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10. singular points and singularity
Seoul National University of Technology
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Deleuze defines singularity as “the distribution of singular points”(“How do we recognize the structuralism”, Desert Islands and other Texts, 176). Singular point is a mathematical concept stemming from the Differential theory, which means a ‘non-differentiable point.’ However, singularity is also a concept used in biochemistry as in ‘enzyme singularity(’specificity’)’, and singular point too is a concept in physics like a material point in a force field from which the force is emitted. Singularity is often mistaken for uniqueness or property that expresses individuality, but Deleuze not only refers to singularity as the pre-individual and the impersonal but also contrasts it with property. Singularity is not particularity either. Besides, it is contrasted with the generic universality and generality of ‘all,’ but also implies a very different kind of ‘universality’ drawn from its repeatability. To understand this, we need to start from singularity as a concept in ‘physica’.
First of all, in mathematics, a singular point is a non-differentiable point, which is, for example, a cusp such as the vertex of a triangle or an endpoint of a broken curve. Differentiability means that ‘the curve is continuous at one point, and the left and right differential coefficient are the same.’ Simply put, there should be only one differential. If, for example, the base of an isosceles triangle with both angles at 45 degrees is placed on the x-axis, the right differential coefficient at the top cusp is 1 and the left one is –1. It has two differentials. In fact, the number of the differentials is not just two. As you know, because the differential is the gradient of the tangent line at one point on a curve, numberless tangents pass through that point and all values between 1 and -1 are differentials. In mathematics, if the number of its differential is not one, it is said that there is no differential. That’s not because it has no differential but because it has too many.
The singular point in physics is the point from which the force is radiated. For example, as often seen in the experiments using magnets and iron powder, the point where a magnet is placed is the singular point of the magnetic field. When the ‘distribution’ of the number or locations of the magnets changes, the magnetic field changes greatly. In other words, the singularity of the magnetic field changes. In a gravitational field, a gravity-bearing entities such as the earth or the sun is the singular point. In meteorology, the center of low or high pressure is a singular point. The distribution of these singular points determines the singularity of the weather for the day. Weather forecast is made through this weather singularity. Some of those are concepts like ‘cold front’, ‘continental wind’, ‘intensive heavy rain’, and ‘dry rainy season’ All these are the concepts that express the singularities of weather that are repeated due to the distribution pattern of the singular points. The structure of an element is also described as a distribution of singular points that are particles.
A singular point is a point from which a certain force radiates. When it comes to force, there are various modalities such as the pulling force paired with the pushing force, and the inertial force and the deviating force. Particles emit different types of forces such as electromagnetic force, weak and strong nuclear force, and gravity. The one and the same electrons pull and push depending on the neighboring particles. Depending on these forces, singular points are combined or decomposed. Singular points transition from one singularity to another by combination and decomposition.
In this sense, singularity can be said to be the neighborhood relation of singular points. However, when an object with a singularity is combined with another singular object, it forms singularity again on the next level. In other words, it becomes the singular point of that singularity. A nucleic acid called cytosine(C), for example, becomes a different amino acid depending on its neighborhood relationship. In other words, It can become serine(UCU), proline(CCU), or alanine(GCU) depending on the neighborhood relation. These amino acids combine with other amino acids to form proteins. If the neighboring amino acid changes, it becomes a different protein. Serine is an amino acid with a determined singularity, but it participates as a singular point when forming the singularity of a protein.
Singular point constitutes a singularity, but conversely, it has a different 'nature' by the singularity that it constitutes. Oxygen atoms participate in the oxygen molecules( ) to constitute the singularity of the quality of making fire, but they also participate in the water molecules( ) to constitute the singularity of the quality of extinguishing the fire. It is important to note that singularity does not refer to this individual property that makes and extinguishes fire, but it is the matrix where these properties arise. Enzyme singularity(’specificity’) is not the catalytic property of an enzyme, but the matrix that enables catalytic reaction. That, of course, doesn't mean that singularity unilaterally determines singular point. The singularity of a group or a compound becomes something different when any singular point is added or omitted. The singularity of Oxygen molecule is different from that of ozone molecule( ) although both are compounds composed of the same oxygen atoms.This relation between singular point and singularity is the same with the relationship between people. One and the same individual becomes a singular point of a soccer team and that of a family or rock band too. Besides, this person can become a singular point that quickly lures in the opponent defenders when in soccer team A, but can become a singular point that makes a frustrating and timid play when in team B. As you know, this is caused by the relationship with other singular points that make up the team. The singularity of a group in which I participate determines my singularity in that group. Of course, that singularity is evidently what I made in that it changes greatly if I get out of the group. If the singularity of a group doesn’t change without me, I’m not a singular point but merely an ordinary point. Even if I participate, I can’t form a singular point. When it comes to a triangle, all but three vertices are ordinary points. Although points such as maximum point, minimum point, and inflection point are differentiable points, they are called remarkable points in that they remarkably show the characteristics of the curve.
Therefore, although a singular group is a ‘whole,’ it is not enough to be called a ‘whole’ because it is a whole the nature of which is made and changed by singular points. It can be said that it is a whole without wholeness and a multiplicity without the One. An organic group in which the center or the ‘whole’ has integration power or domination power has fixed stability, whereas this kind of group in which the forces of disparate singular points are alive can be said to have a ‘metastability.’ In the former case, only the center that integrates the whole is a singular point. On the other hand, the latter has multiple singular points with different forces.
The former has strong internal stability, whereas the latter has high external variability. That’s because it changes every time a singular point comes in and out. This implies that a group or a compound is likely to disintegrate as any singular point is separated. Because a singular point has both attract and repel, sometimes it becomes an attractor that attracts other singular points, and sometimes it becomes a repulsive point that moves away from and repels each other. It is well known that rock bands easily break up or their colors totally change when there’s a change in one of their members. A pack of wolves is said to be the same. For this reason, Deleuze/Guattari affirms the collective form of ‘band’ or ‘pack’ in contrast to organisms(A Thousand Plateaus, 33-35).
The relationship between singular point and singularity is somewhat eccentric. Although a singular point constitutes a singularity, it does so only in such a way the constituted singularity determines the ‘nature’ of the singular point. This is because a singular point has indetermination. A compound with a singularity can become a singular point again because it has indetermination. Even a simple singular point or a compound with singularity has not only determination but also indetermination full of determinabilities. If you know that the concept of virtuality Deleuze says has indetermination, determinability, and determination all together(DR 169), you can see that the concept of singularity corresponds to that of virtuality. Deleuze also defines that sense is an event and event is a singularity(LS 52)
Like other concepts in the philosophy of difference, the concept of singularity also contends with the existing familiar concepts. The first counterparts that this concept strikes are generic universality and the concept of particularity that is the mate of the former. The concept of traditional universality is about certain characteristics common to ‘all things’: ‘all humans die,’ ‘all humans have thinking ability,’ and ‘all humans have two eyes,’ etc. What the concept of universality pays attention to is these characteristics common to ‘all’ humans like this. These are the ones that define the ‘identity’ of humans. Nothing is as obvious and ordinary as this. That’s why Nietzsche once said that there is nothing as insignificant as universality. Particularity is defined as the unity of universal and individual, which means a particular mode in which the universal runs through the individual. This is the way the universal subsumes the individual.
On the contrary, what we seek to see by the singularity is not this ordinary universality common to everyone but the rare aspect of an event. As you know, the word ‘singular’ is in contrast to the word ‘ordinary’ or ’normal.‘ What we really need to pay attention to is this. It is when viewing even a seemingly natural and obvious universality as a singularity different from others that we become to pay attention. Although the word ’all things fall to the ground’ has a universality, no one will pay attention no matter how strongly you emphasize it. However, the situation totally changes when conceptualizing this as a singular force called ‘gravity.’
You may say that it is the universality of gravity that we call Newton’s achievement. However, didn’t the attempts and efforts to use this concept here and there by the attraction of its singular force lead to a ‘universality’? That was the case with the development process of the concept of gravity. At the outset, there were secret traditions between magicians fascinated by the singular force of the magnet. Petrus Peregrinus, who experimented the singularity of magnet through cutting magnet or carving it into a sphere in 1269, was one of them. This interest led to the argument that the earth is a gigantic magnet(William Gilbert). It is well known that Kepler was greatly influenced by this ‘philosophy of magnet.’(Yamamoto, The Birth of Science) Galilei hated it very much. Newton suspected that the sun might have magnetic force because magnetic force disappears when heated. However, it is clear that the idea of the gravity of stars that pull without direct contact stems from the magical interest in the singular force of the magnet. On the other hand, when gravity is connected to acceleration(Einstein), the concept of gravity unfolds a different field of singularity.
The concept of singularity criticizes the concept of generic universality, but implies a different kind of concept of universality. The singularity of magnets contrasts to the ordinary universality of 'all stones.' However, it has a conditional universality because it goes for ‘any stone if it has a pull and push force without direct contact.’ Not all cytosine(C) makes serine(UCU), but any cytosine that connects with uracil (U) on both sides makes serine. The point can be said to be whether to gather ordinary commonalities to form a generic universality or to form a conditional universality through singularity.
Deleuze goes on to emphasize that singularity is impersonal and pre-individual(LS, 98). Singularity is impersonal in that it is not only independent of the individual's personality but also irrelevant to the integrated personal subject 'I.' ‘My’ immune singularity, for example, belongs to not ‘me’ but immune cells. Autoimmune diseases that attack 'my' cells or allergies that react to food that 'I’ need show this well. It is impersonal because it belongs to the ‘under’ of the subject I, and pre-individual because it belongs to the ‘prior’ of the individual I. The singularity of Spinoza’s thinking does not just belong to individual Spinoza. That is shown in the fact that whenever this type of thinking comes up, we call it ‘Spinozian.’ For this reason, Deleuze has said that children are Spinozists, and can be Spinozists even without reading Spinoza. On the other hand, there are persons who have feministic heads but whose hands and feet are patriarchal. Conflicting singularities coexist in an individual’s personality in a split state. Consequently, singularity doesn’t belong to an individual nor personality.
Another concept that singularity contends with is property. Property is what properly belongs to an individual only or a ’property’ an individual exclusively possesses. Those who emphasize what is proper to an individual emphasize the ‘individuality’ of proper noun, namely, proper name, whereas those who emphasize what is proper to humans emphasize the exclusive ‘speciality’ that all humans have. Human speciality, in fact, is an arbitrary and partial selection of some of the universalities that all humans have. It goes like this. The characteristics of having two eyes are excluded because numerous animal species have two eyes. The characteristics of thinking and language use are selected as the nature proper to human because there don’t seem to be such beings as ‘thinking animal’ or ‘animal that uses language.' Why is that selected? That’s because it seems conventionally self-evident and others easily agree with it. There are infinitely many properties common to all humans. So nothing is as arbitrary as the property of humans only. This is because it is just one of the infinite many. A more essential problem is that this ‘proper nature’ shows humans' narcissistic prejudice against non-humans. Other animals and plants too have most of what are thought to be human properties, such as thinking, language, labor, tool, and play, etc.
Some argue that proper name is important because it means personal difference that others do not have. It sounds as if proper name is the essence of the concept of difference. However, even though wearing trendy clothes and pursuing individuality, most are ordinary and normal people who are not different from others. Proper name merely shows mediocrity in the illusion that it belongs to ‘me’ only. It is another name for ‘universality in itself’ that one shares with others unknowingly. Moreover, proper name is confined in a narrow view where it thinks of nothing but human.
If you think that proper name is an object of attention in the philosophy of difference, you’d better recall Deleuze’s word “Difference is not diverse.”(DR 222) Everything ordinary is not what the philosophy of difference concerns whether being proper to someone or being individual. What’s important is always something singular. Even if common to certain people and not proper to an individual, singularity is important. There are proper names that survived the time of extinction thanks to certain singularity. 'Platon,' 'Spinoza,' and 'Marx' are all proper names that are not extinct until now for the singularity of thinking. Spartacus, Marie Antoinette, Stalin, and My Bloody Valentine are probably names that will not be erased for a long time due to their unforgettable singularities. Therefore, proper nouns must also be redefined: ”proper noun is the name of impersonal singularity.“ When someone shows a singularity expressed as a proper noun, the name is called out again. In that sense, singularity has ‘eternality.’ That’s because it’ll be called out every time it’s repeated by someone. However, even if it is called out by the same name, it’ll be called out in a different way each time it’s called out. Just as every repetition is a repetition of a difference.
Just as a singular point emits force, singularity also emits force. It is an attractor that catches our eyes, ears, and hearts. There are those who boast of their properties and claim their rights, whereas there are those who get caught up in them leaving to leave themselves by the fascination with the singularity that they didn’t know. When getting caught up and attracted into the field of singularity, we again attract others by becoming an expression of singularity. Singularity, that is the name of the field in which the force of this fascination and caught up works.
translated by Jung Ki Lee