Final Summary on "All Human Thought Can Be Stored in a Binary Computer"

2006/8/8 12:01:09

The leftist began by asserting: "From the standpoint of mathematical theory, dichotomy—that is, using binary numbers—can express all human thought and laws of motion, because these thoughts can all be stored in a binary computer." Obviously, "because these thoughts can all be stored in a binary computer" is the logical starting point; otherwise the word "because" would be meaningless. And "these thoughts" in Chinese grammar refers back to "all human thought" in the preceding clause "from the standpoint of mathematical theory, dichotomy—that is, using binary numbers—can express all human thought and laws of motion." In other words, the entire statement rests on the premise that "all human thought can be stored in a binary computer."

The absurdity of this premise actually requires no mathematical proof whatsoever, because the prerequisite for storing something in a computer is that it can be linguisticized. But human thought obviously cannot be fully linguisticized. For example, "across the shimmering water, gazing in silent longing"—how do you linguisticize this kind of thought? Furthermore, Daoist thought denies language itself. The Dao transcends all language. Is the Dao a thought? If the Dao is not a thought, then Chinese culture amounts to zero, because the highest category of Chinese culture is precisely this Dao that transcends all language. How do you input this "Dao" into a computer? Do not dare suggest that typing the character "Dao" constitutes "the Dao"—even Laozi's ox would laugh at you! In other words, the thoughts that can be input into a computer have nothing to do with the essence of Chinese culture. What meaning do these inputtable thoughts have? Study the distinction between "Dao" and "Shu" (technique) in traditional Chinese culture and you will understand. To attempt to bury traditional Chinese culture's "Dao" using the Western technicized "Shu" of computers—what kind of intent is that? Can you hear that butterfly Zhuangzi transformed into laughing?

Of course, since this error is so obvious, the leftist then proposed modifying the statement to "'all human thought' refers to 'all human thought expressed through text, sound, or images.'" Obviously this qualification is insufficient—why should "all human thought" in the original statement be restricted to "all human thought expressed through text, sound, or images"? Of course, if the leftist can at least acknowledge that human thought cannot be fully linguisticized, that counts as progress. In that case, this ID will not pursue the matter further, and will modify the original proposition according to the leftist's intent to "all linguisticized human thought can be stored in a binary computer," where "linguisticized" refers to the above-mentioned "text, sound, or images." Then, this ID will proceed to demonstrate that even this weakened, modified proposition is a fallacy!

Originally, this ID overestimated the leftist's mathematical level, so I used mathematical methods to address this issue. Later, upon discovering that the leftist's mathematical level was not very high, I will use a constructive argument here to demonstrate the absurdity of this proposition. The reasoning is actually the same—both use the mathematical diagonal method. I should also note that the diagonal method does not necessarily involve finding a diagonal—that is just a colloquial name. This method has many generalizations and variations. If no one told you they all originate from the diagonal method, an ordinary person probably could not see the connection at all. Moreover, even in numerical arrangements using the diagonal method, one does not actually need to take the diagonal number—any number given by a function satisfying certain conditions will work. This is probably not something most people know, so I will not elaborate.

Because the leftist assumes "all linguisticized human thought can be stored in a binary computer," these thoughts constitute a set A, where the thoughts are denoted by a_n, with n representing natural numbers. Since the universe will eventually perish, and the time interval for humans to produce each thought cannot be infinitely short—otherwise it would violate the principles of quantum mechanics—we know that the number of elements in set A is finite, though the number can be very large. Then we construct the following thought: U(this thought's expression differs from thought a_n), where U represents the logical union, and a_n ranges over all elements of set A. Then this thought is obviously not in set A, and it cannot be simplified to any thought in A, because this thought concerns expression—any logical simplification trick is useless. Since set A is finite, this thought's expression is also finite, and this thought is clearly a human thought. Therefore, this contradiction can only stem from the leftist's assumption that "all linguisticized human thought can be stored in a binary computer"—meaning this assumption is absurd.

In fact, the limitations of instrumentalized language were already profoundly studied in Godel's incompleteness theorems. Computer language is merely one kind of axiomatized human language. The linguistic turn in 20th-century philosophy ultimately declared the failure of the general linguisticization of human thought. This is actually common knowledge—anyone who reads a bit of postmodern philosophy knows this. And the inevitable failure of computerizing human language is essentially the same, because the essence of computer language is an axiomatized logical structure. In mathematics, reflection on the axiomatic method has long since appeared, with Godel's incompleteness theorem being one direction of that effort. Human language cannot be fully axiomatized and therefore even less can it be fully computerized. Those interested in the philosophical implications of this can research it themselves. In particular, one can look at the reflections on scientism within Western philosophy, which form a very important part of postmodernist thought. The dangers of scientism must be guarded against, let alone a minor branch of scientism: computerism. The constructive argument above is merely using the enemy's own spear to pierce the enemy's own shield. But the reflection on scientism is the direction this discussion should extend toward.