On 6/10/2015 7:19 am, John Clark wrote:
On Sun, Oct 4, 2015 5, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>>wrote:
>>
If
the universe is infinite and not just huge then a finite
d
istance away there *IS* a
person identical to our
B
ruce Kellet
in every way EXCEPT he's named John Clark not
Bruce Kellet
In fact there are a infinite number of them.
>
Prove it! And I mean *prove*, not just wave your hands a bit.
I
f the Universe is infinite and if it is "normal"
then
i
t
has to be true.
A
number is called
"
norm
a
l
"
if it is a infinite irrational number
and
the average number of times a di
gits
in base b
occurs
gets closer and closer to 1/b as larger portions of the sequence are
examined. In other words
it's normal if
in the decimal expansion of the number one digit is not more common
than another. If a number is normal then any finite sequence of number
s
you can name exists a finite distance to the right of the decimal point.
We know that almost all real numbers are normal but only a very few
particular numbers have been proven to be so; one that has been proven
to be normal is
Champernowne
's
constant
:
0.12345678910111213141516
1718
192021...
At some finite distance to the right of the decimal point is your
telephone number and your social security and your credit card number,
and if every 2 digits encodes a letter or a punctuation mark in the
English language then at some finite distance to the right of that
decimal point all 7 Harry Potter novels are encoded back to back.
But is the matter in the universe distributed normally? My intuition
says yes but I can't prove it.
That's why I asked you to prove it -- it is not sufficient to say that,
"well, if it were true then it would be true." The type of random
uniformity typified by a normal number is quite hard to achieve, and
even harder to prove. That is why we can't prove that arbitrary reals
such as pi and e are normal. It is easy for Champernowne's number
because that is not a random sequence of digits.
>
PS. If the copy is named 'Bruce Kellet', then it is not me,
because that is not my name!
Agreed, close but no cigar. So there are a infinite number of things
that are
Bruce Kellet
and there are a infinite number of things that are /almost/
Bruce Kellet
.
Not likely. Anything that fails to be me, necessarily fails by a wide
margin.....
Bruce
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