The nature of 0 & 1 as limit cases seem to be fascinating for the theorists. However, in terms of ‘Overcoming Bias’, shouldn’t we be looking at more mundane conceptions of probability ? EY’s posts have drawn attention to the idea that the amount of information needed to add additional cetainty on a proposition increases exponentially while the probability increases linearly. This says that in utilitarian terms, not many situations will warrant chasing the additional information above 99.9% certainty (outside technical implementations in nuclear physics, rocket science or whatever). 99.9% as a number is taken out of a hat. In human terms, when we say ‘I’m 99.9% sure that 2+2 always =4’, where not talking about 1000 equivalent statements. We’re talking about one statement, with a spatial representation of what ’100% sure’ means with respect to that statement, and 0.1% of that spatial representation allowed for ‘niggling doubts’, of the sort : what have I forgotten ? What don’t I know ? What is inconceivable for me ? The interesting question for ‘overcoming bias’ is : how do we make that tradeoff between seeking additional information on the one hand and accepting a limited degree of certainty on the other ? As an example (cf. the Evil Lords of the Matrix), considering whether our minds are being controlled by magic mushrooms from Alpha Pictoris may someday increase the ‘niggling doubt’ range from 0.1% to 5%, but the evidence would have to be shoved in our faces pretty hard first.
tcpkac
Karma: 17
Thanks for the beauty, it feels good. Some thinking out loud. I can’t help but feel that the key is in the successive layers of maps and territories : maths is (or contains) the map of which physics is the territory, physics is the map of which ‘the real world’ is the territory, ‘the real world’ is the map our brains create from the sensory input concerning the territory which is the ‘play of energies’ out there, while that in itself is another map. Antony Garrett Lisi’s proposal, as an example, would be the most elegant meta-map yet. What these maps have in commmon is : being created by the human brain, a wet lump of nervous tissue comprising ad-hoc purpose specific modules. It has specific ways of making maps, so small wonder all these layers of maps are coherent. Now if the ‘mathematics’ layer of maps has unforeseen and self-consistent properties, it could be just a manifestation of the nature of our map-making modules : they are rules driven. So, is the Universe a geometric figure corresponding to a Lie E8 group, or does that just happen to be the way the human brain is built to interpret things ?