a funny measurement:

Indirect measurements of tricky to deal with things, like citadels by their shadows, is such a beautifull discovery of the ancient greeks that I try an other example of the trick:

The town Bad Salzuflen near Bielefeld (see the entry below) has a strange similarity to one of the worst movies, gruesome sound ever made. "I have looked into the future and it doesn't work" is it's message. (Neither did the film, but this review is good) Let's have a look: Bad Salzuflen lives from huge hospital and wellness business in it and it is in a strange way separated into two parts: The run down town itself with the working people (many poor and imigrants), and the wellness parks and hospitals in the early 1960's style, where wealthy 'eternal' guests spend their time with all sorts of new-age-therapies, dining, etc. A kind of invisible boundary separates both, you never see e.g. children of the working population playing in the nice park just a few meters away and open for everyone.

After an accidential ride to it and puzzled upon my impressions, I remembered this film on a somewhat similar idea - from a review: "Only at the fag end of the 1960s could such a simultaneously ambitious and preposterous movie be made. Boorman's thesis - that the middle class hippies cannot retreat to their own bohemian idyll without descending into in-fighting and impotency - draws both from H.G. Wells' 'Time Machine', and no doubt his own observation of the Sixties communes". The idea of these communities materialized in wellness center concepts for the aging career-68'ers and developed out of 19th century medical centers. Their contemporary cases could easily be mistaken for Th. Mann's 'Magic Mountain' with which Bad Salzuflen had some similarities long ago. But that old version was an economically selfsufficient upper class community separated from the normal society and the main economy, whereas the current ones suck money out of all of society and are the political guiding model (at least in the overaged Germany). The old alienation from modernity by separation is exchanged by a generalized stagnation and economic deterioration. E.g. the amazing resistance against an appropriate schooling of lower classes and imigrant children, as schools are the determinant for social status mobility in Germany. Among the film's nice ideas is one, where Connery is tricked into the library, into reading and thinking:

, finally into infiltrating the 'Vortex' by 'Arthur': "I am Arthur Frayn, and I am Zardoz. I have lived three hundred years, and I long to die, I am a fake god by occupation - and a magician, by inclination. Merlin is *my* hero! I am the puppet master." The idea that 'gated communities' turn sometime into 'hidden communities' as part of a crypto-social structure is interesting (anticipated by Lem, comme d'habitude) and apparently discussed among sociologists: "send the richest people—or, probably more efficiently, the poorest people—out of the country or the state. Inequality would go down and well-being would go up. Alternatively, leave the inequalities as they are, but devise ways to hide them from people—censor the media, say (no more Lifestyles of the Rich and Famous)—so that people do not know their relative positions. That should, according to The Spirit Level, bring down crime, disease, obesity, and so forth". The separation of the social classes and their exploitation in the movie fits nicely to the current reality of Germany.

a case of city amnesia

A shallow recent film on a kind of wishfull city amnesia made my friends wonder, so here some ideas on it's psychological background. The film is a late version of some silly internet joke on Bielefeld, a middle sized town in the german provinces, and expresses it's strange longing for amnesia. Being in itself just a typical german town, because of which some big opinion- and market research companies settled there, with history tracing back to the origins of the german founding myths (more, more) and behaving during the past century not worse than everywhere else in Germany: Here you see the Synagoge burning 1938. The population protested against the crude pogroms because it asked for distributing valuable furniture instead of throwing and smashing it into the streets. Camps for slave labour supplied ca. 100 companies in the city, as usual those times. In the weekends, people enjoyed rides to such a camp and this Stalag nearby, watching the inmates running after potatoes thrown over the fence. Some rural people stayed honest (film). After WW2 Bielefeld recivilized quickly and was even considered for becoming Germany's next capital, by the locals again after the german reunification, still causing a strong animosity against it's more successful competitors. Now it is one of the highest appreciated places for living in Germany, making the mentioned desire for amnesia even more puzzling.

The movie version of this wish for nonexistence actually belongs as latest and most weird phase to the particular german way of history-exorcism in post WW2 german popular culture:
Phase 1 from the 1950's on by the comedian Heinz Erhardt, connecting to and then exorcizing nazi patterns of emotions by a kind of stubborn infantilism and anancastic humor at the edge of Goebbels rhetoric (youtube1, youtube 2).

Phase 2 was the psychological core of german criminal telenovellas from the 1960's on, when the calm and rational detective substitutes the shrieking nazi, here a collection of the key scenes, when murder cases, as slightly alienated uncoverings of dark war secrets, are communicated and calmed down. Actually, media specialists know since long that those crime series were invented by a former nazi who tried to overcome his own past by that. An open media secret in Germany. Such series' international success make one wonder ...

Phase 3 was the famous game show by Hans Rosenthal, a jewish Berliner barely escaping the KZ. The show's title "Dalli-Dalli" was the call of the nazi-wards in Poland when they made the jews run more quickly from the final train stations into the camp. "Dalli-Dalli" spread into the german language and had allways an association as the voice of an evil authority imediately before turning to violence. "Dalli-Dalli" was a kind of final warning. Notice the slightely transformed jewish stars in the background.

All that worked well, so why the need of the shallow phase 4 in that movie now? It is because the previous phases only work *retrospectively*, after the dark past is behind. In Bielefeld's case, this did not happen, the boundary was blurred and the past streched into the present.E.g. after WW2 e.g. Himmler's wife and daughter were given a home in Bielefeld by an influential Ex-Nazi-support group, among the recipients of support was probably Mengele. There is a permanent battle on the name of the city art hall local industrialists sponsored. It's architect, co-founder of the american Nazi-party ("He attended one of Hitler's Nuremberg rallies in 1938, and in 1939 he followed the German army into Poland. "We saw Warsaw burn and Modlin being bombed," he wrote afterward. "It was a stirring spectacle." quotes the W-Post): "I have no excuse (for) such unbelievable stupidity ... " Founded by a local member of the Himmler-fan-club, then named for Kaselowski, a friend of Himmler, with opaque involvement in robbing jewish businesses. (The investigating historian felt the need to secure documents from destruction or manipulation by transfering them into an other country.) Now the art hall got rid of that name, but locals succeeded in naming a nearby street after Kaselowski. When Frank Gehry recently participated in designing a new part of that art hall, he too made startling comments: "Ich werde täglich mit großer Dummheit konfrontiert." Until the german reunification, Bielefeld was the dangerous hotspot of german neofaschism, which then moved into the former GDR. Slave work continued until the mid 1970's, but with children in orphanages instead of POW's and ethnic minorities. After a holocaust-memorial lecture in the local university, citizens of neighbouring towns who still hide goods (books, art, etc.) from jews who exchanged them for money and food during their flight had contacted an aquaintance for how to get finally rid of the remains. Supressed into the subconsciousness, weird feelings in visitors express usually just indirectly, e.g. the puzzled reaction when the city's PR dept. asked a gourmet journalist for a visit: "Was tue ich am Rande des Teutoburger Waldes, werden viele Leser jetzt fragen. Die Antwort ist einfach: Ich suche die Herausforderung ..." But now, Bielefeld seeks for salvation in dementia, for relief by nonexistence.


a voice from the basement

Two months ago a ride to Berlin turned into an unexpected encounter with language (e.g. by this antique (clay) mailbox found in a musem), intensified by a visit of a very interesting literary translater's workshop. - At this occasion here the link on a new book on the relevance of literary translations. - One of the workshop's themes was how to translate a short novel by Ludwig Hohl, a Petrarca-awarded hermit thinker hidden in a gastly basement room in Geneva. A hermit needs a yoga, a 'deep work' structuring his life, and so Hohl had his one: His 'Notices', a symphony-like structure of notes and quotes he worked on throughout his life. The theme of this symphony was the creative inner process and it's relation with language and literature. The resulting structure of the 'Notices' looks more like medieval memorabilia or renaissance memory theaters than like a normal book, the few modern analoga could be Valery's Cahiers or Lichtenberg's writings. Goethe and his somewhat similar collections of remarks are frequently quoted by Hohl, so is Spinoza's achievement of intellectual autonomy. Like the magnum opus of some renaissance hermetic, Hohl's and the mentioned mental relative's yoga's can't be consumed passively. Reading through this web (a 'structure', not a 'system') involves solving exercises, given by the author (in contrast to Goethe, who makes finding them an exercise too). The creation of 'true reading' as 'active reading' in the accidential visitor is actually the goal towards this music of thoughts works towards. The issue of 'deep reading' had been discussed by Grothendieck at length, here (from ca. p.35) a survey of his thoughts. Y. André gives here a comparative lecture on reading, writing and creativity, here a historian describing his working method and here on libraries as memorabilia.


a Gremlin finding

I doubt that they like it, but I took a photo of them. Found in the basements of an old Citadel in Spandau, after stumbling over old cannons, forgotten helmets and mysterious gravestones. The figures come from an art class for ca. 12 year old pupils, obviously with much better connection to their creativity than many grown ups. A nice occasion to mention again this museum dedicated to children's creative skills in art.


a local tour:

Three weeks ago, a librarian's letter mentioning travel reports induced me to take a camera and try a miniature version of such a thing too and see what happens. The tour led to Oerlinghausen, a small town nearby and hometown of the sociologist Niklas Luhmann. It's rough idea was to look into a nice archeological museum in Oerlinghausen I remembered vaguely.

It took just a few minutes to stumble across (and into) the unexpected, an art exhibition in the former synagoge, one of the very few still standing, which you see here with the original windows and woodwork. The jewish community of Oerlinghausen declined in the 1920's when many of it's members emigrated to Brasilia, as I was told, and the synagoge had been given up. The last members of the community had later been deportated by the Nazis. Artist Jens Andres' „Was ich fürchte ist die Gedankenlosigkeit“ (= "What I fear is thoughtlessness") can be taken as admonition. There is a kind of discrete tension building up between the long painting on that motto, the pop-artish "Wut" (= "Hate") between the windows and the mysterious and playfull warning signs in the basement. The town's (unsalaried) art organisation which uses the Synagoge now lists among it's connections an interesting polish art group, making me wonder where to the last communities members were deported to. And if Aichinger's "Man überlebt nicht alles, was man überlebt." (= "You don't survive some of the things you survive") happened here too. Her "Herod's children" and this list tell more.

A struggle with the past is a permanent theme too of the archeological museum you see now, the cause of my trip. Founded 1936 on a site of archeological findings, it became part of the Nazi propaganda business, and tried for decades to get away from that past, finally successfully. Today, it has become one of the best archeological open air museums with excellent didactic program and part of a multinational network of similar initiatives. When it's current director Karl Banghard observes "archeology attracts freaks like garbage attracts flies", this refers to contemporary esoteric and new age scenes and popular pseudo-medieval "militainement" happenings. It's exhibition offers a route from paleolithic times to late middle age, each represented by at least one building and pieces of their reconstructed environments. E.g. you start at a paleolithic summer tent, then two mesolithic huts with mesolithic flora around them. One wonders how one could have survived in such conditions, and if the inhabitants may have been Neandertals, but they were as modern humans as we. BTW, here a tool transforming your facial shapes into a Neandertal one. Aside this neolithic long hut one finds the precursers of modern grains harvested by the Rössen culture then and a small puddle around other vegetables used then are plated. The Rössen culture kept cattle, sheep, goats and pigs, which you don't find in the musem, but the parts of the tour on the Iron, Bronce and middle ages contain retro-breeded cattle too. Roughly at those times, lactose tolerance and skin pigmentation changed. The Iron age part shows a small field with plants cultivated for clothes and it's colouring, it's them who collided with the roman civilization. Rome looked like this, the cultural and military collision is theme here. Chimneys had been invented a millenium later only, what that means you find out when you enter a hut where a cooking fire burns. Here you see Gerhard Kalden in a tent build after one of the rare archeological findings from the mesolithicum ca. 60 m further. The upper parts of the tent are modeled after tents in Sibiria and inner Asia, using ethnography for archeological reconstructions. Equally impressive is this bronce age farm house with context. Unfortunately closed were the early middle age parts of the exhibition, including a reconstruction of Charlemagne's plant garden "capitulare de villis" and several houses, most impressive (an shocking) the "sunken hut". This looks like a weird joke - a house sunken nearly until the roof into the mud whose single room is just cut out of the clay. These horribly unhealthy, cold and wet pits were the working places since stone age until early modern times, since their temparature and humidity fitted manufactoring needs. As substitute for fotos from that, here a beautifull and instructive link on an other medieval issue, a 'Motte' whose reconstruction was organized by Karl Banghard too. A 'Motte' is the real thing behind what you probably imagine as medieval castles, those stone castles dominating the public image are (at best) just late medieval 'Disneyland anticipations' for aristocrates in romantic mood. Obviously, history allways was a kind of Rorschach blob-test on which people project their phantasies and madnesses. Only turning to the traces of the facts and admitting the never ending incompleteness of that business offers hope. The Oerlinghausen museum staff, mostly long time voluntaire participants, complements such exhibitions and reconstructions according to the current state of knowledge (recent news) with a broad spectrum of didactic events, like these workshops or special events focussing on e.g. the romans in this region and their lifestyles. The quality and diversity of the museum's activities make one think at the success of open sourse software like Linux: As there, dedicated amateur enthousiasts create an impressive amount of expertise and turn that into action.

The most lasting impression is about the slowness of progress visible from Rössener culture to early modern times. All the houses in the museum look very similar, aside chimneys entering somewhere the late middle ages and the amazing lifestyle anticipations of Rome. One remembers that even the former chancelor Gerd Schröder grew up in this region of Germany in a clay hut whose interior walls were covered with ice each winter morning. Still, for a shocking part of living mankind, basic issues of living are unsolved, even those ones those neolithic groups somehow managed. The strategic planing pressure on those neolithic must have been huge, errors resulting in famines instead of 'bail outs' as economical leadership counts on today. One wonders too, if "personas" extisted at those times, the closeness of living without a sphere of privacy must have turned group living into a permanent "Big Brother" show. "Alone", a polar researchers biography, describes how painfull transparent and predictable other people become when they live under permanent mutual perception. Organized data collection frenzy today makes cultural achievements like discreetness and privacy risking extinction like some strange butterfly (existentialists would call it horsefly) whose existence looks entirely unbelievable when they are finally gone. An other major difference between our and premodern mindsets surely is the later's lack of an idea of culmulative cultural progress. The direct and permanent experience of nature probably resulted in an intuition of the 2nd main theorem of thermodynamics, acc. to which order and structure - the anti-entropic work of civilization - is possible only as local and temporarily violation of nature's tendency towards chaos. The ancient greeks called the anti-entropic work "nous", the entropic nature "chaos" and the 2nd main theorem "ananke", "chaos" had to be temporarily tricked, coaxed to such an exeptional deviation. Socrates expressed it in Gorgias: "The good is possible only as rescue and getting saved". Christianity's salvation promise later was a theological loophole, but even then thought as a loophole outside the normal course of life. An excellent description of that antique christian way of thinking can be found in the novel "A canticle for Leibowitz" and the brilliant "Dream of Scipio". Only the age of enlightment generalized this motive, by unhinging it from the theological frame, towards our modern idea of permanent progress as natural developmental law of mankind. However, early christianity had a specified goal for it's anti-entropic loophole. Enlightment not. It suffers from a fundamental confusion on the concept of cultural goals: Shall they be thought of in analogy to production procedures, being defined by the result independent from the way to it? Or in analogy to human life, e.g. learning and growing, defined by the process alone? Again, a novel best illustrates the first concept and it's usage: "Ypsilon minus"- The author H.W. Franke, a physicist and sci fi writer, observed N. Luhmann's school of thought whose impact on political, administrative thinking in Germany is hard to overestimate. Luhmann went so far as to exclude human beings as part of modern bureaucratic societies. Acc. to him, the boundary between 'culture' and 'nature' shifted drastically, 'human mind' belonging to the later and goal of quantification, selcetion and mastering like other resources. I prefer an other way to draw distinctions, as 'human mind' being the residue of 'culture', who now is targetted by 'bureaucratic societies' as entropic force aside the old 'naure'. The complexities of this can be seen again in a novel: "Snail on a Slope" by the Strugatskii brothers. The battle between individual and bureaucracy are theme of J. Le Carré's novels, the latest one a slightely fictionalized case study in Hamburg. Earler, the philosopher E. Lévinas analysed this and how entropy infiltrates and corrupts the human mind: "His 'freedom of thoughts' expires silently: The thrust of the enemy forces is a slope. The consciousness of sliding downwords gets lost." (from 'Totalité et Infini', p. 214) Decivilization as global tendency is even theme of research now, indicating (like the new attention to psychoanalytic studies as here, or here) a final loss of belief in the selffullfilling idea of cultural progress.


"The Job of Enlightment"

Salomon Maimon (1753 – 1800)

Ca. a decade ago, on a train ride to Berlin, I browsed through and became increasingly fascinated by a book on Salomon Maimon, "the man who understood Kant". Below a short text I wrote then on my impressions. A contemporary analysis of Maimon's philosophy is given in: Gideon Freudenthal (ed.): Salomon Maimon: Rational Dogmatist, Empirical Skeptic. Critical Assessments. Kluwer Academic Publishers, Dordrecht 2003. Quotes of Maimon come from this website. You find his autobiography here, more scans here.

Although his concepts play a decisive role in the history of ideas, only a few specialists bother about Salomon Maimon’s philosophical writings. Much better known is his autobiography written in the early 1790’s – a funny account of 18th century spiritual life in eastern Europe’s Jewish communities, told by a chaplinesque narrator – once a celebrated scholar, then a wandering beggar half mad by hunger and despair. Yet his erratic way of life was governed by a central inner law from which Salomon never deviated, a central question he never lost sight of:

How far reaches human understanding independent from experience?

He perceived all human activities as “being just a kind of, more or less, intense thinking”, deduced all desires from a fundamental “urge to think” whose goal is the “maximisation of thinking” and “sincerity” was the moral value he lived after. The suffering this caused in Maimon’s life let some researchers call him: “The Job of Enlightment”.

He was born as Shlomo ben Yehoshua in Sukoviborg, Lithuania, educated as a rabbi and became quickly famous as a child prodigy. In fact so famous that he was kidnapped by someone who wished to become his father-in-law. Salomon married another girl, but then his mother-in-law developed the habit of beating him up when his reluctance to earn a livelihood became clear. Despite his surrounding’s animosity against modern science, Maimon found and studied a book about mathematical astronomy. Since then, his strongest wish was to learn more about science in Germany. "Man scheint gleichsam zu vergessen, daß man durch Newtons Weltsystem mit weit beßrem Erfolg Krankheiten kurirt, als durch die Electricität, nemlich Krankheiten des Geistes." Another important event for him was the aquaintancy with Maimonides’ “Guide for the Perplexed”, this lead to an unorthodox commentary and to a change of name. Disappointed by his environment - and by the empty promisses of “practical Kabbalah” (the spell for gaining invisibility didn’t work) – he left his home, wandered around in europe and was finally saved from starvation by Moses Mendelssohn when he arrived in Berlin. There, Maimon studied Kant’s “Kritik der reinen Vernunft” which he criticised severely. Kant tried to explain the possibility of experience by exploring the necessary conditions for this possibility. To achieve this, Kant distinguished between the Thing-in-itself and the mind, then within the mind between sensibility and understanding. Maimon reacted with his "Versuch über die Transzendentalphilosophie", "Ad Kantium" and dedicated to the King of Poland with the wish: "den edlen Polen eine vorteilhafte Meinung von meiner Nation, nämlich den unter ihrem Schutz lebenden Juden, beizubringen". According to Maimon, this doesn’t work and Kant’s concepts cannot be separated. E.g. while Kant thought usual space and time as necessary forms of sensibility without understandings interference, Maimon let them result as only one of the mind’s ways of thinking several objects. A spectacular verification of this idea was achieved ca. 100 years later by Ch. Hinton, a mathematician who wondered about the possibility of “absolute knowledge” about arrangements of colored cubes and realised that playing with them in a certain way enables one to “see” 4-D. Luckily, by means of other arrangements the visual system can be stimulated to switch back into it’s usual modus. According to Coxeter in a book about regular solids in 4-space, this has lead to important discoveries. Penrose even tried to construct in this way 3-D analogies to M.C. Escher’s pictures, but found that “a bit insane”. Hinton wrote later strange stories playing in a world with 2-D time.

Maimon suggests an analogy from mathematics for the relation between sensitivity and understanding: If we imagine a smooth plane curve, as perceived by sensitivity, which is then analysed by understanding through the construction of triangles of inclinations, i.e. difference equations, a more and more refined analysis would converge towards the building of differentials, resulting in a dimensionless point (initial condition) and some relations between the differentials (differential equation). So, the curve which was initially perceived mainly by sensitivity, is now mainly perceived by understanding. The properties of analogously build “differentials of sensitivity” are the categories of understanding, their knowledge is a never reached final goal.

This concept of inseparable unity of passive perceivement and mental activity had a great impact on the masterminds of German romantics, the “differentials of sensitivity” being the theoretical basis for the work of Friederich Schlegel, Fichte, Novalis. The most widely read german history of culture, written by Egon Friedell, uses Maimon’s concept as guiding methodological principle without mentioning it’s source.

The same analogy is used by Maimon to clarify the relation between the thing-in-itself and the mind. Whereas Kant’s distinction makes experience impossible, according to Maimon the idea of an extra-mental reality makes no sense. So, experience is possible because - in the infinite mind – subject, object and their interaction fall together, but it can be attained by us only insofar we approximate the former in the course of scientific progress. By doing mathematics we come close to the divine mind since e.g. in arithmetics the subject (number-representing psychological states), the object (numbers) and their interaction (inductive definitions a la Peano) coincide. That human mathematics contains indirect proofs shows that even there true experience is not always reached. By way of discussing the thinkability of noneuclidian geometry and a concept of truth as process, Maimon anticipated Hilberts Formalism.

When Maimon’s critique was send to Kant, he reacted enthusiastically, praised Maimon as the one who had understood him best and organised its publication. Much later, Maimon’s Kant-interpretation was reactivated by Hermann Cohen and lead to a philosophical movement called “Neukantianism”. Together with Maimon’s consideration of Jewish spirituality, again taken up by Cohen, this shaped the thinking of Walter Benjamin.

At Maimon’s time, Berlin’s intellectual life was determined by informal “Salons” outside the academic establishment. Sabattia Joseph Wolff reports in: “Maimoniana oder Rhapsodien zur Charakteristik Salomon Maimon’s”, Berlin 1813, about such a learned society founded by Maimon. Here a summary of its constitution:


The members write essays about subjects of interest in relation to the society’s goal. These – or, if there is a lack of such essays, the best appropriate text aviable – are presented and read at the society’s meetings every month. These lectures are not to be disturbed, but every member can write a critique which is then presented in the same way as the original essay. Finally, the author of the original essay can produce analogously an anticritique.


Each month after the above mentioned lectures, an unstructured communication starts, in which every member can feel free to follow his uncensored imagination and arbitrary association of ideas, however strange they may be. All remarks are recorded, then read and their psychological causes are discussed. In case of doubt, the opinion of the producer of a remark has the priority.


Each month, the administrator of the society, who is elected democratically, poses a subject for a price competition. This is announced in newspapers and non-members are encouraged to participate. The administrator and two democratically elected members decide about the two best of the incoming essays. These are published by the society and the contest-winner gets all possible profit from that publication.

Salomon Maimon on himself: "Ich bin zwar kein großer Mann, kein Philosoph für die Welt, kein Possenreißer; habe auch in meinem Leben keine MandelMäse in die Luftpumpe ersticken keine Frösche auf die Tortur bringen, auch keine Männchen durch die Electrizität tanzen lassen. Aber was thut dieses zur Sache? ich liebe die Wahrheit, und wo es darauf ankommt, frage ich selbst nach dem Teufel und seiner Großmutter nicht. Da ich nun die Wahrheit aufzusuchen, meine Nation, mein Vaterland und meine Familie verlassen habe, so kann man mir nicht zumuthen, daß ich geringfügiger Motiven halber, der Wahrheit etwas vergeben sollte. Persönliche Feindschaft hege ich gegen niemand, wer aber ein Feind der Wahrheit ist, wer sein Ansehen beim Publikum dazu mißbraucht, dasselbe aus niedrigen Absichten irre zu führen, ist eo ipso mein Feind, sollte er auch übrigens mit mir in gar keinem besondern Verhältnß stehen; und ich werde keine Gelegenheit verabsämen dem Publicum sein Betragen in das rechte Licht zu stellen, er mag römischer Bischof, Professor, oder türkischer Sultan seyn."


a context of Gromov's program

Perhaps as gift for curious websurfers, Micha Gromov, geometer (more) at the IHES, posted shortly before last christmas parts of a fascinating essay discussing "real" and "artificial" intelligence, pattern formation and detection, learning, language, of course mathematics and lot's of other interesting topics on his website. Theme of his essay is a sketch of a kind of program for exploring a possible general background structure behind the invention of and dealing with "ideas" and concepts. As the idea of a special cognitive background structure as root of mathematical thinking can be traced back at least to the ancient Platonists, Gromov's essay motivates to take a small tour through it's history for looking if Gromov's thoughts fit to that. Many thanks to Matilde Marcolli and Yuri I. Manin, who kindly allow to include pieces of their art for illustrating some issues, of course this does not imply any sharing of the thoughts expressed here.

The mindset called "Platonism" received more attention recently with Yuri I. Manin's interview in the AMS Notices and his remarks in a following book review on the history of mathematics. Among mathematicians, "Platonism" is about meaningfull mathematical concepts and structures as being "preexistent" and "found", in contrast of being "made" or "invented" - hidden structures as being "revealed" in the course of research instead of being "constructed". Yuri Manin expresses the resulting mental image of mathematics with a beautifull picture:

"... a great castle and you gradually start seeing it's contours through the deep mist, and begin to investigate something. How you formulate what it is you've seen depends on your type of thinking and the scale of what you have seen. And so you begin to blow away the mists, to find appropriate telescopes, seek analogies with edifices that have been discovered before, create a language for the things you see so vaguely ..."

That may sound rather detached from immediate "reality" (whatever that is) and about something like a dodecahedral cloud floating in the air. However, the idea of a screwdriver illustrates the meaning of a "Platonic idea" probably much better. Even a superficial browsing of contemporary mathematics shows that "platonic" programs and concepts are among the leading forces for actual research. E.g. there was hardly ever a more "platonic" insight than Grothendieck's quest for the "mysterious functor" relating different ways to do geometry (="cohomology theories") in number theory, which became one of the most usefull tools in the applied business of cryptography. Many more examples could be given, like the quest of the "field with one element" in the context of treating geometry and number theory in a unified way, or that for the correct definition of "higher categories" as expressing what "spaces" really are. Ca. 20% of Manin/Pachishkin's Encyclopedia volume on number theory present "Analogies and Visions", Kato's beautifull survey on his groundbreaking work is framed in poetical expressions of a platonic mentality: “Mysterious properties of zeta values seem to tell us (in a not so loud voice) that our universe has the same properties: The universe is not explained just by real numbers. It has p-adic properties … We o u r s e l v e s may have the same properties.”

Despite being named after Plato, the "platonic mindset" goes back to far older ancient greek philosophers and there had never been a commonly accepted set of welldefined doctrines for it. Plato maps a road towards it in his dialogues, but carefully makes clear that his real teaching was an esoteric one and never explicitely written down. Perhaps he thought that to be unnecessary because it pervaded all ancient greek philosophy before him and consited more of a mentality instead of specific beliefs. Mentalities can be learned by practice, not by just reading dialogues. And this was his reason for advertizing the yoga of mathematics. Plato distinguished between three levels of thinking: sensation, reason and higher intuition. These levels of thinking correspond different layers of external reality and of internal psychology. The special feature of "ideas" as the reality counterparts of higher intuition was their identity with higher intuition's counterparts in psychology: "ideas" as common foundation of both external reality and internal psychology. They provided the connection between individual thinking and reality which made knowledge possible and consequently, the best knowledge is that which connects most directly with them. For the same reason, "ideas" were considered "more real" than everything else - in contrast to the current view of "ideas" as reduced versions of reality, they were perceived as enrichments. An analogy: Classical greek sculptures were about visualizing ‘abstract’ concepts; 19th century scholars concluded that this forces them to have been colourfree because ‘abstract concept’=’reduced’, ancient greeks made them probably for the same reason very colourfull because for them ‘abstract concept’=’enriched’. This way, "Platonism" solved the epistemological problem and avoided ontological troubles. But it run into other troubles: if higher intuition can't be reduced to rational thinking characterized by verbal reasoning, intuition becomes increasingly incommunicable the more interesting it becomes. Similar, if true knowledge only comes from turning towards the common basis of outside and internal reality, but language is based on distinguishing these and everything else, language itself becomes unfit. Worse - even having a localized, personal ego is incompatible with knowledge. Actually, some antique philosophers teached that knowledge is impossible, if possible then unexpressable, if expressable then incomprehensible. Others turned to expressing in paradoxa, irony and myths, what apparently became a trademark for deep thinking like some millenia later twisted language for german thinkers. An other resulting invariant of greek philosophy is it's insistance that real learning is accompanied by a separation of the personal ego from the egofree part of the mind which only connects to "ideas". Walter Benjamin describes that in his "Ursprung des deutschen Trauerspiels" with "Die Wahrheit ist der Tod der Intention" ("Truth is the death of intention"). He specifies the special relation of language to truth with: "Das ihr gemäße Verhalten ist nicht ein Meinen im Erkennen, sondern ein in sie Eingehen und Verschwinden" ("The language's appropriate behavior is not building opinions, but an immersion into truth and a vanishing in it"). The loss of this connection and the subsequent arbitraryness of normal language in naming and distinguishing things was for ancient philosophers like Parmenides the basic error of the human mind whose stabilization and ramifications created the world of discourse, doubt and pseudoknowledge we live in now. Acc. to Benjamin this original mistake shows up in the faint air of melancholy pervading the images of nature since then. It is the poet's and the philosopher's task to restore the lost connection for brief moments ...

... or to create:
"to name something was to give birth to a new entity .... Humans could exercise Free Will and put in perspective mathematics and philosophy", describe Graham and Kantor in their study on mathematics and religiousity in set theory research in Russia a century ago. Pavel Florensky, 'the Russian da Vinci', argued: "it is the word alone that makes the cognitive process possible, that makes objective what was still subjective, sums up our inward longing for reality and places before us the cognitive urge as a goal and value."

Yuri Manin wrote a very beautifull poem presenting this role of "arbitrary naming" in creating frames of meanings for further creative work. It has been stimulated by real ships he observed and produces instantly a strong image and the complexity of the relation naming/knowing comes without effort precisely when the barges' poetic associations set in. There is probably nothing more arbitrary than the names of the ships - but, well ... just read and notice what happens:

Barges on the Rhine


... I’ve read half–through the catalogue of ships

Ossip Mandelshtam

ANGELUS DEI, with coal humps on his back,
strides along as a forlorn camel that lost sight of his needle’s eye.

IMMACULATA shyly cuddles to the left bank
trying to cover her face with a veil of feeble smoke.

God cannot be comprehended, but can be named.
The Name of God is God himself,
so the Name Worshippers believed. The venerable Illarion,Pavel Florensky.
And infinity cannot be comprehended, but can be named(Georg Cantor’s Alephs).
Who can comprehend barges? Who names them?
He - or She - is beyond the comprehension of mortals as well ...

CURA DEI’s Diesel engine snorts scornfully at INNUENDO.

who fancies himself a kamikaze, the divine wind,
that will smite the dishonorable ones,
heaving in lacerated flames
Hiroshima, Bikini atoll, the World Trade Center, Königswinter.

TOLERANTIE only faintly pants.

DISSIDENTIA ran aground last night,
her clawed belly rumbled on wet stones,
a hundred meters from my balcony.
She will sail again – but whither do we sail, pray, tell me, ZEMBLA!

PANTA RHEI ... everything flows ... πάντα ῥεῖ ...

Translated from the Russian original by Yuri Manin

Angelus Dei (lat.): God's Angel
Immaculata (lat.): the Immaculate, Vrigin Mary
Cura Dei (lat.): God's care
Innuendo (lat.): insulting allusion
Sayonara (jap.): Fare Well!
Mon Désir (fr.): my desire
Banzai (jap.): battle call of japanese warriers
Kamikaze (jap.): "divine wind", military suicide aviators in World War II
Tolerantie (dutch): the tolerance
Dissidentie (lat.): disaccord
Zembla: Imaginary country in Vladimir Nabokov’s novel “Pale Fire”.

A friend just called attention to Eco's recent book "The vertigo of lists", dealing with the many roles that lists of names played in literature and art, from the catalog of ships in Homer to the list of Don Giovanni, touching on a lot of different aspects of abstract or disembodied "naming" too.

A surprising reference to platonic truth is in Werner Herzog's cineastic aesthetics, as the try to catch with the artist's tools the "extatic truth" behind the superficial "truth of the accountants". The method he teaches in his film school is "not for the faint hearted... For those who have a fire burning within." Herzog suggests: "Follow your vision. Form secretive Cells everywhere. At the same time, be not afraid of solitude." His "Bells from the deep" about russian mysticism gives a nice idea, incl. the unintended satire unavoidably attached to such docu.

At least since the mid 19th century, scholars traced these themes back to an even older tradition of shamanism. E.g. Nietzsche's Friend Rohde’s great work “Psyche. Seelencult und Unsterblichkeitsglaube der Griechen” and the small books on the greeks and Nietzsche by G. Colli. Dodds “The Greeks and the Irrational” contains a very interesting chapter on that. Before philosophers, "higher insights" showed in temple slaves, whose blood attracted spirits who then could be eavesdropped by the priests, and the priests then interpreted what they heard with “logos”. In philosophers, both roles became united in one person who performed extatic metempsychoses followed by rational exegesis. The books of Parmenides and Empedocles still start with tales of voyages of their souls. Here is a link conc. the reconstruction of Empedocles’ ideas acc. to Kranz (after he continued the Diels, Kranz edition of Presocratic fragments). Like the extases caused by visiting spirits in shamans, the early philosopher's job was not a voluntarily chosen one, but a vocation. As the separation of the personal ego from the egofree part of the mind connected with "platonism", this needs not to be an enjoyable experience. Yuri Manin tells here his fight with his first math book.

The very forcefull triptych (1 ,2 ,3 ) by Matilde Marcolli, parts of which are reproduced here, exposes this as agonizing condition.You see the painfull complexity there from belonging to more that one world and not to reduce to one's projections on both. The style of renaissance, when science emerged, with moments of surrealism is no coincidence, as is the theme "liberty".

Among the psychological attitudes related to shamanism are "staying vigil", "attentive listening" to the unpredictable whispers of the spirits, keeping the voice of the ego low, "looking for hints". Thomas McEvilley wrote a fascinating book (online scan, youtube interview, thanks to J.H.) about possible connections with ancient indian philosophy, it’s summaries of single theories are very excellent for themself: Sociologically, shamanism was rooted in tribal culture and small communities. Shamanism were one-man operations, restricted to a small clientele. Shamans were "fermions", independent and isolated from each other. When with emerging urban structures in Mesopotamia, temple bureaucracies and career priests in university-style hierarchical organisations (e.g. the Marduk temple employed ca. 7,000 people) stabilized the state, shamanistic practices became tamed to a homeopathic dose of “intrinsic motivation/curiosity in the things for themself”, predictable and finally substituted by an entirely different mindset and communication style. Imagine how career-priests probably felt towards those wandering orphics, fakirs, sorcerers etc.? Bureaucrats are "bosons". Of course, the shaman's relation to language was complex too and the possibility that instead of expressing truth, they misuse their skills to deceive was theme since ages. Yuri Manin analyses here the "trickster"-theme in ancient myths and the possible anthropological background of shaman/tricksters. The platonic concept of knowledge as becoming that what is to be known by an act of immersion and identification comes from shamanistic practices. Shamanistic traditions continue to be a vital part of everyday culture in East Asia, e.g. Siberia, Japan and Korea. In Europe, beyond antiquity and perhaps transmitted through neoplatonic communities in south france, this stayed alife among medieval scholars (beautifully told in M. Yourcenar's "L'Œuvre au noir") and turned into the selfconcept of early scientists. Giordano Bruno used in his essay (La Bibioteca Ideale di G. Bruno) on "heroic frenzies" the myth of Actaeon and Artemis as metapher for the philosopher's hunt for truth: During a hunt, Actaeon meets Artemis, the godess of hunting, and is transformed by her into the stag he runs after with his dogs, who then dismember him. Bruno's essay is highly recommended as selfdescription of the mentality of the early science community in the most crucial piece of it's formation.

L. Graham and J.-M. Kantor describe in "Naming Infinity. A true history of religious mysticism and Mathematical creativity" a very interesting re-emergence of similar traits in the Russian school of set theory in the first third of the XXth century. (google scan, an article by Moore, a review, Bourbaki's history book) From Freeman Dyson's review: "... the puzzling cultural dynamics that converted religious mysticism into mathematical insight. The authors particularly probe the surprising way that a religious heresy (Name Worshipping) emboldened the Russian mathematicians who finally surmounted the theoretical difficulties that had overwhelmed earlier pioneers in set theory." Here are links on Illarion the monk and Pavel Florensky.

In antiquity, the "higher intuition" sketched above was taken for granted and philosophy was largely about it's practical training and stabilization. Modern discussions of "Platonism" focus instead on the ontological status of abstract concepts and their relation with linguistics. Gromov's takes up again the antique route by starting from the existence of an anthropological invariant producing those "higher intuitions", provides plausible reasons aside intuitive evidence, but leaves ontological questions aside. Like the antique platonists. After Gromov singles out the specific mentality, he suggests the existence of a formal backgroundstructure behind it, gives that a name and sketches a program for dealing with it. This is the "modern part" of his program.


some updates:

Homo Erectus (pic):
The Paleoanthropologist John Hawks (blog) remarks: "Don't underestimate the range of body size in H. erectus - the Dmanisi sample is clearly small, maybe Bushman-sized, and the tall East African specimens are accompanied by many short ones as well. The "women invented culture" idea has been pursued in recent years by Chris Knight. He places the crucial events later in our evolutionary history, but is worth looking at as a model for how these events might be integrated." Several of his blog entires are about the Homo Erectus, e.g. these puzzling findings on Crete. This "Guide to Twenty-Two Species of Extinct Humans" tells the "epic of Homo sapiens and its colorful precursors and relatives. The story begins in Africa, six to seven million years ago, and encompasses twenty known human species, of which Homo sapiens is the sole survivor. Illustrated with spectacular, three-dimensional scientific reconstructions portrayed in their natural habitat developed by a team of physical anthropologists at the American Museum of Natural History and in concert with experts from around the world, the book is both a guide to extinct human species and an astonishing hominid family photo album". An exhibition of the Smithsonian Institute. Then I stumbled across an interesting remark on "marrow cults" at the Homo Erectus in Thomas MyEvilley's "The Shape of Ancient Thought" (p.220). McEvilley wonders if such cults continue in !Kung Bushman beliefs in an occult power of a (fictive) spinal channel system and turnes into part of magic physiological doctrins in Sumerian culture, then ancient india and finally entered through the teaching of Alcmaeon of Croton and Democedes of Croton Plato's theory of eros. And here are very interesting news on the simultaneous changes in hominid- and elephant-populations, apparently the homo erectus used fire for preparing meat, but not for preparing vegetables. Only a few weeks ago I found this thesis of Norbert Meuter, who came to similar conclusions about the homo erectus and who gives very interesting links to earlier, rather speculative, but astonishingly good fitting to later archeological data, texts by Susanne Langer. She in turn hints backwords to the developments of greek religion, where this new study was recently recommened, but I the libraries here still process the request...

If you are curious about how living was in the oldest great settlements, try this expert simulation of Çatal Höyük.

social brain:
Aside mirror neurons, the right temporo-parietale junction (rTPJ) shall be crucial for social skills: Rebecca Saxe at the MIT calls it "the core of our ability to read other people's minds" (german article). Here is an other interesting study. Face recognition is studied here. A new study "Cross-cultural recognition of basic emotions through nonverbal emotional vocalizations" is here. About social skill induced brain development a report here.

Technology anticipations:
Richard Sennet reports in his book on handycraft that the described counterintuitive ways how new technologies emerge is rather common. He tells about the history of srewdrivers, which were invented much earlier than one got an idea of it's proper uses and thinks, the internet is an other such case of a technology whose use still has to be found (making me wonder if language could be a similar open case).

Love in the time of dictatorship:
"A book suddenly disappears. Two days after it hits Minsk bookshops and Belarus’s internet retailers, it is suddenly “unavailable”. Neither inquiring readers nor embarrassed sales staff are given any explanation. It is as if the book never existed. But it does." (review, more)