That is true. Let me try one last attempt: you cited a scenario of "a box with 10 holes in the bottom". Consider the scenario of coin flipping. When you flip a coin, you generate 1 bit of random information. So, if you flip a coin 8 times, you should get 8 bits of random information. But suppose that the coin is not a fair coin, e.g., it is weighted on one side. Would you really still get 8 bits of random information after 8 flips?Originally Posted by MK27
The idea here is that you don't, e.g., you get 7 bits of random information. But now, if you take the 8 bits generated from the coin flips and use it in a one time pad to encrypt 8 bits of information, then you would have actually used a key of effectively 7 bits, not 8 bits, to encrypt 8 bits of information.
In theory, this means that the 8 bits of ciphertext do not entirely depend on the 8 bits of key, as the actual information in the key is 7 bits. There is 1 bit of ciphertext that actually depends on both the plaintext and the key. It probably is not enough to deduce the entire plaintext, and in practice may not even be enough to deduce a single bit, but it still does not amount to perfect secrecy.
Relating this back to "plain language text arbitrarily converted (with mod 2) to a bitstream", it means that just because the process is random does not mean that you necessarily get at least as much random information as you need. So, "the very essence of entropy" is a grand phrase, but not necessarily an accurate one.