General put-down #2
These hypothetical situations remind me of a common, everyday-type scenario which has to do with what it means to understand something. When you count, for instance, your footsteps, you do not understand the numbers. You are probably only mentally manipulating the words, and perhaps the symbols, for the numbers. If you truly *understood* the numbers, you would be able to give the number as easily in, say, octal, as in decimal. So do you know the number of steps you have walked? Or only the name and the symbol for the number in your native language and native script? I have tried counting my steps in Japanese, a language foreign to me, and noticed that I was quite often merely reciting number WORDS in the language without thinking of the numbers represented by them. I mention that it was Japanese because if I had been counting in, say, German or Polish, the number words would have been nearly identical to English for the purposes of this experiment and thus would have proven nothing.
When you multiply largish numbers, you almost certainly do not understand what you are doing. The only reason 6*7=42 looks better than 6*7=38 is memorization. If you had not memorized addition and multiplication tables, they would both look equally OK. You do not really multiply the numbers, yet you say you do. The Chinese room experiment is redundant. Do not ask about the Chinese room when you have better to work with.