I'm not reading Max's book, so I don't know exactly what he said, but using FPI as in
Everett QM and writing down which of two equally likely events you actually experience is
an example of bernoulli trials. The proportion of 1s and 0s both converge to 1/2 in
probability. This is exactly the way prediction of probabilities are evaluated
experimentally. It is irrelevant that the proportion of subsequences that have exactly
equally 1s and 0s goes down.
Brent
On 3/3/2014 8:32 PM, chris peck wrote:
Hi Liz
*>> I'm not sure I follow.*
Me neither.
*>> 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 would be no 'about' it were your interpretation right, Liz.
It would be all the time, exactly 50%.
Hes saying that zeros occur about 50%of the time in the zeros and ones you have written
down.
That corresponds to the individual bit strings. Not the entire collection of
them.
*>> I guess the sloppy phrasing is he implies 0s happen half the time in most
sequences?*
I suspect its sloppy interpretation rather than sloppy phrasing that implies
that.
*>> I don't know if that is true (it's true for 6 of the 16 sequences above)*
6/16 isn't half is it? I measured 1 divided by 2 just now and it still seems to come out
as 0.5 here.
*>> or if it becomes more true (or almost true) with longer sequences. Maybe a
mathematician can enlighten me?*
I wrote a little program Liz that collects together all the bit strings that can be made
from 16 bits. Then it counts the number of 1s and 0s in each one. It has a little
counter that goes up by one every time there are 8 zeros.
there are 65536 combinations. 12870 of them have 8 zeros. 12870 / 65536 * 100 =
19%.
6/16*100 = 37%
I don't know about you but 19, being less than 37, suggests to me that the percentage is
going down. But ofcourse ask a mathematician if you're not certain of that yourself.
*
>> I admit Max seems a little slapdash in how he phrases things in the chapters I've
read so far, presumably because he's trying to make his subject matter seem more
accessible.*
Yeah, which is preferable to people with similar ideas being slap dash in order to make
them less accessible.
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