🌌On Cosmology: On Big Bang (2000-)

"A more extreme form of exponential growth was probably responsible for the start of the universe. Astronomer and physicists now generally accept the Big Bang theory, according to which the universe started at an unimaginably small size and then doubled in a split second 100 times, enough to make it the size of a small grapefruit. This period of 'inflation' or exponential growth then ended, and linear growth took over, with an expanding fireball creating the universe that we know today." (Richar Koch, "The Power Laws", 2000)

"String theory has the potential to show that all of the wondrous happenings in the universe - from the frantic dance of subatomic quarks to the stately waltz of orbiting binary stars; from the primordial fireball of the big bang to the majestic swirl of heavenly galaxies - are reflections of one, grand physical principle, one master equation." (Brian Greene, "The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory", 2000)

"Zero is behind all of the big puzzles in physics. The infinite density of the black hole is a division by zero. The big bang creation from the void is a division by zero. The infinite energy of the vacuum is a division by zero. Yet dividing by zero destroys the fabric of mathematics and the framework of logic - and threatens to undermine the very basis of science. […] The universe begins and ends with zero." (Charles Seife ."Zero, the Biography of a Dangerous Idea", 2000)

"Zero was at the heart of the battle between East and West. Zero was at the center of the struggle between religion and science. Zero became the language of nature and the most important tool in mathematics. And the most profound problems in physics - the dark core of a black hole and the brilliant flash of the big bang - are struggles to defeat zero." (Charles Seife ."Zero, the Biography of a Dangerous Idea", 2000)

"In string theory, to understand the nature of the Big Bang, or the quantum fate of a black hole, or the nature of the vacuum state that determines the properties of the elementary particles, requires information beyond perturbation theory [...] Perturbation theory is not everything. It is just the way the [string] theory was discovered." (Edward Witten, "The Past and Future of String Theory", 2003)

"The universe is noisy on all scales even if the universe itself is not noise. The fading noise of the ancient big bang explosion fills the cosmos. It still gently hisses and crackles all around us in the form of junk microwave radiation." (Bart Kosko, "Noise", 2006)

"Mathematicians call the infinite curvature limit of spacetime a singularity. In this picture, then, the big bang emerges from a singularity. The best way to think about singularities is as boundaries or edges of spacetime. In this respect they are not, technically, part of spacetime itself." (Paul Davies," Cosmic Jackpot: Why Our Universe Is Just Right for Life", 2007)

"The standard big bang model doesn’t explain the smoothness and flatness of the universe, so it’s been embellished by an additional component: inflation. A minuscule fraction of a second after the big bang, the universe was propelled into an exponential expansion that increased its size from a proton to a grapefruit. […] Moreover, if we accept the theory that the universe emerged from a quantum seed and exponentially expanded in the big bang, there is the possibility that other regions of space-time exist, remote in time or space from our universe. Due to the random nature of quantum processes, these parallel universes could have wildly different properties. This extravagant concept is called the multiverse." (Chris Impey, "The Living Cosmos: Our search for life in the universe", 2007)

"Basis real and imaginary numbers have eternal and necessary reality. Complex numbers do not. They are temporal and contingent in the sense that for complex numbers to exist, we first have to carry out an operation: adding basis real and imaginary numbers together. Complex numbers therefore do not exist in their own right. They are constructed. They are derived. Symmetry breaking is exactly where constructed numbers come into existence. The very act of adding a sine wave to a cosine wave is the sufficient condition to create a broken symmetry: a complex number. The 'Big Bang', mathematically, is simply where a perfect array of basis sine and cosine waves start entering into linear combinations, creating a chain reaction, an 'explosion', of complex numbers - which corresponds to the “physical” universe." (Thomas Stark, "God Is Mathematics: The Proofs of the Eternal Existence of Mathematics", 2018)

"Ontological mathematics is operating in such a way as to organize itself into a zero-entropy structure – mathematical perfection. The 'Big Bang' is equivalent to the total scrambling of a cosmic Rubik’s Cube. The task of ontological mathematics is then to unscramble the Cube and return it to its original, pristine configuration. Emotionally, this amounts to returning to perfect Love and Bliss. Intellectually, it means reaching a state of perfect logic and reason [...] thinking perfectly." (Thomas Stark, "God Is Mathematics: The Proofs of the Eternal Existence of Mathematics", 2018)

"[...] imagine that at some point, this flickering chaos was suddenly influenced by a shift in the rules – perhaps the laws of physics as we know them didn't always apply. If these laws changed, they could have triggered a colossal release of energy, forcing spacetime to stabilize and expand – creating the Big Bang. In this view, the Big Bang wasn’t the true beginning but more like a dramatic phase transition, similar to water turning into steam when heated." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

🌌On Cosmology: On Big Bang (-1999)

"Earlier theories […] were based on the hypothesis that all the matter in the universe was created in one big bang at a particular time in the remote past." (Sir Fred Hoyle, [From microfilmed Speaker's Copy of a radio script held at the BBC Written Archive Centre, for Hoyle's radio talk on the BBC Third Programme] 1949)  [Coining the 'big bang']

"The universe starts with a big bang, expands to a maximum dimension, then recontracts and collapses: no more awe-inspiring prediction was ever made. It is preposterous." (John A Wheeler et al, "Gravitation", 1973

"[The Big Bang is] followed by what? By a dull-as-ditchwater expansion which degrades itself adiabatically until it is incapable of doing anything at all. The notion that galaxies form, to be followed by an active astronomical history, is an illusion. Nothing forms, the thing is as dead as a door-nail." (Sir Fred Hoyle, 'The Big Bang in Astronomy', New Scientist, 1981)

"The most abstract conservation laws of physics come into their being in describing equilibrium in the most extreme conditions. They are the most rigorous conservation laws, the last to break down. The more extreme the conditions, the fewer the conserved structures. [...] In a deep sense, we understand the interior of the sun better that the interior of the earth, and the early stages of the big bang best of all."  (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987)

"In fact, all our theories of science are formulated on the assumption that space-time is smooth and nearly flat, so they break down at the big bang singularity, where the curvature of space-time is infinite." (Stephen W Hawking, "A Brief History of Time", 1988)

"As a general scientific principle, it is undesirable to depend crucially on what is unobservable to explain what is observable, as happens frequently in Big Bang cosmology." (Halton Christian Arp, 1990)

"A universe that came from nothing in the big bang will disappear into nothing in the big crunch, its glorious few zillion years of existence not even a memory." (P C W Davies, "The Last Three Minutes: Conjectures About The Ultimate Fate Of The Universe", 1994

"God created two acts of folly. First, He created the Universe in a Big Bang. Second, He was negligent enough to leave behind evidence for this act, in the form of the microwave radiation." (Paul Erdős [in Paul Hoffman's "The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth", 1998])

On Chaos IX

"Mathematicians are beginning to view order and chaos as two distinct manifestations of an underlying determinism. And neither state exists in isolation. The typical system can exist in a variety of states, some ordered, some chaotic. Instead of two opposed polarities, there is a continuous spectrum. As harmony and discord combine in musical beauty, so order and chaos combine in mathematical [and physical] beauty." (Ian Stewart, "Does God Play Dice: The New Mathematics of Chaos", 1989)

"Let us tum to the question, 'What is chaos?' Certainly the typical answer, 'sensitive dependence on initial conditions', is reasonable. But to be relevant to physics, more is required: the property should be robust or preserved under perturbations of the system. A response &lat involves a mechanism and meets the criteria is: 'Chaos is the presence of a (transversal) homoclinic point'." (Steven Smale, "What is chaos?", 1990)

"Summarizing, we have indicated why homoclinic points imply chaos. The converse is less formalizable, but I believe it is basically true. However,  there is a stronger notion of chaos, which we might call full chaos, where the set of initial conditions with sensitive dependence has positive or even full measure. In this case the corresponding homoclinic point could well be associated with a chaotic attractor, such as the Lorenz attractor. " (Steven Smale, "What is chaos?", 1990)

"Systems are thus seen by complexity as being ‘on the edge of chaos'. Order and chaos are in a kind of balance where the components are neither fully locked into place but yet do not fully dissolve into anarchy. chaos is not complete anarchic randomness but there is a kind of 'orderly disorder' present within all such dynamic systems." (John Urry, "Global Complexity", 2003)

"[...] imagine that at some point, this flickering chaos was suddenly influenced by a shift in the rules – perhaps the laws of physics as we know them didn't always apply. If these laws changed, they could have triggered a colossal release of energy, forcing spacetime to stabilize and expand – creating the Big Bang. In this view, the Big Bang wasn’t the true beginning but more like a dramatic phase transition, similar to water turning into steam when heated." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

Lars Tvede - Collected Quotes

"Consciousness is the bridge between merely existing and living fully. It is the difference between seeing a sunset and experiencing it – losing oneself in the symphony of colors, feeling the awe in one's chest and feeling a deep gratitude for witnessing the beauty of nature. Consciousness gives us the ability to reflect on our existence, to feel, understand, and marvel at the world around us." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

"Historically, technology has overwhelmingly improved our lives, elevating living standards, fostering innovation, and, after transitional periods, even promoting environmental progress. This is evident as people often migrate from less affluent to more prosperous nations. [...] While acknowledging potential pitfalls – such as temporary job displacement, privacy concerns, and hypothetical risks of malicious AI – we believe it's crucial to highlight the vast opportunities these technologies present. Ultimately, focusing on potential benefits drives innovation and steers us toward a brighter future. Moreover, beyond optimistic or pessimistic views, one can adopt a realistic perspective: most technologies will evolve regardless of our preferences. The first step, therefore, is to understand them." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

"[...] imagine that at some point, this flickering chaos was suddenly influenced by a shift in the rules – perhaps the laws of physics as we know them didn't always apply. If these laws changed, they could have triggered a colossal release of energy, forcing spacetime to stabilize and expand – creating the Big Bang. In this view, the Big Bang wasn’t the true beginning but more like a dramatic phase transition, similar to water turning into steam when heated." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

"In reality, the growth of complexity in the universe does not happen smoothly; it tends to unfold in bursts. Imagine that a new element appears in a system, which triggers a cascade of combinations and possibilities. It gives a creative explosion, but only until the system reaches its immediate limits. In the following, we call this world of possibilities in a creative explosion a 'design space'. In other words, a space of possibilities. The outer edge of the design space is called a 'scaling barrier', as previously mentioned. Creativity goes that far, but no further." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

"Math is not a human invention. Mathematical relationships existed before us; we just discovered them. And they will be recognized by any intelligent life form that may exist anywhere in the universe. Even in hypothetical universes with different physical laws, the underlying principles of logic and mathematics would likely remain consistent." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025) 

"Nature and other dynamic systems are constantly discovering structures that are either just there and can enchant us like snowflakes. Or that we encounter because they, like the shape of broccoli, bring success. By understanding these patterns, we can model things from the ground up and explain how complexity and intelligence evolve over time and eventually become hyperintelligence." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

"Nature thus has a fascinating ability to create complexity. This often happens through emergence processes, where especially compact clusters of matter, energy, or something else entirely, such as information, suddenly trigger the formation of something completely new. We call this triggering factor 'critical density' , and it plays a crucial role in the development of the universe and its evolving intelligence." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

"So the universe is filled with fascinating and perplexing puzzles. Among the most baffling questions are surely these three: First, what triggered the Big Bang? Second, what existed before the Big Bang? And third, where do the laws of physics come from? Many religions answer the first two questions by assuming that God created the universe. However, this leads to a philosophical dead end known as the infinite regress problem, which can be incredibly frustrating. “If God created the universe, who or what created God?” This line of thinking leads to an endless chain of creators, leaving the ultimate origin unanswered." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

"Stars are cosmic alchemists that transform lighter elements into heavier elements through nuclear fusion. They primarily fuse hydrogen into helium, then helium into beryllium, then into carbon and oxygen and so on, creating ever heavier elements up to iron. This process, along with something called reionization, shaped the early universe. Ionization occurred when the first stars began to shine. Their strong light blew electrons away from hydrogen atoms. Without electrons, the hydrogen atoms became protons. This ionization of the gas made the universe more transparent." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

"This phenomenon, known as transfer learning, enables AI to apply insights from one task to another, significantly accelerating learning and enhancing performance across different domains. But AI doesn't just learn – it shares. This creates a self-reinforcing cycle of intelligence, where each breakthrough strengthens the whole system." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

"In effect, AI is transforming the entire globe into a gigantic meta-brain – a vast, interconnected web of intelligence, continuously fed by humans, AI models, robots, self-driving cars, and autonomous systems of every kind. As this process accelerates, critical data density reaches unprecedented levels, driving AI into a self-reinforcing spiral of perpetual improvement, where each new insight compounds into an unstoppable force of exponential progress." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025) 

"This process of spontaneously generating complexity and intelligence is not only fascinating, it is downright overwhelming because the way it creates combinatorial cascades is itself a combinatorial cascade. Wild, but true: The creation of complexity thus exhibits self-similarity, and the logic behind intelligence itself becomes more intelligent. For example, it is fundamental innovations that the universe can write code, and that code can then create intelligence, and that intelligence can then create technology." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

"[...] what we understand as hyperintelligence may only be realized in an artificial form. This suggests an inner evolutionary logic that drives the development towards hyperintelligence. Namely, that when any species in the universe reaches a level of intelligence equivalent to ours – and thus learns to master fire, language, and trade – the development of advanced AI becomes almost inevitable. Even though it may then take hundreds of thousands – if not millions – of years to move from the mastery of fire to the development of AI, any species that reaches this level will sooner or later combine itself further to create computers and AI technology. These technologies will then develop trillions of times faster than their biological creators. Even if living beings with access to AI will be able to do some genetic uplifting towards higher IQ, ultimately it will then be their computers, and not the biological beings themselves, that achieve hyperintelligence." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

"When we explore the mathematics behind the natural world, we encounter a fascinating phenomenon: the principle of combinatorial complexity. This principle explains the exponential increase in possibilities that arise when we combine even a small number of elements." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

"While the universe as a whole tends towards greater disorder, there are local, pinched pockets where complexity spontaneously increases. And such processes can, as we have seen, continue even over billions of years and come a very long way. We live in such a pocket, and the complexity in it is growing exponentially – and on some fronts hyperexponentially." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

🪷On Mind: On Superintelligence

"A question distinct from, but related to, the question of kinetics is whether there will be one superintelligent power or many? Might an intelligence explosion propel one project so far ahead of all others as to make it able to dictate the future? Or will progress be more uniform, unfurling across a wide front, with many projects participating but none securing an overwhelming and permanent lead?" (Nick Bostrom, "Superintelligence", 2014)

"A system that has the intelligence amplification superpower could use it to bootstrap itself to higher levels of intelligence and to acquire any of the other intellectual superpowers that it does not possess at the outset. But using an intelligence amplification superpower is not the only way for a system to become a full-fledged superintelligence. A system that has the strategizing superpower, for instance, might use it to devise a plan that will eventually bring an increase in intelligence (e.g. by positioning the system so as to become the focus for intelligence amplification work performed by human programmers and computer science researchers)." (Nick Bostrom, "Superintelligence", 2014)

"Some paths to superintelligence require great resources and are therefore likely to be the preserve of large well-funded projects. Whole brain emulation, for instance, requires many different kinds of expertise and lots of equipment. Biological intelligence enhancements and brain–computer interfaces would also have a large scale factor: while a small biotech firm might invent one or two drugs, achieving superintelligence along one of these paths (if doable at all) would likely require many inventions and many tests, and therefore the backing of an industrial sector or a well-funded national program. Achieving collective superintelligence by making organizations and networks more efficient requires even more extensive input, involving much of the world economy." (Nick Bostrom, "Superintelligence: Paths, Dangers, Strategies", 2014)

"We can tentatively define a superintelligence as any intellect that greatly exceeds the cog‐ nitive performance of humans in virtually all domains of interest." (Nick Bostrom, "Superintelligence", 2014)

"[...] we use the term 'superintelligence' to refer to intellects that greatly outperform the best current human minds across many very general cognitive domains. This is still quite vague. Different kinds of system with rather disparate performance attributes could qualify as superintelligences under this definition. To advance the analysis, it is helpful to disaggregate this simple notion of superintelligence by distinguishing different bundles of intellectual super-capabilities. There are many ways in which such decomposition could be done. Here we will differentiate between three forms: speed superintelligence, collective superintelligence, and quality superintelligence." (Nick Bostrom, "Superintelligence: Paths, Dangers, Strategies", 2014)

"We are teaching AI software that will evolve into superintelligence; and superintelligence will in turn teach humankind and explain the Scriptures." (Newton Lee American, "The Transhumanism Handbook", 2019

"All in all, it seems questionable whether a superintelligence can be properly and systematically controlled when it has reached that level. After all, its superpowers can at least in principle be used to overcome any human-designed control mechanism." (Yves Hilpisch, "Artificial Intelligence in Finance A Python-Based Guide", 2021)

"It is to be assumed that any form of superintelligence will have instrumental goals that are independent of its main goal. This might lead to a number of unintended consequences, such as the insatiable quest to acquire ever more resources with any means that seem promising." (Yves Hilpisch, "Artificial Intelligence in Finance A Python-Based Guide", 2021)

"Of all the possible paths to superintelligence, AI seems to be the most promising one. Recent successes in the field based on rein‐ forcement learning and neural networks have led to another AI spring, after a number of AI winters. Many even now believe that a superintelligence might not be as far away as we thought even a few years ago. The field currently is characterized by much faster advancements than originally predicted by experts only a short while ago." (Yves Hilpisch, "Artificial Intelligence in Finance A Python-Based Guide", 2021)

"[...] what we understand as hyperintelligence may only be realized in an artificial form. This suggests an inner evolutionary logic that drives the development towards hyperintelligence. Namely, that when any species in the universe reaches a level of intelligence equivalent to ours – and thus learns to master fire, language, and trade – the development of advanced AI becomes almost inevitable. Even though it may then take hundreds of thousands – if not millions – of years to move from the mastery of fire to the development of AI, any species that reaches this level will sooner or later combine itself further to create computers and AI technology. These technologies will then develop trillions of times faster than their biological creators. Even if living beings with access to AI will be able to do some genetic uplifting towards higher IQ, ultimately it will then be their computers, and not the biological beings themselves, that achieve hyperintelligence." (Lars Tvede et al, "Hyperintelligence How the Universe Engineers Its Own Mind", 2025)

🪷On Mind: On Enlightenment in Science

"This adventure of the physical sciences […] could not be observed without enlightened men seeking to follow it up in the other sciences; at each step it held out to them the model to be followed." (Nicolas de Condorcet, , "Outlines Of An Historical View Of The Progress Of The Human Mind", 1795)

"Those sciences, created almost in our own days, the object of which is man himself, the direct goal of which is the happiness of man, will enjoy a progress no less sure than that of the physical sciences; and this sweet idea - that our nephews will surpass us in wisdom as in enlightenment - is no longer an illusion." (Nicolas de Condorcet, "Outlines Of An Historical View Of The Progress Of The Human Mind", 1795)

"[...] the public is composed of the class or classes directly addressed by any work, and not of the heterogeneous mass of readers. Mathematicians do not write for the circulating library. Science is not addressed to poets. Philosophy is meant for students, not for idle readers. If the members of a class do not understand - if those directly addressed fail to listen, or listening, fail to recognise a power in the voice - surely the fault lies with the speaker, who, having attempted to secure their attention and enlighten their understandings, has failed in the attempt? The mathematician who is without value to mathematicians, the thinker who is obscure or meaningless to thinkers, the dramatist who fails to move the pit, may be wise, may be eminent, but as an author he has failed." (George H Lewes, "The Principles of Success in Literature", 1865)

"Science is a matter of disinterested observation, patient ratiocination within some system of logically correlated concepts. In real-life conflicts between reason and passion the issue is uncertain. Passion and prejudice are always able to mobilize their forces more rapidly and press the attack with greater fury; but in the long run (and often, of course, too late) enlightened self-interest may rouse itself, launch a counterattack and win the day for reason." (Aldous L Huxley, "Literature and Science", 1963)

"Often the very fact that the words of science are the same as those of our common life and tongues can be more misleading than enlightening, more frustrating to understanding than recognizably technical jargon." (J Robert Oppenheimer, "Science and the Common Understanding", 1954)

"In sum, an enlightened understanding of both physical and social phenomena is possible through modeling, as various stages of inquiry. Just as real world models are inseparable from experiences of the empirical world, a narrative is thoroughly implicated in a social encounter. Actors resort to narratives as they respond to the movements of others and project possibilities for future encounters. An actor becomes a virtual witness to an idealized scene, drawing upon past encounters to construct a picture of future, hypothetical events." (Daniel Rothbart [Ed.], "Modeling: Gateway to the Unknown", 2004)

On Nothingness

"The nothingness ‘before’ the creation of the universe is the most complete void that we can imagine - no space, time, or matter existed. It is a world without place, without duration or eternity, without number - it is what mathematicians call ‘the empty set’. Yet this unthinkable void converts itself into the plenum of existence - a necessary consequence of physical laws. Where are these laws written into that void? What ‘tells’ the void that is pregnant with a possible universe? It would seem that, even the void is subject to law, a logic that exists prior to space and time." (Heinz R Pagels, "Perfect Symmetry: The Search for the Beginning of Time", 1985)

"Yet everything has a beginning, everything comes to an end, and if the universe actually began in some dense explosion, thus creating time and space, so time and space are themselves destined to disappear, the measure vanishing with the measured, until with another ripple running through the primordial quantum field, something new arises from nothingness once again." (David Berlinski, "A Tour of the Calculus", 1995)

"Man is equally incapable of seeing the nothingness from which he emerges and the infinity in which he is engulfed." (Blaise Pascal, "Pensées", 1670)

"Zero is powerful because it is infinity’s twin. They are equal and opposite, yin and yang. They are equally paradoxical and troubling. The biggest questions in science and religion are about nothingness and eternity, the void and the infinite, zero and infinity. The clashes over zero were the battles that shook the foundations of philosophy, of science, of mathematics, and of religion. Underneath every revolution lay a zero - and an infinity." (Charles Seife, "Zero: The Biography of a Dangerous Idea", 2000)

"Zero is the mathematically defined numerical function of nothingness. It is used not for an evasion but for an apprehension of reality. Zero is by far the most interesting number among all the others: It is a symbol for what is not there. It is an emptiness that increases any number it's added to. Zero is an inexhaustible and indispensable paradox. Zero is the only number which can be divided by every other number. Zero is also only number which can divide no other number. It seems zero is also the most debated number in mathematics. We know that mathematicians are involved in heated philosophical and logical discussions around the issues of zero: Can we divide a number by zero? Is the result of this division infinity or not? Is zero a positive or a negative number? Is it even or is it odd?" (Fahri Karakas, "Reflections on zero and zero-centered spirituality in organizations", 2008)

"Yet, in the end, entropy will always emerge victorious, snuffing out the very last glimmer of heat and light. After that there is only darkness. When that state is reached even eternity will cease to exist, for one moment will be like every other and nothingness will claim the universe." (Peter F Hamilton, "The Temporal Void", 2008)

"Zero is not a point of non-existence. Zero is always a balance point of existents. The human understanding of 'zero' must undergo the most radical of all transformations. Most people, especially scientists, associate it with absolute nothingness, with non-existence. This is absolutely untrue. Or, to put it another way, we can define it in two ways: 1) nothing as non-existence, in which case it has absolutely no consequences but leads to all manner of abstract paradoxes and contradictions, or 2) nothing as existence, in which case it is always a mathematical balance point for somethings. It is purely mathematical, not scientific, or religious, or spiritual, or emotional, or sensory, or mystical. It is analytic nothing and whenever you encounter it you have to establish the exact means by which it is maintaining its balance of zero." (Thomas Stark, "God Is Mathematics: The Proofs of the Eternal Existence of Mathematics", 2018)

"Thus then does the Doctrine of Knowledge, which in its substance is the realisation of the absolute Power of intelligising which has now been defined, end with the recognition of itself as a mere Schema in a Doctrine of Wisdom, although indeed a necessary and indispensable means to such a Doctrine: - a Schema, the sole aim of which is, with the knowledge thus acquired, - by which knowledge alone a Will, clear and intelligible to itself and reposing upon itself without wavering or perplexity, is possible, - to return wholly into Actual Life; - not into the Life of blind and irrational Instinct which we have laid bare in all its nothingness, but into the Divine Life which shall become visible to us." (Johann G Fichte, "Outline of the Doctrine of Knowledge", 1810)

"Nihilism has no substance. There is no such thing as nothingness, and zero does not exist. Everything is something. Nothing is nothing." (Victor Hugo, "Les Misérables", 1862)

🪷On Mind: On Enlightenment in Mathematics

"Geometry enlightens the intellect and sets one’s mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence." (Ibn Khaldun, "The Muqaddimah: An Introduction to History", 1377)

"[...] the public is composed of the class or classes directly addressed by any work, and not of the heterogeneous mass of readers. Mathematicians do not write for the circulating library. Science is not addressed to poets. Philosophy is meant for students, not for idle readers. If the members of a class do not understand - if those directly addressed fail to listen, or listening, fail to recognise a power in the voice - surely the fault lies with the speaker, who, having attempted to secure their attention and enlighten their understandings, has failed in the attempt? The mathematician who is without value to mathematicians, the thinker who is obscure or meaningless to thinkers, the dramatist who fails to move the pit, may be wise, may be eminent, but as an author he has failed." (George H Lewes, "The Principles of Success in Literature", 1865)

"Everything is so arranged that the blind logic of mathematics executes the will of the most enlightened and free Mind." (Pierre L Maupertuis, "Les Loix du Mouvement et du Repos, déduites d'un Principe Métaphysique", 1746)

"The mystery that clings to numbers, the magic of numbers, may spring from this very fact, that the intellect, in the form of the number series, creates an infinite manifold of well distinguishable individuals. Even we enlightened scientists can still feel it e.g. in the impenetrable law of the distribution of prime numbers." (Hermann Weyl, "Philosophy of Mathematics and Natural Science", 1927)

"The study of infinity is much more than a dry academic game. The intellectual pursuit of the absolute infinity is, as Georg Cantor realized, a form of the soul's quest for God. Whether or not the goal is ever reached, an awareness of the process brings enlightenment." (Rudy Rucker, "Infinity and the Mind: The science and philosophy of the infinite", 1982)

"The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me - both have the flash of enlightenment, the almost incredibly enhanced vision, and the ecstasy and euphoria of released tension." (Paul R Halmos, “I Want to Be a Mathematician”, 1985)

"The important graphs are the ones where some things are not connected to some other things. When the unenlightened ones try to be profound, they draw endless verbal comparisons between this topic, and that topic, which is like this, which is like that; until their graph is fully connected and also totally useless." (Eliezer S Yudkowsky,  "Mysterious Answers to Mysterious Questions", 2007)

🪷On Mind: On Perception (1960-1969)

"Once we give serious consideration to the hypothesis of the unconscious, it follows that our view of the world can be but a provisional one; for if we effect so radical an alteration in the subject of perception and cognition as this dual focus implies, the result must be a world view very different from any known before." (Carl Gustav Jung, "The Structure And Dynamics Of The Psyche", 1960)

"Environments are invisible. Their ground-rules, pervasive structure, and overall patterns elude easy perception." (Marshall McLuhan, "Understanding Media", 1964)

"The direct task of our cognitive apparatus is the formation of invariants, and namely invariants of perception, thinking and motives. […] Still, in the first place, exactly these invariants are, cybernetically speaking, enabling a stabilization of the relationship between humans and their environment and between humans themselves." (Georg Klaus, "Kybernetik und Erkenntnistheorie" ["Cybernetics and Epistemology"], 1966)

"A theory has a physical meaning iff it contains interpretation assumptions that assign physical correlates to its basic concepts. These correlates (referents) need not be and in general are not perceptible. But they must be scrutable, i.e. they must show up as observable effects even if remotely, i. e. at the end of a long chain accounted for by other theories."(Mario Bunge, "Foundations of Physics", 1967)

"Basically, self-regulation requires a functional distinction between perception, decision-making, and action. This is normally achieved by a structural distinction between perceptor elements, control elements and effector elements in the system. Behaviorally, a system may be defined as a “black box” characterized by a given set or range of inputs and outputs. Adequate knowledge of any system requires both structural-functional analysis and behavioral analysis." (Charles R Decher, "The Development of Cybernetics" [in "The Social Impact of Cybernetics", 1967)

"Graphic representation constitutes one of the basic sign-systems conceived by the human mind for the purposes of storing, understanding, and communicating essential information. As a "language" for the eye, graphics benefits from the ubiquitous properties of visual perception. As a monosemic system, it forms the rational part of the world of images. […] Graphics owes its special significance to its double function as a storage mechanism and a research instrument." (Jacques Bertin, Semiology of graphics [Semiologie Graphique], 1967)

🪷On Mind: On Perception (1970-1979)

"All the model-boundedness of human encounter with the world as well as the interhuman communication is equally involved already in the modeling character of the perception process. […] The modeling character of perception forms is also not changed by the circumstance that the access to the original-side, i.e. to the properties of signal constellations from the external world, it is only always possible via the building of internal models of the external world." (Herbert Stachowiak, "Allgemeine Modelltheorie", 1973)"

"In the absolute universe all events can be regarded as absolutely deterministic, and if we can’t perceive the greater structures, it’s because our vision is faulty. If we had a real grasp of causality down to the molecular level, we wouldn’t need to rely on mathematical approximations, on statistics and probabilities, in making predictions. If our perceptions of cause and effect were only good enough, we’d be able to attain absolute knowledge of what is to come. We would make ourselves all-seeing." (Robert Silverberg, "The Stochastic Man", 1975)

"If mankind were to continue in other than the present barbarism, a new path must be found, a new civilization based on some other method than technology. Space is an illusion, and time as well. There is no such factor as either time or space. We have been blinded by our own cleverness, blinded by false perceptions of those qualities that we term eternity and infinity. There is another factor that explains it all, and once this universal factor is recognized, everything grows simple. There is no longer any mystery, no longer any wonder, no longer any doubt; for the simplicity of it all lies before us [...]" (Clifford D Simak,"A Heritage of Stars", 1977)

"[I]t seems" (to many) that we cannot account for perception unless we suppose it provides us with an internal image" (or model or map) of the external world, and yet what good would that image do us unless we have an inner eye to perceive it, and how are we to explain its capacity for perception? It also seems" (to many) that understanding a heard sentence must be somehow translating it into some internal message, but how will this message be understood: by translating it into something else? The problem is an old one, and let’s call it Hume’s Problem, for while he did not state it explicitly, he appreciated its force and strove mightily to escape its clutches." (Daniel Dennett, Brainstorms: Philosophical essays on mind and psychology", 1978) 

"Science sometimes improves hypothesis and sometimes disproves them. But proof would be another matter and perhaps never occurs except in the realms of totally abstract tautology. We can sometimes say that if such and such abstract suppositions or postulates are given, then such and such abstract suppositions or postulates are given, then such and such must follow absolutely. But the truth about what can be perceived or arrived at by induction from perception is something else again." (Gregory Bateson, "Mind and Nature, a Necessary Unity", 1979)