All of Brownbat's Comments + Replies

Happy to try to clarify, and this is helping me rethink my own thoughts, so appreciate the prompts. I'm playing with new trains of thought here and so have pretty low confidence in where I ended up, so greatly appreciate any further clarifications or responses you have.

There's a standard trick for scoring an uncertain prediction: It outputs its probability estimate p

Yup, understand that is how to effectively score uncertainty. I was very wrong to phrase this as "we still have to have some framework to map uncertainty to a state" because you don't strictly ... (read more)

This is really interesting. 

To understand this more thoroughly I'm simplifying the high and low quality video feeds to lists of states that correspond to reality. (This simplification might be unfair so I'm not sure this is a true break of your original proposal, but I think it helped me think about general breaking strategies.)

Ok, video feeds compressed to arrays:

We consider scenarios in fixed order. If the diamond is present, we record a 1, and if not, a 0. The high quality feed gives us a different array than the low quality mode (otherwise the low... (read more)

1redbird
Thanks for the comment! There's a standard trick for scoring an uncertain prediction: It outputs its probability estimate p that the diamond is in the room, and we score it with loss −log(p) if the diamond is really there, −log(1−p) otherwise. Truthfully reporting p minimizes its loss. You're saying that giving it less information (by replacing its camera feed with a lower quality feed) is equivalent to sometimes lying to it?  I don't see the equivalence! That's an interesting thought, can you elaborate?

"A number of commenters, yesterday, claimed that the preference pattern wasn't irrational because of "the utility of certainty", or something like that. One commenter even wrote U(Certainty) into an expected utility equation."

It was not my intent to claim "the preference pattern wasn't irrational," merely that your algebraic modeling failed to capture what many could initially claim was a salient detail of the original problem. I hope a reread of my original comment will find it pleading, apologetic, limited to the algebraic c... (read more)

I think I missed something on the algebraic inconsistency part...

If there is some rational independent utility to certainty, the algebraic claims should be more like this:

  • U($24,000) + U(Certainty) > 33/34 U($27,000) + 1/34 U($0)
  • 0.34 U($24,000) + 0.66 U($0) < 0.33 U($27,000) + 0.67 U($0)

This seems consistent so long as U(Certainty) > 1/34 U($27,000).

I'm not committed to the notion there is a rational independent value to certainty, I'm just not seeing how it can be dismissed with quick algebra. Maybe that wasn't your goal. Forgive me if this is my oversight.

The Mantis Shrimp (http://en.wikipedia.org/wiki/Mantis_shrimp) forms a crude wheel to maneuver on land.

But I still can't think of any examples of wheels in nature that use axles and are large enough to be more than a free floating rotating object. Maybe this seems an arbitrary threshold, but I think usually when we marvel at the wheel, we're marvelling at axles, and their ability to support weight and radically reduce friction when moving big heavy things, all while holding the object basically level. While the cellular turbines that power us are pretty fa... (read more)