“butterfly”, by M C Escher
Curran Kelleher rocks recursion:
Gödel, Escher, Bach – Lecture 2: Part 1 of 8
Gödel, Escher, Bach – Lecture 2: Part 2 of 8
Gödel, Escher, Bach – Lecture 2: Part 3 of 8
Gödel, Escher, Bach – Lecture 2: Part 4 of 8
Gödel, Escher, Bach – Lecture 2: Part 5 of 8
Gödel, Escher, Bach – Lecture 2: Part 6 of 8
Gödel, Escher, Bach – Lecture 2: Part 7 of 8
Gödel, Escher, Bach – Lecture 2: Part 8 of 8
This lecture series is available through MIT’s Open Courseware
From an article by Jonathan Amos, “Stonehenge design was ‘inspired by sounds'”
Friedrich Wilhelm Nietzsche, “The Birth of Tragedy, Out of the Spirit of Music”
And now we should not conceal from ourselves what lies hidden in the womb of this Socratic culture! An optimism that thinks itself all-powerful! Well, people should not be surprised when the fruits of this optimism ripen, when a society that has been thoroughly leavened with this kind of culture, right down to the lowest levels, gradually trembles with an extravagant turmoil of desires, when the belief in earthly happiness for everyone, when faith in the possibility of such a universal knowledge culture gradually changes into the threatening demand for such an Alexandrian earthly happiness, into the plea for a Euripidean deus ex machina! People should take note: Alexandrian culture requires a slave class in order to be able to exist over time, but with its optimistic view of existence, it denies the necessity for such a class and thus, when the effect of its beautiful words of seduction and reassurance about the “dignity of human beings” and the “dignity of work” has worn off, it gradually moves towards a horrific destruction. There is nothing more frightening than a barbarian slave class which has learned to think of its existence as an injustice and is preparing to take revenge, not only for itself, but for all generations. In the face of such threatening storms, who dares appeal with sure confidence to our pale and exhausted religions, which themselves in their foundations have degenerated into scholarly religions, so that myth, the essential pre-condition for every religion, is already paralyzed everywhere, and even in this area that optimistic spirit which we have just described as the germ of destruction of our society has gained control.
While the disaster slumbering in the bosom of theoretical culture gradually begins to worry modern man, while he, in his uneasiness, reaches into the treasure of his experience for ways to avert the danger, without himself having any real faith in these means, and while he also begins to have a premonition of the particular consequences for him, some great wide-ranging natures have, with an incredible circumspection, known how to use the equipment of science itself to set out the boundaries and restricted nature of knowledge generally and, in the process, decisively to deny the claim of science to universal validity and universal goals. Given proofs like this, the delusion which claims that with the help of causality it can fathom the innermost essence of things has for the first time become recognized for what it is. The immense courage and wisdom of Kant and Schopenhauer achieved the most difficult victory, the victory over the optimism lying concealed in the essential nature of logic, which is, in turn, the foundation of our culture. While this logic, based on aeternae veritates [eternal truths] which it did not consider open to objection, believed that all the riddles of the world could be recognized and resolved and had treated space, time, and causality as totally unconditional laws with the most universal validity, Kant showed how these really served only to raise mere appearance, the work of Maja, to the single, highest reality and to set it in place of the innermost and true essence of things and thus to make true knowledge of this essence impossible, that is, in the words of Schopenhauer, to get the dreamer to sleep even more soundly (World as Will and Idea, I, 498). With this recognition there is introduced a culture which I venture to describe as a tragic culture. Its most important distinguishing feature is that wisdom replaces science as the highest goal, a wisdom which, undeceived by the seductive diversions of science, turns its unswerving gaze onto the all-encompassing picture of the world and, with a sympathetic feeling of love, seeks in that world to grasp eternal suffering as its own suffering. Let us picture for ourselves a generation growing up with this fearlessness in its gaze, with this heroic push into what is tremendous; let us picture for ourselves the bold stride of these dragon slayers, the proud audacity with which they turn their backs on all the doctrines of weakness associated with that optimism, in order “to live with resolution,” fully and completely. Would it not be necessary that the tragic man of this culture, having trained himself for what is serious and frightening, desire a new art, the art of metaphysical consolation, the tragedy, as his own personal Helen of Troy, and to have to cry out with Faust:
With my desire’s power, should I not call
Into this life the fairest form of all?However, now that Socratic culture has been shaken on two sides and can hang onto the sceptre of its infallibility only with trembling hands, first of all by the fear of its own consequences, which it is definitely beginning to sense and, in addition, because it is itself no longer convinced with that earlier naive trust of the eternal validity of its foundations, it’s a sorry spectacle how the dance of its thinking constantly dashes longingly after new forms in order to embrace them and then how, like Mephistopheles with the seductive Lamias, it suddenly, with a shudder, lets them go again. That is, in fact, the characteristic mark of that “fracture” which everyone is in the habit of talking about as the root malady of modern culture, that theoretical man is afraid of his own consequences and, in his dissatisfaction, no longer dares to commit himself to the fearful ice currents of existence. He runs anxiously up and down along the shore. He no longer wants to have anything completely, any totality with all the natural cruelty of things. That’s how much the optimistic way of seeing things has mollycoddled him. At the same time he feels how a culture which has been built on the principle of science must collapse when it begins to become illogical, that is, when it begins to run back once it is faced with its own consequences. Our art reveals this general distress: in vain people use imitation to lean on all the great productive periods and natures; in vain they gather all “world literature” around modern man to bring him consolation and place him in the middle of artistic styles and artists of all ages, so that he may, like Adam with the animals, give them a name. But he remains an eternally hungry man, the “critic” without joy and power, the Alexandrian man, who is basically a librarian and copy editor and goes miserably blind from the dust of books and printing errors.
Today I digress…just thinking of this old journal entry from May 2005 (again, a rumination generated by Consciousness Explained). I dare you to read it.
In terms of Jesus’ identity as it was self-realized or self-defined, Jesus was not conscious of being simply a person or “I”, but of actually being someone it was thought impossible for him to be. God had been around for a long time, spoken to Moses, David and the prophets, performed miracles in and for Israel, created the universe, etc. Dennett probably would say that Jesus must have been crazy, he must have created this illusory, impossible self (with great ingenuity, by the way), and he must have convinced his crazy followers of same, who then “made up” all kinds of stories. Dennett probably also would say that the people of the time were subject to memes which inclined them to believe such piffle. In fact, Dennett would say, much of the biography of Jesus is probably true, only it is riddled with “local memography”, or conceptual universes developed out of “primitive,” “superstitious,” or whatever, topographies of reality (i.e. myths).
However, Dennett would be guilty of one of his own most-hated logical fallacies – the failure to adequately imagine what this would entail, and so to rule out the truth of it summarily (“…thought experiment depends, illicitly, on your imagining too simple a case, and drawing the “obvious ” conclusion from it…”; or “mistaking a failure of imagination for an insight into necessity”).
First of all, the notion of memology, the “meme”, is largely rooted in Roman culture. Dennett’s novelistic theory of consciousness as a “centre of narrative gravity” flows from the dynamics of this so-called “primitive” culture. You might want to take a look at M.M. Bakhtin’s notion of “heteroglossia”, which is identical to memology, and whose “dialogization of social languages”, which he found to have originated in the Roman Empire, is the very development of consciousness as virtual novel with the centre of narrative gravity Dennett describes. Bakhtin outlines the origin of this type of linguistic process in the cross-cultural and intercultural dynamics of ancient Rome. One might ask whether a society whose inventions Dennett himself is using to enlighten quite a few, quite intelligent and modern people, could be all that naive, now, could it?
Second, when you study Bakhtin [The Dialogic Imagination], it is important to note that memes are specifically a development of the Roman Era, because when one examines literature antedating the rise of Roman novelistic heteroglossia, one discovers, as in the Epic genre for example, a much more closed, monoglossic, memonic world (or “consciousness”). So, one could not argue that memes as such, in all the multifarious diversity and interlocuity that Dennett ascribes to them, really existed, since there is no linguistic evidence for them [and yes, I know, Dennett notes Dawkins in the appropriation of this term]. Epic and other archaic genres exhibit a more formal structure, a literary stone age, if you will, especially in terms of timespace, or “chronotope”, which is fixed and unreal. The audience does not interact with the closed chronotope, it is a finished, entirely past, inaccessible timespace, not a “happening” but a “once upon a time…”. It is these closed genres that become the memes of ancient novels.
Bakhtin is quite adamant about this. It is the social development of theatre, especially parodic, comedic, irreverent, “grass roots”, non-elite productions out of which novel emerged. It is in this realm that the audience enters the narrative and is carried along with it; the chronotope becomes emergent and future-oriented, open-ended, more “consciousness-like.”
Third, in terms of Jesus’ followers “making up stories,” one can hardly imagine why they would risk their lives in this manner. If their leader was publicly executed by Roman authority, it seems very unlikely that the early disciples would defy the Imperial authority, on pain of death, by inventing pure fictions and publicly proclaiming them – openly insulting and provoking the Caesar, denying, illegally, the deity of Augustus, a popular and much loved ruler, and just generally stirring up trouble for themselves to no evidently beneficial purpose. Even the fact that they believed their preposterous claims does not adequately explain their suicidal mania. Thousands upon thousands of Christians were persecuted and executed, or just basically shunned and run out of town – for what? How did following Jesus’ teachings of giving up all worldly goods, sharing everything in common, giving to the poor and just basically helping each other out justify their stubborn bloody-mindedness and lack of survival instinct?
The fact is, it doesn’t! And one must see the basis of the conflict as somewhat more profound than simple naïveté. One must ask the reciprocal question: Why would a powerful regime, a veritably impregnable fortress of religious diversity, tolerance and authority, be provoked to such a degree by a small group of complete lunatics? What possible threat could they pose?
Fourth, in view of the linguistic sophistication of Roman culture, as evidenced by its creation of memes (heteroglossia) and of novels (dialogizations of social languages), narratives that are future oriented, open-ended and accessible, one could argue that consciousness itself underwent an important evolutionary development at this point in history – the very development Dennett describes as the nature of consciousness in the modern world, however broadly or narrowly you may wish to define “modern”.
It seems that the type of consciousness created by living in the environment of Imperial Rome was blossoming from a more tribal, static, limited self-defining narrative to a more democratic, dynamic, diversified self-defining narrative – a paradigm shift. Robert Graves brilliantly characterizes this historical moment in his astounding novel (how ironic), I Claudius. In an argument between two historians, Livy and Pollio, Livy, of the old school, writes epic-like histories, incorporating poetry, eulogies and favoring historical inaccuracies reflecting glory over historical accuracy of negligible narcissistic quality. Pollio, on the other hand, prefers to write history in all its naked, irreverent and boring accuracy, favoring truth over narcissism. The point is not which is better, the point is that this reflects heteroglossia and dialogization in narrative and the development of a more real, temporally accessible, relatable, non-heroizing, novelistic type of history writing.
Variability and dynamism is evident in its development, leading to a diversity of novelistic forms and to the transformation of worldwide culture on the scale of a revolution. All subsequent developments in Western culture owe a debt of gratitude to the imaginative liberty of the Romans.
Fifth, it is the beauty of the wider parameters granted during this period that religious concepts underwent dialogization and became accessible to the common folk, rather than remaining strictly canonical, sacred, codified and basically useless to the average person. These concepts received memonic play in a way they never had before, and hence were examined, batted about and just plain adulterated, resulting in an explosion of intra and inter cultural adaptations, amalgamations, reworkings, translations, new ideas, heretical ideas, brilliant ideas and just plain fun, while yet maintaining some of the more rigid traditions in a state of cultural flux, tension and sometimes outright conflict.
It is into this environment that the consciousness of Jesus emerges. Jesus is able to freely spin self-determining narratives in this environment the like of which would have been impossible just centuries earlier. The material available to him is vast, multicultural, complex – memonic. It is also accessible to a broad spectrum of audiences via the memosphere of the vast empire. Jesus is a sophisticated language user and the historical accounts of his fame as a teacher above all else, reflect the overall sophistication of the average people of his culture in terms of well-developed socio-linguistic consciousness. This was not a naive, primitive, mythocentric group, but rather, a mentally maturing, creative, paradigm-shaping historical force, peopled by individuals who were just as concerned with truth and verification as we ourselves. Claudius himself, as a historian, is a prime example.
And so, when a writer of this era asserts that he is writing a true account, one must not simply dismiss this as the ravings of a village gossip or the superstitious fantasies of a deluded peasant. They may well be, in some cases, but a certain amount of respect for the text must be maintained.
The consciousness of Jesus as presented by the heterophenomenological accounts is not entirely unique in Roman culture. The emergence of such a centre of narrative gravity was not impossible as a derivative of the newly memonic social milieu. The point is that it was an accessible, if not expected, historical meme, a “God-Man” (θειος Ανηρ). Therefore, the stories surrounding and concerning the life and ministry of Jesus were given serious consideration by educated Roman minds, including Paul (who was Saul, a Pharisee), Luke, Roman magistrates (including Pilate), as well as the enemies of Jesus who cited some of the more extraordinary assertions, such as healing a man born blind on the Sabbath – a sophisticated legal abstraction of an apparently impossible, mythological idea – as the basis for his execution as a legal challenge to the authority of the Caesar.
The consciousness of Jesus, therefore, was not composed of linguistic “figment”, but rather, of social, political, historical, memetic, heteroglossic realities, virtual realities, in terms of the developing consciousness of the people of the time. And so, his claims were strongly resonant with the culture, they made sense to people, and in fact, are characterized by Jesus himself (and his followers) as “Good News,” relevant to the significance and meaning of the very society and the individuals of which it was composed. His message, and its concomitant phenomenological assertions, i.e., the presence of a supernatural force, a real, demonstrable, witnessed incidence of the God Man, was earth shattering to these people. The consciousness of Jesus was a memonic earthquake which shook the identity of the Roman Empire to its very core, and which redefined the centers of narrative gravity of thousands upon thousands of people. It eventually transformed the entire empire by its psychological and social power.
So this is no simple case of mythologic naïveté based on the hysterical fabrications of religious zealots. This is a case of a serious development of human consciousness brought about by the paradigm-shifting flood of consciousness raising achieved in and by the dynamic sociolinguistic environment of the Roman Empire. Jesus seems to have appeared at just the right time, at the cusp of these developments, and he seems to have taken control of them, giving direction to an otherwise crumbling and degrading Imperial lineage, resulting in the crumbling and degradation of the society itself. Without the appearance of the consciousness of Jesus, the Roman Empire would have disappeared, like many great civilizations before it.
When Adam asked for a companion in the Garden of Eden, the Lord did not give him a video or a magazine, he gave him a real woman. Now here’s the punchline – even Adam, the perfect man, couldn’t handle her!
May 2005
It seems to be a blind spot among moderns that humanity is “fallen”, that the present status of humanity cannot be used for moral modeling. We all know that the story of the Garden of Eden contains an appropriated Goddess myth, re-modeled as a polemic against the goddess theology and ancient matriarchal paradigms, such as those of the Egyptians, since woman gives birth to, or creates, man. In Eden, man gives birth to woman, and God “gives birth” to both via creation from “dust.” Recursively, God creates life from nothing or, as later writers asserted, from his word. The myth also asserts that “the man” (“Adam”) which God created was able to live eternally in Eden, that there was no death.
Now, where does this notion of eternity come from? And the incredible idea of a human body that is indestructible, that does not age or decay? These notions definitely do not come from observation of anything in nature. Even the ancients could not help but notice that one of the fundamental qualities of nature is that things are “corruptible”, to use a Pauline term, that they decay, or degrade, or explode (as volcanoes), or are subject to catastrophe (disease, injury); that plants die, that nature does not exhibit, even at first glance, “eternal” qualities – mountains erode, sands shift – nature is in a state of flux.
Modern science, in its pursuit of the fundamentals of nature, has discovered that substance is fundamentally unstable. They cannot explain what holds it together, except to say that there is a “force”, defined by the Planck constant, an “energy”, but no particular reason for it.
In the search for fundamentals, the progression can be illustrated by, for instance, the question why there are two sexes. Genesis 1 and 2 also try to explain this theologically. So science asked, what are the fundamentals of humanity? Well, first of all, there are two “kinds” of human, male and female. So the next question was, what is the fundamental cause of this? And they found that, well, there are only two kinds of chromosomal patterns determining sex, xx and xy, a genetic basis. So, what is the fundamental cause of genetic differences? It was found that DNA is a double helix string of protein molecules, four in kind, which are arranged in apparently infinite combinations, like musical notes can be, and that one of these combinations was specific for sexual identity of two kinds. So then, what is the fundamental cause of protein differentiation? Well, it turned out to be that proteins are constructed of fundamental particles called molecules, in different combinations. In fact, all matter is constructed of these particles, so a greater fundamental cause was discovered which not only explained sexual differentiation, but material differentiation and properties, connecting humans and all living things to “the dust”; that is, to inorganic substances because they are made of the same stuff.
So science discovered a fundamental physical principle that placed humans in the universe as a variation of simple substances. But still, where did the life come from? There must be a more fundamental principle than just molecules, because there also exist non-living molecular structures, salt for instance, and “complexity” itself does not seem to explain the difference between living and non-living substance – especially since life could not be produced by experimental means from simple substances (i.e., Alchemy), or found anywhere else except Earth.
So what is the fundamental structure of molecules? Well, atoms and their combinations. So the properties of atoms were investigated to discover what fundamental qualities they exhibited and it was found that they were, in turn, composed of even more fundamental particles – electrons, protons, etc. – which explained how and why they were able to combine to form such a variety of substances, exhibiting such a variety of properties.
In the discovery of quantum physical reality, scientists also discovered that the whole entire universe is “dying”, that the substance of the universe exhibits the quality of entropy – the progression from greater organization to lesser organization, from higher energy states to lower states, and that, eventually, according to any theory (string and wave theories of the universe included) the universe will be destroyed.
So where does the notion of eternity come from if all observations of the world render non-eternal results? In a world that constantly and consistently exhibits death and decay, where could such an idea have come from? How is it even an evolutionary concept, since evolution appears to be a function of death? Evolution seems to require death as the basis for selection in that selection would not be necessary if death were not an inherent property of the world.
The notion of eternity is unexplainable in terms of the universe that we live in. The universe does not naturally present this idea to the mind and neither does evolutionary development. Eternity is an absurd notion from the point of view of the world in which we live. So where did it come from? It could have come from simple opposition – the logic that since things die, perhaps there are things that don’t die, that are opposite in quality. This is a sophisticated logic, not a “survival” logic; it is a playful logic, not a “serious” logic. It is a logic that came from stories, from fictions or myths, that allowed minds to play, to explore, to imagine worlds beyond their own where things were different.
Perhaps the impetus for this was the phenomenon of dreams or of recounting histories for the benefit of the group, or some combination of both, which blossomed into story telling and entertainment – pure mind-based activities that human beings found to be important for social cohesion – to share same understandings (“memes”) for the purpose of communication, so that individuals could operate in the same conscious frames of reference. In this way, they could decrease the options for interpretation, limit the scope of sounds into words that became ever more specific in reference, and place these words in contexts, or juxtapositions, leading to the development of social groups which could command more power by the cohesion produced by the commonality of language and of the epiphenomena of shared understandings of origin, of purpose, of meaning, of the relation between individuals in ever growing, more complex societies, as humans became ever more reproductively successful.
So we are back to reproduction again and the question of eternity. The story of Eden is an example of this playful logic of opposition – that woman is not God, or God is not woman, based on the creation of humans in her womb (related metaphors, “mother earth” or “mother nature”), and that man is not God, or God is not man, because man came from dust. But where did the dust come from? Where did the Earth come from? The ancients reasoned that they must have come from somewhere, from someone, that life has an origin, and it must be a living origin, a “father” metaphorically, because of the new, patriarchal paradigm, and that this father could not, in turn, have a father. A finite recursion of fathers must have had an original father, hence, “In the beginning…”; not the beginning of the father, however, but the beginning of the world. So where did the father come from? Logically, he must have always been, he didn’t come from anywhere – he is eternal (“ageless”).
So, why are his sons and daughters not eternal? A darn good question! Apparently they somehow “lost” this quality of their father, becoming no longer of the same “kind” as him. This seems tragically like punishment, but punishment for what? They must have done something to deserve punishment, and quite a harsh one, it seems, as the difference between living and dying is of primary importance. Why should people die if their original father is eternal?
This is a complex line of reasoning, a moral, intellectual level, which, according to Robert Persig, is higher than social, biological and organic levels (Lila: An Inquiry Into Morals, 1991). It is completely thought-based, conceptual, as opposed to practically or materially based, as in social communication, biological survival and organic existence. Therefore, the answer posed by the Genesis narrative is also posed on a moral level. They died because of a moral reason. This is profound – that physical results are based in moral causes. This reasoning also seems to explain a great many other causes and results: the existence of “evil” in the world and evil inclinations in human disposition. It is asserted that the entire world was degraded on a moral basis and that actual, physical death was the result. Moral degradation was also a result, entangled in the entire, complete separation of humanity from the physical and moral perfection, the “being of the same kind” (speciation) as the father.
The man and woman, humanity, are “cast out” of this state, metaphorically. They “descend” and God “ascends”; reality suffers a symmetry breakage and two realms of being emerge – one destructible and one indestructible. So, the notion of eternity appears to have a moral basis, developed from a sense of alienation created by the tragic reality of death.
That death is a moral tragedy and not just a physical one, is very important. It means that the Fall of humanity, illustrated by the story of Eden, is thought-based, not physically-based; it is moral, not scientific. This is the blind spot. It is our thoughts (consciousness) not our physical actions, that cause death. Thoughts and physical actions are not integral. One cannot derive thoughts from actions and actions cannot be derived from thoughts because it can be demonstrated that people often do not know why they do things. Otherwise, there would be no need for psychology or sociology or anthropology or neurology or cognitive behaviorology, etc., etc. It seems that no one can really say, definitely, what actions are derived from what thoughts.
Hence the moral dilemma of humanity – how to discern moral thoughts from immoral ones, actions being non-determinant or irrelevant. Who can say which thoughts are moral and which are not? No one; hence the studies of philosophy, theology, etc. It is a blind spot, this inability to discern, and people will deny it because it is a true blind spot – it does not register. We seem to think we know, in fact, we are often taught to think we know. However, it is a biblical (narrative) truth that we do not. Our thoughts, which are products of a morally bankrupt physicality, the universe included, cannot be moral of the “kind” that God is moral. We are faced with an impossibility (improbability) – to have moral thoughts. Just how “fallen” are we, some may ask? It is not a viable argument that we are only partially fallen, as death is as complete a punishment as anyone could imagine.
Further, how to discover moral truths from “revelation” or “revealed truth” if our thoughts are completely immoral? “Who will save me from this body of death?” (Paul).
Saved By Gödel 