![\"the](\"https:\/\/goodshare.org\/wp\/wp-content\/uploads\/2010\/10\/emperors-projecting-crown.jpg\" "\\"emperors-projecting-crown\\"")
the emperor's magic-shoe-powered projecting crown<\/p><\/div>\n
There once was an Emperor who ruled the land and all that were in it with an iron fist. \u00a0He was what you might call an \u2018absolutist\u2019.\u00a0\u00a0 In his circle of courtiers was a wizard by the name of Notwen whose teachings, or at least the Emperor’s interpretations thereof,\u00a0 had had great influence on the Emperor\u2019s social and political policies.\u00a0 There is a story that circulates within the land, that explains how it was that the Emperor came to think and rule in the absolutist manner that he did.\u00a0 It is a story that the people call \u2018the Emperor\u2019s new shoes\u2019 and it tells the tale of how Notwen infused magic into these shoes, magic that gave the Emperor special powers and at the same time made it clear to him why authoritarian force was the ideal approach to organizing the activities of the people in his Empire.<\/p>\n
It was early in his youth when the Emperor was very impressionable and when he was under the tutorship of Notwen where the story of the Emperor\u2019s new shoes begins. \u00a0Notwen had by this time imparted much understanding to the young Emperor, like the lesson of the hair-whorl which showed that, without fail, in order for the hairs to follow an orderly orientation over the head-lands, there must be a central figure that will act as a one-of-a-kind direction-giver or \u2018director\u2019 of this order. \u00a0After the Emperor had assimilated this knowledge, Notwen laughed and reversed himself on the hair-whorl interpretation saying that \u201ca good team can make its leader look good, even if he is an empty-headed idiot\u201d.\u00a0 One might say that this was Notwen\u2019s \u2018pedagogic technique.\u2019<\/p>\n
The Emperor appreciated being able to acquire such principle-based wisdom or \u2018software\u2019 from Notwen, but also had a strong interest in \u2018hardware\u2019, tangible technology that he could use to physically amplify his personal powers.<\/p>\n
After persistent nagging and threats to do him violence, Notwen agreed to take the Emperor into his secret laboratory. \u00a0It was at that time that Notwen was experimenting with a technology that we today know as \u2018piezo-electricity\u2019. \u00a0Notwen had grown a matte of these crystals and placing it on the ground, he invited the emperor to stand upon it. \u00a0He then connected two wires to an electric lamp and Notwen then extinguished all of the candles so that they would be in pitch darkness so as to better see what the lamp was doing. \u00a0\u00a0Amazingly every time they heard a cart or horse pass by outside the carefully concealed lab, the lamp flickered and glowed brightly.<\/p>\n
The Emperor was astonished and asked Notwen how this could be. \u00a0Notwen explained that the Emperor\u2019s own inertial mass was like a tamp on top of the piezo-electric matte so that when the rumbling came through the ground in waves, and the matte tried to rise up on the crest of a wave, it’s rising was resisted by the Emperor\u2019s bulk standing on top of it, so that the matte, being caught between the mass of the ground and the mass of the Emperor, as between a rock and a hard place, was compressed and electricity was squeezed out of it which lighted the lamp.<\/p>\n
The Emperor was thrilled by the thought that the reins of such power could be held in his hands (or toes, as the case may be) and he commanded Notwen to make him a pair of shoes with piezo-electric soles and to install jewel-shaped lamps in his crown which the soles could be wired to. \u00a0Then, when his advisors at his council table were not listening closely enough to him, he could dig his heels and soles into the floor so that his crown would flare up and illuminate the council room so that they would \u2018get the message\u2019, that it was time to stop talking and start listening and taking orders.<\/p>\n
Notwen had no choice but to comply with the Emperor\u2019s wishes, but he took the Emperor aside and told him something about the nature of \u2018force\u2019 that he must never allow himself to forget. \u00a0He told him that the forces in the heavens and in nature are always \u2018between\u2019 things and are never of local origination. \u00a0He reminded the Emperor that it was the force of acceleration between the earth and his own inertial mass that generated the (electrical) power and that this was not changed merely by strapping the magic matte to the soles of his feet. \u00a0That is, he could not rightly claim that he was the \u2018source\u2019 of this power he could now manipulate, since the power derived from between things rather than originating locally, from things.<\/p>\n
But the Emperor was in his youth, full of ego and what you might call a bit of a ‘humilityless twit’.\u00a0 While he was in the laboratory, he stole some of Notwen’s notebooks so that he might find some of Notwen’s words that he could twist and thereby claim the new power as his own.\u00a0 Later, in searching through the notebooks, he found three rules that explained what \u2018force\u2019 was. \u00a0The rules were;<\/p>\n
1. force is what makes things move that are not presently moving.<\/p>\n
2. force is what makes things move faster than they are presently moving<\/p>\n
3. force is always reciprocated by equal and opposite force<\/p>\n
The Emperor could see how he could use the first definition of force to claim ownership over his new powers. \u00a0By digging in his heels and imposing force, he became the sole owner and originator, … the sole source(ror) of the force.<\/p>\n
But what had Notwen said? … that the celestial forces and the forces in nature were always ‘between’ things, … that they were \u2018relative\u2019 rather than starting from a particular place as if that place was an absolute local wellspring of force.<\/p>\n
The Emperor pondered; …how was it that Notwen had two definitions of force, one in which force could be just a push or a pull and another in which force was associated with \u2018acceleration\u2019?\u00a0 But no matter, the Emperor had all that he needed in the first rule and he could rightfully say that he was using it precisely as Notwen had formulated it.<\/p>\n
Still, the puzzling nature of ‘force’, though in the background of his thoughts, periodically returned to the foreground and on one of these occaisions, the Emperor remembered how, when he had been ice-skating with friends, when two skaters pushed away from each other, although the force on both was the same, the lighter skater moved off faster than the heavier one, supporting the notion that \u2018force\u2019 was between things or \u2018relative\u2019 rather than \u2018absolute\u2019. \u00a0What had Notwen intended by his warning?\u00a0 Did he mean that a central authority that pushed people out in all directions would find them bouncing off the walls of the Empire and come flying back, and that it was better to inspire organization rather than to impose it?<\/p>\n
No matter, the Emperor was delighted with his new shoes and he decided to go with the first definition of force in spite of Notwen\u2019s warning. \u00a0He henceforth claimed that the force that made things happen started within him, that his force was a locally originating force, an absolute force that could be used to impose order on the movements of all things and persons in the Empire.\u00a0 \u00a0All he needed was his own intellect, will and purpose and the force to back it up and by imposing it on the people, he could make the Empire run like a well-oiled machine.\u00a0 The ones on the lower levels could fight over who would be the ‘treads on the tires’ that would have to support the full weight of the overall edifice.<\/p>\n
He proudly wore his piezo-electric-soled shoes and his electric crown. \u00a0They served to remind him that he was the sole author of his own force.\u00a0 When he was in a particularly forceful mood and people ran from him in all directions to carry out his bidding, he would jump and dance around, radiating out coloured beams of light that illuminated the surroundings and advertised his absolutist, centralist authority to all in range.<\/p>\n
It wasn\u2019t until many years later when the revolutionaries had broken through the castle portals into the outer courtyards that he found himself seriously reviewing his assumptions.\u00a0 It was as if the hair-whorl, his imperial \u2018birdsnest on the ground\u2019, had somehow transformed into a violent vortex that was about to suck him under. Now there was \u00a0a screaming, yelling, torch-carrying mob down in the courtyard, surrounding his palace, \u00a0pointing and shouting up towards his chambers, and erecting some kind of wooden structure that, though he knew not what it was, seemed to be something being prepared especially for him, though it was neither the gazebo nor the hot-tub that were on the palace grounds keepers’ to-do list.<\/p>\n
He went to his desk, unlocked the top drawer, and recovered Notwen\u2019s notebooks.\u00a0 He perused them feverishly, now looking beyond the rules and definitions of \u2018force\u2019 where he had previously stopped.\u00a0 He noticed some carefully scribed text that Notwen had underscored for emphasis,\u00a0 it said:<\/p>\n
\u201cIt must always be remembered that these rules that define force pertain only to the dynamics of systems that have already been formed and in no way address how such systems come into being or are subsumed in the evolution of new systems. \u00a0The harmonies in nature\u2019s dynamic that orchestrate a ceaselessly unfolding innovation imply that movement is not absolute but relational, that things move under one another\u2019s simultaneous mutual influence.\u00a0\u00a0 Those who may chance to read my definitions of force and their relation to motion must always keep this in mind, that these rules are not adequate to address the full complexity of the world dynamic which is in ceaseless innovative revolution, but are merely an after-the-fact way of describing systems that are already established and stable, the rules then giving us some justification for examining and analyzing them in isolation from the celestial dynamics in which they are inextricably included and pervaded by, and which shall at some point regather them into new systems. <\/span><\/p>\n
In order to comprehend and take into account the evolutionary forces, …<\/span><\/p><\/blockquote>\n
The Emperor stopped reading as several letters and slips of paper fell from the back of the notebook to the floor. \u00a0He stooped and picked them up and as he began reading them, realized that they were a dated succession of Notwen’s thoughts, all speaking to this same issue of the relativity of motion. \u00a0On the first raggedy edged note-slip, it said;<\/p>\n
\u201cAn exact solution to the problem of three bodies exceeds, if I am not mistaken, the force of any human mind.\u201d – Notwen
\n<\/span><\/p>\n\u201cIt is inconceivable, that inanimate brute matter should, without the mediation of something else, which is not material, operate upon, and affect other matter without mutual contact; as it must do, if gravitation, in the sense of Epicurus, be essential and inherent in it. And this is one reason, why I desired you would not ascribe innate gravity to me. That gravity should be innate, inherent, and essential to matter, so that one body may act upon another, at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it.\u201d – Notwen
\n<\/span><\/p><\/blockquote>\nAnd on the next, there was a further commentary by Notwen on how he had failed to incorporate the relativity that was inherent in nature\u2019s dynamic yet beyond the scope of his definitions of force and motion;<\/p>\n
“I wish we could derive the rest of the phaenomena of nature by the same kind of reasoning from physical principles; for I am induced by many reasons to suspect that they all may depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles laid down will afford some light either to this or some truer method of philosophy.” -Notwen
\n<\/span><\/p><\/blockquote>\nThe last piece of note-paper seemed to suggest that Notwen had acquiesced to his failure to ‘tie down the ultimate origins of force and motion’, … his failure to\u00a0 capture the mutual influence of things with other things in the harmonically unfolding universe; i.e. the experientially evident conjugate relation between the local inhabitants and the spatial-habitat that was manifest in the overall movement of the stars and planets, in the manner in which they moved under one another\u2019s simultaneous mutual influence as if gravity was a force that acted faster than the speed of light, … signalling to Notwen that gravity was either the divinity itself in the form of an evolutionary force immanent as an energized medium co-extensible with the universe, or a force that derived from beyond nature, the latter choice evidently being the option that Notwen had, at least at the time he had collected these notes and placed them in the book, been opting for;<\/p>\n
\u201c\u2026 and the planets and comets will constantly pursue their revolutions in orbits given in kind and position, according to the laws above explained ; but though these bodies may, indeed, persevere in their orbits by the mere laws of gravity, yet they could by no means have at first derived the regular position of the orbits themselves from those laws. . . . This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. And if the fixed stars are the centres of other like systems, these, being formed by the like wise counsel, must be all subject to the dominion of One.\u201d – Notwen
\n<\/em><\/span><\/p><\/blockquote>\nThe Emperor closed the notebook and put it back in the drawer, as he heard the blunt hollow sound of the battering ram, its deeply sonorous booming echoing loudly through his chambers and down the access corridor as it bashed and splintered the thick wooden doors to his chamber.\u00a0 Something beyond his central command was now calling the shots, announcing that the season for regathering was now descending upon the Empire, … or was this regathering force coming from within the Empire?<\/p>\n
The Emperor’s life was now involuntarily in chronicled review in his head, and his thoughts went back to his youth, … back to that day in Notwen\u2019s laboratory and to \u2018the path not taken\u2019, where he could have accepted that the force which pushed the electricity out of the magic piezo-electric matte was not HIS force, … not an absolute local force of one-sided local origination, but deriving instead from between himself and the universe, from his conjugate habitat-inhabitant relation.\u00a0 \u00a0His people under his direction had been his force but now his people were a force reciprocally impressing against him.\u00a0 It was like the hair-whorl which Notwen had first persuaded him was the source of the order and organization of all the hairs in the head-land, the local organizing power that caused them to bow down and align to this central authority, …an interpretation that Notwen had immediatel, mockingly renounced as if to make the point stronger, … saying that \u201ca good team can make its leader look good, even if that leader is a do-nothing fool\u201d, implying that ‘the force’ is never really locally, centrally originating.<\/p>\n
Though his time was drawing to a close, the Emperor felt compelled to put on his magic shoes and electric crown one last time.\u00a0 But with horror he noted that though he stood still, with every blow of the battering ram against the door, his crown lit up and shone brightly, projecting a kaleidoscope of colours onto the walls, ceiling and floors of his chamber, reminding him, too late, that \u00a0rather than being his own local source of power, he was merely one of the channels through which the universe, the dynamics of the living space he shared inclusion in, was expressing itself.\u00a0\u00a0 The mob was now inside the chamber, the thumping of their boots in their rush towards him eliciting a final flickering of his frozen-footed light-show in curious accompaniment to the terminal fluttering of his heart.<\/p>\n
* * *<\/p>\n
Epilogue: <\/strong><\/p>\n
Some centuries later, history repeated itself, as it often does. \u00a0Laws of force and motion were once again written and people once again misinterpreted them and believed that force was something local that could originate within a local system, rather than being the universe expressing itself through the local system (the ‘local systems’ being flow-features the universe had itself gathered within itself). \u00a0Such belief led to systems of social organization that were directed by force, from a central authority, and it lead to central authorities that believed that they were the source of this locally originating force.<\/p>\n
Of course, \u2018force\u2019 is never locally originating, except in idealized rules and laws.\u00a0 Motion comes before \u2018force\u2019 and \u2018motion\u2019 is inherently \u2018relative\u2019.\u00a0 Without starting from relative motion as in the celestial dynamic, there would be no way to derive the rules of force and motion, yet once these rules have been derived, they are unable to reproduce the motion, characterized by simultaneous mutual influence, that was used to derive them in the first place. \u00a0This is because the implicit force in a system wherein things move under one another\u2019s simultaneous mutual influence is invisible and nonlocal and is commonly referred to as \u2018field\u2019 or \u2018energy-field\u2019. \u00a0\u2018Local\u2019 things and their movement are not the source of \u2018energy-fields\u2019, quite the opposite; energy-fields are the source of \u2018local\u2019 things and their movements, and those \u2018local things\u2019 are not really \u2018local\u2019 but give the appearance of \u2018localness\u2019 or \u2018permanence\u2019 of identity. \u00a0As Emerson has said;<\/p>\n
\u201dThe wholeness we admire in the order of the world is the result of infinite distribution. Its smoothness is the smoothness of the pitch of the cataract. Its permanence is a perpetual inchoation. Every natural fact is an emanation, and that from which it emanates is an emanation also, and from every emanation is a new emanation.\u201d \u201cWe can point nowhere to anything final; but tendency appears on all hands: planet, system, constellation, total Nature, is growing like a field of maize in July; is becoming somewhat else; is in rapid metamorphosis. The embryo does not more strive to be man than yonder burr of light we call a nebula tends to be a ring, a comet, a globe, and parent of new stars.\u201d<\/span><\/p><\/blockquote>\n
So it came to be, once again, that many people choose to follow in the path of the Emperor, to take the path of the absolutist that understands \u2018force\u2019 as a locally originating power to make things happen, rather than acknowledging that \u2018energy\u2019 and \u2018motion\u2019 precede force, and that motion implies, always, a conjugate habitat-inhabitant relation.\u00a0 To assume that motion can be the product of locally originating force is delusion, it is to mistake map-making rules for the territory, as Notwen tried, unsuccessfully to council the Emperor.<\/p>\n
Thus, we are \u2018still inside this story\u2019 and are currently witness to a seemingly endless success of \u2018Emperors\u2019 who would confuse the powers that flow through them for \u2018their own locally originating power\u2019, until, of course, they stand paralyzed like a cow in a locomotive\u2019s headlight, realizing that their being one of the \u2018illuminati\u2019 is a myth, that their luminosity is coming from elsewhere, an enlightenment that may be resisted, short of a powerful emotional experience of the ilk of an encounter with a locomotive.<\/p>\n
As a footnote to this \u2018epilogue\u2019, an excerpt from the writings of Erst Mach \u2018Die Mechanik in ihrer Entwicklung -Historisch-kritisch dargestellt\u2019 (\u2018The Science of Mechanics: A Critical and Historical Account of its Development\u2019), wherein he demonstrates that nature\u2019s dynamics are relative and that the tautological rules and definitions of force and motion are derived from relative motion, meaning that \u2018the force\u2019 flows through us rather than originating \u2018locally\u2019 within us.<\/p>\n
* * *<\/em><\/p>\n
Footnote to Epilogue: <\/strong>
\n<\/em><\/p>\nExcerpt from Ernst Mach\u2019s \u2018The Science of Mechanics: A Critical and Historical Account of its Development\u2019 (Translated by T. J. M. M\u2019Cormack)<\/strong><\/p>\n
[Concerning \u2018absolute\u2019 versus relative motion]<\/p>\n
The view that \u201cabsolute motion\u201d is a conception which is void of content and cannot be used in science struck almost everybody as strange thirty years ago, but at the present time it is supported by many and worthy investigators.\u00a0 Some\u201drelativists\u201d are: Stallo, J. Thomson, Ludwig Lange, Love, Kleinpeter, J.G. MacGregor, Mansion, Petzoldt, Pearson.\u00a0 The number of relativists has very quickly grown, and the above list is certainly incomplete.\u00a0 Probably there will soon be no important supporter of the opposite view.\u00a0 But, if the inconceivable hypotheses of absolute space and absolute time cannot be accepted, the question arises: In what way cane we give a comprehensible meaning to the law of inertia?\u00a0 MacGregor shows in an excellent paper (Phil. Mag<\/em>., vol. xxxvi, 1893, pp. 233-264)1<\/sup>,\u00a0 which is very clearly written and shows great recognition of Lange\u2019s work, that there are two ways that we can take : (I) the historical and critical way, which considers anew the facts on which the law of inertia rests and which draws its limits of validity and finally considers a new formulation ; (2) the supposition that the law of inertia in its old form teaches us the motions sufficiently, and the derivation\u2019 of the correct system of coordinates from<\/em> these motions.<\/p>\n
For the first method it seems to me that Newton himself gave the first example with his system of reference indicated in the fifth corollary, which has been often mentioned above.\u00a0 It is obvious that we must take account of modifications of expression which have become necessary by extension of our experience.\u00a0 The second way is very closely connected psychologically<\/em> with the great trust which mechanics, as the most exact natural science, enjoys.\u00a0 Indeed, this way has often been followed with more or less success.\u00a0 W. Thomson and P. G. Tait (Treatise on Natural Philosophy, vol. i, part 1, 1879, \u00a7 249)1<\/sup> remark that two material points which are simultaneously projected from the same place and then left to themselves move in such a way that the line joining them remains parallel to itself.\u00a0 Thus, if four points O, P, Q, and R are projected simultaneously from the same place and then subject to no further force, the lines OP, OQ, and OR always give fixed directions.\u00a0 J. Thomson attempts, in two articles (Porc. Roy. Soc. Edinb., 1884, pp. 568, 730), to construct the system of reference corresponding to the law of inertia, and in this recognises that the suppositions about uniformity and rectilinearity are partly conventional<\/em>.\u00a0\u00a0 Tait (loc. cit., p. 743), stimulated by J. Thomson, takes part in the solution of the same problem by quaternions.\u00a0 We find also MacGregor in the same path (\u201cThe Fundamental Hypotheses of Abstract Dynamics, \u201c Trans. Roy. Soc. of Canada, vol. x, 1892, \u00a7 iii, especially pp. 5 and 6).<\/p>\n
The same psychological motives were certainly active in the case of Ludwig Lange, who has been most fortunate in his efforts correctly to interpret the Newtonian law of Inertia.\u00a0 This he did in two articles in Wundt\u2019s Philos. Studien<\/em> of 1885.<\/p>\n
More recently Lange (Philos. Studien<\/em>, vol. xx, 1902) published a critical paper in which he also worked out the method of obtaining a new<\/em> system of co-ordinates according to his principles, when the usual rough reference to the fixed stars shall be, in consequence of more accurate astronomical observations, no longer sufficient.\u00a0 There is, I think, no difference of meaning between Lange and myself about the theoretical <\/em>and formal value of Lange\u2019s expressions, and about the fact that, at the present time, the heaven of fixed stars is the only practically usable system of reference, and about the method of obtaining a new system of reference by gradual corrections.\u00a0 The difference which still subsists, and perhaps will always do so, lies in the fact that Lange approaches the question as a mathematician<\/em>, while I was concerned with the physical<\/em> side of the subject.<\/p>\n
Lange supposes with some confidence that his<\/em> expression would remain valid for celestial motions on a large scale.\u00a0 I cannot share this confidence.\u00a0 The surroundings in which we live, with their almost constant angles of direction to the fixed stars, appear to me to be an extremely special case, and I would not dare to conclude from this case to a very different one.\u00a0 Although I expect that astronomical observation will only as yet necessitate very small corrections, I consider it possible that expression would remain valid for celestial motions on a large scale.\u00a0 I cannot share this confidence.\u00a0 The surroundings in which we live, with their almost constant angles of direction to the fixed stars, appear to me to be an extremely special case, and I would not dare to conclude from this case to a very different one.\u00a0 Although I expect that astronomical observation will only as yet necessitate very small corrections, I consider it possible that the law of inertia in its simple Newtonian form has only, for us human beings, a meaning which depends on space and time.\u00a0 Allow me to make a more general remark.\u00a0 We measure time by the angle of rotation of the earth, but could measure it just as well by the angle of rotation of any other planet.\u00a0 But, on that account, we would not believe that the tempora<\/em>l course of all physical phenomena would have to be disturbed if the earth or the distant planet referred to should suddenly experience an abrupt variation of angular velocity.\u00a0 We consider the dependence as not immediate, and consequently the temporal orientation as external<\/em>. Nobody would believe that the chance disturbance — say by an impact — of one body in a system of uninfluenced bodies which are left\u00a0 to themselves and move uniformly in a straight line, supposing that all the bodies combine to fix the system of co-ordinates, will immediately have a disturbance on the others as a consequence.\u00a0\u00a0 The orientation is external here also.\u00a0 Although we must be very thankful for this, especially when it is purified from meaninglessness, still the natural investigator must feel the need of further insight — of knowledge of the immediate<\/em> connections, say, of the masses in the universe.\u00a0 There will hover before him as an ideal an insight into the principles of the whole matter, from which accelerated and inertial motions result in the same <\/em>way.\u00a0\u00a0 The progress from Kepler\u2019s discover to Newton\u2019s law of gravitation, and the impetus given by this to the finding of a physical understanding of the attraction in the manner in which electrical actions at a distance have been treated, may here serve as a model.\u00a0 We must even give rein to the thought that the masses which we see, and by which we by chance orientate ourselves, are perhaps not those which are really decisive.\u00a0 On this account we must not underestimate even experimental ideas like those of Friedlander1<\/sup> and Foppl,2<\/sup> even if we do not yet see any immediate result from them.\u00a0 Although the investigator gropes with joy after what he can immediately reach, a glance from time to time into the depths of what is uninvestigated cannot hurt him.<\/p>\n
A small elementary paper of J. R. Sch\u00fctz (\u201cPrinzip der absoluten Erhaltung der Energie,\u201dGottinger Nachrichten, math.-physik, Klasse<\/em>, 1897) shows, on simple examples, that Newton\u2019s laws can be obtained from the principle spoken of.\u00a0 The term \u201cabsolute\u201d is only meant to express that the princinple is to be freed from indeterminateness and arbitrariness.\u00a0 If we imagine the principle applied to the central impact of elastic masses m1<\/sub> and m2<\/sub> in the form of points, of initial velocities u1<\/sub> and u2<\/sub> and final velocities v1<\/sub> and v2<\/sub>, we have<\/p>\n
m1<\/sub>u1<\/sub>2<\/sup> + m2<\/sub>u2<\/sub>2<\/sup> = m1<\/sub>v1<\/sub>2<\/sup> + m2<\/sub>v2<\/sub>2<\/sup>.<\/p>\n
We can calculate v1<\/sub> and v2<\/sub> from u1<\/sub> and u2<\/sub> if we suppose that the principle of energy holds for any velocity of translation c directed in the same sense as u and v.\u00a0 We then have<\/p>\n
m1<\/sub>(u1<\/sub> + c)2 <\/sup>+ m2<\/sub>(u2<\/sub> + c)2<\/sup> = m1<\/sub>(v1<\/sub> + c)2 <\/sup>+ m2<\/sub>(v2 <\/sub>+ c)2 <\/sup>.<\/p>\n
If we subtract the first equation from the second, we get the equation of the principle of reaction<\/p>\n
m1<\/sub>u1<\/sub> + m2<\/sub>u2<\/sub> = m1<\/sub>v1<\/sub> + m2<\/sub>v2<\/sub>.<\/p>\n
in which c has dropped out.\u00a0 From the first and third equation we can calculate v1<\/sub> and v2<\/sub>.\u00a0 By an analogous treatment of the \u201cabsolute\u201d principle of energy, we get Newton\u2019s equation of force for a mass-point, and finally the law of reaction, with its corollaries of the conservation of the quantity of motion and the conservation of the centre of gravity.\u00a0 The study of this paper is very much to be recommended, since even the conception of mass can be derived by the help of the principle of energy.\u00a0 Cf. the section on \u201cRetrospect of the Development of Dynamics\u201d in my Mechanics<\/em>.<\/p>\n
Revisions:<\/p>\n
XXII<\/p>\n
[To p. 242, line 6 up, add:]<\/p>\n
What is pleonastic and tautological in Newton\u2019s propositions is psychologically comprehensible if we imagine an investigator who, setting out from his familiar ideas of statics, is in the act of establishing the fundamental propositions of dynamics.\u00a0 At one time force is in the focus of consideration as a pull or pressure, and at another time as determinative of accelerations.\u00a0 When, on the one hand, he recognises, by the idea of a pressure which is common to all forces, that all forces also determine accelerations, then this twofold notion leads him, on the other hand, to a divided and far from unitary representation of the new fundamental propositions.\u00a0 Cf. Erkenntnis und Irrtum, 2nd<\/sup> ed., pp. 140, 315.<\/p>\n
XXV<\/p>\n
[To p. 245, beginning of VIII, add :]<\/p>\n
Dynamics has developed in an analogous way to statics.\u00a0 Different special cases of motions of bodies were observed, and people tried to put these observations in the form of rules.\u00a0 But just as little as, from the observation of a case of equilibrium of the inclined plane or the lever, can be derived a mathematically exact and generally valid rule for equilibrium — on account of the inaccuracy of measurement, — so little can the corresponding thing be done for cases of motion.\u00a0 Observation only leads, in the first place, to the conjecturing of laws of motion, which, in their special simplicity and accuracy, are presupposed as hypotheses<\/em> in order to try whether the behaviour of bodies can be logically derived from these hypotheses.\u00a0 Only if these hypotheses have shown themselves to hold good in many simple and complicated cases, do we agree to keep them.\u00a0 Poincar\u00e9, in his La science et l\u2019hypoth\u00e8se<\/em>, is, then, right in calling the fundamental propositions of mechanics conventions<\/em> which might very well have fallen out otherwise.<\/p>\n
* * *<\/p>\n","protected":false},"excerpt":{"rendered":"
There once was an Emperor who ruled the land and all that were in it with an iron fist. \u00a0He was what you might call an \u2018absolutist\u2019.\u00a0\u00a0 In his circle of courtiers was a wizard by the name of Notwen whose teachings, or at least the Emperor’s interpretations thereof,\u00a0 had had great influence on the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-873","post","type-post","status-publish","format-standard","hentry","category-apn","count-0","even alt","author-emile","last"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/goodshare.org\/wp\/wp-json\/wp\/v2\/posts\/873","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/goodshare.org\/wp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/goodshare.org\/wp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/goodshare.org\/wp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/goodshare.org\/wp\/wp-json\/wp\/v2\/comments?post=873"}],"version-history":[{"count":12,"href":"https:\/\/goodshare.org\/wp\/wp-json\/wp\/v2\/posts\/873\/revisions"}],"predecessor-version":[{"id":877,"href":"https:\/\/goodshare.org\/wp\/wp-json\/wp\/v2\/posts\/873\/revisions\/877"}],"wp:attachment":[{"href":"https:\/\/goodshare.org\/wp\/wp-json\/wp\/v2\/media?parent=873"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/goodshare.org\/wp\/wp-json\/wp\/v2\/categories?post=873"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/goodshare.org\/wp\/wp-json\/wp\/v2\/tags?post=873"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}