On 3/2/2014 11:36 PM, 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.
Naah. The *fractional* deviation from 50/50 keeps going down as 1/sqrt(n).
Brent
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