If I took the scenario at face value—in other words, treating the question as one of pure mathematics—the mathematical answer is of course BusyBeaver(me).
In reality, if I received some sensory input sequence that somehow led me to believe some relevant approximation to the offer was being truthfully made with probability greater than epsilon, then my answer would depend on the actual input sequence, because that would determine the model I had of the probability distribution of resources available to ‘Omega’ in the event of the offer being at least semi-truthful, and of the relationship between the offered utils and my actual utility function (which is of course itself not formally known). Depending on that input sequence, I could see myself saying “eh, 1” or “umm… the Bekenstein bound of the Hubble radius; if you would be so gracious as to correct my assumption that this is your lab account quota, I would be grateful” or a great many other things.
If I took the scenario at face value—in other words, treating the question as one of pure mathematics—the mathematical answer is of course BusyBeaver(me).
I presume that (me) is supposed to be some large number here. This leads to a separate question- is Omega limited to Turing computable calculations? It isn’t normally relevant to what Omega can do, but I’ll be slightly annoyed if I say to Omega BusyBeaver(1000) and Omega gets embarrassed for having limits.
If I took the scenario at face value—in other words, treating the question as one of pure mathematics—the mathematical answer is of course BusyBeaver(me).
In reality, if I received some sensory input sequence that somehow led me to believe some relevant approximation to the offer was being truthfully made with probability greater than epsilon, then my answer would depend on the actual input sequence, because that would determine the model I had of the probability distribution of resources available to ‘Omega’ in the event of the offer being at least semi-truthful, and of the relationship between the offered utils and my actual utility function (which is of course itself not formally known). Depending on that input sequence, I could see myself saying “eh, 1” or “umm… the Bekenstein bound of the Hubble radius; if you would be so gracious as to correct my assumption that this is your lab account quota, I would be grateful” or a great many other things.
I presume that (me) is supposed to be some large number here. This leads to a separate question- is Omega limited to Turing computable calculations? It isn’t normally relevant to what Omega can do, but I’ll be slightly annoyed if I say to Omega BusyBeaver(1000) and Omega gets embarrassed for having limits.
I think he’s saying the largest number he could come up with.
Yes.