Francis Bacon, Lucian Freud, Frank Auerbach

In my infancy I used to say that what Francis Bacon was doing in painting, Samuel Beckett (Comment c´est) was doing in literature and Swans in popular music: Showing that the body/the subject/the individual is constituted by forces/flows/streams (of desire) that are older than the subject, that distort it in its compactness and that trangress it (with or without elevating it to catharsis) and that remain after its demise, i.e. the body/subject as a condensation/force field/way station/relay of forces that come from the outside/primordial chaos/nature/culture, constitute some kind of semi-self-referential loop and then, after demise, fall apart and combine anew – the entity formed by/being a way station for streams of desire crawling through greater streams of mud, decomposing: that´s How It Is. A reading of Lacan (and Schopenhauer) favors such a perspective – and of Deleuze who wrote a cool book investigating how Bacon´s art is about making invisible forces (that stem out of „the virtual“) visible. The subject/body as a force field … Numerous other connotations come to mind with Bacon: A „sinister“ painter (contrasted by the personal appearance of a jovial hedonist) who seems to make existential horror and crucifixation explicit – respectively (as an ultimate mode of being affected) vulnerability / and who establishes „zones of indistiguishability“ between man and animal (suffering, tormented man becomes animal / suffering, tormented animal becomes man) and, possibly, a communion of living creature. The erection of (apparently frail and multidimensional and enigmatic) figure within a historical context dominated by abstraction. A figure ghost-like and robust like the artist himself. References to van Gogh by a similarly intense painter, who solitarily creates out of himself. The idea of the body that wants to get „rid of itself“ (most notably exemplified in the Scream motif) and wants to transform into something else (but, obviously, can´t quite). A novel depiction of contour (in an interplay with occasionally violent brushwork). – David Sylvester complains that the relationship between motif and background is a bit unpleasant with Bacon: But herein Bacon is also some kind of originator: The background is nothing the figure emerges from or whatever: The background isolates and depicts the figure: You can also ruminate whether it is meant to express the neutrality of the many forces of the world with which the figure will never interact – at any rate: What a fabulous background! What beauty of colours! (You have to see the paintings in the original to get adequate idea.) Great Monoliths.

Francis Bacon, Lucian Freund and Frank Auerbach were friends and influenced each other and were dominating figures in the english art scene of their time. Cross out Francis Bacon, and there remains Lucian Freund and Frank Auerbach. – Lucian Freud was a grandchild of Sigmund and, as a chaser of girls, produced numerous offspring of his own. He was described as „electric“, „breathing like an animal“, and „feeling free to do whatever he liked“. As a figurative painter he rose to full maturity when he combined the violent brushwork of Francis Bacon with sharpness of contour and immersion into detail. Freud gets intensely close to his sitters, has an invasive gaze, often portrays them in unusual, and frail, positions. He himself claims that he would like his portraits to actually be the persons portrayed, and that his colour functions as skin – and at any rate, the portraits seem close and the skin seems so thin that you think it could tear apart and the body mass could fall out – while at the same time it is stabilised by the many folds and brushstrokes. However, his paintings seem quite ambivalent, and actually more uncanny than Bacon´s. Freud´s personnel doesn´t exactly deliver a spiritual impression. Their individuality derives from peculiar looks (at the verge of oddity) and unusual gestures. They´re individual but appear relatively empty (and stupid!), they usually look down and seem uncomfortable when confronted with the invasive gaze of the painter at their supposedly innermost secret (note however that they´re captured in the way sitters look like after long sessions – silently annoyed and fatigued). When they´re together in a room there seems to be no true bond between them, respectively that the bond between them seems to be one of shame or guilt or a dirty (though not sensational) secret that has to be hidden behind closed doors. Isolated individuals. – As a child, Lucian liked to be alone, and he preferred animals (horses) over people. He did not treat his first wife good and was a controlling, maybe sadistic husband (who could not, however, dominate his second wife so easily). When painting others he „wanted to see the whole animal“, and he said a lot of his sitters „are girls who have some sort of holes in their lives that is filled by posing for an artist“. He had a difficult relationship with his intrusive mother but could handle her and painted her when after the death of her husband she was a shadow of herself. – Sylvester asked Francis Bacon whether he would provoke feelings of ambiguity in his sitters he did not portray so favorably – but with Freud this seems to be more at hand. Freud´s portrayal of man provokes empathy and  remind us of taking the other as an individual (maybe even in a Levinasian sense), but they´re also humiliating, even if that´s a portrayal of the human condition. When Freud painted the Queen (over a period of 19 months), the Queen was not amused about the product (although it is actually one of the more favorable portraits in Lucian´s oeuvre).

Francis Bacon, Lucian Freund and Frank Auerbach were friends and influenced each other and were dominating figures in the english art scene of their time. Cross out Francis Bacon and Lucian Freud, and there remains Frank Auerbach. Like Lucian Freud, Frank Auerbach was a (German) jew whose family had to flee the Nazis, and they settled to England, where he would study under David Bomberg (who had been a celebrated painter in his younger years but, due to his intellectual and creative versatility, annoyed and overcharged art critics and so became „the most brutally excluded artist in Britian“ – described as the most intelligent man of the academy, Bomberg was „certainly no one who deliberately wanted to impress someone“ but an authentic man). Although Auerbach´s individual works are often highly different from each other, his general style (or: stylistic approach) has not changed much over the decades. His motives are sparse in variety as he mainly paints scenes in London/Camden and portraits. He maintains a small circle of sitters who he may portray over and over again. Although his intention is to get to the „essence“ of the sitter, the portaits of the same sitter are often extremely distinguished from each other – and often he would work on a painting for a very long time, painting layer over layer. Auerbach´s ability to create a comprehensive portrait out of blunt brushwork and colour fields is amazing, yet often the density of layers is what is most striking (making his paintings occasionally very heavy and difficult to exhibit) – through the layers the paintings gain haptic quality, and remind us of the multiple layers of reality/perception as well as the sheer materiality of the physical world. – Bacon rose to fame (relatively) early (in the 1950s), Freud in the last quarter of his life, Auerbach is the least popular of them. His constant investigation of painting and his high versatility seems to have prevented a signature style or his stuff becoming iconic. – I mean, if you have an intelligence for the arts you will understand that in a virtual painting there is a fluctuation and a vibration/vibrating intensity between different layers respectively between the actualised and the virtual. That brings stuff into motion. This is how an artwork „lives“ and is brought to life. And that´s how you have it in Auerbach paintings who takes this eventuality of getting a grasp on art to very extremes. Auerbach eventually/primordially sees the world as chaos, and the task of the painter as to impose order. Auerbach is interested in „raw“ perception, and, so to say, in an immediate dialogue with the audience which forms the image partially on own terms. A „continuum of perception“. He solidifies form which carries the possibility of its dissolution within itself and offers perceptions that include their own variations. – In this radical approach, Auerbach considers himself a loner (within schools and trends in painting) and a workaholic who seemingly never stops adding the next layer.

„When I saw Frank Auerbach´s works for the first time, I thought that there was really happening something new and extraordinary, and that´s what actually happened … Wonderful portraits in dense colour – but he could not sell any of them at that time. I often ask myself how many people have an eye for art at all. They buy when an artist is famous – and probably does not create his best works anymore. But when something wonderful and innovative happens, they don´t see it.“ (Francis Bacon, Interview with Michael Peppiat, 1897; translated from German back to English by me, fuck off)

Winckelmann, Sulzer, Füssli, Mengs

… were artists and/or theorists who had something to say about art and who were important/conductive in intellectually institutionalising a discourse about art and aesthetics – as an autonomous subject – in Germany in the 18th and 19th century, respectively at the time of era-defining genius Goethe. Their writings are largely out of print. What did they say?

Johann Joachim Winckelmann (1717-1768), offspring of a shoemaker who loved art and especially the ancient Greeks, had a difficult life for many years and he had to live in humble circumstances. The hardships he faced as a scholar (shittily equipped libraries which were, in addition to that, accessible only one hour a day) are beyond our imagination: Acknowledge the effort behind his undertakings and bow down! – Notably in his main work Geschichte der Kunst des Altertums he lay the foundation of regarding the ancient Greeks as the most perfect people and their art as the most perfect art – and indeed ancient Egypt or the Etruscans, which he also discussed, weren´t exactly of such caliber. He attributed this to specific climatic and geographic conditions and to the Periclean democracy and, in doing so, tried to understand the emergence of art out of a greater social context. According to Winckelmann the end of art is beauty, and the ancient Greeks were the most harmonious of men. – Winckelmann´s legacy, and his work itself, was ambiguous. On the one hand he said that the ideal of Greek art could never be reached again, on the other hand he lay foundations for classicism which tries to imitate the Greeks. This was to come in a more formal, and anemic, fashion, but also fresh, original and abyssal-ethereal as e.g. in the case of the good Hölderlin. While Winckelmann resented anemic academic pedanticism his writings seem hard going by today´s standards. Originality and genius were, more or less, foreign categories to Winckelmann, but he also lived before the Geniezeit in Germany – his thoughts were more revolving around the collective genius of a people and about conditions under which great art can arise.

Anton Raphael Mengs (1728-1779) was an eminent classicist painter and nicknamed as the „German Raphael“. His Gedanken über die Schönheit und über den Geschmack in der Malerey (1762) was used as a „textbook“ in many academies. Also Mengs says that the end of art is beauty – as beauty is a tangible expression of perfection (which is, in itself, intangible and only to be found in God). Beauty is achieved as the artist tries to imitate nature and as the artist is carefully selective not to display more or less in his paintings than nature would require. By careful selection, he may create art that is even more beautiful than nature! While also affirmative of the notion that the Greeks are the apex (because they had direct access to the ideal whereas all others only can have an indirect access to the ideal), Mengs is discussing three artists in detail: Raphael, Corregio, and Titian, and he announces that, on the whole, Raphael is the greatest of them (while the others may be the leaders in specific areas e.g. Titian concerning colour) because Raphael is the greatest and well-rounded of individuals, including the „downside“ of Raphael only being able to confront also malice and triviality in the human realm with generosity and greatheartedness (i.e. a bit inappropriately). – Mengs himself confronted less criticism than Winckelmann or Sulzer and, as a great artist, also appeared as a somehow more monolithic figure. His notion of the true artist imitating nature is somehow understandable as true creativity appears natural, stemming out of itself, relatively immune to the diktat of culture and the expectations of the audience, and powerful, overflowing and diverse. Therein, it creates its own harmony.

Johann Georg Sulzer (1720-1779) was a theologian, a philosopher and a man of stupendous erudition. His Allgemeine Theorie der Schönen Künste (1771-1774) was designed to be both a theoretical work as well as an encyclopedia about everything related to art and aesthetics, it contains ca. 900 articles and ranges from music and poetry to architecture and garden art. Sulzer says art is about adding beauty to things (stemming out of an aesthetic drive in man) and that the end of art is moral purification and betterment of mankind – he dismisses a cult of pure reason and says that the (educational) power of art lies in its sensuality and the power with which it adresses the senses and the emotions i.e. the whole of man (although Sulzer does not seem to have a well-formulated theory about that). Sulzer speaks of the genius and says the chief characteristic of the genius is enormous sensitivity and ability to be affected by and to get immersed into things. – The most prominent critique directed at Sulzer came from Goethe: Goethe dismissed the notion that art can be a main vehicle for the betterment of mankind – art originates from the „fire within the artist“ i.e. from the artist´s self expression and happens relatively independent from the (self-unconscious) audience. Of course Goethe was not entirely dismissive about the audience, but – in contrast to the democratic Sulzer – he favored the conaisseur of art over the general audience (which may be natural and unspoiled but, in fact, neither very understanding nor commited).

Johann Heinrich Füssli (1741-1825), who called himself Henry Fuseli when he was an emigrant in England, was a painter, poet and professor at the Royal Academy of Arts. His Aphorisms, Chiefly Relative to the Fine Arts are condensations of his lectures. Confronted with the French Revolution and its aftermath, Füssli became dismissive of the notion that art could do a lot about true refinement of humanity. While he was a fan of the ancient Greeks (as the only people who were able/lucky enough to truly authentically relate to ideals), he was also aware that art is also/mainly about reacting to the challenges posed by the contemporary. As a painter Füssli often made reference to nightmares, horror and otherworldly stuff, as a theorist he emphasised the importance of expression in art (Winckelmann said that an artwork is/should be about expressing beauty/ideal but also about expression (Ausdruck) i.e. the emanation of the (beautiful) subject within circumstances – and he somehow favored the „static“ element of beauty/ideal over the „dynamic“ (quasi-contaminative) of expression: Füssli was inclined to think otherwise). The Aphorisms are a cool document, and they´re insightful also concerning the genius whose qualities are discussed at length. Füssli also thought the highest instance is (not a classicist ideal but) nature – in its infinity (i.e. also containing supposedly nasty elements), and that the genius is someone who is able to profoundly understand/imitate certain aspects of nature (where beauty and the ideal is one element but nothing art should be restricted to). Claims about the „death of art“ or cultural decay prominent at, more or less, every time, can be effectively countered by proclaiming that with every great genius art starts anew (and that due to the infinity of nature there is acutally no competition between them, just an ever ongoing growth and illumination of infinite nature). Hahahahaha! That will feel good.

About Art in Ancient Greece, about Modern Art and about Contemporary Art

Winckelmann said, in the mid-1700s, that the highest purpose of art is to display beauty and that art has its apex in ancient Greece (under specific geographic and climatic conditions as well as under the conditions of democracy). Winckelmann was, of course, aware that the concept, and perecption, of beauty, is ambiguous. So he said that beauty emanates in the perfect harmony of a being with its intentions and a harmonious subsumption of its parts under the whole. The highest beauty is to be found in God and the highest beauty in art can be reached when man is approximated to the ideal, rounded off and harmonious, resting in itself, somehow innocently and naive as well as heroic, stemming immediately out of himself. „Edle Einfalt, stille Größe“ – Winckelmann was dismissive of the purely lovely, the enjoyable or that which is overly playful or pompous (characteristic of Baroque or Rococo). With this works Winckelmann was highly influentual at his time, and it is true that he somehow intellectually instituted a discourse of the autonomy of art and what art actually is/should be about. What he says was both fresh and virgin but also carried the seeds of institutionalising an empty, overly formal, anemic classicism. Hölderlin and Nietzsche were very fond of the Greeks in which they say an image of perfect humanity – such a fascination isn´t very easy to imagine today. Marxistic scholars claim that Winckelmann´s ideas and ideals and visions of a heroic, natural man, living free from constraints and under conditions of democracy refer to the (half-conscious) sentiments of the (half-)dormant bourgeoisie at this time and, therefore, stand and fall in history with the bourgeoisie being a revolutionary class (and it would be interesting to know how we could approach this when referring to Piaget´s model of the cognitive development of the infant when we try to look at historical stages that way – I hope I can do this somewhere soon). Winckelmann was also influential concerning cyclical models of looking upon cultures/historical entities (e.g. Spengler) and about viewing peoples as cultural units (both in a „progressive“ and a „reactionary“ sense), more generally we can think about developments in art when we try to look at it from a Winckelmannian perspective. That the end of art is beauty, and beauty is, ideally, to be found in God and in free man – well, looks superseded; that this is so because of decay – well: a more filigree perspective is needed.

There is this book „Verlust der Mitte“ (originally published 1948) by Hans Sedlmayr I read a long time ago and now came to remember on that occasion. Sedlmayr makes up a conservative scholar who sees modern art as a process of cultural degeneration (he mourns loss of unity/harmony/completeness that he thinks existed somewhere back in time). – Sedlmayer was a member of the NSDAP and later in his life reportedly had some affiliations to the Green party; indeed, he was hooked on ideas of Ganzheitlichkeit, (reactionary) spiritism and nostalgia for some kind of ideal of embeddedness of man in the cosmic whole; although he is also kind of a misfit within such partisanship and intellectually trangresses partisan affiliations: At the core Sedlmayr mourns the loss of a relationship between man and God. In the modern era, man is cut off from God and becomes dangerously „autonomous“ and makes a mess, resulting not least in dissolution, fragmentation and atomisation of his modes of self-reflection (including art) and developing a mirror image full of self-loathing. Harmony corruption. Definitely no beauty. – Even if you find this unconvicing, „Verlust der Mitte“ is a worthwhile read, many insights and eruditions it carries, and Sedlmayr has a lot of empathy e.g. for van Gogh or Paul Klee.

That the end of art is beauty seems to be quite superseded – although the quest for beauty is inherent to art and has always been there. Since beauty is actually not definable, visionary artists have been aware that what we perceive as beautiful is, to some degree, malleable; and great, visionary artists have expanded our notion and perception about what is to be considered as beautiful. In an accelerating society, within modernity, the quest for beauty also accelerates, and may become overwhelmed by a larger conquest for meaning – as modern art is, as can be said, foremost about locating meaning. Beauty is but an element within meaning.

Illuminatingly, young contemporary German philosopher Markus Gabriel philosophises that art is about evocation of things in a different context, in a context different from normal. By showing stuff in unusual context, meaning is added and transformed (concerning both motif and background), respectively, within such dislocations, meaning per se emanates. The true artwork shows meaning per se (indeed, objects of contemporary art appear somehow fluctuating between being silent and empty and on the other hand so charged with meaning and so uncanny and talkative). It shows how the meaning of things is dependent on context and on interpretation within contexts and that it is linked to the imaginary i.e. to the great wide open. Remember how Angell de la Sierra from Omega Society says that by showing the many facets of a thing in multiple contexts the true artist shows the existential ontology of a thing, and while maybe not showing the „thing in itself“ in a scientific/kantian sense, art shows the meta-noumenon of a thing (respectively „meaning“ as Gabriel says). – It is true that art is highly about displaying intelligence at divergent thinking i.e. at seeing many associations to a given thing which then establishes context and fixation. It is about sensitivity to nuances and tolerance for ambiguity. And the meaning that is revealed in the artwork usually is ambiguous and ambivalent in nature. That is so because art is an investigation of the (so-called) irrational aspects of existence, about man in the universe. Shades of God.

This diversification of meaning probably has always been prominent in art yet while in more „ancient“ art you have a tendency towards holism and rounding things off, in the most contemporary art the trajectory of production of meaning is permanent evasion and establishment of meta-levels. While the one thing may appear boring and conservative in our time the other one risks losing substance and degenerating into farce and derision. As Francesco Bonami, curator at the Biennale, says: „The great curators had an almost Christian attitude with respect to the exhibition, as though attempting the moral and cultural conquest of the world, while the curator´s attitude today must be more pagan.“ (Likewise, when I read Greenberg or Carl Einstein I sense there is some coolness in the harsh verdicts of semi-ancient art criticism of days bygone, supposedly something that is absent in today´s „anything goes“ tolerance within a degeneration of standards … then, I also probably don´t miss it so much, since lenience and tolerance have some things going for them (if this is a correct idiom at all, I don´t care atm, because I like it right now and people going to understand it anyway).) – „It is – and perhaps always has been – the function of art to take us to the margin of contemporary experience, to try on what seems far-fetched, peculiar, different, and new so as to explore what may be on the verge of becoming essential to know“, it says at the end of „Art since 1940 – Strategies of Being“ by Jonathan Fineberg. – The problem is that, under such a flag, we today seem to be, under the disguise of art, confronted with too many empty peculiarities and „objects that resemble objects of art“ („kunstähnliche Gegenstände“, as the Merowinger says) replacing (true) objects of art. True objects of art are a rare thing however, as you recognise when you gaze back through space and time. Yesteryear´s epochs seem so great and monolithic because only the masterpieces are still around, while we can see a lot of trash and ephemeral stuff of our epoch. Some day we will be equalised along these lines (and e.g. Basquiat or Duncan Wylie will remain).

So, alongside the trajectory of opening, there are the demons of banality. Once, when I was young, I appeared bitter over that, but over time I seem to see it more casually, and I am grateful to live in this fantastic epoch. It is good, and underappreciated, that we are living in great times today! That when we go to the museum there we find the half-inflated rubber raft on the floor, a magnetic tape which displays „Ha Ha“ in an endless loop and a camera which films the scenery supposedly forever, as an artwork called („The Illusion of) Permanence“ or so. Ahh, exciting, ahh, eccentric; the meaning of it rests in a superposition. – Tbh this stuff from ancient Greece is, indeed, harmonious, but also not very exciting. The endless production of meaning (and making it collapse) is cooler. Incipit Zarathustra.

I do not want to throw it under the table that – as it appears to me – this note is not written as good as I would have wanted it to be. It is a bit tattered, I suppose. It was not written as easily as other notes and not in straight line but from accumulation via different spots. Then again, I think it is actually quite okay and nothing to be worried about. Maybe some will think that some of the stuff in here is banal, but it is not; is very deep and I have left out some mental leaps that are probably explicative, but also a nuisance, as I intend to write concise and relatively short notes which are nevertheless very comprehensive; I do not like verbose stuff, I am maybe too lazy to write verbose and I hate long conversations anyway. These notes about art are designed to aesthetically as well as intellectually display compactness – that is the idea.

A conclusive remark about the question of who is right: the Christian priest or the pagan? In art, s/he will be right who carries spiritual truth (and this usually means transcending the supposed pagan/priest opposition and being universal). What spiritual truth is, respectively how it is displayed, cannot be stipulated. You will, however, easily notice it when you finally see it, death to false metal. – The final conclusion of Sedlmayr´s „Verlust der Mitte“ is that there is an „empty throne“ which shall be occupied by the perfect man, the Gottmensch. – I  have also half-erratically ruminated about an Omega Man that will come and will provide a solution to the contemporary art problem and to the contemporary philosophy problem (and that the solution will, likely, come in unexpected fashion and be poorly understood). The ongoing vacany of the throne is probably due to the Gottmensch of today needs to be quite more comprehensive and all-encompassing than even Picasso or Michelangelo – although this may be an erroneous assumption since the times of Michelangelo or Imhotep probably weren´t less complex than ours; and for the Omega Man the complex (e.g. metaphysics, science…) is simple while the simple (e.g. politics or everyday human interactions) seems complex and stuff for endless ruminations to him/her. Apart from that the Gottmensch of today will need, among his powers, extraordinary mental strength, since s/he will have to try to establish connection in a world that is, forever, atomised and very superficial, and old ideas that art or philosophy are going to save us aren´t applicable anymore and the Gottmensch cannot shelter behind such illusions anymore. Technology is the prime mover and, as always, will produce both order and wreckage. History is some form of chaos and will continue to be. In some years I may have a 3D printer and my home will be „smarter“ than me.

About Numbers

.A while ago in the intellectual communities on Facebook there was a discussion in which someone came up with the idea that God necessarily needs to exist because only God could read (infinite) irrational numbers like pi. Another one countered that Gödel´s incompleteness theorem would allow that (i.e. that stuff exists that cannot be proven or verified). Somehow both assertions seem inadequate, but make you think about the nature of numbers (and mathematics) which is actually a mysterious and haunting subject. However, upon reflection, numbers simply express how quantifiable properties relate to each other. Out of an r you can construct a circle with pi, an ever more perfect circle with the more digits of pi you know, the perfect circle, constructed with infinite precision, cannot be constructed in a finite universe. Likewise, if you have a basket with two apples and want to have one with three, you can do that, with infinite precision, by adding one apple to the basket. Numbers, in themselves, are neither platonic nor are they real, they are virtualities / virtual entities.

I have thought about the continuum hypothesis, the orders of the infinite, the incompleteness theorem, whether the universe is a mathematical system or a logical syllogism a while ago. Some say that by applying logics they can see it all, and maybe that is true, nevertheless with logics you can construct pretty much anything of your liking (apart from that a logically correct conclusion need not be based on a correct assumption). Lots of stuff, for instance proofs of God, have been constructed with logic – but all of them can also be refuted by using logics (see, comprehensively, John Mackie´s The Miracle of Theism if you´re interested). Usually the philosophers and theologians coming up with their proofs of God were thinking that they did not prove the existence of God by using logic but, literally, that they were proving the necessary existence of God out of logic, although to every neutral observer it was apparent that there was something wrong, wobbly, uncanny in their proofs, although it is not necessarily easy to exactly tell what the problem is. Often it may require an entirely new heuristics, and for instance it took centuries to exactly tell what is wrong with Zeno´s paradoxa. Metaphysical questions may be undecidable, not least because they´re paradoxical in nature.

And then, the incompleteness theorem… Despite its apparent gravity and the mysteriousness it seems to imply the incompleteness theorem hardly affects professional mathematician´s business. I have never read Gödel´s original paper and maybe would not understand it since maths, among other things, is not my speciality, however as far as I can see it is about the „paradox“ of the barber who shaves anyone but himself or the Cretans lying. Despite there is no logical solution to that paradoxes they will somehow be solved in practice without too many trouble (or if we applied „fuzzy logics“ we could formalize stuff or so, idk…). Maybe a kind of solution to it, respectively shedding some light on the mystery the incompleteness theorem seems to imply, comes in a way Cantor „solved“ the mystery of infinite sets – when he made the „paradoxes“ they carry their defining element. There is also this stuff: hyperinfinite sets. They can be constructed, but their existence cannot be proven, and under Occam´s Razor they may seem a nuisance (because they seem to add more orders of the infinite that seems to be needed). Given the incompleteness theorem, the mysterious hyperinfinite sets may either exist or not. However, certain mathematical objects, like knots, can be better conceptualised under the assumption that hyperinfinite sets do exist, be their existence only theoretical (under the assumption of hyperinfinite sets something is possible to construct about the understanding of knots, as an „indirect“ proof that would lead to the possibility of a more direct proof that could eventually do without the assumption of hyperinfinite sets). Apparently, the virtual again. When you think about numbers (and mathematical objects), especially about odd numbers, complex numbers – or negative numbers, or zero, or infinite sets that have puzzled humans for so long, you may become aware that they´re virtual entities.

WIthout the concept of the virtual we´re actually pretty fucked up if we tried to understand the nature of numbers, I guess. It can be argued that numbers are, e.g., platonic, and there are some indications to it, likewise there are other indications that taking them as platonic entitities does not actually apply. With Virtual Reality the notion of the virtual has become somehow more mainstream. Before that it has been prominent within the philosophy of Gilles Deleuze. In thinking and conceptualising about the virtual Deleuze draw on fellow philosopher Henri Bergson – and on Marcel Proust, i.e. neither a philosopher nor a scientist nor a mathematician but a literary genius who, concerning the virtual, was ruminating about how to grasp the qualities of memory. I cannot remember who it was but it was some eminent mathematician who noted that even the most abstract and aloof maths sooner or later is bound to somehow become applicable when trying to get a grasp on something in reality. It is all a gigantic network, hahahahaha.

In his book Infinity and the Mind Rudy Rucker described how it was when he had a personal encounter with Gödel. Despite popular beliefs that he was bizarre the elderly Gödel had, as it seemed to Rucker, the statue of a very wise man who seemed to have thought about everything in life, thoroughly and concise; something that people would also remark about the elderly Wittgenstein. Rucker noted that Gödel had the habit that when completing a sentence or statement he would often exalt his voice and break into a ringing laughter, in an obvious gesture of adding some irony and leaving room for calling into question the things he just stated with such rigid logic and that seemed to be so perfectly concise – bravo, that´s the spirit! Wittgenstein was also so eminent at logics that he used logic for accelerating perplexedness. When the elderly Wittgenstein displayed the profoundly wise man to others the effect was ambiguous, as Wittgenstein on the one hand seemed to have thought about everything, including the more mundane things in life, but would enter a discussion about everything with great intensity, devotion and sternness (including conversations about the more mundane things in life), so that people usually on the one hand felt enriched and that they had received valuable advice but that they sort of had been overrun by a tank on the other hand (conversations with Emily Dickinson seemed to have been of a similar quality). – A while ago I have noticed that Kripke is considered as one of the definitely most important philosophers of the last 200 years. Kripke explained Wittgenstein to a more general population after Wittgenstein´s death. Kripke is an analytical philosopher and so far I have not read much about him. I read however that most of his (more recent) works are lectures and he himself does not seem to care so much about them being published, because his mind is obviously working too fast for caring about such mundane things – bravo, that´s the spirit! Kripke however is silent about many other things a philosopher would be expected to be vocal about. I have read that, in personal encounters, Kripke appears like a very intelligent person, yet something somehow is missing, a certain human element. – I said this about Kripke because as an association it came to my mind, it also somehow fits into this note and it is, apart from that, informative, and I like to inform people about all kind of stuff because I like to get informed about all kind of stuff myself.

This note about numbers may be dilettante, I am not a professional mathematician, I have not thought a lot about it, and I am occupied with doing other things at the moment. But I don´t see an error with conceptualising numbers as virtual entities. So far for now.


Does Time Really Flow? New Clues Come From a Century-Old Approach to Math.