I meant that they were functionally booleans, as a single condition is fulfilled “is rich”, “has anvil”, “AGI achieved”. In the anvil example, any number past 1 corresponds to true. In programming, casting positive integers to booleans results in “true” for all positive numbers, and “false” in the case of zero, just like in the anvil example. The intuition carries over too well for me to ignore.
The first example which came to mind for me when reading the post was confidence, which is often treated as a boolean “Does he have confidence? yes/no”. So you don’t need any countable objects, only a condition/threshold which is either reached or not, with anything past “yes” still being “yes”.
A function where everything past a threshold maps to true, and anything before it maps to false, is similar to the anvil example, and to a function like “is positive” (since a more positive number is still positive). But for the threshold to be exactly 1 unit, you need to choose a unit which is large enough. 1$ is not rich, and having one water droplet on you is not “wet”, but with the appropriate unit (exactly the size of the threshold/condition) these should be functionally similar.
I’m hoping there is simple and intuitive mathematics for generalizing this class of problems. And now that I think about it, most of these things (the ones which can be used for making more of themselves) are catalysts (something used but not consumed in the process of making something). Using money to make more money, anvils to make more anvils, breeding more of a species before it goes extinct.
I meant that they were functionally booleans, as a single condition is fulfilled “is rich”, “has anvil”, “AGI achieved”. In the anvil example, any number past 1 corresponds to true. In programming, casting positive integers to booleans results in “true” for all positive numbers, and “false” in the case of zero, just like in the anvil example. The intuition carries over too well for me to ignore.
The first example which came to mind for me when reading the post was confidence, which is often treated as a boolean “Does he have confidence? yes/no”. So you don’t need any countable objects, only a condition/threshold which is either reached or not, with anything past “yes” still being “yes”.
A function where everything past a threshold maps to true, and anything before it maps to false, is similar to the anvil example, and to a function like “is positive” (since a more positive number is still positive). But for the threshold to be exactly 1 unit, you need to choose a unit which is large enough. 1$ is not rich, and having one water droplet on you is not “wet”, but with the appropriate unit (exactly the size of the threshold/condition) these should be functionally similar.
I’m hoping there is simple and intuitive mathematics for generalizing this class of problems. And now that I think about it, most of these things (the ones which can be used for making more of themselves) are catalysts (something used but not consumed in the process of making something). Using money to make more money, anvils to make more anvils, breeding more of a species before it goes extinct.