I know. Utility is a number. But ‘value is fragile’ teaches us that it can’t be a 1-dimensional number like the reals. It’s a many dimensional value, so I guess that to formally reason about complex value you need to use higher maths—such as hypercomplex numbers.
We care about lots of things, but that is all gathered up in the utility function, which adds up all the things we care about and puts it onto a single utility scale.
In context it looked like you meant something like numbers described by Knuth arrow notation or something similar.
Taking your clarification- note that just because something is complicated does not mean it is complex in the technical sense. There are many other generalizations of the reals such as the surreal numbers. In this particular context, ordinal lists of reals (which can be thought of vector spaces of the reals with a privileged basis) seem to work pretty well. Beware the superficial similarity of words.
“Many dimensional values” are called “vectors”. Hypercomplex numbers are a particular kind of vector, but there’s no reason at all to think they’d have something to do with complexity of value.
But ‘value is fragile’ teaches us that it can’t be a 1-dimensional number like the reals.
This is not in fact what “value is fragile” teaches us, and it is false. Without intending offense, I recommend you read about utility a bit more before presenting any arguments about it here, as it is in fact a 1-dimensional value.
What you might reasonably conclude, though, is that utility is a poor way to model human values, which, most of the time, it is. Still, that does not invalidate the results of properly-formed thought experiments.
Um, that term doesn’t mean very big numbers or anything similar. It has to do with extensions of the complex numbers.
I know. Utility is a number. But ‘value is fragile’ teaches us that it can’t be a 1-dimensional number like the reals. It’s a many dimensional value, so I guess that to formally reason about complex value you need to use higher maths—such as hypercomplex numbers.
That’s wrong. Utility is one dimensional.
We care about lots of things, but that is all gathered up in the utility function, which adds up all the things we care about and puts it onto a single utility scale.
In context it looked like you meant something like numbers described by Knuth arrow notation or something similar.
Taking your clarification- note that just because something is complicated does not mean it is complex in the technical sense. There are many other generalizations of the reals such as the surreal numbers. In this particular context, ordinal lists of reals (which can be thought of vector spaces of the reals with a privileged basis) seem to work pretty well. Beware the superficial similarity of words.
“Many dimensional values” are called “vectors”. Hypercomplex numbers are a particular kind of vector, but there’s no reason at all to think they’d have something to do with complexity of value.
EDIT: Also, what nyan_sandwich said.
This is not in fact what “value is fragile” teaches us, and it is false. Without intending offense, I recommend you read about utility a bit more before presenting any arguments about it here, as it is in fact a 1-dimensional value.
What you might reasonably conclude, though, is that utility is a poor way to model human values, which, most of the time, it is. Still, that does not invalidate the results of properly-formed thought experiments.