Mathematics falls from grace (Part 2)
By the time modern Statistics arose, the mechanical conception of nature (discussed in Part 1) had already greatly broken down, under the impact of its own achievements. Three great nineteenth century advances were critical in this respect: the law of the conservation of energy, the discovery of the organic cell as the common unit of both plant and animal life, and Darwin’s theory of evolution.
Engels says of these developments: “…empirical natural science made such an advance and arrived at such brilliant results that not only did it become possible to overcome completely the mechanical one-sidedness of the eighteenth century, but also natural science itself, owing to the proof of the inter-connections existing in nature itself between the various fields of investigation (mechanics, physics, chemistry, biology, etc.), was transformed from an empirical into a theoretical science and, by generalising the results achieved, into a system of the materialist knowledge of nature… The unity of all motion in nature is no longer a philosophical assertion, but a natural-scientific fact.”
The first result of the breakdown of the old, rigid certainties and “mechanical one-sidedness of the eighteenth century”, however, was a step in the opposite direction: increasing challenges to the materialist assumptions (still mostly unconscious) of the natural scientists, and a strident re-assertion of idealist philosophy in science, based partly on the findings of modern physics. This was initiated by the physicists themselves, as they struggled to comprehend their own findings. The discovery of X-rays, and of the new radioactive elements polonium and radium, and more accurate measurements of time and the speed of light, raised some very fundamental questions about long-held beliefs about the nature of matter, space and time, and thus set this process in motion.
The French mathematician and physicist Henri Poincaré, for example, whose own investigations of time had raised questions about the Newtonian postulate of absolute time and space, wrote, “These principles on which we have built all, are they about to crumble away in their turn? This has been for some time a pertinent question. When I speak thus, you no doubt think of radium, that grand revolutionist of the present time… It is not alone the conservation of energy which is in question; all the other principles are equally in danger…”(The Foundations of Science, p303) Discussing recent experiments to determine the mass of electrons, Poincare concludes that at least in relation to the electron, “Mass disappears.” And Poincaré’s idealist conclusions include the following in regard to time and space: “It is not nature which imposes them upon us, it is we who impose them upon nature because we find them convenient.” (The Foundations of Science, p207)
This is where Vladimir Lenin entered the debate.
We generally think of Lenin as the architect of the Bolshevik Party, rather than as a philosopher. But in 1907, in the wake of the defeat of the 1905 revolution in Russia, with consequent moods of despair and disorientation deepening among a layer of revolutionists, questions of philosophy became a central issue in the fight to build a revolutionary party in Russia. A leader of the Bolsheviks, Alexander Bogdanov, had embraced the idealist epistemology circulating under the name Empirio-Criticism, and had asserted that it was compatible with Marxism. Much in the same way that he did later with The State and Revolution, Lenin undertook an exhaustive survey of the current literature on the question, holding it up against the writings of Marx and Engels. Lenin’s polemic against Bogdanov and the other champions of Empirio-Criticism was published in 1909 under the title Materialism and Empirio-Criticism (MEC).
The chief philosopher of Empirio-Criticism was the Austrian professor Ernst Mach. A physicist like Poincaré, Mach thoroughly explored and critiqued the weaknesses in the Newtonian ideas of absolute time and space. (Albert Einstein credited Mach with helping his thinking while he was developing the Special Theory of Relativity.) But Mach also presented an idealist view of the relationship between mental images and the sensations from which they were formed, claiming that “Sensations are not symbols of things. The ‘thing’ is rather a mental symbol for a complex of sensations of relative stability.” (quoted in MEC p40).
Lenin observes, “…Mach’s doctrine that things are complexes of sensations is subjective idealism… it inevitably follows that the whole world is but my idea. Starting from such a premise it is impossible to arrive at the existence of other people beside oneself: it is the purest solipsism.” (MEC p42)
In his philosophical work, The Grammar of Science, Karl Pearson, the theorist of modern Statistics, expressed his full agreement with Mach. Lenin describes Pearson as “conscientious and honest opponent of materialism.” (MEC p189) “The philosophy of Pearson,” writes Lenin “as we shall repeatedly find, is distinguished from that of Mach by its far greater integrity and consistency… Pearson fights materialism with great determination.”(MEC p52) “Pearson spares no effort in combating the concept of matter as something existing independently of our sense-impressions.” (MEC p92) “…the Englishman Karl Pearson, expresses himself with characteristic precision: The laws of science are products of the human mind rather than factors of the external world… [On] the question of causation, Pearson formulates the following thesis: The necessity lies in the world of conceptions, and not in the world of perceptions.” (MEC p160-61 – quoting Pearson’s The Grammar of Science, p243) In Pearson’s view, Lenin summarises, “it is man who dictates laws to nature, and not nature that dictates laws to man.”
Pearson rejected the idea of causation as a fact of nature. “…law in the scientific sense only describes in mental shorthand the sequences of our perceptions. It does not explain why those perceptions have a certain order, nor why that order repeats itself; the law discovered by science introduces no element of necessity into the sequence of our sense-impressions; it merely gives a concise statement of how changes are taking place. That a certain sequence has occurred and recurred in the past is a matter of experience to which we give expression in the concept causation; that it will continue to recur in the future is a matter of belief to which we give expression in the concept probability. Science in no case can demonstrate any inherent necessity in a sequence, nor prove with absolute certainty that it must be repeated.” (The Grammar of Science, p113) This is nothing but a re-statement of the skepticism of David Hume.
Gathering together all the contradictions and expressions of doubt of the physicists who were struggling to understand the new discoveries, Pearson declared that “matter as the unknowable cause of sense-impression is a metaphysical entity as meaningless for science as any other postulating of causation in the beyond of sense-impression” (The Grammar of Science, p251-52)
Regarding the ‘disappearance of matter’ much discussed by physicists, Lenin responds: “’Matter disappears’ means that the limit within which we have hitherto known matter disappears and that our knowledge is penetrating deeper; properties of matter likewise disappearing which formerly seemed absolute, immutable, and primary (impenetrability, inertia, mass, etc) … are now revealed to be relative and characteristic of only certain states of matter. For the sole property of matter with whose recognition materialism is bound up is the property of being an objective reality, of existing outside the mind…. It is mainly because the physicists did not know dialectics that the new physics strayed into idealism. They combated metaphysical … materialism and its one-sided ‘mechanism’ and in doing so, threw out the baby with the bathwater. Denying the immutability of the elements and of the properties known hitherto, they ended by denying matter, i.e. the objective reality of the physical world. Denying the absolute character of some of the most important and basic laws, they ended by denying all objective law in nature…Insisting on the approximate and relative character of our knowledge, they ended by denying the object independent of the mind, reflected approximately-correctly and relatively-truthfully by the mind.” (MEC p260-62)
Lenin concludes: “Modern physics is in travail; it is giving birth to dialectical materialism. The process of childbirth is painful.” (MEC p313)
The process of childbirth proved both painful and protracted. But in the decades that followed, Physics regained its foothold in the material world, on the basis of a radically altered image of nature. This was a true scientific revolution. While it would require a great stretch of the imagination to say that it gave birth to a conscious dialectical materialism, dialectical laws such as the interpenetration of opposites became part of the common language of advanced physics, such as with the dual wave-particle theory of light. Some individual figures among the leading physicists, such as Niels Bohr of the Copenhagen school, eventually adopted philosophical positions close to dialectical materialism (see M. E. Omelyanovsky, Dialectics in modern physics p47).
With Statistical theory, the outcome has been less fruitful. While very few scientists or statisticians today would accept Pearson’s idealist views in toto, his rejection of causation has nonetheless become an axiom of Statistical theory.
Today, the technical advances of computerisation have not only greatly increased the volume and quality of statistical data, but have facilitated its analysis – to the point where any high school student with a spreadsheet can throw up a scatterplot and calculate the correlation coefficient in seconds, tasks which would have required hours of tedious calculation for Pearson himself. Despite all this, Statistics still shies away from the question of causation.
“Correlation does not imply causation” is its watchword – true enough as far as the mechanical conception of causation goes, but it really leaves us at a shallow level of understanding. Moreover, it condemns those who depend on statistical evidence to constant misinterpretation. If, for example, a study finds that a diet high in some particular type of food is associated with a high incidence of some medical condition, the inference is made by many journalists and readers of the report that the food is necessarily the cause of the medical condition, no matter how carefully the authors caution against such a conclusion. For a public hungry to know causes of complex phenomena – and justifiably so – yet which has no model of causation beyond the mechanical one, this kind of misunderstanding is absolutely inevitable.
Statistical theory will not be able to tackle the question of causation without transcending the one-sided mechanical model and developing a dialectical conception of causation. Statistical investigations typically involve complex and multiple causes and effects, where cause and effect transform one into the other. Engels explains: “Reciprocal action is the first thing that we encounter when we consider matter in motion as a whole from the standpoint of modern natural science. We see a series of forms of motion, mechanical motion, heat, light, electricity, magnetism, chemical union and decomposition… all of which…pass into one another, mutually determine one another, are in one place cause and another effect, the sum-total of the motion in all its changing forms remaining the same….Only from this universal reciprocal action do we arrive at the real causal relation. In order to understand the separate phenomena, we have to tear them out of the general inter-connection and consider them in isolation, and then the changing motions appear, one as cause and the other as effect.”
For example, the process of increasing aridity and desertification which threatens many regions is accompanied by retreat of forests. Is the retreat of the forests a cause of the increasing aridity, or is it an effect of it? The answer is: it is both cause and effect (and only one of many causes and effects). But in order to act to halt the desertification, it is necessary to tease apart this reciprocal action further. Statistical methods could be used in this disentangling process, to discover under what conditions one is cause and the other effect. The many feedback loops encountered in ecological and environmental problems are in crying need of such teasing apart.
Ultimately, the activity of human beings forms the test of causality (and of the objective truth of human knowledge in general). Understanding causes enables human beings to produce desired effects. Humanity learned that friction causes heat through making fire by means of friction. This imperative to modify nature to meet human needs is what drives the hunger for knowledge of cause and effect.
It is also why such questions were of such interest to Frederick Engels, Vladimir Lenin, and other working class fighters, and why they placed the defence of scientific thinking – materialist and dialectical thinking – so high among their priorities. The proletariat’s fight for freedom reaches far beyond the fight against oppression and exploitation. It is a fight for conscious control over the processes of both human society and nature. The rise of the working class to power will necessitate a second flowering of science, one that will make the 16th and 17th centuries look like little more than a brilliant anticipation.
As the proletariat moves to wrest control of the processes of production from the dictates of the blind laws of the market, and to put the production of food and fibre and the transformation of energy to meet human needs on a truly scientific basis for the first time, the life sciences and earth sciences – Biology, Ecology, Genetics, Geography, Physiology, Medicine and Epidemiology, among others – become the central natural sciences of the day. Alongside these, their handmaiden science, the materialist mathematics of Statistics, can expect to advance rapidly. Similarly, the sciences of human society, presently so clouded by the obfuscations of a class which has little to gain and much to lose by their development, will make rapid advances. Science will cease to be the exclusive preserve of a professional elite, and will become the common heritage and daily practice of educated, toiling humanity.
As Engels says, “Thus, at every step we are reminded that we by no means rule over nature like a conqueror over a foreign people, like someone standing outside nature, but that we, with our flesh, blood, and brain, belong to nature, and exist in its midst, and that all our mastery of it consists in the fact that we have the advantage over all other creatures of being able to learn its laws and apply them correctly.” (Engels, The part played by labour in the transition from ape to man)