Presentation of the text Mathematics by Sandor Ferenczi ## edited by Jorge Canestri e Silva OlivaThe text we are presenting, It does not appear as a completed paper, but rather as a series of notes that are original but sometimes enigmatic observations that are not easy to decypher. We have no information on the origins of the theme dealt with in the essay and taken up again a few years later in 1926 in the article: Ferenczi had a tendency to bring back to psychoanalytic investigation specialized debates that were considered external to it, and this seemed to cause Freud a certain amount of dissappointment (M.Stanton, 1990, p.66). This interest can be testified by the fact that one of his dearest and most brilliant scholars, Imre Hermann, carried out a thorough investigation of the principal themes of this article: the problems regarding the origin of talent and logical-mathematical thought through specific texts on the nature and function of logical thought. Among the cultural circumstances that may have favoured Ferenczi’s attention towards mathematics, we may recall the international debate that arose at the beginning of the century regarding the foundations of mathematics, during which (in 1902) the great logician G.Frege, following the criticisms by B.Russel, decided not to publish the second volume of his The key word to a comprehension of the text is the term Through repeated self-observation, Silberer had discovered that at the moment of the passage between being awake and going to sleep he produced clear images that could be interpreted as symbolic descriptions of what happened at the moment when his effort to think of a given topic contrasted with his incipient sleepiness. This discovery was very favourably accepted by Freud who had already previously hypothesized the possibility of an " According to Silberer, the typical phenomenon of the Although explicitly referring to Silberer’s functional phenomena, Ferenczi again transforms the concept that oversteps the boundaries of the Regarding the origin of mathematics, or at least of arithmetic, Ferenczi believes that it consists in the unaware perception of the functioning of the various physiological apparatus responsible for sensorial perception. Thus, the operations of addition and subtraction of the sensorial stimuli at the cellular and neuronal level (that give rise to the perception of the stimulus itself: intensity, form, color, etc.), considering only and specifically their "formal" aspect, would give rise to a symbolic production of the mind as the first elementary part of mathematics, i.e. arithmetic. Similarily, certain traditional sub-divisions of the discipline such as arithmetic, algebra or logic, would become psychic projections of the developmental stages that, starging from the perceptive functions of addition and subtraction of the stimuli typical of the sensory organs, lead through progressive abstractions to symbolisation, conceptualisation, and finally to the formulation of conscious thought. A proof to this thesis are the so-called "idiot savant", people who often have a low intelligence but manage to do exceptionally complex calculations (square roots, individuation of primary numbers, etc.) without having any idea of the reasoning behind what they are calculating and without knowing the algorithms that lead to the desired results. Although the author’s main thesis that mathematics "is interior self-perception of one’s own conscious functioning" of which only the formal aspects are grasped, belongs in it’s simplicity to the archeology of the topic, it can in any case be included in the present debate about the nature of mathematics and its discoveries. As is well known, the universality of some of the mathematical rules (eg. the Pythagoras’ theorem, discovered in the same form by populations who were far apart and of different historical and cultural levels), poses the everlasting problem about the nature of the discipline itself. Is mathematics an invention of the mind that, being common to all humanity, sooner or later produces the same results; or does mathematics form a world of its own, with rules that are independent of common reality (e.g. the discover of non-Euclidean geometry), to which people with particular capacities can accede in order to discover the rules of its functioning? This is a matter of great actuality today that so far does not appear to have been definitely solved, as is witnessed by the ongoing debate between the two points of view, in which astrophysicists such as Barrow, neuroscientists such as Changeux and mathematicians such as A.Connes take one side or the other.
Sandor Ferenczi : Mathematics (c. 1920)
1. Pcs and cs: Organs for ucs psychic qualities. Ucs: Organ for physiological qualities (perception-recollection). Sense organs: Organs for physical qualities. ( (ii)Physiological reality is algebraically(iii) Ucs reality is symbolically (paralogically) (Primary process) - (iv)Pcs reality is logically (Secondary Individuation
- (v)Cs (?) reality is process)
measured. Counting machine ‘Comparison with the study of quantities’ (Mathematics). 3. Mathematician-knocked down. No idea of mathematics-skilful.
4.
5.
* * * 6. Mathematics is * * * 7. Mathematician not necessarily clever. (Idiots): peculiar combination (introspection). * * * *Genius*: combination of strongly-developed introspection with strong
instincts. (i) Manifestations of instinctual beings are elaborated by a (syst.) cs capable of combination. (ii) Genius elaborates his own inst. ‘ideas’.
* * * 9.
1O. The second great epoch in psycho-analysis is connected solely with the name of Freud and deserves to be called a ‘theory of libido’. For the first time, the following-up of the 11. The third, the present-day, phase of Freud’s psycho-analysis is characterized by It is to be expected that this trend of development in psycho-analysis, which takes into account, in addition to the congenital factor, also the formal and quantitative moments, will further the investigation of the various ‘talents’ which until now have been regarded only as rather more or less of one essentially uncertain (anatomical) ‘disposition’. Such researches, however, are not yet in existence. I have prefaced my article with this cursory survey of the place of mental talent in psycho-analytical theory in order to demonstrate the narrow foundation on which research into one particular talent has to be built, and the various, often completely heterogeneous, strong-points which would have to be used in such building. The furthering and inhibiting post-natal influences, constitutional factors of the ego, and of sexuality, metapsychological considerations, must all help in motivating a special talent.
12. The foundations on which such a construction could be built up were too narrow and the whole building was too labile and insecure to justify any attempt at systematic investigation. Thus we must content ourselves with trying, armed with the tools of psycho-analytical knowledge, to bring nearer to our understanding one special talent, that of mathematics. 13. (i) Arithmetic = Physics (ii) Algebra = Physiology (sensory qualities) (symbol!) (iii) Higher mathematics (differential -integral calculus) = Symbolism (iv) = Logic Arithmetic = Physics Algebra = Physiology Symbolism = UCS Psychic Logic = Pcs cs
Progressive abstraction (screening) with the help of phylo- genetically acquired functions. - Proof for the reality of the external world.
The * * * 15. Inter-relation of physical, physiological and psychological forces during the whole life, perhaps also
Sense organs are screens (mathematical). Not objective.
- Auto-arithmetics: perception of the individual sense
- Symbolism: summation of sense impressions (amphi-mixis-condensation).
- Logic: regression to arithmetics at a higher level.
Impressions
Reckoning with Reckoning with symbols (notions) is
* * * 16. The Summation of The The closer connexion of action based on cautious thinking with the 17. The fusion of numerous single impressions of the external world into a In the ucs the fusions (elementary process) happen according to the principle of 18. * * * 19. (i) *Thinker*: trial admission to action ‘under displacement of minimal qualities’.- Much more important are psychiatric observations on the coincidence of great mathematical ability with otherwise strong backwardness of the other kinds of intellectual and moral development, often amounting to imbecility, or even idiocy.
(iii) 20. (Thinker=transitional type between mathematician and man of action. ‘Sicklied o'er with the pale cast or thought'). 21. (Description of the two types.) 22.
Scientific works to date on mathematical talent dealt with: (i) (ii) Connexion between musical and mathematical talent -an obviously secondary question. * * * 23. 24. (i) A (ii) These simple perceptions are summed up into a (iii) The elimination (a further screening) of the differences, another (iv) The relating of these conceptions to each other and the trial admission of action based on them (conception of the consequence)=thinking. 25. The psychologist is in the last instance a self-observer (?) + object, "oscillating" between introspection and observation of objects.
* * * 26. Inhibition as a 27. A ‘Weltanschauung’, as far as possible faultless, demands a utraquistic attitude (oscillating between introspection and object observation) out of which a reliable reality can be constructed. * * * - The pure logician is the mathematician among the psychologists. He has interest only for the formal in the pcs and projects it into the external world. The psychologist must, in addition to logic, also take into account the
*sub-intellectual*, the ucs ideas and their (fantastic) interplay, also the*instincts*which are the basis of everything psychic -for it is only the aims of the instincts and their derivatives which form the*content*of the mind. The psyche is ruled by the tendency to care that the instincts receive satisfaction, and are steered eventually into certain harmless channels which prevent unpleasure, that disturbing external stimuli be removed either by adaptation or by changing the external world, or be diminished as far as possible.
The psychologist must not be the mathematician of the mind, for he must take into account the contents of the mind (which are basically illogical and determined by the instincts). * * * 29. Logic = mathematics of the pcs Pleasure principle = mathematics of the ucs * * * 30. Insensitive bodies are the most real calculating organs (photography, expressionism). * * * 31. Where this mechanism is present the processes of excitation occasioned by the physiological and psychological stimuli must each time go through a new screening, i.e. being sorted and classified according to quantities. (Light filters in co1our photography: (1) separation, (2) synthesis.) Cs memory systems of the pcs Sorting into the Excitation of the senses * * * *Conceiving*would mean then a function which strives to condense all
these impressions separated into their elements into a unit (conception).
The principal systems of the ucs: Sense organs separate the world into elements, the mind restores it. This * * * 33. Very primitive, approximative mathematics of similarities, but mathematics nevertheless. Mathematics of the 34. The mathematician must therefore gain insight into the processes of his pcs mental systems, if his results are to correspond with external reality. (Children's mathematics?) No! (Idiot's mathematics?) Arithmetic: addition, subtraction-function of the sense organs. Algebra : combination of higher order; permutation, geometrical calculations, reckoning with time-function of the ucs. (This is to be supposed also in animals: the dive of the eagle on his prey, the spring of the tiger-demand calculation. Differential and integral calculus, geometrical functions, even though no *Mathematics*is a*psychic*organ projection in the same way that mechanics appears to be a*physiological*organ projection.*Music*is likewise a projection outwards of the*metapsychological*processes which accompany the affective and emotional processes; the congeniality of the musician and the mathematician is based on the same ability for fine self-observation.
36. A second screening seems to take place within each * * * 37. Condensation is the process corresponding to association in the ucs. The 38. The work of an acting man is a magnificent 39. The mathematician is a man who has a fine capacity for self-observation of this condensation process, i.e. of the formal, of the ‘functional’ phenomena in 40. First function of the psychic: 41. Such ‘ * * * - The mathematician appears to have a fine self-observation for the metapsychic (also probably physical) processes and finds formulas for the operation in the mind of the condensation and separation functions,
*projects them*, however,*into the external*world, and believes that he has learnt through*external experience*.
A very strong argument against this is the eminently 43. Surprisingly these formulas prove valid as ‘applied’ mathematics also in the physical world (technique). Indeed, an argument for the ‘monism’ of the universe, at least for the identity in essence of the metapsychic with the physical. 44. Query: is mathematics Solution of this problem perhaps: self-observationis in itself an inner ‘experience’, out of which mathematics is abstracted. That is, on both sides of the P-system mathematical abstractions do occur. In other words : is mathematics * * * 45. It is not improbable that we must think of the screening work of the sense organs as a prototype of what happens in the higher mental field, in the ucs. The sorting according to certain categories characterizes the whole memory system, which constitutes the ucs, according to The memory systems of the ucs are still sorted-with regard to (achronic) time, to space, etc.-according to the principle of similarity. What
With the help of ‘ Cs is after all no system, but a special mental act (?). |