Abstract
George Sarton had a strong influence on modern history of science. The method he pursued throughout his life was the method he had discovered in Ernst Mach’s Mechanics when he was a student in Ghent. Sarton was in fact throughout his life implementing a research program inspired by the epistemology of Mach. Sarton in turn inspired many others in several generations (James Conant, Thomas Kuhn, Gerald Holton, etc.). What were the origins of these ideas in Mach and what can this origin tell us about the history of science and science education nowadays? Which ideas proved to be successful and which ones need to be improved upon? The following article will elaborate the epistemological questions, which Charles Darwin’s “Origin” raised concerning human knowledge and scientific knowledge and which led Mach to adapt the concept of what is “empirical” in contrast to metaphysical a priori assumptions a second time after Galileo. On this basis Sarton proposed “genesis and development” as the major goal of his journal Isis. Mach had elaborated this epistemology in La Connaissance et l’Erreur (Knowledge and Error), which Sarton read in 1911 (Hiebert in Knowledge and error. Reidel, Dordrecht, 1976; de Mey in George Sarton centennial. Communication & Cognition, Ghent, pp. 3–6, 1984). Accordingly for Sarton, history becomes not only a subject of science, but a method of science education. Culture—and science as part of culture—is a result of a genetic process. History of science shapes and is shaped by science and science education in a reciprocal process. Its epistemology needs to be adapted to scientific facts and the philosophy of science. Sarton was well aware of the need to develop the history of science and the philosophy of science along the lines of this reciprocal process. It was a very fruitful basis, but a specific part of it Sarton did not elaborate further, namely the erkenntnis-theory and psychology of science education. This proved to be a crucial missing element for all of science education in Sarton’s succession, especially in the US. Looking again at the origins of the central questions in the thinking of Mach, which provided the basis and gave rise to Sarton’s research program, will help in resolving current epistemic and methodological difficulties, contradictions and impasses in science education influenced by Sarton. The difficulties in science education will prevail as long as the omissions from their Machian origins are not systematically recovered and reintegrated.
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Notes
This is a part-quotation only. Because of the complexity of Huxley’s initial text, it is more economic to quote this way. Any reader may feel free to look up the actual quotation.
The concept of atom certainly has strong inherent metaphysical aspects. Mach always asked “Have you seen one?” with the irony implied in using a strong Austrian accent “Ham’s eens g’sehn?”.
Similarly, the social perspective might not be very helpful in analyzing individual “errors” in the knowledge process. It is not the social construction of the world, but the individual construction of the world, i.e. adaptation to individual experiences (Mach 1905), which possibly lead to inconsistencies or methodologically sub-optimal approaches in the world view. The social parts of the process tend to be important in individual construction, but they do not replace the generality of the world view. Sensual experiences are individual.
Of course, maybe some elites might have the feeling of losing their influence in the short-term and instinctively fear such a democratic approach. The Greek scientists inherently supposed that they benefitted from the institution of slavery and therefore, elite knowledge was institutional for them. They also, like Plato, sometimes argued for defending the specific knowledge of their “polis” against the knowledge of other city-states and send pupils unfit for “initiation” to be “secretly dispersed among the inferior citizens” (Plato 360–380B.C./1871/1892 Timaeus, p. 439). Mach suggested that in some aspects, modern science teaching still inherently defends some of such attitudes, though for him science can only grow in a cosmopolitan atmosphere where many different ways of thinking contribute their experiences and criticisms (Mach 1914).
Also Sarton argued that the most important contributions to Greek science after the famous schools had been sufficiently established, such as Archimedes, were mostly coming from the periphery and not the initial location of the schools of thought (Sarton 1959). It was the Macedonian Alexander and his successors, not a Greek ruler, who implemented Diogenes’ idea of the “cosmopolitan” on a larger political level. In medieval times, similar attitudes of the Catholic Church to defend its quasi-monopoly on knowledge can be argued to have contributed to the much attested scientific sterility of scholasticism (see also Mach 1905 or Zilsel 1976). Maybe it is not by chance that some empirically oriented authors, such as Berkeley and Mach used the concept of “vulgar” thinking not as diminutive, but as an integral concept for understanding the genesis of scientific knowledge (see Berkeley 1705; Mach 1886/1914).
Actually, every philosopher has his private natural science and every natural scientist has his private philosophy. Only that these private sciences tend to be of a slightly antiquated kind. […] At some places, [the ages-old paths] seem to be blocked by quite natural, instinctive philosophical and natural science prejudices that have remained as rubble from older attempts, failed work. It would be recommendable to clear these heaps of rubble from time to time or to build a bypass around them.” (Mach 1905/2002 p. 4) More recently, gestalt psychologists such as Lipmann and Bogen (1923) and system theoreticians, such as Hayes (1978) have used the concept of “naïve physics” in order to make a similar genetic analysis, but based on a slightly less “offensive” concept.
The German Erkenntnistheorie literally translates as “theory of knowledge/cognition”. The meaning in the Machian sense is different from, but related to epistemology (which will be elaborated later). In order to gestalt-psychologically denote this difference, the usage of the German term “erkenntnis” will be kept. The term “erkenntnis-theoretical” will be used as an adverb. Mach used the terminology of erkenntnis-psychology in order to clarify—like Sarton with his concept of humanism (Sarton 1931/1962)—that he considered his view mainly derived from his experiences of natural sciences and not from classical philosophy.
See part I regarding Mach’s definition of an enlarged (generalized) concept of genesis based on Lamarck, Spencer, Darwin (Erasmus and Charles), Wallace, Mendel, etc.
One has to be careful to extract the teleological and anthropomorphic parts from this argument. Is the most reproductive and selfish individual the survivor? Or is it a free rider, like a bacteria culture in a petri dish producing hazardous waste until all die? What is the meaning of “survival” in a transformative world?
This concept is at least partly based on a confusion of the “experience of the individual” with the “construction of the concept of self”; in this confusion, science and religion are intermingled, so that a specific religious concept of “self” is set at the bottom or rather “top”, from which then the concept of scientific reasoning—and science in general—is derived (see for instance Plato 1871/1892 Vol. III, p. 463).
Many human “reflexes” are largely adaptive as a combination of congenital reflexes and psychical gestalt adaptations. In sucklings the sucking, gripping, walking, etc. are thus plastic also in being a reciprocal psycho-physiological process. Ch. Bühler (1935) wrote: “Instinctive actions [of the suckling] are not excluded because the child does the imitational actions only rudimentary, namely laboriously, cumbersome and incompletely. Also other actions regarded as instinctual, such as the sucking, are initially produced laboriously and in conjunction with excess, wrong or even hindering co-actions.” The gestalt concept initially derives from Mach. Its current use in psychology tends to reduce it to a “holistic” concept, i.e. a concept of fixed Aristotelian “form” instead of Darwinian process transformations. For more details on the discussion between Bühler and the Finnish gestalt psychologist Eino Kaila around the gestalt concept, see Siemsen (2010a). Mach, Kaila and this discussion were very influential for Finnish science education. Mach’s concept of gestalt is centrally used in it (see Kurki-Suonio 2011).
This seems to be different for humans at least compared to many species of apes. The biological hypothesis of neoteny (the retention of juvenile characteristics into adulthood) suggests that humans partly evolved by mutations, which caused earlier discontinuation of ontogenetic development in childhood. Therefore, also the adult human skeleton is more similar to young great apes than to adult ones. Haeckel had observed this by adapting the idea from Huxley to show Human and great ape skeletons next to each other. Haeckel replaced some of Huxley’s skeletons by adolescent versions (see Haeckel 1905). This neotenic adaptation made reflexes less important relative to cultural learning, but culture became thereby also more central for the survival of sucklings. Humans “lost” survival reflexes in order to “gain” flexibility in learning. The result is a higher plasticity of the total process.
See part I: “I have lectured on Greek science and civilization, for instance, to boys whose whole past—whose living past—was at most two centuries deep: the depth of a skin. […] I prefer, however, to lecture to more sophisticated people, who have already obtained some sort of historical background and a sense of perspective.” Sarton (1922b, p. 242) Due to the time-frame in science education (from professor to teacher to student), ideas that are produced and propagated nowadays need a lot more than 20 years until they have a chance to be empirically discussed and settled.
So in as far as Mach was the role model for Sarton in science education (see part I), Mach then is the indirect (3rd generation) role model for many countries in the world. Are they aware of this? Should they be? What effect does forgetting one’s intellectual roots have on the actual quality of education? Could this be improved by rediscovering those roots? For Sarton’s own understanding of the role of history of science (and for the understanding of History and Philosophy of Science by this journal), this certainly seems so.
This should not overrate Sarton’s role in science education. There were also other influences from philosophy, from psychology, etc. Nevertheless, several of these influences, like for instance the logical positivism of the Vienna Circle, or of gestalt psychology had similar influences from Mach as well as making similar abstractions from Mach’s foundational ideas. One could argue that as a result, the inconsistencies, especially those found in science education, increased rather than decreased (see especially Siemsen 2011a). Only in Mach’s publications as a monistic endeavor, a consistent version of his ideas can be found.
The problem is exemplified in an article by Philipp Frank, which was presented at the foundation of the “Institute for the Unity of Science” (founded 1947). The institute was considered something like an institutionalization of the emigrated Vienna Circle. Conant gave the inauguration speech (Conant 1951). In his introductory speech, Frank quoting Quine regarding analytical and synthetic propositions depending ultimately on pragmatic criteria, declares that “[…] we have to consider science as a human enterprise by which man tries to adapt himself to the external world. Then a “pragmatic” criterion means, exactly speaking, the introduction of psychological and sociological considerations into every science, even into physics and chemistry. […] It is widely felt in the Institute for the Unity of Science that by the combination of the logical and the sociological approach to science all the needs which have produced traditional philosophy and metaphysics can be satisfied.” (Frank 1951, p. 8). Thus, unfortunately at the end of the speech, psychology was dropped, like in Sarton’s initial articles, and subsumed under sociology. Thus, there were many sociologists of science, such as Holton, Merton, etc. and many books written on the sociology of science. But basically no-one continued research on erkenntnis-psychology (except for one singular book by Maslov 1966, and some recent works titled as such but actually dealing only with psychology and not with erkenntnis-psychology, such as Feist 2006).
As Mach notes (1890, p. 2) a word only has “value and meaning by the conceptions it awakens, by the psychological content, which is given to it, without which it remains empty sound. This content might be very different, depending on the conceptual richness of the speaker and the listener.” Thus, for teacher and learner it is probably more different than for two scientists from the same specialization. But even here, experiences and empirical meanings remain central.
For instance, readers of the same article might have very different experiences and a very different world view as a result. Thus what one reader regards as a “play with empty words” can for another be “rich in suggestions”. Of course what is to be understood or evaluated in an article, i.e. in how far it complies with scientific motives (and maybe specific motives of the journal), does not change. But the readers will nevertheless probably come to very different conclusions regarding it. In this case, the experience of the second reader empirically disproves the intuition of the first. But for regarding this result as empirical, one has to include psychological or rather erkenntnis-psychological considerations. From a purely logical or sociological perspective, the two views are equivalent. The motive for the focus on erkenntnis-psychology for Mach and in this article is thus to include valuable experiences into a then clearer and more generalizable view. If the experiences are valuable can be “seen” empirically (i.e. it is made explicit for comparison with the experience of the reader) from the general applicability of the examples provided in the article as well as the more detailed elaborations by Mach in Appendix 1 and 2 and additionally the statistically tested quasi-Machian method in Appendix 3. Further empirical examples are provided by Siemsen (2011a), especially for the case of Finland. In the case of the teaching of Fourier, there is even a nearly direct methodological and empirical comparability of Sarton’s, Mach’s and K. H. Siemsen’s (1981) science teaching.
Because of the erkenntnis-psychological implications of some wordings in the quotations used, these are marked by the author here and in the following. As the different original texts quoted use all possible markings, the markings by the author will be locally defined, normally by underlining or by using bold fonts.
“Snoopy” here stands for a dog as a common child companion as well as a prominent iconic figure of modern children’s literature often regarded as “simple” by adults. Describing children as “snoopy” interestingly highlights their seemingly vulgar way of enquiry as seen from a scientific perspective. Mach’s question would be, if the vulgar is not actually empirically better than some highly abstracted metaphysical scholarly approaches. Thus the vulgar might already contain much of the scientifically refined methodology, but in a more basic, less directed (and thus also not overly narrowed) form.
See for instance Rubin (1921) on a gestalt psychological concept of “background”. As mentioned later, this concept is not entirely consistent with Mach’s concept as it is not genetic in a post-Darwinian sense, i.e. it is not transformative. Transformative means that by adaptive changes, gestalts can acquire new meanings, like species continuously transform into new ones. Any form (gestalt) is never ideal or absolute, but only temporary. It seems to exist because of the observational time frame, but it is actually a process.
See part I and Hohenester (1988) for an overview.
This of course is based on pure speculation, as the author currently has no indication about the actual school books used by these physicists. One can only state that Mach’s school books were used in the areas and times when these people went to school, though the books were not the only ones in use. Just the case of Pauli is sure, because as Mach’s godson, he received Mach’s books as presents from Mach himself (see Laurikainen 1989).
By request, Mach even sent his school books to an Indian physics professor, P. Lakshmi Narasu. Narasu was a colleague of the father (Iyer) of India’s later physics Nobel laureate C.V. Raman at a college in Trichinopolis (Narasu later worked in Madras, i.e. Chennai). Narasu wanted to translate the books. What happened of this project still needs to be researched in detail (the letters from Narasu are in the Mach archive at the German Museum, Munich, NL 174/2305–2307). If Raman knew enough German to read Mach’s school books is not clear, but he himself proclaimed to have been early influenced by Helmholtz, probably one of the other books Mach had sent to Narasu. The mother’s milk effect makes such details difficult to entangle. Often ideas acquired from one person later on in memory become ascribed to someone else as both were initially read at the same time. Raman’s interest in science education, erkenntnis-theory and science institutions would point into this direction.
The idea of general science education is much older though (see for instance Jenkins 1979, pp. 70). The Nuffield project in the UK has also been influenced by it. Again, what is understood as “general” is a critical point and often ambiguous.
It was based on Holton’s “Introduction to concepts and Theories in Physical Science” (1952).
Rogers was also a close friend and neighbour of Einstein at Princeton (see Jennison and Ogborn 1994). Einstein was strongly influenced by Mach’s ideas (see part I). Sterrett (1998) described Mach’s influence on Einstein when he was 17 by reading the Popular Science Lectures. Euler (2006) has already recommended using the genetic effect of the Popular Science Lectures again. This might be taken further: why not translate and use Mach’s school books again (with some careful updating)?
It was also spread to many other countries (see Holton 2003, p. 784).
From this program, Gerome Bruner derived his experience of the cultural dependency of logical learning, i.e. that it is not universal, but depends on previously laid meanings of concepts (see Bruner et al. 1966/1967). From this he developed his criticism of Piaget's "stages" concept not being universal, but only applying approximately to middle-class children from Geneva. Bruner's criticism thus also applies to Zacharias' approach (empirically, it is an outcome of it as Bruner did his experiments in the wake of Zacharias' African venture).
“The instructor on the history of science [must be able] to explain not only the full signification of the idea, but also of each step which led to its discovery […] in the most concrete and specific way. [In order to be able to do this] he should be given all the paraphernalia necessary for the explanation of the scientific facts involved, such as maps, charts, pictures, models and various apparatus.” (Sarton 1918, p. 198) The term “paraphernalia” is used in order to denote the “necessities” for an activity. Historically, this was a legal term concerning the dowry of women, which described items necessary to denote her status. They remained her possession also after marriage.
In German, the concept of “Gelsenkirchener Barock” mocks decorated objects, which were made for the newly-rich factory owners at the times of industrialization. As a result of the emulation process, the initial cultural implications of the objects and its decoration (intended by the Aristocracy) often became lost or grotesque. Such a process can also sometimes be observed when scientific objects become adapted for teaching. The result is that students become puzzled and distracted by phenomenally irrelevant “features” of a nicely-made bronze gadget with many screws and buttons. Such objects are often “magical”, i.e. they work only in the classroom when manipulated by the teacher (if they work at all, see Siemsen 2011c).
The same problem applies to the empiriogenetic process of the teacher as well. The reason for Holton (2003, p. 783) for the “multimedia cornucopia” of the Project Physics course “was to let each teacher decide what part to use for the class.” The “cornucopia” certainly has the side-effect of providing dazzling details for the teachers. The tools might initially have been methodological and genetic in design, such as the short (within minutes) “time-loops” Holton (2003, p. 783) describes. They visually repeat a specific process in order to abstract it from its concrete time dimension. But overall—for the majority of teachers at least—the “cornucopia” probably had the effect of distracting from the central erkenntnis-theoretical problem. Thus the tools in their totality lost any focus they might have had regarding what is important for a genesis teaching process and what is not.
Maybe Mach was a bit over-optimistic in this assumption.
One such cleared-up concept is Newton's idea of "interaction", which nowadays is completely lost in most physics teaching courses, which tend to focus on "force". But Newton's concept of force cannot be understood without thoroughly understanding interaction and the more intricate concept of "interaction at a distance" (see Kurki-Suonio 2011).
Holton in an email 12/08/2011.
It is probably not by chance that Holton (1992) in his article on Mach's fortunes in America in the part on William James does not mention the development of James' "radical empiricism" in contrast to pragmatism and its potential connection to Mach's Knowledge and Error. Holton mentions though that Perry, James' biographer, states that James got his empiricism from Mach. But the more interesting question is, in how far does this also apply for his "radical empiricism"?
Also the influence in the US of the (Machian founded) gestalt psychology is not mentioned in the article, just Mach's influence on B. F. Skinner's rather materialistic "radical" behaviorism. Even Mach's influence on anthropology in the US through Franz Boas' students (who later influenced Bruner) is not mentioned in the article, a strange omission for someone so interested in the concept of culture. Also A. V. Ahlfors, long-time mathematics professor in Harvard and didactics researcher, a student of Kaila and Nevanlinna in Finland is not mentioned, though he certainly influenced US mathematics education with at least some Machian erkenntnis-theory.
Actually, both observations are connected. Holton is a historian of ideas, but like Sarton he surprisingly does not apply his methodology when it comes to his own science teaching. If he wanted to design a course "parallel to major ideas of Mach", spending several years of his time on it and a lot of research money, why didn't he go to Vienna in the beginning and spend a week or two on researching Mach's ideas on science education, especially his physics books (how he did it). Maybe methodologically, Holton in this respect remains a bit too much of a student of the physicist Bridgeman and does not systematically analyze questions from their Machian erkenntnis-psychological perspective, though he intuitively uses this view sometimes.
"Besides “pure physics”, the course shows how physics connects with other sciences, particularly astronomy and chemistry, and includes aspects of the philosophy and history of science that put the development of the major ideas of physics into a humanistic and social context." (Project Physics 1971, p. 1) Rabi defines humanism as "historical understanding, in the sense of the biography, the nature of the people who made this construction, the triumphs, the trials, the tribulations" (quoted after Project Physics 1971, p. 1). The necessity of understanding the psychology of the students is nowhere mentioned, not even for the teacher. Psychologists (but probably no Machian gestalt psychologists) seem to have, like artists, teachers and others, helped in some detail development, but were seemingly never involved in the philosophy and the overall design of the course (Project Physics 1971, p. 3). Even the definition of humanism excludes humanistic psychology, such as developed by Charlotte Buehler (also from Machian roots, see Siemsen 2011a).
For humanism of course one needs—in order to describe humans—a psychology. But the private psychology used here is nowhere consciously reflected. Such an intuitive psychology, like naive physics, often seems to work approximate for the most day-to-day cases, such as discovered in their children by any parents, but not for more elaborate cases, such as science education. Like in the Project Physics course, Galileo is regarded as a hero of science, because he criticizes the inconsistencies of Aristotelian physics, one could criticize Sarton's, Rabi's or Holton's tacit Aristotelian psychology.
Holton keeps very close to the texts by Galileo, which is—according to Mach—a good approximate approach, but by itself without (gestalt) psychology not sufficient for teaching. For instance, scientists tend to omit or cover their own errors and deviations in research, but it is these which tend to provide some of the most important insights (also according to Sarton, see Part I), because they show the misleading alternative gestalts.
The approach from Holton (as compared to Mach or Rogers) starts from physics and then links the other sciences, hoping to create a whole at the end of the process. But, as gestalt psychologists argue, one has thereby already a priori destroyed the inner structure of (unified) science by chopping (categorizing) it into little pieces (the cardinal mistake of Comte from Mach's perspective was to start science with categorization). Mach starts from the erkenntnis-theory, from the whole sensual experiences and from there focuses the attention towards a physical perspective, a psychical perspective, a chemical perspective, the different senses, etc. (see Appendix 2). The phenomenon remains whole thereby and does not have to be artificially (re-)constructed from "chemistry, astronomy, technology, …".
It is amazing with how much effort and care for details the Project Physics course has been designed. It has largely achieved its self-set goals by dramatically increasing enrolment in high-school physics courses (see Project physics 1971; Ahlgren and Walberg 1973; Holton 2003). The criticism here is that the course and its goals were improving on the symptoms instead of the problem. If the problem is the "understanding" of science in the sense of Huxley—which is why so many high school students were not taking physics in the first place—making more of them enroll, but not significantly improving their understanding, will not help. The top students do not need it and the low achievers have nothing from it, either because they still belong to the 50 % who do not take it, or because they still do not understand science even after the course.
As Siemsen (1981) already showed experimentally, interest is not necessarily positively correlated to understanding. Otherwise Azerbaijan and Mexico should also top the PISA grades list, because they were found best in "motivation", while the more careful Finns are low in the latter, but top in the former list (see OECD 2007). The problem is that the intuitions of students and teachers about how learning works tend to be only partly positively and sometimes even negatively correlated to the statistically measurable learning. These intuitions are therefore a poor indicator to rely on (see Bruner 2004; Siemsen 2011a).
For instance one category according to which students evaluate courses is the perceived "speed of learning". Of course it is very hard for beginners in a topic to distinguish between the speed of learning and the superficiality of learning. Because genetic courses have an exponential learning course, instead of the usual (and therefore expected) linear development, they seem to be slow in the beginning (though they soon become much "faster", even in many areas not covered by standard tests). As a result, the quality of a genetic-adaptive course tends to be extremely underestimated by students before they take such a course, while for instance tutorial courses are overestimated by them, even after such courses have been offered for several semesters (see Siemsen 1981).
The students' estimations tend to change dramatically after their first hours in a genetic course. As the genetic learning effect seems counterintuitive for students (and teachers), they will not believe in the effects until they themselves have experienced it. Even though their estimates are then more accurately reflecting the empirical results, they are still off the mark, because they use another category "difficulty of the subject" as a measure. But with a genetic course, "difficult" problems become apparently "easy". The students therefore tend to ask the teacher, why he or she has "left out the difficulties" (see Siemsen 1981). If they easily pass the same "difficult" test in which many of their fellow students fail, this is in their interpretation due to their inherent genius, independent of the genetic course. As the learning in Machian genetic courses works unconsciously (by self-constructing hapts, enacts and iconic gestalts) and is very different from the learning usually applied in school or university, students tend to have difficulties in making sense of it in their self-reflection. The process of making sense in self-reflection (and with it changing one's world view as a prerequisite) can take years.
The following calculations are only rough estimates. The figures used here and in the following passages are comparable only in a very indirect way. They should therefore not be used as an absolute measure of comparison, but as a rule-of-thumb indicator, showing the magnitude of the differences probably involved here. Probably specialists on US education know the figures in much better detail. Nevertheless, the estimate shows that the effects of Kurki-Suonio's field experiment in Finland roughly equals the lab experiment of Siemsen (1981) and that the measurable effects of both are leagues apart from the measurable effects of Project Physics.
If 20 % of high-school students in the USA improved their knowledge of physics by 6 %, the statistical impact on all high-school students (2,5 Mio.) was a bit more than 1 %, on the total age-group in the USA therefore about 1 % (with 87 % graduating high school). If similar watering-down effects are supposed for Finland (see Siemsen 2011a), the large difference between Finland and USA in PISA indicates an even larger difference between the initial impacts of Project Physics and Kurki-Suonio's course. The final impact of both courses on their country seem to have been roughly comparable as far as the figures are known, though the final impact of one course in much smaller Finland was probably higher (reaching 20 % of high-school students in USA vs. reaching 30 % of science teachers in Finland). Nevertheless, a larger final statistical impact of a 6 % improvement would not make much of a difference compared to the final impact of a 40 % (or more) improvement, as long as the latter effects a minimum of the overall population.
PISA considers this a one grade difference on their grade-scale from 0 to 6.
The test from 2006 is a better indicator than the 2009 test, because "science" was tested for the first time and there have been less possibility for "improving" the scores by training students to the PISA-type phenomenological questions. Such a "dressage" tends to artificially improve scores in the sense of Huxley without improving understanding of science.
Could a genetic course improve all students to an average of about 35 on the 40-point scale used by Project Physics' self-evaluation? As genetic learning is exponential and not linear, there is no problem in principle speaking against such an improvement, if one teaches a whole one-year course genetically, though this will probably require successive improvements. The Finns already noticed that the PISA scale is not sufficient to measure their improvements anymore as they are reaching the upper limits of the scale.
Darling-Hammond (2009, p. 16) evaluates the Finnish development in science education as "Once poorly ranked educationally, with a turgid bureaucratic system that produced low-quality education and large inequalities, it now ranks first among all the Organization for Economic Cooperation and Development (OECD) nations on the Programme for International Student Assessment (PISA) assessments in mathematics, science, and reading. The country also boasts a highly equitable distribution of achievement, even for its growing share of immigrant students. In a recent analysis of educational reform policies in Finland, Pasi Sahlberg describes […]" Pasi Sahlberg was one of the first students of Kurki-Suonio. Darling-Hammond (2009, p. 16) compares the US and Finnish science education from the 70's to now: "While Finland continues to experience problems and challenges, it has created a much more consistently high-quality education system for all of its students than has the United States. And while no system from afar can be transported wholesale into another context, there is much to learn from the experiences of those who have addressed problems we encounter." Thus in her evaluation, the US has stagnated since the 70's, while Finland coming from behind has not only overtaken the US and other European countries, but excelled them by far in science education. It was a singular process in Finland, not something innate in culture. It must therefore be reproducible elsewhere within a reasonable time-frame.
According to PISA, the influence of the educational background of the parents' accounts for less than half of the student's performance in Finland compared to many other countries, including the USA, UK and Germany.
It would be interesting to research, how many of these assumed "good physicists" actually excel because of an eidetic memory, which allows them to reproduce exactly the same words instead of understanding physics in Huxley's way.
Some theory of physics is necessary for any world view. Without physics, one could not say anything about the world, just as psychology is necessary to say anything about human beings (and animals). Thus, anybody has a private physics. The question is, how naïve or scientifically developed this private view is. A scientifically developed view can certainly describe more phenomena of the “world” more consistently. This seems to become increasingly necessary as more and more technology permeates everyday life and democracies require informed decisions by their citizens about technology-related questions. Scientifically sophisticated concepts prevent the influence of “pop”-science (i.e. pseudo-scientific and scientifically one-sided elaborations), while improving the possibilities of the popularization of science (see Siemsen 2010c).
Though the British elite education system scores better in terms of top performers (grade 6) than the USA or the OECD average, still Finland is better, even much better if the “good” students are included in the definition of what a “top performer” is (i.e. grade 5 or 6, see Appendix 3).
Holton in an email 12/08/2011.
A self-centered perspective holds similar pitfalls as it depends on the self as a construction. Mach proposes an individual perspective, which largely abstracts from the self, but not from individual sensual perceptions.
There might always be an alternative description, but then one would need to identify a single "social factor", which can consistently describe all the general empirical effects measured in PISA and described by Siemsen (1981), Černohorský, Laemmel, Schwarzwald, Binet, Kurki-Suonio, etc.
Though Kurki-Suonio describes that it took him a year to change the world view of teachers, until they resolved their intuitive resistance and became enthusiasts. According to some experiences this can probably be brought down to 1–3 weekends (see Siemsen et al. 2012). The method will work (applicable by the teacher doing the right thing) after the first, but it becomes stable (consciously understandable with a minimal Machian theory to the teacher) only after several sessions.
Accentuations in italics are in original, by underlining from the author.
For Mach this is the main function of philosophy in science: to learn to be able to think outside of one’s mental box. Nevertheless, as mentioned before one needs to be also careful with the metaphysical assumptions involved in erkenntnis-theoretical reconstructions. All attempts of reconstructing genetic processes in retrospect are prone to error (a problem of which Mach specifically warns). Highlighting this cautiously by no means implies that one cannot or should not try, but that a critical attitude is especially necessary for these processes.
The following parts are taken from Mach (1873/1969, pp. 479–481) unless stated otherwise.
The origin of this concept lies in the Aristotelian idea of air “hindering” the ascent of a thrown body and at the same time “supporting” the descent of a falling body (the traveler hastens when approaching his destination). This leads to a differentiation between natural and forced motion (Mach 1872/1911, p. 24/25). “But it was only when Galileo gave up this supposition of a gradual and spontaneous decrease of the impressed force and reduced this decrease to resisting forces, and investigated the motion of falling experimentally and without taking its causes into consideration, could the laws of uniformly accelerated motion of falling appear in a purely quantitative form.” (Mach 1872/1911, p. 26) This shift first requires an adaptation in the concept of gravity as “continually communicating impulses” (Mach 1872/1911, p. 26). The empirical meanings of fundamental concepts are often integrally related.
Kurki-Suonio commented to the author (email 11/06/2010) that he found a “long set of terrible-looking trigonometric expressions which Kepler had tried in his search for a mathematical representation for the law of refraction without being able to find the correct one known as Snell’s law.” This is an interesting example of the difficulties of the later discussed “naïve empiricism”.
This last statement from Mach is conceptually very complex and acquires very different meanings depending on which erkenntnis-theory of physics and mathematics one uses. For instance Mach’s use of “and” is not meant as equivalence in the true–false sense. Therefore, the “and” does not imply an empirical symmetry between the concepts “velocity and time” or “velocity and distance”. Also Mach’s concept of mass is different, which also changes what Mach means with “opposing” and with “bodies”. This might be taken as an example, why Mach has so often been misunderstood.
With the inclined planes, Galileo varies the time-frame of the observation of the free fall to make the time of observation better suited to the physiology of human visual observation. Varying time (repetition, slow motion, quickening of slow processes or retarding fast processes) is often essential for learning processes.
What is often seen as “errors” by science teachers is not so for Mach. The definition of an error depends on the frame of reference. From a different point of view, most errors become adequate descriptions, though their field of application might actually be very limited (as in the case of “naïve” empiricism, see later). It might seem tedious for a teacher to follow them, but it can produce major progress for the learner.
Except if one subscribes to “naïve” empiricism. “Naïve” should here not be misunderstood in a pejorative sense, but as a description, which accounts for fewer facts (Mach used the term “private” or “vulgar”, depending on the circumstances, see Mach 1905). It is usable within a limited domain of reference. One should though be very careful, not to overstep this domain and apply it in general. Thus, some naïve empiricist science education might indeed be successful, while the method applied for science education in general, often under general labels, such as “enquiry”, “student centered” or “constructivist”, can be very detrimental. The concepts of such labels are not adequate to make useful distinctions about the concept of empiry actually used. The question as to when this is or is not the case and what conceptual remedies could be used instead shall be briefly discussed at the end of the article.
The concept of sensation is used here in the very broad Machian sense of comprising the whole relation of the physical, the physiological and the psychical. For whom this Machian usage is too broad to feel comfortable with it, may temporarily replace “sensation” with “perception”.
The pragmatist argument of “usefulness” is inherently dependent on the perspective one has. The criteria for the usefulness of empirical facts for Galileo are obviously not the same as for Einstein. The criteria of usefulness for scientists cannot be the same as for students. The latter point will become important later in the article. Often in the psychology of science, convenience is mistaken for (empirical) usefulness. Thus Sarton regards it as useful to let others teach the uninitiated students while this attitude is actually convenient as it does not require a rethinking of his teaching method.
Aristotle actually introduces the principle of rationality as the scientific way of thought. This requires two important assumptions: mind-matter duality and logic as the basis of human scientific psychology. For Mach, both assumptions are contradicted by later psychophysical observations and therefore need to be abandoned (these of course as well as Darwin’s insights were not known at the time of Aristotle). If mind-matter dualism is a basis for the concept of rationality, it is not surprising that different forms of dualism are still predominant as world views, even though they are less thought-economical.
One might add, even at the present time today (see Wilczek 2002, 2004a, b). The interesting question is, if we know that the concept of force is an auxiliary and not an empirical concept, how does this change our use of the concept of force in science education? How does teaching the changed concept of force also change the way students use and apply it?
Duhem notes that an experiment without its theory is unintelligible. Mach adds that “indeed, one can only advise to pay attention, if the result of the experiment fits at all to the theory brought along” (Mach 1905/1926/2002, p. 202). “Theory” for Mach of course includes “erkenntnis-theory”.
According to Mach, the elements could in principle also be called “physical elements” (they are actually psychophysical). He avoids this, because it tends to lead too much to one-sided physicalistic interpretations.
His concept of “reality” is thus very similar to James’: resulting from all sensual experiences (James 1905/1977).
“Darwin’s theory” here denotes a consistent theory economically describing the facts from geology, fossils, biology or breeding, which have been described for instance by Darwin, Lamarck, Spencer, Wallace and their intellectual successors. Mach generalizes this by including the facts of science, especially physics, psychology, anthropology, etc.
Gestalts are formed in relation to other gestalts. These clusters form an experiential frame of reference, the domain of their applicability (what the Danish gestalt psychologist Rubin called “background”, see Rubin 1921). The frame is a property of the gestalt. This property can be (partly) abstracted from in the process of using the gestalt analogously. Herein lies the high thought-economic value for teaching and research of gestalts once they are formed, given that the gestalts initially learned are generalizable, i.e. applicable with many of their properties within a larger domain of facts.
Specific modes or methods of learning designed to focus on the one or the other part of the process might thus reduce the bottleneck in the learning process in this part of the process, while inadvertently increasing it in another. For instance inquiry learning might introduce too much of the new without providing adequate learning tools to make sense of it. Problem based learning might narrow too much on a specific experiential frame, etc. For Mach it is not the specialization into one method of thinking, but the generality of the learning process, which enables a scientific world view. Too early specialization and abstraction is detrimental for knowledge development (see Mach 1876 or Wittenberg 1968). Specialization is unable to (trans-)form the syntheses for a fundamental understanding of science. Situations of many new phenomena at once might for instance be necessary to enable gestalt changes in generally applied methodological gestalts, while a specific observation in an experiment might concentrate attention and thus enable a gestalt switch which initially seems counterintuitive.
It can thus be observed even in initially passive or unresponsive students that once this process of thought is initiated, the attitude of the student is suddenly transformed. The “problem” for the teacher becomes rather to somehow “end” the thinking process at the end of the lesson. This effect has been aptly observed by many Machian educators, even and especially for the students supposed to be “laggards”, for instance Binet (1911, p. 116/117) “[…] mental orthopaedics exercises […] can make it possible to assimilate any kind of knowledge. This is so because any knowledge is summarized into an action which this very knowledge enables one to execute. Consequently it is possible to learn through action […].” Sarton’s method was in this regard not as general as Mach’s and Binet’s, because he admitted to have repeatedly despaired at whole classes of laggards (Sarton 1922b).
As friends of board and computer games can verify, puzzles are in the long run relatively boring games. The games topping the “long-term playability” lists are those which involve optimizing competing variables. These are again topped by games which transform their character due to inherent processes depending on external factors in combination with the results of previous optimizations. Mach’s “many-sided way” (see Appendix 1, part I) unknowingly implemented thereby has unfortunately not been explored much in formal educational software. This still tends to focus on simple puzzles as method. Their long-term educational value might be improved manifold by implementing a Machian genetic method.
See Schwarzwald (2005).
For accounts on this, Mach himself repeatedly told of people he saw for a single exam, who heard or read a single lecture and who afterwards, through this experience, had a different perspective on life (see for instance Mautner, cited in Thiele 1978, p. 158). There are similar accounts from former candidates of Černohorský (in personal interviews with the author). Kurki-Suonio, Černohorský and K. H. Siemsen hold many long-term relations to former students, which at the occasions of meetings can be interviewed for their experiences (which has often been done by the author). Their stories share a common narrative in terms of erkenntnis-theory. They experienced it as transformational for their personality and as broadly applicable within their professional and often also personal life as described by Mach (see Appendix 1, part I).
The Aristotelian concept of empiry is based on a distinction between sensation and judgment. Aristotelian judgment is made on the logical basis of the “excluded third”, i.e. on a clear-cut true–false distinction. Mach disposes of this distinction, of the implied introduction of logicism at the basis of the psychical as well as of the implicit epistemological wedge in regarding the skin as the “borderline” of the self. Mach’s elements radically comprise the whole relation from the light-source to the interpretation of the resulting visual perception. What these elements are, needs to be inquired though.
Thus, science like science education tends to proceed in genetic/transformative “loops” (in days, weeks or months).
The concept of memory here is again much broader than commonly used. It is meant as a general function of (at least) everything “living” in the sense Ewald Hering (1870/1902) and Richard Semon (1923) used it. This concept of memory thus encompasses physiology and culture. The sociological perspective of the concept was elaborated by Zilsel (1976).
It can obtain a general point of view though, which fits all sub-sciences. As Mach (1893a/1960) stated about his concept of empiry, “The most supreme philosophy of a natural scientist is to endure an incomplete world view.”
This analysis of facts from different fields in turn requires an erkenntnis-theoretical consistency between these fields for which Mach offers a natural philosophy solution without arbitrary epistemological “cuts” (like dualism) or disregarding a larger number of facts (like materialism does).
Conant was for instance rector at Harvard University from 1933 to 1953 and head of the National Defense Research Committee during WWII.
Mach’s initial version of this idea of Sarton reads “What our classical institutions pretend to give can and actually will be given to our youth with much more fruitful results by a competent historical instruction, which must supply, not names and numbers alone, nor the mere patriotically and confessionally tainted history of dynasties and wars, but be in every sense of the word a true cultural history.” (Mach 1893b/1986, p. 350) It should be noted here that the English translation for instance changed Mach’s use of “culture” as in “cultural history” (Kulturgeschichte) into “history of civilization”. Should this translational adaptation without an obvious necessity actually be the origin of later disputes regarding the concepts of culture and civilization? Civilization certainly is more teleological and limiting in its basic assumptions than the more general concept of culture.
Maybe instead of observations, Aristotle and others, such as Democritus, already did experiments on this question. For instance it seems to be interesting to ask how Aristotle came to the suggestion that “all dry things which become moist and all moist things which become dry engender animals” (Pasteur quoted by Conant 1957a, p. 494). Pasteur does not write on this question, but it seems to reverberate in the writings and those of his opponents. Judging from Aristotle writings, he did make experiments (Aristotle 350/1930), but then Conant’s exclusive focus on Pasteur’s own writings prevents him to become aware of it. Instead Conant seems to agree with Pasteur’s suggestion that “such errors [of antiquity and the middle ages] could not, however, long survive the spirit of inquiry which took hold of Europe in the sixteenth and seventeenth centuries” (Pasteur quoted by Conant 1957a, p. 494). Also Conant strangely omits the invention of microscopes with high resolution by Leeuwenhoek in 1674 and Leeuwenhoek’s following observations of millions of “very little animacules” where before one could not see anything without such a microscope. This observation (and some subsequent experiments) certainly did contribute to the question of spontaneous generation. What is general here is not the method of experimenting, but changing the spatial dimensions of our observational domain to the “very little”. Pasteur mostly confirmed this further than Leeuwenhoek by making more specific experiments. What was actually new was the question of the transmission by air, which Leeuwenhoek did not exclude, but admits not to have specifically observed. Pasteur is then known for his method of preventing the initial unintended existence and the transmission of the “very little animacules.”
Italics are by Conant, underlining by the author.
Even though here a critical attitude is taken towards Conant, this should not diminish his achievements for science and science education. What is to be criticized is that after the perceived empirical “failure” of General [science] Education to actually become general and not only an education of the top 20 %, the initial goal was seemingly seen as unattainable (see Holton 2003). No further attempts were made towards this goal. It was tacitly given up. The reasons for this failure have not been critically reviewed or analyzed in terms of history and philosophy of science. If the errors—as described—are prevented, the initial goal can probably be achieved, as other educational experiments with less errors demonstrate.
For consistency reasons, the evolutionary process itself has to be considered adaptive and transformational. But this is not only a question of erkenntnis-theory. Also the biological evolutionary process is not random, but meta-adaptive. For instance, mutation rates are not only a means of adaptation, but are adaptable to changes in the environment (called second-order selection, see for instance Sniegowski et al. 2000).
Like finding one optimum does not say much about other optima.
As reconstruction of genesis, especially of long-past processes can only search for the most probable solution according to current evidence, the answer cannot be final. A single origin is the more economic hypothesis though.
This insight is actually a corollary of Darwin’s idea that the genesis process is adaptive and transformational, but not teleological. Mach (in Appendix 1, part I) shows that this is also applicable to science as humans are a result of the evolutionary process, human thinking and scientific thinking therefore as well. The evolution process might have adapted to these transformations from the process observable in other biological evolutionary processes, but it still has to be considered non-teleological. God’s thoughts might be used in prophecies, but this is the domain of religion and not of science.
James’ strong words indicate why he later called his philosophy “radical empiricism”. It is therefore surprising that he takes a much more conciliatory position towards logicism for founding pragmatism. This dichotomy can probably still be regarded as the main inconsistency of pragmatism, with James’ version vs. Pierce’s (and Dewey’s). Nevertheless, because of James, pragmatism is never fully logicistic, though how empirical it is varies very much for each pragmatist. As pragmatism can be regarded as the dominant US American philosophy, at least at the times of the General Education movement, this is important for the “background” enculturation and the resulting adaptations of specific ideas. For reasons of stringency, these relations will not be considered further in this article. For details on the relation between Mach and James, see for instance Siemsen (2010a).
It is interesting to note that similar absolutisms have especially been introduced after Darwin by biologists, who should have known much better. For instance the hypothesis of “ontogeny recapitulating phylogeny” from Haeckel initially used for finding “genetic trees” later became a “law” (see Haeckel 1905). The hypothesis from Weissmann that genes would constitute the exchangeable and mutable elements of cells and therefore organisms, later included the additional assumption that this was the only way of transmission (see also Mach 1886/1919; the so-called “Weissmann-Barrier” seems now being contradicted by epigenetic observations).
Conant describes this influence from Sarton as something quite deeply felt and not only as a matter of courtesy. In a metaphor, Einstein in his obituary to Mach (1916, p. 102/103) noted that all the eminent physicists of his generation had been strongly influenced by Mach (mainly through the Mechanics and maybe through Mach’s widely used physic’s school books), even though some even might not want to remember it: “I think that even those who think of themselves as enemies of Mach, don’t remember how much of Mach’s approach they have—so to speak—imbibed with their mother’s milk.” Similar to Conant’s description of Sarton’s influence on him, Einstein’s metaphor implies that the earlier one “imbibes” fundamental ideas, the more they will influence one’s thinking, but the less one will remember how it came to this influence. It is another metapsychical phenomenon.
The case studies start their in-depth analysis in the 16th/17th century the earliest.
In this sense, the generally observed problem of low achievement of students with “migrant” (or worker) background in countries such as Germany might be an epiphenomenon: the students whose parents have less background in the basic concepts of “Western” science and the empirical meanings of its pre-scientific concepts, have the largest problems to bridge the gap to where school science starts. This is not the problem of migrants (or workers), but of the history and philosophy how school science is taught. Many years of special migrant support programs in Germany and other countries have not improved the situation. The actual problem, i.e. the internalization of gestalts and developing those gestalts by successive “loops” from basic experiences, is overlooked by an initial a priori sociological focus.
Around the question of experience and experiment, different educationalists close to Mach’s ideas have taken quite diverging directions. For instance H. E. Armstrong, strongly influenced by Huxley, favored the “heuristic” approach, i.e. in principle based on experience, but strongly biased towards experiments, taking historical questions little into account. Late in his life, he noted that he had done an empirical mistake and that his approach would not work for many students “The majority [of the students] proved incapable—it is not in us to be logical.” (see Armstrong 1934 and Bradley 1975). In spite of this, Nuffield was modeled on Armstrong’s earlier ideas (see Jenkins 1979). See Siemsen (2011d) about the Czech version of this problem. Also Piaget had a similar late-in-life insight, questioning if his approach actually works for low-achieving students (see Siemsen 2010a). Furthermore Binet, from whom Piaget took over many ideas, developed his “mental orthopedics” approach for the laggards only late in his life, much after the intelligence test (see Siemsen 2010b). Martin Wagenschein, a German physics educator, favored natural phenomena, but rejected the very idea of statistically measuring results extracted from educational experiments.
The time Finns and US-Americans spend in school remains the same, but in the end, the Finns have gained ¾ to 1½ years of school to the OECD average (see OECD 2006). So the “long-winded” way is not longer, at least in the “long run” of several school years, but actually shorter, because of the exponential effects from genetic learning (see Siemsen 2011a and K. H. Siemsen 1981).
Therefore, if one only focuses on the “handcraft” aspects of science as Sarton has suggested, the process of the intellectual refining becomes hidden.
In a metapsychical analysis, Sarton metaphorically describes the psychical phenomenon of a gestalt shift, although he is certainly not consciously aware of this fact. The idea of the metapsychical analysis should have lead to a careful deliberate scientific undertaking instead of a tacitly implied one.
It is interesting to compare this statement with the one from Hans Hahn, student of Mach, mathematician and teacher of Gödel, Carnap, Popper and Karl Menger: “If the mathematicians have, since the days of Euclid, already learnt to put themselves up with the fact that there is no royal road to their science, so on the other side the access to it must not lead over the longest and steepest high mountain paths, so that most people would have to fail underway, but the few who manage to pass, being exhausted to death, finding themselves not at the goal, but at the beginning, where true mathematics would be supposed to start.” Sarton’s analogy of a tunnel reminds one on the contrary of Mach’s suggestion “to build a tunnel” between the physical and the psychical view of phenomena. Genetic “loops” might provide an alternative to the “high mountain paths” of learning.
In the history of psychology, for instance, the gestalt concept did not take hold in the US within the concept of thinking (or epistemology). Gestalt psychology became intermingled with (erkenntnis-theoretically not fitting) physicalism and logicism. The gestalt concept had to be reinvented or relabelled, for instance as “emergence” concept. Both concepts, gestalt and emergence, give explanations for a “holistic” view. But the gestalt concept—at least in its original non-physicalistic version—postulates a consistent psychological (thought economical) explanation which one can research, while the “emergence” concept relies on a more mystical appeal to an a priori inexplicability of complexity. The central question of what are the empirical meanings of complexity and simplicity remains unresearched. The difference belongs to the areas of metaphysics and “metapsychology”. The main problem is that the epistemological origins of the gestalt concept by Mach became forgotten.
The term here is used in the sense of Jerome Bruner as a dual process of adaptation. The idea is adapted to a different culture and the culture can also become adapted to the idea (see Cole 2000).
The labels with which the sides are categorized, such as “constructivism” or “inquiry learning” often do not fit the facts described and can be used nearly interchangeably. In the sense of Mach, the theories they are bringing with them do not fit to their experimental results. Although the US science education fares very bad in international comparisons, such as the OECD PISA study (see Appendix 3), US science education is internationally considered the standard from which everybody learns. High quality science in the US is by no means translated 1:1 into high quality science education. This discrepancy should merit at least a careful analysis, which of the ideas in the US system are beneficial and which ones are not. It should also lead to a careful evaluation, if for countries like Finland, which fare much better in PISA than the US, the adoption of US ideas into their science education will actually lead to the deterioration of their system instead of its improvement. Finally, one should ask the question, if the US science education system can learn from other countries, such as Finland in its current state (see also Darling-Hammond 2009 and the “administrative solution” proposed there). For the empirical evaluation of such questions of course one needs a theory and an erkenntnis-theory specifically fitting to the questions and the statistics fitting to these questions in the first place (for example "cold statistics" or Wagenschein's rejection of applying statistics to education do not fit well).
See quotation before by Mach (1915, p. 28) that “the method of Galileo consists in the careful and complete exposition of the mere facts.”
See Siemsen (2011b).
This is an approximation from the publication of Galileo’s Mechanics in 1600 to Newton’s Principia in 1687 and Huygens’ change in his concept of mass resulting from Richter’s pendulum observations 1671–1673 (see also Mach 1883/1915).
These ideas can be found in Rogers’ “Physics for the Inquiring Mind”. From a genetic perspective, the book contains many aspects, which are neither found in the P.S.S.C. courses nor in the Project Physics courses, the two other comparable programs of the General Education movement (see Table 1). The erkenntnis-theoretical aspects can be found much more developed in the Finnish science school book series “Galileo” (the similarity of the title with the topic of this article is no coincidence, but the result of strong erkenntnis-theoretical relations as found by Kurki-Suonio, see Kurki-Suonio 2011; Siemsen and Siemsen 2009; Siemsen 2011a). On the historical-genetic relation between the history and philosophy of science and erkenntnis-theoretical ideas of these books (Kaarle Kurki-Suonio’s Galileo and Roger’s Physics), see also Siemsen and Siemsen (2009) and Siemsen (2011a).
The numbers vary depending if the numbers from field experiments or lab experiments are used. Field experiments, such as the PISA results from Finland, produce more diluted results, though nobody has yet tried to optimize them. Probably the Finnish results could then still be substantially improved, nearer to the lab results. With some more experience, research and funding, the lab results can probably also still be substantially improved.
In the USA, the gestalt psychologist and student of Wertheimer Abraham Luchins (1993) described similar extreme results during the teaching experiments for his dissertation at New York State University. The results were so extreme that one member of the commission did not believe them, even when Luchins performed the experiment with his students under his supervision. As another member of the commission, a statistician then noted: if one measures an elephant with a gold scale, one should not wonder about extreme results. A similar disbelief was reported by Siemsen (1981) regarding his supervising professor.
Unfortunately, it seems that Luchins had not seen the possibility to generalize the results. Even publication was difficult. He initially left the results with Wertheimer during his WWII army service. Wertheimer died before he could retrieve them and the faculty denied him access afterwards.
Mach is probably thinking of coins, which most students probably have with them.
Mach scholars might notice that the example is nearly identical with the teaching example from Mach’s father, who had asked his son carrying a flower pot, if the pot was empty. When Mach answered positively, his father asked him to turn the flower pot, hold it underneath a water surface and then turn it again. Mach described that he was actually surprised by the air bubbling out from the flower pot.
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Acknowledgments
I would like to thank especially Marc de Mey, Gerald Holton, Richard Kremer, Michal Kokowski, Lisa Martin and Edgar Jenkins for the information they provided on many specific historical details discussed in this article as well as Gabriel Szász for his suggestion of the “bizarreness” property of theory and the experiment of a Machian course in Astronomy. Also the College Archives and Corporate Records Unit at Imperial College London, especially Anne Barrett and Catherine Harpham, as well as the British Library, especially Jeremy Nagle, and Emilie Tesinska in Prague have been very supportive in aiding the research and accessing some of the rarer items. Additional thanks goes to the Philosophical Archive at the University of Konstanz for permitting the translation of Mach’s teacher instruction (Appendix 1 in part I). Michael Matthews helped with many suggestions, which added to the initial version and shifted the general focus of the article. I would also like to thank Kaarle Kurki-Suonio and my father, Karl Hayo Siemsen for their invaluable help in proofreading.
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Because of its length, this article is published in two parts. Part I (“Ernst Mach, George Sarton and the Empiry of Teaching Science”) focuses on Sarton’s teaching ideas and how he was influenced and not influenced by Mach. This part II will look into Sarton’s influences on successors in science education, i.e. which ideas of Sarton were continued and how this process further dilutes Mach’s educational epistemology. This dilution especially concerns the concepts of genesis and empiry, which have undergone a substantial shift in their empirical meanings with Mach. These concepts then in turn change the empirical meanings of important questions for science education, such as what is an experiment. In the succession of Sarton, the inconsistencies introduced by him become empirically observable on a larger scale. Some issues might only be fully understandable when reading both parts, though both can be read by themselves.
Appendices
Appendix 2: Excerpts from Ernst Mach’s First School Book (Grundriss der Naturlehre für die unteren Klassen der Mittelschulen)
1.1 Mach and Odstrcil (1887)
1.1.1 Foreword
Following the wish of the editor, who wanted to present the school with a book which would comprise academic and pedagogical-didactic requirements at the same time, we have agreed to write the following Grundriss. […] We hoped to best fulfill our task by observing the following basic principles:
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1.
Everywhere we start from the phenomena [Erscheinungen], so that the concepts arise in a natural way, by themselves so to speak.
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2.
As far as possible we use the often very naïve, simple and classical observations and thoughts from which the great scientists have built physics. The account thereby given becomes not only most understandable, but the historical moment fits itself into this account quite naturally and not only superficially.
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3.
We strive for an account as coherent as possible. The student should with each theorem which he learns be reminded of his previously acquired knowledge, apply it and learn to feel its value.
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4.
The phenomena are not only presented in special singular forms, but—where it is helpful and useful—we try to give the student an overview on the richness of possible cases.
It will in general not be necessary to use the whole instructional text. The text is structured in a way which easily allows the teacher to make an excerpt, to leave out what seems too difficult or less important (which is marked by smaller font size) or use it for a closer cohesion or better insight only in a repetition. […]
Because of the great interest, which the [astronomical-meteorological] topic commands among the youth, this appendix will also bear fruit if it needs to be largely left for private studies [because of too little time during the school lessons], if the teacher once-in-a-while provides the most important clues necessary for understanding.
Such clues would be:
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(a)
On an evening in the beginning of the school year, the students are made acquainted with some constellations (great and small dipper, Cassiopeia) and their attention is drawn to the daily rotation of the starry sky and the stagnancy of the celestial pole.
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(b)
On the 23rd of September, the western point of the horizon is determined with the students from a place with a sufficient look-out. Also the equality of day and night duration can be established.
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(c)
These observations are repeated at the time of the solstices and the spring day and night equality in order to enlarge the knowledge of the constellations and to show the yearly changes in the declination and rectascension of the sun.
Thereby, depending on the opportunity, the phases of Venus, Mars, Moon, Jupiter, the ring of Saturn as well as the sunspots can be shown with a telescope.
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(d)
In the geometrical lessons (which often is also done by the physics teacher) one can in the chapter regarding the position of the straight line and the plane explain in more detail against each other the position of the vertical, the horizon, the world axis, the meridian, the plane of the celestial equator, at the discussion of spheres, the vertical and noon circles, parallel circles, celestial equator and horizon, at the inclined cylinder and the angles, which the sides of such one include with the radiuses of the base, the always parallel direction of the axis of the earth and the explanation of the seasons. Through this the geometrical lesson will not be diminished, but deepened and made more attractive.
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(e)
Once in a while a question can be posed to the students in the end of the physical and mathematical lessons, which stands in connection with what has been dealt with during the lesson, such as: When does the moon arise today, which phase does it have? Where is Venus? Which planet is visible, in which constellation can it be found? How high today is the barometer and the thermometer? Which kind of wind do we have? Etc. Also once per school year (for instance if the barometer is part of the lesson) a drawing of the barometric pressure lines in Europe taken from the newspaper will prove to be very instructive.
Of course we tried to accord with the Ministerial Instructions.
Prague and Teschen, March 1886
The authors
1.2 Introduction
§ 1. The epitome of all, which we perceive through the senses, we call Nature or sensual world.
What do we perceive through the eye? The color, the shape [gestalt], the place of an object. What do we get to know through the sense of touch? The shape, the roughness, smoothness, warmth, cold, the place of a thing. What do we get to know through the hearing, the smell, the taste?
When our fingers at a specific location in space perceive something tactual, we can most of the time also see something there, can provoke a sound by knocking, etc.
§ 2. What under fitting circumstances can excite several of our sensual organs at once, we call matter. The matter filling a limited space is called body.
Give examples of bodies. A piece of copperFootnote 107 is a body. We can touch and see it. If we drop the piece of copper on the table, we hear it. Because of the solvable chemical compounds, which are to be found on its surface, we can taste it and because of the volatile compounds, which emerge there from, even smell it. A piece of silver we can equally touch, see and hear, but not taste and smell.—The air is also a body. The air we usually do not perceive through touch. But if we move our hand fast through the air, or if we expose it to the moving air, the wind, we can feel it immediately. But also the quiet air, if it is warm or cold acts on our sense of touch. Normally we don’t see air. But very hot air, for instance which which is heated by electrical discharge, glows and shines, becomes visible. Hot air, which emanates from a heated body, throws in sunlight a visible shadow on a plain white wall.
§ 3. All bodies have several properties in common, which is why they are called general properties (Newton 1686). A body fills the space, which it occupies, or its volume in such a way that it makes the intrusion of other bodies into the same space impossible. This is the general property of impenetrability.
A body by resisting the penetration of another body, also resists the tactual fingers, it becomes touchable. If one puts a stone in a glass completely filled with water, part of the water is pushed away and flows over. Through a funnel, which closes exactly around the neck of the bottle, no water can be filled into the bottle. Why? If one submerges a corked bottle with removed bottom (like in figure) into water, it does not fill up. A light on a cork continues to burn underneath it. If also the neck is put under the water and one pulls the cork out or tilts the bottle, then the air escapes in big bubbles with sound and the bottle immediately fills up with water.Footnote 108 Diving bell. Skaphander [heavy diving equipment]. 
Appendix 3
The Finnish curve (Fig. 1) seems to be typical for a genetic “Machian” teaching effect (see also K. H. Siemsen 1981, partially translated in Siemsen 2011a for a lab experiment consistently producing similar curve-shifts): In Finnish science education, there are very few students who “don’t understand” (in Huxley’s words from the beginning), and additionally many students who understand science issues very well (i.e. former average students, who suddenly become very good). Other countries included in the PISA study do not show this typical shift or at least much less pronounced. In this regard, the US has an ‘anti-curve’: more students understand little or no science, while fewer students understand science issues very well. It would be interesting to see, if using a fully Machian approach to science teaching would be especially effective for tackling US PISA problems by overproportionately decreasing the ‘laggards’, while increasing the number of top performers.
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Siemsen, H. Ernst Mach and George Sarton’s Successors: The Implicit Role Model of Teaching Science in USA and Elsewhere, Part II. Sci & Educ 22, 951–1000 (2013). https://doi.org/10.1007/s11191-012-9454-8
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DOI: https://doi.org/10.1007/s11191-012-9454-8