John Stuart Mill’s Tendency Laws: are they contradictory to his determinism?

Introduction
By reconstructing Mill’s argument, I will show that there is no contradiction between Mill’s determinism and his views on tendency laws. Mill was consistent in his approach. In the context of his deterministic method, he provided adequate explanation of why we should be viewing the phenomena of the world as tendencies, both in the physical and the (mental or moral) social sciences, without negating causality. However, at the same time, Mill outlines the limitations of causality and its laws.
This essay has two parts. In the first part I consider Mill’s tendency laws in the natural sciences, while in the second part I focus on tendency laws in the social sciences.
I have sourced Mill’s original material from ‘System of Logic’ (SOL) and ‘On the Definition of Political Economy and on the Method of Investigation proper to it’ (DPE). Both are included in Nagel (1). In the text I use ‘social science’ to denote Mill’s ‘mental or moral science’, or ‘political economy’.
Part I: The physical sciences
Mill’s determinism is based on ‘the various uniformities of the course of nature, which when ascertained by what is regarded as a sufficient induction, we call he laws of nature’ (SOL, Book III, Chapter IV, § 1; 1, 187). The law of causation dictates that every fact which has a beginning has a cause. He proceeds to define ‘the cause of a phenomenon to be the antecedent, or the concurrence of antecedents, on which it (the phenomenon) is invariably and unconditionally consequent’. (SOL, Book III, Chapter V, § 3; 1, 197-198). The repeating, invariable and unconditional consequence of the phenomenon enables us to generalize, inferring its cause.
A phenomenon will occur again and again, as long as the phenomena comprising its cause occur again, and provided that ‘no other phenomenon having the character of a counteracting cause shall exist’. (SOL, Book III, Chapter V, § 5; 1, 203).
The concept of a counteracting cause is opening the door to tendency laws. It so happens that in some cases: ‘There are often several independent modes in which the same phenomenon could have originated… Many causes may produce mechanical motion; many causes may produce some kinds of sensation; many causes may produce death’. (SOL, Book III, Chapter X, § 1; 1, 239).
Given the multitude of causes in some phenomena, it is possible that diverse causes act simultaneously, in composition; in such case ‘two or more laws interfere with one another and apparently frustrate or modify one another’s operation, yet in reality all are fulfilled’. (SOL, Book III, Chapter X, 4; 1, 246).
Therefore, when a phenomenon may be explained by a multitude of causes and opposing causes occur simultaneously, we cannot be certain about the outcome. This does not mean that the laws are not valid. They are fulfilled, but the outcome of the acting of opposing causes may produce different outcomes. For this reason: ‘All laws of causation, in consequence of their liability to be counteracted, require to be stated in words affirmative of tendencies only, and not of actual results.’ (SOL, Book III, Chapter X, 4; 1, 248).
Part II: The social sciences
In the social sciences we have to cope with two major issues: great complexity and our ignorance, to degrees that are by far higher than in the physical sciences. ‘We study nature… in circumstances… of great complexity and never perfectly known to us, and with the far greater part of the processes concealed from our observation.’ (DPE; 1, p.427).
Causes will operate in a certain manner unless they are counteracted. ‘We may be able to conclude, from the laws of human nature applied to the circumstances of a given state of society, that a particular cause will operate in a certain manner unless counteracted; but we can never be assured to what extent or amount it will so operate, or affirm with certainty that it will not be counteracted; because we can seldom know even approximately, all the agencies which may co-exist with it, and still less calculate the collective result of so many combined elements’. (SOL Book VI, Chapter IX, § 2; 1, 334).
It is impossible to be ‘quite sure that all circumstances of the particular case are known to us sufficiently in detail and that our attention is not unduly diverted from any of them.’ The unknown circumstances, the ones that ‘have not fallen under the cognizance of science, have been called “disturbing causes”’. (DPE; 1, p.429).
We can never be assured to what extent or amount the disturbing causes will operate, or affirm with certainty that a particular cause will not be counteracted. ‘We may be able to conclude, from the laws of human nature applied to the circumstances of a given state of society, that a particular cause will operate in a certain manner unless counteracted; but we can never be assured to what extent or amount it will so operate, or affirm with certainty that it will not be counteracted; because we can seldom know even approximately, all the agencies which may co-exist with it, and still less calculate the collective result of so many combined elements.’ (SOL, Book VI, Chapter IX, § 2; 1, 334).
Having established the existence of disturbing causes, Mill proceeds to preserve the integrity of causality, by claiming that: ‘The disturbing causes have their laws, as the causes which are thereby disturbed have theirs; and from the laws of the disturbing causes, the nature and amount of the disturbance may be predicted “a priori”, like the operation of the more general laws which they are said to modify or disturb, but with which they might more properly be said to be concurrent. The effect of the special causes is then to be added to, or subtracted from, the effect of the general ones.’ (DPE; 1, p.430).
As the last sentence reminds us, what makes all of this line of argumentation valid is the compounding of causes. ‘When an effect depends upon a concurrence of causes, those causes must be studied one at a time, and their laws separately investigated, if we wish, through the causes, to obtain the power of either predicting or controlling the effect; since the law of the effect is compounded of the laws of all the causes which determine it.’ (DPE; 1, p.421).
We have now arrived at the conclusion of the argument. ‘It is evident that the social sciences considered as a system of deductions a priori, cannot be a science of positive predictions, but only of tendencies’. (SOL, Book VI, Chapter IX, § 2; 1, 334). This is the same conclusion Mill arrived at when considering causality in the physical sciences. One might say though, that the tendencies are more evident in the social compared to the physical sciences, due to the higher complexity of the phenomena and our ignorance.
Mill closes the “loop” of the scientific process with verification using the “a posteriori” method. The “a priori” method of investigation is supplemented by the “a posteriori” method as a means of verifying truth and ‘reducing to the lowest point that uncertainty before alluded to as arising from the complexity of every particular case, and from the difficulty (not to say impossibility) of our being assured “a priori” that we have taken into account all the material circumstances.’ (DPE; 1, p.431).
Social phenomena are complex, and there are potentially many disturbing causes, most of which, if not all, we do not know of. Therefore the relevant laws governing the phenomena can only be stated as tendency laws which we verify using the “a posteriori” method. The verification process may give us knowledge about some of the disturbing causes and their laws.
Epilogue
Having shown that Mill was consistent in his approach, I want to conclude by briefly considering the legacy of “tendency laws”.
‘When things are not ceteris paribus, the laws in question still apply. But they now describe tendencies – partial elements of a complex situation. (Therefore) ceteris paribus laws and tendencies go hand in hand – and that seems reasonable enough’ (2). Kincaid’s statement practically attributes the “ceteris paribus” approach to Mill. And many economists and philosophers agree with him. Given the importance of ceteris paribus laws in economics, we can conclude that Mill’s “tendency laws” have played a very important role in the shaping and the development of economics.
However, the limits to our knowledge and understanding of complex phenomena must not be underestimated. As Hayek argues: ‘…we can reasonably claim that a certain phenomenon is determined by known natural forces and at the same time admit that we do not know precisely how it has been produced… It would then appear that the search for the discovery of laws is not an appropriate hallmark of scientific procedure but merely a characteristic of the theories of simple phenomena as we have defined these earlier; and that in the field of complex phenomena the term ‘law’ as well as the concepts of cause and effect are not applicable without such modification as to deprive them of their ordinary meaning.’ (3)
When it comes to complex social phenomena, “tendency laws” may in addition to providing some explanations, reveal the limits of causal determinism, and enhance “our knowledge of our ignorance” (4, quoted by Hayek in 3).
References
1. Nagel, Ernest. John Stuart Mill’s Philosophy of Scientific Method. Hafner Publishing Company. New York, 1950.
2. Kincaid, Harold. Defending Laws in the Social Sciences, in: Martin, Michael and McIntyre, Lee (eds.) Readings in the Philosophy of Social Sciences. MIT Press, 1994.
3. Hayek, F.A. The Theory of Complex Phenomena, in: Martin, Michael and McIntyre, Lee (eds.) Readings in the Philosophy of Social Sciences. MIT Press, 1994.
4. Popper, K. R. “On the Sources of Knowledge and Ignorance”, Proceedings of the British Academy. 46, 1960.

 

On the Dark Side: A “Fluxus Eleatis” Discourse

Ludwig Wittgenstein: “In a conversation: one person throws a ball; the other does not know whether he is supposed to throw it back, or throw it to a third person, or leave it on the ground, or pick it up and put it in his pocket,…Any interpretation still hangs in the air along with what it interprets, and cannot give it any support. Interpretations by themselves do not determine meaning.”

Socrates: So it is that the good man too could sometimes become bad, either through age or toil or disease or some misfortune – for doing badly is nothing other than being deprived of knowledge – but the bad man could never become bad – for he is bad all the time – but if he is to become bad he must first become good.

MM: Are you a good man?

Mr. FFF: I am good and bad at the same time. And not because of lack of knowledge.

Mrs. T: Are you then disagreeing with Socrates?

Mr. FFF: Good and bad is only one of the “dialectical” dichotomies of man. Others being: reason / faith,  bright / dark, rational / irrational, sacred / profane, Apollonian / Dionysian, nature / culture. Dialectics dictate that both sides are taken together, and dealt with as a whole.

Friedrich Nietzsche: Every human embodies a compound of nature and culture, chaos and order, instinct and reason… symbolised by Dionysus and Apollo.

Mrs. T: What are the origins of bad, of the dark side? Was man in the past a unitary entity? How did this dichotomy of bright and dark come about?

Mr. FFF (Reads from Genesis): “Now the serpent was more crafty than any beast of the field which the Lord God had made and he said to the woman, ‘Indeed, has God said you shall not eat from any tree of the garden?’  And the woman said to the serpent, ‘From the fruit of the trees of the garden we may eat, but from the fruit of the tree which is in the middle of the garden, God has said you shall not eat from it or touch it lest you die.’  And the serpent said to the woman, ‘You surely shall not die for God knows in the day you eat from it your eyes will be opened and you will be like God, knowing good and evil.’  And when the woman saw that the tree was good for food and that it was a delight to the eyes and that the tree was desirable to make one wise, she took from its fruit and ate.  She gave also to her husband with her and he ate.  Then the eyes of both of them were opened and they knew that they were naked.  And they sewed fig leaves together and made themselves loin coverings.”

St. Augustine: We took away an enormous quantity of pears, not to eat them ourselves, but simply to throw them to the pigs. Perhaps we ate some of them, but our real pleasure consisted in doing something that was forbidden. .. the evil in me was foul, but I loved it. I loved my own perdition and my own faults, not the things for which I committed wrong, but the wrong itself. My soul was vicious and broke away from your (God’s) safe keeping to seek its own destruction, looking for no profit in disgrace but only for disgrace itself.

Mrs. T: Surely the Judeo-Christian view is not the only one.

Mr. FFF: Of course not. To take an example, daemons were benevolent spirits in the time of Hesiod. It was Plato and his pupil Xenocrates, who first characterized daemons as dangerous spirits. This was later absorbed by the Christians.

Mrs. T: Is the dark side a moral construct?

Mr. FFF: The dark side is a multifaceted construct. It has moral and religious connotations to say the least.

MM: The seductress of Juliette claimed immediately after the act that morality and religion are meaningless.

Mr. FFF: Lets put two of the prominent “dark side” attributes on the table: sin and evil.

MM: Juliette’s aim in life is to to enjoy oneself at no matter whose expense. What is the meaning of sin and evil for Juliette?

Clairwil: I expect Juliette to do evil – not to quicken her lust, as I believe is her habit at present, but solely for the pleasure of doing it…one must proceed calmly, deliberately, lucidly. Crime is the torch that should fire the passions.

Mephistopheles: Das beste, das du wissen kannst, / Darfst du den Buben doch nichts sagen.

(Mephistopheles: The best of what you know may not, after all, be told to boys.)

Georges Battaile: Sexual reproductive activity is common to sexual animals and men, but only men appear to have turned their sexual activity into erotic activity. Eroticism, unlike simple sexual activity, is a psychological quest independent of the natural goal: reproduction and the desire for children…Eroticism always entails a breaking down of established patterns, the patterns, I repeat, of the regulated social order basic to our discontinuous mode of existence.

Adolfo Bioy Casares (Reads from “The Diary of the War of the Pigs”): “Την κοιτουσε απο κοντα. Καρφωνε το βλεμμα του στα χειλη, στις λεπτομερειες της επιδερμιδας, στο λαιμο, στα χερια που του φαινοντουσαν εκφραστικα και μυστηριωδη. Ξαφνικα καταλαβε πως αν δεν τη φιλουσε, η στερηση θα ηταν ανυποφορη. Ειπε μεσα του: “Ειμαι τρελος”. Κι επανελαβε πως αν την φιλουσε, θα κατεστρεφε ολη αυτη την τρυφεροτητα, που τοσο αυθορμητα του προσφερε εκεινη. Θα εκανε ισως τη λαθος κινηση, που θα την απογοητευε και θα τον εμφανιζε σαν ενα ατομο χωρις ευαισθησια, ανικανο να ερμηνευσει σωστα μαι πραξη γενναιοδωριας, σαν ενα υποκριτη που παριστανε τον καλο, ενω μεσα του κοχλαζουν οι χυδαιες ορεξεις, σαν εναν ανοητο που τολμα να τις εκφρασει. Σκεφτηκε: “Αυτο δε μου συνεβαινε αλλοτε” (και ειπε μεσα του πως αυτο το σχολιο του ειχε γινει πια εμμονη ιδεα). “Σε μια παρομοια κατασταση εγω θα ημουν ενας αντρας μπροστα σε μια γυναικα, ενω τωρα…” Κι αν τωρα εκανε λαθος; Αν εχανε εξαιτιας μιας αγιατρευτης ντροπαλοσυνης την καλυτερη ευκαιρια; Γατι να μη δει τα πραγματα απλα, να μην αφησει τον εαυτο του να καταλαβει πως η Ν κι εκεινος…”

Adolfo Bioy Casares (Reads from “The Diary of the War of the Pigs”): He was watching her from a close distance. His stare was penetrating her lips, the details of her skin, the neck, the hands, mysterious and ever so expressive. He told himself: ” I am mad”. And repeated that if he were to kiss her, he would destroy all the tenderness that she was so spontaneously offering to him. He might make the wrong move, that would disappoint her and present him in her eyes as a person without sensitivity, unable to interpret correctly an act of generosity, like an hypocrite who was pretending to be good, while inside him burn all sorts of vile desires, like a fool who dares express them. He thought: “this was not happening to me in the past” (and told himself that this was becoming now a persistent thought). “In a similar situation in the past, I would be a man in front of a woman, while now…” And if he were wrong? If  because of this incurable shyness he was to miss the best chance? Why not see things in the simple way, not let himself understand that N and himself…”

Michel Foucault: …transgression is not related to the limit as black is to white […] the outside to the inside […] their relationship takes the form of a spiral which no simple infraction can exhaust…sexuality is a fissure – not one which surrounds us as the basis of our isolation or individuality, but one which marks the limit within us and designates us as a limit…transgression and the limit has replaced the older dichotomy of the sacred and the profane.

Marlow: And perhaps in this is the whole difference; perhaps all the wisdom and all the truth, all the sincerity, are just compresses into that inappreciable moment of time in which we step over the threshold of the invisible.

Brother Medardus: One morning when I was going to the choirmaster for my music lesson, I caught his sister by surprise in a light negligee, her breast almost completely bare. She swiftly covered it up, but my prying eyes had already seen too much. Words failed me. New, unknownfeelings welled up within me and drove the red-hot blood through my veins so that my pulse beat out loud for all to hear. My heart was held in a convulsive grip and nearly bursting, until I eased my torment with a gentle sigh.
Georges Bataille:  …eroticism fell within the bounds of the profane and was at the same time condemned out of hand. The development of eroticism is parallel with that of uncleaness. Sacredness misunderstood is readily identified with evil.
Michel Foucault: If it is extremely dangerous to say that reason is the enemy that should be eliminated, it is just as dangerous to say that any critical questioning of this rationality risks sending us into irrationality… if critical thought itself has a function…it is precisely to accept this sort of spiral, this sort of revolving door of rationality that refers us to its necessity… and at the same time to its intrinsic dangers.

Mr. FFF: The spiral negates the dichotomy. A new paradigm is born. I am a descendant of Gerard de Nerval.
Friedrich Nietzsche:…morality takes good and evil for realities that contradict one another (not as complementary value concepts,which would be true), it advises taking the side of the good, it desires that the good should renounce and oppose the evil down to its ultimate roots – it therefore denies life which has in all its instincts both Yes and No.
Alexander Nehamas: The essential unity of what we commonly distinguish as good and evil is one of the most central themes in Nietzsche’s writing.
Georges Bataille:  If they want to elevate sexuality above its organic matrix and turn it into a spiritual activity, human beings cannot but conceive erotism as a gateway to death and the diabolical. The taking over of evil is an extreme and sovereign value. This process would not require the excision of morality, rather it would bring forth a higher level morality, an a-theological “hypermorality”.


Marlow: We penetrated deeper and deeper into the heart of darkness.
Mr. Kurtz: The Horror, the Horror!
Marlow: I saw the inconceivable mystery of a soul that knew no restraint, no faith, and no fear, yet struggling blindly with itself.
Friedrich Nietzsche: It is with people as it is with the trees. The more they aspire to the height and light, the more strongly do their roots strive earthward, downward, into the dark, the deep – into evil.
Marlow: The mind of man is capable of anything – because everything is in it, all the past as well as all the future… Droll thing life is – that mysterious arrangement of merciless logic for a futile purpose. The most you can hope from it is some knowledge of yourself – that comes too late – a crop of unextinguishable regrets.
Friedrich Nietzsche: Human beings need what is most evil in them for what is best in them… whatever is most evil is their best power and the hardest stone for the highest creator… human beings must become better and more evil.

Adolfo Bioy Casares (Reads from “The Diary of the War of the Pig”): “Πιστεψε πως δεν ειχε πια ουτε δυναμεις ουτε ψευδαισθησεις για ν’αντεξει τη ζωη. Η φιλια ηταν αδιαφορη, ο ερωτας ποταπος και απιστος και το μονο που περισσευε ηταν το μισος. … του περασε απο το μυαλο μια λυση που αξιζε τον κοπο να την μελετησει κανεις¨το ιδιο του το χερι, οπλισμενο μ’ ενα φανταστικο ρεβολβερ να τον σημαδευει στον κροταφο.”

Adolfo Bioy Casares (Reads from “The Diary of the War of the Pig”): Adolfo Bioy Casares (Reads from “The Diary of the War of the Pig”): “He felt that he no longer had any powers or illusions to stay alive. Friendship was indifferent and love unworthy and vile and the only thing in abundance was hatred… a solution emerged in his mind to be further explored “his own hand, armed with a imagined revolver, aiming his temple”.

Participants

Georges Battaile, French writer and philosopher

Adolfo Bioy Casares, Argentine writer

Clairwil, character in de Sade’s “Juliette”

Mr. FFF, wanderer

Michel Foucault, French philosopher

Mr. Kurtz, half-English, half-French, ivory merchant and commander of a trading post

Marlow, main character in Conrad’s Heart of Darkness

Brother Medardus, a Capuchin Friar

Mephistopheles

MM, partner

Alexander Nehamas, professor of philosophy

Friedrich Nietzsche, German philosopher

Socrates, Greek philosopher

Mrs. T, unknown ethinicity, gourmant

Heidegger-Weg (Heidegger's Path) – Part II: The French Connection

It is now more than five months since I have posted the first part of my tribute to Heidegger, following my visit to his hometown and the mountain retreat in the Black Forest. It is time to continue with the second part, which focuses on two French friends who became very important for Heidegger after the Second World War. One is a philosopher, Jean Beufret, and the other is a poet, Rene Char. Until the 1970’s Heidegger had a major impact on French intellectual life and philosophy. His two French friends, in their own way, have played a major role in this.

Thor Seminar, 1968: Heidegger in the middle, Beaufret far right

The Philosopher Jean Beaufret

Jean Beaufret is the French philosopher who played a key role in introducing and developing Heidegger’s ideas in France. Heidegger’s ideas were introduced in France in the 20’s and 30’s, but became highly influencial only after the second world war. Heidegger and Beaufret met in 1946 in Todtnauberg. Beaufret introduced Heidegger to French existentialism, and posed to him some questions with regard to Sartre’s address “Existentialism is a Humanism”, given earlier in the year. Beaufret wrote the questions hastily on a piece of paper in a Paris cafe so as to be delivered by a friend ready to leave for Freiburg. Heidegger in response to these questions wrote the “Letter on Humanism” and dedicated it to Beaufret. It was written at a time of great personal struggle for Heidegger: he had just been indefinitely banned from teaching following the Nazi war-crimes hearings, and he had undergone a kind of emotional breakdown as a result.

Jean Beaufret and Martin Heidegger

Beaufret taught philosophy at the Ecole Nationale Superieure from 1946 to 1962 and was in the core of Parisian intellectual life, being friend with among others Maurice Merleau-Ponty, Jacques Lacan, and Louis Althusser. In 1955, with Kostas Axelos, a Greek philosopher who was teaching in Paris, Beaufret organized the conference “What is Philosophy?”, in which Heidegger was welcomed by the leading French Philosophers.

Beufret edited and published some of the letters he exchanged with Heidegger in four volumes of “Dialogue with Heidegger”. The first volume is on Greek Philosophy.

The Poet Rene Char

It is not an accident that two of Heidegger’s most celebrated acquaintances are poets: the French Rene Char and the Romanian – German – Jewish Paul Celan.  As Heidegger observes in “Letter on Humanism”:

“Be[-ing], as what has come down <to us> which becomes truth, remains hidden. But the fate of the world is presaged in poetry, without its having as yet emerged as the history of be[-ing].”

In 1955, Jean Beaufret introduced Heidegger to the French poet Rene Char, during one of his to France. Prior to his arrival in France, Heidegger stated that the person he most wanted to meet was Char, whom he regarded as the most important contemporary thinker. They became friends and met many times in Provence, the birthplace of Char.

Rene Char and Martin Heidegger

One of his “surrealist” poem collections, written in the 30’s is “The Hammer without a Master”. Some of its verses, were set to music by Pierre Boulez. Here is one of them.

The furious handicraft

The red caravan on the edge of the nail
And corpse in the basket
And plowhorses in the horseshoe
I dream my head on the point of my knife is Peru

“There are those who leave behind poisons while others leave remedies. Difficult to tell which is which. You have to taste.
The immediate yes or no is healthy in spite of the corrections that will follow.”

[Rene Char: In a crude mountain shelter, translated by Susanne Dubroff]

Char has influenced Heidegger deeply. As Michael Worton comments “…this friendship led Heidegger to write his Gedachtes sequence of poems, which are among his last writings and bear the marks of Char’s poetic practice of thinking-through-language”.

Rene Char

Heidegger was so captivated by the landscape in Thor, the place of residence of Char, that he organized philosophy seminars there in 1966, 1968, and 1969. In the mornings the participants would sit under the trees in front of the house and discuss the topic of the seminar, while in the afternoons they would visit the surroundings. One topic was young Hegel’s words: “A torn stocking is better than a darned one; not so self-consciousness”. Another one discussed Marx’s eleventh Feuerbach thesis: “The philosophers have merely interpreted the world. The issue is to change it.”

 

 

Gravity

Today’s post subject is gravity.  It all begun yesterday morning, when I wanted to see a pictue of David Hockney’s, and run by accident into Garrowby Hill, the picture you see below.

I immediately felt the instinctive need to jump on the winding road and let gravity do the rest of the work, propelling me down the twisted path without regard for time and speed. It was after this delirium that lasted for a few seconds that I started thinking about gravity.

This took me back to Newton’s theory of gravity: gravity is a force, that is directly proportional to the mass of the objects involved.

Newton’s law of universal gravitation states that every massive particle in the universe attracts every other massive particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The second theory is Einstein’s General Theory of Relativity. Einstein realized that Newton’s theory of gravity had problems. He knew, for example, that Mercury’s orbit showed unexplained deviations from that predicted by Newton’s laws. However, he was worried about a much more serious problem. As the force between two objects depends on the distance between them, if one object moves closer, the other object will feel a change in the gravitational force. According to Newton, this change would be immediate, or instantaneous, even if the objects were millions of miles apart. Einstein saw this as a serious flaw in Newtonian gravity. Einstein assumed that nothing could travel instantaneously, not even a change in force. Specifically, nothing can travel faster than light in a vacuum, which has a speed of approximately 186,000 mi/s (300,000 km/s). In order to fix this problem, Einstein had not only to revise Newtonian gravity, but to change the way we think about space, time, and the structure of the Universe. He stated this new way of thinking mathematically in his general theory of relativity.

In a nutshell, Einstein set forward the hypothesis that “Gravity” is a curve in space-time.   

Many of the predictions of general relativity, such as the bending of starlight by gravity and a tiny shift in the orbit of the planet Mercury, have been quantitatively confirmed by experiment.

Einstein said that a mass bends space, like a heavy ball making a dent on a rubber sheet. Further, Einstein contended that space and time are intimately related to each other, and that we do not live in three spatial dimensions and time (all four quite independent of each other), but rather in a four-dimensional space-time continuum, a seamless blending of the four. It is thus not “space,” naively conceived, but space-time that warps in reaction to a mass. This, in turn, explains why objects attract each other. Consider the Sun sitting in space-time, imagined as a ball sitting on a rubber sheet. It curves the spacetime around it into a bowl shape. The planets orbit around the Sun because they are rolling across through this distorted space-time, which curves their motions like those of a ball rolling around inside a shallow bowl. (These images are intended as analogies, not as precise explanations.) Gravity, from this point of view, is the way objects affect the motions of other objects by affecting the shape of space-time.

Without matter, space-time is flat (left), but it curves when matter is present (right).

Einstein’s general relativity makes predictions that Newton’s theory of gravitation does not. Since particles of light (photons) have no mass, Newtonian theory predicts that they will not be affected by gravity. However, if gravity is due to the curvature of space-time, then light should be affected in the same way as matter. This proposition was tested as follows: During the day, the Sun is too bright to see any stars. However, during a total solar eclipse the Sun’s disk is blocked by the Moon, and it is possible to see stars that appear in the sky near to the Sun. During the total solar eclipse of 1919, astronomers measured the positions of several stars that were close to the Sun in the sky. It was determined that the measured positions were altered as predicted by general relativity; the Sun’s gravity bent the starlight so that the stars appeared to shift their locations when they were near the Sun in the sky. The detection of the bending of starlight by the Sun was one of the great early experimental verifications of general relativity; many others have been conducted since.

One can imagine how many measurements have ben carried out in order to validate and/or refute einstein’s theory and its components, one of which is “frame-dragging”.

I quote one of the reports on such measurements (BBC NEWS):

“Frame-dragging” is the effect wherein a massive body like Earth drags space-time around with it as it spins.”Frame-dragging” is the effect wherein a massive body like Earth drags space-time around with it as it spins.

Ignazio Ciufolini and Erricos Pavlis measured frame-dragging by studying the movements of two satellites in Earth orbit over a period of 11 years.

Ciufolini, from the University of Lecce, Italy, and Erricos Pavlis from the Joint Center for Earth Systems Technology in Baltimore, US, analysed millions of laser range-finding signals that are reflected by the satellites Lageos and Lageos 2.

These reflected signals are normally used to map variations in the Earth’s gravitational field.

But the researchers analysed them for evidence that the satellites’ orbits were altered by frame-dragging, also known as the Lense-Thirring effect after the Austrian physicists who predicted it in 1918.

Ciufolini and Pavlis say their result is 99% of the value predicted by Einstein’s theory, plus or minus 5%. This result has an uncertainty of about 10% say the scientists.

Commenting on the research, Neil Ashby of the University of Colorado, US, said the result was “the first reasonably accurate measurement of frame dragging.”

He added: “Further analysis is anticipated as additional geodesy missions are undertaken to improve our knowledge of Earth’s gravity field.”

The same researchers reported preliminary findings in 1998, which were roundly criticised. But reaction to the latest measurements has been broadly positive. The new work is based on a new gravity map released last year.

And so the story goes. the good news for Newton’s theory is that it is still good for most cases, as it starts having problems when the mass involved is huge. So we can continue having Newton in our everyday lifes, while Einstein is waving at us from a distant star, riding a light beam.

P.S. I am not going to join Albert this time. I return to Garrowby Hill to visit David Hockney and have a beer at the local inn. And now that we talk about it, I have a small contribution to make to the theories of gravity. I have noticed that after the third pint of ale, my feet are heavier. I have therefore prepared an amendment to the Newtonian theory: the force of gravity is also directly proportional ot the alcohol content of the masses involved. Cheers!!!

Gravity booster