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%. -Gabe On Monday, March 3, 2014 1:36:11 AM UTC-6, chris peck wrote: > > *>> If you repeated the cloning experiment from Figure 8.3 many times and > wrote down your room number each time, you'd in almost all cases find that > the sequence of zeros and ones you'd written looked random, with zeros > occurring about 50% of the time.* > > > There's something strikes me as very strange about this idea. > > Tegmark's method is just a means of writing down binary sequences. > > Being strict, already with binary sequences just 4 digits long, only 37.5% > of those contain half zeros. This drops the longer the sequences get. So, > with sequences 6 digits long, only 31.25% contain half zeros. With > sequences 8 digits long only 27% and with 16 digits only about 19%. > > If his experiment continued for a year, (365 digits) many people would > find that either room 1 or room 0 was dominating strongly. For these people > a change in room would seem very odd, a glitch in the matrix that wouldn't > be of any great concern vis a vis prediction once 'normality' kicked back > in the following night. For others, a change in room would occur at regular > intervals and would seem very predictable. There would be the guy who > changed room every night. There would be all the guys whose room changed > every night except for the one time when it stayed the same. A little > glitch is all. > > In truth, the longer you continued the game and the more people got > involved the less chance a person would have of finding room assignment > random at all. There would be increasingly few people willing to bet 50/50 > on a particular room assignment. > > ------------------------------ > Date: Sun, 2 Mar 2014 17:13:23 +1300 > Subject: Re: Tegmark and UDA step 3 > From: [email protected] <javascript:> > To: [email protected] <javascript:> > > "Hello, dear, looking for a bit of multi-sense realism?" > > On 2 March 2014 16:35, <[email protected] <javascript:>> wrote: > > > heh heh heh I love this place. It's like walking through an eccentric > street market where traders call out their wares > > "GETCHYOUR P-TIME 2 for 1 logico-computational really real structure > today only" > > "Assuming comp only, that's right comp only. Theology but done like > science. Madam you are ugly but I will be sober in the morning. You there, > you reek of not-comp, get lost. Ah sir, did you like the dreams? Same > again?" > > "GETCHOR P-TIME..,." > > > > > -- > 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] <javascript:>. > To post to this group, send email to [email protected]<javascript:> > . > 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.
