Let Me Help Miss Chan Straighten Out the Thinking for Mr. Mathematics!

Since Miss Chan's post stated this was her final summary on the topic, truth must nonetheless be made clear. So I'll take the trouble to help Miss Chan straighten out Mr. Mathematics' thinking! Mathematics' reply to Miss Chan, "Another attempt to straighten out Miss Chan's thinking," completely dodged Miss Chan's proof itself, and only used "Since they're finitely many, of course finite computer capacity can store them all -- what's there to argue about?" to make his case. This is not a proof of any kind, merely an assertion -- a taken-for-granted assertion. It's like assuming that if two different lines intersect they must have only one intersection point, but this seemingly obvious conclusion is not necessarily true in mathematics. One can find certain types of spaces where this obvious conclusion fails. So Mathematics' rebuttal is invalid!

As for Mathematics saying "But isn't your post stored right now in the Qiangguo Forum server?" -- what kind of argument is this? Does a post being stored on a server prove that all human thoughts can be stored on a server? A post is merely a tiny fraction of human thought, not all of it. Using the part to cover the whole -- this logic obviously has problems.

Mathematics also said: "Once it's finite, there's no difficulty whatsoever." This is clearly not something someone with professional mathematical training could say. There are many undecidable problems that involve finite things. Finite things can still present difficulties, even undecidable ones.

Mathematics said: "But Miss Chan insists on applying contradictions derived from infinity onto the finite, when the finite case is simple -- since it's finite, just calculate the capacity and store them in a computer." But Miss Chan's proof involves no infinity at all. What Miss Chan constructed is entirely a finite situation. Mathematics should look at this more carefully.

It seems Mathematics himself is riddled with errors, yet insists on declaring: "Yesterday I made a mistake, I didn't remember my other post. But wrong is wrong -- I won't apologize either, because my posts are full of errors anyway. And I'm a scoundrel -- scoundrels naturally never apologize." But Miss Chan never asked Mathematics to apologize. Mathematics is a bit presumptuous -- Miss Chan asked Mathematics to acknowledge his error. Acknowledging an error is not necessarily the same as apologizing.

Finally, let me quote Miss Chan's relevant proof below, and see whether it involves any infinite situation:

Because the leftist hypothesis states that "all linguistically expressible human thoughts can be stored in a binary computer," these thoughts constitute a set A, where thoughts are denoted by an, with n representing natural numbers. Since the universe will perish, and the time interval for humans to produce a thought cannot be infinitely short (otherwise it would violate the principles of quantum mechanics), we can know that the elements in set A are finite, though the quantity can be very large. Then we construct a thought as follows: U (the expression of this thought differs from thought an), where U represents logical conjunction, and an represents all elements of set A. This thought is obviously not in set A, and it cannot be simplified into any thought in A, because this thought speaks of expression, so any tricks of logical simplification are useless. Since set A is finite, the expression of this thought is also finite, and this thought is obviously a human thought. The contradiction can only come from the leftist hypothesis that "all linguistically expressible human thoughts can be stored in a binary computer" -- meaning this hypothesis is absurd.

There is also a passage unrelated to the proof but particularly brilliant, which I quote as well:

The absurdity of this premise actually requires no mathematical method to demonstrate, because the prerequisite for being storable in a computer is that it can be linguistically expressed. But human thought obviously cannot be entirely linguistically expressed. For example, "With a glimmer of water between us, gazing in silence, unable to speak" -- how can such a thought be linguistically expressed? And then there's Daoist thought, which negates language. The Dao is apart from all language. May I ask, is the Dao not 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 would you input this "Dao" into a computer? Please don't say that typing the character "Dao" is the Dao -- even Laozi's ox would laugh at you for that! In other words, the thoughts that can be input into a computer have nothing to do with the essence of Chinese culture. What significance do these inputtable thoughts have? Study the distinction between "Dao" and "Shu" (technique) in traditional Chinese culture and you'll understand. Attempting to use the Western technicized computer's "Shu" to bury traditional Chinese culture's "Dao" -- what kind of intentions are these? Can you hear Zhuangzi's butterfly laughing uproariously?