Intro to the math chapter

Here is the rough draft of the introduction to my chapter in my thesis about mathematics:

It is not the results but methods that can be transferred with profit from the sphere of the special sciences to … philosophy. – Bertrand Russell

Although Bertrand Russell’s idealist philosophy in the massive Principia Mathematica of a complete codification of the universally acceptable modes of human reasoning (that is, those modes without contradictions), at least as they applied to mathematics, came crashing down with Kurt Godel’s tiny “On Formally Undecidable Propositions in Principia Mathematica and Related Systems I” (1932), his methodology is still useful and pertinent today in literary criticism. The gap between the sciences (whether “hard sciences,” such as mathematics, physics, chemistry, biology, or the social sciences, such as political science, sociology, economics, linguistics) and the humanities (literature, philosophy, art theory) has seemed impassable for ages given the stereotype of scientists as the kings of the temple of objective truth and knowledge and humanists as jesters entertaining others in flights of fancy and make-believe. Every year at the time of the MLA conference, there is a mocking article in the New York Times about the fanciful ideas humanists have come up with. Perhaps some of the mocking is justified. Of course, such stereotypes are not true, but one discovers a kernel of truth given the Alan Sokol affair. Sokol played a famous hoax on the postmodern academic world when he submitted a pseudoscientific paper to Social Text entitled “Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity” with the goal of seeing whether a humanities journal would “publish an article liberally salted with nonsense if (a) it sounded good and (b) it flattered the editors’ ideological preconceptions.” The footnotes contain even more obvious jokes:
Just as liberal feminists are frequently content with a minimal agenda of legal and social equality for women and 'pro-choice', so liberal (and even some socialist) mathematicians are often content to work within the hegemonic Zermelo-Fraenkel framework (which, reflecting its nineteenth-century liberal origins, already incorporates the axiom of equality) supplemented only by the axiom of choice. (242-243).
The Zermelo-Fraenkel axioms with the addition of the axiom of choice, which states that given any set of mutually exclusive non-empty sets, there exists at least one set that contains exactly one element in common with each of the non-empty sets, are the standard axioms of axiomatic set theory, and hence, are unrelated to political questions of equality and choice. In the end, the Sokol affair demonstrated that some humanities scholars lack a basic understanding of science and mathematics. Of course, the converse is also true: some scientists and mathematicians lack a basic understanding of literary criticism and theory, so we must return to the divide between the physical and human sciences.

What is Called Thinking in America?

The smart way to keep people passive and obedient is to strictly limit the spectrum of acceptable opinion, but allow very lively debate within that spectrum - even encourage the more critical and dissident views. That gives people the sense that there's free thinking going on, while all the time the presuppositions of the system are being reinforced by the limits put on the range of the debate.



          -- Noam Chomsky (1998)

Brilliance

You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won’t believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!


—Richard Feynman, as quoted by D.L. Goodstein in his forward to vol. II of the Feynman Lectures in Physics

Introduction

Not an introduction of my self, but an introduction of my essay on Calvino:

Archaeologists have discovered clues about the origin of writing in an 11,000-year-old Ishango (central African) bone with lines scored into the surface. The short parallel lines look like human fingers, the corresponding “words” for counting. Hence, one can equivalently read the strokes pictorially as standing for fingers held up or scriptorially as standing for a certain numeral. The signifier and the signified in both cases remain the same and remain linked. However, the signifier changes when humans began recording sixty sheep by means of one “sheep” sign followed by sixty strokes to recording the same information by means of one “sheep” sign followed by a second sign indicating “sixty.” In other words, a “token-iterative” sign-system, which is in effect equivalent to a language which is restricted to messages of the form “sheep, sheep, sheep, sheep…” progresses to an “emblem-slotting” system, which is equivalent to a language which permit messages of the form “sheep, sixty.” The former system conflates the signifier, viewed as a visual image, and the signified, viewed as a mental image, whereas the latter system condenses the signifier and the signified. Token-iterative lists are, in principle, lists as long as the number of individual items recorded. With a slot list, on the other hand, one gets no information simply by counting the number of marks it contains. The slot-list system conveys information so long as a reader knows the symbol for sixty and the “grammar” of the system. In other words, the reader must understand the significance of each slot because, unlike the token-iterative system, the meaning of each slot is not necessarily the same.
Therefore, to read a slot list, one must be able to read symbols as such. Instead of reading multiple marks, each representing one sheep, we must be able to read marks as symbols (numbers) without a material basis. For numbers are things no one has ever seen, heard, or touched. Yet, somehow, they exist, and their existence can be confirmed in everyday terms by all kinds of everyday procedures that allow mere mortals to agree beyond any shadow of doubt as to “how many” eggs there are in a basket or “how many” loaves of bread are on the table. This magical quality reveals the slot-system’s power because writing is possible when one can manipulate signs to “slot,” or identify anything whatsoever.