Hi Jason/Gabriel Thanks for the posts. They were both really clear. I can see that it was a mistake to hedge my bets on exact figures and also, given Jason's comments, to think that seemingly regular sequences were quite common.
I do maintain that proportions of roughly 50/50 splits are a spurious measure of 'seemingly random' though and that irregularity of change is a better one. There also seems to me to be a big difference between Tegmark's game as described in the quote below, and flicking coins. Tegmark's game is a process guaranteed to generate (over 4 iterations) 16 unique and exhaustive combinations of 0s and 1s (heads or tails). If 16 people were to flick a coin 4 times and write down the results there is only a low probability that the resulting set would map on to that generated by Tegmarks game. There is fair chance there would be some repetition. Jason, you say: >> Even if your pattern were: 0 1 0 1 0 1 0 1 0 1, you still have no better >> than a 50% chance of predicting the next bit, so despite the coincidental >> pattern the sequence is still random. I disagree here. In Tegmarks game you know a particular outcome is not exclusive and that you'll have two successors who get one and the other. The next outcome is (01010101010 AND 01010101011) not (01010101010 XOR 01010101011). Now this might influence how you bet. If you care about your successors you might refuse to make a bet because you know one successor will lose. If we rolled dice rather than flicked coins and were to bet on getting anything but a 6, in a modified Tegmark game we might still refuse to bet knowing that one successor would certainly lose. Its a bet we almost certainly would take if we were rolling die in a classical world without clones. More dramatically, if you play Russian roulette in Everettian Multiverse you always shoot someone in the head. Crossing the road becomes deeply immoral because vast numbers of successors trip and get run down by trucks. A final confusion: Does anything ever seem 'apparently random' in a Marchalian/Tegmarkian game? Given that you know outcomes are generated by a mechanical process and given you know exactly what the following set of outcomes will be, how can they seem random? Even 1001111010110011 isn't looking very random anymore. :( Date: Thu, 6 Mar 2014 10:21:47 +1300 Subject: Re: Tegmark and UDA step 3 From: lizj...@gmail.com To: everything-list@googlegroups.com On 6 March 2014 06:45, Gabriel Bodeen <gabebod...@gmail.com> wrote: Brent was right but the explanation could use some examples to show you what's happening. The strangeness that you noticed occurs because you're looking at cases where the proportion is *exactly* 50%. binopdf(2,4,0.5)=0.375 binopdf(3,6,0.5)=0.3125 binopdf(4,8,0.5)=0.2374 binopdf(8,16,0.5)=0.1964 binopdf(1000,2000,0.5)=0.0178 binopdf(1e6,2e6,0.5)=0.0006 Instead let's look at cases which are in some range close to 50%. binocdf(5,8,0.5)-binocdf(3,8,0.5)=0.4922 binocdf(10,16,0.5)-binocdf(6,16,0.5)=0.6677 binocdf(520,1000,0.5)-binocdf(480,1000,0.5)=0.7939 binocdf(1001000,2e6,0.5)-binocdf(999000,2e6,0.5)=0.8427 binocdf(1000050000,2e9,0.5)-binocdf(999950000,2e9,0.5)=0.9747 Basically, as you flip a coin more and more times, you get a growing number of distinct proportions of heads and tails that can come up, so any exact proportion becomes less likely. But at the same time, as you flip the coin more and more times, the distribution of proportions starts to cluster more and more tightly around the expected value. So for tests when you do two million flips of a fair coin, only about 0.06% of the tests come up exactly 50% heads and 50% tails, but 84.27% of the tests come up between 49.95% and 50.05%. Thank you, that's exactly what I was attempting to say in my cack-handed way. (And it is almost certainly what Max intended to say.) -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
