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Netizen "Math," If You Have Any Academic Integrity, Step Up and Admit Your Error!

[Chán Zhōng Shuō Chán] posted on 2006-08-07 10:40:24

Chán Zhōng Shuō Chán

This is a perfectly normal academic question. Netizen "Math" proposed that all human thought can be represented in binary digits. This ID used a very simple method to prove it wrong. Netizen "Math," if you have any academic integrity, step up and admit your error!

Peking University and Tsinghua have been competing for a long time, but when it comes to mathematics, Tsinghua has no contest with Peking University. I hear Netizen "Math" is from Tsinghua, though not a mathematics major, so having some academic errors is not surprising. But anyone from Tsinghua, no matter how brilliant they think they are, should still admit mistakes when they make them. At the very least, anyone from Peking University would never try to cover up an error!

As for the clamoring of others, those people don't even have the most basic mathematical knowledge. This ID has no time to wrangle with them. Some things are too kindergarten-level, and this ID has no obligation to teach them. Even if they remain forever unenlightened, that's their problem — this ID will just enjoy the show. But if Netizen "Math" still has a shred of academic conscience, please step up and admit the error, or academically demonstrate that this ID is wrong. If this ID is truly wrong, this ID will certainly admit the mistake. But on this particular question, that's impossible. Because if this ID were wrong, then the method used to prove this ID wrong would necessarily also prove that set theory and some of the most foundational mathematics contain errors. In that case, Netizen "Math" would become a great master — but the chance of that happening is probably zero, even if you wait until the end of the universe!

The proof is appended below once more:

As for that Math ID who routinely makes logical blunders, he recently claimed as if he'd discovered a new continent: "From the standpoint of mathematical theory, dichotomy, that is, the use of binary numbers, can express all human thought and laws of motion, because these thoughts can all be stored in binary computers." I have no idea what kind of "mathematical theory" this so-called math ID is referring to. Does merely calling yourself a Math ID entitle you to spout mathematical nonsense? Very well then, let us very mathematically examine this so-called discovery or claim by the Math ID:

Let us assume his claim holds — that all human thought and laws of motion can be represented in binary numbers. Then let us line up all these binary numbers representing all human thought and laws of motion. Now consider this binary number: its Nth digit differs from the Nth digit of the Nth binary number in the lineup above (for example, if the latter is 1, the former is 0, and vice versa). Clearly, this binary number is not among those representing all human thought and laws of motion, yet this binary number represents the following thought: "its Nth digit differs from the Nth digit of the Nth binary number in the lineup." In other words, this thought is not contained in the totality of human thought and laws of motion — which is a contradiction. By the simplest proof by contradiction, the assumption "all human thought and laws of motion can be represented in binary numbers" does not hold. All human thought and laws of motion cannot all be represented in binary numbers.

The proof method above is actually not this ID's invention. It is a classic mathematical proof technique with a common name: the "diagonal method." It first appeared in Cantor's series of proofs regarding set theory in the 19th century. Not to mention the 20th century's mathematical development that surpassed the sum of all previous centuries — anyone with a basic understanding of this 19th-century mathematical knowledge could not possibly assert such an absurd proposition.