By Kumar David –
A month and 100 years ago in November 1915 Albert Einstein spoke at four weekly meetings at the Prussian Academy in Berlin; at the fourth on 25 November he put forward the general theory of relativity (GR). On 16 and 20 November eminent mathematician David Hilbert presented a strikingly similar formulation to the Gottingen Academy and at a still uncertain date sent a paper much the same as GR except on an abstruse point better appreciated only by the cognoscenti. (Hilbert’s formulation was non-covariant while Einstein’s was covariant; Greek to laymen). There is confusion about the date of Hilbert’s paper as some original printer’s proof pages have been lost but it appeared in print on 6 December. Einstein’s was published on the 2 December. Einstein and Hilbert were friends and had corresponded and shared ideas about the difficulty of formulating the GR equations. Hilbert invited Einstein to Gottingen in June-July 1915 where he stayed with Hilbert and gave two 6-hour lectures.
Unfortunately there was bad feeling from Einstein towards Hilbert about getting priority credit for GR. It was settled after Hilbert included the acknowledgement in a March 1916 paper, where he too adopted a covariant approach, which said his (Hilbert’s) “differential equations seemed to agree with the magnificent theory of general relativity established by Einstein in his later papers”. The truth is that though Hilbert the brilliant mathematician may or may not have piped Einstein in polishing GR to formal perfection only physicist Einstein grasped its earth-shattering implications. He had been working towards an overturn of the gravitational paradigm since 1913. Quite rightly GR is called “Einstein’s theory”. But this apart great scientists are not free of human foibles.
In recognition of the centenary event that motivated this piece I thought it ok to include a popularised recapitulation of an eye-catching aspect of GR, but since not all readers may care for scientific mumbo-jumbo I have relegated it to the end where it may be skipped.
Who first proposed evolution theory?
The common view that Alfred Russell Wallace was a lightweight naturalist tramping South American and East Asian forests is wrong. He was an outstanding scientist with major contributions to biology, geography, geology and anthropology. His honours include the Société de Géographie Gold Medal, Founder’s Medal (Royal Geographical Society), Darwin-Wallace and Linnean Gold Medals (Linnean Society), two Royal Society Gold Medals, and the Order of Merit the highest British civilian honour.
The unforgettable story is how one day in June 1858 Darwin received a letter from Wallace (they corresponded from time to time and Wallace even sent Darwin birds) enclosing a paper which he asked Darwin to forward to Charles Leyll, president of the Linnean Society, for publication “if he thought it sufficiently interesting”; the understatement of the century! Darwin was thunderstruck! The paper replicated the concepts of natural selection and evolution on which he had been working for 20 years but not dared to publish, terrified of a conservative and Christian backlash. Leyll, Joseph Dalton Hooker and Darwin’s bulldog Thomas Huxley devised a solution. They hurriedly organised a meeting of the Linnean Society on 1 July at which Wallace’s paper and an abstract of Darwin studies and conclusions were presented. The Society published both on 20 August. Darwin got back to his book the monumental Origin of Species, published in November 1859.
There has been a long fallout shadow with agitators declaring that Wallace had been denied priority as his paper had been submitted first and that he was entitled to the evolution theory mantle. This is not correct because, though Wallace’s eureka moment was brilliant, nay a stroke of genius, he had nothing like the wealth of detailed studies that Darwin had accumulated over 20 years to establish the theory beyond dispute. As Wallace wrote “this vast, unprecedented (achievement) is the result of the work of one man in the short space of twenty years”. Neo-Darwinism, alongside general relativity and quantum mechanics has become one of the three pillars on which modern science stands.
Isaac’s smear campaign against Gottfried
Yes, yes it’s true that by any yardstick, in any “greatest scientist of all time” stakes, Isaac Newton (IN) will win by a landslide and Philosophiæ Naturalis Principia Mathematica is justifiably saluted as the most significant of all scientific works. Alexander Pope’s intended epitaph is a typical encomium: “Nature and Nature’s laws lay hid in night: God said, ‘Let Newton be’ and all was light”. But as a person Newton was a queer bird. He experimented with alchemy hoping to turn base metal into gold, dabbled in the occult, and his recently published secret religious notebooks reveal that he rejected the Trinity as apostasy and declared that worshiping Christ as God was idolatry. Maybe to be a genius absolutely, one’s pursuits need to be dotty completely – what does neuroscience say?
So it is not surprising that IN and his acolytes engaged in a smear campaign to besmirch Gottfried Leibniz (GL), co-inventor of the calculus, the most important tool of higher mathematics. In the late 1670s IN developed what he called the Method of Fluxions, a geometrical version of the calculus (tangents) as a device for his physics studies, but in keeping with his introverted nature, never publicised it. In 1684 however GL, one of the greatest of mathematicians ever, presented the differential calculus and followed it with the integral calculus in 1686. He also set-out beautiful symbols (the dy/dx and ∫ of your schooldays). British mathematicians resisted these symbols for a century before capitulating. A year later in 1687 Principia was published where IN used the calculus in Fluxion form to capture the grandeur of the heavens.
The smear campaign was ugly and Newton of godlike status, with his hangers-on, buried poor GL whose reputation was resurrected by posterity only much later. In a full-blooded surge of Brit patriotism the Royal Society adopted a resolution in 1715 recognising IN as the sole inventor of the calculus and tried in many ways to smear GL as a plagiarist! It is tempting to trace the decline of British mathematics for the next century to its reluctance to accept GL’s superior symbols. By then mathematics had powered ahead on the Continent (the Bernoulli family, Euler, Lagrange, Laplace, and of course the prince of mathematicians Gauss) but it languished in Britain. The one exception to deserve the epithet great, George Boole, devoted himself to an entirely new field, symbolic logic.
What is the verdict on the priority debate? Newton’s vision was action, motion and dynamics, Leibniz’s geometry and formalism; we behold a physics emphasis versus a mathematics emphasis. Newton the great scientist contrasts with Leibniz the great mathematician. As for chronological priority, it is certain that the two discovered the calculus independently and in the same time period.
Equalisation of the rate of profit
In Kapital III Marx grapples with the ‘Transformation Problem’. The Labour Theory of Value (LTV) declares that all commodities bear a value, corresponding to the labour contained in them, and are exchanged at this value. However in the real world commodities are sold at prices that (in theory and at equilibrium) equalise the rate of profit across the economy. Therefore prices do not necessarily equal values and there is a contradiction between LTV and real world economics. Marx grappled for no less than twelve chapters (including background chapters) but failed to resolve the contradiction. Actually he was ahead of his time and groping towards a Money Theory of Value (MTV), implicit in Volumes II and III but never explicitly articulated – see my piece ‘Marx’s Money Theory of Value’ in Colombo Telegraph, 11 October, 2015, but leave that to one side today.
The point for today is that Volume III was published posthumously by Engels in 1884 and in 1885 a Professor Wilehlm Lexis of Freiburg and Gottingen Universities, better known for the Lexis ratio and Lexis diagram, published a piece claiming that he was the forerunner who had explored this before Marx. Engels in a Preface to Volume III written in 1894 concedes that Lexis had independently worked similar partial positions but says nothing about precedence. As with previous examples there is a difference in clout; Marx located his problem historically and in society, Lexis’s approach is an economic technicality. Anyway it’s a half-hearted priority dispute.
Bending of light
‘Curvature of space’ (space-time to be proper) is a better rendition but ‘bending of light’ is more catchy so I have opted for it to discourage you from turning the page. First you must put two everyday habits out of mind. There are more dimensions to reality (that is GR theorists’ reality) than the three we are content with, secondly gravity is not a force of attraction between masses as Newton told us, no, it’s a kind of geometrical curvature of space. Don’t worry, I will explain with diagrams.
Imagine a bug, a strange fellow who knows only two dimensions, he cannot imagine up and down. If he lives on a globe he will crawl all over the sphere unaware that he is on a two dimensional surface wrapped around a third dimension. Likewise if three-dimensional ‘we’ inhabit a high-dimension universe we too would be clueless if wrapped around the higher dimensions. OK, that’s enough affront to your common senses for one day.
Now for gravitation. If there are no big masses around, space is nice and ‘flat’ as in the smooth outer parts for fig.1 which is familiar three-dimensional space. However is there is big mass present, according to GR our three dimensions will ‘sag’ into the higher dimensions. Gravity, GR says, is not a force, it is a geometric effect; you roll down towards the mass for geometric reasons, not because you are tugged by a force. Next fig.2 explains the bending of light. Light from a distant star (A), if it passes very close to the sun, must travel through the “sag”, so it is “bent” on its way to earth (E). It will then seem to us that the direction of the star is B. Of course one can’t see any of this by day, the glare of sunlight blanks out all the stars. Except, that’s right, except during a total solar eclipse, when the whole starlit sky springs into view behind the darkened solar disc.
So if during an eclipse you look at star A whose position is well known and hey presto its not there, it seems to have moved to B, you have an anomaly, an aberration. All observations of the star-sky during eclipses have confirmed such aberrations, tiny though they be – just s few arc-seconds. (An arc second is one degree of angle divided by 3600; but astronomers are terribly clever and can measure these tiny shifts). The shift has been thoroughly established indisputably anchoring one of GR’s most startling predictions (the other exciting predictions are the expanding universe, black holes, gravitational lensing and to an extent the big-bang). General relativity is a cornerstone of cosmology in the current epoch in the evolving history science.