On Hegel's 'Philosophy of Nature' : A Free Reflex of Spirit - part thirty.

'Eternity'

by Anna Laetitia Barbauld (1743 – 1825)

------ The year has run

Its round of seasons, has fulfilled its course,

Absolved its destined period, and is borne,

Silent and swift, to that devouring gulf,

Their womb and grave, where seasons, months and years,

Revolving periods of uncounted time,

All merge, and are forgotten. —Thou alone,

In thy deep bosom burying all the past,

Still art; and still from thine exhaustless store

New periods spring, Eternity.—Thy name

Or glad, or fearful, we pronounce, as thoughts

Wandering in darkness shape thee.

Thou strange being,

Which art and must be, yet which contradict'st

All sense, all reasoning,—thou, who never wast

Less than thyself, and who still art thyself

Entire, though the deep draught which Time has taken

Equals thy present store—No line can reach

To thy unfathomed depths. The reasoning sage

Who can dissect a sunbeam, count the stars,

And measure distant worlds, is here a child,

And, humbled, drops his calculating pen.

On and still onward flows the ceaseless tide,

And wrecks of empires and of worlds are borne

Like atoms on its bosom.—Still thou art

And he who does inhabit thee.

Georg Wilhelm Friedrich Hegel, (1770 - 1831). 'Philosophy of Nature'. 'Physics'.

The Solar System.

In his philosophical 'Dissertation on the Orbits of the Planets', 1801, the greatest philosophical mind that there has ever been and yet his dissertation was on something quite straightforward, Hegel explains to begin with what he is trying to do, three things in all, to discuss those primary concepts upon which the physical part of astronomy is ordinarily taken to depend (vulgo pendere solet), then to expound what true philosophy establishes about the structure of the solar system in particular with respect to the orbits of the planets, and then finally to demonstrate how valuable philosophy is even for determining the mathematical ratios of quantities, by offering a well known example from ancient philosophy.

'All of nature’s earthly creations show their inadequacy in the face of her first force, gravity. Subdued by the pressure of the whole, they perish however perfectly they may, after their own fashion, embody the image of the universe. Like gods, in contrast, the heavenly bodies wander so serenely through the light aether precisely because they bear their centre of gravity fully within themselves and are not bound to the earth. No expression of reason could be purer nor more sublime than that organism we call the solar system and nothing could be worthier of philosophical contemplation. Thus is Cicero’s praise of Socrates, that he brought philosophy down from heaven into the lives and hearths of men, to be judged rather meagre unless we understand it as saying that philosophy can bring no benefit to our lives and our homes without, once descended, exerting all its energy to ascend once again back up into heaven'.

'The brief space of a dissertation is hardly suitable to the treatment of so august an object of enquiry. Indeed, only the elements can be given here. I will attempt to do that by first discussing the concepts usual to the physics contained in the science of astronomy. Then I move on to present what true philosophy has established concerning the structural bonds of the solar system with particular reference to the planets’ orbits. Finally, I demonstrate the real strength of philosophy in the mathematical determination of quantitative relations by citing a famous example from ancient philosophy'.

- 'On The Orbits of the Planets'

There is a pattern here in that to begin with Hegel intends to argue that the proper use of mathematics in physical theory must be determined by theory and should not determine it and then he will expound the physical theory that accords with the true philosophy and to end with he will demonstrate that the true philosophical physics is itself mathematically fruitful.

'Whoever approaches this part of physics soon realises that it is rather a mechanics than a physics of the heavens and that astronomy’s laws derive their origin from another science, from mathematics, rather than actually having been teased from nature or constructed by reason. Our great countryman Kepler, blessed with the gift of genius as he was, discovered the laws according to which the planets circulate in their orbits. Later, Newton was celebrated for proving these laws not from physical, but from geometrical grounds, and also, despite that, for integrating astronomy into physics. Now Newton certainly did not introduce the force of gravity, which he wants to identify with centripetal or attractive force, into this part of physics. All physicists before him regarded the relationship between the planets and the sun as a true one, i.e. as a real and physical force. What Newton did was to compare the magnitude of gravity shown by experience for bodies forming part of our earth with the magnitude of celestial motions; he then proceeded to deal with everything else using mathematical reasoning from geometry and calculus1. We must be especially wary of this binding of physics with mathematics; we must beware of confusing pure mathematical grounds with physical ones; namely, of blindly taking lines deployed by geometry as helps to construction in proving its theorems for forces or force directions. We must surely all agree that mathematics as a whole is not merely ideal or formal, but no less real and physical'.

- 'On The Orbits of the Planets'

Hence the first part of the dissertation is an assault upon the vulgar view that physical theory depends upon mathematical principles an error that results in the reduction of physics proper to mechanics. So, Johannes Kepler, (1571 – 1630), Kepler gave the laws of planetary motion their proper mathematical form. Sir Isaac Newton's, (1642 – 1726/27), geometrical analysis which decomposed the simple planetary ellipse and displayed it as the product of a parallelogram of forces is philosophically misleading in virtue of there being no real forces corresponding to the lines in his diagrams, the planets are not pulled different ways by impulse and we hold that impulse belongs to mechanics not to true physics:

'Not only was Newton careful to call his famous text, in which he describes the laws of motion and gives examples of them from the world system, ‘mathematical principles of natural philosophy;’ he also reminds us repeatedly that he uses the expressions ‘attraction,’ ‘impulse’ and ‘propensity towards a centre’ indiscriminately and interchangeably taking these forces not in the physical but only in the mathematical sense3. The reader must not expect, then, on the basis of such terminology, to find definitions of the types and modes of action, causes, or physical grounds anywhere in Newton’s work. Neither may he attribute true and physical forces to the centres, which are only mathematical points, even when Newton speaks of forces strongly attracting to the centre or of these as central forces4. Just what concept Newton had of physics is clear alone from his assertion that perhaps in purely physical terms instead of ‘attraction’ it would have been more correct to say ‘impulse’. We, however, maintain that ‘impulse’ belongs in mechanics and not in the true physics'.

- 'On The Orbits of the Planets'

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Lucrezia Orsina Vizzana, (1590 – 1662), 'Ave stella matutina'

Ave stella matutina,

peccatorum medicina

mundi princeps et regina,

virgo sola digna dici,

contra tela inimici,

clipeum pone salutis

tui titulum virtutis.

Tu es enim virga Iesse

in qua Deus fecit esse

Aaron amygdalum,

mundi tollens scandalum.

Tu es area compluta,

coelesti rore imbuta,

sicco tamen vellere:t

u nos in hoc carcere

solare propicia.

Dei plena gratia

O sponsa Dei electa,

esto nobis via recta

ad aeterna gaudia

ubi pax et gloria.

Tu nos semper aure pia

Dulcis exaudi Maria.

Hail, morning star,

a cure for all sins,

ruler and queen of the world,

alone worthy to be called a virgin,

against the spears of the enemy

interpose the shield of salvation,

the sign of your virtue.

For you are the staff of Jesse,

the rod of Aaron,

who take away the temptation of the world.

You are watered earth,

imbued with celestial dew,

like a dry fleece:

therefore console us in this prison

You are full of the grace of God

O chosen spouse of God:

be to us a straight path to eternal joy,

where peace and glory are found.

You will always have a pious ear for us.

So listen to us, sweet Mary.

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The fact that a certain pattern of motion can be produced experimentally through the composition of mechanical impulses does not in the least prove that the unchanging courses of the planets are produced by that kind of composition. A principle is not to be accepted because of its utility and fertility, nor are lines to be given a physical significance on grounds of mathematical convenience.

That science comprising mechanics and astronomy depends almost exclusively upon this resolution, on the construction of the parallelogram of forces,7 and the vast reach of this science, complete in itself and consistent with the appearances of nature, seems to confirm this hypothesis. The result is that the highest confidence is placed in this principle because its wide-ranging utility is clear despite the fact that, considered in its own right, there is no plausible reason to support it. However, we shall see later the true reason why the effects of a force anywhere must be represented by a square, and why all magnitudes referring to it must be represented by relations arising from the construction of a square. Here let it suffice to note that the resolution of a unitary phenomenon represented by a line, straight or curved, into other lines is a mathematical postulate. While its enormous utility in mathematics is certainly a great recommendation, it is nevertheless extremely important to keep in mind that this means that the principle of resolution depends on a different science8. Now, a principle may not be judged according to its utility or consequences; neither can it be acceptable to ascribe a physical meaning to the lines into which a line representing a force direction is resolved according to this postulate simply because they prove mathematically convenient.

- 'On The Orbits of the Planets'

Instead of constructing a mechanical model in which the centrifugal force is added to the pull of gravitational attraction the whole motion must be seen as expressing the gravity of the bodies themselves and the centripetal and centrifugal forces must be interpreted as opposite aspects of gravity. True philosophy repudiates the principle of the experimental philosophy which is derived from mechanics, or the imitation of nature in dead matter, and the production of a synthesis of absolutely distinct forces in a certain body for whatever pertains to the imitation of nature is to be entirely set aside in the cognition of nature itself, and no place must be given in physics to chance and caprice; but if the motions of the sun, the planets, and the comets are explained through the ratios of centripetal and centrifugal force, they must be said to have found their places, not by any necessity but simply by some chance.

'In truth, however, philosophy ascribes this difference of forces to matter in such a way that it makes gravity or identity itself their precondition. Why a construction of planetary motion from this premise is so sorely lacking becomes clear given that the centrifugal force acts in rectilinear motion; it is not a cause lying deep in the interior of a central body; and, indeed, it is attributed to another body. Hence, also, not even a principle of connection is possible. And since these forces have the character of contradictory opposites, neither is it possible to explain why they cannot be set against each other in a straight line, but only at an angle that splits the straight line of opposition in two13. So long as they lack a common principle then, it is undeniable that these forces are merely ideal and not at all physical. This experimental philosophy should not therefore rely on true philosophy’s opposition of forces when trying to derive phenomena from forces which obviously have nothing in common and are simply alien to each other. Their relationship is completely different. True philosophy rejects experimental philosophy’s principle taken from mechanics, which uses only dead matter for its imitations of nature and effects the synthesis of absolutely distinct forces in some arbitrary body. Anything that serves the imitation of nature, however, must be thoroughly abandoned in the pursuit of knowledge of nature itself, and in physics there can be no place for chance or arbitrariness. If, then, the relationship between centripetal and centrifugal forces is used to explain the motion of sun, planets and comets, clearly this means that these bodies come together without necessity at all through nothing more than some kind of coincidence'.

- 'On The Orbits of the Planets'

The compositive method of Newtonian mechanics is not at all like the method of geometry itself which does not construct a curve from straight lines and this point was important to Hegel because the Identity Philosophy leaned heavily upon mathematical analogies and especially upon the geometric method of Spinoza. Geometry takes some whole as given and deduces unknown properties and relations from known ones and this should be the method of physics likewise and Hegel endeavoured to demonstrate both from the procedure of mathematical calculation and through the examination of empirical cases that the distinction between centripetal and centrifugal force is quite empty.

'The centripetal force is only equal to the centrifugal force when the magnitude of the complete motion actually can be correctly expressed by the magnitude of the one or the other force. And the relation between these forces, their difference and their names are all vacuous'.

'As for the emptiness of the distinction, first it will surely be accepted that centripetal force and gravity are one; Newton’s whole concern was to demonstrate their identity. The physical construction of the phenomenon of motion among the heavenly bodies, attributing it all entirely to gravitation, with centripetal and centrifugal forces as gravity’s two factors, one of which is set equal to the total force, is thus also void15. Then there is the law of centripetal force. It diminishes with distance and Newton wants to account for the total quantity of motion with this law, so it includes the tangential direction imputed to centrifugal force. The assumption is that the circular motion is not effected by means of the propensity to the centre alone, but is composed of one direction to the centre and one on the tangent16. Since, however, the total quantity of motion is attributed to centripetal force and is determined by its magnitude, clearly centripetal force is not opposed to centrifugal force; rather it expresses the entire phenomenon. This after all is the reason why in the geometrical construction the effect of centripetal force is represented by the area of a complete triangle, one of its factors being the tangential line, or by a sector. Just how vital it is then in mathematical terms to take one force as equal to the other, or rather as actually the whole, becomes clear from the fact that the total magnitude of the opposing forces is not simply to be measured by the real effect of only the one of them, it must also include the effect that force would have if not hindered by its opponent. In the calculation, to each must be added the effect of the other. Thus, the actual magnitude of centripetal force may not be represented solely by the versed sine, but must also include the tangent or the diagonal line resulting from these two. Similarly, the actual magnitude of centrifugal force cannot be represented by the tangent alone, but must include the versed sine or the diagonal product of these two. This all includes the claim that centrifugal force stands in inverse ratio to distance. Whether one explains the phenomenon with centripetal or centrifugal force, the solution to all and any problems will always be the same'.

- 'On The Orbits of the Planets'

Kepler's account of planetary motion which does not depend on this distinction but only on ratios of space and time is therefore preferable and Kepler's strength comes from having always considered the Solar System as a whole and Newton's weakness from his conviction that a whole can be built up out of finite bits. The story of the apple has become an appropriate mythic presentation of this, but Hegel suggests that we ought to realize that Newton's Apple was as baleful as the apples in those other older myths of the Fall of Man and the Fall of Troy. Newton's Apple belongs to the myth of the Fall of Reason into understanding.

M. J. Petry the translator of the 'Philosophy of Nature' provides the facts concerning Newton's apple even down to a description of how the apple looks and tastes.

'Newton's favourite niece Catherine Barton married John Conduitt in 1717, and for the last ten years of his life the couple lived with him. In 1727 John Conduitt wrote to B. L. B. de Fontenelle (1657-1757) correcting certain errors in the latter's eloge of Newton written for the French Academy, 'In the year 1665, when he retired to his own estate, on account of the plague, he first thought of his system of gravity, which he hit upon by observing an apple fall from a tree ... The apple tree is now remaining, and is shewed to strangers'. In 1732 the manor and estate of Woolsthorpe in Lincolnshire, where this event took place, was bought from the Newtons by the Turnor family, and it was Edmund Turnor (1755 ?-1829), the Lincolnshire antiquary and fellow of the Royal Society, who published Conduitt's letter in his 'Collections, for the History of the Town and Soke of Grantham' (London, 1806) pp. 158-167. The original is in the Portsmouth collection of papers: see L. T. More 'Isaac Newton' (London, 1934)'.

'The original apple tree was blown down by a storm in 1820, but a grafted scion was propagated at the Royal Botanic Gardens at Kew. It is an old variety of cooking apple called the 'Flower of Kent': the apples are flavourless, red streaked with yellow and green, and shaped much like a pear: see H. P. Macomber 'Catalogue of the Babson Newton Collection' (2 vols. New York, 1950-1955) vol. II p. 85. Newton did not announce the law of universal gravitation until 1686, because until 1685 he was not aware of the importance of the centre of gravity in the attraction of a sphere: see H. H. Turner's letter to 'The Times' March 19, 1927: F. Cajori 'Newton's twenty years' delay in announcing the law of gravitation' in 'Sir Isaac Newton 1727-1927'-'The History of Science Society' (London, 1928) pp. 127-188. Cf. The Portsmouth Collection, Cambridge University Library, Additional Manuscripts 3968, no. 41, bundle 2'.

-'Philosophy of Nature', Petry's footnote

Petry also supplies a translation of the passage here referred to.

'See the reference to the apple story in Hegel's 'De Orbitis Planetarum' (Iena, 1801, ed. Lasson, Leipzig, 1928) p. 378, 'The general public was reconciled to the concept of gravitation less by the way in which the force which is common to the whole universe gives meaning to the expositions of Kepler and other thinkers, than by the teaching that the everyday force which causes a stone to fall to the ground, also moves the celestial bodies in their orbits. The story of Newton's having seen the apple fall has so captured the popular imagination, that it has been quite forgotten that the fall of the whole human race, as well as the subsequent fall of Troy, also began with an apple-a bad omen for the philosophic sciences'. Cf. Sir Thomas Browne (1605-1682) 'Pseudodoxia Epidemica' (London, 1646, German tr. C. Rautner, Frankfurt and Leipzig, 1689) bk. 7 ch. i.'

-'Philosophy of Nature', Petry's footnote

As it happens the dissertation I am working on is an Hegelian reading of James Joyce's 'Finnegans Wake', a novel about falling, the Fall of Man and the Fall of Troy, the Fall of Lucifer and the Fall of Humpty Dumpty, and so Newton's Apple features in the Wake and in my dissertation I play upon this Hegelian notion of the Fall of Reason to the understanding as exemplified through Newton's apple.

'What secondtonone myther rector and maximost bridgesmaker was the first to rise taller through his beanstale than the bluegum buaboababbaun or the giganteous Wellingtonia Sequoia; went nudiboots with trouters into a liffeyette when she was barely in her tricklies; was well known to claud a conciliation cap onto the esker of his hooth; sports a chainganger’s albert solemenly over his hullender’s epulence; thought he weighed a new ton when there felled his first lapapple; gave the heinousness of choice to everyknight betwixt yesterdicks and twomaries; had sevenal successivecoloured serebanmaids on the same big white drawringroam horthrug; is a Willbeforce to this hour at house as he was in heather; pumped the catholick wartrey and shocked the prodestung boyne; killed his own hungery self in anger as a young man; found fodder for five when allmarken rose goflooded; with Hirish tutores Cornish made easy; voucher of rotables, toll of the road; bred manyheaded stepsons for one leapyourown taughter; is too funny for a fish and has too much outside for an insect; like a heptagon crystal emprisoms trues and fauss for us; is infinite swell in unfitting induments; once was he shovelled and once was he arsoned and once was he inundered and she hung him out billbailey; has a quadrant in his tile to tell Toler cad a’clog it is; offers chances to Long on but stands up to Legge before; found coal at the end of his harrow and mossroses behind the seams; made a fort out of his postern and wrote F.E.R.T. on his buckler; is escapemaster-in-chief from all sorts of houdingplaces; if he outharrods against barkers, to the shoolbred he acts whiteley; was evacuated at the mere appearance of three germhuns and twice besieged by a sweep; from zoomorphology to omnianimalism he is brooched by the spin of a coin; towers, an eddistoon amid the lampless, casting swannbeams on the deep; threatens thunder upon malefactors and sends whispers up fraufrau’s froufrous;..... '

- 'Finnegans Wake'

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Jacques Arcadelt, (c. 1507 – 1568), 'O Felice Occhi miei'

O felici occhi miei, felici voi

Che sete care al mio sol,

perche sembianze avete degli occhi

Che gli fur si dolci e rei.

Voi ben voi sete voi felici,

Ed io io non che per quetar vostro desio

Corre a mirar l'onde mi struggo poi.

O happy eyes of mine, happy you

What thirsts are dear to my sun,

because you look like you have eyes

Which was so sweet and guilty to him.

Well you are happy,

And I do nothing but to quench your desire

He runs to look at the waves and then I pine.

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Hegel's theory of the pendulum of nature gives no indication of having been influenced by Jakob Böhme, (1575 – 1624), doctrine of the two centres as that model provides merely a compositional account of the planetary ellipse and Hegel discourses upon the planets in Platonic mode which is somewhat distanced from any consideration of the fall of Lucifer or the Eitelkeit of being-for-self and the Hellenic influence of Kepler has to be distinguished from the Protestant Newtonian influence of Böhme and for this reason we must question Marshall Brown's assumption that the elliptical image of life of German Romanticism is always to be traced to the latter, Böhme probably never became important for Johann Christian Friedrich Hölderlin, (1770 – 1843), as he did for Hegel and given Böhme's influence upon Hegel from 1801 onwards the characterization of the second pole of the ellipse is to be taken as blind and merely mathematical, see 'Erste druckschriften', another indication that the Dissertation was conceived and drafted at Frankfurt.

Hegel neither denies nor belittles the extent of Newton's achievement as a mathematical construction and he was an enthusiastic student of mathematics himself and there is no doubt that he studied Newton's theorems and proofs carefully, his beef is with the underlying assumptions of the experimental philosophy. Newton seeks to explain an organism with mechanical assumptions, and is therefore driven to ascribe the force of gravity and the origin of the mysterious centrifugal force to a God of whose creative activity he can give no account and the mechanical approach assumes that matter is an inert stuff to which contrary impulses are somehow imparted. Rather, Hegel believes we must assume that the contrary impulses that God is said to have imparted to matter really express the nature of matter and we must conceive matter itself as a unity of opposite forces and only upon this assumption can we construct a properly physical theory.

In the second part of the dissertation Hegel sketches the outline of a properly physical theory of the Solar System. Matter he says is objective gravity.

'Gravity constitutes matter such that matter is objective gravity. It is one and the same matter dividing itself into poles and thereby creating a line of cohesion, generating diverse shapes in a series of evolutions with different relations between the factors. This is gravity’s real difference, from which we distinguish the other, ideal difference, that of the potentials of time and space. One double thus implies another: one of poles, the other of potentials; and that makes four regions. Let us first consider the cohesion line. Gravity draws this line by asserting itself at all points, each of which is distinct in itself due to the reciprocal relations of factors, producing a series of nodes and centres for itself. In each of these points there is no lack of that multiplicity of relations to the others, now drawn together under the law and organisation of each, bundled by the power of its own principle. The solar system draws a line so much greater than the rest, which makes it so much more powerful, for where the cohesion line is broken, the body at that point carries its centre of gravity within itself; not with an absolute power certainly, but with greater force than that of the other bodies. No body, no matter that it is a whole in itself, is completely independent of the others and each is part and organ of the larger system. Still, the heavenly bodies enjoy, if not perfect, surely the greatest possible freedom and independence from gravity. The planets were not wandering aimlessly through infinite space on rectilinear paths, when they just happened to be flying in the neighbourhood of the sun and were forced under its law onto their orbits. And that hypothetical centrifugal force is not what holds them back from the sun. Rather, because they form an original system with the sun, the true cohesion force holds them firmly in place and keeps them apart'.

- 'On The Orbits of the Planets'

As a physical phenomenon gravity is already in itself objective or in Friedrich Wilhelm Joseph Schelling's, (1775 – 1854), terminology it is part of the real series yet from the Difference essay we have learned to expect that the great conceptual oppositions between the sides of the Absolute Identity will be reflected on each side hence according to the Difference essay itself philosophy of nature is theoretical and philosophy of mind is ‘practical but each of the absolute sciences has a theoretical and a practical part. The subjective/objective distinction and the particular/universal distinctions similarly appear on both sides and Hegel's conception of philosophical method in this period derives from this principle of absolute reflection.

Whatever metaphysical problem he is dealing with has the two sides: real/ideal, particular/universal, subjective/objective, intuitive/conceptual, theoretical/practical, and these two sides have to be brought into a perfect equilibrium which is the totality of the Idea and Hegel applied the method in detail to the practical sphere proper when we come to the 'System of Ethical Life' but for present concerns we merely need to take note that the consistent application of all these antitheses to both the ideal and the real series is bound to produce some unexpected and even paradoxical interpretations for these familiar terms. Hence in the present instance 'Faith and Knowledge' provides the essential clue that gravity qua subjective or particular is body but qua objective, or universal, it is motion and the physical body is the particular centre of gravitational force, and as exerting force it is a subject but the universal law of gravity, its objective reality, is revealed only in the motion of bodies where the Moon appears as the satellite of the Earth, the Earth of the Sun, and so on. And finally the totality of subjective force and objective law is revealed in the perfect equilibrium of the Solar System in which motion is brought to rest without being brought to a stop as it is when a projectile falls to earth.

We are being asked to conceive of matter in such a way that it contains motion within itself and matter here means not body but extension and the most primitive model for this is a line of bodies in space and yet if the line is to be self-maintaining then the bodies must neither fall together nor fly apart, they must cohere somehow across the interval between them and applying this conceptual requirement to our line of bodies we can deduce that they must have different gravities and yet difference of gravity is what is revealed as motion and motion involves a third real spatial dimension and the ideal dimension of temporal sequence hence we have four dimensions, three of space and one of time required for the realization of the force of gravity or its complete display as the law of motion.

What has been achieved here is that which is involved in the Idea of the Solar System is analysed, or in terms of the Kantian theory of space and time as the forms of intuition and of mathematics as the constructive science of pure intuition Hegel has constructed the Idea out of the pure intuition of gravitational force and this is his preferred way of expressing it but either way will only work if there is a whole, the Idea, which can be comprehended intuitively and Newton's compositive approach presupposes that rest in space is more intuitive than motion and Hegel's construction substitutes the resting whole of motion as what is intuited. The four dimensions of the absolutely resting motion are the squareness of Nature and according to Hegel's third thesis: ‘The square is the law of nature, the triangle of spirit.’ Whereas the essence of nature is a motion that is perfectly at rest, spirit is a motion that is absolutely restless, the dimensions of nature are four, three spatial and one temporal; the dimensions of Spirit are but three, the three inner dimensions of time, past, present, and future. The philosophical intuition of the Absolute is the moment when past and future are comprehended in an eternal present but this perfectly one-dimensional resumption of the whole is radically different from the four-dimensional cyclic oneness or eternity of nature.

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Barbara Strozzi (1619 – 1677), 'Il Romeo', 'The Wanderer'

Vagò mendico il core

tutto il regno d'amore,

dimandando pietà, chiedendo aita

nell'infelice sua povera vita.

Ne per ben salda fede

poté trovar mercede,

ché di quante egli amò

crudeli a torto ch'il fuggì,

ch'il tradì, ch'il volle morto.

Tornò dal suo cammino

il mio cor pellegrino,

ne pietoso favor ha mai trovato

per il mendico suo misero stato.

Femminil cortesia

forz'è che spenta sia,

ch'ogni ricca beltà resa tenace

non l'udì, nol mirò, lo mandò in pace.

My heart wanders begging

through the dominions of love,

seeking kindness, asking for help

for its wretched unhappy life.

Not even for steadfast faithfulness

could it find mercy,

for the more it loves wrongfully cruel women,

the more they flee, betray, wish it dead.

My wandering heart

returned from its ramble,

not having found the least compassion

for its miserable deprived condition.

The affection of women

is perhaps so wearied

that all who are rich in beauty remain unfeeling:

not hearing or seeing, they send my heart away

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The dividing line between nature and spirit is mortality and death cuts off time from space by making the temporal dimension finite and in mortal consciousness infinity must now become inward or ideal and this inwardness is its liberation. The four-square cycles of celestial nature repeat themselves identically while living terrestrial nature does not and even the life of the Earth itself in the cycle of the four elements, and the four seasons is endlessly various yet this standing variety is the background for the moving variety of mortal life. Hegel believed in the permanence of species but since he was so deeply aware of the conceptual significance of mortality he drew the boundary between nature and spirit in a way that can readily accommodate the Darwinian assumption that living variety is the expression of radical contingency and hence provides the raw material for a self-directed process of selection in time.

This discussion of the placement of spirit within nature is a digression however, what of the theory of the Solar System? Regarded as a line of cohesion the planets form a pendulum of nature, and their elliptical orbits are the swinging of this infinite pendulum. Since they do not swing in a single line it might seem more natural to speak of each of them as a separate pendulum yet Hegel wants to bring the mechanical conception of the pendulum under the more organic sway of the concept of magnetism, the planets do not swing from their centre independently, their motions express the field of force generated by their communal gravity, and it is the notion of this field of force that Hegel wants to express by his combination of the idea of an infinite pendulum with that of a magnetic field. His fifth thesis says: ‘As the magnet is the natural lever, so the gravitation of the planets toward the sun is the pendulum of nature’. Why put these two analogies together?. The reason only emerges when we discover that he wants to interpret the elliptical orbits of the planets as the field of a celestial magnet, a magnet exerts force from its divided poles, not from its point of indifference, it is like a lever that contains its own Archimedes. In the pendulum of nature this infinite lever has also achieved its own place to stand and the gravitational centre is an indifference point from which no force is exerted and the centre of force is the ideal line that connects the umbilica of the planetary ellipses. And Hegel claims that physical philosophy teaches that the true centre of force(s) is necessarily the fount of light, and that the true force and virtue of the sun is to be posited in that fact.

'In Book I, Section XI of the Principia, where Newton describes the motion of bodies mutually attracting each other by centripetal force, he requires that action between attracting and attracted bodies should be reciprocal such that neither can remain at rest, and further that both would be moved through that mutual attraction as if around a common centre of gravity. Here he appeals to the fourth corollary of the law, which in fact only says that the state of motion or rest of the common gravity centre of two or more bodies is not affected by reciprocal action between them. But there is nothing there that suggests the necessity of a true and actual centre or of a central body. That common gravity centre is thus merely a mathematical point and the fact that the sun is the force centre, or in its neighbourhood, is not down to necessity, but to mere chance, which has given it the greatest mass. Now, the enormous mass of the sun, whose concept includes density, is determined once again from the hypothesis that all force depends on mass. Physical philosophy, however, teaches us that the true force centre is necessarily the light source and that this is what constitutes the true force and power of the sun'.

- 'On The Orbits of the Planets'

But in fact the Sun is the locus of only one of the umbilica and it is for this reason that the pendulum analogy is more fundamental than the magnetic one, what makes the light-focus the significant one in the discussion of the aether (see previous article). The theory of the absolute magnet or pendulum is the formal displaying of the line that defines the first two dimensions. The concept of a centre of force upon which the whole line swings brings us to the exposition of the point itself as a non-spatial reality, a ‘subject, relative to which motion in space is defined and the line of cohesion provides us with the bare objective or abstract concept of matter in the void. In order that the physical and real concept of matter may be comprehended, it must be posited subjectively. The subjective motion of our planet is its axial rotation, from which our defnition of East and West are derived. North and South derive from the stable axis of the pendular motion. The cycle of day and night which this axial rotation produces is our first immediate experience of the necessity of change and motion.

'No matter how the bodies of the solar system are separated and the fixed cohesion line is overcome turning into motion, it is absurd to suggest that this line’s force would be dissipated in the indifference of all diameters of a formal circle. On the contrary, the line demonstrates its force precisely by asserting itself as the orbital axis, creating a polarity in the variation of motion; one pole reducing and the other accelerating it. Motion slows to the aphelion, where the force of the culmination point, the sun, is greatest; while to the perihelion, with that force minimal and the planet’s immanent force maximal, it accelerates. Disturbances in planetary motion must be referred to this as they are effects of a weak and brief cohesion readily subjugated by the primary cohesion'.

'Finally, we have contrasted an ideal difference of potentials with the real magnetic difference and now we must observe briefly that the real difference itself exists in the form of a double difference, that namely the real east-west line is formed as well as the line of bodies we call comets, circulating in orbits with immeasurable apsides, precisely because east and west stand under the law of potential difference'.

- 'On The Orbits of the Planets'

Our experience contracts into the darkness of merely subjective consciousness, and expands again into the daylight world of objects and the comprehension of this cycle is the work of mens, mind, mind itself is the real existence of time but as the original subject of motion mens is not simply a moving point in the single dimension of time. ‘t takes its perfect and natural form in its contrary, or by passing over into space and constituting a plane, which because we posit nothing else but the difference of mind and extension itself, lacks every other difference and is a square.

This proposition explain what it means to say as Hegel does that the square is the law of nature. The eternal reality for theoretical contemplation by the mind is a four dimensional spatio-temporal equilibrium. Squareness is the simplest schema for this that we can construct in pure intuition. Mathematics is the mind's reflective capacity to reconstruct in a purely ideal realm, the real process which we have thus far merely observed and analysed as a physical reality. Since it is only reflection mathematical construction appears to be an arbitrarily free activity, quite alienated from all real content yet because of the necessity of mathematical propositions we know that our mathematical calculations must hold good in any possible world and thus in the real one too and the moment of subjectivity involved in the transition from one dimension to another appears in mathematics as the incommensurable. The mathematical point itself is the primitive intuition of this, the reflective form of what we have already learned to call the negative infinite and the simplest model for the reflective Darstellung of subjectivity is a line and the square is the mathematical schema of natura naturans (nature creating). Following this process of intuitive construction the schema for natura naturata (nature created) will be the cube. Hegel's adoption of this mathematical model for the genesis of space confirms the interpretation of the proposition ‘quadratum est lex naturae’; and it helps us to understand the occasional mysterious references to the cube of Spinoza but it also testifies to Hegel's interest in the mathematical formulations of the laws of motion.

One would have supposed that the alternative series: radius, circle, sphere, would interest Hegel more yet quite apart from the fact that the celestial orbits are elliptical not circular his interest in the line, square, cube sequence was determined by the fact that when the cohesion of the line fails the rate of free fall toward the centre is the square of the distance involved. When the separate bodies remove that difference that is their separateness falling upon one another into one body, they change the line into a square hence the law of falling is the ratio of the square of the distance, that is of the line changed to a square.

'.. the so-called higher geometry reduces the plane to the line and both to the infinitely small, that is to the point, while analysis forms the line from points, the infinite line. But how the line arises from the points and the plane from the line and so on, that is not comprehended in any other way than by resort to the extraneous concept of motion, i.e. after the identity of space and time has been asserted. Now we have seen that the line is mens/Geist/spirit/mind generating itself in the subjective form appropriate to it; also that its transition into objective form is in fact the square, which is why on the other hand its product in natura naturata is the cube. After all the abstractions of mind are done, when space generates itself there are three dimensions and the body in emergence is the square, while the body in existence is the cube. Since the relation between bodies separated from each other is the line, a subjective relation lacking objective form, as one falls onto the other they turn the line into the square by abolishing the difference and regrouping into one body. Hence the law of falling bodies features the square of the displacement or the square into which the line mutates'.

- 'On The Orbits of the Planets'

Even more significant is the fact that Kepler's third law the law of the planetary periods involves the cubing of a square root, for these planetary periods constitute the ideal body, that is, the total gravitational field of the solar system. In effect Hegel is arguing for a return to the neo-Pythagorean assumptions of Kepler in the quest for the most elegant mathematical theory of the measured data of planetary astronomy and Kepler's own discoveries have convinced him that the true theory must be expressed in powers and roots. The three powers, linear, square, and cubic are the organic potencies of extension as a living expression of Reason and its image and if this view is accepted it provides a theoretical basis for the framing of mathematical equations in physical theory and it tells us what potency-relations to expect and to look for in our raw data. Hegel's own endeavour to frame a mathematical expression for the line of cohesion itself is both the natural coping stone of his theory since it involves the complex ratio of a squared square and a cube and a demonstration of its general utility.

We can understand that the distance-ratios of the line of cohesion ought not to be accidental upon Hegel's view. Upon any view at all, once the general law of gravitational attraction is recognized, the search for a mathematical pattern in the planetary intervals is a matter of some interest. It was, of course, a subject of burning interest, in its own right, to the first scientifc observers of the heavens in our own Western tradition and Hegel's aim is to integrate the newest mathematical results into the context of their assumptions and methods and his outstanding example drawn from ancient philosophy is the Pythagorean sequence which the Demiurge is supposed to have employed for the creation of the World-Soul in the likely story recounted by Plato's Timaeus. This series is the first three integers and their first three powers: 1, 2, 3, 4, 8, 9, 27. Hegel wanted to generate the required interval-ratios from this series by a potency operation upon it and the required intervals ought to be the cube root of the fourth power of the successive terms of the Pythagorean sequence but in order to get a series with an appropriate interval sequence Hegel had to remove 2 and replace it by 4. His other emendation is made without any such obvious reason and in his table of results he replaces 1 by the cube root of 3 which means that he really required the fourth root of 3 in his generative series and he provides no philosophical explanation for either of these changes but the implication of his breviter ut reliqua tradamus is that he is hasting towards a conclusion and does not wish to give explanations. In some measure we can plausibly infer what his reasons were, the removal of a cube in the middle and the insertion of the fourth root of three at the beginning to balance the cube of three at the end and to mirror the fourth power of three in the final result is not a happy accident.

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Isabella Leonarda, (1620 – 1704), 'Care plage'

Care plage, cari adores,

Quantum estis suave per me.

Nihil mage, quam adores

Care Jesu clamo a te.

Si tu ardes, ardendo beas,

Et delectat, dum plagas nos.

In hoc corda dum flammas creas,

Tunc in anima cadit ros.

Probo aliquando deliquia, tormenta et pina, sed cito

veniunt ad me, divine consoliationes.

Un sola delectia gratia

Fugat cito dolorum milia.

Tunc tormenta vedentur vilia,

Quando corditu donas solatia,

Faces tua delecta, candida,

Facit cor un non restet in jubilo,

Et tu vivant repeta jubilo

Etiam penis corda plus languida.

Ah, amantissime, Jesu si ista est,

Amores fulmine, vulnera me,

Dum frontis lumina tu beas me.

Si me Jesus scis beare,

Ne cesses quaeso, cor meum plagare.

Alleluia.

Dear wounds, dear flames,

How pleasant you are to me.

Dear Jesus I cry for nothing more

than fires from you.

If you burn, you bless by burning,

and you are pleasing while you wound us.

As you create flames in this heart,

then dew falls in the soul.

As you bless the flames in this heart,

then dew falls in the soul.

Sometimes I experience fainting,

torments and punishments,

but divine consolations come quickly to me.

One single loving grace from you

quickly causes thousands of sorrows to flee.

Then torments seem paltry,

when you give comfort to my heart.

Your beloved, dazzling face,

makes my heart not resist joy,

and even hearts more weak from pains

live full of joy.

Ah, most loving Jesus, if that is so,

wound me with the lightning of love,

while you bless me with the light of your countenance.

If you know how to bless me, Jesus,

do not cease, I beg you,

to wound my heart.

Alleluia.

___________________________________________

The story so far. The fourth root of three is to be thought of as the square root of a square root, and the fourth power of three is the square of a square and the whole pattern of squares and cubes of 2 and 3 both roots and powers is determined by the fact that Kepler's third law which gives the formula for the generation of the ideal body of the Solar System involves the ratio of a square and a cube and although this is the reason why the fourth and third roots of three replace unity as the first term in the generative and the generated series the replacement of the unit by some surd was necessary because the finite is to be generated by the Infinite. Zero and One the negative and positive expressions of the pure Absolute, are not generative and the substitution of 16 for 8 was not only dictated by the empirical data but by the fact that a cube cannot belong inside the series and the square that does belong there is to be thought of in that position as a simple square, not as the fourth power of two.

The wish to establish a general physical theory is demonstrated by the fact that these results are applied to the two planets with enough known satellites to make the application significant, the first three moons of Jupiter fit the theory well enough ... but the fourth? We can leave that hanging but given the rather special character of the final term in his full series it is amenable to explanation. The satellites of Saturn are of greater interest, here we have a full set of seven, and the best series of cubes discoverable began with the unit and proceeded in powers of two at first regularly then irregularly terminating with 2 and the holistic character of this philosophical approach to physical theory requires that one's empirical data must in the relevant sense be complete yet it can be complete for the purpose of theory construction without being empirically correct and in the Hegelian perspective the mistaken assumption that the Moon was a planet was a fortunate error for the Pythagoreans and its correction was a misfortune for Kepler since with only six moving bodies he was doomed to spend a lifetime trying to fill the five intervals with the five regular solids.

They were all operating with incomplete data, Hegel wanted to demonstrate that the simple series (he calls it an arithmetic progression but once the initial interval (3) is established it actually proceeds by powers of 2), originally formulated by Christian Wolff (1679 - 1754) but generally called ‘Bode's Law’ ‘does not in any way pertain to philosophy, for according to the Wolff-Bode series there ought to be a planet between Mars and Jupiter and in the very months in which Hegel was turning back to his German manuscript and calculations, the Sicilian Piazzi, was reporting the successful verification of the law to the Berlin astronomer, J. E. Bode. Their correspondence about the discovery of the asteroid Ceres was published almost exactly contemporaneously with Hegel's dissertation and within a few years four asteroids were known and Hegel duly takes account of them in his Berlin lectures on celestial physics.

This misfortune for his procreative numbers has brought a lot of unwarranted obloquy directed towards Hegel's head for he was not guilty of an alleged apriorism that have so often been credited to him for he admits that the discovery of planets and their distances is a matter for empirical inquiry he merely claims as any scientific investigator should that the empirical inquiry is carried on in the belief that natural phenomena conform to a rational pattern. Having found a mathematical formula that not only fits the facts but is consistent with his general theory he declares that his opponents are wasting their time. and if with the benefit of hindsight you wish to condemn him for this he is laying it down that we must always look for something without finding it before we are entitled to say that it is not there. Bode and the astronomers who found what his law told them to look for had no theoretical foundation for their position and there is still no theoretical justification for the series which does not work for Neptune.

Some lessons regarding the theory of scientific method to be drawn from this, first that a useful hypothesis must always go beyond the facts so that it will suggest its own tests yet its applicability to the philosophic endeavour to render a coherent system of all the metaphysical assumptions and basic presuppositions of science is up for debate. The attempt to avoid conflict with known facts is quite a task and this attempt which Hegel conscientiously made appears somewhat preferable to the confidence with which Schelling presented his speculative physics as a guide for research suggesting that where there were no known facts that answered to his theoretical requirements further research would bring them to light. The Hegelian rigorous focus upon rendering coherent what is definitely known or believed is more sensible given enough unsolved difficulties and problems will always remain to ensure continued growth and so the important lesson is that even if our hypothesis is open to testing we can have no secure grounds for believing that it is self-correcting in the relevant respects for in so far as our hypothesis fits the known facts we cannot be certain what the relevant respects are and the hypothesis may point as Hegel's did directly away from the crucial line of inquiry and since we cannot pursue all lines of inquiry we must resign ourselves to the fact that we are bound to keep on looking where our theories tell us to. One thing that follows from this is that the development of a variety of competitive theories is healthy and it must be admitted that the thrust of Hegel's philosophy of nature is rather opposed to that precisely because of the wish to embrace the actual data of science in his coherently organized philosophical account.

Mechanism, Chemism, and Organism. The Dissertation has a limited objective, even from the internal evidence for instance the remark about what physical philosophy teaches regarding the necessary identity of the gravitational centre with the source of light we can see that there was more in Hegel's general theory of the body of the Idea than can be securely recovered from this source yet we are better off with respect to this first part of his earliest philosophy of nature than with respect to any other and the career of the Idea when, to employ Hegel's theological metaphor, it comes down to Earth, is illumined for us in its details only by some fairly direct remarks and illustrations in the Difference essay and the Divine Triangle report and by a few more oblique references elsewhere.

One important fact indicated by Hegel's summary for the ‘Introduction to Philosophy’ of 1801 is that the straightforward opposition between physics as a speculative concept and mechanics as a reflective one was not maintained even in his first course at Jena, a simple opposition typical of the Frankfurt standpoint and forming a link between the Dissertation and the ‘System-Programme’. The Idea comes on Earth to the organic or to individuality after it has comprehended the ideal moments of the concept of the organic, namely the mechanical as it is posited on Earth, and the chemical and thus the polemic against Newton begins to be framed in terms of a contrast between absolute or infinite mechanics and finite mechanics and no longer in terms of the simpler opposition of speculative physics and reflective mechanics and this conceptual development is directly coherent with the establishment of absolute refection as a bridge between finite thought and speculation in the Difference essay and the fact that it has not already happened in the Dissertation is evidence enough that the main body of that work is older than the Difference essay.

Finite or Newtonian mechanics is evidently the first moment in the life of the Earth as a universal individual. Chemism, as the second moment, embraced all the polarized phenomena of magnetism, electricity, and chemical affnity. The totality of mechanism and chemism, the individuality’ of the Earth itself, is reached in the meteorological process of the physical elements. Hegel took an interested in this since he was convinced that climate conditions the temperament of the Volksgeist and so influences all the higher manifestations of spiritual culture yet information on his views about meteorology in the early Jena period is hard to find and he indeed held that the chemism of the Earth-process is total or infinite or, in other words that the process of elementary tension can produce an absolute transmutation in particular of air into water and water into air.

This meteorological process is the formative context for the mineral system of the Earth and geology is of interest to Hegel since in the sporadically ordered variety of geological formations he observed a frozen image of the dynamic processes of meteorology and in the self-shaping of crystals he observed an anticipatory hint of the self-generation and self-maintenance of the organism, and the mineral kingdom reveals in this way the life that is present in its apparent petrifaction which our labour can only mechanically disturb when we sow seeds and plant things in the appropriate soil and climatic conditions. The Earth-process moving in the meteorological cycle and stabilized in the mineral kingdom brings forth plants which are living species not properly individuated since they are rooted in the universal individual (the Earth) and as a rule the whole plant can be propagated from a small part sometimes even from any par of a living specimen. Hence the plant is life generally as an objective intuition that is to say without subjective sensibility subsumed under the Concept. Hegel was an enthusiastic botanist yet the peculiarly ambivalent logical character of plants is responsible for his constant appeal to flowers and fruit as analogical metaphors both for celestial structures far lower in the scale and for spiritual phenomena much higher up.

The animal is the Concept of the living thing subsumed under intuition and the concept is particularized in the two sexes so one needs a pair ideally a pair coupling for the complete intuition (instantiation in perception) of the concept and in their mating relation even a human couple is merely an empirical universal and with the theory of the self-aware and self-moving but not yet rational animal organism the philosophy of nature arrives at its final totality the point of contraction or unified centre of force which is the axis around which everything rotates, and here the evidence of the Difference essay is direct, the construction of the organism resumes the whole process of the Earth's individuality especially the stages of the chemical process and Mesmer's theory of animal magnetism provided a sort of gravitational’ context here for Hegel's own chemistic theory of sexual differentiation and attraction. In the 'Natural Law' essay he had adopted the view that organic health involves a kind of warfare of the functioning sub-systems and that disease arises when this struggle of the members gets out of hand.

The inwardness expressed by the animal's cry its inarticulate demand for recognition is the moment of the birth of consciousness where nature passes over into spirit and this dawning of independent consciousness in the struggle for recognition is directly alluded to in the Difference essay and in the 'System of Ethical Life', the animal's cry for recognition is connected with the approach of death and all of these themes, animal magnetism, sexual chemism, the war of the organs, and the mortal struggle for recognition, become permanent features of Hegel's philosophy of organism and/or of subjective spirit.

Yes, nature passes over into spirit with the cry of the animal, and we are animals of course, but with us nature passes over into spirit with music too ... our rather sublime animal cry ...

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Antonio Archilei, (1543 - 1612), Dalle più alte sfere ... from the highest spheres ...

Dalle più alte sfere Di celeste

Sirene amica scorta

L’armonia son, ch’a voi vengo, ò mortali,

Poscia, che fino al

Ciel Battendo l’ali

L’alta fiama n’apporta,

Che mai si nobil coppia il sol non vide

Qual voi nuova Minerva, e forte Alcide.

From the highest heavenly spheres

Mermaids escort, friend I am harmony,

who come to you, oh mortals, Then, until

Heaven flapping its wings

The high flame brings us,

The sun has never seen such a noble couple

What, you new Minerva, and strong Alcide.

___________________________________________

Dedicated to my lovely one. There is certainly one absolute in this world. I absolutely love you.

An animal cry:

Ba ba ba doo. Ba ba ba doo. Ba ba ba doo.

I've nothing much to offer

There's nothing much to take

I'm an absolute beginner

But I'm absolutely sane

As long as we're together

The rest can go to hell

I absolutely love you

But we're absolute beginners

With eyes completely open

But nervous all the same

If our love song

Could fly over mountains

Could laugh at the ocean

Just like the films

There's no reason

To feel all the hard times

To lay down the hard lines

It's absolutely true

Nothing much could happen

Nothing we can't shake

Oh, we're absolute beginners

With nothing much at stake

As long as you're still smiling

There's nothing more I need

I absolutely love you

But we're absolute beginners

But if my love is your love

We're certain to succeed

If our love song

Could fly over mountains

Sail over heartaches

Just like the films

If there's reason

To feel all the hard times

To lay down the hard lines

It's absolutely true

David Bowie, 'Absolute Beginners:

Coming up next:

The fluidity of matter.

It may stop but it never ends ...