On 04 Mar 2014, at 04:49, LizR wrote:
I'm not sure I follow. Tegmark said "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."
That seems to me to be correct. If you do the experiment 4 times you
get the sequences I typed out before, except I seem to have
accidentally doubled up! The correct sequences should read:
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010
1011 1100 1101 1110 1111
Depending on how you decide something looks random, I'd say quite a
few of those sequences do. And 0s do occur 50% of the time overall,
for sure.
I guess the sloppy phrasing is he implies 0s happen half the time in
most sequences? I don't know if that is true (it's true for 6 of the
16 sequences above) or if it becomes more true (or almost true) with
longer sequences. Maybe a mathematician can enlighten me?
Imagine you throw a billions of coins. You can understand intuitively
that getting *exactly* half tails and half heads would be a lucky
event. Then you can do the math, and it confirms this. You will get
"white noise", most of the case. With big number, such sequence of
P=1/2 events gives a "grey" white noise, which confirms Tegmark
statement that most sequence will have approximately the same number
of head and tail, but the "about" here is important. The deviation
from this will be non null, but non significant. It drops like 1/
sqrt(n) as Brent said. Indeed, if you get too many heads, or too many
tails, that would make you believe that the coins are biased. All
correlation studies in experimental physics are based on this.
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.
Yes, I have often met that problem. I like to be slightly non rigorous
for helping people to grasp the main idea, but then nitpickers jumps
on the details. If you expose the point in taking all details into
account, then you are accused of making things less accessible, or to
hide difficulties in jargon.
Some people just try hard to not understand, and this usually, I
guess, for private agenda or some ideologies, I'm afraid.
Bruno
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