> On 11 Mar 2019, at 03:16, [email protected] wrote:
>
> They say if information is lost, determination is toast.
That is not correct. If information is lost, reversibility is toast, but
determination can be conserved.
Typically the Kestrek bird K is irreversible, as it eliminates information Kxy
= x. From KSI you get S, but from S, even knowing it comes from the application
of K, you cannot retrieve I. Similarly with addition and multiplication in
arithmetic. From 18 you can’t guess it cames from 7 and 11. Erasing information
is common.
Some does not tolerate that, so Church works in the base {I, B, W, C}, where I
is [x]x, B is [x][y][z] x(yz), etc.
That base is not combinatorial complete, but is still Turing complete,
illustrating that we can do computation without eliminating any information.
(None of I, B, C and X eliminates information)
But the quantum eliminates even the combinator W (Wxy = xyy), or the lamda
expression [x][y]. xyy. That is, we cannot eliminate information, but we cannot
duplicate it either!
Now, the problem is that the BCI combinator algebra are not Turing-complete. It
is the core of the physical reality, and Turing universality needs the addition
of modal “combinators”.
> But doesn't QM inherently affirm information loss? I mean, although, say, the
> SWE can be run backward in time to reconstruct any wf it describes, we can
> never reconstruct or play backward Born's rule, in the sense of knowing what
> original particular state gave a particular outcome. That is, there is no
> rule in QM to predict a particular outcome, so how can we expect, that given
> some outcome, we can know from whence it arose? AG
You can run backward by discarding information. Born rule, or the projection
inherent in the measurement discard information, when you abandon the collapse
postulate. That is why “fusing” histories can be done by relative amnesia, and
also that is how Church emulate “local kestrels” capable to “apparently
eliminate information”, but only with selected objects, like the numbers. K n m
= n
A quantum computer (essentially irreversible during the processing) is Turing
complete, and so can simulate all classical computers discarding information
all the times, but in the details, everything is locally determinist and
reversible.
Bruno
>
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