🪷On Mind: On Reasoning (1750-1799)

"Especially when we investigate the general laws of Nature, induction has very great power; & there is scarcely any other method beside it for the discovery of these laws. By its assistance, even the ancient philosophers attributed to all bodies extension, figurability, mobility, & impenetrability; & to these properties, by the use of the same method of reasoning, most of the later philosophers add inertia & universal gravitation. Now, induction should take account of every single case that can possibly happen, before it can have the force of demonstration; such induction as this has no place in establishing the laws of Nature. But use is made of an induction of a less rigorous type ; in order that this kind of induction may be employed, it must be of such a nature that in all those cases particularly, which can be examined in a manner that is bound to lead to a definite conclusion as to whether or no the law in question is followed, in all of them the same result is arrived at; & that these cases are not merely a few. Moreover, in the other cases, if those which at first sight appeared to be contradictory, on further & more accurate investigation, can all of them be made to agree with the law; although, whether they can be made to agree in this way better than in any Other whatever, it is impossible to know directly anyhow. If such conditions obtain, then it must be considered that the induction is adapted to establishing the law." (Roger J Boscovich, "De Lege Continuitatis" ["On the law of continuity"], 1754)

"We think only through the medium of words. Languages are true analytical methods. Algebra, which is adapted to its purpose in every species of expression, in the most simple, most exact, and best manner possible, is at the same time a language and an analytical method. The art of reasoning is nothing more than a language well arranged." (Abbé de Condillac, "System of Logic", cca. 1781)

 "The mathematician pays not the least regard either to testimony or conjecture, but deduces everything by demonstrative reasoning, from his definitions and axioms. Indeed, whatever is built upon conjecture, is improperly called science; for conjecture may beget opinion, but cannot produce knowledge." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

"In every chain of reasoning, the evidence of the last conclusion can be no greater than that of the weakest link of the chain, whatever may be the strength of the rest." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

"In mathematics it [sophistry] had no place from the beginning: Mathematicians having had the wisdom to define accurately the terms they use, and to lay down, as axioms, the first principles on which their reasoning is grounded. Accordingly we find no parties among mathematicians, and hardly any disputes." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

"In metaphysical reasoning, the process is always short. The conclusion is but a step or two, seldom more, from the first principles or axioms on which it is grounded, and the different conclusions depend not one upon another.

"It is otherwise in mathematical reasoning. Here the field has no limits. One proposition leads on to another, that to a third, and so on without end. If it should be asked, why demonstrative reasoning has so wide a field in mathematics, while, in other abstract subjects, it is confined within very narrow limits, I conceive this is chiefly owing to the nature of quantity, […] mathematical quantities being made up of parts without number, can touch in innumerable points, and be compared in innumerable different ways." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

"The mathematician pays not the least regard either to testimony or conjecture, but deduces everything by demonstrative reasoning, from his definitions and axioms. Indeed, whatever is built upon conjecture, is improperly called science; for conjecture may beget opinion, but cannot produce knowledge." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

"The reader will find no figures in this work. The methods which I set forth do not require either constructions or geometrical or mechanical reasonings: but only algebraic operations, subject to a regular and uniform rule of procedure." (Joseph-Louis de Lagrange, "Mechanique Analytique", 1788)

 "The only method of preventing such errors from taking place, and of correcting them when formed, is to restrain and simplify our reasoning as much as possible. This depends entirely upon ourselves, and the neglect of it is the only source of our mistakes." " (Antoine-Laurent de Lavoisier, "Elements of Chemistry in a New Systematic Order", 1790)

 "We think only through the medium of words. Languages are true analytical methods. Algebra, which is adapted to its purpose in every species of expression, in the most simple, most exact, and best manner possible, is at the same time a language and an analytical method. The art of reasoning is nothing more than a language well arranged." (Antoine-Laurent Lavoisier,"Elements of Chemistry", 1790)

"We must trust to nothing but facts: These are presented to us by Nature, and cannot deceive. We ought, in every instance, to submit our reasoning to the test of experiment, and never to search for truth but by the natural road of experiment and observation." (Antoin-Laurent de Lavoisiere, "Elements of Chemistry", 1790)

[...] mathematicians obtain the solution of a problem by the mere arrangement of data, and by reducing their reasoning to such simple steps, to conclusions so very obvious, as never to lose sight of the evidence which guides them." (Antoine-Laurent Lavoisier, "Elements of Chemistry In a New Systematic Order", 1790)

We must trust to nothing but facts: These are presented to us by Nature, and cannot deceive. We ought, in every instance, to submit our reasoning to the test of experiment, and never to search for truth but by the natural road of experiment and observation." (Antoine Lavoisier, "Elements of Chemistry", 1790)

We ought, in every instance, to submit our reasoning to the test of experiment, and never to search for truth but by the natural road of experiment and observation." (Antoine-Laurent Lavoisier, "Elements of Chemistry in a New Systematic Order", 1790)

In mathematics, such processes [of reasoning] are much longer than in any other science; and hence the study of it is peculiarly calculated to strengthen the power of steady and concatenated thinking, - a power which, in all the pursuits of life, whether speculative or active, is one of the most valuable endowments we can possess. This command of attention, however, it may be proper to add, is to be acquired, not by the practice of modern methods, but by the study of Greek geometry, more particularly, by accustoming ourselves to pursue long trains of demonstration, without availing ourselves of the aid of any sensible diagrams; the thoughts being directed solely by those ideal delineations which the powers of conception and of memory enable us to form." (Dugald Stewart, "Elements of the Philosophy of the Human Mind", 1792)

"Whoever limits his exertions to the gratification of others, whether by personal exhibition, as in the case of the actor and of the mimic, or by those kinds of literary composition which are calculated for no end but to please or to entertain, renders himself, in some measure, dependent on their caprices and humours. The diversity among men, in their judgments concerning the objects of taste, is incomparably greater than in their speculative conclusions; and accordingly, a mathematician will publish to the world a geometrical demonstration, or a philosopher, a process of abstract reasoning, with a confidence very different from what a poet would feel, in communicating one of his productions even to a friend." (Dugald Stewart, "Elements of the Philosophy of the Human Mind", 1792)

🪷On Mind: On Reason (1725-1749)

"For chemistry is no science form’d à priori; ’tis no production of the human mind, framed by reasoning and deduction: it took its rise from a number of experiments casually made, without any expectation of what follow’d; and was only reduced into an art or system, by collecting and comparing the effects of such unpremeditated experiments, and observing the uniform tendency thereof. So far, then, as a number of experimenters agree to establish any undoubted truth; so far they may be consider'd as constituting the theory of chemistry." (Hermann Boerhaave, "A New Method of Chemistry", 1727)

"[…] our reasonings about the wonderful and intricate operations of Nature are so full of uncertainty, that, as the wise-man truly observes, hardly do we guess aright at the things that are upon earth, and with labour do we find the things that are before us." (Stephen Hales, "Vegetable Staticks", 1727)

"It hath been an old remark, that Geometry is an excellent Logic. And it must be owned that when the definitions are clear; when the postulata cannot be refused, nor the axioms denied; when from the distinct contemplation and comparison of figures, their properties are derived, by a perpetual well-connected chain of consequences, the objects being still kept in view, and the attention ever fixed upon them; there is acquired a habit of reasoning, close and exact and methodical; which habit strengthens and sharpens the mind, and being transferred to other subjects is of general use in the inquiry after truth." (George Berkeley, "The Analyst; Or, A Discourse Addressed to an Infidel Mathematician", 1734)

"All the perceptions of the human mind resolve themselves into two distinct kinds, which I shall call impressions and ideas. The difference betwixt these consists in the degrees of force and liveliness, with which they strike upon the mind, and make their way into our thought or consciousness. Those perceptions, which enter with most force and violence, we may name impressions; and under this name I comprehend all our sensations, passions and emotions, as they make their first appearance in the soul. By ideas I mean the faint images of these in thinking and reasoning. I believe it will not be very necessary to employ many words in explaining this distinction." (David Hume, "A Treatise of Human Nature", 1738)

"But to form the idea of an object, and to form an idea simply is the same thing; the reference of the idea to an object being an extraneous denomination, of which in itself it bears no mark or character. Now as it is impossible to form an idea of an object, that is possessed of quantity and quality, and yet is possessed of no precise degree of either; it follows, that there is an equal impossibility of forming an idea, that is not limited and confined in both these particulars. Abstract ideas are therefore in themselves individual, however they may become general in their representation. The image in the mind is only that of a particular object, though the application of it in our reasoning be the same, as if it were universal." (David Hume, "Treatise of Human Nature", 1738)

 "Do not expect to arrive at certainty in every subject which you pursue. There are a hundred things wherein we mortals […] must be content with probability, where our best light and reasoning will reach no farther." (Isaac Watts," The Improvement of the Mind", 1741) 

 "It is not therefore the business of philosophy, in our present situation in the universe, to attempt to take in at once, in one view, the whole scheme of nature; but to extend, with great care and circumspection, our knowledge, by just steps, from sensible things, as far as our observations or reasonings from them will carry us, in our enquiries concerning either the greater motions and operations of nature, or her more subtile and hidden works." (Colin Maclaurin, "An Account of Sir Isaac Newton's Philosophical Discoveries, in Four Books", 1748)

It seems evident, that men are carried, by a natural instinct or prepossession, to repose faith in their senses; and that, without any reasoning, or even almost before the use of reason, we always suppose an external universe, which depends not on our perception, but would exist, though we and every sensible creature were absent or annihilated. […] It seems also evident, that, when men follow this blind and powerful instinct of nature, they always suppose the very images, presented by the senses, to be the external objects." (David Hume, "An Enquiry Concerning Human Understanding", 1748)

There is no method of reasoning more common, and yet none more blameable, than, in philosophical disputes, to endeavour the refutation of any hypothesis, by a pretence of its dangerous consequences to religion and morality. When any opinion leads to absurdities, it is certainly false; but it is not certain that an opinion is false, because it is of dangerous consequence. Such topics, therefore, ought entirely to be forborne; as serving nothing to the discovery of truth, but only to make the person of an antagonist odious." (David Hume, "An Enquiry Concerning Human Understanding", 1748) 

🪷On Mind: On Reason (1700-1724)

"The mathematics are the friends to religion, inasmuch as they charm the passions, restrain the impetuosity of the imagination, and purge the mind from error and prejudice. Vice is error, confusion and false reasoning; and all truth is more or less opposite to it. Besides, mathematical truth may serve for a pleasant entertainment for those hours which young men are apt to throw away upon their vices; the delightfulness of them being such as to make solitude not only easy but desirable." (John Arbuthnot, "An Essay on the Usefulness of Mathematical Learning", 1701)

"[…] even if someone refuses to admit infinite and infinitesimal lines in a rigorous metaphysical sense and as real things, he can still use them with confidence as ideal concepts" (notions ideales) which shorten his reasoning, similar to what we call imaginary roots in the ordinary algebra, for example, v-2." (Gottfried W Leibniz, [letter to Varignon], 1702)

“It is easy to perceive that the prodigious variety which appears both in the works of nature and in the actions of men, and which constitutes the greatest part of the beauty of the universe, is owing to the multitude of different ways in which its several parts are mixed with, or placed near, each other. But, because the number of causes that concur in producing a given event, or effect, is oftentimes so immensely great, and the causes themselves are so different one from another, that it is extremely difficult to reckon up all the different ways in which they may be arranged, or combined together, it often happens that men, even of the best understandings and the greatest circumspection, ale guilty of that fault in reasoning which the writers on logic call the insufficient, or imperfect enumeration of parts, or cases: insomuch that I will venture to assert, that this is the chief, and almost the only, source of the vast number of erroneous opinions, and those too very often in matters of great importance, which we are apt to form on all the subjects we reflect upon, whether they relate to the knowledge of nature, or the merits and motives of human actions. It must therefore be acknowledged, that that art which affords a cure to this weakness, or defect, of our understandings, and teaches us so to enumerate all the possible ways in which a given number of things may be mixed and combined together, that we may be certain that we have not omitted any one arrangement of them that can lead to the object of our inquiry, deserves to be considered as most eminently useful and worthy of our highest esteem and attention. And this is the business of the art, or doctrine of combinations." (Jakob Bernoulli,"Ars Conjectandi" [“The Art of Conjecturing"], 1713) 

"[...] this subject] has a relation to almost every species of useful knowledge that the mind of man can be employed upon." (Jacob Bernoulli,"Ars Conjectandi"[“The Art of Conjecturing"], 1713)

"There are two kinds of truths: those of reasoning and those of fact. The truths of reasoning are necessary and their opposite is impossible; the truths of fact are contingent and their opposites are possible." (Gottfried W Leibniz, "Monadology", 1714)

“Reasoning will never make a Man correct an ill Opinion, which by Reasoning he never acquired." ( Jonathan Swift,"A Letter to a Young Gentleman, Lately Enter’d Into Holy Orders by a Person of Quality", 1721)

🪷On Mind: On Reasoning (1600-1699)

"The long chains of simple and easy reasonings by means of which geometers are accustomed to reach the conclusions of their most difficult demonstrations, had led me to imagine that all things, to the knowledge of which man is competent, are mutually connected in the same way, and that there is nothing so far removed from us as to be beyond our reach, or so hidden that we cannot discover it, provided only we abstain from accepting the false for the true, and always preserve in our thoughts the order necessary for the deduction of one truth from another." (René Descartes, "Discourse on the Method", 1637)

"So there arise two kinds of variation: complexion [combinations] and situs [permutations]. And viewed in themselves, both complexion and situs belong to metaphysics, or to the science of whole and parts. If we look at their variability, however, that is, at the quantity of variation, we must turn to numbers and to arithmetic. I am inclined to think that the science of complexions pertains more to pure arithmetic, and that of situs to an arithmetic of figure." (Gottfried Leibniz,"Dissertatio de arte combinatoria" [“Dissertation on the Art of Combinations"], Leipzig, 1666)

"It is obvious that if we could find characters or signs suited for expressing all our thoughts as clearly and as exactly as arithmetic expresses numbers or geometry expresses lines, we could do in all matters, insofar as they are subject to reasoning, all that we can do in arithmetic and geometry." (Gottfried W Leibniz, 1677)

" Mathematics in gross, it is plain, are a grievance in natural philosophy, and with reason: for mathematical proofs, like diamonds, are hard as well as clear, and will be touched with nothing but strict reasoning. Mathematical proofs are out of the reach of topical arguments; and are not to be attacked by the equivocal use of words or declaration, that make so great a part of other discourses, - nay, even of controversies." (John Locke, "An Essay Concerning Human Understanding", 1690)

“Even the wisest and most prudent people often suffer from what Logicians call insufficient enumeration of cases." (Jacob Bernoulli , 1692)

"The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc’d to a Mathematical Reasoning; and when they cannot it’s a sign our knowledge of them is very small and confus’d; and when a Mathematical Reasoning can be had it’s as great a folly to make use of any other, as to grope for a thing in the dark, when you have a Candle standing by you." (John Arbuthnot, "Of the Laws of Chance", 1692)

🪷On Mind: On Reasoning (600-1499)

"To master this instrument the religious thinker must make a preliminary study of logic, just as the lawyer must study legal reasoning. This is no more heretical in the one case than in the other." (Averroes, "The Decisive Treatise", 1178)

"Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth, unless the mind discovers it by the path of experience.(Roger Bacon, "Opus Majus", cca. 1267)

"There are two modes of acquiring knowledge, namely, by reasoning and experience. Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth unless the mind discovers it by the path of experience." (Roger Bacon, Opus Majus", 1267)

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

"Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence." (Ibn Khaldun, cca. 14th century)

"Among all the studies of natural causes and reasoning, Light chiefly delights the beholder; and among the great features of mathematics the certainty of its demonstrations is what preeminently tends to elevate the mind of the investigator: Perspective, therefore, might be preferred to all the discourses and systems of the human learning." (Leonardo da Vinci, 1497)

🪷On Mind: On Reasoning (-599)

"Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it." (Eudoxus, cca. 4th c. BC)

"But in synthesis, reversing the process, we start from the point which we reached last of all in the analysis, from the thing already known or admittedly true. We derive from it what preceded it in the analysis, and go on making derivations until, retracing our steps, we finally succeed in arriving at what is required. This procedure we call synthesis, or constructive solution, or progressive reasoning." (Pappus of Alexandria, cca. 4th c. BC)

"In analysis, we start from what is required, we take it for granted, and we draw consequences from it, and consequences from the consequences, till we reach a point that we can use as starting point in synthesis. For in analysis we assume what is required to be done as already done" (what is sought as already found, what we have to prove as true). We inquire from what antecedent the desired result could be derived; then we inquire again what could be the antecedent of that antecedent, and so on, until passing from antecedent to antecedent, we come eventually upon something already known or admittedly true. This procedure we call analysis, or solution backwards, or regressive reasoning." (Pappus of Alexandria, cca. 4th c. BC)

"It is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician demonstrative proofs." (Aristotle, cca. 4th c. BC)

"Thus, of all the honorable arts, which are carried out either naturally or proceed in imitation of nature, geometry takes the skill of reasoning as its field. It is hard at the beginning and difficult of access, delightful in its order, full of beauty, unsurpassable in its effect. For with its clear processes of reasoning it illuminates the field of rational thinking, so that it may be understood that geometry belongs to the arts or that the arts are from geometry." (Agennius Urbicus,"Controversies about Fields", cca. 4th c. BC)

[...] so external sensation is the image of this perception of the soul, which is in its essence truer and is a contemplation of forms alone without being affected. From these forms, from which the soul alone receives its lordship over the living being, come reasonings, and opinions and noetic acts; and this is precisely where ‘we’ are." (Plotinus, "Enneads", cca. 270 AD)

📁On Data: On Clusters

"The logarithmic transformation serves several purposes: (1) The resulting regression coefficients sometimes have a more useful theoretical interpretation compared to a regression based on unlogged variables. (2) Badly skewed distributions - in which many of the observations are clustered together combined with a few outlying values on the scale of measurement - are transformed by taking the logarithm of the measurements so that the clustered values are spread out and the large values pulled in more toward the middle of the distribution. (3) Some of the assumptions underlying the regression model and the associated significance tests are better met when the logarithm of the measured variables is taken." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"Exploratory data analysis (EDA) is a collection of techniques that reveal (or search for) structure in a data set before calculating any probabilistic model. Its purpose is to obtain information about the data distribution (univariate or multivariate), about the presence of outliers and clusters, to disclose relationships and correlations between objects and/or variables." (Ildiko E  Frank & Roberto Todeschini, "The Data Analysis Handbook", 1994)

"While classification is important, it can certainly be overdone. Making too fine a distinction between things can be as serious a problem as not being able to decide at all. Because we have limited storage capacity in our brain (we still haven't figured out how to add an extender card), it is important for us to be able to cluster similar items or things together. Not only is clustering useful from an efficiency standpoint, but the ability to group like things together (called chunking by artificial intelligence practitioners) is a very important reasoning tool. It is through clustering that we can think in terms of higher abstractions, solving broader problems by getting above all of the nitty-gritty details." (Joseph P Bigus,"Data Mining with Neural Networks: Solving business problems from application development to decision support", 1996)

"Data clusters are everywhere, even in random data. Someone who looks for an explanation will inevitably find one, but a theory that fits a data cluster is not persuasive evidence. The found explanation needs to make sense and it needs to be tested with uncontaminated data." (Gary Smith, "Standard Deviations", 2014)

"The general design choice of hierarchical aggregation is to construct the derived data of a hierarchical clustering of items in the original dataset and allow the user to interactively control the level of detail to show based on this hierarchy."  (Tamara Munzner, "Visualization Analysis and Design", 2014)

"Cluster analysis refers to the grouping of observations so that the objects within each cluster share similar properties, and properties of all clusters are independent of each other. Cluster algorithms usually optimize by maximizing the distance among clusters and minimizing the distance between objects in a cluster. Cluster analysis does not complete in a single iteration but goes through several iterations until the model converges. Model convergence means that the cluster memberships of all objects converge and don’t change with every new iteration." (Danish Haroon, "Python Machine Learning Case Studies", 2017)

"A form of machine learning in which the goal is to identify regularities in the data. These regularities may include clusters of similar instances within the data or regularities between attributes. In contrast to supervised learning, in unsupervised learning no target attribute is defined in the data set." (John D Kelleher & Brendan Tierney, "Data science", 2018)

"Unsupervised learning or clustering is a way of discovering hidden structures in unlabeled data. Clustering algorithms aim to discover latent patterns in unlabeled data using features to organize instances into meaningfully dissimilar groups." (Benjamin Bengfort et al, "Applied Text Analysis with Python: Enabling Language-Aware Data Products with Machine Learning", 2018)

📓On Literature: On Hallucinations (From Fiction to Science-Fiction)

"Kings are not born: they are made by artificial hallucination." (George B Shaw, "Man and Superman", 1903)

"It must be, I thought, one of the race's most persistent and comforting hallucinations to trust that 'it can't happen here' - that one's own time and place is beyond cataclysm." (John Wyndham, "The Day of the Triffids", 1951)

"An hallucination is not, strictly speaking, manufactured in the brain; it is received by the brain, like any 'real' sense datum, and the patient act in response to this to-him-very-real perception of reality in as logical a way as we do to our sense data. In any way to suppose he only 'thinks he sees it' is to misunderstand totally the experience of psychosis."" (Philip K. Dick, "Drugs, Hallucinations, and the Quest for Reality", 1964)

"Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts. [...] A graphic representation of data abstracted from banks of every computer in the human system. Unthinkable complexity. Lines of light ranged in the nonspace of the mind, clusters and constellations of data." (William Gibson, "Neuromancer", 1984)

"He’d used decks in school, toys that shuttled you through the infinite reaches of that space that wasn’t space, mankind’s unthinkably complex consensual hallucination, the matrix, cyberspace, where the great corporate hotcores burned like neon novas, data so dense you suffered sensory overload if you tried to apprehend more than the merest outline." (William Gibson, "Count Zero", 1986)

📓On Literature: On Cyberspace (From Fiction to Science-Fiction)

"Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts. [...] A graphic representation of data abstracted from banks of every computer in the human system. Unthinkable complexity. Lines of light ranged in the nonspace of the mind, clusters and constellations of data." (William Gibson, "Neuromancer", 1984)

"He’d used decks in school, toys that shuttled you through the infinite reaches of that space that wasn’t space, mankind’s unthinkably complex consensual hallucination, the matrix, cyberspace, where the great corporate hotcores burned like neon novas, data so dense you suffered sensory overload if you tried to apprehend more than the merest outline." (William Gibson, "Count Zero", 1986) 

"In cyberspace, she noted, there are no shadows." (William Gibson, "Mona Lisa Overdrive", 1988)

"All I knew about the word 'cyberspace'when I coined it, was that it seemed like an effective buzzword. It seemed evocative and essentially meaningless. It was suggestive of something, but had no real semantic meaning, even for me, as I saw it emerge on the page." (William Gibson, No Maps for These Territories", 2000)

"Although personally, I think cyberspace means the end of our species." (Michael Crichton, "The Lost World: A Novel", 2001)

"We need to bridge our sense of loneliness and disconnection with a sense of community and continuity even if we must manufacture it from our time on the Web and our use of calling cards to connect long distance. We must log on somewhere, and if it is only in cyberspace, that is still far better than nowhere at all." (Julia Cameron, "God is No Laughing Matter", 2001)

"That's how it is online - there's no time in cyberspace. It's almost like everything physical evaporates, and it's just your mind and the different sites floating in a void." (Tim Tharp, "The Spectacular Now", 2008)

🌌On Cosmology: On Planets (1850-1899)

"The circle is one of the noblest representation of the Deity, in his noble works of human nature. It bounds, determines, governs, and dictates bounds, dictates space, bounds latitude and longitude, refers to space, the sun, moon, and all the planets, in direction, brings to the mind thoughts of eternity, and concentrates the mind to imagine for itself the distance and space it comprehends. It rectifies all boundaries; it is the key to information of the knowledge of God." (John Davis, "The Measure of the Circle", 1854)

"The genuine spirit of Mathesis is devout. No intellectual pursuit more truly leads to profound impressions of the existence and attributes of a Creator, and to a deep sense of our filial relations to him, than the study of these abstract sciences. Who can understand so well how feeble are our conceptions of Almighty Power, as he who has calculated the attraction of the sun and the planets, and weighed in his balance the irresistible force of the lightning? Who can so well understand how confused is our estimate of the Eternal Wisdom, as he who has traced out the secret laws which guide the hosts of heaven, and combine the atoms on earth? Who can so well understand that man is made in the image of his Creator, as he who has sought to frame new laws and conditions to govern imaginary worlds, and found his own thoughts similar to those on which his Creator has acted?" (Thomas Hill, "The Imagination in Mathematics", The North American Review Vol. 85 (176), 1857)

"SYSTEM (σύστημα, σύν ἵστημιavu, to place together) - is a full and connected view of all the truths of some department of knowledge. An organized body of truth, or truths arranged under one and the same idea, which idea is as the life or soul which assimilates all those truths. No truth is altogether isolated. Every truth has relation to some other. And we should try to unite the facts of our knowledge so as to see them in their several bearings. This we do when we frame them into a system. To do so legitimately we must begin by analysis and end with synthesis. But system applies not only to our knowledge, but to the objects of our knowledge. Thus we speak of the planetary system, the muscular system, the nervous system. We believe that the order to which we would reduce our ideas has a foundation in the nature of things. And it is this belief that encourages us to reduce our knowledge of things into systematic order. The doing so is attended with many advantages. At the same time a spirit of systematizing may be carried too far. It is only in so far as it is in accordance with the order of nature that it can be useful or sound." (William Fleming, "Vocabulary of philosophy, mental, moral, and metaphysical; with quotations and references; for the use of students", 1857) 

"The pursuit of mathematical science makes its votary appear singularly indifferent to the ordinary interests and cares of men. Seeking eternal truths, and finding his pleasures in the realities of form and number, he has little interest in the disputes and contentions of the passing hour. His views on social and political questions partake of the grandeur of his favorite contemplations, and, while careful to throw his mite of influence on the side of right and truth, he is content to abide the workings of those general laws by which he doubts not that the fluctuations of human history are as unerringly guided as are the perturbations of the planetary hosts." (Thomas Hill, "The Imagination in Mathematics", The North American Review Vol. 85 (176), 1857)

"Although the astronomer has achieved many successes in studying comets, yet these objects still remain outside the surveyed fields of astronomy - now, as in the old days when men spoke of sun and moon, planet and stars, as including all the members of the heavenly host." (Richard A Proctor, "The Twentieth Century, Whence Came the Comets?", Vol. 29 (111), 1886)