Emergent Order

"The infinite variety of forms which we observe in the realm of organic life not only delight our senses with their beauty and diversity, but also excite our curiosity, in suggesting the problem of their origin and connection. [...] The unity of the organic structure, which expresses itself everywhere in the fundamental features of living things and in the chemical composition and constructive power of their plasm, is also seen in the laws of symmetry in their typical forms. [...] In the protists … the constructive force of the elementary organism, the individual cell, determines the symmetry of the typical form and the special form of its supplementation; but in the histons … it is the plasticity of the tissue, made up of a number of socially combined cells, that determines this. [...] All the various fundamental forms that can be distinguished and defined mathematically are found realized in the graceful flinty skeletons of these unicellular sea-dwelling protozoa. [...] The great majority of organic bodies show a certain regularity both in their outer configuration and the construction of their various parts, which we may call ‘symmetry’ in the wider sense of the word. [...] These two branches of investigation have the common aim of detecting an ideal law of symmetry in the bodies they deal with and expressing this in a definite mathematical formula."

- Ernst Haeckel (1834 - 1919)
The Wonders of Life

Borrowed Ascent

"The growth of climbers, even more than all other plants, is upward towards the light. In the shade of the forest they rarely or never flower, and seldom even produce foliage; but when they have reached the summit of the tree that supports them, they expand under the genial influence of light and air, and often cover their foster-parent with blossoms not its own.

Here, as a rule, the climber’s growth would cease; but the time comes when the supporting tree rots and falls, and the creeper comes with it in torn and tangled masses to the ground. But though its foster-parent is dead it has itself received no permanent injury, but shoots out again till it finds a fresh support, mounts another tree, and again puts forth its leaves and flowers.
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Mr. Darwin has now shown us the marvelous interdependence of every part of nature. Not only is each organism necessarily related to and affected by all things, living and dead, that surround it ... [The the natural world is a system of] complex relations and mutual interdependence, which link together every animal and vegetable form … into one grand organic whole."

- Alfred Russel Wallace (1823 - 1913)

Radiant Geometry

"If we wander over the moor, where we tread on Nature's carpet, we find that all the little plants which nestle in the short mossy grass are "radiating ornaments" - that is, they are pretty objects which consist of parts spreading regularly from a center.

I cannot too strongly advise the young ornamentist to study the principles on which Nature works. Knowledge of the laws which govern the development of plant-growth is very desirable; but it is not our place to imitate even the most beautiful of plant-forms - this being the work of the pictorial artists. Yet it is ours to study Nature's laws, and to observe all her beauty, even to her most subtle effects, and then we may safely pillage from her all that we can consistently adapt to our own purposes. But in order that we produce ornament, we must infuse mind or soul into whatever we borrow from her."

- Christopher Dresser (1834 - 1904)
Principles of Decorative Design

Mycelial Dreams

"In the best interpreted dreams we must often leave one portion in obscurity because we observe in the interpretation that it represents the beginning of a tangle of dream thoughts which cannot be unraveled but which has furnished no new contribution to the dream content. This, then, is the keystone of the dream, the place at which it mounts into the unknown. For the dream thoughts which we come upon in the interpretation must generally remain without a termination, and merge in all directions into the net-like entanglement of our world of thoughts. It is from some denser portion of this texture that the dream-wish then arises like the mushroom from its mycelium."

- Sigmund Freud (1856 - 1939)
The Interpretation of Dreams

A Diagram of Forces

"The form, then, of any portion of matter, whether it be living or dead, and the changes of form that are apparent in its movements and in its growth, may in all cases alike be described as due to the action of force. In short, the form of an object is a ‘diagram of forces,’ in this sense, at least, that from it we can judge of or deduce the forces that are acting or have acted upon it: in this strict and particular sense, it is a diagram,—in the case of a solid, of the forces that have been impressed upon it when its conformation was produced, together with those that enable it to retain its conformation.

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In an organism, great or small, it is not merely the nature of the motions of the living substance that we must interpret in terms of force … but also the conformation of the organism itself, whose permanence or equilibrium is explained by the interaction or balance of forces."

- D’Arcy Wentworth Thompson (1860 - 1948)
On Growth and Form

Visible Invisible

"The great aspiration of the Human Race is to gain a knowledge of the Reality, the Noumenon behind the phenomenon; but the fact that from infancy we have been accustomed to confine our attention wholly to the objective, believing that to be the reality, has surrounded us with a concrete boundary wall through which we can only at times, with difficulty, get transient glimpses of that which is beyond. It is only in recent years that we have been able to realize that it is the Invisible which is the Real, that the visible is only its shadow or its manifestation in the Physical Universe, and that Time and Space have no existence apart from our physical senses, in short, that they are only the modes or limits under which those senses act or receive their impressions and by which they are necessarily rendered finite.

The difficulty is that our physical senses only perceive the surface of our surroundings, and that we have hitherto been looking at the Woof of Nature as though it were the glass of a window covered with patterns, smudges, flies, &c., comprising all that we call physical phenomena and which, when analyzed in terms of Time and Space, produce the appearance of succession and motion. It requires a keener perception, unbounded by these limitations, to look through the glass at the Reality which is beyond.

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Although we have no words to express, nor indeed minds to grasp, the wonders and glories of that which is behind the Veil, it is possible for some of us to get a glimpse of it through our Window. [...] We have seen that it is the Invisible which is the Real, that the visible is only its shadow; that the Invisible, as distinguished from the Visible, is not in a place apart from the Physical, but is the Reality of which the visible constitutes the boundary lines or planes in our consciousness."

- Sydney Turner Klein (1853 - 1934)
Science and the Infinite

Heart Divine

"The willing into being the primordial particle, has completed the act, or more properly the conception, of Creation. We now proceed to the ultimate purpose for which we are to suppose the Particle created - that is to say, the ultimate purpose so far as our considerations yet enable us to see it - the constitution of the Universe from it, the Particle.

This constitution has been effected by forcing the originally and therefore normally One into the abnormal condition of Many. An action of this character implies reaction. A diffusion from Unity, under the conditions, involves[31] a tendency to return into Unity - a tendency ineradicable until satisfied. But on these points I will speak more fully hereafter.

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But are we here to pause? Not so. On the Universal agglomeration and dissolution, we can readily conceive that a new and perhaps totally different series of conditions may ensue - another creation and irradiation, returning into itself - another action and reaction of the Divine Will.

Guiding our imaginations by that omniprevalent law of laws, the law of periodicity, are we not, indeed, more than justified in entertaining a belief - let us say, rather, in indulging a hope - that the processes we have here ventured to contemplate will be renewed forever, and forever, and forever; a novel Universe swelling into existence, and then subsiding into nothingness, at every throb of the Heart Divine?

And now - this Heart Divine -
what is it? It is our own."

- Edgar Allan Poe (1809 - 1849)

Eureka: A Prose Poem

Starry Space

"Considered from the point of view of a minute observation of nature, the Infinite might figure as ‘the infinitely little;’ no blade of grass being like another, as there was no limit to the complexities of an atom of earth, cell, sphere, within sphere.

But the earth itself, hitherto seemingly the privileged center of a very limited universe, was, after all, itself but an atom in an infinite world of starry space, then lately displayed to the ingenuous intelligence, which the telescope was one day to verify to bodily eyes.

For if Bruno must needs look forward to the future, to Bacon, for adequate knowledge of the earth - the infinitely little; he looked back, gratefully, to another daring mind, which had already put the earth into its modest place, and opened the full view of the heavens. If God is eternal, then, the universe is infinite and worlds innumerable.

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And his consciousness of unfailing unity and order did not desert him in that larger survey, making the utmost one could ever know of the earth seem but a very little chapter in that endless history of God the Spirit, rejoicing so greatly in the admirable spectacle that it never ceases to evolve from matter new conditions. The immovable earth beneath one’s feet! one almost felt the movement, the respiration of God in it. And yet how greatly even the physical eye, the sensible imagination (so to term it) was flattered by the theorem. What joy in that motion, the prospect, the music, the music of the spheres! - he could listen to it in a perfection such as had never been conceded to Plato, to Pythagoras even."

- Walter Pater (1839 - 1894)
Giordano Bruno

Shared Essence

"The spiritual source shines clear in the light;

the branching streams flow on in the dark.

Grasping at things is surely delusion;

according with sameness is still not enlightenment.

All the objects of the senses

interact and yet do not.

Interacting brings involvement.

Otherwise, each keeps its place.

Sights vary in quality and form,

sounds differ as pleasing or harsh.

Refined and common speech come together in the dark,

clear and murky phrases are distinguished in the light.

The four elements return to their natures

just as a child turns to its mother.

Fire heats, wind moves,

water wets, earth is solid.

Thus with each and every thing,

depending on these roots, the leaves spread forth.

Trunk and branches share the essence;

revered and common, each has its speech.

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In the light there is darkness,

but don’t take it as darkness;

in the dark there is light,

but don’t see it as light.

Light and dark oppose one another

like front and back foot in walking.

Each of the myriad things has its merit,

expressed according to function and place.

Phenomena exist, like box and lid joining;

principle accords, like arrow points meeting."

- Shitou Xiqian (700–790)

Overtones and Vibrations

"String theory is an attempt at a deeper description of nature by thinking of an elementary particle not as a little point but as a little loop of vibrating string. One of the basic things about a string is that it can vibrate in many different shapes or forms, which gives music its beauty. If we listen to a tuning fork, it sounds harsh to the human ear. And that’s because you hear a pure tone rather than the higher overtones that you get from a piano or violin that give music its richness and beauty.

So in the case of one of these strings it can oscillate in many different forms - analogously to the overtones of a piano string. And those different forms of vibration are interpreted as different elementary particles: quarks, electrons, photons. All are different forms of vibration of the same basic string. Unity of the different forces and particles is achieved because they all come from different kinds of vibrations of the same basic string."

- Edward Whitten (1951 - )

Universal Consciousness

"A spiritual evolution, an evolution of consciousness in Matter in a constant developing self-formation till the form can reveal the indwelling spirit, is then the keynote, the central significant motive of the terrestrial existence. This significance is concealed at the outset by the involution of the Spirit, the Divine Reality, in a dense material Inconscience; a veil of Inconscience, a veil of insensibility of Matter hides the universal Consciousness-Force which works within it, so that the Energy, which is the first form the Force of creation assumes in the physical universe, appears to be itself inconscient and yet does the works of a vast occult Intelligence.
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They are the seven colours of the light of the divine consciousness, the seven rays of the Infinite, and by them the Spirit has filled in on the canvas of his self-existence conceptually extended, woven of the objective warp of Space and the subjective woof of Time, the myriad wonders of his selfcreation great, simple, symmetrical in its primal laws and vast framings, infinitely curious and intricate in its variety of forms and actions and the complexities of relation and mutual effect of all upon each and each upon all. These are the seven Words of the ancient sages; by them have been created and in the light of their meaning are worked out and have to be interpreted the developed and developing harmonies of the world we know and the worlds behind of which we have only an indirect knowledge. The Light, the Sound is one; their action is sevenfold."

- Sri Aurobindo (1872 - 1950)
The Life Divine

Underlying Manifestations

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

- Ian Stewart (1945 - )

Broken Symmetry

"The state of a really big system does not at all have to have the symmetry of the laws which govern it; in fact, it usually has less symmetry. [...] In my own field of many-body physics, we are, perhaps, closer to our fundamental, intensive underpinnings than in any other science in which non-trivial complexities occur, and as a result we have begun to formulate a general theory of just how this shift from quantitative to qualitative differentiation takes place. This formulation called the theory of 'broken symmetry' may be of help in making more generally clear the breakdown of the constructive converse of reductionism."

- Philip W. Anderson (1923 - 2020)

Principial Unity

"All that exists, in whatever mode this may be, necessarily participates in universal principles, and nothing exists except by participation in these principles, which are the eternal and immutable essences contained in the permanent actuality of the Divine Intellect. Consequently, it can be said that all things, however contingent they may be in themselves, express or represent these principles in their own way and according to their order of existence, for otherwise they would be purely and simply nothingness. Thus, from one order to another, all things are linked together and correspond, to come together in total and universal harmony, for harmony is nothing other than the reflection of principial unity in the manifested world."

- René Guénon (1886 - 1951)

Crumpled Manifolds

"The whole process of applying this complex geometric transformation to the input data can be visualized in 3D by imagining a person trying to uncrumple a paper ball: the crumpled paper ball is the manifold of the input data that the model starts with. Each movement operated by the person on the paper ball is similar to a simple geometric transformation operated by one layer. The full uncrumpling gesture sequence is the complex transformation of the entire model. Deep learning models are mathematical machines for uncrumpling complicated manifolds of high-dimensional data. [...] Our own understanding of images, sounds, and language, is grounded in our sensorimotor experience as humans -as embodied earthly creatures. Machine learning models have no access to such experiences and thus cannot 'understand' their inputs in any human-relatable way [...] this mapping is just a simplistic sketch of the original model in our minds, the one developed from our experience as embodied agents—it is like a dim image in a mirror."

- François Chollet (1989 - )

Seed Unfolding

"The One, perfect in seeking nothing, possessing nothing and needing nothing, overflows and creates a new reality by its superabundance. [...] The process is like the unfolding of a seed, moving from simple origin to termination in the world of sense, the prior always remaining in its place, while begetting its successor from a store of indescribable power - power that must not halt within the higher realm [...] but continue to expand until the universe of things reaches the limit of its possibility, lavishing its vast resources on all its creatures, intolerant that any one should have no share in it. Nothing is debarred from participation in the Good, to the extent of its receptivity. "

- Plotinus (c. 204/5 – 270 CE)
The Enneads

Possible Worlds

 "As there are an infinity of possible worlds,
there are also an infinity of laws,
certain ones appropriate to one; others,
to another, and each possible individual
of any world involves in its concept
the laws of its world."

- G.W. Leibniz (1646 - 1716)

Fleeting Vortices

"[Physicists and naturalists cannot] look down from a great height upon a world which their consciousness could penetrate without being submitted to it or changing it. [...] a more complete study of the movements of the world will oblige us ... to discover that if things hold and hold together, it is only by reason of complexity, from above.

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Hence we find our minds instinctively tending to represent energy as a kind of homogeneous, primordial flux in which all that has shape in the world is but a series of fleeting 'vortices'. [...] each new being has and must have a cosmic embryogenesis ...

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Science, philosophy and religion are bound to converge ...
but without merging, and without ceasing, to the very end,
to assail the real from different angles
and on different planes."

- Teilhard De Chardin (1881- 1955)
The Phenomenon of Man

More is Diferent

"At each level of complexity entirely new properties appear, and the understanding of the new behaviors requires research which I think is as fundamental in its nature as any other. That is, it seems to me that one may array the sciences roughly linearly in a hierarchy, according to the idea: The elementary entities of science X obey the laws of science Y. But this does not at all imply that science X is 'just' science Y. At each stage entirely new laws, concepts, and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one."

- Philip W. Anderson (1923 - 2020)
More is Different

Unfolding Forms

"The essential order of movement is not that of an object translating itself from one place to another, but rather, it is a folding and unfolding, in which the object is continually being created again, in a form generally similar to what it was, though different in detail. The explicate order of movement of the object is thus not independent, substantial, and self-existent. We suggest instead that it is an appearance, abstracted from the implicate order, on which it depends and from which it derives its whole form and set of characteristic relationships.

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What all this means is that the flux of the holomovement is the implicate source of all forms, both physical and mental. That is to say, the whole of existence, including inanimate matter, living organisms, and ‘mind,’ arises in a single ground, in which these are all enfolded, or contained implicitly. 

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It is clear that, in this view, living organisms are to be regarded as particular manifestations of what is ultimately enfolded in the inward depths of the holomovement. We are suggesting here that a living organism has a more direct contact with what is thus enfolded in the holomovement than does inanimate matter. [...] One can appropriately call the holomovement the life energy, which is the ground that ultimately creates and sustains all matter and all mind, as two relatively autonomous and independent streams that may move in parallel."

 - David Bohm (1917 - 1992)
The Implicate or Enfolded Order
Quoted from Chapter 1 in Mind in Nature: the Interface of Science and Philosophy