Norman Samish wrote:
> ----- Original Message -----
> From: "Brent Meeker" <[EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]>>
> Brent, you say, ". . . It seems to me that an information theoretic 
> analysis should be able to place a lower bound on how small a 
> probability can be and not be zero."
> Doesn't a lower limit on probability repudiate the notion of Tegmark, 
> Vilenkin, et al, that there are necessarily duplicate worlds to ours, if 
> only we go out far enough?  

I don't see why these questions are related.  There are only *necessarily* 
duplicate worlds if there is an infinity of worlds of a higher order than the 
information content of a world.

>If you repudiate duplicate worlds, do you 
> also repudiate infinite space?

Space could be infinite without there being duplicate worlds.  "Repudiate" is 
too strong a word.  I doubt they are relevant.

> E.g., Alex Vilenkin ("Beyond the Big Bang," Natural History, July/August 
> 2006, pp 42 - 47) says, "A new cosmic worldview holds that countless 
> replicas of Earth, inhabited by our clones, are scattered throughout the 
> cosmos." 
> Vilenkin's view is that this conclusion arises from Alan Guth's theory 
> of inflation and "false vacuum" put forth in 1980.  The unstable false 
> vacuum (which eternally inflates exponentially) has regions where random 
> quantum fluctuations cause decay to a true vacuum.  

You can't "go to" those different universes.  Their supposed existence is 
entirely dependent certain theories being correct.  But those theories are 
contingent on suppositions about a quantum theory of spacetime - which is not 
hand.  So, while I'm willing to entertain them as hypotheses, I neither accept 
nor deny their existence.

>The difference in 
> energy of the false vacuum and the true vacuum results in a "big bang."  
> In the infinity of the false vacuum there are, therefore, an infinity of 
> "big bangs."  The big bangs don't consume the false vacuum because it 
> inflates faster than the big bangs expand.  Vilenkin figures the 
> distance to our clone at about 10 raised to the 10^90 power, in meters.  
> (This roughly agrees with Tegmark's number.)  (An unanswered question is 
> where and why did this initial infinity of high-energy false vacuum 
> originate?)

If one can originate, then any number can.  But I don't see that such an 
infinity has any implications.

> Now 10 raised to the 10^90 power is a big number.  Therefore the ratio 
> of duplicate Earths to all worlds is exceedingly small - but not zero!  
> Do you think it should be zero?

I think it might be of measure zero.  Or there might not be any duplicate 

Brent Meeker

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