[ExI] The unlimited size of qubits.

[Stuart LaForge]

Mike Dougherty wrote:

> I guess the distinction is one of scope or possibly bandwidth.  A
> separate space would be 3 of those original axis taken as a tuple, right?
> :)  maybe 3+1 is 6 taken as 3 + a checksum of another 3.  Call it a
> spacetime RAID.  many worlds is redundancy and the posited bifurcation in
> world lines is perspective-induced distortion.

That is an interesting notion. Although generally it is the differences
between  Everett branches that is considered informative rather than the
redundancy. How do exactly half of the universes know to show you the
electron being spin-up while the other half know to be spin down?

It is the completeness of the multiverse that is the mystery. How do the
Everett branches ensure that every possible outcome is realized somewhere
unless they were coordinating with one another?

I mean sure one can just throw infinity at it and say given an infinite
number of chances any highly improbable event will be realized somewhere.
But if you do that, then there is no need for bifurcation to take place
because all possible universes are already there a priori.

> to the blind spot caused by the optic nerve that our processing equipment
> simply edited out of normal awareness.
 
No bifurcation means no need for a blind-spot to prevent you from sensing
all those copies of you out there since you are not spawning them every
time you flip a coin. They are already out there somewhere. It seems that
infinity is one assumption that makes for fewer overall assumptions. Such
as a mechanism to store and organize all the exponentially bifurcating
universes.

>> Shannon information exists whether one understands the context or not.
>> Semantics and meaning are relative but information itself seems to
>>  be absolute and independent of ones ability to understand it or even
>> just see it. A closed book still contains information even if it is in a
>> language you don't understand.

> Yeah, agreed.  However, to strain the analogy some... you read 1984 when
> you were X years old.  It contained a string of bytes that represembles
> the exact text authored by Orwell.  You read it again when you are 2X
> years old; same exact bytes so it's the same information - but you
> experience a slightly different story thanks to additional X years of
> subjective context.

Yes but that is because the meaning has changed, not the information
content. Information and meaning are largely independent of one another.
Information is  a constant in that everyone who reads "1984" in a given
language will have the same number of bits communicated to them

While meaning is like a variable, in that no two people will interpret
"1984" identically. Not even you at two different ages. Consider how in
the English language terrible and terrific used to mean the same thing. Or
how in English "pan" means a type of cookware while in Latin it means
bread.

> You might also learn there is a steganographic
> encoding of another message inside those bytes.   Knowing the cypher
> grants additional layers of story,  perhaps even changing the A story
> because of the B story ... or does that simply create a C story?  Or are
> we assuming the bytes already literally "mean" every permutation of
> cypher and harmonic/overtones possible for byte stream of length N? 
> (Including resequencing bytes or groups of bytes)

Neither. The meaning of a message lies first in the sender and then the
recipient, but never in the symbols themselves. The symbols are arbitrary.
Furthermore, the sender's meaning i.e. the purport is not guaranteed to be
at all the same as the recipient's meaning i.e. the import. For example,
you calling for "help!" in the jungle might be interpreted as "dinner!" to
a hungry tiger with almost the same degree of urgency. Or you might see a
cloud that looked like the letter "I". Context is everything.

> This reminds me of a thought I had as a child: how many ways can you write
> the number 8?  4+4, 10-2, etc with all the ways you learned in 1st grade,
> but also 2^3 and sqrt(64) and such that you learn later.   Also encodings
> like binary or hexadecimal.  Etc.  The point was that "8" is only one
> convention for how to express the idea of eight.

There are an uncountably infinite number of possible ways to express the
number 8.

Proof:

Let A = x+y = 8 represent the set of ordered pairs of integers (x,y) where
the sum of the two integers x & y  are equal to 8. This can be represented
as a function F from the set of integers to the set of integers such that
F:Z->Z | F(x) = y = 8-x.

Clearly on can see there is a unique integer y for every integer x. Since
there are a countably many integers there are therefore a countably
infinite number of pairs of integers such that x+y = 8. Therefore the
cardinality of the set A is Aleph-zero.

Now consider the arithmetic mean or average of the elements of all
possible subsets of A. Each such average would itself be an expression
that was equal to 8. e.g. the average of any number of 8s will itself be
8. Therefore there are 2^(Aleph-null) possible expressions for the average
of ways to express 8 as the sum of two integers. Therefore therefore there
are at least as many ways to express the number 8 as there are real
numbers. Or in other words there are at least Aleph-1 possible ways to
express the number 8.

> Maybe this comes back to the Platonic realm?

Or maybe it comes back to infinity. :-)

Stuart LaForge