On “Quantification”

6,778 characters2007.12.11

What is “quantification”? This word is easy to understand, but it is not at all easy to explain just how the modern worldview has been “quantified.” “Quantification” was certainly not invented by modern science; “quality” and “quantity” are indispensable when human beings observe things, or one could say they are a priori—if we do not regard things in terms of qualitative or quantitative relations, then the world can only be a mass of chaos. Human beings always “partition” this world through quality and quantity, so that the world can be understood and described.

Natural history, one might say, takes an approach that emphasizes partitioning by “quality.” At first, people may only have known “a kind of” “tree,” except that some trees were tall and some short, some had broader leaves and some larger fruit, and so on. Through natural history, however, people came to understand these originally quantitative relations as qualitative relations, and thus could distinguish this is a pine, that is a cypress.

The approach of modern science, by contrast, goes in the opposite direction: it seeks to reduce what were originally qualitative relations to quantitative relations, to recognize the force between the Earth and the Moon and the force by which apples fall to the ground as one and the same, to reduce the differences among the properties of various substances to differences in quantity at the level of molecular structure, to regard all phenomena as the motion of particles, and finally to strive to use a set of formulas to interpret the essence of all change.

The key requirement of “quantification” is to make things measurable and comparable, and to make the standards of measurement and comparison objective and abstract. Even without quantification, people can compare the length, size, or weight of things; one need only put two things together and compare them. But such comparison does not appeal to a standard independent of the act of comparison itself. And the establishment of such a standard requires long-term human practice—this process was also discussed in the course on political economy: at first, people only engaged in barter, for example, I am willing to exchange one sheep for your five axes. But the problem is that the person who owns five axes may not necessarily need a sheep; he may prefer to trade for ten eggs, while the person with ten eggs may in turn want something else. Rather than searching back and forth for a suitable counterpart in this way, it is better to establish a universal medium—for example, I first exchange a sheep for twenty shells, and then use the shells to exchange for an axe; that is much more convenient. In the end, the standard of measurement independent of any specific exchange activity—“money”—comes into being. And the formation of standards of measurement such as length, volume, and weight is similar to the formation of money: through long-term practical activity, people select something most convenient and most precise as the standard of measurement—for instance, setting the freezing point and boiling point of water as standards of temperature, and taking the interval between two noons as the standard of time.

Fundamentally speaking, any measurement is nothing more than comparison. To say that something weighs 10 kilograms means that it is equivalent to ten times the mass of 1 cubic decimeter of pure water at 4°C. But the consequence of “quantification” is that it can make you forget “comparison,” as if the various quantitative attributes of any thing were inherent in the thing itself and existed objectively without needing comparison with any other object.

Of course, if we trust certain aspects of modern science, then perhaps we should acknowledge that some quantitative properties are indeed inherent to things; there is no need to discuss these issues here. The more crucial issue is not “quantification” itself, but the loss of limits on quantification. Not only the length and weight of things, but also human intelligence, emotion, and talent; the work of government; the soundness of society; and so on—“quantification” is abused in the case of any kind of measurement.

Since what needs to be measured and compared does indeed require quantification to a proper degree, there is nothing objectionable about that. For example, when evaluating academic performance, one can use “A, B, C, D, E,” or “excellent, good, average, poor,” or “pass, fail,” and so on; in any case, giving a symbol as an evaluation is not a bad thing. This is of course also a kind of quantification, or one could say the initial form of quantification, because it abstracts and objectifies the standards of evaluation. But although it may seem equivalent, once “ABCDE” is changed to a five-point scale, the meaning is already somewhat different; if it is changed to a hundred-point scale, this becomes even more obvious. Why do I say this? Because numbers have “magic.”

Because of the intervention of numbers, the question of measurement and comparison is transformed into the question of measurement and calculation. “ABC” or “excellent, good, average” can on the one hand be regarded as quantitative relations, but on the other hand they can also be regarded as qualitative relations; this preserves a certain degree of uncertainty. Yet once numbers are adopted, any hazy veil is lifted away, and what remains are those clear and unmistakable quantitative relations. If I received a “good” on my midterm, had “excellent” performance in class, and only “average” on my final, then what should my overall grade be? — It is hard to say. But if I got 80 on the midterm, 90 in class, and 70 on the final, and then calculated them according to weights of 20%, 30%, and 50% respectively for class performance, midterm, and final, then it is easy to conclude that my overall grade should be 77; of course, scores from different subjects can also be put together and averaged. In other words, the intervention of mathematics not only homogenizes the evaluation of a single grade for a single course at a single time, but further homogenizes all grades and all subjects. That is to say, the expansion of “quantification” not only makes things that were originally compared in an indeterminate way clear and definite, but also makes things that were originally incomparable with one another comparable.

My reflections on “quantification” are still very superficial; these are just random thoughts, written down offhand.

2007-12-11