My 1996 lecture in the theory of science

My 1996 lecture in the theory of science
intended for the doctorate degree at the University of Bergen

John Bjarne Grover

Kuhn's paradigms and the simultaneity of scientific discoveries

In this lecture, I discuss two concepts pertinent to the history of philosophy which it is my intention to show the mutual relevance of. The first is the one which has persisted in philosophy, and, even more, in religion, throughout all ages and cultures in various forms, and which can be associated with a concept of a shared social consciousness in a community, whether this be interpreted in the form of shared knowledge in the broad sense of CULTURE, or whether it is taken in a more narrow philosophical frame, from Platonism in antiquity to the idealism of the previous century, and, more recently, in the novel views advocated by Rupert Sheldrake, David Bohm, and others. We can easily trace it in mythological reality and in any outlook which considers FATE pertinent to knowledge, which even today is a widespread conception in the subjective and everyday interpretation of reality (in such forms as 'why does this always happen to me...'), and the question of FREE WILL has followed philosophy through all ages. Archetypes, whether in Jung's form or such as Eliade conceived of them already in 1949/52 (in 'The myth of the eternal return'), when he identified them with exemplary models and paradigms, is perhaps the most obvious theoretical formulation of the notion of a shared consciousness. The concept which is most relevant in the present context is, nevertheless, Thomas Kuhn's concept of scientific paradigms from 1962, whether this concept be carried over from Eliade or not.

A second concept I am about to discuss is another one of Thomas Kuhn's, which he deals with in a paper from 1959, entitled 'Energy conservation as an example of simultaneous discovery'. It is reprinted in the 1977 collection entitled 'The essential tension'. This paper discusses the phenomenon of simultaneous discovery in science, when at least two scientists make the same discovery simultaneously, and independently of each other. Kuhn's example is the closely connected hypotheses on energy conservation which were advanced independently by altogether 12 European physicist, in three groups of four each, in the years from 1830 to 1850. On the cluster of these 12 independent scientists making very similar discoveries independently of each other, he remarks that "the history of science offers no more striking instance of the phenomenon known as simultaneous discovery" (p.69). He ends the paper with the question: "Why, in the years 1830-1850, did so many of the experiments and concepts required for a full statement of energy conservation lie so close to the surface of scientific consciousness?" (p.104).

This question, from 1959, was answered in a general form three years later, in his Structure of scientific revolutions, from 1962. It is the connection between these two papers, that I will elaborate on here. I will refer to his 1962 paradigm concept as 'shared consciousness', and to his 1959 concept as 'simultaneous discovery'.

The awareness of a shared consciousness was a prominent feature in nineteenth century idealist philosophy - which also Kuhn seems to suggest in his 1959 paper. I find it convenient to consider the period between the end of the nineteenth century and the appearance of Kuhn's philosophy of science (that is, roughly the period 1900-1960) as an intermediate stage reserved for a highly specialized cultural development. That development is, needless to say, the development of the information technology in the computer and the cultural formalization needed to interpret it. The mid point in this period between 1900 and 1960 is the thirties, with Gödel at the centre in 1931. My interpretation is this: In order to develop the new technology and its supporting epistemology, the metaphysical parts of scientific epistemology had to be abandoned. The new technology, even if it trespassed the old information technology vastly, could not be expected to formalize God. So, in order to interpret the new computers, the boundary to the knowledge which was to count as computable was defined in a first form almost exactly at the turn of the century, by the discoveries of new logical paradoxes and Cantor's proof for the existence of a transfinite domain essentially out of reach for the enumerative powers of those natural numbers which came to be the foundation for the new computers. It is probably important to notice that it was Cantor's explicit intention to study the theological interpretation of mathematics when he defined his transfinite numbers. With this boundary to the computable, a compartmentation of the knowledge-space was introduced, such that everything inside the boundary came to count as computable, and everything outside was - if not principally uncomputable, so at least - not computable in that sense of it which Alan Turing defined formally in the thirties. Metaphysics was pushed well beyond this boundary, and the logical positivists attempted to capture knowledge in protocol sentences - which in effect would have made everything within this scope computable.

Then, in 1931, Gödel proved that any such formal system, have it only the slightest complexity, will be incomplete and inconsistent. This achievement can be interpreted as signalling that all theory beyond a certain level of complexity ultimately is tied up to a realm beyond the scope of the theory itself, and consequently that any theory within the Turing boundary must be tied up knowledge outside this boundary. In the present framework, Gödel's proof entailed, in 1931, that the boundary could no longer be pushed any further. After this, the prerequisites for an epistemologically valid interpretation of the computer technology were made in the thirties. Tarski defined the new semantics, the new computability boundary was defined, and the computer was developed as the technical tool to handle this new knowledge within the scope of the Turing boundary.

In this interpretation, the socalled cognitive revolution in the latter half of the 1950's is not the beginning of a completely new era: It is, rather, the beginning of the return to a reopening of that not all too spacy knowledge which the new computability had confined us in, to reassociate it with a larger metaphysical attachment to a shared social consciousness, which it had been the marxists' task to keep in store while the logicians did the mechanical work.

This is where I see Thomas Kuhn. In the early sixties, computability within the scope of the Turing boundary had already started to grow a little boring, and Kuhn took a bold leap forwards and called his essay the Structure of scientific revolutions. In assuming that such revolutions, which represent transitions between mutually incommensurable paradigms and consequently should not be computable by any Turing machine, while still maintaining that they possess sufficient structure to be addressed in the manner he does, Kuhn has assigned to them a computability on a higher level than the Turing-computable. Hence if a Thought Filter Machine works in the background of Kuhn's paradigms, it must be in the form of what we could call a Cantor machine. Let us assume that anything which can be transmitted from one scientist to another in the form of a consistent scientific theory is also definable in the form of a Turing machine. This is today generally acknowledged in the practice of computer implementation and testing of hypotheses. A paradigm is then a sort of Cantor machine governing scientific thought beyond the scope of the Turing machine. This is how I interpret the cognitive revolution in the latter half of the fifties: The new science addresses the knowledge-space beyond the Turing-computable.

An example will make this clearer: After the onset of the computer technology, linguistics has been split into two branches: 1) Computational linguistics, which works with elaborating grammars in algorithmic form, implementable in computers, and 2) all the rest of linguistics, being left with a vague and seemingly uncomputable domain which comprises both the computer-implementable grammars in addition to its more vague domains. We should perhaps expect to find that any successful scientific theory of grammar should be implementable in computer programs, and that this is a convenient test on the successfulness of a grammatical theory: If we do expect to find this, then linguistics as a science is just a short-hand label for computational linguistics. If not, we must ask what distinguishes ordinary natural-language linguistics from the branch of computational linguistics. My answer follows from the above: Natural-language linguistics adds something to the branch of computational linguistics to the extent that it works with the linguistic representation of the social space, in particular those aspects of it which is concerned with the shared consciousness, or, in Kuhn's terminology, with paradigms. The non-computational linguists work with describing the units and nature of the signification in this social space (in the mind of what Orwell called the Big Brother). Linguistics subsists currently as an important representation of the era of cognitive science just as much by virtue of the role which Chomsky assigns to it in his Syntactic structures from 1957, when he explicitly rejects any discovery procedures for the working linguist. We are not, according to this programme, expected to account for how we make our scientific discoveries. This is where we transcend the Turing machine and enter the domain of the new Cantor machine. The linguist of natural languages is supposed to work by means of intuition and inspiration. This means that the non-computational linguist is supposed to address the mind-space which transcends what can be captured in protocol sentences. I suppose that this explicit internalization of grammar, which is the hallmark of Chomskyan grammar, heralds the entering of the new space for science, transcending the realm of the Turing-computable languages of rational explication. If this is not only the retreat to the previous century, which it probably isn't, then it is the beginning of a reformulation of that old perennial problem of the shared mind and consciousness which Western culture had to relegate to the communists while working out the design of the new computers.

This reformulation is the project which also Kuhn embarks upon around the same time. In his 1959 paper on the 12 simultaneous discoveries in physics in 1830-50, he advances a hypothesis of three factors relevant to the simultaneities which he finds plausible. These factors are:

1. The availability of conversion processes, such as the technical conversion of heat to work and vice versa.
2. The general concern with engines, as the technological mastering of the conversion processes
3. The philosophy of nature in the nineteenth century

Kuhn discusses these three factors in turn, and repeatedly refers to the views advanced by Faraday and Grove as essential to all of them. The years 1830-1850 saw a remarkable convergence of those sciences which contributed to the understanding of energy conservation through the mastering of the concept of physical work. Kuhn quotes a paper written by Mary Sommerville from 1834, about the connection between the new physical sciences and the convergence among these which had lasted from about 1829 (according to her). This produced a network of disparate scientific disciplines converging on these phenomena of physics. Kuhn says about the first factor, the availability of conversion processes:

"Faraday and Grove achieved an idea very close to conservation from a survey of the whole network of conversion processes taken together. For them conservation [i.e, of energy] was quite literally a rationalization of the phenomenon Mrs.Sommerville described as the new 'connexion'" (p.75).

This is the point which runs through Kuhn's paper, and which has perhaps the strongest explanatory force relative to his later concept of 'disciplinary matrices': The idea of energy conservation, which was conceived of simultaneously by this group of 12 different independent scientists scattered over Europe, could in itself be traced to the rationalization of this network of converging but disparate scientific disciplines. The simultaneous discoveries had an empirical basis, but the phenomenon of simultaneity of discovery must be traced to the rationalization which shifts the theories from their empirical physical basis to their exact interpretation in mathematical form. This essentially lends an aspect of idealism, which is the third factor, to Kuhn's interpretation as well.

I return to the point below, but I will mention that in the context of his discussion of the German 'Naturphilosophie', Kuhn cannot resist the temptation to make notice of the concern which several of these physicists also nourished relative to the phenomenon of the light colour of venous blood in the tropics (a slightly surprising - but possibly important - point), in light of the conclusions which could be drawn as to the relation between oxidation and loss of heat from the body, relevant to the concept of physical work. This conversion process (relation between the colour of blood in the veins and the surrounding physical temperature conditions) is discussed by Kuhn in the context of the third factor, the natural philosophy, concerning the view that object and subject converge in an idealist reality wherein such conversion processes may take place.

He takes recourse to the approach of Faraday and Grove and the rationalization of the scientific network of the highly disparate approaches not only when he discusses conversion processes and natural philosophy, but also when he considers the second factor, the concern with engines. His discussion leads to the conclusion that the historical phenomenon of simultaneity of scientific discovery must be traced to this shared component in the three factors.

When the rationalization of the network of the converging empirical scientific disciplines leads to simultaneity of scientific discovery, we should indeed expect to find that the simultaneity phenomenon is most prominent in the most rationalizing discipline itself, that is, in mathematics. The connection between mathematics and the concept of a shared consciousness can in fact easily be traced in the philosophy of mathematics. There are three main schools of thought generally acknowledged as prominent when it comes to the ontological status of mathematical objects. The majority of mathematicians probably subscribe to the classical Platonist or logistic schools, in modern form represented in Bertrand Russell and the tradition from him. These mathematicians assume that the objects of thought which the mathematical symbols and expressions refer to have independent existence in some platonic realm, and therefore have existence independently of whether they are addressed by humans or not. Hence when this is accessible to all mathematicians, we have a counterpart to the shared consciousness in it. The two other prominent schools are the intuitionists, who presume that mathematics derives from a primordial intuition which has a universal status, and the formalists, which was the progressing problemshift in the twenties, but which suffered particularly from Gödel's proof, signalling a social dependency on all sufficiently complex formal systems.

Hence we may safely assume that most mathematicians are inclined to acknowledge an epistemological level beyond the individual mind as essential to the nature of mathematics, and therefore that, if anywhere, the hypothesized shared consciousness should be found as pertinent to mathematics, as the primary example from the sciences. Accordingly, simultaneous discoveries should be a prominent feature in the history of mathematics, and it is here that we find a possible test condition for the hypothesis: If there is a shared consciousness relevant to science, major revolutionary shifts in the history of mathematics should be characterized by simultaneous discoveries.

The story is quickly told: Leafing through the textbooks on the history of mathematics soon convinces the reader that this indeed is the case. Unfortunately, I have, in spite of extensive searches, not been able to find any systematic studies of the phenomenon of simultaneous discovery in the history of mathematics, but I have made my own superficial studies. I cannot present any statistics from this, but I can suggest that the overwhelming number of reported cases met with in the literature will provide any such study with the needed basis for making what I assume will contribute to the supporting evidence for the hypothesis of such a characteristic feature in the science and history of mathematics. If the study is not already made, I suppose it will be.

I will here restrict myself to the mention of a few important and fairly well-described cases essential to revolutionary shifts in mathematics. The most famous example is the priority dispute which followed the grand paradigm shift inherent in Leibniz' and Newton's discoveries of the infinitesimal calculus in the latter half of the seventeenth century (around 1670-80). The opening of this field of mathematics counts as a true turning point in the history of Western mathematics, and one may well consider everything preceding it and everything succeeding it as two radically different compartmentations of the history. It is crucial that this profound discovery, which entails working with infinitesimally small values approaching zero, was made by two outstanding mathematicians at the same time, but in different countries. This case is telling by its profound importance and the far-reaching effects of the priority dispute which followed. It is well described in the literature.

Another very telling case is the discovery of the non-Euclidean geometry after some 2000 years of mathematical uneasiness by Euclid's fifth postulate. It is true that there had been some increased attention to the problem of deriving the fifth postulate from the other four in the decades preceding the solution of the problem, and this could have contributed to the eventual solution, but the simultaneity of it, by Nicolai Lobachevski in Russia and János Bólyai in Hungary, consisting in omitting the fifth postulate entirely and thereby creating a novel geometry, is nevertheless impressive in light of the 2000 years preceding it. The story is, though, possibly telling for another important aspect as well: Carl Friedrich Gauss has traditionally been credited with priority to this discovery, but he never published the finding. This may, as insinuated by some historians, possibly be traced to the young János Bólyai as a source of his discovery. The father of Bólyai was also a mathematician and a close friend of Gauss, and the son told his father in 1823 about some plans he had for solving the fifth postulate problem by just omitting the postulate and creating a completely new geometry instead. Some time after, Gauss let it sift out to the mathematical world that he had come across a solution to the problem (even if he humbly refrained from publishing it), but the young János was occupied with other tasks and could not find the concentration and opportunity to work out his theory, even if his father started to urge nervously on him. Then, in 1829, seven years later, it happened that Nicolai Lobachevski, who likewise had common acquaintances with Gauss, published the same solution, albeit in a Russian journal which was sufficiently remote to keep the solution out of European attention for still some years. It was nevertheless in that same year 1829 that János suddenly got the spur to write his theory down. His theory was published in 1832 as an appendix to a mathematical work of his father. This revolutionary turn in nineteenth century mathematics was the solution to a puzzle which had rid the mathematical world through 2000 years. János later discovered that he could have been deprived of the priority to the discovery, and he did not manage to publish anything more in mathematics in the course of his lifetime. Unfortunately, many of János Bólyai's mathematical works are still unpublished. The librarian at the manuscript collection in Budapest has promised to send me a list of the titles.

This story may be telling for a certain logic of discovery characteristic for the attachment to and impact from a hypothesized shared social consciousness which recurs with considerable anecdotal similarities in a somewhat related process, taking place a few years later, but still in that same period of time which Kuhn deals with in his 1959 paper. This was the discovery and elaboration of the modern hypercomplex numbers in 1843-44, an event which led to a true revolution in algebra. Sir William Hamilton, who as a child was a prodigy and was said to have mastered 13 languages when he was 13 years old, got his famous 'flash of genius' on an evening stroll together with his wife, after fifteen years of fruitless pondering on the problem of complex numbers. He suddenly received the solution in the form which he termed quaternions (with three imaginary components instead of one), and he immediately inscribed the solution into the bridge stone wall he happened to pass in the same moment. Meanwhile, in Stettin, Hermann Grassmann sat working with his grand 'Ausdehnungslehre', a theory of socalled extension which defined a much more general and far-reaching algebra, but in important respects identical in the sense of making use of numbers as classes of numbers. It is from Grassmann's work, which was started in 1840 and published in 1844, that the modern algebra derives. Hamilton's more narrow solution soon became famous, while Grassmann's work fell into oblivion - and he finally left mathematics and turned to the study of Indo-European linguistics instead, where he wrote a Sanscrit dictionary still in use, and discovered the wellknown Grassmann's law. Today, though, Hamilton's quaternions are quite 'out', while Grassmann's algebra is certainly 'in'.

These three cases of simultaneous discovery all rest on the turning points to large and revolutionary paradigm shifts in mathematics. It would be an interesting topic of study to investigate all the major paradigm shifts in the history of mathematics, from the point of view of verifying whether such simultaneity of discovery occurs systematically in these turning points. Kuhn's 1959 paper, taken together with his theory of paradigms or disciplinary matrices, seems to suggest that such simultaneity should expectedly be found in such cases, the more prominent the more important the discovery is. We may well stop and ponder the question: If indeed there is such a logic of discovery in the exact sciences, what is the rationale behind it?

I will not attempt to answer this question here, and neither does Kuhn provide any explicit suggestion to its solution, but I will point out that a certain ambiguous use of language in his paper seems to be telling for an important aspect of the problem. In the majority of cases where he refers to the concept of physical work (that is, in the technical sense of it), he uses the somewhat strange way of expression 'THE CONCEPT WORK' - that is, instead of the expected form 'THE CONCEPT OF WORK'. This ambiguous term refers both technically to physical work (the concept work) and to the idea of work with concepts (the concept work). I find, by a close reading of the paper, that this ambiguity is far from unimportant for the question. The most striking use of it is found on the pages 86-87 in the 1977 collection, where the following wording is found in the context of discussing the eighteenth century's pendant to the concept of work, in the concept of the socalled VIS VIVA (that is, 'living force' as a technical term), and the reinterpretation of it in the first half of the nineteenth century:

"Nor was this new dynamical view of the concept work really worked out or propagated until the years 1819-39, when it received full expression in the works of Navier, Coriolis, Poncelet, and others. All these works are concerned with the analysis of machines in motion. As a result, work - the integral force with respect to distance - is their fundamental conceptual parameter" (p.86f, my emphases).

This and similar passages clearly indicates that the formulation THE CONCEPT WORK, running through the paper, is deliberately intended to have the ambiguity of meaning which he later assigns to the Gestalt switches of his paradigm shifts in 1962. The ambiguity of this expression carries in fact a considerable part of the explanatory force in this paper.

As suggested in a paper by David Bloor, we may turn to Wittgenstein for support of the contention that mathematics is the concept work: In the Remarks on the foundations of mathematics (book V section 46), Wittgenstein says: "Mathematics form a network of [social] norms". Bloor interprets this in the sense that the ontological status of mathematics is the same as that of a social institution. Consequently, mathematical work has repercussions in the social space. This seems to bring us somewhat closer to a rationale behind the phenomenon of simultaneous discovery: We make the daring leap of assuming that revolutionary work with mathematical concepts is also revolutionarily present in the (more or less) platonic regions of the shared consciousness, which consequently means that the work can be perceived by other mathematicians working in the same regions of mathematics, even if they are in considerable geographical distance from the source of this revolution. Furnished with this bold working hypothesis, we can turn to an interpretation of the phenomenon of simultaneous discovery with more incisive tools. For example, we can hypothesize that the young János Bólyai, in order to work out his non-Euclidean geometry, for some reason needed somebody to collaborate with in the platonic realm. I will not speculate on the reason, beyond the somewhat trivial assumption that if mathematical concepts are essentially social, or coincide with social concepts, then the elaboration of new mathematical concepts may also require social collaboration in some form or other. János first tried his father, who could not help him much, but who leaked the project to Gauss, who neither was really cooperative. However, Gauss seems to have hinted to the mathematical world that some support was needed here. János did not find the metaphysical support he needed until 1829, when somebody occurred in those same metaphysical regions, when Lobachevski in Russia, completely unknown to János, started working in the same parts of the mathematical paradise. This gave to János the incentive and socio-metaphysical support which his contemporaries thought he needed, and he quickly wrote his hypothesis out.

In this interpretation, I assume that the revolutionary paradigm shift in geometry was to be socially implemented in the form of a simultaneous discovery with contribution from at least two mathematicians. It adds to the irony that these two minds, even if the present interpretation seems to assume an interdependency in the metaphysical realm, nevertheless had to be independent in the observable realm, since neither his father nor Gauss could function as the needed support for this revolutionary discovery.

These traits recur strongly also in the way the story about Hamilton and Grassmann usually is told. Gauss seems in fact to have had a metaphysical finger in this story as well: From his own scattered hints and his own copies of the letters which he had sent to friends, it seems as if he had discovered equivalents to quaternions even before William Hamilton started pondering the problem. Hamilton probably started the concept work in 1828, but without much success. Then, after Grassmann had started to work out his impressive 'Ausdehnungslehre' in 1840, Hamilton got the flash of genius in 1843, just before Grassmann, who never got a chair at a university, had finished his work. Hamilton hurried to the local mathematical society and announced his discovery. Again, it seems as if Hamilton could not really make the discovery without Grassmann's work and metaphysical impact.

There is divine irony in a farcical priority dispute which arose shortly after the Dubliner Sir William Hamilton had announced this revolutionary discovery of the quaternions. Another man with the same name - Sir William Hamilton, a Scottish philosopher with a strong interest in logic and metaphysics - had been lecturing on the quantification of predicates since 1839. In 1846, around the time when Grassmann sent his 'Ausdehnungslehre' to Cauchy in Paris, the metaphysical Hamilton got a letter from the Englishman Augustus de Morgan (one of the socalled founders of symbolic logic), who was just about to publish a work on the quantification of predicates, and who wanted some additional information from Hamilton before the publication. The metaphysical Hamilton sent him some of his papers, which de Morgan made use of in his publication, and a furious priority dispute arose: The metaphysical Hamilton accused de Morgan for plagiarism, in making use of the material he had sent him. The metaphysical Hamilton got so upset by the ensuing priority dispute that he almost lost his mind, as the story-tellers know to phrase it. De Morgan succeeded in prolonging the horrible dispute untill the metaphysical Hamilton finally retired from the world in 1856, and he even managed to prolong it after that, against the students and supporters of the metaphysical Hamilton. This lasted until 1862, when finally everybody was tired of the nonsensical and noisy dispute, and it silenced.

Then, in 1862, Grassmann, who had been left in oblivion in Stettin, made a second edition of his 'Ausdehnungslehre'. He wrote in the preface to this and to a later reprint of the first edition that he was very disappointed by the neglect and complete silence which had followed the first edition, and by the fact that he never got an academic chair, and that, in 1854, he had written to the Academy in Paris with a request for considering a possible plagiarism by Cauchy, to whom he had sent his 'Ausdehnungslehre' around 1845-46. However, the committee never answered his letter, and the request was left in silence. After the publication of Grassmann's second edition, de Morgan in London (who, of course, knew who the mathematical Hamilton was) once again tried to start the dispute with the metaphysical and now expired Hamilton, but after a few unsuccessful attempts, he gave up. Grassmann then left mathematics and turned disappointed to the study of languages instead.

This sad and absurd interpretation, associating Grassmann with the metaphysical Hamilton, as a kind of shadow representative in the platonic regions of the exact sciences, or as the one whom the mathematician Hamilton mistook for himself in 1843, seems perhaps far-fetched in the light of traditional constraints on historical interpretation, but it should be tolerable as a possible account under the assumption of a platonic or social realm accessible to all, such as most mathematicians are inclined to believe in. It is my contention that linguists who are not computational linguists must be ready to acknowledge such slightly absurd accounts, if the bold working hypothesis finds empirical support from studies in the history of science.

There is also a story about priority disputes from considerably more paradisial regions than has been discussed so far, with obvious relevance here. This is the one found in the Bible, in Genesis chapters 25-35, in the story of Esau and Jacob, with their female counterparts Rachel and Leah. The story of the twins Jacob and Esau is well known, how Jacob acquired Esau's birthright with a dish of stewed circular lentils (and a little bread) when Esau came hungry home from the fields. It was this which later made it possible for Jacob to acquire his father's blessings in Esau's place with some shade of legitimacy. He made use of young goat fleece to imitate Esau's hairy skin, in order to deceive his father of the blessing which rightly should have befallen Esau. Jacob took Esau's blessing from their father, as had the divine providence already foreshadowed long before. Rebecca told him that the priority dispute which came to follow was too harsh for Jacob to remain in Isaac's land, so he had to flee to his father-in-law Laban, where he stayed for fourteen years. He was supposed to stay for seven years and then marry Laban's daughter Rachel. But on the wedding night after these seven years, he got Rachel's elder sister Leah instead, and when, in the next morning, he reproached Laban for having made a mistake, Laban just answered that they usually married the older daughter before the younger one in his country. So Jacob had to work another seven years to get Rachel as well. This mistake was, of course, a copy of his own replacement of Esau's birthright with his own.

The sojourn in Laban's land is a copy of the events in his father's land: When Jacob is about to return to Isaac's country, Rachel steals her father Laban's god images, as a counterpart to Jacob's own stealing of his father's blessing. When they approach Isaac's land and are about to meet Esau again, he wrestles for a whole night with an angel who finally touches and displaces his hip. Again, this is Esau's representative in the social/angelic realm (a kind of platonic region, we may assume), somewhat like the metaphysical Sir William Hamilton who occurred instead of Grassmann in the priority dispute.

This aspect of TWO instantiations of the same person runs through all of this story about the twins Esau and Jacob. The story is not interrupted by Jacob's stay in Laban's land, but, rather, it is here that it touches directly on the three factors which Kuhn suggests as essential to such cases of simultaneity. Before they leave Laban, Jacob is allowed to pronounce his wish for wages for the fourteen years of labour. He suggests the following conceptual division line as defining for his wages: Every goat in Laban's flock which is striped or speckled or spotted, and every lamb which is dark-coloured, shall be his, and every animal which does not possess this geometrical pattern in Jacob's flock shall be considered stolen. But Laban removes all these animals from the flock before Jacob gets the chance to select them, and Jacob is left with nothing. All animals in the flock are suddenly without these geometric patterns.

Now Jacob creates the technology which is the counterpart to a new revolutionary discovery. He tends Laban's flocks, and in the course of this work, he takes rods from poplar, almond and plane trees and peels the bark in streaked geometric patterns to expose the white wood underneath. These patterned rods he handles like a machine to generate the conversion process he needs: He puts the streaked rods into the watering trough when the strong animals are in heat, and - somewhat miraculously - these strong animals conceive young which possess precisely this defining geometric property on their sheepskin, as transferred from the pattern on the peeled rods. However, when the weak animals are in heat, he does not put the peeled rods into the water trough, which has the consequence that the young of the weak animals do not acquire these defining geometrical patterns on their sheepskin.

That is, Jacob puts the rods in and take them out somewhat like a mechanical engine. Jacob then separates the strong young with this property from the weak young without it, and gradually his share of the flock is shifted into a strong and healthy and growing part, while Laban's share of the flock weakens and sickens away. This is the conversion process which shifts the wealth from Laban to Jacob.

This technology possesses exactly the three defining factors which Kuhn lists as relevant to the simultaneity of discoveries:

1) The selective exposition of the peeled rods before the strong animals in heat only, and their removal before the weak animals. This is what Kuhn calls THE CONCERN WITH ENGINES.

2) The fact that this selective exposition produces a transference of strength or power from Laban's share to Jacob's share of the flock. This factor is what Kuhn calls THE AVAILABILITY OF CONVERSION PROCESSES.

3) The idealism ('Naturphilosophie') in the Jacob story appears in the moment of transference of similarity from the sensory impression of the streaked rods onto the young of the conceiving animal (that is, the animal doing THE conceiving or CONCEPT WORK). This is exactly the same point which Kuhn makes, when he takes recourse to the observation that venous blood (that is, supposedly, the blood in the veins, and not the blood of Aphrodite) is lighter in tropical areas than normal, due to less loss of heat from the body. This was Kuhn's sheepskin in his 1959 paper: Indeed, Jacob made use of the same trick when the animals were in heat (that is, sexual heat rather than tropical or technical heat). This represents the moment of identification of subject and object which is typical for the idealist absolute: Subject and object are identifiable when the objective rods leave their imprints on the young of the perceiving and conceiving animals. Hence, the transference of similarity from the peeled rods to the sheepskin represents THE NATURAL PHILOSOPHY WITH IDENTIFICATION OF OBJECT AND SUBJECT.

These three factors have an important role to play when Jacob is away from his twin Esau, who has an essentially HAIRY skin in the story: When Jacob appeared before Isaac, who could not see him, he was disguised in young goat's skin to imitate Esau. The flocks he tended in Laban's land is a consciousness or subconsciousness he initially shared with Esau, and which he gradually acquired.

Jacob's household eventually gave him their lentil-circular earrings together with their images of foreign gods, which he all buried under an oak at Schechem. Jacob then had his name changed to Israel: He was the head from which all of Israel's twelve tribes descended, indeed the root vertex of the Jewish society.

Hence, the Jacob story represents the Biblical version of the relationship between simultaneous discoveries and paradigms. The priority dispute which followed the mistaken blessing of Jacob is a part of the authority relegation in the major revolutionary paradigm shift in the early mythological history of Israel: Isaac gave his authority over to his follower in the moment when the nation of Israel was born, and divine providence had already at the outset secured that he would give it to the wrong man. Isaac 'trembled very exceedingly' when he discovered the mistake.

It is pertinent to the history as well as to the theory of science to observe that the Jacob/Esau story has remarkable similarities not only with important events in the history of mathematics, but also with the central moments in Kuhn's 1959 paper, making way for his concept of paradigms a few years later (consult for example Margaret Masterman's overview of this concept in the Lakatos/Musgrave collection, including even the concept of 'an anomalous pack of cards'). The acknowledgement of a shared social consciousness wherein paradigms produce their thoughts would be a considerable leap forwards, if this entails that we are allowed to make such inferences on historical dependency as in the example with Bólyai and Lobachevski, or with Hamilton and Grassmann. If we can indeed approximate such knowledge scientifically, then we have entered a radically new space of knowledge - presumably to be identified with the new knowledge-space inaugurated by Chomsky.

I have not touched much upon the corollaries for the theory of science which follow from the assumption of such a shared social consciousness, governing conjectures and refutations as well as the general confidence which the scientific community takes in empirical and theoretical results. No doubt, the mastering of this knowledge-space will belong to future, but we should nevertheless be able to perceive the traces of this shared consciousness and its knowledge even today. I would like to make some comments on how I believe that we can interpret the assumptions advanced here in everyday situations and scientific work. It goes without saying that the paradigms in Kuhn's sense hold a certain sway over our thoughts in manners which we are normally not really aware of: We acquire the thoughts we do, because these are in conformity with the current paradigm, and we simply do not think of other thoughts. I think that we sometimes can come across evidence for the paradigm emerging as a shared consciousness in rather trivial situations. Assume that you are writing a letter and go to mail it in the mailbox. As you approach it and prepare for the letter to be put in, you suddenly experience this vague but still strong resistence to it. You feel that you should not mail the letter, even if it looks perfectly appropriate to do so, and the addressee supposedly will appreciate the letter. The irrational resistence nevertheless convinces you that there must be something wrong, and you give in to the incentive and put the letter back in your bag again. The resistence never gets an explanation, and you never send the letter.

I believe that many people would behave in this manner, and give in to such irrational incentives without knowing why. Many would do so without even knowing about it consciously, and many would also think that such resistance signals a kind of genuine noblesse, a sort of aristocratic remains which still heralds a residual dignity for mankind on earth. There are of course many ways to interpret such 'signals', if we may call them so, but in the present framework, I am inclined to interpret them as expressions of the current paradigm, holding its members with a kind of split and conquer strategy. This point is, I believe, of importance for the theory - and, in particular, for the practice - of science. We can, in fact, contribute to an understanding of the working of the hypothesized shared consciousness even today by relating in a more conscious and mature manner to this social paradigm. An example from my own experience is telling: I experienced over and over again in the course of my first year as a doctorate student that queries and questions to the university institutions remained unanswered, somewhat in the manner of the letter I just spoke about. In this period, and, in particular, in the period when I came to work on this lecture, I had, due to the obscurity of the state I was assigned in the system, to send a number of requests to various instances in the university system. I counted that the accumulated span of time which I had to wait for answers to these questions ran to something close to four years altogether, summed up in the course of only the first year of my project, and distributed over, say, ten such requests. The resistance and silence was so immense that I had to conclude that irrational powers were at work. Repeated requests led to nothing, and the practical difficulties which ensued from this came to hamper my scientific progress. I conjecture that this was the effect of the scientific paradigm control in its self-preserving function, and the irrational resistance was to be explained along the lines of the letter which was never sent. Probably, the administrators and colleagues who were supposed to answer would have been overcome with irrational anxiety (produced by the Big Brother) if they had ignored the resistance and dropped the letter in the mailbox. The overt rationales behind the delays may still have been well-founded in the traditions of the university institution, but could, I believe, hardly stand a test of scrutiny as to its scientific purpose.

This is a kind of problem which the theory of science has perhaps neglected too much, but it is clear that a contribution which allows for a heightened consciousness as to the impact from a shared consciousness also may improve science in this very practical and immediate sense of it, in addition to the far wider perspectives which open by a future formalization of this knowledge-space (the Cantor machine), wherein conjectures and refutations are thoughts in the mind of the more or less capricious community. In order to master the knowledge of the shared social consciousness, we must probably transcend that Western tradition which goes all the way back to patriarchal times of conquering persons rather than the scientific problems we are out to solve. For example, competition and career are the worst possible drives for gaining such scientific knowledge. Wittgenstein and Kuhn seem to converge on the view that exact sciences, preparing the path for the less exact sciences such as physics, come down to a matter of social consciousness. This is, I believe, a very important point to observe for the theory of science.

Finally, I would like to mention that, in immediate succession to my preparatory work with the Jacob story in this lecture (from the beginning of September), the university was visited by Kjartan Slettemark, who made a performance at the university square on the 19th of September. I failed to see the performance, and I had no knowledge of it in advance, but I afterwards saw the report in the university newspaper, which convinced me that he had worked with similar concepts in the course of my work: Together with the two sisters Karin and Marie Grønlund (representing something like Rachel and Leah Grove), he painted twelve pictures, in close parallel to the pictures which Rachel stole from her father, and to the twelve tribes of Israel. The slogan reported from the performance was: I AM STUEREN, to be interpreted: I AM THE STEWER, that is, Jacob with his lentil stew. After having read the report in the newspaper, I understood the importance of Slettemark's contribution in the shared social consciousness to my own preparatory work to this lecture, and the institutionalization it received during the performance. This is evidently also a part of the function of his performance art and his art in general, addressing the same social knowledge-space as I have been concerned with here.

The university director bought the twelve pictures, and Jacob, Rachel and Leah left Bergen without them.

My thanks for Slettemark's contribution and for your attention.

This lecture is printed in the booklet 'Doktorgraden' and its translation 'The doctorate', both Bergen 1998, as well as in part 3 of the dissertation 'A waist of time' which is included also in volume 3 of my works published in 2013.

Added on 18 june 2019: Of course I do not want a 'similar' or 'competitor' e.g. on basis of things stolen or 'borrowed' from my workdesk. That would be swindle and nothing good can come out of that. What I meant with the example of Bolyai/Lobachevski was that mathematical discoveries may perhaps tend to arise if there is a counterpart in the platonic space - but not if the counterpart reads material stolen by e.g. surveillance or is organized by some administration. If e.g. Lobachevski got his material by swindle, that is, lifted from Bolyai's work in some way or other, that could perhaps (I dont know if that were the case) have been a part of the reason for the miserable career of Bolyai. And my own miserable career does of course not thrive well with such.

Some sources:

Bloor, D. (1983): Wittgenstein: a social theory of knowledge. Macmillan Press, London.

Chomsky, N. (1957): Syntactic structures. Mouton, The Hague.

Eliade, M. (1949/52): The myth of the eternal return. Transl. from the French by Willard R.Trask. Pantheon, New York.

Gödel, K. (1931/70): On formally undecidable propositions of Principia Mathematica and related systems. In: Heijenoort, J.(ed.): Frege and Gödel. Two fundamental texts in mathematical logic. Harvard University Press, Cambridge, Mass.

Grassmann, H. (1844/1911): Gesammelte mathematische und physikalische Werke. Edited by Friedrich Engel. Teubner, Leipzig.

Kuhn, T. (1962/70): The structure of scientific revolutions. 2nd edition, enlarged. International encyclopedia of unified science. Vol.2, no.2. University of Chicago Press, Chicago.

Kuhn, T. (1958): Energy conservation as an example of simultaneous discovery. In: Kuhn, T. (1977): The essential tension. Selected studies in scientific tradition and change. The University of Chicago Press, Chicago. Reprinted by permission from Clagett, M. (ed.) (1959): Critical problems in the history of science. University of Wisconsin Press, Madison.

Lakatos, I. / Musgrave, A. (1970): Criticism and the growth of knowledge. Cambridge University press, Cambridge.

Wittgenstein, L. (1953): Philosophical investigations. Macmillan, New York.