[4] I looked up a commentary on Cardano’s probability research to see if it’s actually plausible that he thought that calculating probabilities in games of dice was intractable. Apparently he drew a distinction between “chance” and “luck,” claimed they were both at play in dice games, and suggested that one cannot have “rational knowledge” of luck. This seems like a really interesting mistake, which might be intertwined his supernatural/non-mechanistic view of the world.
It’s not clear that he’s wrong, or what he’s wrong about. What did he call “luck”, and what did he call “chance”?
To be charitable to Cardano:
1. If you buy a lottery ticket you probably won’t win.
2. But someone will win.
3. In other words, chance are your odds before. If “Lucky” is being the unlikely case, then to say ‘one cannot have rational knowledge of luck’ is to say ‘you can’t (rationally) know you’re going to win the lottery, the odds are against you.’ It is precisely that understanding which conveys why buying the lottery ticket is a fool’s errand: because you don’t know you will be lucky. You don’t know you ‘have a chance’.
I also think that examining past beliefs about progress can help to inform present-day debates. If historical people have tended to severely underestimate opportunities for future progress, then we should be wary of making the same mistake. We should, for example, feel some reflexive skepticism toward the predictions of growth pessimists like Robert Gordon, who worry that most really important inventions have already been developed. Like Cardano reacting to the inventions of the 1400s, they look out at electricity and plumbing and the internet and ask: “What lack we yet unless it be the taking of Heaven by storm?”
You have outlined that in context that phrase was pessimistic. But, today it sounds very different. It sounds like someone saying a) “We have everything we need to start colonizing the stars.” b) that’s our next goal.
It’s not clear that he’s wrong, or what he’s wrong about. What did he call “luck”, and what did he call “chance”?
To be charitable to Cardano:
1. If you buy a lottery ticket you probably won’t win.
2. But someone will win.
3. In other words, chance are your odds before. If “Lucky” is being the unlikely case, then to say ‘one cannot have rational knowledge of luck’ is to say ‘you can’t (rationally) know you’re going to win the lottery, the odds are against you.’ It is precisely that understanding which conveys why buying the lottery ticket is a fool’s errand: because you don’t know you will be lucky. You don’t know you ‘have a chance’.
You have outlined that in context that phrase was pessimistic. But, today it sounds very different. It sounds like someone saying a) “We have everything we need to start colonizing the stars.” b) that’s our next goal.