The Philosophy of Nature and Philosophy of Physics in the Writings of Marian Smoluchowski

1.1.1. Smoluchowski in citation lists

The year 2017 saw the hundredth anniversary of the death of outstanding Polish physicist Marian Smoluchowski. Over the more than a hundred years since his death, this great scholar has been widely forgotten. Few researchers, even among physicists, are able to cite any of Smoluchowski’s scientific achievements on an ad hoc basis, and outside science circles his name is not associated with physics at all. Scientific, biographical or memorial publications about Smoluchowski have appeared so rarely over the last hundred years that the memory of him has been erased. The hundredth anniversary of his death passed practically unnoticed. Meanwhile, had it not been for his untimely death, Smoluchowski would probably have become a Polish Nobel Prize winner. His scientific achievements are impressive and undoubtedly entitled him to receive the prize. This monograph is primarily an attempt to demonstrate the contribution of the physicist Smoluchowski to philosophy, and especially to the philosophy of nature, but also to raise awareness of the position he occupies in the world of modern science, despite the passage of over a hundred years since his death.

Smoluchowski’s presence in today’s science is impressive. His equations are among the foundational equations of the theory of stochastic processes. In his book Stochastic Processes in Physics and Chemistry, Nico van Kampen writes that the Chapman-Kolmogorov equation, which relates to homogeneous Markov processes, is also often called the Smoluchowski equation but he will not use that name because it is used interchangeably with several other closely related but non-identical equations¹. Elsewhere, he states that the Fokker-Planck equation, which describes the temporal evolution of the probability density function, is also sometimes called the ‘Smoluchowski equation’². The Smoluchowski continuity equation is one of the most frequently used in descriptions of sedimentation and coagulation processes. This is the equation into which Fick’s law (the diffusion law) was inserted, and in which the operation of the external field was taken into account. Smoluchowski was the first to note that the phenomenological laws of macroscopic diffusion could be applied to probability. The diffusion process is the result of the superposition of the Brownian motion of individual particles of a substance³. The Smoluchowski continuity equation is used in a wide variety of contexts, ranging from theoretical work to industrial applications, for example for industrial water purification, calculations determining the formation of soot deposits in aircraft engines, milk coagulation, the formation of gel barriers, the growth of nanotubes, granulocyte aggregation, and leukocyte adhesion. This equation is often referred to as the ‘Smoluchowski equation’ (for example, when measuring zeta potential and deviations of the current-time relationship in electroosmotic flow). It also appears as the ‘Smoluchowski limit’ in applications of diffusion-limited chemical reaction kinetics and in the study of the class of systems of stochastic differential equations describing diffusion phenomena⁴.

Smoluchowski’s works are cited in publications on the issues of simulation of potassium channels in cell membranes, liquid mechanics (droplet collisions), protein electrophoresis, rotational diffusion, the impact of viscosity on electron transfer kinetics, analysis of the effects of cholera toxins, information thermodynamics (numerical calculations) and Brownian dynamics.

Marian Smoluchowski is the most cited Polish scientist in world scientific literature for the period from 1996 to 2001 – in scientific works globally he was cited 553 times. Also, in the article Contemporary applications of Smoluchowski’s equations, Andrzej Fuliński points out that in the years 1996–2002⁵, Smoluchowski was cited 836 times, though this statistic does not include those publications which only referred to the term ‘Smoluchowski’s equation’. It follows that not only would the number of citations of Smoluchowski not decrease but would even increase.

Publications citing Smoluchowski’s works or referring to his equation could recently be found in a variety of journals, from the most serious physical journals – both general (such as Physical Review Letters and Physical Review) and specialised (Applied Physics Letters, Astronomy and Astrophysics, Colloid Journal, Journal of Aerosol Science, Journal of Chemical Physics, ‘Journal of Crystal Growth or Journal of Fluid Mechanics), through influential chemical journals (such as Dyes Pigments, Industrial & Engineering Chemistry Research, The Journal of Physical Chemistry, The Chemical Society of Japan or Journal of Colloid and Interface Science), biological ones (for example, Biochemistry, Biochemical Engineering Journal, The Journal of Biochemistry Molecular Biology and Biophysics and Journal of Biomedical Engineering), to publications of the calibre of Archive for Rational Mechanics and Analysis, Journal of Engineering for Gas Turbines and Power, Statistics – Theory and Methods, Computational Mechanics or Journal of Computational Physics⁶. This list of scientific journals is impressive, especially considering that they relate to the achievements of a scholar who lived a hundred years ago and that physics has been one of the most dynamically developing fields of science over the last century.

In the article ζ Potential and the Smoluchowski equation, Marek Kosmulski writes that the name Smoluchowski is associated in modern science mainly with the ζ (zeta) electrokinetic potential and the Smoluchowski equation, which allows the calculation of this potential on the basis of measurable quantities, for example electrophoretic mobility. This is not the physicist’s only, or even most important, scientific achievement, but due to the renaissance of interest in colloidal particles—currently called nanoparticles—it is in this context that Smoluchowski’s name very often appears. In the last decade, the correctly spelled name ‘Smoluchowski’ has appeared on average in 1,500 publications per year, published by Elsevier, Springer, the American Chemical Society or Wiley (excluding all other publishers). The search for scientific literature referring to Smoluchowski’s achievements is very difficult, as his name is often misspelt. According to Kosmulski, articles indexed by the Web of Science include the following spellings of his surname: Schmoluchowski, Schmolukowski, Smolucbowski, Smoluchoski, Smoluchovski, Smoluchowiski, Smoluchowsi, Smoluchowsky, Smoluhovski, Smoluhowski, Smolukhovskii, Smolukhovskiy, Smolukhovsky, Smolukhowski, Smolukovski, Smolushovski—and this list, according to Kosmulski, is probably only the tip of the iceberg⁷.

According to the Web of Science, the number of citations of Smoluchowski’s works in the years 1894–2014 amounted to 7,235. For comparison, in a slightly longer period, i.e. in the years 1880–2015, the number of references to the works of Maria Skłodowska-Curie (1867–1934) is 1,582⁸.

The numbers given by the Web of Science are constantly growing and will continue to grow. This is made possible by the situation in industry, especially in chemistry and pharmacy, where a large part of the current research concerns coagulation processes. The basis for this research is the formulae and rules developed by Smoluchowski. The most frequently cited article is from 1917, in which he presented a new theory of colloid solidification, published after the author’s death in 1918 in Zeitschrift für Physikalische Chemie (Journal of Physical Chemistry) entitled Study of a Mathematical Theory for the Coagulation Kinetics of Colloidal Solutions. This article has been cited more than 5,500 times. Three discourses on diffusion, Brownian movements and the coagulation of colloid particles, given in 1916 at the Wolfskehl Congress in Göttingen, are still being cited. To this day, they are considered the best introduction to the issues of coagulation.

In 2005, Jorge E. Hirsch, an Argentinean physicist working at the University of California, San Diego, proposed an index reflecting the distribution of citations to a particular scientist’s publications and the number of their best papers. The h-index is a way of measuring scientific achievements taking into account the number of publications and the number of citations. The h-index (index h, Hirsch index, Hirsch number) for a given author is the number of publications cited ≥ h times⁹. This indicator also shows that Marian Smoluchowski is the most cited Polish scientist. The Hirsch index for his publications was 29 at the time of writing, while Maria Skłodowska-Curie’s was 16.

In 1990, two scholars from the Max Planck Institute in Stuttgart—philosopher Werner Marx (1910–1994) and physicist Manuel Cardona (1934–2014)—began a research project called ‘Blasts from the past’. The study was to answer the question of how the importance or usefulness of a scientific article can be measured.

The researchers decided to check how many times a given publication was on the reference lists of other articles. According to the researchers, the number of citations cannot be equated with the overall importance or usefulness of a publication, which applies especially to recent articles, the long-term significance of which may not yet be clear. This also applies to many older articles that are not cited because their results are now so well known that they appear in textbooks without the sources being given. It would be easy to theorise and speculate on this topic, but as the idea’s initiators have stated, there is a satisfactory way to proceed, especially in the case of physics: collecting and analysing data. They analysed a huge proportion of the publications that have appeared in modern times, until 1930. Nearly ten thousand names of scientists—mainly in the exact sciences—were taken into consideration and the citation of their papers in contemporary scientific publications in the years 1990–2003 was examined.

The results of the research indicate the extremely high position of Marian Smoluchowski, whose works are referred to very often today. Out of ten thousand scientists, Smoluchowski was in sixth position, being the first person on the list without a Nobel Prize:

1. Albert Einstein (1921 Nobel in physics) – 3,025 citations (died 1955; lived 76 years);
2. Peter Debye (1936 Nobel in chemistry) – 1,592 citations (died 1966; lived 82 years);
3. Max Born (1954 Nobel in physics) – 1,575 citations (died 1970; lived 88 years);
4. Irving Langmuir (1932 Nobel in chemistry) – 1,564 citations (died 1957; lived 76 years);
5. William John Strutt (1904 Nobel in physics) – 1,503 citations (died 1919; lived 77 years);
6. Marian Smoluchowski – 1,356 citations (died 1917; lived 45 years)¹⁰.

Although Smoluchowski never won a Nobel Prize and lived for 30–40 years less than the other scholars mentioned, the number of publications of the first five scientists listed after Einstein is similar. In this context, an obvious question arises—what would the scientific achievements of our physicist have been if he had lived to an old age?

1.1.2. A Nobel for Smoluchowski?

Another issue that arises after analysing Marx and Cardona’s results is the question of whether Smoluchowski had a chance of being awarded the Nobel Prize. To answer this, it is helpful to realise that at least three Nobel Prize winners—Richard Zsigmondy (1865–1929, Nobel Prize in Chemistry in 1925), Jean Baptiste Perrin (1870–1942, Nobel Prize in Physics in 1926) and Theodor Svedberg (1884–1971; Nobel Prize in Chemistry in 1926)—received the Nobel Prize for the results of work in which they directly or indirectly used Smoluchowski’s research. Bogdan Cichocki writes that he believes Smoluchowski did not receive the Nobel Prize because he died young and the prize is not awarded posthumously. In 1925, the Nobel Prize in Chemistry was awarded to Richard Zsigmondy, a professor at the University of Graz in Austria, for his research in the field of colloids. His work was experimental and closely related to Smoluchowski’s theoretical achievements. The following year, as many as two Nobel Prizes were indirectly related to the great Polish academic. In the field of physics, the prize was awarded to Frenchman Jean Baptiste Perrin for experimental work on Brownian motion, confirming the validity of the Einstein-Smoluchowski molecular theory, while in the field of chemistry the prize went to Theodor Svedberg from Uppsala, Sweden, whose experimental work on suspensions ran concurrently to Smoluchowski’s theoretical considerations related to them¹¹.

Richard Zsigmondy received the Nobel Prize “for his demonstration of the heterogenous nature of colloid solutions and for the methods he used, which have since become fundamental in modern colloid chemistry”¹². Smoluchowski’s contribution to this research is spectacular. Zsigmondy, being an experimentalist, needed a theoretical foundation for his research and took it from Smoluchowski. During his Nobel lecture in Stockholm, he said:

“This induced me to ask the theoretical physicist M. von Smoluchowski to derive an experimentally verifiable formula by which the presence of spheres of attraction could be deduced from the speed of coagulation; von Smoluchowski willingly agreed to my suggestion and gave, in addition, a complete theory of coagulation on a mathematical basis¹³.”

It is therefore likely that it could have been a joint prize for both scientists.

Theodor Svedberg received the Nobel Prize “for his work on disperse systems”¹⁴. Dispersion systems are colloidal dispersed systems, composed of at least two phases, of which at least one is a strongly fragmented material, dispersed in a second phase of a continuous nature, called a dispersion medium. Svedberg and his colleagues published a series of papers devoted to the issue of fluctuation. In the introduction to the first article—A new method of testing the validity of Boyle-Gay-Lussac’s law for colloidal solutions¹⁵—he writes that to interpret the results of the measurements obtained, a theory was needed that would be able to link the observed quantities with the concepts of the kinetic theory of matter. Svedberg found this theory in two of Smoluchowski’s works. These were two articles, the first of which, Über Unregelmässigkeiten in der Verteilung von Gasmolekülen und deren Einfluss auf Entropie und Zustandsgleichung¹⁶ (On irregularities in the distribution of gas molecules and their impact on entropy and on the equation of state), was included in a commemorative publication of 20 February 1904 to celebrate the 60th birthday of Ludwig Boltzmann (1844–1906). In it, Smoluchowski formulated the theory of particle density fluctuations in gas and considered the impact of fluctuations on the equation of state. In the second text,¹⁷ from 1907, entitled A theory of kinetic opalescence of gases in a critical state and other related phenomena, he dealt with the application of his theory to the phenomenon of gas opalescence in the vicinity of a critical state and to the phenomenon of a blue sky and other related effects in which the influence of molecular fluctuations is revealed on a macroscopic scale¹⁸.

Bronisław Średniawa (1917–2014) writes in a paper devoted to both scholars:

The collaboration between Smoluchowski and Svedberg lasted seven years, from 1907 to 1914. In those years, the two conducted scientific correspondence with one another. Beginning in 1908, Smoluchowski cited and discussed, sometimes critically, Svedberg’s results in all his works on Brownian motion and fluctuations. In his works devoted to these issues, Svedberg also mentioned Smoluchowski’s publications and letters¹⁹.

In a speech at the Nobel Prize awards ceremony on May 19, 1927, Svedberg presented the results of research he had conducted in the years 1923–1926 (i.e. a few years after Smoluchowski’s death). In discussing them he did not have the opportunity to mention collaborating with Smoluchowski. It was mentioned by Professor Henrik Gustaf Söderbaum, secretary of the Royal Academy of Sciences. Presenting Svedberg’s merits, he said:

As we have recently heard, Einstein evolved a theory for this so-called Brownian movement which was then developed to a high degree by the now late Smoluchowski… If we now consider a very small volume fraction, the result is that, as Smoluchowski has calculated in detail, the number of particles present simultaneously within this volume can change from one moment to another. Svedberg and his collaborators have been able to confirm this extremely interesting conclusion that a ‘few-molecular’ system having definite limits within a large volume of a material with a definite mean temperature may contain a varying number of particles, partly by counting the colloidal particles, partly in the case of solutions of radioactive substances by counting the number of so-called scintillations²⁰.

Jean Baptiste Perrin, the great French physicist, received the Nobel Prize in 1926 “for his work on the discontinuous structure of matter, and especially for his discovery of sedimentary equilibrium”²¹. The work concerned research that experimentally confirmed the Einstein-Smoluchowski theory. In his essay On Thermodynamic Fluctuations and Brownian Motion, Smoluchowski writes: “Among the experimenters who undertook this research, Svedberg and Perrin and their colleagues should be mentioned above all. “This last scholar in particular managed to verify with great accuracy the theoretical formulae related to Brownian motion.” In 1913, Perrin published Atoms²². He described in it the scope of research, as well as the conclusions and thoughts resulting from the experiments carried out, intended to de facto falsify the Einstein-Smoluchowski theory. In Atoms, Perrin repeatedly cites Smoluchowski’s research work in the field of the theories of Brownian motion, fluctuations and opalescence, which were a theoretical complement to Einstein’s previously published works. Separately, Perrin devoted the entire fifth chapter, Fluctuations, Smoluchowski’s Theory to Smoluchowski’s fluctuations²³. In it, he describes in a matter-of-fact way the theoretical results obtained by Smoluchowski, which he used in his experiments:

We have already indicated one of these phenomena in speaking of the definite though very feeble thermal inequalities which are produced spontaneously and continuously in spaces of the order of a micron, and which are, indeed, a second aspect of the Brownian movement itself. These thermal fluctuations, of the order of a thousandth of a degree of such volumes, seem in practice to be inaccessible to our measurements. The density of a fluid in equilibrium, like its temperature or molecular excitation, should vary from point to point. A cubic micron, for example, will contain sometimes a larger and sometimes a smaller number of molecules. Smoluchowski has drawn attention to these spontaneous inequalities, and has been able to calculate the fluctuation in density…²⁴.

Elsewhere in Les Atomes (Atoms) we read:

No longer confining himself to the case of rarefied substances, Smoluchowski succeeded a little later (…) in calculating the mean density fluctuation for any fluid whatever, and proved that, even with condensed fluids, the fluctuations should become noticeable in spaces visible under the microscope when the fluid is near the critical state. He thus succeeded in explaining the enigmatic opalescence which is always shown by fluids in the neighbourhood of the critical state. This opalescence, which is absolutely stable, indicates a permanent condition of fine-grained heterogeneity in the fluid²⁵.

In Les Atomes, Perrinrepeatedly recalls Smoluchowski’s research, thus proving the importance of his theoretical deliberations and the scientist’s contribution to proving the atomistic structure of matter. However, it should be noted that the works of Einstein were crucial for Perrin: Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten²⁶ (On the movement of small particles suspended in stationary ­liquids required by the molecular-kinetic theory of heat) of May 11, 1905, and Zur Theorie der Brownschen Bewegung (On the Theory of Brownian Motion) of May 19, 1906.²⁷ This approach of Perrin to the work of both scientists demonstrates that shortly after the publications, Smoluchowski was not treated as equal to Einstein in being responsible for the discovery of Brownian motion, despite the fact that—as it may seem—Smoluchowski’s approach to the proof of Brownian motion should have been more persuasive to Perrin as it presented mathematical evidence of these movements from the microscopic perspective.

Smoluchowski’s research used in the works of the aforementioned Nobel Prize winners are not the only examples of the scholar’s scientific achievements that could have brought him the Nobel Prize. A discovery that brought about an almost paradigmatic change in physics was undoubtedly the development of the foundations in the field of stochastic processes and the introduction of probabilistics to the exact sciences. This was an achievement worthy not only of the Nobel Prize, thanks to which the Polish scientist’s name should be permanently inscribed in the history of science.

Mark Kac notes:

Smoluchowski may not have been aware of it but he begun writing a new chapter of Statistical Physics which in our times goes by the name of Stochastic Processes… (…) The novelty and originality of the Smoluchowski approach lie in his bold replacement of an impossibly difficult dynamical problem (…) with a relatively simple stochastic process²⁸.

Smoluchowski also provided the first correct equations linking the ζ potential to measurable quantities, i.e. electrophoretic mobility, flow potential and pressure difference in electro-osmosis. In world literature, these are known as the Smoluchowski equations²⁹, which also qualified him for the Nobel Prize.

Many years later, a great advocate of Smoluchowski, Indian astrophysicist, mathematician and Nobel Prize winner Subrahmanyan Chandrasekhar (1910–1995), argued that only the Polish physicist’s premature death prevented him from winning the Nobel Prize.

In 1973 Chandrasekhar was awarded the Marian von Smoluchowski Medal of the Polish Physical Society in appreciation of his contributions to stochastic methods in physics and astrophysicsand, especially, the Review of Modern Physics 1943 article which covered Smoluchowski’s contributions. In his speech at the award ceremony, Chandrasekhar noted that the Nobel prizes in chemistry awarded to R. Zsigmondy in 1925 and to T. Svedberg in 1926 were for experimental confirmation of Smoluchowski’s theoretical predictions on colloidal and disperse systems and that if Smoluchowski had been still alive he would certainly have been a Nobel laureate himself³⁰.

Unlike another Polish physicist, Karol Olszewski (1846–1915), Smoluchowski was never nominated for the Nobel Prize. Olszewski had two nominations in physics and one in chemistry and is often cited in Polish literature as the only outstanding European physicist working in Poland at the turn of the 19th and 20th centuries. Considering how much his research work gained in importance in the first ten years after his death, Smoluchowski would have had a better chance of winning the prize.

An interesting fact that should be mentioned is the first Solvay Conference, which took place in Brussels in October 1911. It was a meeting of the most outstanding minds in physics and chemistry, devoted to the most important issues of science. This and subsequent Conferences are named after Ernest Solvay—a Belgian industrialist, passionate about science, who organised and financed the event. Among the twenty-one invited guests were such scientists as Albert Einstein (1879–1955), Maria Skłodowska-Curie, Max Planck (1858–1947) and Ernest Rutherford (1871–1937), as well as Jules Henri Poincaré (1854–1912). The event was chaired by Dutch Nobel laureate Hendrik Anton Lorentz (1853–1928). Smoluchowski did not participate in either this or the next Conference in 1913, which was rather surprising given that at that time he was one of the most outstanding physicists in Central and Eastern Europe. The argument presented in this context that physicists from the nations of Central Europe or from those belonging to the multinational empires of the time, i.e. Prussia and Austria-Hungary, is less than convincing as Emil Warburg (1846–1931) from Berlin participated in it. It is much more convincing that the main topic of the conference was the theory of radiation and quanta, i.e. issues that were not directly related to Smoluchowski’s research, but this is an issue we shall return to in subsection 7.5, ‘Perrin’s Experimental Evidence.’

1.2.1. Memory of Smoluchowski

Smoluchowski was not only an outstanding physicist conducting research at the universities of Vienna, Paris, Glasgow and Berlin, and a scholar working with Gabriel Lippmann (1845–1921), William Thomson, Lord Kelvin (1824–1907) and Warburg. He was a person moving in the circles of European scientific elites, working with the most outstanding European physicists and participating in scientific research that had an impact on the development of modern science. He was a forerunner of many methodological solutions in the field of conducting scientific research. We are indebted to him for our basic successes in promoting and improving the teaching of science in secondary and university education. His philosophical interests deserve special attention, in particular his deliberations in the fields of the philosophy of nature and the philosophy of science, which were often ahead of their time.

The recollections of many people from his social circle, as well as those who wrote about him based on the memories of others, are astonishing in their unanimity. An almost unreal figure emerges from them in which it is difficult to find blemishes or flaws. Undoubtedly, Smoluchowski’s untimely and unexpected death, as is usually the case in such situations, prompted more benevolent, idealising recollections, but monographs and articles, such as the extract from an essay by Stanisław Loria (1883–1958) cited below, written on the 35th anniversary of the scholar’s death, depict a unique figure. Loria wrote:

the development of Smoluchowski’s scientific work and the content and value of his most accurate dissertations draw a profile of this most outstanding Polish physicist as a researcher of pioneering initiative, equipped not only with extraordinary abilities, but also with willpower and the ability to overcome difficulties. Dedicated with all his soul to science, however, he was not of the erudite type, carefully collecting and storing information in case of need. Faced with a clearly formulated problem, he did not waste time looking to see whether there existed ready-made solutions that may have slipped his mind, but pursued his own, short, sometimes bumpy and difficult, path to the goal. At the same time, he was characterised above all by the courage and apposite instinct of the seeker and the will to accomplish a task through his own creativity and assiduous work³¹.

A thesis that well defines the essence of Marian Smoluchowski’s thought was included in an article by Władysław Kapuściński (1898–1979), who noted that in the history of the rational knowledge of nature there are two trends that constantly complement one another and intertwine in the ongoing process of learning about nature. The first is the development of detailed subject research, consisting of discovering the laws of nature based on experiment. In the 17th century, this trend led to the creation of the so-called exact sciences. The second trend is philosophical research, which has developed as the philosophy of nature. For a significant period of the development of European thought, the philosophical trend played a dominant role, the situation only having changed in modern times. Research in the exact sciences, carried out with great success, accelerated the development of science, at the same time weakening the philosophical trend. This does not mean that philosophical reflection has disappeared from the view of supporters of rational knowledge of nature³². Both intertwining epistemological trends can easily be found in Smoluchowski’s works. It is obvious that strictly scientific research is dominant, but theoretical considerations are supported by elements of the philosophy of science, methodology, epistemology and the philosophy of nature. Smoluchowski’s philosophical reflections do not appear on the periphery of his work in the field of physics but form an important, integral part of his scientific activity, without which his achievements in the field of physics would not be fully understood or may even not exist at all. They can be seen, for example, in the 1923 article On the Concept of Chance and the Origin of the Laws of Physics Based on Probability³³, in which physics, mathematics and philosophy merge into one another.

In trying to characterise Smoluchowski’s philosophical views, we encounter several problems, one of which is the dispersion of philosophical thoughts. Smoluchowski included philosophical reflections in numerous lectures, dissertations and essays, as well as in specialised works in the field of physics. They can be found both in scientific papers and in popular science works addressed to a wider audience. They are not always expressed directly, but an in-depth reading can reveal them between the lines. They are usually found in works strictly related to the problems of physics. Smoluchowski speaks most extensively and directly on philosophical topics in the introduction to the Physics section of his Self-Study Handbook.

Despite his many achievements, Marian Smoluchowski, as already mentioned, is not a well-known or appreciated figure in Polish science, not to mention in philosophy. In 1952, Stanisław Loria wrote about this state of affairs:

Unfortunately, it must be said that Smoluchowski’s fame does not match his merits and the importance of his achievements for the development of the methods and cognitive capabilities of modern physics. Apart from a relatively small handful of trained physicists, among the broad mass of Polish intelligentsia today there are few educated people who know as much as they should about Smoluchowski³⁴.

Unfortunately, little has changed in this respect over the years. Among philosophers, there is even less awareness of Smoluchowski’s achievements. One of the reasons for this situation is the small number of publications that have appeared in the nearly one hundred years since his untimely death. Such sparse interest in the general achievements of the Polish scientist is incomprehensible, and particularly surprising is the lack of publications on the Polish market relating to Smoluchowski’s research used in modern science in the field of the application of probabilistics in physics, stochastic processes, fluctuation processes, opalescence or the ever-increasing importance of his theories regarding coagulation processes.

1.2.2. Smoluchowski in publications

It should be emphasised at the outset that the bibliography devoted to Smoluchowski or referring to his scientific achievements is extremely modest. It is possible that the following discussion does not include all studies, however the purpose of this summary is not to create an exhaustive compendium of Smoluchowski’s works, but rather to illustrate the scale of publications devoted to him. It should also be added that some of the works mentioned here contain numerous interpretative simplifications and even conscious manipulations.

Tadeusz Godlewski (1878–1921)—a physicist and professor at the Lviv Polytechnic—produced a brochure entitled Maryan Smoluchowski published by Mathematical News. His life and scientific work³⁵ had previously featured in Muzeum magazine in May 1918. The author’s intention was to recall Smoluchowski and his achievements in the fields of physics and mathematics.

In 1921, one of the issues of Taternik, the magazine of the Tourist Section of the Polish Tatra Society,³⁶ was dedicated to the memory of Marian Smoluchowski—the mountaineer. However, these works form part of the sui generis epigraphic literature.

After Smoluchowski’s death, his article Several remarks on physical analogies, especially in theories of electric currents, thermal currents and the phenomenon of diffusion, appeared in Mathematical News³⁷. In 1923, with the consent of his widow, Zofia Smoluchowska, a translation from German was also published in Mathematical News of Smoluchowski’s extremely important work On the concept of chance and the origin of the laws of physics based on probability.

In the 1920s, the Polish Academy of Arts and Sciences in Kraków decided to collect and publish all Marian Smoluchowski’s works by, which had been developed by professors Władysław Natanson (1864–1937) and Jan Jakub Stock (1881–1925). Individual volumes were published in 1924, 1927 and 1928 under the title The Writings of Marian Smoluchowski³⁸. This is the most serious collection to date—it includes 90 works.

The 1950s were exceptional for publications devoted to Smoluchowski. In 1951, a short article by Armin Teske, Marian Smoluchowski, appeared in the third issue of the bimonthly magazine for teachers Physics and Chemistry³⁹. A year later, Władysław Krajewski (1919–2006) published an article entitled The Great Physicist and Materialist Philosopher (On the 80th Birthday of Marian Smoluchowski). The article appeared in the People’s Tribune⁴⁰, and was later reprinted in seven other newspapers. In the second half of 1952, the Philosophical Thought quarterly printed an essay, Marian Smoluchowski as a philosopher-materialist, by the same author⁴¹. While Armin Teske’s article recalled Smoluchowski the person, Krajewski focused on his worldview, considering and analysing the physicist’s beliefs in the light of Marxist ideology. Krajewski developed this concept in a book entitled The Worldview of Marian Smoluchowski, published four years later⁴².

The culmination of celebrations of the 80th anniversary of the scholar’s birth was the last (published in 1952), twelfth issue of the popular scientific monthly magazine Problems, which contained three articles devoted to Smoluchowski by Loria and Krajewski as well as extracts (in the form of an article) from the Self-Study Handbook.