🥀On Grace (Trivia)

"[Intuitive] Understanding is consequent upon deliberation, and firmly embraces the better part. For [intuitive] understanding concerns itself with divine truths, and the relish, love, and observance of the latter constitutes true wisdom. Rather than being the [mere] product of nature, these successive steps are the result of grace. The latter, according to its own free determination, derives the various rivulets of the sciences and wisdom from the fountainhead of sense perception. Grace reveals hidden divine truths by means of those things which have been made, and by that unity which belongs to love, communicates what it has made manifest, thus uniting man to God." (, "Metalogicon", 1159)

*Orators and Philosophers treat Nature after a very different manner […] with all her graces and ornaments, and if there be anything which is not capable of that, they dissemble it, or pass it over slightly. But Philosophers view Nature with a more impartial eye, and without favor or prejudice give a just and free account [of] how they find all the parts of the Universe, some more, some less perfect." (Thomas Burnet,"The Sacred Theory of the Earth" 2nd ed.,1691)

"In order to depict nature in its exalted sublimity, we st not dwell exclusively on its external manifestations, but we must trace its image, reflected in the mind of man, at one time filling the dreamy land of physical myths with forms of grace and beauty, and at another developing the noble germ of artistic creations." (Alexander von Humboldt, "Cosmos: A Sketch of a Physical Description of the Universe" Vol. 2, 1869)

"[...] science gives Man from time to time a greatly increased mastery over Nature; science, with its analytical triumphs, ever tends to diminish, in the shallowminded, the saving grace of wonder; and science is ever dispelling the darkness that oppresses the mind." (J Arthur Thomson, "The System of Animate Nature" Vol 1, 1920) 

"What the world needs is a fusion of the sciences and the humanities. The humanities express the symbolic, poetic, and prophetic qualities of the human spirit. Without them we would not be conscious of our history; we would lose our aspirations and the grace of expression that move men’s hearts. The sciences express the creative urge in man to construct a universe which is comprehensible in terms of the human intellect. Without them, mankind would find itself bewildered in a world of natural forces beyond comprehension, victims of ignorance, superstition and fear." (Isidor I Rabi, [address] 1954)

"There was a moment when I knew how nature worked. It had elegance and beauty. The goddam thing was gleaming." (Paul K Feyerabend, 1967)

"Ever bigger machines, entailing ever bigger concentrations of economic power and exerting ever greater violence against the environment, do not represent progress: they are a denial of wisdom. Wisdom demands a new orientation of science and technology towards the organic, the gentle, the non-violent, the elegant and beautiful." (Ernst F Schumacher,"Small Is Beautiful", 1973)

"While Occam’s razor is a useful tool in the physical sciences, it can be a very dangerous implement in biology. It is thus very rash to use simplicity and elegance as a guide in biological research." (Francis H C Crick, "What Mad Pursuit: A Personal View of Scientific Discovery", 1988) 

"We move from part to whole and back again, and in that dance of comprehension, in that amazing circle of understanding, we come alive to meaning, to value, and to vision: the very circle of understanding guides our way, weaving together the pieces, healing the fractures, mending the torn and tortured fragments, lighting the way ahead - this extraordinary movement from part to whole and back again, with healing the hallmark of each and every step, and grace the tender reward." (Ken Wilber, "The Eye of Spirit: An Integral Vision for a World Gone Slightly Mad", 1997)

🥀On Grace in Mathematics

"The mathematician is perfect only in so far as he is a perfect man, in so far as he senses in himself the beauty of truth; only then will his work be thorough, transparent, prudent, pure, clear, graceful, indeed elegant." (Johann Wolfgang von Goethe, 1829)

"Proportion, or symmetry, is the basis of beauty; propriety, of grace." (Henry Fuseli [in "The Life and Writings of Henry Fuseli", 1831])

"It [mathematics] is in the inner world of pure thought, where all entia dwell, where is every type of order and manner of correlation and variety of relationship, it is in this infinite ensemble of eternal verities whence, if there be one cosmos or many of them, each derives its character and mode of being, - it is there that the spirit of mathesis has its home and its life. [/] Is it a restricted home, a narrow life, static and cold and grey with logic, without artistic interest, devoid of emotion and mood and sentiment? That world, it is true, is not a world of solar light, not clad in the colours that liven and glorify the things of sense, but it is an illuminated world, and over it all and everywhere throughout are hues and tints transcending sense, painted there by radiant pencils of psychic light, the light in which it lies. It is a silent world, and, nevertheless, in respect to the highest principle of art - the interpenetration of content and form, the perfect fusion of mode and meaning - it even surpasses music. In a sense, it is a static world, but so, too, are the worlds of the sculptor and the architect. The figures, however, which reason constructs and the mathematic vision beholds, transcend the temple and the statue, alike in simplicity and in intricacy, in delicacy and in grace, in symmetry and in poise. Not only are this home and this life thus rich in aesthetic interests, really controlled and sustained by motives of a sublimed and supersensuous art, but the religious aspiration, too, finds there, especially in the beautiful doctrine of invariants, the most perfect symbols of what it seeks - the changeless in the midst of change, abiding things hi a world of flux, configurations that remain the same despite the swirl and stress of countless hosts of curious transformations." (Cassius J Keyser, "The Universe and Beyond", Hibbert Journal, 1904-1906)

"Geometry, whatever others may think, is the study of different shapes, many of them very beautiful, having harmony, grace and symmetry. […] Most of us, if we can play chess at all, are content to play it on a board with wooden chess pieces; but there are some who play the game blindfolded and without touching the board. It might be a fair analogy to say that abstract geometry is like blindfold chess – it is a game played without concrete objects." (Edward Kasner & James R Newman, "New Names for Old", 1940)

"When you are told that something is an average you still don't know very much about it unless you can find out which of the common kinds of average it is-mean, median, or mode. [...] The different averages come out close together when you deal with data, such as those having to do with many human characteristics, that have the grace to fall close to what is called the normal distribution. If you draw a curve to represent it you get something shaped like a bell, and mean, median, and mode fall at the same point." (Darell Huff, "How to Lie with Statistics", 1954)

"The theory of the visual display of quantitative information consists of principles that generate design options and that guide choices among options. The principles should not be applied rigidly or in a peevish spirit; they are not logically or mathematically certain; and it is better to violate any principle than to place graceless or inelegant marks on paper. Most principles of design should be greeted with some skepticism, for word authority can dominate our vision, and we may come to see only though the lenses of word authority rather than with our own eyes." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"Music and higher mathematics share some obvious kinship. The practice of both requires a lengthy apprenticeship, talent, and no small amount of grace. Both seem to spring from some mysterious workings of the mind. Logic and system are essential for both, and yet each can reach a height of creativity beyond the merely mechanical." (Frederick Pratter, "How Music and Math Seek Truth in Beauty", Christian Science Monitor, 1995)