Part I: Who Is Afraid Of Mathematics?
The Problem Of Terror And How To Use A Holophrase To Be Dogmatic
What do all four of the questions below have in common?
- Have you heard that Lacanian analysis is done by people who graduate from university with a psychology degree, then try to analyze society and help others by analyzing their unconscious?
- Have you heard that logic is about normative thought?
- Have you heard that mathematics is about certitude, calculation, abstract thinking, and number?
- Have you heard that madness is a psychosis that is a kind of mental illness characterized by disorganized behavior, delusions, hallucinations, and disorganized speech?
These questions, all composed from rumor and gossip, can be shown to produce a mis-recognition of the tradition. In an initial step, this article aims to describe why this is so. In Part II — The Psychotic Dimension Of Education, we set out a clinical analysis.
By mis-recognition of the tradition, I mean such questions are nothing more than cliches that avoid a more precise entry into what is at stake in the transmission of a civilization. Before defining what this more precise entry and transmission entails, let me give an example. To discover what is being avoided by the cliches on mathematics as number, all you need to do is reflect on your education to recognize the real difficulties with mathematics do not begin with number or arithmetic, but with the introduction of a letter, a variable, or constant in algebra. Things become more complicated, however, with the introduction of the integral sign in calculus in high school. Yet, the majority of people still speak of their fear of numbers and associate mathematics with their educational experience with calculation and boring repetitive exercises. It is rare, for instance, for anyone to speak of their fear of variables, constants, and glyphs, √, ∂, ∫, π … or the concrete formation of a mathematical construction, but it is precisely here the real mathematical problem begins¹.
Terror And The Ghost of Abstraction
Of course, people continue to speak of mathematics as if it were ‘abstract’. No doubt, without taking into account Frege’s damaging critiques of Husserl’s and Cantor’s psychological use of abstraction: removing the color, teeth, and whiskers of a mouse by a process of abstraction that claims to remove any particularity of the mouse, does not result, for Frege, in an abstract mouse, but a dead and bloodless phantom. What Frege wants to do, without quite succeeding, is to replace abstraction with a concrete procedure of nomination. Only later, in the formulation of Russell’s theory of definite descriptions, Hilbert’s epsilon calculus, and Bourbaki’s tau-box abbreviation would such a concrete writing procedure succeed. It is important to recognize, however, the gist of Frege’s critique of abstraction is systematically repeated elsewhere.
When Kandinsky was asked why he painted abstracts, he claimed that there was nothing abstract in his paintings, they were concrete, there were traits of green, red, and blue. And that what is abstract are the representational paintings that proceed by perspective and a complicated framework of optical presuppositions that are assumed, but never explained.
Frege’s and Kandinsky’s attempt to re-read and re-write the tradition out from under the ghosts of philosophy and psychology is an example of what we call here de-monumentalization: a dis-assimilation of a text and the tradition from its cliches and silent dogmatism. It is short wonder, in the lack of such a de-monumentalization, that there would still be people not only fascinated, but terrorized by the ghosts of tradition, and not the tradition as such.
How To Use A Holophrase And Be Dogmatic
In its most simple definition, a tradition is a writing act: an act of structure that fixes a reading. Yet, a tradition can become so codified and monumentalized that it falls silent and becomes a kind of ghost or cliche for tourists, if there were not a new generation to re-read and re-write it. Moreover, in the lack of such an effort of re-reading and re-writing there can be no de-monumentalization and de-codification. Thus, it is difficult for the youth of today to invent anything new if the tradition has become either a form of:
• dogmatism — a silent assumption of meaning on what everyone must know;
- holophrase — a two-dimensional statement that seems to be three-dimensional.
These two modes of trivializing speech and language often accompany each other in forms of tourism. When an airline hostess greets you by saying, “Hello, how are you today?” she has just spoken in the use of a holophrase. Whether she is really interested or actually speaking to ‘you’ or not is doubtful, but it may sound and look like it. Yet, should ‘you’ find yourself addressed by a holophrase it is difficult to disregard or not take it seriously. So much so that ‘you’ are often forced into either another holophrase, “I am doing fine!”, or the silent dogmaticism of a smile, just in order not to feel out of place or a-social.
The problem being posed here is whether or not the four questions above on Lacanian analysis, logic, mathematics, and madness, are not all forms of dogmatism and holophrase. When someone mentions, “I am a Lacanian analyst getting a psychology degree”, “Logic is about the norms of thought”, “Mathematics is about number and abstraction”, or “Psychosis is Madness” are they using a holophrase? And if they are, what is being mis-recognized of the tradition and what are its consequences? A professional calling card? Or a ready-made delirium? The articles that follow in this series will address these questions.
In speaking today it has become essential to know how to use a holophrase and be dogmatic especially in the most professional and liberal of environments. For it seems most do not need to use the personal pronoun ‘I’ anymore. It is more sympathetic to assume an underlying understanding that is accepted by everyone and speak of oneself with a ‘you’ that functions at the place of the Other: “Like, you know how it is when you find someone next to you that you really like, then …like … you just know what they are thinking like.” Who is this ‘you’ floating everywhere in a speech? And what is assumed about a mutual understanding here and the constant use of ‘like’ ? A quick use of language may seem to facilitate an identification and codification of the Other, but it also carries with it an automatic charge of paranoia when messages actually come back from the Other in a way that is not entirely one’s own. Indeed, how could it be otherwise, since in adopting a holophrastic manner of speech, the ‘I’ is never speaking, it is more like a marionette being spoken by the place of language. Call this place of language the Other²
The Place of Terror in Mathematics
The problem of madness today is not one of hearing voices, but when these voices begin to speak and think for ‘you’. Indeed, the shift from fear to terror occurs here: when one does not simply hear a voice or see something scary, but when this voice tries to tell ‘you’ what to do by actually saying ‘I’ in your place over something banal. “Oh, ‘you’ want to take a plane to NYC, well, just know this … ‘I’ will always be there with ‘you’. Maybe ‘you’ should just stay home.” Notice how this rhetoric of terror, is the preferred mode of speech for any monotheistic God: “Know the fear of the Lord, and you shall receive wisdom”[Proverbs 2:5]. So much so, that it is only a step from the religious commandments of the God of Abraham and Issac, to the universal laws of the God of Nature as they were espoused in modern science by a Galileo, Descartes, and Newton: “Philosophy is written in this grand book — I mean the universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth” (G.Galileo, translation in The Philosophy of the Sixteenth and Seventeenth Centuries (1966) by Richard Henry Popkin, p. 65). If we take such a monumental statement at face value, as a form of ‘mathematical tourism’, then we can read it as a function of a holophrase whether it be found in the language of an airline hostess, terrorist, theologian, or scientist. I will return in Part III: Machines, Gods, and Animals — to trace this language “written in the Book of Nature”, by first asking whether God actually writes anything — it is certain he speaks and gives commandments — and whether Freud’s discovery of the unconscious frees us from the need of such a hypothesis.
When the majority of people speak of their fear or fascination of numbers and associate mathematics with calculation and abstraction today, it becomes obvious at some point that they are not speaking about mathematics, but are being spoken by a philosophy or ‘idea’ of mathematics that is constantly on the verge of holophrase. Indeed, such ‘ideas’ often go beyond mere fear and fascination, but express a kind of panic or anxiety of being terrorized or in love with the Other. Education, Paternalistic Law, Metaphysics, God, and Science, are just a metonymy of monuments that can serve to mis-recognize the Other in the mathematical tradition. Further still, many debutants and savants alike confuse mathematics with a mere ‘technical writing’ . If true, this would reduce mathematics to being nothing more than a form of coding and decoding writing. If false, then the question remains on how to de-monumenalize the tradition, how not to reduce mathematics to a mere code or technical writing, while constructing the tradition in a less holophrastic and less dogmatic way? As we will show in Part IV —The World Without Limits: §4 Strategies: it is a question of introducing the Other into mathematics in a more neutral, that is to say, less terrorizing and fascinating manner.
 In Part IV: Welcome To The World Without Limits, we situate a more precise entry into mathematics following M. Heidegger’s exegesis on the original Greek definition of the Mathemata: “What one knows already and teaches itself with excellence”. See Heidegger’s What is a Thing?: A. Modern Science, Metaphysics, and Mathematics; Eng. Translation, D.F. Krell, Harper & Row; p.249–257.
 See the end of Part IV: Welcome To The World Without Limits, for a construction of the Other in an optical-geometrical example.
Why write here on Medium? It is an experiment. It is an attempt to communicate with a different audience and in a different way than those I habitually address in the field of logic, mathematics, and Lacanian analysis in the U.S. and France. It is also the admission of a sigh: that I am dissatisfied with the level of the work that has been published under the epitaph of Lacanian analysis for quite sometime now. Needless to say, I have no illusions as to what I am publishing here will change things in those contexts. But it does make room here for an experiment in hearing and saying something new but simple in public about important subjects. Since I have just started writing here, I will use the pseudonym Simplicus until I become familiar with the site. You can, however, find here the clinic-school that I work at: www.topoi.net