It is said that all good things correlate, and all bad things correlate. This is difficult to square with the idea that all weird things correlate, given some are good and some are bad. Between the options, I’m more convinced by the goodness and badness clusters than the weirdness cluster.
It is possible for it to be simultaneously true that all good, bad, and weird things form correlated clusters, even if some weird things are good and some bad. For example, being rich correlates with being old, even though being rich is good (correlates with being healthy, happy, smart, etc.) and being old is bad (correlates with cancer, death).
I consider it to be not only possible but plausible that both options are true.
Why do you think that both options can’t be true? Is your line of thinking something like this?
Both options can’t be true, by reductio ad absurdum.
If all good things correlate then a given good thing will correlate with a given weird good thing. If all weird things correlate then this weird good thing will correlate with a weird bad thing. If all bad things correlate then this weird bad thing will correlate with all bad things. If we assume that correlation is transitive, then we’ve just shown that any good thing must correlate with every bad thing, including the absence of good things, so it must anti-correlate with other good things, which contradicts our premise.
This argument doesn’t hold because correlation isn’t necessarily transitive. For an intuitive example: lefthandedness correlates with winning swordfights (because the typical opponent has more experience sparring against righthanded people). Being tall correlates with winning swordfights (because tall people tend to have longer limbs and more reach). Yet lefthandedness doesn’t correlate with being tall.
Very strong correlations are transitive, so this might be where the confusion is coming from. As the famous syllogism has it, being a man correlates with R=1 with being mortal, being Socrates correlates with R=1 with being a man, and therefore being Socrates correlates with R=1 with being mortal.
The weird cluster hypothesis is that weird things tend to correlate across a variety of domains—not that they strongly correlate. Likewise for “all good things correlate, and all bad things correlate.” I think that this makes them compatible.
It is said that all good things correlate, and all bad things correlate. This is difficult to square with the idea that all weird things correlate, given some are good and some are bad. Between the options, I’m more convinced by the goodness and badness clusters than the weirdness cluster.
It is possible for it to be simultaneously true that all good, bad, and weird things form correlated clusters, even if some weird things are good and some bad. For example, being rich correlates with being old, even though being rich is good (correlates with being healthy, happy, smart, etc.) and being old is bad (correlates with cancer, death).
I consider it to be not only possible but plausible that both options are true.
Why do you think that both options can’t be true? Is your line of thinking something like this?
This argument doesn’t hold because correlation isn’t necessarily transitive. For an intuitive example: lefthandedness correlates with winning swordfights (because the typical opponent has more experience sparring against righthanded people). Being tall correlates with winning swordfights (because tall people tend to have longer limbs and more reach). Yet lefthandedness doesn’t correlate with being tall.
Very strong correlations are transitive, so this might be where the confusion is coming from. As the famous syllogism has it, being a man correlates with R=1 with being mortal, being Socrates correlates with R=1 with being a man, and therefore being Socrates correlates with R=1 with being mortal.
The weird cluster hypothesis is that weird things tend to correlate across a variety of domains—not that they strongly correlate. Likewise for “all good things correlate, and all bad things correlate.” I think that this makes them compatible.
All things correlate (positively or negatively) if you check sufficiently many decimal places.