On 3/3/2014 11:55 PM, chris peck wrote:
*>> I'm not reading Max's book, so I don't know exactly what he said,*
Im reading the quote Jason kindly provided and responding to exactly what
Tegmark 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. *
and the figures I've been stating reflect bernoulli trials precisely.
*>> The proportion of 1s and 0s both converge to 1/2 in probability. *
but in doing so call in to question definitions of 'about' 'roughly' and 'almost all'.
But then you haven't read the Tegmark quote so you won't be able to add anything
substantive about that.
I read Jason's quote: "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. In other words, causal physics will produce the illusion of randomness from your
subjective viewpoint in any circumstance where you're being cloned." But I don't know
what Figure 8.3 is.
*>> It is irrelevant that the proportion of subsequences that have exactly equally 1s
and 0s goes down.*
Whats irrelevant is the use of proportion of 1s and 0s in determining 'apparent
randomness'. It doesn't. Which is my point. The figures for exact proportions were just
my arse about tit way of getting there.
That's true. The proportions of 1s and 0s doesn't determine randomness, it just
determines the relative measures of experiencing room 1 and room 0. But what Max wrote is
true also; there would be 2^N "you"s and most of them would have written down sequences
that were within z/sqrt(N) of 50/50 and looked random (i.e. incompressible) where you can
choose z to be whatever you want to define "most of them". But whatever you choose for z,
z/sqrt(N) still goes toward zero as N->inf.
Brent
But still, even though I seemed to get there on my tod, at least I know what a Bernoulli
trial is now. Thanks for that.
------------------------------------------------------------------------------------------
Date: Mon, 3 Mar 2014 21:43:29 -0800
From: [email protected]
To: [email protected]
Subject: Re: Tegmark and UDA step 3
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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