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Sir Isaac Newton - mathematical laws Black Box theory

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Isaac Newton (1642-1727) was a great mathematician and a great physicist, and probably the most incisive thinker ever known. He chiefly established that natural phenomena generally follow determinate mathematical laws in demonstrating consistent laws of motion, of gravity and of other phenomena. He produced his 'black box' theory of science as explaining only how things happen but not why things happen. Newton may have seen that as simply a more rigorous definition of experimental science from William Gilbert's earlier requirement that science could not go beyond what can be deduced directly from experience and experiment. (Though supported by some other physicists, and by George Berkeley in his 1721 De Motu, Newton's black-box physics was 're-interpreted' by many like Einstein as a 'dead-matter plus ether or forcefield' why-physics). Newton's main works were his Latin 1687 Philosophiae Naturalis Principia Mathematica, and The Opticks published in English in 1704 and in Latin in 1706.

Newton's science theory.

Though Newton had earlier tried to develop a Descartes-like mechanical physics, his major physics work seems to have involved combining laws of force and motion in mechanics with a Gilbert-like attraction theory, to develop laws of gravitational orbital motion around 'centres of force'. Newton saw gravity as governing the motions of the celestial bodies as well as of apples falling from trees. He used the 'force' terminology perhaps more readily associated with Galileo-Descartes mechanics AND the 'attraction' terminology associated often with William Gilbert attraction theory, and allowed that gravity might be due to unseen signals acting across empty space in line with Gilbert's physics OR might be caused by the impact force of unseen ether particles or fluid in line with Descartes' physics.

Hence, in the Principia final Scholium to Book 1 Section 11, after showing that planet orbits can be explained by some centripetal force directed towards the sun, Newton concludes that the existence of gravity as a property of bodies can be deduced from the proven existence of magnetism as a property of bodies ;

"These propositions naturally lead us to the analogy there is between centripetal forces, and the central bodies to which those forces used to be directed ; for it is reasonable to suppose that forces that are directed to bodies should depend on the nature and quantity of those bodies, as we see they do in magnetical experiments."

Also in this scholium Newton states that he is not committing to any particular manner of operation of 'at-a-distance' forces or of 'contact' forces.

"I here use the word attraction in general for any endeavour, of what kind soever, made by bodies to approach each other ; whether (as Gilbert) that endeavour arise from the action of the bodies themselves as tending mutually to or agitating each other by spirits emitted ; or whether (as Descartes etc) it arises from the action of the aether or of the air or of any medium whatsoever whether corporeal or incorporeal any how impelling bodies placed therin towards each other. In the same sense I use the word impulse, not defining in this treatise the species or physical qualities of forces but investigating the quantities and mathematical proportions of them"

Clearly to Newton bodies moved, but experiment could not decide if they were actually moving themselves or were being pushed by others - there is no evidence to decide between active matter and dead matter or between 'A moves B', and 'B moves itself in response to A'. (Modern science-english translation would not be 'emitted spirits' but 'energy emissions' or 'signal emissions'.)

Of course this conclusion was not accepted by many physicists (who Newton noted in Principia's introduction to Book 3, had "prejudices to which they had been many years accustomed"), and was maybe too difficult for Einstein or anyone else to address. But Newton saw his laws of science as correctly predicting natural events without needing to know why things happened, in the manner of 'black box' behaviour laws that relate only inputs or stimuli to outputs or responses without considering any mechanisms connecting them. Newton considered hypotheses regarding currently unseens as being matters of philosophy or logic and not science, and not currently provable or disprovable by science. Newton concluded that though he had disproved substantial elements of Galileo-Descartes mechanical physics, like ether vortex motion gravity and motion tides, some modification of a mechanical ether theory might correctly explain gravity, magnetism, electricity and light. But Newton himself seemingly prefered to use Gilbert-style attraction theory in thinking about physics, which he also thought might perhaps more likely correctly explain gravity and other forces.

Newton's considerations on Descartes push-physics as against Gilbert response attraction physics is maybe best put in his Principia Book 3 Rule 3. Here he first shows how we can reason that matter has solidity and exclusive-space-occupancy, then how "we must universally allow that all bodies whatsoever are endowed with a principle of mutual gravitation." Then he concludes that the argument is stronger for the universal gravitation of all bodies than for their impenetrability. But in finding that Gilbert-like physics was somewhat more likely the true option, Newton concluded that the evidence did not exist to decide between the two theories and might well never exist, continuing with "In bodies we see only their figures and colours, we hear only the sounds, we touch only their outward surfaces, we smell only the smells, and taste the savours : but their inward substances are not to be known either by our senses or by any reflex act of our minds" - Newton could see no evidence for Descartes 'certain knowledge'. He basically concluded that the evidence did not exist to decide between taking 'mass' as the measure of the size and pushability of bodies or as the measure of bodies ability to produce and respond to gravity signals - though he seems clearly to have privately favoured the latter. But of some interest Newton's words above also allow that incorporeal bodies or media might either excite responses from matter or might somehow push matter though lacking any push property in Cartesian physics.

Newton also did useful work on light and sound, and produced a theory of fluids that solved problems of fluids in movement and of motion through fluids. This he applied to Descartes' supposed unseen universal fluid ether, in which many physicists came to believe, but Newton disproved substantial aspects of that and never conceded any kind of mediating ethers or signals as proven entities though granting that action-at-a-distance needed some kind of mediation. He did in his 'Opticks' and elsewhere use both ether explanation and attraction explanation to help clarify his new physics ideas, especially for physicists who supported either one of such explanations and their 'unseens'. Many at the time saw Newton as developing Gilbert's theory which supporters of Descartes' Cartesian push-physics had made very unpopular by name-calling only, but one of Newton's great originalities was in his seeing particular explanations as unnecessary to science and seeing hypotheses on unseens as being unscientific - and being the first clear proponent of a blackbox science simply predicting everything. Copernicus, Galileo and others had earlier done some black-box science, but excluded explanation only either as being more politic or as to be perhaps done later.

Mathematics was also advanced by Newton's work on calculus, which many of his peers falsely claimed was stolen from Leibnitz. But his science was presentationally mathematical and distinctly in the style of Euclid, though Newton always required that experimental facts must be decisive in science and not mere logical deduction or mathematics alone. Newton's published physics mathematics was, like most early mathematics, presented geometrically rather than algebraically.

Newton was the chief proponent of defined mathematical behaviour laws with undefined-explanation 'black-box science', maybe chiefly because he could see no way to decide between the alternative Gilbert and Descartes physics explanations ('Newton's Dilemma') or between alternative explanations of light. If different theories could fit the same mathematics then they were either really the same theory or were compatible image theories and descriptions that only appeared different. Newton did convince a few other scientists of his time into favouring Black Box physics that could predict everything without relying on explanations, as being the best physics possible as long as there were no proven physics theories without unseens. But explanation-theory retained its popularity among scientists and was even credited to Newton ironically. Black-box theory was maybe fine while nature was seen as being relatively simple, but it perhaps looked less intelligible when nature became seen as being more complex - so it could be argued that defined explanation is then needed to help make a theory more understandable ? Or maybe some correct science theory cannot be understandable to many anyway ? Of course a science theory cannot be only a bare mathematics with no physical meaning, but it can be a mathematics whose physical meaning is not fully uniquely defined.

Newton knew how badly Gilbert's earlier physics theory had been treated, and correctly expected that his theory substantially based on it would likely be equally badly received especially if he referred to Gilbert. (but maybe someone still has evidence connecting him to Gilbert ?) Newton did try publishing one short paper on a part of his optics work submitted in 1672 to the Royal Society. This first paper in 1672 was only a small correct non-theory technical paper on colours, colour abberation and Newton's new reflecting telescope - fully proving all that it said. But amazingly the eminent scientist peer Robert Hooke immediately tried to stop the Royal Society publishing this first paper of Newton, and himself published a ridiculous factually-wrong criticism of it that was widely backed. In response to Newton amplifying/defending his light ideas in December 1675 an angry Robert Hooke threatened to form his own Royal Society. Yet most science historians expect people to believe that it was Newton who was unreasonable ! See Newton 1672. Then in 1684 Gottfried Leibniz began publishing some of Newton's key mathematics as his own and by 1690 many were claiming that Newton had stolen Leibniz maths. Newton decided against publishing further papers, and though he held a higher opinion of some earlier thinkers like Euclid, he was very wary of putting his ideas to most of his peers. With a few minor mostly anonymous exceptions and private letters to a few friends, Newton waited until he could publish his science himself complete in book form - his Principia in 1687 and his Opticks in 1704. And when they were very badly received by largely Descartes-supporter peers of whom Newton held a low opinion, Newton finished with science and took the job of running the British Mint. Attraction physics was rubbished as being anthropomorphic, with silly claims that it required all matter to have eyes, minds and legs - ridiculous claims that themselves involve anthropomorphic thinking. (Gravity being simple can clearly need only the simplest response, and the relative nature of attraction theory really gave it more scientific power.) And Newton's black-box theory was soon simply ignored as though it did not exist.

To quote 'A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball, on Newton, from www.maths.tcd.ie -
" His theory of colours and his deductions from his optical experiments were at first attacked with considerable vehemence. The correspondence which this entailed on Newton occupied nearly all his leisure in the years 1672 to 1675, and proved extremely distasteful to him. Writing on December 9, 1675, he says, `I was so persecuted with discussions arising out of my theory of light, that I blamed my own imprudence for parting with so substantial a blessing as my quiet to run after a shadow.' Again, on November 18, 1676, he observes, `I see I have made myself a slave to philosophy; but if I get rid of Mr.Linus's business, I will resolutely bid adieu to it eternally, excepting what I do for my private satisfaction, or leave to come out after me; for I see a man must either resolve to put out nothing new, or to become a slave to defend it.' "

A majority of Newton's peers were strong Descartes push-physics supporters who would not consider alternative theories, and especially would not consider the old enemy Gilbert attraction theory. They saw Newton as an anti-Descartes Gilbert theorist and believed that Newton's blackbox position was a just a fraudulent cover to disguise his backing for the hated Gilbert theory. The minority of Newton's peers who would reasonably consider alternative theory ideas, mostly took Newton at face value as supporting blackbox theory and not attraction theory - and only few of them accepted black-box theory. Nobody other than Newton gave any real consideration to attraction theory, not even to attempt disproofs of it. And Newton himself produced no disproofs of it, only disproofs of parts of Descartes mechanical physics which suffered from more rigid requirements as do many other physics theories. Newton firmly held to his blackbox-science line dividing scientific knowledge from non-scientific knowledge - with religion and explanations of gravity both being areas of great interest outside science. (Newton privately tried unsuccessfully to develop his physics to fit with his religious ideas, and to develop its effluvia/spirits and chemistry. But his religious ideas were much more specific and detailed than those of Descartes, his published attraction theory ideas were less precise than those of Gilbert and chemistry was in need of so much more experimenting that it was still being called alchemy.)

Newton like Gilbert became acclaimed as a great scientist, while the theories of both were rejected without disproof (much later Einstein did produce his 'disproof of Newton' which was eagerly accepted with nobody looking closely at exactly what theory was supposedly being disproved). The failure of Gilbert and Newton theory among physicists was not reflected among non-physicists, so that even today most people see their signal-attraction physics theory as correctly explaining magnetism and gravity. A caricature of part of Newton's physics theory became acclaimed somewhat slowly, with his real theory rejected with Gilbert's by the mob of scientific pigmy peers - and that process passed into physics history continues still now. Or maybe, being really generous, it could be said that the world was just not really ready to look at a physics that was not some simple mechanical push physics - and maybe the world is still not ready ?! Certainly it remains rare today to find an even half-reasonable view of Newtonian physics outside of this website.

For comparison with other physics theories, Newton's three laws of motion were ;

1. Every body will remain at rest, or in a uniform state of motion unless acted upon by a force.

2. When a force acts upon a body, it imparts an acceleration proportional to the force and inversely proportional to the mass of the body and in the direction of the force.

3. Every action has an equal and opposite reaction OR the mutual actions of two bodies on each other are equal and opposite.

Newton's view of 'a force acting' allowed of either some kind of Descartes 'dead-matter' push action or Gilbert 'robot-matter' signal attraction action from another body. It requires the existance of 1.a force from one body AND 2.a second body acted upon by the force, with the actions of each being relative to each other. He is maybe here not clear enough that his 'force' gives RELATIVE change of motion, relative acceleration, rather than giving absolute change of motion and that all motion is DIRECTIONAL or vectoral. While push-physics requires all forces to be directly associated with an originating body, attraction physics allows some forces to exist in signals separated from an originating body though allowing that the signals themselves may be some kind of body. But for both, forces acting need BOTH an originating body AND a body acted on and forces persist (as with collision, spring and gas-pressure forces) for only as long as they are opposed. Newton did with substantial success mathematise Gilbert attraction physics in these respects. But the spacetime vectoral mathematics later developed by Minkowski would maybe better suit it than being wasted on some merely geometrical physics.

Current mainstream physics commonly seems to say that the gravitational force between two bodies in Newton's physics is given by the formula F=G((m₁m₂)/r²)) which may imply that their mutual attraction is proportional to the product of their masses. But a pebble doubled in mass does not fall to the ground at double the acceleration, showing only an infinitesmal increase. Though now used as an approximation for mutual gravitation in terrestrial gravitation for masses tiny compared to Earth's mass, this mainstream 'mis-equation' is only about the hypothetical one-way effect of one gravitational mass on another inertial mass and might better reflect the physics, and Newton, as F=Gm₁(m₂/r²). And, as Newton required, the mutual attraction of two bodies is the simple sum of the gravities of each. This mere force addition may seem to some to undermine mutual causation, though push action-reaction mere force addition may not seem to undermine mutual causation there. Newton did use an explicitely stated approximation for calculating the gravity of actual objects by taking the objects as zero-size point objects rather that their actual size. He concluded that experiment proved that using such center-of-gravity points commonly gives an adequate accuracy for gravity calculations, and does not give infinite gravity where two bodies touch as some still falsely claim.

There is often some misunderstanding of Newton's third law of motion - action and reaction or mutual actions being equal and opposite. Does this merely state that the inertia of a body will oppose any force applied to it ? Push reactions can seem simply explained as due to inertia plus exclusive-space-occupancy in a Galileo-Descartes type push-physics. So when A pushes on B with some force-action, B's inertia then pushes back on A with an equal and opposite force-reaction - if bodies actually can contact and push. (What determines the extent to which A and B actually accelerate here, is then the strength of the forces on each relative to the strength of their inertias.) But the equality and oppositeness of attractions or repulsions of bodies separated by some distance may seem to rule out the inertia of B causing any reaction force on A, and somehow require some different action-mutuality so that if A attracts B with some force-attraction then B must attract A with an equal and opposite force-attraction. And for a 'remote-control robot', the 'remote' body can send a signal that causes a physical action in the 'robot' body without there being any physical reaction on the 'remote' body. Newton showed that his laws of motion do apply to gravitating bodies far apart, but was maybe less clear as to exactly how they applied then.

Newton's physics, maybe like quantum mechanics and general relativity, can seem to assume or require instantanaeous reactions to forces or simultaneous action and reaction - though nowhere does he make that a specific exact requirement. If one (Cartesian) body collides with a second such body then they clearly collide at the same instant and the 2 bodies will seemingly exert collision forces on each other at the same instant, and give equal and opposite changes of momentum to the 2 bodies. Instantanaeous reaction may still look reasonable (though maybe less exactly certain) if 'collision' involves proximity repulsion without any actual contact, but does look more doubtful for forces acting between bodies that are far apart and not in contact at a common point.

Given an observer body and another body, an observer body clearly generally detects motion in the other body only relative to its own motion and generally detects its own motion only relative to the motion of the other body so that no motion can be determined as being absolute motion. From that it follows that generally neither can absolute motion energies be determined. Laws of relative motions, relative energies and relative forces alone can generally be determined. But if an observer body has some indeterminate motion then other bodies nearby may well share that same motion. And any net motion can be viewed a sum of several different component motions so that any uniform motion might be viewed as composed of (or include) cancelling opposite accelerations, and a motion uniform for a time might yet be begun and/or ended with accelerations. But a net uniform motion can seem to be a net acceleration motion, or viceversa, to an observer body that itself has some appropriate motion. A body can be at rest or in uniform motion when a force is acting on it, only if it is acted on also by some second exactly equal and opposite force. And motion energies, or kinetic energies, are subject to similar requirements.

For an overview of a 'Gilbert-Newton' view of gravity and like forces see The Attraction Theory of gravity and other forces.

MOTIONS.

The chief evidence of the operation of most physical laws of nature is found in different motions, as considered in the studies of many concerning physics such as Galileo, Gilbert, Kepler, Descartes, Newton and Einstein.

The perseverance of much natural motion like planet orbits helped convince Gilbert and Newton that space offers no resistance to, or drag on, the motion of bodies in it - and cannot affect bodies motion. But both Descartes and Einstein assumed that space can somehow push bodies and so also drag on bodies motion. The perseverance of natural planet orbits seems to some to require at least some steady force such as gravity. However, natural orbits and spins to some seemed like rest and uniform straight line motion in requiring no force to maintain them. And some even thought that uniform straight-line motion does need a force to maintain it.

Spin or rotation of a body about a central fixed point within itself, is commonly considered as for a 'perfectly solid body' though no multi-atom body may actually be such so perhaps little is really known of actual solid body spin. Spin is physically similar to the circular motion of bodies about an external point, as of the Earth and Mars about the Sun, called orbiting or orbital revolution. Both are non-uniform motions that require forces to maintain them as well as to change them - but some forces can be persistent, like the Sun's gravity, and can be internal to a body or a system. If any multi-part object or system held together by limited forces is made to spin fast enough then its parts will fly apart. A 'perfectly solid body' is generally now taken as having parts held together by some infinite force, though short-range strong forces may actually be involved and Descartes physics unreasonably assumes that uni-part bodies need no holding-together force.

Some natural uniform motion velocities are probably central-attraction escape velocities and probably include atomic escape velocities of which the 'velocity of light' may well be an example. Other major natural uniform motion velocities include those for wave transmission through mediums as for the 'velocity of sound'.

Another basic type of natural motion is deflection or reflection, as where the path of motion of something moving is changed when it meets another object - eg when a moving ball meets a wall or when a light ray meets a mirror. One possible explanation of some or all reflections is contact collision, of two things being unable to occupy the same space so that the parts of any motions directed to occupying the same space have their direction reversed. A second possible explanation of some or all reflections is proximity repulsion, as bodies increasingly repel each other as the distance between them falls. Interestingly for light reflection Newton suggested the further possible explanation of post-contact proximity attraction, where a surface strongly attracts something passing into it and pulls it back out of it. Of course it is maybe not clear what atomic forces would be needed for that, and Newton might perhaps have done better with repulsion which has attraction mathematics but with an opposite sign. And if billiard ball collisions are in fact proximity repulsions, could the extent of currently known atomic repulsion forces fully explain billiard ball collisions ? And would a perfectly elastic collision require an infinite repulsion force or just repulsion with the inverse square law ?

It follows from Newton's laws of motion that objects with similar velocities relative to some inertial frame of reference can attain different relative velocities only if forces do different work on them. The 'kinetic energies' of objects are measures of the work required to bring them to rest relative to some inertial frame of reference - and by definition more decelleration being required by a faster object, kinetic energies are the products of objects masses and their velocities relative to the inertial frame of reference. It follows that kinetic energies are not absolute properties of objects, but are only relative properties. But it is generally assumed that objects do have some absolute properties, which might or might not include such things as maybe 'mass' or other properties.

Motions common in larger visible objects may also be common in less easily seen microscopic objects - or may not. Hence microscopic objects do commonly show one apparently random motion called Brownian motion which may or may not have a real equivalent in larger object motion. And there is always the issue of the absoluteness and the relativity of any motion. Newton saw uniform motion as not distinguishable from a state of rest if the observer had the same uniform motion or state of rest, ie was in the same inertial frame of reference, and from that concluded that an observer could not know if his inertial frame of reference was a state of rest or some undeterminable state of uniform motion. And if gravitation is universal and necessarily non-uniform and accelerating, then perhaps nowhere can really exist any actual inertial frame of reference.

You should be able to read here Sir Isaac Newton's 1687 Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) but somehow the original seems not available online anywhere. But an online English version is available and linked to and discussed in our Newton's Principia section .

Or if you might want to buy Newton books in our USA Newton books or UK Newton books sections.

Or for now you could maybe read online or download free 'The War of the Worlds' by HG Wells, PDF 0.61mb to load. (you may need the FREE PDF reader available from www.Adobe.com.)

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