Introjection and Science: Beyond Subjectivity & Objectivity

In the documentary Fractals: The Colors of Infinity, Benoît Mandelbrot describes how after discovering the eponymous ‘Mandelbrot set’ and working with it for two or three days, he noticed that the strange new object he was dealing with had begun to seem uncannily familiar, as if he had known it all his life. From there the documentary segues into a brief introduction to Jungian archetypes and how patterns similar to fractals often appear in ancient art, then goes on to explain how fractals are ubiquitous throughout nature, from crystals to cauliflower to the prices of cotton throughout a century. It is somewhat disturbing to observe such otherwise rigorous scientists descending into groundless speculations about fractals as archetypes, but they are not completely to blame for this, since the connection between a transcendental mathematical shape and a transcendental archetype seems too obvious for them to resist. I will argue, however, that Mandelbrot’s uncanny feeling is better explained by the psychoanalytical phenomenon of introjection, and that this relation to objects provides new insight into the relation of scientists to their work, perhaps even allowing for something close to objectivity.

Introjection is a notion introduced by Freud in his theorizing of the libidinal economics of the unconscious, i.e. into what objects the unconscious allots and expends its affective energy. Introjection roughly proceeds as follows: a person comes into contact with an external object (a person, concept, sensory impression, etc.), is attracted to it, and proceeds to identify itself with the external object.* In fact, the Ego is defined by Lacan as ‘what of the subject can be seen in his or her objects’. In other words, a person identifies (usually involuntarily) with various objects, and then from these objects identifies commonalities (‘my personal style/taste’) in order to retrospectively construct for themselves an imaginary ego, a person’s concept of themself. For an everyday illustration, there are many people who are proud of naturally having blonde hair: these people have introjected the concept of blonde hair, thus they identify themselves as ‘blondes’. Conversely, there are many natural blondes who dye their hair a different color: these people have not introjected the concept of blonde hair, and instead identify themselves with another hair color. In this case, one’s choice of whether to introject one’s hair color strongly depends on the value attached to blonde hair by a person’s culture; otherwise, it would rarely if ever occur to people that they should be dissatisfied with their hair color. This same relationship can be found between every person and every object that each person comes into contact with, particularly those objects that a person owns.

As a person walks through a crowded store, a complex process is taking place where he identifies or does not identify with each object & person who he meets; his subjectivity is being shaped by everything in his vicinity, as his unconscious decides whether or not each object is worth bringing to conscious attention. These mass introjections cause minimal change; however, using the notion of habitus such small changes become more notable.

Habitus is a notion popularized by the work of Pierre Bourdieu and can roughly be described as “an internalized mental or cognitive state through which people deal with the social world. The habitus both produces and is produced by society”. One’s habitus acts as an integrated schema of one’s tastes, preferences, and abilities (more specifically, the amount of individual social, symbolic, cultural, & economic capital that an individual possesses); it differs from the ego in that many of the objects that are incorporated into a habitus are unconscious. In our example with the store, then, habitus acts as a filter which predetermines which objects are to be introjected and which are not. It would immediately seem that habitus, as a deterministic schema, precludes any shaping of subjectivity from external objects. Indeed, we can see how this shaping of one’s subjectivity is reduced quite a bit, but at the same time habitus is not all-intelligent: a habitus, for example, may pick up on a prominent detail (e.g. poor posture in an otherwise beautiful woman) and reject this ‘flawed’ object simply on that ground, without which said object would undoubtedly have been introjected. Similarly, many objects cannot be neatly fit into a judgeable category, and thus these categories are constantly expanding & contracting to deal with new stimuli, usually at the unconscious level.

On rare occasions, however, one encounters a phenomenon that is entirely different from anything one has encountered before: foreign food, skydiving, the Mandelbrot set. Habitus has no adequate categories, and is forced to turn to its context, the field, in order to try and locate some sort of value judgement to base itself upon. However, such examples are, for the average person, ineffable. Professional food tasters are taught a diverse vocabulary which breaks the elements of taste into extremely subtle categories (e.g. there are fourteen different criteria by which the flavor of mayonnaise is judged), but the layperson is entirely incapable of expressing these differences. Indeed, in one experiment by Consumer Reports, food experts and college students were told to judge forty-four different brands of strawberry jam; when they simply had to order them from best to worst, the choices of both groups were quite similar. When they were asked to explain their choices, however, the college students choices began to strongly diverge from those of the food experts, e.g. the experts’ best jam was ranked second-last, and the experts’ worst jam was ranked third. The students began to approve of those brands which could be more easily described, and became lost in abstract categories rather than focusing on raw sensory impressions (Gladwell, 63-4). In a somewhat similar way, the feeling of skydiving is entirely incapable of being expressed in typical discourse: all that the non-expert can hope to do is to silhouette the ineffable: “Your eyes don’t know how to focus when faced with such depth, and it’s just crazy.” Although these experiences in themselves cannot be categorized, connotations have arisen surrounding the idea of foreign cuisine (adventurousness, worldliness, distinction), the idea of skydiving (bravery/recklessness, a carpe diem mentality), and it is these connotative categories that help a person introject these experiences. Indeed, one cannot help but wonder whether at times it is only these abstract personal qualities which are introjected rather than the sensory impressions themselves.

The Mandelbrot Set

What I want to argue is that for Benoit Mandelbrot, his Mandelbrot set was one such ineffable phenomenon. It was entirely new when he discovered it, so in itself it could not be categorized. Given Mandelbrot’s place in the professional and mathematical fields, his context provided him with positive connotations for such a discovery: it was potentially a heuristic tool which would come very much in handy. This positive connotation was all that was needed to motivate his unconscious to introject this foreign object: Mandelbrot experienced an uncanny (unheimlich, in the Freudian sense) openness to this object, to the point where he committed himself to introject whatever further discoveries he would make about this new class of object; in an indescribable, abstract manner, Mandelbrot became the Mandelbrot set, became fractal. Just as people have historically tended to use the most developed technology as a metaphor for their brain (clockwork, engine, computer, internet), and just as the artist witnesses their own artwork for the first time after creating it in a state of semiconscious impulsion and (retrospectively) judges herself according to her art, so Mandelbrot shaped his notion of himself according to fractals: new metaphors were available to him, new patterns in the external world were revealed to him, new problems became manifest for him.

This sort of occurrence , I argue, provides a third option beyond the duality of objectivity and subjectivity. A ‘wormhole’ is formed between subjectivity and its object, where rather than imposing categories upon an object until it is made familiar, the object imposes itself upon the subjectivity, forcing it to develop new concepts & schemata. There are some remnants of doxa, of course: fractal geometry is confined to Euclidean geometry, excluding the equally valid non-Euclidean sphere. Nevertheless, the relation of subjectivity to object cannot be completely explained through the terms subjectivity/objectivity, and warrants some thought. Most of all, it suggests a new way of thinking about scientific paradigms and the praxis of scientific discovery.


*: This is an oversimplified explanation, mostly because the author personally does not believe in the subject. Substituting ‘habitus’ for ‘person’ might be the best compromise, but this brings in a deterministic impulse counter to my later argument. By way of countering this, the reader is asked to keep in mind that there are some objects of study the substance of which cannot be adequately accounted for by the notion of habitus. (Attraction to the form of these topics, however, can near-unfailingly be explained by habitus.)


  • Benoît Mandelbrot felt a strange familiarity with fractals when he first discovered them. 
  • Mandelbrot & others tried to explain this by reference to Jungian archetypes, ideas which are imprinted in the human brain from birth which provide people with a ‘collective unconscious’.
  • We do not have to content ourselves with these groundless speculations, but can explain Mandelbrot’s uncanny feeling by the psychoanalytical notion of introjection.
  • Introjection roughly proceeds as follows: a person comes into contact with an external object (a person, concept, sensory impression, etc.), is attracted to it, and proceeds to identify itself with the external object.
  • Every person has an integrated set of preferences that has been conditioned into them by their social class, culture, etc. This set of preferences is called a person’s habitus. Habitus acts as a filter to judge whether or not various objects and stimuli are worth caring about.
  • Our categories of judgement sometimes get in the way of what we really feel (as in the case of the jam taste testing above). Language gets in the way of our senses, and we become lost in abstract categories, preferring those senses that can be more easily described.
  • Sometimes one encounters a stimulus that is so new that they have no way of judging & categorizing it. Still, there may be connotations surrounding the idea of it (e.g. the connotation of courage for skydiving) that are capable of being judged (“Am I really the sort of person who would go skydiving?”).
  • When Mandelbrot first discovered the Mandelbrot set, the positive connotations that he gleaned from the mathematical and professional fields were enough to convince his unconscious to introject the Mandelbrot set.
  • Mandelbrot, in a somewhat indescribable way, identified himself with the Mandelbrot set, which provided him with new metaphors, patterns, and problems.
  • Introjection cannot be fully described in terms of objectivity and subjectivity, and indeed acts as a ‘wormhole‘ between them. Therefore, the notion of introjection has interesting repercussions for the philosophy of science, e.g. the construction of scientific facts.



  • Bourdieu, P. & Wacquant, L. (1992). An Invitation to Reflexive Sociology. New York: Polity Press.
  • Evans, D. (1996). An Introductory Dictionary of Lacanian Psychoanalysis. London: Routledge.
  • Fractals: The Colors of Infinity. Lesmoir-Gordon, N. (Dir.). (1995). Films For The Humanities & Sciences.
  • Freud, S.; Strachey, J. (Ed.). (1967). Beyond The Pleasure Principle. New York: Bantam Books.
  • Freud, S.; Brill, A. (trans.). (1938). The Basic Writings of Sigmund Freud. New York: Random House.
  • Freud, S.; Riviere, J. (trans.). (1960). The Ego & The Id. New York: W.W. Norton & Co.
  • Gladwell, M. (2005). Blink: The Power of Thinking Without Thinking. New York: Little, Brown, & Co.
  • Gleick, J. (1987). Chaos: Making A New Science. New York: Penguin Books.
  • Wilde, O. (1889). “The Decay of Lying”, in Intentions (1891).

About Graham Joncas

We are a way for capital to know itself.

Posted on August 8, 2011, in Language, Psychoanalysis, Science and tagged , , , , , , , . Bookmark the permalink. 1 Comment.

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