I appreciate that these are being used as simple analogies, but since they are phrased as real-world scenarios I feel that it weakens my visualisation of the situation in hand by not explicitly commenting on the time-scales over which the teacher/pupil wishes to maximise their utility.
Each example refers to the impact of the initial setup, or decision made when faced with an excuse, to the overall utility of the outcome but fails to convey to me clearly the success or failure criteria.
I would find it valuable if we were able to split the scenarios into a timeline decision tree to show how the impact of initial setup and decisions made would affect the utility over time, which would allow me to visualise the most beneficial path once I had decided on the timescale over which I wish to consider. (Taking this even further I would most likely attribute different weightings to my utility function depending on time-horizons and then attempt to maximise over the whole.)
What variation would there be in setup and decision if my consideration was for a one-shot decision versus a long-term career?
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There seem to be far too many people hung up on the mathematics which ignores the purpose of the post as I understand it.
The post is not about truth but about conviction. Eliezer is not saying that there could be a scenario in which the rules of mathematics didn't work, but that there could be a scenario under which he was convinced of it.
Deconstructing all elements of neurology, physics and socialogy that make up the pathway from complete ignorance to solid conviction is not something I could even begin to attempt - but if one were able to list such steps as a series bullet points I could conceive that the manipulation of certain steps could lead to a different outcome, which appears to me to be the ultimate point of the post (although not hugely ground-breaking, but an interesting thought experiment).
It is not a claim that the strongly held conviction represents fact or that the conviction would not be shaken by a future event or presentation of evidence. As a fundamental believer in scientific thought and rationality there is much that I hold as firm conviction that I would not hesitate to re-think under valid contradictory evidence.