Comrade Haldane Is Too Busy to Go on Holiday

by Gavan Tredoux

  Calling variation the “synthesis” of the “antithesis” mutation and the “thesis” heredity is empty, given that variation is exactly what mutation produces; there is no synthesis. Stabilizing selection, by far the most common kind of selection, does not produce evolution; it produces stasis, the opposite of evolution, since it immediately eliminates the variation introduced by selected-against mutation, leaving things as they were before. And in the rare cases when evolution really is the result, because the mutation is selected for, that is immediately provided by the “antithesis”; merely relabeling it “synthesis” is not helpful. As A. P. Lerner put it, this approach “clearly does not improve the interpretation of biological facts for students who are not suffering from an overpowering emotional urge to embrace the dialectic.”94

  Engels felt confident that dialectical materialism could conquer mathematics, too, and Haldane’s treatment of this excursion-without-compass-or-map anticipates his later response to the innovations of Soviet biology under Lysenko. Engels had some trouble with calculus, which he attempted to teach himself late in life, from scratch, apparently working from a textbook published in the 1790s. This text still employed the system of infinitesimals, which gave the right results if used in the right ways, but lacked rigorous justification. Augustin-Louis Cauchy would supply a rigorous reworking of calculus in the 1820s by discarding infinitesimals and formalizing the notion of limits. In the twentieth century, infinitesimals even reemerged in a completely different rigorous formalization as a result of advances in mathematical logic and model theory. But Engels did not know about Cauchy, and persuaded himself that infinitesimals and consequently differentiation were “contradictions” in mathematics, which should just be embraced as part of the dialectical process.

  Meanwhile, Marx had also been trying to work mathematics out from scratch, armed only with the dialectical method, and had concluded after much labor that y = ax could be differentiated, which he conceived of as a kind of symbolic computation, by first writing it as y/x = a, and then imagining that at x := 0 (where “:=” means “assigned”) this gave 0/0 := a. Since dy/dx = a, as the textbooks taught, he concluded that mathematicians had simply defined dy/dx := 0/0 as the next symbolic computational step—something like the progression of history. Engels wrote to Marx enthusing that this demonstrated how the “contradictions” in mathematics simply had to be accepted, since the ratio of “vanished quantities,” 0/0, made no sense. “I compliment you on your work. The matter is so perfectly clear that we cannot be amazed enough how the mathematicians insist with such stubbornness upon mystifying it. But that comes from the one-sided way of thinking of these gentlemen.”95 The poly-sided Engels found many other “contradictions” in mathematics involving things he did not understand—for example, complex numbers, and the fact that square roots are powers of ½.

  Haldane’s account of all this, from his preface to the English translation of The Dialectics of Nature (1940), needs considerable unpacking and unwrapping.

  Engels’ remarks on the differential calculus, though inapplicable to that branch of mathematics as now taught, were correct in his own day, and for some time after. He points out that it actually developed by contradiction, and is none the worse for that. To-day ‘rigorous’ proofs are given of many of the theorems to which he refers, and some mathematicians claim to have eliminated the contradictions. Actually they have only pushed the contradictions into the background, where they remain in the field of mathematical logic. Not only has every effort to deduce all mathematics from a set of axioms, and rules for applying them, failed, but Gödel has proved that they must fail. So the fact that the calculus can be taught without involving the particular contradictions mentioned by Engels in no way impugns the validity of his dialectical argument.96

  It is not true that Engels, who was writing in the late 1870s, was “correct” in his own day. As we have seen, he was at least forty years out of date. Nor is it true that the formalization of calculus was “developed by contradiction” unless that means nothing more than that a rigorous treatment was postponed until one could be found. The fact that Cauchy and others worked hard to place calculus on a rigorous footing shows rather that they did not accept a “contradiction.” The idea that mathematicians have only “pushed” the “contradictions” a level up into mathematical logic is an early, and very egregious, example of the sort of misuse that Gödel’s theorems have suffered.97 This sense of “contradiction” is not something we don’t understand yet, or something Engels does not understand, but logical inconsistency within a formal system, the statement ‘p and not-p’. The fact that a formal system powerful enough to construct integer arithmetic with both addition and multiplication cannot be used to prove its own consistency—so that the system cannot derive ‘p and not-p’—is not an invitation to embrace contradictions in mathematics. For example, if someone were to discover an inconsistency in Zermelo-Frankel set theory today, considerable effort would go into devising a new system. Otherwise that theory would literally prove everything, since a false statement implies anything, and the system would be no use—at least, to a non-dialectician. And calculus is not merely “taught” using rigorous methods today—as if this is a matter of pedagogical style—but was completely rebuilt to use those methods by 1830, even if the new system took a little longer to reach England.

  The thing to notice here is the way in which Haldane engages in special pleading on behalf of Engels. Since Haldane was a skilled mathematician himself (putting the Gödel flummery to one side as a bit of overambitious dabbling), he could certainly recognize the concerted mathematical illiteracy displayed by Engels, who was out of his depth here at the shallow end. Jean van Heijenoort, who was once Trotsky’s bodyguard in Mexico but became an eminent logician after he renounced Marxism and gave up politics, wrote an amusing essay that surveys the impressive dimensions of this illiteracy—it has even been said that van Heijenoort finally gave up Marxism when he encountered Engels on mathematics.98 Instead, Haldane screened Engels behind an evergreen hedge that few of his readers would have been able to poke through, leaving them with the idea that Engels was not bad for his era, even partly correct, maybe well ahead of his time in some ways, with an argument valid in parts. Later, he would say much the same about Trofim D. Lysenko.

  Another interesting episode throws some light on Haldane’s knowledge of Soviet practices at this time. In an intercepted letter to the Marxist historian Dona Torr, dated November 3, 1938, Haldane thanked her for lending him a copy of a Soviet edition of the Dialectics of Nature. He was taking it with him to Spain, but he had spotted some excisions from an earlier edition he had seen. “I am inclined to think that somebody in Moscow had quietly suppressed some passages in the earlier edition. If not I must have imagined them. Granted that they were passages where Engels backed the wrong horse in a scientific controversy, but I don’t think we have any right to suppress them without mentioning the fact. As a matter of fact his mistakes were most interesting, and as he did not publish the stuff he cannot be held responsible for the mistakes.”99

  4. STALINOPHILIA

  On December 1, 1937, the Daily Worker announced “J.B.S. Haldane to Make Science Plain for You . . . a special and exclusive series of articles dealing with science from the point of view of the progressive thinker. . . . He treats his subject from the point of view of the active fighter for Socialism.” In case these public announcements were not enough, a few months later the MI5 informant M/2, who had been talking to Marjorie Pollitt, reported that “it is clear that J.B.S. Haldane is in the closest touch with the more intellectual leaders of the Communist Party. He apparently sees Harry Pollitt and Emile Burns quite frequently.”1 Haldane would go on to write hundreds of articles for the Daily Worker, up until the 1950s. Most of these were written in the style of popular science that he had based on H. G. Wells and perfected by the early 1930s—only now with Marxism, the Soviet Union, Lenin, and Stalin drawn in at every possible opportunity for inordinate praise. H
e republished most of these articles in book form, adding an occasional footnote or addendum, so that they were more generally available.

  Haldane ranged far and wide to find interesting topics, from biology to physics, cosmology, mathematics, medicine, physiology, statistics, geography, chemistry, and beyond. Connecting all these topics to politics sometimes required acrobatics. For example, when explaining the rudiments of calculus, Haldane simply asserts that the Soviets know more about it: “To judge from the technical books which sell by tens of thousands in the Soviet Union, a bigger fraction of the people understand it there than here. In a society where workers are encouraged to understand their work it is natural that it should be widely studied.”2 Or, when considering statistical samples, that the Soviets got more political sampling done: “in the Soviet Union today all citizens get at least some political education from attending public meetings to decide on local as well as national affairs.”3 An article on controlled experiments presented an opportunity for flights of fancy about Soviet “experimentation” and Stalin’s History of the Communist Party.

  Marxism became more scientific as it developed in Leninism and Stalinism. The Bolsheviks had a correct political and economic theory. But that was not enough. They experimented on a great scale. For example they tried state farms and collective farms. The latter worked better in most cases. . . . They were able to compare the results of different experiments, for many types of productive relation are possible under Socialism. Above all, as any reader of the History of the C.P.S.U. finds out, they learned from their mistakes in a truly scientific manner. Leninism is not only a historical science like geology. It is an experimental science because Leninists make history as well as studying it.4

  Psychology? “Though Marxism will certainly benefit from advances in individual psychology, it is already a genuine and scientific analysis of human behaviour in the mass.”5

  Geology? “Marxists think that history is moving towards universal Socialism and the breakdown of barriers not only between classes but between nations. And one solid block of two hundred millions in the Soviet Union is working towards these goals.”6

  Probability? “You can never be sure that you will not die before you get home, or that when you do you will not find that your wife has gone mad or your child been run over. Society should be organised so as to make such events as these as unlikely as possible. It is a striking fact that in the Soviet Union the theory of probability plays a big part in planning.”7

  Weed control? “In a socialist country all applied science is public service, and the gap between theory and practice is narrowed. That is one reason why more and more scientists are becoming socialists.”8

  Newts? “In the Soviet Union, aquaria were very well developed. . . . In 1934 it was easier to buy small tropical fish in Moscow than it was in London.”9 Even in the case of flying ants, we are informed along the way that “under socialism the average citizen will have more, not less, private property than to-day, besides his or her share in the public property.”10

  But what about mining? “It was not merely uneconomic to take steel for thousands of miles from Ukraine to Siberia, when it could be made on the spot, or to take raw cotton from Tashkent to Moscow, and send cotton goods back again. Stalin saw that the formerly subject peoples had a right to industrial development.”11

  And gas? “Near Moscow the most remarkable of all the developments of gas liquefaction is in progress. Some of the coal seams are near ground level and only a foot or two thick. The Soviet people do not want miners to work in such narrow seams [so they turn the coal into gas.] . . . It is wonderful to think what this will mean from the human angle. Instead of coalmines working under dangerous and dirty conditions, and gas-works which belch out smoke and can be smelt a mile away, there will be spotlessly clean factories with machinery controlled by a few skilled men and women. Under capitalism the worker is subordinated to the machine. Under socialism the machine becomes the servant of man as it should be.”12

  Surely not cooking? “Rational cooking on a factory scale is more likely to start in the Soviet Union than elsewhere.”13

  Apparently, in the Soviet Union even small children, when they were not savoring “rational cooking on a factory scale,” were scientists too. “In Britain many school children learn science, but they have little chance of making any discoveries for themselves. In the Soviet Union some children make discoveries. . . . [M]any birds fly south in autumn . . . to discover what routes they took the children in hundreds of country schools started trapping birds. The traps were carefully designed so as not to hurt them. Each bird had a numbered ring put on its leg and was then let loose. Results began to come in when the same bird was caught two or three times in the same place.”14 But this is just a foretaste of the scientific enlightenment that is to come. “With the combination of scientific education and leisure to which we may look forward as Leninism spreads over the world, we can look forward to a day when about one person in twenty will be a naturalist, and many mysteries of nature will be a mystery no more.”15

  There hardly seem to be any limits. In the context of an article about the mathematician G. H. Hardy, a self-declared enemy of all applications of mathematics, universal versatility emerges instead.

  Lenin aimed at something quite different, a society of ‘men who can do everything,’ where professors can and do mend their own cars, and mechanics investigate the scientific principles involved in their jobs. The Soviet Union has not yet reached this goal, but it is well on the way to it. Foreign engineers who brought over complicated machinery to the Soviet Union were often horrified because the workers insisted on taking it to bits, even if it took a month to put it back together again. This meant a delay in starting production, but it meant that the workers were able to mend the machines if they went wrong, and often to improve on their design fairly quickly. Soviet intellectuals are mostly drawn from the ranks of the manual workers, and proud to show that they are still capable of tackling skilled jobs. Clearly a society of this kind can switch from peace to war, and will switch over from war to peace again, much more quickly than our own; quite apart from the fact that there are no landlords and other vested interests to impede these changes. . . . This is why Marxism is rightly called scientific socialism. It is based not merely on an analysis of the breakdown of capitalism, and what is needed to replace it, but on a study of how social changes actually do occur. Before 1917 it had not had an adequate experimental test. But Lenin, Stalin and their collaborators, have given it the test which every scientific theory requires, and it has proved to work in practice. No wonder that Marxism is spreading among scientists to an extent that alarms many people.16

  In case human instincts might seem like a hurdle here, Haldane is confident that man’s very nature can be remade, quickly. Indeed, this had already happened. “Human character can be changed in one generation. The younger generation in the Soviet Union will work together for the public good. They regard the struggle for one’s own interests which is inevitable under capitalism, as being not so much wicked as ridiculous selfishness.”17 And so when considering human needs, the Soviet Union pointed the way to prosperity, though the example may be harder to emulate elsewhere.

  The Soviet Union was so backward technically at the time of the revolution that it was only entering the age of universal plenty in 1941. Britain could enter it within a year of establishing socialism. . . . For the younger people in the Soviet Union, brought up under socialism, mostly take it for granted that it is pleasant and honourable to work for the community. They are therefore ripe for communism. We will not be so till socialism has taught us the same moral lesson.18

  Fortunately, “the example of the Soviet Union will lead other countries to adopt socialism. . . . If we are not afraid of applying the ideas current in the Soviet Union to our own affairs, we too have a splendid future ahead of us.”19 Part of the secret of this “universal plenty,” apparently, was planning.

  There are two S’s in U.S
.S.R. One stands for Socialist and implies planning from above; the other for Soviet, means initiative and criticism from below. The two-way traffic of ideas is as vital to science as it is to industry. Without planning, Soviet science would not have shown the greatest growth in a generation which has ever been recorded, and, to take only one example, the Red Air force would have been many years behind the Luftwaffe in design. Without democracy the Soviet scientists would have made few original discoveries, and would not have had the initiative needed to tackle war problems.20

  Haldane was quite definite about who was responsible for the universal plenty. “No living man has a clearer grasp of the nature of society than Stalin, who has played a leading part in two great changes, the overthrow of capitalism, and the building up of socialism.”21 But these developments did not come at the expense of freedom, which was rapidly improving under communism, approaching American levels. “I am inclined to think that the average man has a greater freedom of movement in the United States than anywhere else, and that this freedom is increasing most rapidly in the Soviet Union, where it is already fairly high. This, if correct, is due to the great development of transport and the real high wage in the U.S.A., and to the system of holidays with pay and workers’ holiday resorts in the U.S.S.R., together with the fact that, as there is no unemployment there, workers tend to move very freely from one job to another.”22

  Freedom of movement in the land of universal plenty was accompanied by freedom of expression, up to a point.