|
Author
|
Topic: paradoxical impact
|
Wade
Member
Member # 1713
|
posted 17. September 2005 18:01
There's probably a mathematical term for functions where A(x) > B(x) for all x, and yet the integral
of B (area under the curve) is larger than the integral of A. Even if there isn't, it seems this forum needs to define such a type of "integral" operator in the real world, where the contributing components to the integral decay with time and space differentially.
In particular, we can observe that locally, "bad" people can beat / trump "good" people - and there is a local edge and advantage to cheating. In the short run crime pays. However, bad behavior also sets in motion counter-actions, whereas good behavior sets in motion supportive feedback, so, viewed from way back in a larger time scale (perhaps 100 years), "good" triumphs over "evil".
I'm reminded of battles in the educational world over certain strict educational practices that were viewed as harmful in the short run, and yet, were the things that students came back 20 years later and thanked you for as having ultimately changed their lives.
The fact that, in the real world, (a) no event can be set in motion without external consequences that may not be evident, and (b) anything decays with time and develops "noise" unless refreshed, means that, in theoretical terms, the arguments based on "Turing machines" - with infinite tapes that are infinitely reliable, are interesting, but inapplicable. Anything that's actually computable has to overcome counter-moves, decay, and degradation.
IP: Logged
|
|
Christopher D. Beling
Member
Member # 723
|
posted 03. October 2005 23:42
Hi Wade; I know what you are aiming at in this post and I agree with the general idea - so I wish to give some comments and ideas:
1) First a critique. It is a mathematical certainty that if A(x)>B(x) for all x then
2) I think for your general idea you need to develop the same kind of maths that is used in population genetics. Here a new gene enters the system (the analogy would be a new idea(hypothesis) comes into society). This gene may be deleterious with respect to the local environment giving rise to negative selective advantage s<0. Alternatively the gene may advantageous with respect to the local environment given rise to a positive selective advantage s>0. By analogy we understand that the idea(hypothesis either grows or contracts in society - according to the prevailing metaphysical beliefs, the amount of scientific evidence - and probably many other factors).
With this analogy - and following your idea - the idea(hypothesis) may in the short term have poor survivability but in the long term may get approved - and finally get "fixed" in the society. Conversely an idea(hypothesis) that falls initially on good (fertile) ground [perhaps because there is an error in metaphysical perception] may flourish for a while, but as time progresses society becomes more mature and the survivability factor "s" turns from positive to negative. The initially s>0 idea(hypothesis) is thus finally destined to the category "extinct".
The way to formalize this is along the lines used by Fred Hoyle in Mathematics of Evolution using a "propagator function" G(s;x,t(i+1);x',t(i)) that maps the initial probability vector phi(x',t(i)) representing the probability that fraction x' of the population will have accepted "the idea" at time t(i) onto the elements of the new probability vector phi(x,t(i+1)) that fraction x will have "the idea" at time t(i+1). This mapping is produced by the integral:
Note that in this equation function G(s;x,t(i+1);x',t(i)) is a function of s, and s - the selective advantage for "the idea" is a function of the time - through the environment which is changing (metaphysical commitments + scientific knowledge). Indeed of great importance is that the presence of "the idea" in society can in fact influence the environment - a kind of feedback as you say. This means that an idea originally with s<0 can gain popularity and eventually become s>0 - with subsequent fixing.
The probabilities of final acceptance (fixing) of "the idea" or alternatively the final rejection (extinction) of "the idea" are given by:
Richard Dawkins is famous for his "idea" of the "meme" (in analogy to the gene of molecular biology) which in the above description would represent "the idea". Indeed the above analogy follows Dawkins - that some "memes" get tried and ultimately fixed in human society and some do not. Dawkin's "meme" has come under heavy attack from a number of directions in the recent book Dawkins' God by Alistair McGrath. Of these critiques the one which I feel relevant here is that the "meme" as described by Dawkins does not relate to a separate human will and intelligence (design) - it only relates to natural law (as with the gene). My personal take is that we humans are creatures that take truth seeking seriously (by noting logic and evidence and their interplay) and although this is hard to discover this truth seeking faculty operating within the G propagator function will lead us to eventually fix correct ideas (memes) and delete wrong ones. But am I being too naive?
- Chris
[ 04. October 2005, 08:47: Message edited by: Christopher D. Beling ]
IP: Logged
|
|
|
Printer-friendly view of this topic