Thread:User talk:Tmtoulouse/Bump: You know that obnoxious thing people do on the internet when they've said something and they feel they haven't been paid enough attention? I'm doing that./reply (21)

Let me put it this way: The giant lolipop theory (GLT) claims that on 26th March 2014, we will make some observation which clearly supports its claims (e.g. we will see the giant's tongue through our telescopes.) More formally, at some time tg, where tg > tnow, we will have some observation og; but predicts no observations for times t < tg. And, GLT specifies tg as 26th March 2014.

Anti-GLT theory claims that on that same date, we will see no such observations (e.g. we look out our telescopes, and no giant tongue can be seen). More formally, at tg, we will have some observation o~g, which by its nature is incompatible with having observation og.

So, both theories predict different observations at tg, og and o~g. Why should we assume anti-GLT is more likely than GLT? Because, our existing knowledge + anti-GLT is simpler than our existing knowledge + GLT. Let O = {all ot for all t0 <= t <= tnow}. In other words, O is all the observations we have had so far. Anti-GLT is more likely, because C(O + o~g) < C(O + og), where C(x) is a measure of complexity. (I would say Kolmogorov complexity, or some computable approximation thereto.) Hence, parsimony leads us to prefer anti-GLT, since anti-GLT is a simpler theory than GLT.

Now, the God+afterlife theory (GA theory) says that post mortem, I will make certain observations. Unlike GLT, it doesn't predict a precise date for its observations, but that is fine. Consider the theory "My cat will die one day". That theory predicts certain observations in the future. It doesn't specify a precise date, but it can provide a function p(t) = probability we have had those observations by time t. Obviously, all animals, my cat included, have a finite lifespan, and the longer they live, the more likely they'll die now (to simplify things a bit). So, the fact that the afterlife theory doesn't precisely specify a time for my own death is fine, since that is analogous to the case when dealing with the death of my cat. It simply claims that, whenever my death occurs, then observations of a certain sort will follow, reasonably promptly thereafter, measured in subjective terms. Depending on one's theology, maybe one believes in soul sleep, and I will be unconscious post mortem for thousands or millions of billions of years before God returns me to consciousness; but, since the theory references subjective time, that duration doesn't count.

So, GA theory says I'll have certain observations oGod at time tpm, where tpm > tdeath > tnow.

What does no-God-no-afterlife theory (NGNA theory) predict at tpm? Well, interestingly, it doesn't predict any observation at all. It predicts, not an observation, but this strange entity called observing nothing, a null set of observations. This is why, GLT and anti-GLT are symmetric, in a way which GA and NGNA aren't. So, comparing the GLT/anti-GLT pair to the GA/NGNA pair isn't really valid.

Should parsimony prefer NGNA to GA theory? Using the same logic we used for the GLT/anti-GLT case, we have to compare C(O + GA) to C(O + NGNA). Now, NGNA is essentially a null set, so we are basically comparing C(O + GA) to C(O + null), and it seems reasonable to assume that C(O + null) = C(O). So, if C(O) < C(O + GA), then NGNA wins by parsimony.

Can adding an observation make the set of observations simpler? Indeed it can. Consider a program which generates all the digits of pi, call any program meeting this description P1. Consider instead a program which generates the first n digits of pi, where n is a large but finite arbitrary number (say one on the order of Graham's number); call this program P2. Now, is the shortest P1 program shorter than the shortest P2 program? Yes; a P1 program must just encode an algorithm to calculate pi; a P2 program must also encode some large number n, and the logic to stop the generation when that many digits have been output. The Kolmogorov complexity of a finite initial substring of pi will be greater than the Kolmogorov complexity of pi itself, when that initial substring is long enough.

Furthermore, let me present the following theory, call it universe extinction theory (UET). UET claims, that at some time tend, where tend >= tnow, the universe, and everyone and everything within it, will suddenly cease to exist, and thus time will end, and nothing will exist at all, ever thereafter. Of course, UET is not a single theory, but a family of theories, for differing values of tend. At one extreme, where tend is many billions or trillions of years in the future, UET may match various theories from cosmology of the end of the universe (e.g. the Big Crunch). On the other hand, if tend is next week, or next second, or this very instant, well now we are in reverse Last Thursdayism territory - Next Thursdayism rather than Last Thursdayism.

Won't the principle of parsimony prefer UET(tnext Thursday)? Isn't it simpler to assume the universe suddenly ceases to exist next Thursday, than it exists for billions, trillions of years to come. That is an immense extra volume of spacetime we are adding to the universe, an immense subsequent series of observations - surely, that immense addition is not perfectly compressible, and even if combined with O it compresses significantly, it seems likely that C(O + a tiny bit extra) << C(O + billions of years extra). But, if the principle of parsimony leads us to prefer the hypothesis that the universe will end next Thursday, doesn't it lead us to believe in preference to that, that right now is the last moment of the universe's existence? But, clearly that is preposterous; so something must be wrong with the principle of parsimony.

Furthermore, no-afterlife theory (NA theory) is very similar to UET(tmy death), except the U (the universe) is my personal universe rather than everybody's. If UET has problems, why won't NA have similar problems?

Now, maybe my presentation of the principle of parsimony is wrong; but if so, I challenge you to explain why, and provide an alternative.