On Wed, Mar 5, 2014 at 6:52 PM, chris peck <[email protected]>wrote:
> 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. > Interesting, I wonder what difference in the decision theory is required to weight the two cases differently, the ANDs vs. the XOR.. Are there any? Perhaps there is an argument for some quantum suicide experiments. > 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. > But from the first person view, the existence of clones changes nothing that you can detect. It is a difference that makes no difference. > > 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. > Everything you do affects an infinite number of future selves, choose wisely. :-) > > 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. > > :( > A related question is, is there any such thing as true randomness at all? Or is every case of true randomness an instance of FPI? Jason > > > ------------------------------ > Date: Thu, 6 Mar 2014 10:21:47 +1300 > > Subject: Re: Tegmark and UDA step 3 > From: [email protected] > To: [email protected] > > > On 6 March 2014 06:45, Gabriel Bodeen <[email protected]> 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 [email protected]. > To post to this group, send email to [email protected]. > 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 [email protected]. > To post to this group, send email to [email protected]. > 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. 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