Hey gts, I think this topic is more appropriate for
[email protected] which you can sign up for at the same place as you signed up for this Singularity email list. The reason is that foundations of probability is a highly technical issue of relevance to AGI engineering; whereas this email list is intended more for general discussion of Singularity-related issues... Anyway, to respond to your point: Yep, I agree that exchangeability is different from, but closely related to Chaitin randomness, in the sense that for finite series it seems to be the case that * Chaitin randomness "almost always" implies exchangeability * Exchangeability "almost always" implies Chaitin randomness -- Ben On 1/19/07, gts <[EMAIL PROTECTED]> wrote:
Ben wrote on ExI: > However, exchangeability likely does NOT imply Chaitin randomness.... I think you're right about that, though I confess my understanding of Chaitin randomness is still sketchy. My understanding is that exchangeability in the de Finneti sense implies only the sort of randomness defined by the more conventional axiom of randomness, which I sent to you and a few others in private email this morning: "Axiom of Randomness: the limiting relative frequency of each attribute in a collective C is the same in any infinite subsequence of C which is determined by a place selection." (http://plato.stanford.edu/entries/probability-interpret/) This is only the ordinary frequentist view of randomness. De Finneti viewed exchangeability as a reduction of the objectivist notion of independence, i.e., on his view we can and should reduce the allegedly metaphysical notions of 'objective probability' and 'independence' to his equivalent notions of 'subjective probability' and 'exchangeability'. Nothing there as far as I know about the sort of maximum-entropy randomness that I think incompressible Chaitin-random sequences are thought to be. -gts ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=11983
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