The article ends by noting that even with colored ink, the number of distinguishable symbols is finite. Indeed, if there is a limit to the number of values held by each of the variables, that would limit what you could write.
If we're looking for theoretical ways around that constraint, you could allow inks that change over time, so you would have to observe each character for a certain amount of time in order to see what it was representing as its ink changed (or didn't).
The "New Riddle of Induction," proposed by Nelson Goodman in 1955, challenges our understanding of inductive reasoning and the formation of scientific hypotheses. Goodman introduced the concept through his famous "grue" example.
Imagine a property "grue," defined as "green up to time t, and blue thereafter." All emeralds examined before time t are both green and grue. The riddle asks: Why is it rational to predict that future emeralds will be green rather than grue?
This paradox highlights the problem of choosing between competing hypotheses that equally fit past observations. It questions our basis for preferring "natural" predicates (like green) over "artificial" ones (like grue) in inductive reasoning.
Goodman's riddle challenges the idea that induction is based solely on observed regularities. It suggests that our choice of predicates in forming hypotheses is influenced by factors beyond mere observation, such as simplicity, familiarity, or projectibility.
The New Riddle of Induction has significant implications for philosophy of science, epistemology, and artificial intelligence. It raises questions about the foundations of scientific prediction, the nature of natural kinds, and the role of language in shaping our understanding of the world.
There are crystal structures that simply won't form anymore, even though they did a few decades ago. Real life Ice-9? Could make an incredible sci-fi book.
If the observation time is finite, and the time resolution of the observation is limited, then you'd still only have a finite number of distinguishable symbols, wouldn't you?
That's true if the time resolution is limited. Theoretically there could be no limit. It would not make for a very practical alphabet, but it would still be an unlimited alphabet.
Just as Rorschach's mask always changes in Watchmen. We would have books with changing alphabet. In the library of babel, Harry Potter would be located in one section at a given time T1 but maybe at a different section at time T2.
If we're looking for theoretical ways around that constraint, you could allow inks that change over time, so you would have to observe each character for a certain amount of time in order to see what it was representing as its ink changed (or didn't).