peterdjones.domain.name.hidden wrote:
> "Hal Finney" wrote:
> The first is that numbers are really far more complex than they seem.
> When we think of numbers, we tend to think of simple ones, like 2, or 7.
> But they are not really typical of numbers. Even restricting ourselves to
> the integers, the information content of the "average" number is enormous;
> by some reasoning, infinite. Most numbers are a lot bigger than 2 or 7!
> They are big enough to hold all of the information in our whole universe;
> indeed, all of the information in virtually every possible variant of our
> universe. A single number can (in some sense) hold this much information.
How ? Surely this claim needs justification!
~~~~~~~~~~~~~~~~~~~~~
The single number can be of infinite length, with infinite digits, and can therefore contain unlimited information. One could compare the single number to a tape to a Universal Turing Machine. Granted, the UTM needs a head and a program to read the tape, so the tape by itself is not sufficient to hold information.
Norman
~~~~~~~~~~~~~~~~`
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups "Everything List" group.
To post to this group, send email to everything-list.domain.name.hidden
To unsubscribe from this group, send email to everything-list-unsubscribe.domain.name.hidden
For more options, visit this group at
http://groups.google.com/group/everything-list
-~----------~----~----~----~------~----~------~--~---
Received on Fri Mar 17 2006 - 16:32:17 PST