http://existentialrisks.tribe.net/thread/26e7e7f4-71b8-441e-a9e3-8b98bcdb054f?format=rss Tribe.net. Local Connections http://existentialrisks.tribe.net/thread/26e7e7f4-71b8-441e-a9e3-8b98bcdb054f#5eeb118d-9b2c-42ea-a943-d0da0ba694df I'd love to discuss... but I'll need to digest first..... Tue, 04 Apr 2006 19:19:21 GMT http://existentialrisks.tribe.net/thread/26e7e7f4-71b8-441e-a9e3-8b98bcdb054f#5eeb118d-9b2c-42ea-a943-d0da0ba694df Amy 2006-04-04T19:19:21Z http://existentialrisks.tribe.net/thread/26e7e7f4-71b8-441e-a9e3-8b98bcdb054f#912b8c04-60b4-4759-90d7-127fef5d96f3 The Fermi Paradox and Singularities Robert Pisani Department of Statistics University of California Berkeley, California robert pisani <r.pisani@mac.com> There are many billions of galaxies that contain even more billions of star systems that can support life. The universe has existed for 13+ billion years, and the time that humans needed to grow from single celled creatures to what they are today is just a few million years, an instant in the life of the universe. If life is as common as is now thought, we would not be the first civilization to have arisen in the universe. Any civilization that has advanced to our stage must produce radio waves, microwaves, etc. But we don't find any. Enrico Fermi said, "Where is everybody?" It was thought at one point in the 1950's that nuclear weapons had the potential to end human life on earth. Knowledgeable insiders assessed the chance of reaching the 21st Century as "about 50%". Whether or not such thinking was justified, new technologies like DNA manipulation and nanotechnology and molecular manufacturing clearly do have such potential. These technologies and others could cause extinction of the human race, and in fact all life on our planet, either through deliberate application or technical malfeasance. Following is a framework for beginning to think rigorously about the Fermi Paradox. Kurzweil's Law says that technology grows at a double exponential rate. Denote the level of technology at time t by yt. (0) yt = exp(exp(t)). Given a sequence of times t0 < t1 < t2 < . . . define (1) Epoch(n) = the period from tn to tn+1 and (2) pn = the chance of total annihilation during Epoch(n) Assuming that survival chances in different Epochs are independent, given that a civilization has survived to the end of Epoch(k-1) and thus the beginning of Epoch(k), if n „ k the chance that it will survive until the end of Epoch(n) is: (3) s(n) = ½ {(1-pi), i = k, n} And the chance it will survive for an infinite number of epochs is (4) lim n ý ƒ s(n) = lim n ý ƒ ½ {(1-pi), i = k, n}, which is greater than 0 if and only if (5) _ ln (1-pi) converges. For small p, ln(1-p) ~ - p, so (loosely) for small p, (5) converges if and only _ pi converges. If (5) diverges, the probability of ultimate extinction is 1.0. Let yn = the number of different weapons available at time n which will cause extinction if used. Certainly defensive measures against such weapons will also be available. If the probability of any given weapon being applied successfully against all of its defenses in Epoch(n) is q > 0, then the chance that any given weapon is not used successfully in Epoch(n) is 1-q, and the chance that at least one is used successfully, and the civilization perishes, is pn = 1 - (1-q)x, where x = yn. Since ln(1-q) < 0 and yn ý ƒ , ln(1 - pn) =ln (1-q)x = x ln(1-q) = yn ln(1-q) ý - ƒ, and (5) diverges Suppose that defensive measures yield Epoch(n) probabilities qn which decline to 0 as n grows larger. Still, if (5) is to converge, we must have yn ln(1- qn) ~ - yn qn ý 0. and to avoid extinction, we must have necessarily (but not sufficiently) qn < 1/ yn = 1/exp(exp(n)) for n> n0, some n0 Even more restrictively, we must have yn qn < 1/n, and thus qn < 1/nyn = 1/(n exp(exp(n)) for all n larger than some value. And so on. Clearly the qn must decline to 0 very rapidly, and (0) clearly places an extreme burden on any program of defense that seeks to avoid the annihilation of the civilization. Should other considerations show that such rapid decline is structurally not possible, (4) will then necessarily equal 0, explaining the Fermi Paradox. ========= Discuss... Thu, 30 Mar 2006 02:30:34 GMT http://existentialrisks.tribe.net/thread/26e7e7f4-71b8-441e-a9e3-8b98bcdb054f#912b8c04-60b4-4759-90d7-127fef5d96f3 Mike 2006-03-30T02:30:34Z