🅲Nicolaus Copernicus - Collected Quotes

"The center of the earth is not the center of the universe, but only of gravity and of the lunar sphere." (Nicolaus Copernicus, "Commentariolus" [Little Commentary"], cca. 1514)

"Although all the good arts serve to draw man's mind away from vices and lead it toward better things, this function can be more fully performed by this art, which also provides extraordinary intellectual pleasure." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"Among the many and varied literary and artistic studies upon which the natural talents of man are nourished, I think that those above all should be embraced and pursued with the most loving care which have to do with things that are very beautiful and very worthy of knowledge." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"At rest, however, in the middle of everything is the sun. For, in this most beautiful temple, who would place this lamp in another or better position than that from which it can light up the whole thing at the same time?" (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"But we should rather follow the wisdom of nature, which, as it takes very great care not to have produced anything superfluous or useless, often prefers to endow one thing with many effects.Books & Literature." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"For a traveler going from any place toward the north, that pole of the daily rotation gradually climbs higher, while the opposite pole drops down an equal amount." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"For it is the duty of an astronomer to compose the history of the celestial motions through careful and expert study." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"For when a ship is floating calmly along, the sailors see its motion mirrored in everything outside, while on the other hand they suppose that they are stationary, together with everything on board. In the same way, the motion of the earth can unquestionably produce the impression that the entire universe is rotating." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"Hence I feel no shame in asserting that this whole region engirdled by the moon, and the center of the earth, traverse this grand circle amid the rest of the planets in an annual revolution around the sun. Near the sun is the center of the universe. Moreover, since the sun remains stationary, whatever appears as a motion of the sun is really due rather to the motion of the earth." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"I shall now recall to mind that the motion of the heavenly bodies is circular, since the motion appropriate to a sphere is rotation in a circle." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"[...] if the worth of the arts were measured by the matter with which they deal, this art - which some call astronomy, others astrology, and many of the ancients the consummation of mathematics - would be by far the most outstanding. This art which is as it were the head of all the liberal arts and the one most worthy of a free man leans upon nearly all the other branches of mathematics. Arithmetic, geometry, optics, geodesy, mechanics, and whatever others, all offer themselves in its service." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"More stars in the north are seen not to set, while in the south certain stars are no longer seen to rise." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"Of all things visible, the highest is the heaven of the fixed stars." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"The earth together with its surrounding waters must in fact have such a shape as its shadow reveals, for it eclipses the moon with the arc of a perfect circle." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"The earth also is spherical, since it presses upon its center from every direction." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"The massive bulk of the earth does indeed shrink to insignificance in comparison with the size of the heavens." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"The strongest affection and utmost zeal should, I think, promote the studies concerned with the most beautiful objects. This is the discipline that deals with the universe's divine revolutions, the stars' motions, sizes, distances, risings and settings... for what is more beautiful than heaven?" (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"Therefore I would not have it unknown to Your Holiness, the the only thing which induced me to look for another way of reckoning the movements of the heavenly bodies was that I knew that mathematicians by no means agree in their investigation thereof." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543) 

"Those who devised the eccentrics seen thereby in large measure to have solved the problem of apparent motions with approximate calculations. But meanwhile they introduced a good many ideas which apparently contradict the first principles of uniform motion. Nor could they elicit or deduce from the eccentrics the principal consideration, that is, the structure of the universe and the true symmetry of its parts." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"We find then in this arrangement an admirable harmony of the world, and a dependable, harmonious interconnexion of the motion and the size of the paths, such as otherwise cannot be discovered. For here the penetrating observer can note why the forward and the retrograde movement of Jupiter appears greater than that of Saturn, and smaller than that of Mars, and again greater with Venus than with Mercury; and why such retrogression appears oftener with Saturn than with Jupiter, less often with Mars and Venus than with Mercury. Moreover, why Saturn, Jupiter, and Mars, when they rise in the evening, appear greater than when they disappear and reappear [with the sun] [...]And all this results from the same cause, namely the motion of the earth." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"We regard it as a certainty that the earth, enclosed between poles, is bounded by a spherical surface." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543) 

"Whatever motion appears in the firmament arises not from any motion of the firmament, but from the earth's motion. The earth together with its circumjacent elements performs a complete rotation on its fixed poles in a daily motion, while the firmament and highest heaven abide unchanged." (Nicolaus Copernicus, "On the Revolutions of the Heavenly Spheres" ["De revolutionibus orbium coelestium"], 1543)

"And as far as hypotheses go, let no one expect anything in the way of certainty from astronomy, since astronomy can offer us nothing certain, lest, if anyone take as true that which has been constructed for another use, he go away from this discipline a bigger fool than when he came to it." (Andreas Osiander, "Ad lectorem de hypothesibus huius operis" [To the Reader Concerning the Hypotheses of this Wor"], [in Nicolaus Copernicus' "On the Revolutions of the Heavenly Spheres", 1543], 1943)

📒🆆John Wyndham - Collected Quotes

"The humans have a curious force they call ambition. It drives them, and, through them, it drives us. This force which keeps them active, we lack. Perhaps, in time, we machines will acquire it." (John Wyndham, "The Lost Machine", 1932)

"There are so many disadvantages in human construction which do not occur in us machines. [...] Some little thing here or there breaks - they stop working and then, in a short time, they are decomposing. Had he been a machine, like myself, I could have mended him, replaced the broken parts and made him as good as new, but with these animal structures one is almost helpless." (John Wyndham, "The Lost Machine", 1932)

"And we danced, on the brink of an unknown future, to an echo from a vanished past." (John Wyndham, "The Lost Machine", 1932)

"I don't think it had ever occurred to me that man's supremacy is not primarily due to his brain, as most of the books would have one think. It is due to the brain's capacity to make use of the information conveyed to it by a narrow band of visible light rays. His civilization, all that he had achieved or might achieve, hung upon his ability to perceive that range of vibrations from red to violet. Without that, he was lost." (John Wyndham, "The Day of the Triffids", 1951)

"There is an inability to sustain the tragic mood, a phoenix quality of the mind. It may be helpful or harmful, it is just a part of the will to survive - yet, also, it has made it possible for us to engage in one weakening war after another." (John Wyndham, "The Day of the Triffids", 1951)

"Knowing makes all the difference... It's the difference between just trying to keep alive, and having something to live for." (John Wyndham, "The Chrysalids", 1955)

"The essential quality of life is living, the essential quality of living is change; change is evolution; and we are part of it." (John Wyndham, "The Chrysalids", 1955)

"But, as I understand it, your God is a universal God; He is God on all suns and all planets. Surely, then, He must have universal form? Would it not be a staggering vanity to imagine that He can manifest Himself only in the form that is appropriate to this particular, not very important planet?" (John Wyndham, "The Midwich Cuckoos" 1957)

"Knowledge is simply a kind of fuel; it needs the motor of understanding to convert it into power." (John Wyndham, "The Midwich Cuckoos" 1957)

"Some quotations are greatly improved by lack of context." (John Wyndham, "The Midwich Cuckoos" 1957) 

🅿Louis Pasteur - Collected Quotes

"In the fields of observation chance favors only the prepared mind." (Louis Pasteur, [lecture] 1854)

"As in the experimental sciences, truth cannot be distinguished from error as long as firm principles have not been established through the rigorous observation of facts." (Louis Pasteur, "Étude sur la maladie des vers à soie", 1870)

"Analogy cannot serve as proof." (Louis Pasteur)

"Man’s first glance at the universe discovers only variety, diversity, multiplicity of phenomena. Let that glance be illuminated by science - by the science which brings man closer to God, - and simplicity and unity shine on all sides." (Louis Pasteur)

"The arguments […] by which you support my theories, are most ingenious, but not founded on demonstrated facts; analogy is no proof." (Louis Pasteur)

 "[…] the notion of the infinite […] forces itself upon our mind and yet is incomprehensible. When this notion takes possession of the understanding we have only to bow before it." (Louis Pasteur)

🅿Pythagoras of Samos - Collected Quotes

"All was numbers." (Pythagoras of Samos, cca. 6th century BC)

"Geometry is knowledge of the eternally existent."  (Pythagoras of Samos, cca. 6th century BC)

"Number is the ruler of forms and ideas, and the cause of gods and demons." (Pythagoras of Samos, cca. 6th century BC)

"Number rules the universe." (Pythagoras of Samos, cca. 6th century BC)

"Number was the substance of all things." (Pythagoras of Samos, cca. 6th century BC)

"The learning of many things does not teach intelligence […]." (Pythagoras of Samos, cca. 6th century BC)

"There is geometry in the humming of the strings; there is music in the spacing of the spheres." (Pythagoras of Samos, cca. 6th century BC)

🅿Edgar E Peters - Collected Quotes

"Because we hate living with uncertainty, we often try to make complex systems, such as the economy, more predictable and less uncertain. However, making a complex system more predictable also makes it less resilient to shocks, and less creative. Lowering uncertainty reduces complexity, often with disastrous effects." (Edgar E Peters, "Patterns in the dark: understanding risk and financial crisis with complexity theory", 1999)

"Complex systems, then, have local uncertainty and global certainty. They generate change, and they are resilient to unexpected shocks. They turn uncertainty into order, and they reverse order back into uncertainty. They evolve and change through time, and they do so without a central planner. Complex systems are everywhere. In fact, real life is one huge complex system. How is such behavior possible? First, we need to understand the general class of complex systems. By understanding their nature, we will see the important role uncertainty plays in maintaining stability. When we understand natural systems, we will understand the role of uncertainty in a free society." (Edgar E Peters, "Patterns in the dark: understanding risk and financial crisis with complexity theory", 1999)

In a free-market economy, then, uncertainty is a necessary element. Only when the economy is in a state of uncertainty can the participants efficiently search for solutions to problems and find creative answers. In addition, only a system that depends on uncertainty can survive unexpected shocks. A complex process can take multiple paths to an optimal solution. It does not require 'ideal' conditions; in fact, shocks often force it to find a better solution, a higher hill in the fitness landscape. The 'creative destruction' identified by the Austrian school suggests that a free-market economy is not only resilient to shocks, but is also creative and capable of generating innovation. It can only do so while in a high state of uncertainty." (Edgar E Peters, "Patterns in the dark: understanding risk and financial crisis with complexity theory", 1999)

"It seems obvious that uncertainty reigns during times of crisis. However, crisis itself can be a positive development. It is only negative in that it specifies that change is coming. Most people are uncomfortable with change and equate it with hard times. Mainstream economics tends to take the same view, calling such events 'shocks'. They are even referred to as 'exogenous' - outside of the system. If it were not for change, according to the mainstream school, everything would continue along in perfect balance, a 'circular flow'. Change is like an alien invasion. The mainstream view ignores the fact that change is necessary." (Edgar E Peters, "Patterns in the dark: understanding risk and financial crisis with complexity theory", 1999)

"Uncertainty is not necessarily bad or synonymous with risk. Complex systems use uncertainty to their advantage as they adapt to changes in their environment and learn to be resilient to unexpected shocks. Uncertainty then, rather than being the source of so many problems, becomes a necessary element if a market and a society are to remain free." (Edgar E Peters, "Patterns in the dark: understanding risk and financial crisis with complexity theory", 1999) 

🅿John Napier - Collected Quotes

"Seeing there is nothing that is so troublesome to mathematical practice, nor that doth more molest and hinder calculators, than the multiplications, divisions, square and cubical extractions of great numbers. [...] I began therefore to consider in my mind by what certain  and ready art I might remove those hindrances." (John Napier, "Mirifici logarithmorum canonis descriptio", 1614)

"A Logarithmic Table is a small table by the use of which we can obtain a knowledge of all geometrical dimensions and motions in space, by a very easy calculation. It is deservedly called very small, because it does not exceed in size a table of sines; very easy, because by it all multiplications, divisions, and the more difficult extractions of roots are avoided; for by only a very few most easy additions, subtractions, and divisions by two, it measures quite generally all figures and motions."  (John Napier, "The Construction of the Wonderful Canon of Logarithms", 1889)

"And if any number of equals to a first sine be multiplied together producing a second, just so many equals to the Logarithm of the first added together produce the Logarithm of the second." (John Napier, "The Construction of the Wonderful Canon of Logarithms", 1889)

"Any desired geometrical mean between two sines has for its Logarithm the corresponding arithmetical mean between the Logarithms of the sines." (John Napier, "The Construction of the Wonderful Canon of Logarithms", 1889)

"To decrease geometrically is this, that in equal times, first the whole quantity then each of its successive remainders is diminished, always by a like proportional part." (John Napier, "The Construction of the Wonderful Canon of Logarithms", 1889)

🆃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)

🅽Mark Needham - Collected Quotes

 "A random walk, in general, is sometimes described as being similar to how a drunk person traverses a city. They know what direction or end point they want to reach but may take a very circuitous route to get there. The algorithm starts at one node and somewhat randomly follows one of the relationships forward or backward to a neighbor node. It then does the same from that node and so on, until it reaches the set path length. 'We say somewhat randomly because the number of relationships a node has, and its neighbors have, influences the probability a node will be walked through.)'" (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Adding graph features and context improves predictions, especially in situations where connections matter. [...] Unfortunately, many machine learning approaches today miss a lot of rich contextual information. This stems from ML’s reliance on input data built from tuples, leaving out a lot of predictive relationships and network data. Furthermore, contextual information is not always readily available or is too difficult to access and process. Even finding connections that are four or more hops away can be a challenge at scale for traditional methods. Using graphs, we can more easily reach and incorporate connected data." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"At the most abstract level, graph analytics is applied to forecast behavior and prescribe action for dynamic groups. Doing this requires understanding the relationships and structure within the group. Graph algorithms accomplish this by examining the overall nature of networks through their connections. With this approach, you can understand the topology of connected systems and model their processes." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Betweenness Centrality makes the assumption that all communication between nodes happens along the shortest path and with the same frequency, which isn’t always the case in real life. Therefore, it doesn’t give us a perfect view of the most influential nodes in a graph, but rather a good representation." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Centrality algorithms are used to understand the roles of particular nodes in a graph and their impact on that network. They’re useful because they identify the most important nodes and help us understand group dynamics such as credibility, accessibility, the speed at which things spread, and bridges between groups." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Community formation is common in all types of networks, and identifying them is essential for evaluating group behavior and emergent phenomena. The general principle in finding communities is that its members will have more relationships within the group than with nodes outside their group. Identifying these related sets reveals clusters of nodes, isolated groups, and network structure. This information helps infer similar behavior or preferences of peer groups, estimate resiliency, find nested relationships, and prepare data for other analyses. Community detection algorithms are also commonly used to produce network visualization for general inspection." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Feature extraction is a way to distill large volumes of data and attributes down to a set of representative descriptive attributes. The process derives numerical values (features) for distinctive characteristics or patterns in input data so that we can differentiate categories in other data. It’s used when data is difficult for a model to analyze directly - perhaps because of size, format, or the need for incidental comparisons. Feature selection is the process of determining the subset of extracted features that are most important or influential to a target goal. It’s used to surface predictive importance as well as for efficiency." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Graph algorithms provide one of the most potent approaches to analyzing connected data because their mathematical calculations are specifically built to operate on relationships. They describe steps to be taken to process a graph to discover its general qualities or specific quantities. Based on the mathematics of graph theory, graph algorithms use the relationships between nodes to infer the organization and dynamics of complex systems. Network scientists use these algorithms to uncover hidden infomation, test hypotheses, and make predictions about behavior." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Graph embedding is the representation of the nodes and relationships in a graph asfeature vectors. [...] Graph embedding uses graph data slightly differently than in connected feature extraction. It enables us to represent entire graphs, or subsets of graph data, in a numerical format ready for machine learning tasks. This is especially useful for unsupervised learning, where the data is not categorized because it pulls in more contextual information through relationships. Graph embedding is also useful for data exploration, computing similarity between entities, and reducing dimensionality to aid in statistical analysis." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"In classic graph theory, an acyclic graph that is undirected is called a tree. In computer science, trees can also be directed. A more inclusive definition would be a graph where any two nodes are connected by only one path. Trees are significant for understanding graph structures and many algorithms. They play a key role in designing networks, data structures, and search optimizations to improve categorization or organizational hierarchies." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Keep in mind that centrality measures represent the importance of a node in comparison to other nodes. Centrality is a ranking of the potential impact of nodes, not a measure of actual impact. For example, you might identify the two people with the highest centrality in a network, but perhaps policies or cultural norms are in play that actually shift influence to others. Quantifying actual impact is an active research area to develop additional influence metrics." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Machine learning is not artificial intelligence (AI), but a method for achieving AI. ML uses algorithms to train software through specific examples and progressive improvements based on expected outcome - without explicit programming of how to accomplish these better results. Training involves providing a lot of data to a model and enabling it to learn how to process and incorporate that information." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Make it a habit to run Connected Components to test whether a graph is connected as a preparatory step for general graph analysis. Performing this quick test can avoid accidentally running algorithms on only one disconnected component of a graph and getting incorrect results." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Sometimes the most important cog in the system is not the one with the most overt power or the highest status. Sometimes it’s the middlemen that connect groups or the brokers who the most control over resources or the flow of information. Betweenness Centrality is a way of detecting the amount of influence a node has over the flow of information or resources in a graph. It is typically used to find nodes that serve as a bridge from one part of a graph to another." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Putting together the right mix of features can increase accuracy because it fundamentally influences how our models learn. Because even modest improvements can make a significant difference [...]. Connected features are features extracted from the structure of the data. These features can be derived from graph-local queries based on parts of the graph surrounding a node, or graph-global queries that use graph algorithms to identify predictive elements within data based on relationships for connected feature extraction." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Use Degree Centrality if you’re attempting to analyze influence by looking at the number of incoming and outgoing relationships, or find the 'popularity' of individual nodes. It works well when you’re concerned with immediate connectedness or near-term probabilities. However, Degree Centrality is also applied to global analysis when you want to evaluate the minimum degree, maximum degree, mean degree, and standard deviation across the entire graph." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Using graphs for connected feature extraction can significantly improve our predictions. The ideal graph features and algorithms vary depending on the attributes of the data, including the network domain and graph shape. We suggest first considering the predictive elements within your data and testing hypotheses with different types of connected features before fine-tuning." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"When using community detection algorithms, be conscious of the density of the relationships. If the graph is very dense, you may end up with all nodes congregating in one or just a few clusters. You can counteract this by filtering by degree, relationship weights, or similarity metrics. On the other hand, if the graph is too sparse with few connected nodes, you may end up with each node in its own cluster. In this case, try to incorporate additional relationship types that carry more relevant information." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Without peripheral and related information, solutions that attempt to predict behavior or make recommendations for varying circumstances require more exhaustive training and prescriptive rules. This is partly why AI is good at specific, well-defined tasks, but struggles with ambiguity. Graph-enhanced ML can help fill in that missing contextual information that is so important for better decisions." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

🆂William L Schaaf - Collected Quotes

"A formula is simply a mathematical statement of a principle or a rule describing the relation between two or more quantities. This mathematical statement shows that there is an equality between certain quantities; in other words, the formula translates a verbal rule into algebraic symbols. Thus a formula is very similar to an equation." (William L Schaaf, "Mathematics for Mechanics", 1942)

"A graph, as the name itself suggests, can go a step further than the formula - it can make visible what the formula represents - it can give an actual picture of the mathematical relationship. The relationship literally becomes more graphic; the relative magnitudes of the variables become apparent to the eye, as do extreme maximum and minimum values, if any; so do the rates at which they change; trends become clear; extrapolation and interpolation become more meaningful; any special features of the relationship are emphasized; general types of relationships are recognizable; two or more relationships can frequently be directly compared with one another." (William L Schaaf, "Mathematics for Mechanics", 1942)

"A type of picture-graph less commonly used than formerly is the pictorial representation of an object which has been arbitrarily subdivided to show certain numerical relationships; as, for example, the pictorial representation of the food values of beefsteak. This is a very poor type of graphic representation, and should definitely be avoided. The irregular outline of the picture as a whole, and of each of the shaded areas, makes a comparison of the areas difficult, if not altogether impossible; the shading only to the confusion." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"Geometric lines are fictions in the sense that, while we draw them, we think of them as having no width, simply length. Lines may be curved or straight." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"Graphs showing time changes, or the increases and decreases in the amount of something over a period of time, are generally of two kinds: (1) vertical bar graphs, and (2) broken- or smooth-line graphs. Both kinds differ from the categorical charts [...] in that they have two scales instead of only one; that is why it is preferable to call them graphs rather than charts, although these terms are used rather freely and interchangeably, and there is no standard convention." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"If a number or a quantity is thought of as being broken up, or subdivided into any number of equal parts, and then a certain number of those parts is considered separately in relation to the total number of such parts, we arrive at the idea of a fraction." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"In [...] horizontal bar-charts, showing comparisons between different kinds of things, or between different places, only one numerical scale is required, viz., the scale representing the amounts involved. No other numerical scale is needed, since we are dealing with various categories. While not always the most effective device for exhibiting such comparisons, horizontal bar-charts are simple and convenient." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"In mathematics, a definite quantitative relation between two or more variables, whether expressed verbally, by a formula, or by a graph, is called a functional relationship, or simply a mathematical function. Each variable is said to be a function of the other. The word function, as used here, has nothing to do with use or purpose; it simply calls attention to the fact that the quantities in question are quantitatively related to each other in a definite manner." (William L Schaaf, "Mathematics for Mechanics", 1942)

"It is clear that for any given point on a graph, its horizontal distance from the vertical scale (abscissa) represents the magnitude of the independent variable, while the vertical distance above or below the horizontal scale (ordinate) represents the corresponding magnitude of the dependent variable. Thus the position of the curve with respect to the axes depicts the actual magnitudes of the variables. But in studying changing variables and functional relationships, it is frequently desirable to inquire as to the rate at which a quantity is changing, i.e., how fast it is increasing or decreasing, rather than how large or how small it is. Rate implies a ratio; a rate of change means the amount of change in the function (or dependent variable) per unit change in the independent variable." (William L Schaaf, "Mathematics for Mechanics", 1942)

"Many forms in Nature exhibit the geometric property of symmetry. Anything symmetrical, whether natural or manmade, is usually pleasing in appearance, since it is 'balanced', and appeals to the eye. Symmetry is one of the most important principles of ornament, design and architecture. It is not, however, the only one; others are repetition and rhythm." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"The mathematical concept of chance, or probability, must not be confused with the psychological notion of likelihood. If a coin upon being tossed six times in succession has come up 'heads' each of the six times, we may be impelled to feel that upon the seventh toss it is 'more likely' to turn 'tails' in view of the six previous heads; but this is only an emotional reaction and not a mathematical probability. Mathematically [...] on any single throw, the chances are even for heads or tails, irrespective of what the previous trials may have been. In the long run, the greater the number of trials, the more nearly equal will become the number of heads and tails." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"The methods of algebra are essentially an extension of arithmetic. In other words, the numbers, symbols and operations used in algebra are the same as those used in arithmetic, only they are more general in character. This means (1) that letters as well as numbers are are “used te to represent quantities, and (2) that ‘numbers are re‘garded as having quality as well as quantity." (William L Schaaf, "Mathematics for Mechanics", 1942)

"There is no such thing as an absolute or perfect measurement. An object can be thought of as having an actual, real, or 'true' length; but that length can never be found completely, it can only be found approximately. How 'exact' any particular measurement happens to be depends upon the nature of the instruments used, the skill of the operator, and the conditions under which it is made. The difference between the true length and the measured length is technically known as the error. An error is not a mistake. The careless use, or the misuse, of a measuring instrument leads to mistakes. The proper use of a measuring instrument always involves errors. The errors may be large or small; they can never be completely eliminated. The extent of the approximation is known as the degree of accuracy of the measurement; a numerical measure of the extent of the error is known as the precision of the measurement. What particu. lar degree of accuracy is sought depends chiefly upon the purpose for which the measurement is made, or the "use to which the object is to be put." (William L Schaaf, "Mathematics for Mechanics", 1942)

"Practical geometry deals with the nature and properties of various geometric forms, such as rectangles, triangles, circles, etc., and emphasizes especially the measurement of such figures. Hence the chief value of practical geometry is in problems of design and construction." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"The operation of adding two numbers is essentially a process of grouping, or, more accurately, regrouping. When we add two numbers we do not increase anything; we regroup the numbers in accordance  with the standard pattern or number system based on groups of ten." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"When statistical data are of such a nature that it is permissible to assume that 'in-between values' vary continuously and uniformly (or very nearly so) from one observed or measured value to the next, a modification of the broken-line graph may be used. Instead of connecting the plotted points with straightline segments, a 'smooth' curved line is drawn between the points [...]. Such curvedline graphs may be drawn either 'free hand' or with the aid of drafting instruments known as French curves." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"You may expect to find graphs anywhere: in books, in periodicals, in newspapers, in pamphlets, on show cards in advertisements, in business reports, and so on. Their use, however, is sometimes limited. For one thing, they are of necessity less accurate than the figures on which they are based, which, of course, doesn’t matter too much in many cases. In the second place, they are sometimes misleading, which may or may not be intentional. It is also possible that the reader of a chart or graph may misinterpret it." (William L Schaaf, "Mathematics For Everyday Use", 1942)

"A mathematical point is an idea - an abstraction - something we can think about. It cannot be defined logically. Fortunately, our common experience with physical objects makes it relatively certain that each of us has the same idea in mind when he uses the word point, and so the lack of a logical definition presents no particular difficulty." (William L Schaaf, "Plane and solid geometry for home study", 1944)

"Having brought our story down to the present, we may well ask: What is geometry? Is it a system of logic, of pure mathematics, or is it a practical art to serve as the handmaiden to science, engineering, astronomy, and kindred technical fields? The answer is simple: it is both a logical science and a practical art." (William L Schaaf, "Plane and solid geometry for home study", [forward] 1944)

"No step should ever be taken, and no statement should ever be made, without giving a legitimate reason therefor. A 'legitimate' reason means a reference to a definition, to an assumption, or to a proposition previously proved; it may also include reference to a statement in the hypothesis, or to a line arbitrarily drawn at the outset of the demonstration." (William L Schaaf, "Plane and solid geometry for home study", 1944)

"To define a term adequately means to describe it in such a way that no doubt or ambiguity arises as to its meaning when that term is used. A good definition should indicate to what larger group of objects the object defined belongs, as well as how that object differs from other objects of that group. The larger group is sometimes called the genus, and the smaller, special group is called the species. Geometric objects, i.e., figures, are for the most part easy to define with precision." (William L Schaaf, "Plane and solid geometry for home study", 1944)

"Whenever we discuss a geometric statement in order to prove it, we refer to previously proved statements for 'evidence'. In this process of referring back to earlier statements that have already been established by proof, it is clear that some few of the earliest statements must of necessity remain unproved - that is, they have to be taken for granted, since we must begin our chain of reasoning somewhere. It is not possible to prove every statement. Those statements which are thus taken for granted without proof are called assumptions. Hence in all logical reasoning, two considerations are of prime importance: (1) the meanings of the terms used, and (2) the basic assumptions made." (William L Schaaf, "Plane and solid geometry for home study", 1944)

"Mathematics is on the artistic side a creation of new rhythms, orders, designs, harmonies, and on the knowledge side, is a systematic study of various rhythms, orders." (William L Schaaf, "Mathematics: Our Great Heritage: Essays on the Nature and Cultural Significance of Mathematics", 1948)

"A cylinder is a quadric surface if and only if its right section is a conic. As will be seen shortly, a quadric surface is one whose equation is of the second degree. A quadric cylinder is called parabolic, elliptic, or hyperbolic according as its right section is a parabola, an ellipse, or a hyperbola. The cylinder of revolution, or circular cylinder, is a special case of the elliptic cylinder." (William L Schaaf, "Analytic Geometry; a college course guide", 1962) 

"A cylindrical surface is any surface generated by a moving straight line which constantly intersects a given fixed curve and which remains parallel to a fixed straight line. The fixed curve is called the directrix, and the generating line is known as the generatrix. Thus a cylinder is a ruled surface, that is, the surface is comprised of straight lines (the generators), all of which are parallel." (William L Schaaf, "Analytic Geometry; a college course guide", 1962) 

"A transformation by translation has the effect of moving the origin to a new position without changing the directions of the axes. A transformation by rotation has the effect of turning the axes through an angle about the origin as a pivot, but without changing the position of the origin. Either transformation may be effected by itself, or both may be effected jointly; although, in such case, the rotation is normally performed first and the translation second." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"If each segment of a broken line in space be given the direction determined in passing continuously from one terminal to the other, then the algebraic sum of the projections of the segments upon any directed line equals the projection of the closing line. If the broken line in question should be a closed polygon, the sum of the projections of the sides upon any directed line is zero." (William L Schaaf, "Analytic Geometry; a college course guide", 1962) 

"In algebra, when we plot the graph of an equation, the curve so obtained represents the locus of the equation. In analytic geometry, the word 'curve' refers to any locus; it may be a straight line, a curved line, or a group of lines. We therefore see that: (1) The locus of an equation is a curve containing all those points, and only those points, whose coordinates satisfy the given equation. (2) The equation of a locus is an equation such that the coordinates of every point on the locus satisfy the equation, and every ordered pair of numbers which satisfy the equation are the coordinates of a point on the locus." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"It is possible, however, to determine the general shape and salient features of a curve by a more searching method. This is accomplished by examining more closely the equation of the curve, rather than by computing a more extensive table of values. Certain characteristic features of curves can be determined by inspection of the form of the equation, and by computing only certain special values of the variables. These characteristic properties include the intercepts, extent, symmetry, and asymptotes of the curve." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"It is possible, however, to express geometric facts by using algebraic methods. In other words, the properties of figures and the relationships between them can be described by means of numbers and equations. Conversely, algebraic expressions and equations can be represented or interpreted geometrically. When we translate from the language of geometry to the language of algebra, or vice versa, we are using analytical methods. Geometry when studied in this way is called analytic geometry." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"It is to be understood that by an algebraic equation is meant an equation which involves only integral and fractional powers of the variables x and y. If the equation is of degree higher than two, the equation represents an algebraic higher plane curve. Any equation which is not algebraic is known as a transcendental equation; functions defined by such equations are said to be transcendental functions. For example, y = cos x, y = a log x, and y = k"" are transcendental functions."  (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"The empirical data are usually available in the form of a table exhibiting pairs of corresponding values of the variables. Since the given values do not lie exactly along a straight hne, a parabola, an exponential curve or a power curve, it is necessar}' to find a curve that fits the given data approximately. This process is called curve fitting, and the equation of the curve which fits the data approximately is called an empirical equation. When fitting a curve to a set of given points, we must assume a general form for the equation which we are going to use to represent the curve." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"Very little can be learned about the nature of a surface merely by locating points on the surface. Instead, we study (1) its intercepts and traces in the coordinate planes; (2) its extent; (3) its symmetry, and (4) plane sections." (William L Schaaf, "Analytic Geometry; a college course guide", 1962) 

"When either the translation or the rotation transformations are applied to an equation, they change the coordinates of all points in the plane (except the origin in the case of a rotation). These transformations actually move the axes with relation to the curve, but they do not alter the shape of the curve represented by the original equation and by the transformed equation. Beside this constant or unvarying feature, i.e., the preservation of the geometric form of the curve, there are also certain algebraic expressions whose values remain unchanged in both equations. Mathematical forms which are preserved or do not vary when other changes take place are called invariants." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"When plotting or drawing the locus of a given equation, the position selected for the coordinate axes is, of course, immaterial. Hence, after the locus has been drawn, we may change the position of the axes arbitrarily, as we wish. Naturally, if the locus remains where it was drawn, but the position of the axes is changed, then the equation will have to be changed to correspond to the new position of the axes if the equation is to describe the same locus. In other words, a given locus may be described by more than one equation; each of the equations describes the locus in question with reference to a different set of axes."(William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"A maximum value of a function is one that is greater than any values immediately preceding or following; a minimum value of a function is one that is less than any values immediately preceding or following."  (William L Schaaf, "The Calculus, a college course guide", 1963)

"Emerson once said that it didn’t matter much where a man was, so long as you knew the direction in which he was moving. In somewhat the same way, the significance of a graph or curve often lies not so much in what height a point on the curve has reached, as it does in how fast its height is changing, and whether it is increasing or decreasing." (William L Schaaf, "The Calculus, a college course guide", 1963)

"If a function increases as the independent variable increases, or decreases as the independent variable decreases, the function is said to be increasing; if the function decreases as the independent variable increases, or increases as the independent variable decreases, the function is decreasing." (William L Schaaf, "The Calculus, a college course guide", 1963)

"When a curve approaches an axis or any other straight line in this fashion, the line is said to be an asymptote of the curve. As a working definition, we may say: An asymptote of a curve is any straight line which a curve approaches continuously as the curve moves on to infinity." (William L Schaaf, "The Calculus, a college course guide", 1963)

"In other words, we may think of the instantaneous speed at a certain instant as the limiting value which the average speed would approach tf the interval were indefinitely shortened, while always including the instant in question." (William L Schaaf, "The Calculus, a college course guide", 1963)

"It hardly need be pointed out that to use the calculus skillfully requires considerable practice with standard formulas for differentiating various functions. Among the most commonly used formulas are those for the power function, for a product, and for a quotient. The exercise below affords further practice in the use of these formulas" (William L Schaaf, "The Calculus, a college course guide", 1963)

"It is apparent, therefore, that for a function to have a maximum or a minimum value, it is necessary for the value of f’(x) to be zero or infinite, but that this alone is not a sufficient condition. In addition to f’(x) having a zero or infinite value, f’ (x) must change in sign as it passes through zero (or infinity)." (William L Schaaf, "The Calculus, a college course guide", 1963)

"Once more we must remind the reader not to confuse the amount of change with the rate of change. A function may increase or decrease by a very small amount in a short interval, and yet be changing very rapidly - just as a bullet may travel only a small distance in one thousandth of a second and yet be moving at a very high speed." (William L Schaaf, "The Calculus, a college course guide", 1963)

"The creation of Analytic Geometry by Descartes in the early part of the seventeenth century was a milestone of tremendous significance. Indeed, it was the beginning of modern mathematics in the broad perspective of history. ('Modern' mathematics in the sense of contemporary mathematics did not commence until about 1900, with the advent of functional analysis, abstract spaces, set theory, and symbolic logic.) This great step of recognizing the relation between the numbers of algebra and the entities of geometry once having been taken, it is perhaps not surprising that further advances were soon to follow, culminating in the invention of the Calculus by Isaac Newton and by Gottfried Leibniz. This was a classic illustration of nearly simultaneous, but presumably independent creation." (William L Schaaf, "The Calculus, a college course guide", 1963)

"Thus far we have regarded integration as the inverse of the operation of differentiation, and the integral was thought of as an anti-derivative. It is possible, however, to consider integration from another point of view, namely, as a process of summation, or as the addition of many similar elements. Indeed, it is largely from this point of view that the Integral Calculus developed historically, growing out of early attempts to determine the area bounded by various curves. A given area was subdivided into many small parts, and these 'infinitesimal parts' were then added." (William L Schaaf, "The Calculus, a college course guide", 1963)

"When comparing infinitesimals, we refer to their order. This is a relative term, suggesting comparative degree of smallness. If the limit of the quotient of two infinitesimals is a constant, not zero, they are said to be of the same order; if this limit is zero, the first differential (the numerator) is said to be of higher order than the second, and the second of lower order than the first. If the limit is infinite, the first differential (the numerator) is said to be of lower order than the second, and the second of higher order than the first." (William L Schaaf, "The Calculus, a college course guide", 1963)

"Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number π." (William L Schaaf, "Nature and History of π", 1967)

🅽Alessandro Negro - Collected Quotes

"A graph is a simple and quite old mathematical concept: a data structure consisting of a set of vertices (or nodes/points) and edges (or relationships/lines) that can be used to model relationships among a collection of objects." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"A widely adopted technique for solving the data sparsity issue and the cold-start problem is based on graph representation, navigation, and processing. Graph navigation methods (like the pathfinding example [...]) and graph algorithms (such as PageRank) are applied to fill some gaps and create a denser representation of [a] dataset." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"GNNs are capable of generating representations of nodes that depend on the structure of the graph as well as on any feature information we have. These features could be nodes’ properties, relationship types, and relationship properties. That’s why GNNs could drive the final tasks to better results. These embeddings represent the input for tasks such as node classification, link prediction, and graph classification." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"[...] graphs are extremely useful for encoding information, and data in graph format is increasingly plentiful. In many areas of machine learning - including natural language processing, computer vision, and recommendations - graphs are used to model local relationships between isolated data items (users, items, events, and so on) and to construct global structures from local information. Representing data as graphs is often a necessary step (and at other times only a desirable one) in dealing with problems arising from applications in machine learning or data mining." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs are powerful structures useful not only for representing connected information, but also for supporting multiple types of analysis. Their simple data model, consisting of two basic concepts such as nodes and relationships, is flexible enough to store complex information. If you also store properties in nodes and relationships, it is possible to represent practically everything of any size." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs are useful for representing how things are either physically or logically linked in simple or complex structures. A graph in which we assign names and meanings to the edges and vertices becomes what is known as a network. In these cases, a graph is the mathematical model for describing a network, whereas a network is a set of relations between objects, which could include people, organizations, nations, items found in a Google search, brain cells, or electrical transformers." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs can be used to model and analyze the relationships between entities as well as their properties. This aspect brings an additional dimension of information that graph-powered machine learning can harness for prediction and categorization. The schema flexibility provided by graphs also allows different models to coexist in the same dataset." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs can support machine learning by doing what they do best: representing data in a way that is easily understandable and easily accessible. Graphs make all the necessary processes faster, more accurate, and much more effective. Moreover, graph algorithms are powerful tools for machine learning practitioners. Graph community detection algorithms can help identify groups of people, page rank can reveal the most relevant keywords in a text, and so on." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs, with multiple node types and different types of relationships, are far from being a Euclidean space. This task is where graph neural networks (GNNs) comes in. GNNs are deep learning-based methods that operate on a graph domain to perform complex tasks such as node classification (the bot example), link prediction (the disease example), and so on. Due to its convincing performance, GNN has become a widely applied graph analysis method." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"In many areas of machine learning, graphs are used to model local relationships between data elements and to build global structures from local information. Building graphs is sometimes necessary for dealing with problems arising from applications in machine learning or data mining, and at other times, it's helpful for managing data. It's important to note that the transformation from the original data to a graph data representation can always be performed in a lossless manner. The opposite is not always true." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

🆂James G Scott - Collected Quotes

"A model is a metaphor, a description of a system that helps us to reason more clearly. Like all metaphors, models are approximations, and will never account for every last detail. A useful mantra here is: all models are wrong, but some models are useful." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"[...] always remember that the construction of an ANOVA table is inherently sequential. For example, first we add the clutter variable, which remains in the model at every subsequent step; then we add the distance variable, which remains in the model at every subsequent step; and so forth. Thus the actual question being answered at each stage of an analysis of variance is: how much variation in the response can this new variable predict, in the context of what has already been predicted by other variables in the model? This point - the importance of context in interpreting an ANOVA table - is subtle, but important." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"An obvious question is: do bootstrapped confidence intervals satisfy the frequentist coverage property? If your sample is fairly representative of the population, then the answer is a qualified yes. That is, the bootstrapping procedure yields nominal X% intervals that cover the true value 'approximately' X% of the time. Moreover, as the size of the original sample gets bigger, the quality of the approximation gets better. Alas, it is necessary to appeal to some very advanced probability theory to put both of these claims on firm footing." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"At the core of the resampling approach to statistical inference lies a simple idea. Most of the time, we can’t feasibly take repeated samples of size n from the population, to see how our estimate changes from one sample to the next. But we can repeatedly take samples of size n from the sample itself, and apply our estimator afresh to each notional sample. The idea is that the variability of the estimates across all these samples can be used to approximate our estimator’s true sampling distribution. This process - pretending that our sample is the whole population, and taking repeated samples of size n with replacement from our original sample of size n - is called bootstrap resampling, or just bootstrapping" (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"By themselves, sums of squares are hard to interpret, because they are measured in squared units of the Y variable. But their ratios are highly meaningful. In fact, the ratio of PV to TV - or what fraction of the total variation has been predicted by the model - is one of the most frequently quoted summary measures in all of statistical modeling. This ratio is called the coefficient of determination, and is usually denoted by the symbol R2 [...] The correct interpretation of R2 sometimes trips people up, and is therefore worth repeating: it is the proportion of variance in the data that can be predicted using the statistical model in question." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"Good estimators are those that usually yield estimates close to the truth, with minimal variation. Therefore, we typically summarize a sampling distribution using its standard deviation, which we refer to as the standard error. In quoting the standard error of an estimator’s sampling distribution, you are saying: 'If I were to take repeated samples from the population and use this estimatorfor every sample, my estimate is typically off from the truth by about this much.' Notice again that this is a claim about a procedure, not a particular estimate. The bigger the standard error, the less stable the estimator across different samples, and the less you can trust the estimate for any particular sample." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"In fitting statistical models, we typically equate the trustworthiness of a procedure with its stability under the influence of luck, and we seek to measure the degree to which that procedure might have given a different answer if the forces of randomness had made the world look a bit different. Specifically, the question we seek to answer is: 'if our data set had been different merely due to chance, would our answer have been different, too?'" (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"Model-building requires much more than just technical knowledge of statistical ideas. It also requires care and judgment, and cannot be reduced to a flowchart, a table of formulas, or a tidy set of numerical summaries that wring every last drop of truth from a data set. There is almost never a single 'right' statistical model for some problem. But there are definitely such things as good models and bad models, and learning to tell the difference is important. Just remember: calling a model good or bad requires knowing both the tool and the task." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"[...] complexity sometimes comes at the expense of explanatory power. We must avoid building models calibrated so perfectly to past experience that they do not generalize to future cases." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"It is common to view a statistical model as nothing more than a recipe for calculating the fitted values, and to think that the residuals are just the errors made by this model. But we’ll have a richer picture if instead we view the residuals as part of the model. If you’ve ignored the variation in the residuals, then you really haven’t specified a complete forecast." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"Resampling won’t yield the true sampling distribution of an estimator, but it is often good enough for approximating the standard error (which you’ll remember is just the standard deviation of the sampling distribution). We use the term bootstrapped standard error for the standard deviation of the bootstrapped sampling distribution. The bootstrapped standard error is an estimate of the true standard error." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"Tables are almost always the best way to display categorical data sets with few classifying variables, for the simple reason that they convey a lot of information in a small space." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"The residuals from a regression model are sometimes called 'errors'. This is especially true in experimental science, where measurements of some Y variable will be taken at different values of the X variable (called design points), and where noisy measurement instruments can introduce random errors into theobservations. But in many cases this interpretation of a residual as an error can be misleading. A regression model can still give a nonzero residual, even if there is no mistake in the measurement of the Y variable. It’s often far more illuminating to think of the residual as the part of the Y variable that it is left unpredicted by X." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

📒🅼Walter M Miller Jr. - Collected Quotes

"There is some wisdom, and some foolishness in every people’s way." (Walter M Miller Jr., "The Soul-Empty Ones", 1951)

"Space is my harp, and I touch it lightly with fingers of steel. Space sings." (Walter M. Miller, Jr, "The Big Hunger", 1952)

"A lot of human thinking occurred beneath the level of consciousness, downin the darker regions of the mind where it was not allowed to become conscious lest it bring shame to the thinker. And perhaps he had reasoned it all out in that mental half-world where thoughts are inner ghosts, haunting the possessed man with vague stirrings of uneasiness, leading him into inexplicable behavior." (Walter M Miller Jr, "Way of a Rebel", 1954)

"The machinery of civilization was a living body, with organismic Man as its brain." (Walter M Miller Jr., "Way of a Rebel", 1954)

"The 'romance' of space - drivel written in the old days. When you’re not blasting, you float in a cramped hotbox, crawl through dirty mazes of greasy pipe and cable to tighten a lug, scratch your arms and bark your shins, get sick and choked up because no gravity helps your gullet get the food down." (Walter M Miller Jr., "Death of a Spaceman", 1954)

"A man could change his politics, his friends, his religion, his country, but Men’s tools were a part of his body. Having used a high-powered rifle, the man subsumed the weapon, made it a part of himself. Trading it for a stone axe would be like cutting off his arm. Man was a user of tools, a shaper of environments." (Walter M Miller Jr, "Way of a Rebel", 1954)

"Earth - it was a place where you could stop being afraid, a place where fear of suffocation was not, where fear of blowout was not, where nobody went berserk with the chokers or dreamed of poisoned air or worried about shorthorn cancer or burn blindness or meteorite dust or low-gravity muscular atrophy. A place where there was wind to blow your sweat away." (Walter M Miller Jr, "The Lineman", 1957)

"There were still some meteorites coming in, making bright little winks of fire where they bit into the plain. Deadly stingers out of nowhere, heading nowhere, impartially orbiting, random as rain, random as death. The debris of creation." (Walter M Miller Jr, "The Lineman", 1957)

"Apparently the expectation of humor was enough to produce the illusion of humor, and the comedian could elicit laughter with gesture and expression, regardless of what he said." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959)

"During the last age of reason, certain proud thinkers had claimed that valid knowledge was indestructible - that ideas were deathless and truth immortal." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959)

"Insofar as thought could be governed at all, it could only be commanded to follow what reason affirmed anyhow; command it otherwise and it would not obey." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959)

"It was a species which often considered itself to be, basically, a race of divinely inspired toolmakers; any intelligent entity from Arcturus would instantly have perceived them to be, basically, a race of impassioned after-dinner speech-makers." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959)

"Men must fumble awhile with error to separate it from truth, I think - as long as they don’t seize the error hungrily because it has a pleasanter taste." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959)

"Objective evidence is the ultimate authority. Recorders may lie, but Nature is incapable of it." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959)

"The laws of society are what makes something a crime or not a crime." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959)

📒🆂Robert Silverberg - Collected Quotes

"It was beyond him how someone could voluntarily let himself get involved in this game of dimension-shifting and mutant-battling. But it takes all sorts to make a continuum." (Robert Silverberg, "MUgwump 4" 1959)

"He swung dizzily along the line of time, as he had done so often before. He saw himself, here and here, and saw others, shadow-figures, dream-figures, lurking behind the curtains of time." (Robert Silverberg, "Open the Sky", 1966)

"Forget it. No, don't forget it. Don't forget anything. Take a lesson from it: collect all the data before shouting nonsense." (Robert Silverberg, "The Man in the Maze", 1969)

"The universe is a perilous place. We do our best. Everything else is unimportant." (Robert Silverberg, "The Man in the Maze", 1969)

"You can make no meaningful evaluations of the universe without the confidence that you are seeing it clearly." (Robert Silverberg, "The Man in the Maze", 1969)

 "You have come to the place where all times are one, where all errors can be unmade, where past and future are fluid and subject to redefinition." (Robert Silverberg, "Breckenridge and the Continuum", 1973)

"He didn't have to observe the niceties of etiquette when talking to a computer." (Robert Silverberg, "Born with the Dead", 1974)

"To a dead the whole universe is plastic, nothing’s real, nothing matters a hell of a lot, it’s all only a joke." (Robert Silverberg, "Born with the Dead", 1974)

"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)

"We are born by accident into a purely random universe." (Robert Silverberg, "The Stochastic Man", 1975)

"The only workable time machine ever invented is the science-fiction story." (Robert Silverberg, [introduction] "Trips in Time", 1977)

"The infinite fullness of time brings about everything, he thought: even intelligent lobsters, even a divine octopus." (Robert Silverberg, "Homefaring", 1983)

"Time devours everything. Entire histories vanish. What matters is endurance. The spirit survives and goes onward when the palaces crumble and the kings are forgotten." (Robert Silverberg, "Letters from Atlantis", 1990)

📒🅻Clive S Lewis - Collected Quotes

"This is called the inductive method. Hypothesis, my dear young friend, establishes itself by a cumulative process: or, to use popular language, if you make the same guess often enough it ceases to be a guess and becomes a Scientific Fact." (Clive S Lewis, "The Pilgrim’s Regress: An Allegorical Apology for Christianity, Reason and Romanticism", 1933)

"If you find my arithmetic correct, then no amount of vapouring about my psychological condition can be anything but a waste of time. If you find my arithmetic wrong, then it may be relevant to explain psychologically how I came to be so bad at my arithmetic, and the doctrine of the concealed wish will become relevant - but only after you have yourself done the sum and discovered me to be wrong on purely arithmetical grounds. It is the same with all thinking and all systems of thought. If you try to find out which are tainted by speculating about the wishes of the thinkers, you are merely making a fool of yourself. You must first find out on purely logical grounds which of them do, in fact, break down as arguments. Afterwards, if you like, go on and discover the psychological causes of the error." (Clive S Lewis, "Bulverism", 1941)

"Humans are amphibians - half spirit and half animal. [...] As spirits they belong to the eternal world, but as animals they inhabit time." (Clive S Lewis, "The Screwtape Letters", 1942)

"The Historical Point of View, put briefly, means that when a learned man is presented with any statement in an ancient author, the one question he never asks is whether it is true. He asks who influenced the ancient writer, and how far the statement is consistent with what he said in other books, and what phase in the writer’s development, or in the general history of thought, it illustrates, and how it affected later writers, and how often it has been misunderstood (specially by the learned man’s colleagues) and what the general course of criticism on it has been for the last ten years, and what is the 'present state of the question'. To regard the ancient writer as a possible source of knowledge - to anticipate that what he said could possibly modify your thoughts or your behavior - this would be rejected as unutterably simple-minded. And since we cannot deceive the whole human race all the time, it is most important thus to cut every generation off from all others; for where learning makes a free commerce between the ages there is always the danger that the characteristic errors of one may be corrected by the characteristic truths of another. But thanks be to our Father and the Historical Point of View, great scholars are now as little nourished by the past as the most ignorant mechanic who holds that 'history is bunk." (C. S. Lewis, "The Screwtape Letters", 1942)

"A sum can be put right: but only by going back till you find the error and working it afresh from that point, never by simply going on." (Clive S Lewis, "The Great Divorce", 1945)

"A world of automata – of creatures that worked like machines – would hardly be worth creating." (Clive S Lewis, "Mere Christianity", 1952)

"It is not impossible that our own Model will die a violent death, ruthlessly smashed by an unprovoked assault of new facts […]." (Clive S Lewis, “The Discarded Image: An Introduction to Medieval and Renaissance Literature”, 1964)

"The laws of thought are also the laws of things: of things in the remotest space and the remotest time." (Clive S Lewis, "Christian Reflections", 1967)

“Education without values, as useful as it is, seems rather to make man a more clever devil.” (Clive S Lewis)

"Of course all children's literature is not fantastic, so all fantastic books need not be children's books. It is still possible, even in an age so ferociously anti-romantic as our own, to write fantastic stories for adults: though you will usually need to have made a name in some more fashionable kind of literature before anyone will publish them." (Clive S Lewis)

📒🅲John W Campbell Jr. - Collected Quotes

"Can you appreciate the crushing hopelessness it brought to me? I, who love science, who see in it, or have seen in it, the salvation, the raising of mankind - to see those wondrous machines, of man’s triumphant maturity, forgotten and misunderstood. The wondrous, perfect machines that tended, protected, and cared for those gentle, kindly people who had - forgotten." (John W Campbell Jr, "Twilight", 1934)

"No average mind can either understand or enjoy science-fiction; it takes an amount of imagination beyond the average man." (John W. Campbell Jr, "Science-Fiction", 1938)

"Too darned good a machine can be a menace, not a help." (John W. Campbell Jr, [introduction] "Cloak of Aesir", 1951)

"Science fiction is the literature of the Technological Era. It, unlike other literatures, assumes that change is the natural order of things, that there are goals ahead larger than those we know." (John W Campbell Jr, [introduction to "The Astounding Science Fiction Anthology"] 1952)

"Science is not a sacred cow - but there are a large number of would-be sacred cowherds busily devoting quantities of time, energy and effort to the task of making it one, so they can be sacred cowherds." (John W Campbell Jr, "Prologue to Analog", [introduction] 1962)

"Science fiction is, very strictly and literally, analogous to science facts. It is a convenient analog system for thinking about new scientific, social, and economic ideas - and for re-examining old ideas." (John W Campbell Jr., "Prologue to Analog", 1962)

"That group of writings which is usually referred to as 'mainstream literature' is, actually, a special subgroup of the field of science fiction - for science fiction deals with all places in the Universe, and all times in Eternity, so theliterature of here-and-now is, truly, a subset of science fiction." (John W Campbell Jr, [introduction] Analog I, 1963)

📒🅻Howard P Lovecraft - Collected Quotes

 "I have often wondered if the majority of mankind ever pause to reflect upon the occasionally titanic significance of dreams, and of the obscure world to which they belong. [...] We may guess that in dreams life, matter, and vitality, as the earth knows such things, are not necessarily constant; and that time and space do not exist as our waking selves comprehend them. Sometimes I believe that this less material life is our truer life, and that our vain presence on the terraqueous globe is itself the secondary or merely virtual phenomenon." (Howard P Lovecraft, "Beyond the Wall of Sleep", 1919)

"Ocean is more ancient than the mountains, and freighted with the memories and the dreams of Time." (Howard P Lovecraft, "The White Ship", 1919)

"Hasheesh helped a great deal, and once sent him to a part of space where form does not exist, but where glowing gases study the secrets of existence. And a violet-coloured gas told him that this part of space was outside what he had called infinity. The gas had not heard of planets and organisms before, but identified Kuranes merely as one from the infinity where matter, energy, and gravitation exist." (Howard P Lovecraft, "Celephais", 1922)

"The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the light into the peace and safety of a new dark age." (Howard P Lovecraft, "The Call of Cthulhu", 1926)

"There is a sense of spectral whirling through liquid gulfs of infinity, of dizzying rides through reeling universes on a comet’s tail, and of hysterical plunges from the pit to the moon and from the moon back again to the pit, all livened by a cachinnating chorus of the distorted, hilarious elder gods and the green, bat-winged mocking imps of Tartarus." (Howard P Lovecraft, "The Call of Cthulhu", 1928)

"Non- Euclidean calculus and quantum physics are enough to stretch any brain; and when one mixes them with folklore, and tries to trace a strange background of multi-dimensional reality behind the ghoulish hints of Gothic tales and the wild whispers of the chimney-corner, one can hardly expect to be wholly free from mental tension." (Howard P Lovecraft, "The Dreams in the Witch House and Other Weird Stories", 1933)

"Scientific study and reflection had taught us that the known universe of three dimensions embraces the merest fraction of the whole cosmos of substance and energy. In this case an overwhelming preponderance of evidence from numerous authentic sources pointed to the tenacious existence of certain forces of great power and, so far as the human point of view is concerned, exceptional malignancy." (Howard P Lovecraft, "The Shunned House", 1937)

"Men of broader intellect know that there is no clear distinction between the real and the unreal, that things appear as they seem only by virtue of the delicate physical and mental instruments through which we perceive them." (Howard P Lovecraft)

📒🆅Alfred E van Vogt - Collected Quotes

"There is nothing more futile than arguing with someone who has no basis for his opinions but a vague backlash of emotions." (Alfred E van Vogt, "The Gryb", 1940)

"What system do men follow if not that of logic?" (Algfred E van Vogt, "Vault of the Beast", 1940)

"He knew where the seesaw would stop. It would end in the very remote past, with the release of the stupendous temporal energy he had been accumulating with each of those monstrous swings. He would not witness, but he would cause the formation of the planets." (Alfred E van Vogt, "The Seesaw", 1941)

"Of all the energies in the universe, time is the most potent." (Alfred E van Vogt, "The Seesaw", 1941)

"Amnesia is the best method of escaping from reality." (Alfred E van Vogt, "The Players of Null-A", 1948)

"And the more technically developed a nation or race is, the more cruel, ruthless, predatory, and commercialized its systems tend to become [...]" (Alfred E van Vogt, "The World of Null-A", 1948)

"Words were subtle, and frequently had little connection with the facts they were supposed to represent." (Alfred E van Vogt, "The Players of Null-A", 1948)

"Space was vast, the journeys through it long and lonely, landing always a stimulating experience, with its prospect of new life forms to be seen and studied." (Alfred E van Vogt, "The Monster", 1948)

"It must be that robots predated all other life. It’s the only logical conclusion." (Alfred E van Vogt, "Final Command", 1949)

"When a people lose the courage to resist encroachment on their rights, then they can't be saved by an outside force. Our belief is that people always have the kind of government they want and that individuals must bear the risks of freedom, even to the extent of giving their lives." (Alfred E van Vogt," The Weapon Shops of Isher", 1951)

"Science fiction is a field of writing where, month after month, every printed word implies to hundreds of thousands of people: 'There is change. Look, today's fantastic story is tomorrow's fact.'" (Alfred E van Vogt)

📒🅾George Orwell - Collected Quotes

"The energy that actually shapes the world springs from emotions - racial pride, leader-worship, religious belief, love of war - which liberal intellectuals mechanically write off as anachronisms, and which they have usually destroyed so completely in themselves as to have lost all power of action." (George Orwell, 1941)

"All animals are equal, but some animals are more equal than others." (George Orwell, "Animal Farm: A Fairy Story", 1945)

"The point is that we are all capable of believing things which we know to be untrue, and then, when we are finally proved wrong, impudently twisting the facts so as to show that we were right. Intellectually, it is possible to carry on this process for an indefinite time: the only check on it is that sooner or later a false belief bumps up against solid reality, usually on a battlefield." (George Orwell, "In Front of Your Nose", Tribune, 1946)

"Doublethink means the power of holding two contradictory beliefs in one's mind simultaneously, and accepting both of them." (George Orwell, "1984", 1949)

"Freedom is the freedom to say that two plus two make four. If that is granted, all else follows" (George Orwell, "1984", 1949)

"How could you communicate with the future? It was of its nature impossible. Either the future would resemble the present, in which case it would not listen to him: or it would be different from it, and his predicament would be meaningless." (George Orwell, "1984", 1949)

"If you want to keep a secret you must also hide it from yourself." (George Orwell, "1984", 1949)

"In general, the greater the understanding, the greater the delusion; the more intelligent, the less sane." (George Orwell, "1984", 1949)

"In the long run, a hierarchal society was only possible on a basis of poverty and ignorance." (George Orwell, "1984", 1949)

"It is impossible to found a civilization on fear and hatred and cruelty. It would never endure." (George Orwell, "1984", 1949)

"The best books [...] are those that tell you what you know already." (George Orwell, "1984", 1949)

"Throughout recorded time, and probably since the end of the Neolithic Age, there have been three kinds of people in the world, the High, the Middle, and the Low. They have been subdivided in many ways, they have borne countless different names, and their relative numbers, as well as their attitude toward one another, have varied from age to age; but the essential structure of society has never altered. Even after enormous upheavals and seemingly irrevocable changes, the same pattern has always reasserted itself, just as a gyroscope will always return to equilibrium, however far it is pushed one way or the other." (George Orwell, "1984", 1949)

"We shall meet in the place where there is no darkness." (George Orwell, "1984", 1949)

"Who controls the past [...] controls the future: who controls the present controls the past." (George Orwell, "1984", 1949)

📒 🅱Ray Bradbury - Collected Quotes

"There they go, off to Mars, just for the ride, thinking that they will find a planet like a seer’s crystal, in which to read a miraculous future. What they’ll find, instead, is the somewhat shopworn image of themselves. Mars is a mirror, not a crystal." (Ray Bradbury," A Few Notes on The Martian Chronicles", 1950)

"Coming out of space was like coming out of the most beautiful cathedral they had ever seen." (Ray Bradbury, "The Fire Balloons", 1951)

"The Machine howled. Time was a film run backward. Suns fled and ten million moons fled after them." (Ray Bradbury, "A Sound of Thunder", 1952)

"A book is a loaded gun in the house next door." (Ray Bradbury, "Fahrenheit 451", 1953)

"Books were only one type of receptacle where we stored a lot of things we were afraid we might forget. There is nothing magical in them, at all. The magic is only in what books say, how they stitched the patches of the universe together into one garment for us." (Ray Bradbury, "Fahrenheit 451", 1953)

"The books say nothing! Nothing you can teach or believe. They’re about nonexistent people, figments of imagination, if they’re fiction. And if they’re nonfiction, it’s worse, one professor calling another an idiot, one philosopher screaming down another’s gullet." (Ray Bradbury, "Fahrenheit 451", 1953)

"They are so confident that they will run on forever. But they won’t run on. They don’t know that this is all one huge big blazing meteor that makes a pretty fire in space, but that some day it’ll have to hit." (Ray Bradbury, "Fahrenheit 451", 1953)

"We must all be alike. Not everyone born free and equal, as the Constitution says, but everyone made equal. Each man the image of every other; then all are happy, for there are no mountains to make them cower, to judge themselves against." (Ray Bradbury, "Fahrenheit 451", 1953) 

"What traitors book can be! you think they’re backing you up, and they turn on you." (Ray Bradbury, "Fahrenheit 451", 1953)

"You don't have to burn books to destroy a culture. Just get people to stop reading them." (Ray Bradbury, "Fahrenheit 451", 1953)

"The universe is full of matter and force. Yet in all that force, amongst all the bulks and gravities, the rains of cosmic light, the bombardment of energy - how little spirit, how small the decimal points of intelligence." (Ray Bradbury et al, "Mars and the Mind of Man", 1973)

"Life is a magic show or should be if people didn’t go to sleep on each other. Always leave folks with a bit of mystery." (Ray Bradbury, "Colonel Stonesteel’s Genuine Home-Made Truly Egyptian Mummy", 1981)

"That’s all science fiction was ever about. Hating the way things are, wanting to make things different." (Ray Bradbury, "No News, or, What Killed the Dog?", 1994)

"Do you know why teachers use me? Because I speak in tongues. I write metaphors. Every one of my stories is a metaphor you can remember. The great religions are all metaphor. We appreciate things like Daniel and the lion's den, and the Tower of Babel. People remember these metaphors because they are so vivid you can't get free of them and that's what kids like in school." (Ray Bradbury, The Paris Review, [interview] 2010)

"At base, science is no more than an investigation of a miracle we can never explain, and art is an interpretation of that miracle." (Ray Bradbury)