1/17/2021

Transcendental Numbers


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π written with its own digits

Transcendental Numbers

Into the Unknown

This subject is one of the most intriguing and mind-blowing in all of mathematics. A lot of ground is uncovered in this area and despite intensive research, we have still a lot to learn and a long way to go.

Let’s warm up by thinking about the number line.

The Number Line

The numbers as we normally think of them, that is, as a number line stretching from negative infinity to positive infinity with 0 right smack in the middle and a lot of famous numbers in between like e, π, etc. are called the real numbers and the set of real numbers is denoted by ℝ.

The set contains many well-studied subsets of numbers including the natural numbers ℕ = {1, 2, 3, …}, the whole numbers ℤ = {…-2, -1, 0, 1, 2, …}, and the rational numbers which are numbers that can all be expressed as a fraction of two whole numbers. This set is denoted by ℚ.

Before moving on, let’s introduce some notation. That a set of numbers say 𝔸 is contained in another set of numbers say 𝔹 is written as 𝔸 ⊂ 𝔹. In this notation, we have

ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ.

which are natural, whole, rational, real, and complex numbers respectively. Note that a whole number can always be written as a fraction, so all whole numbers are rational.

About 500 B.C., there was a community (closer to a cult in our day's terms) called the Pythagoreans and they believed that all numbers were rational numbers. But then one of their own philosophers, Hippasus proves that the square root of 2 is not rational.

The proof is brilliant and simple and is one of the pearls of mathematics and the stars of the history of mathematics for sure. The Pythagoreans were so outraged by Hippasus’ proof that they drowned him.

To be clear, Hippasus proved that


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This proof implies that there exist numbers that cannot be expressed as a fraction of whole numbers. We call these numbers irrational numbers.

The set of irrational numbers is a subset of the real numbers and amongst them are many of the stars of mathematics like square roots of natural numbers, π, ζ(3), and the golden ratio ϕ.

This divides the real numbers into two non-intersecting sets. The rational and irrational numbers.

Of course, there are infinitely many irrational numbers and infinitely many rational numbers but for a mathematician, saying that a set is infinite is simply not good enough. Because of Georg Cantor’s investigations into the theory of cardinality (or infinities), we know that sets come in different infinities and it turns out that the set of irrational numbers is not just “bigger” than the set of rational numbers, it is a different and bigger kind of infinity.

Transcendental Numbers

It turns out that some of the irrational numbers come from roots of polynomials with whole-number coefficients.

For example, the square root of 2 is a root in the polynomial f(x) = x² -2.

Such numbers are called algebraic numbers. And they include all the rationals because any fraction is a root of a linear polynomial on the form ax+b. Complex numbers can also be algebraic e.g. the imaginary unit is algebraic because it is a root of the polynomial x² +1.

Many of the famous irrational numbers are algebraic as e.g. the golden ratio ϕ since ϕ is a root in the following polynomial

x² − x − 1.

A real number that is not algebraic is called transcendental.

Since they are non-intersecting i.e. you cannot both be algebraic and transcendental, the real line can be partitioned into two non-intersecting subsets, the algebraic numbers, and the transcendental numbers.

Transcendental numbers had been conjectured to exist for a long time before anyone found one. Joseph Liouville first proved the existence of transcendental numbers in 1844, and later he even constructed such a number.

Georg Cantor proved with a simple argument that there were countably many algebraic numbers (so that the cardinality of the algebraic numbers is the same kind of infinity as the cardinality of the natural numbers) and as we know that there are uncountably many real numbers (also proved by Cantor using his famous diagonal argument), we can deduce that almost all real numbers are transcendental!

Up until the end of the 19’th century, people had only found transcendental numbers by constructing them. They hadn’t really proved that any famous and well-studied numbers were transcendental.

However, that all changed when Ferdinand von Lindemann proved something remarkable.

He showed the following:


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It’s hard to fully appreciate and grasp the usefulness and beauty of this theorem. He instantly found infinitely many transcendental numbers many of which were well-known to us and some of which we had been studying for thousands of years but the transcendentalness of these seemed far away.

Sometimes the contrapositive version of the theorem is useful. It states:


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The Most Famous Equation in Mathematics

Of course, Lindemann knew of Euler’s Identity which has been called the most beautiful equation in the world. It states the following.


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By the contrapositive version of Lindemann’s theorem, we now get that πi is transcendental, but since i is algebraic, π must be transcendental.

This follows from the fact that algebraic numbers are closed with respect to multiplication i.e. if a and b are two algebraic numbers then ab is algebraic. This is not completely obvious but one can use symmetric polynomials and some cleverness to show this.

After this, π has been proven transcendental many more times in different proofs.

Future Challenges

We don’t really know much about transcendental numbers and we don’t have many useful tools that we can use to prove that certain candidates are transcendental.

We don’t even know if eπ or e + π is transcendental. We also don’t know if the Euler-Mascheroni constant γ is transcendental — we don’t even know if the Euler-Mascheroni constant is irrational!

It is a catastrophe and quite embarrassing that we know so little about such an important number.

And in general, we know of very few transcendental numbers, especially taking into account how many there are. Even if we know that a number is irrational, in general, it doesn’t help us much towards proving that it is transcendental.

If you prove a number to be transcendental, that wasn’t known to be before, you will be very famous.

In mathematics the art of asking questions is more valuable than solving problems

~ Georg Cantor

 

 

 

Kasper Müller

Written by

Mathematician and Data Scientist interested in the mysteries of the Universe, fascinated by the human mind, music and things that I don’t understand.


1/15/2021

1/13/2021

A Voyage of Discovery to the Golden Age of Comic Books

 

Thursday, August 9, 2012

Reprints: Part 6: DC from the 1930s & the Originals of Marvel Part I


The New Reprints: A Voyage of Discovery to the Golden Age of Comic Books

Part 6: DC from the 1930s and the Originals of Marvel, Part I

This Chapter was too long so I have to present it in two parts. 

This project will be presented in twelve parts. Unfortunately, I can’t change the order, so later posts will appear first. Please try to check this out in order! And your comments are important. Please post how you became aware of comics and their history!
  1. Introduction/Comics in "real" books.
  2. 1960s: Reprints from the Comic Companies: 80 Page Giants & Marvel Tales!
  3. 1960s: The Great Comic Book Heroes
  4. 1960s: The Paperback Era
  5. 1970s: The Comic Strips AND the Comic Book Strips! 
  6. 1970s: DC from the 1930s and the Origins at Marvel Part I
  7. 1970s: DC from the 1930s and the Origins at Marvel Part II
  8. 1980s until Today: Horror We? How's Bayou! The EC Age of Comics
  9. 1990s until Today: The Archives and Masterworks
  10. How The West Was Lost
  11. When Comics Had Influence: Public Service, Education & Promotion
  12. Journeys End, What We Leave Behind: A Century of Comics
So let us continue our voyage to and from the 1960s and discover the world of comics once almost forgotten. Our expedition is mostly into the world of reprints that were available OUTSIDE the newsstands and comic book stores but we will have a few detours on the way.



While the 1970s began the earnest reprinting of comic strips, the humble comic book was still the prodigal son who had not yet returned.

The decade began with a major event:the comic book shot heard around the world. Jim Steranko created and produced a remarkable two part collection of “The History of Comics” which was just brilliant. The super-large, black and white books, told the story of comics in great detail, going back to their pulp beginnings. Steranko gave us superb images, in black and white, and told the early stories of both DC and Marvel. Volume 2, published in 1972, picks up where the first volume left off, using terrific images to tell us about Blackhawk comics, Plastic Man, Captain Marvel and his family. A highlight of the second volume is a full Spirit story, all seven pages. It also had a compendium of the fascinating Steranko pages from his Marvel work. I had expected and hoped for a part 3, but it is now 40 years later and no dice. But, in all this time, nothing has topped this work, or the beautiful covers created by Steranko. And what was the price for this gorgeous huge paperback book? $1.98.





 “All in Color For a Dime” edited by Dick Lupoff and Don Thompson, was published in 1972, and it featured mostly essays that concentrated on Comic Books. Popeye, the first super-hero of them all, is also featured. Here, in eleven chapters, authors such as Roy Thomas, Ted White and Harlan Ellison discuss the original Captain Marvel, the war comics of the 1940s, and the second-banana heroes such as Johnny Quick. What a great and important read! While the book is almost all text, there is a small color section of covers mostly from the Golden Age. The book cost $11.25 in hardcover then! Three years later it was followed by a sequel, “The Comic Book Book,” which covered topics such as Jack Cole and Plastic Man, Will Eisner and The Spirit, Tarzan, EC comics and Frankenstein.



                       
This page is from the Color section of All in Color for a Dime. It was important to me because I had heard that Marvel's Daredevil got his name from this character, but I had never seen a picture of him.
 I recently asked Roy Thomas about his involvement in “All in Color…”: “Jerry Bails sent me Julie Schwartz's copies of the early XERO (probably #1-3), which alas were lost in the mail when I sent them back. I contacted the Lupoffs to get #4 forwarded, and Dick asked me to do the article about the non-Marvel Fawcett heroes, using a few comics I had and a number that he sent me, plus my memories... not much more.  He even gave me a title, "Captain Billy's Whiz Gang," and a first paragraph or so of history about Fawcett, which I used virtually intact, though he didn't seem to care to be credited for it. I was too busy when the book version was done to revise the article at all, but I'm happy to have been a part of the series... even though I gave Dick conniption fits with my lateness, as I related back in AE #18.  See that issue for more quotes from me re XERO. I had to decline being in the second book (THE COMIC BOOK BOOK), as well... I think I was supposed to write about the "commercial" super-heroes in the old comics, like Captain Tootsie and Volto, etc... not dissimilar to what was eventually done in ALL-STAR COMPANION, VOL. 2.”



 “Jerry Robinson’s The Comics, An Illustrated History of Comic Art,” (1974)   was a wonderful, detailed look at the history of comic strip art, by an artist himself. This was a 250 page, highly illustrated black and white book which had wonderful color section. It was a bit of a disappointment in only one way, Robinson was one of the greatest and most important comic book artists, the first to draw the Joker and Robin in the Batman series. Yet, there isn’t a piece in here about comic books. Sigh.
 
Robinson discussed the artists and even the technology that drove the art form at the beginning of the century. He divides the book into several chapters, such as “A New Art Form.” “The Golden Age” (which for him was 1910-1919) and the “Cavalcade of Color.” In each chapter he allows artists including, Milton Caniff, John Hart, Leonard Starr to leave their comments about the era.

Charles Schulz: When people talk about "putting meaning" into comic strips, too often they mean political meaning or refer to crime. In the first case, it seems to me that the meaning is directed into too narrow an area; in the second, it deals with something which plays a relatively minor role in the lives of most people.
It is surprising, therefore, that so many cartoonists working in such a marvelously flexible medium have not dealt more closely with the real essential aspects of life such as love, friendship, and day-to-day difficulties of simply living and getting along with other people.
 
Comic strip language is notoriously simple, and, of course, this is understandable when one considers the small space to which we are confined in the newspaper. As strips have been reduced in size, due to newsprint shortage and other such difficulties, dialogue has been reduced and real conversations have all but disappeared.

Lack of space, however, is not the only reason for this. I believe that a more important reason is simply a lack of desire and imagination. One of the most delightful aspects of life is conversation. Talking with a new friend, discovering new ideas, and learning about each other can be one of the great experiences of life.

Good writers know this and make use of it in other media. I have been trying to introduce this into the Peanuts strip for the past several years because I feel it is an area that has not been well cultivated.

Dark Horse, in 2011 published an updated and totally redone version of this book. of this one entitled, “Jerry Robinson’s The Comics, An Illustrated History of Comic Art 1895-2010.” Wow, this a very different book, in full color throughout. There is so much added, including the strips that gained popularity since the first addition  such as Doonesbury.  Robinson, in the second edition also touches on certain themes that were taboo in the past, such as the integration of comics, an important subject.



After Robinson's volume, comic books would no longer be dismissed.  Pierre Couperie’s “A History of the Comic Strip” (1968), was written with Maurice Horn. This book doesn’t just reference comic strips that were American, it acknowledges and explains the European influence on the media. This had been ignored in most other books, including the ones I presented in the introduction. For some reason, the progression of comic illustrated storytelling is most often presented as a totally American art form, and creators consistently looked to England to have their efforts validated partially because of an inferiority complex and because Europe had developed their own comics. To fully understand the evolution comic books this book takes us to the mid 1800s. Rodolphe Topffer, a Frenchman, was an early innovator of the comic strip and he was able to foresee the future: the “comic book” and the “graphic novel:” In describing the comic book as a novel he wrote:
The drawings without their text, would have only a vague meaning; the text, without the drawings, would have no meaning at all. The combination of the two makes a kind of novel, all the more unique in that it is no more like a novel than it is like anything else.”

Topffer understood that the drawings and the text must be symbiotic. Some may dispute this, but it makes no difference whether the text is in balloons or at the bottom of the page. What is important is that they are dependent on each other, not where they are placed.

This scan is from "Rodolphe Topffer, The Complete Comic Strips" Compiled, Translated and Annotated by David Kunzle. University Press of Mississippi, 2007. $65 on Amazon




Les Daniels authored,“Comix, A History of Comic Books in  America” in 1971. By today’s standards, this would not be considered great reprint book. It is in black and white, with a small color section, and the comic pages printed two on a page that had to be turned 90 degrees to read. But it was truly a gold mine then of Golden Age material. Daniels fully discusses the history of comic BOOKS. Of course, he leads off with what will become the obligatory essay on the Yellow Kid (featured at the beginning of all books about comics), but he swiftly gets into Superman, comic books and the Golden Age. He doesn’t just discuss the well known characters such as Batman, but he discusses Blackhawk and Chop-Chop, The Spirit and Ebony, Captain Marvel and Steamboat Willie, and many others. Daniels writes about the genre of Funny Animals, which he calls Dumb Animals, and the 1960s and 1970s Underground comics. He also examines EC comics and crime comics, such as Lev Gleason’s “Crime Does Not Pay” that led up to them. The book contains many stories and, finally, a Crime Does Not Pay tale is one of them.

Daniels writes: “Gleason and Biro also brought a new and very controversial slant to comic books with Crime Does Not Pay. Beginning in 1942, this comic book featured factual accounts of conflicts between criminals and the law. In a broad sense, this was the same theme the superheroes had explored. Conflict is, after all, the basis of plot, but Crime Does Not Pay, minus the fantasy element, really sharpened the impact. The tone was sternly, even dogmatically realistic, and grim details were never lacking. The story reprinted here, "Baby Face Nelson vs. The U. S. A." (No. 52, June 1947) represents this publication during its period of greatest popularity. The artwork is by George Tuska. It seems certain that the intention of this comic book was sincere; certainly its new approach was successful, as it gained huge circulation during the postwar years. Perhaps as a result of the mixed emotions it inspired, perhaps because comic books had been around long enough to gain general recognition, there were rumbling resentments against the industry as a whole.” 

These are not two pages put together by me, this is how the pages were printed, two on a sheet.
  Daniels then looks at the aftermath of the Comics Code and discusses how publishers tried to reinvent adult comics with Humbug and the Warren Publications titles of Creepy and Eerie. It would take until 2009 for Humbug to be reprinted. Creepy, which was widely available in the 1960s, began being reprinted in 2008 by Dark Horse.

On the left is a copy of the original page from Humbug #9, 1958. The image on the right is from the Humbug book from Fantagraphics, 2009.

This is as good a place as any to bring up this point. I know many of us are collectors and having the originals is a good thing. Many originals are worth a lot of money. But keeping and reading the reprint books do have a few advantages:

  • Often, the reprint books are clearer, sharper and just plain easier to read.
  • All the issues are in one place.
  • The books are not fragile like old comics. Old comics also may lose some value with use and they tear and stain easily.
  • They are cheaper than buying the originals. Further, if you like the comics and want to keep them to read, keep the reprints and sell the comics! Of course, for collectors, you’d only sell the comics you are not attached to.
  • Many dealers have told us that when a Masterwork or reprint comes out the comis in those titles go down greatly in value.
 Oh, yes, there is a chapter on Marvel!
 Sadly, Les Daniels died on Nov. 5, 2011, at his home in Providence, R.I. He was 68.


I don’t want to underestimate the importance of these volumes; they were the beginning of a long list of successful and interesting books about COMIC BOOKS! And the Golden Age!


 DC Travels from the 1930s to the 1970s

Bonanza Publishing published four books in 1971 that finally brought us back to the Golden Age of  Superman, Batman, and Captain Marvel (Shazam). These three had volumes released which presented stories “From The 30s to the 70s.” Superman and Batman were DC characters; Captain Marvel was a creation of Fawcett Publications, purchased by DC. What a treasure it was to get these books! The volumes contained stories that were spread out over 30 years, mostly in black and white. There were some color features, (“36 Pages in Full Color”), but these older stories were just wonderful. The books presented many of the origin stories, not just of the heroes, but also of the villains such as the Joker, and the supporting characters, such as Alfred the butler. Some of the tales in the Batman volume (including his first appearance from Detective Comics #27, as well as the Alfred story referred to above) were reprints from anniversary and 80 page giant issues from the '60s, which had been traced from their original Golden Age printings.



             
 
The introductions, all by E. Nelson Bridwell, were very interesting. Perhaps the most compelling part of the books was to see how the characters changed, especially after the Comics Code was introduced. Batman, for example, became less dark and the stories got lighter. Superman became less of a wise-guy and more interplanetary.




 
This was an important reprint.  If you recall I wrote in chapter 3, The Great Comic Book Heroes that a lawsuit had prevented anyone from printing the Origin of Captain Marvel, or any other of his marvel tales.
Finally, I get to read his complete origin!
 All in color for $11. Bonanza Books in 1976 also gave us “Secret Origins of the Super DC Heroes.” At first glance, I was happy to see another book that had Golden Age stories in it. Sadly, there were far too many Silver Age origin stories, including Superman from 1975. Many of the Golden Age origins, including the ones of the Flash, Green Lantern, Superman, Plastic Man, Captain Marvel and Batman had shown up in other reprints, including the The Great Comic Book Heroes.  This book of secret origins had previously “unreprinted” stories from Batman #47, and the Golden Age origins of Green Arrow, Hawkman and the Atom.  Carmine Infantino wrote the introduction.



 When published, these were the only Golden Age reprints available in bookstores. They were placed in the "Humor" section. And, with two exceptions, it would remain that way for the rest of the decade.

The next book of Golden Age reprints to be found in bookstores during the 1970s was probably more famous for its introduction than its stories. Gloria Steinem, a leader for the civil rights for women, wrote the introduction to Wonder Woman, typing her into the ongoing “woman’s movement.” She wrote that Wonder Woman “symbolizes many of the values of the woman’s culture that feminists are now trying to introduce into the mainstream.” Ms. Steinem never mentions bondage as one of their goals.

Here's another small detour from the book store. By the mid 1970s, Comic Book Stores were becoming  common. Soon there would be 10,000 of them, now we have less than 3,000.  Since they had more space for comic book related material, more reprint comics began to come out. Marvel was now regularly publishing, Where Monsters Dwell, Beware and other comics featuring stories from their 1950s Atlas Era. By the mid 1970s about 25% of Marvel’s output were reprints. None were from their Golden Age of the 1940s.

As the new Comic Books stores opened they all had their own price lists, which would later be called price guides. These lists were rexographed or mimeographed using the cheapest forms of reproduction available at the time. The lists were not made to last long, their inventory and pricing changed almost daily. Their lists became invaluable, revealing important information!




In 1979 and 1980 DC gave us a taste of the Golden Age with three trade paperbacks: America and War, Mysteries in Space and Heart Throbs. These comics feature the “best” of war, science fiction and romance comics respectively. The volumes also featured complete checklists for their respective genres.








Not all the stories were from the Golden Age of the 1940s and early 1950s, some were Silver Age Tales.
     
But we are running out of space, so I have to divide this topic into two chapters. Too bad, I won't have the space to explain the importance of the next two panels to our voyage of discovery until next time. 


Or how a few stamped, self-addressed envelopes began to uncover the mysteries of the Golden Age.


So now go to part II!


3 comments:

  1. Things are really beginning to heat up now, Barry. Roll on the next instalment. I'm surprised you haven't had more comments about these labours of love, but I'm sure your readers are appreciating them none-the-less.

    Reply
  2. Thanks Kid, and thanks for you help again.

    I notice people respond on other sites, I guess they are shy about responding here. I am very interested in finding our about their experiances, especailly those in other countries.

    Reply
  3. Wonderful. The original Steranko history, though, did not have the title on the cover. That was added for later printings.

    I just recently sold my copy of the Batman volume. Never had or even saw the Wonder Woman or Secret Origins volumes.

    I can't tell you how influential ALL IN COLOR...was for me! I was able to tell Dick Lupoff a few years back though, and Don Thompson some years before that.

    Here's a piece I published 6 years back on a few of my influences. http://booksteveslibrary.blogspot.com/2006/01/comic-book-books.html

Julien Gracq, Nœuds de vie.


Les heures retrouvées de Julien Gracq

Extraits par Bernhild Boie des nombreux inédits accessibles de Julien Gracq (selon le vœu de ce dernier, le gros de ses réserves ne pourra paraître qu’après 2027), les textes courts offerts dans Nœuds de vie sont groupés en quatre chapitres : « Chemins et rues », « Instants », « Lire », « Écrire », qui reprennent les principales rubriques présentes dans ses ouvrages non romanesques. Ce livre posthume est à proprement parler une merveille, mot qui renvoie tant au vocabulaire du roman médiéval (Chrétien de Troyes) qu’aux chefs-d’œuvre du récit d’enfance (Lewis Carroll) et, plus près de nous, à l’enchantement surréaliste prodigué par le meilleur d’André Breton (Arcane 17).


Julien Gracq, Nœuds de vie. Avant-propos de Bernhild Boie. José Corti, 167 p., 18 €


Un livre qui aurait constitué le moins cher et le plus envoûtant des cadeaux de Noël pour un jeune lecteur (une jeune lectrice) soucieux de s’abstraire des réalités pesantes et des perspectives utilitaires. Car il s’agit d’un ouvrage gratuit, en ce qu’il n’a pas pour visée l’amélioration du monde, bien qu’il ne s’interdise nullement l’analyse ou le jugement. Tout y est subordonné au travail de l’écriture, auquel il est demandé d’abord de produire de la beauté.

Nœuds de vie propose des parcours descriptifs de paysages, principalement français et plus spécifiquement peints sur le motif en revisitant les pays de Loire, berceau et refuge ; des réflexions de toutes sortes, d’humeur, de politique, d’Histoire ; des notules critiques concernant des écrivains sans cesse lus et relus (Rousseau, Stendhal, Proust, Valéry, une foule d’autres et d’abord des poètes) ; enfin, des aperçus souvent fulgurants sur la pratique, personnelle ou non, du métier littéraire.

Chaque amateur d’Un balcon en forêt ou de La presqu’île, ces textes étranges d’une rare puissance magnétique, aura sa préférence, même si l’ensemble est délectable en toutes ses parties. La mienne va d’emblée au chatoiement irrésistible du vagabondage diurne et nocturne à travers la France. Les « vues » y sont détourées par un regard de géographe d’une précision si extraordinaire que le paysage semble se construire sous les yeux du lecteur, s’animer comme dans la célèbre image des papiers japonais de Proust, d’où (de leur dépliage et de leurs contorsions dans l’eau) est sorti tout Combray. Image vivante, fluctuante, odorante, sensuelle, jamais statique sauf si l’observateur déçu la juge sans intérêt.

Nœuds de vie : les heures retrouvées de Julien Gracq

Julien Gracq © Dekiss

Gracq parcourait les routes, de préférence secondaires, à l’allure sans hâte de sa deux chevaux, attentif au moindre accident de terrain, aux vallonnements et aux mares, à la couleur et à la texture des sols, aux infinies nuances de la végétation, sensible aux changements de lumière, aux intempéries, à tous les imprévus d’une nature qu’il avait naguère, dans sa jeunesse, quadrillée et balisée à pied et à bicyclette. Le charme de sa prose tient en partie à cette proximité du concret, du tangible, qui n’est donnée qu’aux enfants de la campagne. D’ailleurs, qu’est-ce qui n’est pas d’enfance chez Gracq, dans la faculté d’éprouver la sensation au ras de la peau, des papilles, des cinq sens ? Le miracle réside là tout entier, c’est l’avènement, dans une langue à la fois cérébrale et charnelle, de la merveille constituée par ce mixte instable et pourtant solide de perception physique du réel et de sa métamorphose en phrases claires et flexibles, toujours inattendues et vibrantes.

Mais l’esprit d’enfance qui anime ces pages s’y infuse, s’y épanouit, est aussi ce qui évite à l’œuvre de tomber dans le maniérisme d’un figuratif trop léché, et lui permet de dépasser le trop de clarté qu’aurait une perfection simultanée de chacune des données du réel (la perfection froide d’un Jules Renard, d’un Louis Pergaud, miniaturistes fort estimables mais sans génie). Comme pour l’enfant, le paysage de Gracq est plein de choses non dites, d’êtres cachés, lourd de manigances redoutables, jamais loin de l’éternelle forêt de Brocéliande. Seul Henri Michaux parfois lui ressemble, chez qui « la nuit remue ». Gracq excelle à transformer le panorama français le plus paisible en un théâtre mystérieux hanté par les gnomes et les magiciens. Au cœur de sa bibliothèque la plus intime, Jules Verne et Tolkien ne tiennent-ils pas autant de place que Baudelaire et Rimbaud ?

On trouvera dans les sections du livre plus consacrées à la réflexion qu’à la description mainte autre raison d’admirer, en particulier la lucidité d’un artiste que l’évolution de l’univers, au cours du dernier tiers du XXe siècle et des premières années du nôtre, inquiète de façon prémonitoire. Partisan d’une vie retirée loin des honneurs médiatiques, modeste et heureuse, Gracq voit loin dans ses convictions écologiques et il est justement horrifié par la monstrueuse dynamique de la démographie humaine. La science-fiction pessimiste trouve donc en lui un défenseur, qui se remémore avec nostalgie l’immense liberté de se mouvoir seul sur les routes de France et de Navarre, surtout – et c’est un constat qu’ont pu faire même des gens bien plus jeunes que lui – pendant la période régressive de l’Occupation, où la circulation avait été partout réduite à presque rien.

Cette tendresse pour les heures enfuies, cette allergie à la foule, font-elles de Gracq un passéiste et un misanthrope ? Pas vraiment ; et, s’il trouve suspecte la notion de « prochain », ce n’est pas pour une célébration morose des écrivains d’autrefois, envers lesquels il conserve, comme pour jauger l’actualité littéraire de son temps, une liberté totale d’appréciation.

Mais, comme Proust, s’il considère souvent que sa vieillesse – à la fin des années 1970, il a près de soixante-dix ans – manque de grands écrivains, c’est parce qu’il est lui-même, en émule de l’auteur de la Recherche, un écrivain absolu, c’est-à-dire délié de toute obligation de respect, sauf à l’égard de ce que Breton appelle, dans l’Introduction au discours sur le peu de réalité, « mon beau langage ».

Pas plus que Proust ou Breton, Gracq n’est un précieux enchaîné à une écriture normée par les académies, ou même par les avant-gardes. En revanche, ce qu’il écrit repose sur une connaissance exhaustive de toutes les strates du français. C’est un écrivain rare, admirable praticien de la langue, d’une clarté lumineuse mais difficile aujourd’hui pour bien des lecteurs à cause de sa richesse même, car seule la beauté du style compte à ses yeux, ce qui est devenu tristement anachronique.

Cette beauté est maçonnée à partir de la luxuriance et de la polysémie (aujourd’hui peu exploitées, même en poésie) du vocabulaire et de la syntaxe. La création stylistique de Gracq aboutit à une splendide architecture d’images, de nature fondamentalement poétique. Ainsi d’une journée de mai : « À cette saison épanouie de l’herbe haute, la puissante encolure cornue [des vaches] qui émerge engluée de la verdure réjouit l’œil comme un attribut naturel et achevé du gonflement immobile de la sève, autant qu’un dauphin qui jaillit de la mer en rumeur. »

Image surprenante et pourtant immédiatement convaincante, parce qu’elle est de part en part pertinente (mer et herbes qui gonflent dans le vent ; vert de la prairie et vert marin qui se mêlent ; sève qui monte comme monte la vague avant que le dauphin n’en jaillisse, la portant sur son encolure). De ces phrases singulièrement parfaites, d’une rigueur et d’une invention absolues, on trouve des dizaines dans ce livre des merveilles. Personne n’écrit plus aussi bien que cela de nos jours. C’est un fait, et c’est une perte de substance dont on peine à deviner comment la littérature saura se relever.