Hi Liz >> 0000 0001 0010 0011 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1010 >> 1011 1100 1101 1110 1111
Of which I'm fairly sure half the digits are 0 and half 1! What am I missing here? If you concatenate all those strings together you'll get a bigger string in which the proportion of 1s to 0s is exactly 50/50. And that will always be the case no matter how long the individual bit strings are. If they are 8 bits long then you'll have 256 individual strings. When concatenated together the proportion will be exactly 50/50. But it looks to me like you're misconstruing Tegmark's method here. Its each individual string that matters. What is the proportion of 1s to 0s in 0000, or in 1011, or 1100 etc. Because each string represents a sequence of room - wake ups. In your example, 16 people live through room-wake ups over 4 nights. Each person's experience represented by an individual string. Even over 4 nights you'll see, just by counting, that the number of occasions where the proportion of 1s to 0s is 50% is 6. Not 8. Not half. How does that square with his claim that almost all people will experience a 50/50 distribution of 0s to 1s? not even half will. Now as the individual strings get longer, as more nights are encountered, that proportion goes down. Not up. When individual strings are 16 bits long, there are 65,536 combinations (people). Of whom less than 20% experience a 50/50 split of 1s and 0s over those 16 nights. Now Brent, and Bruno with customary obtuseness, correctly point out that: 1) Tegmark talks about 'roughly half', so not an exact 50/50 split. 2) if you take that into account, then you can get a figure approaching 'almost all'. in the 16 bit example, if you include strings where there are 7 ones (or zeros) and you take strings where there are 6 ones (or zeros) then about 78% of people will experience 'roughly' 50% ones or zeros. Ofcourse now we're in a situation where personal opinion rears its head. Is 78% 'almost all'? Is 37% (6/16) 'roughly half'? Right and wrong don't really preside over these kinds of opinions, but 37% doesn't look like 50% to me. In any case both Bruno and Brent miss the bigger picture: Consider the following 16 bit strings: 1010101010101010 - does that look random? how about 0101010101010101 how about this: 1100110011001100 Seems to me Tegmark is confusing a roughly equal distribution of 1s and 0s with apparent unpredictability. A better approach considers irregularity of change in 1s and 0s. So where there is irregular change : 0100111101010011 it looks unpredictable, but where change is regular : 1111000011110000 it doesn't. The proportion of 1s and 0s is irrelevant. So has Tegmark convinced me that in his thought experiment I would assign 50/50 probability of seeing one or the other room each iteration? Not really. I'm sure Tegmark's world won't be shaken too much by any of this, I'm even more certain that I have something wrong. Though it does seem to have sent Bruno running for cover behind his little sums. So perhaps I am on to something.... All the best Chris. Date: Tue, 4 Mar 2014 11:59:05 +1300 Subject: Re: Tegmark and UDA step 3 From: lizj...@gmail.com To: everything-list@googlegroups.com I should also mention that in the quote, Max says that you wake up in room 0 or room 1, so if we WERE omitting leading zeroes, we'd write "1111111111..." ! Shurely shome mishtake! -- 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.
