Sniffnoy comments on The benefits of madness: A positive account of arationality - Less Wrong

101 Post author: Skatche 22 April 2011 07:43PM

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Comment author: Sniffnoy 24 April 2011 05:47:39AM 7 points [-]

One was a metric on the space of events over a given probability space; it popped into my head as I was waking from a dream during the peak of my mania. If you're interested: for events A and B, we can define d(A,B)=1-P(A|B)P(B|A).

This doesn't appear to actually be true. :-/ Say we take our probability space to be [0,1], and we take A=[0,2/3], C=[1/3,1], and B=[0,1]. Then d(A,B)=d(B,C)=1/3, so d(A,B)+d(B,C)=2/3, but d(A,C)=3/4>2/3. Any ideas on how to fix?

(Also strictly speaking it would be a pseudometric on the set of positive probability events, with two events being equivalent if they differ by a set of probability 0, but that's nitpicking.)

Comment author: Skatche 24 April 2011 03:28:33PM 2 points [-]

Eeeesh. You're right. In my defense, I think I checked the properties while I was still half-asleep, and I must have fudged the triangle inequality. I fiddled with it a bit, but couldn't find any obvious way to make it work. Thanks for your correction.

Comment author: abramdemski 25 April 2011 02:58:17AM 11 points [-]

Happens to the best of us. However, it is worth emphasising that you have provided little evidence with your writing that the actual ideas coming from peak experiences are worth much. You have provided a great deal of indication that the motivational aspect of these ideas is useful, though.

Comment author: Skatche 26 April 2011 11:19:56PM 3 points [-]

However, it is worth emphasising that you have provided little evidence with your writing that the actual ideas coming from peak experiences are worth much. You have provided a great deal of indication that the motivational aspect of these ideas is useful, though.

You may be right. I will have to think about this. A lot of the imperative ideas ("Go do this!") that I've had while manic have had decidedly positive results - notably my bike trip to Georgia and the decision to devote a lot more of my time and mental energy to mathematics, founding the communal house I currently live in, but I'm going to have to try and remember some concrete examples of declarative ideas that have come to me in that state before I continue to make that claim.

Comment author: Sniffnoy 27 April 2011 12:29:13AM 4 points [-]

BTW, I must say I would love to hear about the founding of this communal house, even if this isn't necessarily the place for it.

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