretended to use their expression, that they found the holy grail of theoretical physics by calculating the four dimensionalities of spacetime from first principles using a desktop computer. One of our associates joked about them by calculating the same dimension using a pocket calculator. In fact using the golden mean you can find everything by counting on your fingers, that is if you know the rules of the golden mean arithmetic. The rest is history and you can read it on the comments of this work in Scientific American.
3.An exceptional member of the mainstream who does not normally work in quantum mechanics is Prof. Tim Palmer of the University of Oxford. This professor realized the importance of fractals for quantum mechanics. His first paper did not refer to our group at all. Later on he revised his stance and he referred to Garnet Ord, Laurent Nottale and Mohamed El Naschie on the first page of his revised ArXived paper. Later on when this paper appeared in the Royal Society, the three names were relegated to the very rear of the paper. Never the less, the man at least had sufficient objectivity to acknowledge our priority. Of course he should have noticed that there is no difference between our work using Rene Thom/El Naschie VAK and his proposal. Spacetime and phase space are exchangeable at this high energy where time is spatialized. Anyway this was at least one of the establishment acknowledging that we were there first. On a personal level we have the greatest respect for Prof. Tim Palmer who is an exceptional meteorological scientist.
4.There is at least one earlier attempt to use elements out of our work and overlook mentioning our group. The first which comes to my mind is that of Dr. Garrett Lisi. He is not a mainstream scientist at all but he was supported by some people from Perimeter Inst. in Canada. Needless to say, most of what Lisi wrote about E8 was well known to us long ago and was published in Chaos, Solitons & Fractals years before Lisiâs paper. Of course the establishment in general neither likes Lisiâs nor our work and thus we and Lisi were equal although we were more equal than Lisi in being disliked by the establishment for reasons which have no scientific basis.
5.Here I must now mention the discovery of the important utility of the multiverse. The objective of this comment is really to talk about this subject. What I have written so far was just a summary of the past. I would like to show clearly that the multiverse theory is nothing but a new label for our Cantorian spacetime theory particularly when we couple it with the holographic principle of âtHooft.
ON THE EQUIVALENCE BETWEEN THE MULTIVERSE THEORY OF RAPHAEL BOUSSO AND E-INFINITY THEORY
A multiverse is a universe with an infinite number of pocket universes. Please note that the most important thing here is infinity. Fractal spacetime in the E-infinity version is an infinite dimensional universe. To avoid contradictions and inconsistencies, Bousso introduced causal patch measures. This measure corresponds to the relative topological probability used in E-infinity theory. However the really interesting point comes when you apply to both theories the holographic principle. You recall from E-infinity theory that the holographic manifold of E-infinity is Kleinâs modular curve. This curve has 336 triangles. These 336 correspond to SL 2,7 which constitutes 336 isometries in two dimensions being the surface. They also correspond to 336 kissing points of 10 dimensional spheres. This in turn corresponds to 336 quantum curvatures in 8 dimensions. You can think of the 336 of Kleinâs modular curve as cutting the 10 dimensional spaces of the kissing spheres and flattening them to a surface. You see know the equivalence between particle like states and isometries. Since the kissing points are the points of interactions, they can be regarded as messenger particles or massless gauge bosons. In fact following the holographic principle, they represent all that is going to be particle physics of the standard model later on at lower energy. To see the connection you just compare the 496 of E8 E8 of super string theory to the sum of the electromagnetism as represented by the 137 alpha bar when you add to it Einsteinâs gravity in four dimensions which is 20 and the 336 of particle physics. Now you see that it does not completely add up. There are 3 missing. This 3 can be taken care of in two ways. Either you think of them as the only electromagnetic photons which are massive, namely W minus, W plus and Z zero. Thus we have 3 plus 336 equal 339. Plus 137 plus 20 which exactly matches the 496 of super strings as should be. But there is a better geometrical way to look at that which agrees exactly with the holographic multiverse interpretation of Raphael Bousso. Remember that we have to compactify Kleinâs modular curve to come to a picture similar to that of Escherâs devil and angel. This is the hyperbolic structure well known from hyperbolic geometry. To reach the boundary we could walk for ever. If there is something like an outside observer he will find that we are nearing the boundary but becoming slower and slower and never ever reach the boundary which lies at infinity. Thus although we have a finite area, we have infinite distance to the boundary. If we identify this infinite distance with infinite time then our theory becomes identical to that of Bousso. The famous chaos scientist Otto Rössler compared the situation to a pseudo sphere of a certain cosmological model. In other words, Boussoâs theory, probably unknowingly, adopts words for word our theory and there is a one to one correspondence between our terminology and the new terminology. E-infinity is a multiverse theory. It always was and it will always be. You see we are at the cutting edge of everything in theoretical physics. In addition we can calculate things and not only philosophize about it. That is why some find El Naschie more than irritating and are extremely upset that we have been supporting him because quite honestly, without this help, he could not have achieved anything. In fact without our moral support he would not have survived the last operation which he had in London.
We must think about all these things and develop them further and keep each other informed. Let us, following Leo Tolstoy, try to forgive our opponents and wish them peace of their soul so that they can leave us in peace to complete our work.
Best wishes to everyone,
E-Infinity Communication

E-infinity communication No. 2
Why the golden mean?

Dear All,
Encouraged by the balanced and civilized remark of Dr. Munroe we will attempt to update you on anything new in E-infinity which comes to our attention and answer any reasonable well posed question which anyone of you has as far as we can. We hope that arguments and tone will remain within what you would do in a scientific conference or a discussion in a learned journal. By all means you can make the odd witty remark or polite joke. Just consider that you are not anonymous and that you are responsible for what you are saying. Science is a worthwhile and respectable endeavor. Even non religious people do not commit scandalous actions in a house of worship whether it is a church, synagogue, mosque or a budhist temple. Science is a kind of temple for us scientists and even if you do not believe in that, please out of respect to other believers, leave this site for science and let us discuss science without resorting to personal hidden agendas, irrational hate or jealousy and inferiority complexes. If you would love to see a trial you will have a long one in the High Court of London. Here we talk only about science. Thank you for understanding and now I can move to the next item.
I would like to give here a plausibility explanation of why the golden mean popped up in quantum mechanics. To understand our point of view you must know a little bit of nonlinear dynamics. The most important thing which you have to know in that respect is the KAM theorem. For instance you could consult a book by Heinz Georg Schuster called Deterministic Chaos, published by VCH Verlag, 1989 but any other book on nonlinear dynamics would do. KAM is an acrynomn relating to the name Kolomogorov, Arnold and Moser, the three mathematicians who developed it. Loosely speaking it states that the last periodic orbit which can be destroyed by perturbation is the one which has the most irrational winding number. You can think of a winding number as the ratio of two frequencies as in resonance. The more irrational the winding number is, the more stable the orbit is. Since there is nothing more irrational than the golden mean because it is the least well approximated by a rational as you can see from continued fraction expansion it follows then that this orbit is the most stable. The stationary states which can be observed experimentally is therefore connected as close as possible to the golden mean. You can think of elementary particles as a stationary state of quantum mechanics. When you connect quantum mechanics to KAM then you are effectively making Rene Thomâs VAK hypothesis. Rene Thom conjectured that the Hamiltonian quantum mechanics has a form of attraction although it is non-dissipative and conservative. This strange attraction has a vague resemblance to strange attractors of dissipative systems. That is why it was called the vague attractor of Kologomorov by Rene Thom. El Naschieâs work and the subsequent experimental confirmation of the golden mean in quantum mechanics in the Helmholtz Centre is the proof that the VAK conjecture is correct. You see this is all mathematically perfect and correct but of course we are extending mathematics to physics. When ever you extend mathematics to physics you leave the secure ground of absolute logic and enter into the messy realm of reality. But that is why theoretical physics is for us far more interesting than pure mathematics. In theoretical physics you need not only maths but something more difficult to pin down given to man by God if I may say so and this thing is called intuition. That is the reason why the golden mean will keep coming out in every measurement of quantum mechanical phenomena. Thank you for your patience and we await your questions if you have any before we move to the next point.
E-infinity communication.

E-Infinity Communication No. 3

Further reasons why the golden mean?

Dear Ray

There may be a slight misunderstanding here. Irrationality of Phi is expressed by the fact that the fraction expansion involves only unity. In other words this is 1 divided by 1 plus 1 and 1 is divided again by 1 plus 1 and so on indefinitely. At infinity the result is the golden mean. Some call the inverse of the golden mean the golden mean. This is only semantics and totally irrelevant. We should also not loose sight of what we want to talk about. Whether the Fibonacci progression is more fundamental or the golden mean may be a question of interest to a number of theoreticians involved in a learned discourse. It is also irrelevant that John Baez had a vested interest to draw attention to the work involving the golden mean published by a Russian scientist in a far more restrictive area as compared to the fundamental generalization of E-Infinity. Important are only the facts that a fundamental theorem about stationary states relates elementary particles to the golden mean. The theorem is the VAK which as we said an extension of KAM to quantum mechanics. The experimental verification is a fact. Scientists engage in an honest historical analysis of science will show at some time who was first and who was not. Now let me go back to the fundamental question of why the golden mean?

A Slovenian scientist and mathematician following Mohamed El Naschie expand the idea of mechanical oscillators. Many papers have been published on this subject by L. Marek-Crnjac. Take a two degree of freedom oscillator. Two masses connected by two linear springs. Write the equation of motion. Set the value for the masses as well as the spring constants equal unity. The secular equation is then simply a quadratic equation. The Eigen values are golden mean related. The only positive real Eigen value is the golden mean. Imagine now that you have infinitely many such oscillators connected together. Consequently you can estimate the Eigen value using two well known theorems on Eigen values. These are the Southwell theorem and the Dunkerly theorem. They correspond to what we have studied in school about joining electrical resistance of Omeâs law. When they are successive you add the inverses and when they are parallel you add them. Eigen values are frequencies. Frequencies are energy and energy is mass. Extrapolating the whole thing to quantum mechanics as argued by El Naschie and Marek-Crnjac you have another plausibility explanation for why the golden mean will pop up in any accurate measurement in quantum mechanics phenomenon.

You can see all this theorem in any good book on Mechanical Vibration. There are of course many other ways to argue the appearance of the golden mean which I will discuss next as soon as you have made your comment.

Best regards,

E-Infinity communication

E-Infinity Communication No 4

Mathematical reason for the golden mean in quantum physics

Dear Ray

You are right. But like all of us you are right to a point. We and science exist because philosophy exists. We lose track of things for the same reason. Do not fall in love in general in eloquent formulations no matter how beautiful a sentence is. Reality is indeed fractal. But then you can lose track of reality when you gloss over. You do that when your observation is inaccurate. Your observation ergo reality is as good as the resolution of your instrument. The whole idea of random cantor set as a building block of spacetime is that it is the reality which we were not able to observe directly until now. But it is there. For the first time it manifested itself in quantum mechanics indirectly through the golden mean. Let me first give you some more demanding reasons why the golden mean is there.

We will have to make a jump. It is not systematic. It does not follow from what I said in previous communications. Please accept it for now on its face value. The most fundamental thing which we have for the whole shebang is Kline modular curve in the compactified version. I am not sure of this great man if this great man Roger Penrose knew that he rediscovered the same thing from a far more fundamental viewpoint as far as quantum mechanics is concerned. The entire world of quantum mechanics is encoded in Penrose universe. I know that theoretical physicists can be quite impatient with Penrose and secretly they curse him. I know that his twistor program has come to a halt. And he sometimes said something to the effect that it has failed. But that does not apply to his fractal tiling. Not at all. There is another mathematician who is interested in physics and who is truly an exceptional man. Not as general as Penrose but he runs in the same direction. The work of Alain Connes on non-commutative geometry is best illustrated by Penrose Universe. The work of both men derives its essence from Von Neumann Continuous Geometry. For the sake of this communication, I will refer to page, verse and chapter of Alain Connes Noncommutative Geometry published by Academic Press, copyright 1994. Please look at page 89. Examine figure II.3 entitled Penrose Tilings. Move to page 90. When you read the second paragraph your mind will lit. He says x is a quantum space and then he says that the entire thing is described as tiling. Then he gives an unheard of elementary equation which he calls dimensional function. The dimensional function is z plus the inverse golden mean multiplied by z. It was El Naschie who noticed the profound meaning of this equation and realized that applying some elementary matrix analysis to it, he obtained his bijection formula. You recall that the bijection formula relates the Hausdorff dimension for an n topological space to the backbone or Hausdorff dimension of a zero dimensional space. It is difficult to explain these things without mathematics on this blog. Let me give you a small example: a random cantor set has a golden mean as a Hausdorff dimension. The Menger Uhryson dimension which is nothing but an extended topological dimension for this set is zero. To find the dimension for n = 4, we take the inverse golden mean to the power of 4 â 1 equal three. This means the Hausdorff dimension is 4.23606799 or 4 plus the golden mean to the power of three. You met this famous formula before. But this time we are driving it from the work of Alain Connes. The same thing can be done using von Neumannâs Continuous Geometry which is the basis of Alain Connes work. However nothing can rival the simplicity of Penrose Fractal Tiling. This fractal tiling is the holographic boundary of the theory of everything. And now comes the unexpected expected result. It is impossible to have a Penrose Universe without golden mean proportionality. Penrose kit and dart inside kit and dart inside kit and dart and so on indefinitely could not be designed without the golden mean. In terms of the mathematics of Hamiltonian system, we say we could not have smooth tiling without gaps or overlapping unless we have golden mean proportionalities. Please read the elementary but fascinatingly beautiful Penrose Tilings. Penrose did not stop at that. He has driven a fantastic formula called the isomorphic length. The isomorphic lens was popularized by Martin Gardner. Believe it or not, when you multiply this length by 2 what do you get? You get exactly 4.23606799. In other words you get half of the Hausdorff dimension of the expectation value of El Naschie E-Infinity space. Remember this Hausdorff dimension is found in the most elementary fashion by putting a 4 dimensional cube inside another dimensional cube and so on indefinitely. To get the value you write a continued fraction. That is 4 plus one over four plus one over four and so on indefinitely in the familiar fashion and the final result after infinitely many iteration is 4 plus the golden mean to the power of 3. I will repeat again, this is double as much as we have with a Penrose isomorphic length. The isomorphic length is a wonder which is not a wonder. You stand anywhere in a Penrose universe holographic boundary. You look around yourself and see the world. You close your eyes and move a distance. At a distance not larger than the isomorphic length, you open your eyes again and you will think you have not moved at all. You have a recurrence of the whole universe around you giving you the illusion you have not moved. That is where infinity and finiteness become exchangeable. That is what Mohamed El Naschie observed and used. All very simple. This is the wonder of the hyperbolic geometry in compactified form. You have used related ideas in driving your E12 Exceptional Lie group. I have looked at your paper in Chaos, Solitons & Fractals. I have seen some of your figures. This is all thanks to the work of von Neumannâs noncommutative algebra and Alain Connes noncommutative geometry and Penrose incredible geometrical intuition and knowledge. Mohamed El Naschie, the engineer gave all these subjects the time they needed to digest and reproduce them in his own language in what we call today E-Infinity. I know this communication is far more complex than the previous one. There may be many gaps in my explanation. But I will come back to everything once again and my next communication will be far more comprehensive and far more elementary. But I would like to draw your attention to the last informal review which Mohamed El Naschie wrote on the subject. It is called: The theory of Cantorian spacetime and high energy physics (an informal review), published in Chaos, Solitons & Fractals 41(2009) 2635-2646. As for the golden mean and the symplictic character of quantum vacuum, I advise you to read a short and very simple and beautiful paper by Mohamed El Naschie relating the whole thing to the Banach-Tarski paradox and the no squeezing theorem. The paper is titled: New elementary particles as a possible product of a disintegrating symplictic vacuum published in Chaos, Solitons & Fractals 20(2004) 905-913.

I hope I was of some help and I advise to experiment yourself by doing some elementary calculations yourself. E-Infinity is hands on mathematics. We bring everything we know to bear on the problem. We start from absolutely abstract mathematics and go down without any problem to numerics as well as plausibility explanation. We need all the help we can get. Anything goes as long as it is logical and helpful to our understanding.

E-Infinity communication

E-infinity communication No. 5
Deriving the basic equations of E-infinity
Part I â Elementary introduction
Ignoring nonsense and concentrating on science I would like to explain how to derive the basic dimensional equations of E-infinity. I will start for simplicity with what is more familiar to people not acquainted with E-infinity as a starting point. Later on we will give the accurate, exact derivation and finally we will look into the correspondence to noncommutative geometry and other mathematical theory.
Dimension is the most important topological invariant we have. It is more fundamental than the Euler number or what have you. We start with topology to construct what Wheeler rather loosely calls pre-geometry. We imagine an infinite number of Cantor sets to be joined together statistically to form a pre-geometry and we use for this purpose a Gausian-like distribution which is called gamma distribution. There is some contradiction here because we are joining discrete sets but we use continuous distribution. Later on we will introduce the correct discrete gamma distribution. OK. What we are distributing now is not the sets but the Hausdorff dimension of the sets. We distribute them like Wheelerâs bucket of dust. You can check that in the literature. What is the expectation value of a Hausdorff dimension for the whole collection of this dust? Wheeler calls it Borel mix. I do not think Wheeler had exactly a Borel set in mind, but never mind. To find this average or expectation dimension you have to know the multiplier lambda and a shape factor r. The expectation value is given by r divided by the natural logarithm of lambda. A little contemplation will show that lambda must be the inverse golden mean because we are taking only random elementary Cantor sets in our Borel mix. Taking the simplest camel hump shape we see that r must be equal to two. You can find that in any text book on statistics and probability theory for instance the book of Pitman. Divide now two by ân the inverse golden mean. This gives you 4.156174. Please do this yourself using a pocket calculator. You will remember the exact value should have been 4.236067977. Well this is the price in accuracy which you have to pay for using the continuous gamma distribution. If you want to have the exact result then you have to get rid of the spurious nonlinear terms in the expansion of the natural logarithm. Mohamed El Naschie pointed out that the linear terms of the expansion correspond to the exact discrete distribution. If you do that and make no mistakes then the two divided by the logarithm of lambda changes to 1 plus the golden mean all divided by 1 minus the golden mean. When you do this you will find the exact solution which is 4.236067977.
Let me show how we get that from first principles exactly. You assume you have a random Cantor set with a golden mean Hausdorff dimension. You add to that all the Cantor sets in the world, that is to say infinitely many, each having a Hausdorff dimension equal to the golden mean to the power of n, where n goes from zero to infinity. This would give you a sum which when summed correctly then it is equal to 1 divided by 1 minus phi, namely the golden mean. To compare that with the initial Cantor set which you started with, you have to divide the whole sum again by phi. The result is the well known expectation value of the Hausdorff dimension of E-infinity. Suppose we do not know that phi is the golden mean. Leave it be just a formula for the expectation value of the Hausdorff dimension. This formula now reads 1 ÷(1-Ï) Ï. Remember we had another formula from the gamma distribution which says (1 + Ï) ÷(1-Ï). Now comes the most important condition we have. The first dimension is the Hausdorff dimension, namely an expectation value. The second dimension is an expectation value of a topological dimension. To have a space worth the name space you should have no gaps and no overlapping. The requirement for that is that both preceding dimensions should be equal. Equating both formulas you find a quadratic equation for Ï. Solving this equation you find that Ï is indeed the golden mean, namely 0.618033989. This is space filling condition which Mohamed El Naschie introduced to derive this formula. Inserting the value for Ï in any of the two formulas you always find that the dimension is equal to 4.236067977 as should be.
You can find the detailed derivation in many papers of El Naschie as well as in the work of Marek-Crnjac and others. We see that E-infinity pre-geometry is described by more than one dimension. We have a topological dimension on the average which is equal to the Hausdorff dimension on the average equal to 4 + the golden mean to the power of 3. In addition you have exactly four dimensional topologically speaking. However formally you have been adding infinitely many Cantor sets so that you really have infinitely many dimensions. To understand that the topological dimension is exactly four, I have to refer you to the bijection formula which is connecting El Naschieâs work with noncommutative geometry. In this particular case the formula says that the correction dimension is obtained from raising the inverse golden mean to the power of n minus one. To get the correct result, namely 4.236067977 you have to have n equals 4. When n is equal n then n minus one is equal 3 and hey presto, you see that the inverse golden mean to the power of 3 gives indeed the correct expected dimension, namely our familiar 4.236067977. I urge every reader to do it himself using the pocket calculator. Working yourself through all these little calculations you will start having a feel for the golden mean symphony which is governing quantum mechanics and high energy physics. In the next communication we will go deeper into all the subjects once more from a higher view point. This was just an elementary taste of what it is all about.

E-infinity communication No. 6
Derivation of the fundamental equations of E-infinity Part II
As Confuscious says, ignore perturbation and like Mohamed says, may peace be upon all of you. Let us continue with our scientific discussion.
We would like to tie up some loose ends and unintentional omission of some important aspects of the main equation as discussed so far in communication No. 5.
El Naschie draws attention to an important interpretation of the approximate formula of the expectation value of the gamma distribution of E-infinity. You recall that it was 2 divided by ln lambda. Taking lambda to be the inverse golden mean then ln lambda will have an important interpretation in terms of an entropy which mathematicians call topological entropy. The topological entropy for a certain map turns out ln 1.6180333 equal 0.481212. If you interpret the 2 as being the Hausdorff dimension of a quantum path following Abbot and Wise famous paper, then dividing 2 by this topological entropy is giving you the entropic content of a quantum path. In other words the approximate solution for the expectation value of the Hausdorff dimension, namely 4.156174 is effectively an entropic content. We see the important interplay between different notions which are not different at all when seen from a higher level. Those familiar with string theory and Brane theory may find an analogy for this in the fact that P-Brane and D-Brane which were thought to be different are in fact not different at all. The difference is in the eye of the beholder.
In this context we should apply the same interpretation but this time using a different lambda of a different map. The value of this lambda is itself our 2. Consequently we have 2 divided by ln2. This is a different entropic content using again a topological entropy definition. The value in this case is 2.885390. Try to remember this for later use because this value approximates the missing part needed to compactify chi 7. I mean the part you need in order to make 336 come nearer to 339 by compactification. Of course I am running ahead of my story but please remember this bit for later on.
Now let me give you the exact E-infinity derivation of our 4.23606799 dimensions which we can obtain without making any reference to anything except the pre-geometry we are constructing and the center of gravity theorem of probability theory. Let us take all integers from 0 to infinity. Let us regard this as infinite dimensions. Now we give each dimension a weight. This weight is equal to the golden mean to the power of n where n runs from 0 to infinity. What then is the center of gravity of the whole thing? This is a very simple problem in probability theory which mechanical engineers like to think of as searching for the resultant of many forces. It is now very easy to guess that the resultant which acts at the center of gravity will be given by the sum from 0 to infinity of n multiplied with the golden mean to the power of n and all multiplied with n again, where the last n is now the arm of the force while the force is n multiplied with the golden mean to the power of n. You have to divide this now by the sum of all forces which is sum from 0 to infinity of n multiplied with the golden mean to the power of n. In other words you have a sum of moments divided by the sum of forces. This gives you the expectation value of the average arm of the resultant. This arm is the expectation value of our dimension of the space made of these infinitely many weighted topological dimensions. These infinite series can be summed exactly as shown by El Naschie and it is an elementary matter to show that the final sum is simply 1 plus the golden mean all divided by minus the golden mean which all comes exactly to the well known and familiar value of 4 plus the golden mean to the power of 3. In sum pure mathematical communication Mohamed El Naschie was able to show that this is a well known result in the theory of the Coxeter groups. You can find this paper in Elsevierâs Science Direct.
In a forthcoming communication we promise to show you that all these results are derivable from the theory of subfactors as well as Alan Connesâ noncommutative geometry.
Now to close this 6th communication I would like to give you the exact derivation of the dimension of the holographic boundary of E8 E8 in the case of complete compactification. You recall that we started with 336. Then we keep adding triangles indefinitely in a hyperbolic way. To understand how to find a finite value for this compactification to infinity, you have to be familiar with the theory of Kleinâs modular curve. You have to know that there is an important orbit with 42 points in the 336 curve. This 42 can be thought of as 4 and 0.2 lifted to 10 dimensions by taking 10 copies. That is to say it is 4.2 multiplied with 10. A little contemplation will make it evident that 4.2 is just an approximation to 4.23606799. Taking 10 copies of that you get 42.3606799. Now this is the exact coupling constant of unification in the absence of super symmetry. Thus in the ordinary case of non-compactified Kleinâs modular curve, you get 336 from 42 multiplied with 8. In the exact transfinite case you get the correct result by multiplying 8 with 42.3606799. When you do that you get 338.885438. This is exactly 2.885438. You see now how close this is to what I told you earlier, namely 2 divided by ln2 equals 2.885390. Very close but not completely correct. The exact expression is well known from the theory of transfinite corrections as developed by Mohamed El Naschie following a similar theory dealing with operators due to Fritz John. The exact expression is 16k. Here k is equal to the golden mean to the power of 3 multiplied with 1 minus the golden mean to the power of 3. When you do that you find that it is 0.180340. Now you take 16 copies of it and you have your exact result 2.885438. Now let us derive the exact theoretical inverse electromagnetic constant using Mohamed El Naschieâs fundamental equation and the previous exact transfinite value. The number connected with Einsteinâs gravity Reimannian tensor will remain 20. However the dimension of E8 is no longer exactly 248 but 247.983739. This is 248 minus k square divided by 2. Now our equation should read E8 E8 minus holographic boundary minus Einstein gravity equal inverse electromagnetic constant. Taking the appropriate dimension we have 495.967478 minus 338.885438 minus 20 equals 137.082039325. This is the exact theoretical value as promised. It is the integer value 137 plus a transfinite correction equal to k o where this new constant is equal to the golden mean power 5 multiplied with 1 minus the golden mean power 5 equals 0.082039325. You see the extent of our precision and how the constants of nature are obtained as a probability resulting from summing over infinitely many states but I think it is enough for now and promise to come back in our next communication in due course.

E-infinity communication No. 7
Derivation of the fundamental equations of E-infinity Part III
For the benefit of those who appreciate scientific discussion as opposed to defamatory allegations and those who would like to learn something about E-infinity as opposed to hearsay and parrot repetitions of misconceptions, we continue our discussion by giving literature which we omitted to mention in detail in Communication No. 6.
Pre-geometry and the main idea of Borel mix as used by Wheeler can be found on page 1205 of his monumental book Gravitation, by Charles W. Misner, Kip S. Thorne and John Archibald Wheeler, published by Freeman, New York 1973. You can find everything about gamma distribution in the book Probability by Jim Pitman, published by Springer, Berlin 1993. The expectation value of the gamma and other distributions are conveniently summarized in the table on page 476-477.
Now let me reminisce about Mohamed El Naschie and his lectures when I was just about to finish my Ph.D. He said something very remarkable about the Cantor sets. He said it is something which is there and yet not there. In his youth Mohamed was a friend and follower of Jean Paul Sartre. He was greatly influenced by Sartreâs major book Being and Nothingness (original title LâEtre et le neant: Essai dâontologie phenomenologique). Mohamed read the book in the German translation, having German as quasi his mother tongue (Das Sein und das Nichts). He was even acquainted with it at the tender age of 12 in the Arabic translation by Abdul Rahman Badawi, the famous Egyptian philosopher at that time. In fact Mohamedâs father who was an army general was quite concerned and worried that his young son is reading these things of which he could not make out head or tail. Education is never in vain, even if it is philosophy. The Cantor set made quite an impression on Mohamed and he instantly connected it with what he had read in Sartreâs book. He even mentioned the work of Sartre as well as Martin Heidegger in one of his most profound very early papers on the subject. This particular paper was cited by many pure mathematicians thinking that Mohamed is a pure mathematician. In his review of E-infinity theory Mohamed likened the Hausdorff dimension of the Cantor set with the spirit of a body which has long decayed. He likened it with this famous ghost story by Oscar Wilde. This particular review which is highly cited and although it is only five years old and despite all the negative propaganda artificially created in certain quarters, A Review of E-infinity Theory is found on Google Scholar to have been cited 328 times.
I recall something similar which was said by Leibnitz about imaginary numbers. Leibnitz said there are amphibian between being and not being. This is a remarkable formulation which covers almost exactly Mohamedâs notion of a Cantor set. It is an amphibian between being and nothingness to use the terminology which he borrowed from Jean Paul Sartre. There is no shame in borrowing things from famous as well as lesser mortals. What is shameful is to attempt to hijack other peopleâs ideas and deliberately calling them your own.
Now I would like to go back to the derivation of the fundamental equations. I must warn from the outset however from a major mistake which some could easily commit because they judge in haste. There is no element in Mohamed El Naschieâs work which is numerology. We agree fully with what Dr. Ray Munroe said on certain blogs that numerology is a pattern of numbers for which we have not yet discovered the real underlying reality, physics or theory. However nothing is further from the truth when it comes to E-infinity theory. If you still suffer from this delusion then you have not yet understood the theory. That would be a real pity because the theory is not difficult at all when you free yourself from all prejudice.
Now we give yet another derivation of the expectation value of the Hausdorff dimension. You have to start with the well known dimension of noncommutative geometry. The dimension is given as index or dim of N and M. It is written however as [M:N]. This is given by 1 divided by L plus 1 divided by 1 minus L. Here L is trace of E. From the theory of subfactors we have a very similar formula but this time giving [M:N] by 1 divided 2d-1. Now set L equal d and you will find a quadratic equation for d or L showing that it is equal to the golden mean or minus the inverse golden mean. For the positive value we get our 4 plus the golden mean to the power of 3. I leave it to you to have fun with Alain Connes and the great mathematician of the theory of subfactors. I leave it to you now to work out for yourself the four dimensional fusion algebra which has 1, 1, golden mean and golden mean again as a solution. It sounds like a puzzle but the next communication will make it clearer. Let me end in the same way that some of the rather pleasant commenters on the Munroe blog end their comments by saying, have fun and I add try to ignore perturbation.
E-infinity

E-infinity communication No. 8
The E-infinity counterpart of calculus â and Wyle scaling
It is my intention to start by making specific reference to the literature concerning the last communication which was omitted. The important noncommutative dimension which we used was given in detail in Connes marvelous book Noncommutative Geometry, Academic Press, 1994. The formula is given on page 506. He uses slightly different notation but everything is explained lucidly. You can understand subfactors from the wonderful book by V. Jones and V.S. Sunder called Introduction to Subfactors by Cambridge University Press, 1997. You may recall that Jones is the man who found the remarkable relation between knot theory and statistical mechanics. Much of what Mohamed El Naschie did could be reinterpreted in terms of Jonesâ work. The relevant formula may be found on page 31 of this book. Several other important formulas may be found on page 143 and you can move from there to study how quantum field theory can be derived from subfactors. Believe me it all sounds far more complex than it is. Oh and there is an important paper by Mohamed El Naschie which has much of this stuff published in the Int. Journal of Theoretical Physics, Vol. 37, No. 12, 1998 entitled Superstrings, Knots and Noncommutative Geometry in E-infinity Space. The Editor in Chief of this journal at the time was no one less than the legendary David Finkelstein. David you will recall is one of the main people responsible for introducing set theory in quantum mechanics. Following Heisenberg and Finkelstein, Prof. Heinrich Saller excelled in developing a highly mathematical theory starting from a combination of symmetry groups and set theory. We warn however that this is very demanding mathematically for the average physicist. However if you would at least have a glance at the work of Saller, you will see high energy physics and quantum mechanics from a profoundly important and different view point which is not that dissimilar from that of what El Naschie is doing using what is comparatively humble mathematical tools.
Some of our members think I should move now to explaining the main tools of computation which we have in E-infinity theory. This would be Wyle scale. Other members think that we should no introduce the transfinite theory of dimensions which is the mathematical founding of E-infinity theory. A sizeable minority think we should outline the connection to wild topology and a few other disciplines used frequently in E-infinity theory. We will have to do all of that in the few coming communications. However I am inclined to think that it is time to introduce at least one simple example of the scaling analysis.
If you look to the beginning of the work of Nottale you realize that this eminent and great French scientist agonized about differentiation. He was slightly on the loose side when he equated fractals with non-differentiability. That brought him into conflict with fractal experts like the great Israeli scientist Itamar Proccacia. However the dispute is merely a misunderstanding when temperament takes over reasoning. Nottale like Ord and later on El Naschie realized the need for calculus machinery but he also realized that differentiation and similarly integration covers up all the interesting phenomena and leads us in the wrong direction. Ord in particular realized that taking the limit is the source of all contradictions in quantum mechanics. That is how Nottale decided for a compromise, albeit an ingenious one. Nottale does not give up continuity. For him a Cantor set is excluded a priori as the basis of the calculation. Therefore he used non-standard analysis in his calculations. That is how he came to most of his excellent results. Garnet Ord somehow managed to avoid taking the limit of his difference equations. In a manner of speech and in a way which Ord does not particularly like, you could say that he invented his own quantum calculus. Of course Garnet sees it completely different nowadays and he has grown more sophisticated about these things but for the purposes of this communication, it is sufficient to think of it in this way.
In noncommutative geometry Alain Connes was faced with similar problems like the pioneers of E-infinity. Being one of the greatest pure and applied mathematicians in the history of mathematics he had of course a sophisticated solution. Without going into the detail, let me give you a very short dictionary of the noncommutative solution. Alain Connes introduced a quantized calculus for which the following short dictionary applies. First infinitesimal is replaced by compact operators. Second integral is replaced by a Dixmier trace which is incidentally also used by El Naschie. The table for classical quantum correspondence in noncommutative geometry is given on page 20 of Alain Connes book which we mentioned earlier.
El Naschie as well as Ji-Huan He and Marek-Crnjac and occasionally Goldfain use something else. They return to Wyle scaling. Fractals has a marvelous character expressed in Bidenharn conjecture. The conjecture says the obvious that there are no a priori scales, man or God given, in a fractal spacetime. Therefore the counter argument of Einstein against Wyleâs idea does not apply in a fractal spacetime. The history of the whole controversy and its solution in E-infinity theory is duly explained in several papers by Mohamed El Naschie as well as a review by L. Marek-Crnjac. I will give you the exact reference later on. The final result is disarmingly simple. You are more or less scaling down when you want to differentiate and scaling up when you want to integrate. The words differentiate and integrate should not be now taken literally. Prof. Ji-Huan He likes to say that scaling is everything. In E-infinity at least, this is as near to the truth as anything could be. Let us discuss one example demonstrating the application of this idea and generating El Naschieâs hierarchy of Heterotic strings. You recall in classical mechanics when you want the equation of equilibrium you write a Lagrangian, then the vanishing of the first variation of this Lagrangian gives you the equation of equilibrium or motion. In very simple cases when the Lagrangian is a function rather than a functional, variation is replaced by simple differentiation. In E-infinity things are far simpler than that to the extent that some who expect to lift heavy weights are shocked and left in a state of disbelief because of the simplicity which they did not expect. For certain manifolds involving E-infinity the curvature may be given by very simple expressions. Squaring the curvature you find a normalized energy. If you can identify a certain parameter as a loading and you can calculate the distance which this loading can potentially move, then you have an equilibrium equation. Alternatively if somehow you convince yourself that you have what is equivalent to a Lagrangian, then repeated scaling gives you the answer for equilibrium equation or equation of motion. Suppose I convince you that half of the inverse of the electromagnetic fine structure constant may be regarded physically and correctly as the numerical value of the Lagrangian. In this case repeated scaling using the golden mean will give you the solution of corresponding equilibrium equation or equation of motion. Again this sounds far more complex than when you really do it. Let us do it.
Half alpha bar is equal to 137.082039325 divided by two equal to 68.541020. Multiply this now repeatedly with the golden mean 0.618033989.
The result is then the following hierarchy 42.360680, 26.180340, 16.180340, 10, 6.180340, 3.819660 and so on. This is the well known Heterotic string hierarchy in the transfinite form. The first value is the inverse coupling constant for non-super symmetric unification of all fundamental forces. The second is the coupling constant for super symmetry or the number of bosonic strings. The 16.180340 relates to the additional dimensions added. The 10 are the super string dimensions. The 6.180340 are compactified dimensions and the final number is 4 minus k where 4 are the dimensions of spacetime and k is equal 0.18034 which appears in all other numbers. The explanation of all that is given in detail somewhere else but obtaining the result is less than elementary as far as computation is concerned. Let me show you first how we obtain the original equation. El Naschie showed long ago that the average curvature of Cantorian spacetime at the core is equal to 26.18033989. Squaring this you get the energy in normalized form which is 685.410197. If you remember, this is the dimension of Ray Munroeâs E12. Not quite but very near. It is also very close to the sum of the dimension of all the 17 two and three Stein spaces. Not quite but very near. Introducing a loading lambda index I, then we can define a potential distance equal to the square root of the sum of all theoretical values of the coupling involved in reconstructing the inverse electromagnetic fine structure constant. This is 60, 30, 8 + 1 = 9, and the quantum gravity coupling 1. Adding altogether comes to exactly 100. The square root is therefore 10. Lambda I is therefore equal to 685.410197 divided by 10. This gives us exactly the value we started with namely 68.5410197. When you scale it you get lambda 1 equal to 42.360680, lambda 2 equal to 26.180340 and so on. This is extremely simple isnât it? It is simple but difficult to understand. It is only difficult to understand because of our habits of thinking which we do not want to get rid of easily. Remember we must free ourselves from all ties as Prof. M. B. once said. I am sure you have hundreds of questions. I can assure you if you are not shocked and if you have no questions, then could not possibly have understood anything.
Best regards,

E-infinity communication No. 9
Wyle scaling and deriving the spectral dimension 4.02 of Loll, Ambjorn and Jurkiewicz using E-infinity
There is no reason why we should not continue with our discussion and give further examples of the use of golden Wyle scaling in E-infinity. We have to take the opportunity first to draw the attention of the readers to the literature where details are given. The most important three papers which can be consulted on this subject are the following: From classical gauge theory back to Weyl scaling via E-infinity spacetime by M. S. El Naschie, Chaos, Solitons & Fractals (CS&F), 38, 2008, p. 980, A Feynman path integral-like method for deriving the four dimensionality of spacetime from first principles by L. Marek-Crnjac, CS&F, 41, 2009, p. 2471 and Density manifolds, geometric measures and high-energy physics in transfinite dimensions by S.I. Nada, CS&F, 42, 2009, p. 1539.
To explain the main idea in the most excessively simplistic terms you could say the following. There is a fundamental difference between changing direction in space and stretching a line in space. In the first case nothing really physical happened while in the second case something almost physical happened. That was the crux of Einsteinâs objection against Wyleâs gauge theory. Lacking a natural scale, in a fractal setting a stretching can be set on the same footing as changing an angle. You read the rest please in the relevant literature. By the way many people know this trick and that is why fractal spacetime is becoming fashionable and will become even more fashionable as time goes by, so you can play it again Sam.
Let me now return to examples of Wyle scaling and we can do two things for the price of one. We give another example and derive the spectral dimension given for instance in the paper of Ambjorn, Jurkiewicz and Loll in Scientific American or the improved version they published in a book Edited by Daniele Oriti entitled Approaches to Quantum Gravity, published by Cambridge, 2009 a few years after the first derivation by El Naschie using Bose Einstein statistics. The excellent paper by the three authors who are world renowned for simplictic triangulation, in other words, tiling the space with simplexes which again means Regge calculus or finite element of John Argyris who was one of Mohamed El Naschieâs teachers in Stuttgart, Germany and Imperial College, London is entitled Quantum Gravity: the art of building spacetime on page 341-359. The important formula is on page 352.
Letâs begin at the beginning. In Heterotic string theory anomaly cancellation requires either O(32) or E8 E8. In this theory there are left and right moving sectors. The left is purely bosonic. We start with 26 dimensional strings where 16 have been compactified on a lattice, for instance E8 E8 lattice or spin 32 divided by Z2 lattice. The right movers on the other hand are super symmetric. Thus the right movers are explicitly spacetime symmetric. Recall that spacetime symmetry of super space is found until this moment by trial and error. Now in the right moving sector at the lowest level we have 8 plus 8 equals 16 states. In the left moving sector we have three distinct objects leading to 8 states plus 16 states plus 480 states. This makes altogether 504 states. To obtain the entire spectrum we follow Fock space rules of quantum field theory and multiply left movers with right movers. That way we obtain from 504 times 16 the well known 8064 states. This is a very well known result. You can find this result in popular literature like Scientific American or text books on string theory like Kakuâs book. Knowing that there are truly childish people hanging around on internet blogs with an enormous chips on their shoulders, we would like to give you the literature to check everything yourself so that these children do not write that we are telling you fibs. OK, here they are. Scientific American, Superstrings by M.B. Green, p. 183-203, in the caption of Figure 11.14. Reprinted in a book called Particles and Forces, Editor Richard A. Carrigan, published by W. Freeman, New York (1990). M. Kakuâs book Introduction to Superstrings and M-theory, published by Springer, 1999, see page 384. Now enter Mohamed El Naschie. He realized that the same result is easily obtained in an entirely different manner and in some respects a far simpler geometrical way by assigning the right amount of instantons to each site of Kleinâs modular curve as a holographic boundary of string theory. Without going into details the instanton number in this case is 24. The number of triangles as you know from earlier communications is 336. Multiplying the two numbers you get the total number of instantons, namely 8064. Mohamed was under the false impression that this must be a well known method. He published it and mentioned the whole thing just as a marginal thing. He published it a few times without paying too much attention to any novelty. It was then after heated discussion that Nobel laureate Gerard âtHooft convinced him that it is an entirely new theory. I forgot to mention some of the extensions and the insight which El Naschie gave to this point also without realizing that it is an entirely new theory. First look at 504. This was realized by Mohamed as the summing of an exceptional Lie group. Here is a sum about which some people who are ignorant about the exceptional Lie group hierarchy rejected off hand and of course wrongly so. Add the dimensions of E8, E7, E6 and E5 together then you will have 248 plus 133 plus 78 plus 45 equals exactly 504. What most people did not know is the fact that E5 is nothing else but SO(10) of grand unification which is competing with SU(5). SO(10) is really an E5 based on its Dykin diagram. This fact was known to El Naschie as well as many other careful people which do not include of course John Baez who had too much to do on his shows on his diverse blogs for entertaining people. It was of course a mistake to stop at E5. In mathematics it would mean you are not using a complete set. To use a complete set you have to take all the exceptional groups. The sum of that as everyone knows in the meantime was found by El Naschie to be 4 times 137 equals 548. Similar reasoning would show that classical Heterotic strings are only approximation and the real numbers of massless states is not 8064 but 8872 when we ignore everything after the dot. Now El Naschie did not calculate it in this way. He reasoned differently using the holographic boundary. Taking compactification into account you do not have 336 triangles but 338.885438 weighted number of triangles. In addition he derived the exact instanton density and found that it is not 24 but exactly 26.18033989. Multiplying both exact numbers you find 8872.135951. Wonderful. This is now our numerical Lagrangian or potential or whatever you want to call it. Sixteen times differentiation is an E-infinity equal to sixteen times scaling with the golden mean. Multiplying our Lagrangian with the golden mean to the power of sixteen, you get 4.01999999 on a pocket calculator. This is Loll, Ambjorn and coâs result. For all practical considerations it is 4.02. Please do this calculation yourself.
It is interesting to ask why the pioneer of the holographic boundary did not find this result first. I do not know but we cannot all work on everything simultaneously. A reasonable explanation may be the following. The expert on the holographic boundary did not care about the 336 because they know once they compactify we get infinity and physicists do not like infinity and do not work with it. Mohamed El Naschie on the other hand took a gamma distribution weighted infinitely compactified Klein modular curve which added approximately 3 to the 336 to get approximately 339 which is a finite result and meaningful. He was also able to deal with a fuzzy K3 manifold and find the instanton number to change from the classical 24 to 26.18033. This is incidentally equal to the dimension of transfinite Heterotic strings as well as the corresponding Euler constant as well as the curvature which we discussed in an earlier communication. 26.18033 turned out to be an extremely important number. People interested in number theory knew that much earlier but did not know about any relevance in physics. Nobel laureate David Gross must be credited with super natural intuition to have invented Heterotic string theory. Witten and his friends were probably the first to introduce K3 to physics. So you can see string theory is not in any way as useless as some of its opponents want us to believe. Nothing is useless except underestimating people. Nothing is as harmful as belittling the achievements of other people. Nothing is as revolting as the yello

Wow. Post the rest, E-infinity.