Sender: EPR (Gu Bu | JOKER | Pingtian Dasheng | the homebody who wants to become the Pirate King), Board: KXTS标 Subject: My own conjecture about the second essay question
Posting site: Peking University Weiming BBS (2009-12-28 22:20:24, Monday), internal message
This year’s short-answer questions were relatively easy. The first essay question was a homework problem from previous years, and the third homework question was fairly open-ended. Only the second question was especially difficult; I was completely stumped by it at first. Still, it is quite interesting. Although I didn’t set the question, I also want to try to guess at a possible line of thought.
First, the question asks about “the internal reasons for the fusion of the mathematical tradition and the experimental tradition (Newtonian science may be taken as an example).” In reading the question, the first thing to note is that it asks for “internal reasons”; thus, it is not asking about concrete manifestations. How the fusion of the two traditions is reflected in modern science can be left aside and discussed less. Second, it is not asking for “external” reasons, such as Newton’s own genius, or the intellectual and cultural or social and economic background of Europe at the time. These are external causes; however indispensable they may be, they are not the focus of this question. What are called internal reasons should be sought in the respective logical developments of the two traditions themselves. As for “Newtonian science,” that is merely a hint; it does not mean one must write strictly around Newton, but rather that one should grasp the logical content of the two traditions.
By “logic” here, I mean that once a certain “tradition” has been established, it will contain a certain internal developmental tendency, revealing a seemingly necessary demand that drives that tradition forward. For example, the tradition of industrial technology implies a developmental logic of efficiency and intensification, and so on.
So let us look separately at the logic implied within each of the two traditions, in order to see the root of why they fused. Put simply, the so-called mathematical tradition implies the mathematization of nature—that is, a mechanical view of nature. Pushed further in this direction, the resulting view of nature will be: material objects are knowable, measurable, and calculable. Treating natural objects according to the natural attitude developed by the mathematical tradition leads to the experimental method. On the other hand, the so-called experimental tradition requires research methods that are operable, recordable, analyzable, and, most importantly, repeatable. This in turn leads to an analytic and quantitative mode of operation, and mathematical language is obviously best suited to the recording, analysis, and repetition of experiments, which then leads to a mathematical style.
In short, “mathematization” is the key hinge. The mathematical tradition begins from “intelligibility” and thus demands a mathematical picture of the world; the experimental tradition begins from “repeatability” and thus demands a mathematical language. When the two are fused in this way, it is simply a matter of course.
…I don’t know how many points I’d get according to my line of thought, but if everyone has different ideas, feel free to bring them up and discuss them…
Translated from the Chinese original with AI assistance. The original text is authoritative.
Leave a Reply