Re: Dark energy-powered devices

[John Clark]

On Sun, Apr 7, 2019 at 7:35 PM Lawrence Crowell <
goldenfieldquaterni...@gmail.com> wrote:

>> There are important differences that need to be explained. You can solve
>> the problem of figuring out if Schrodinger's Cat is alive or dead simply by
>> opening the box and looking, but there is no box you can open to figure out
>> what the 8000th Busy Beaver number is.
>>
>
> > You can't compute outcome prior to an observation.
>

Even if you can't compute Schrodinger's Cat you can still find out stuff
about it but that is not the case with non-computable functions, and that
makes me suspect they have no part to play in physics. Computation can not tell
you what the fate of Schrodinger's Cat was however observation can, but you
can't figure out what the 8000th Busy Beaver number is and probably not
even the 5th. And even if I told you what it was you'd have no way of
varying that what I told you was true.

 John K Clark


>

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Re: Dark energy-powered devices

[Lawrence Crowell]

On Sunday, April 7, 2019 at 5:03:07 PM UTC-5, John Clark wrote:
>
> On Sun, Apr 7, 2019 at 2:26 PM Lawrence Crowell  > wrote:
>  
>
>> > there is no comprehensive axiomatic system for Diophantine equations. 
>> Quantum numbers as Gödel numbers for integer solutions to Diophantine 
>> equations are then not entirely computable and there can't exist a 
>> Turing machine (in the classical sense a q → ∞ convex set) that computes 
>> quantum outcomes.
>>
>
> I think the connection between Quantum Mechanics and  Godel's uncertainty 
> is pretty tenuous. Neither a Quantum Computer or a conventional computer 
> can compute the 7918th Busy Beaver number, and even though its computable 
> and finite its very unlikely a Quantum Computer could compute the Ackermann 
> function in polynomial time which effectively makes it non-computable for 
> practical purposes.   
>  
>
>> > I then maintain the solution to the quantum measurement problem is 
>> that there can't exist such a solution. It is an unsolvable problem.
>>
>
> There are important differences that need to be explained. You can solve 
> the problem of figuring out if Schrodinger's Cat is alive or dead simply by 
> opening the box and looking, but there is no box you can open to figure out 
> what the 8000th Busy Beaver number is.
>
> John K Clark  
>


You can't compute outcome prior to an observation. Quantum interpretations 
are meant to gives some explanation for quantum outcomes, but they all 
contradict each other, but are still consistent with QM. This sound very 
similar to forcing conditions on undecidable propositions.

LC 

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My book "I Am" published on amazon

[za_wishy via Everything List]

My book "I Am" has been published on amazon. It deals with my ideas about 
the emergent structure of consciousness and the nature of self-reference 
which gives birth to the emergent structure, which as far as I know, are 
new ideas, so they might prove useful in opening new paths in the attempt 
of obtaining a theory of consciousness.

Kindle version: https://www.amazon.com/dp/B07Q4LZVFH
Paperback version: https://www.amazon.com/dp/1092284397

(also available for the other amazon national websites)

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Re: Dark energy-powered devices

[John Clark]

On Sun, Apr 7, 2019 at 2:26 PM Lawrence Crowell <
goldenfieldquaterni...@gmail.com> wrote:


> > there is no comprehensive axiomatic system for Diophantine equations.
> Quantum numbers as Gödel numbers for integer solutions to Diophantine
> equations are then not entirely computable and there can't exist a Turing
> machine (in the classical sense a q → ∞ convex set) that computes quantum
> outcomes.
>

I think the connection between Quantum Mechanics and  Godel's uncertainty
is pretty tenuous. Neither a Quantum Computer or a conventional computer
can compute the 7918th Busy Beaver number, and even though its computable
and finite its very unlikely a Quantum Computer could compute the Ackermann
function in polynomial time which effectively makes it non-computable for
practical purposes.


> > I then maintain the solution to the quantum measurement problem is that
> there can't exist such a solution. It is an unsolvable problem.
>

There are important differences that need to be explained. You can solve
the problem of figuring out if Schrodinger's Cat is alive or dead simply by
opening the box and looking, but there is no box you can open to figure out
what the 8000th Busy Beaver number is.

John K Clark

>
>

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Re: Dark energy-powered devices

[Lawrence Crowell]

An infinite processing does not necessarily require an infinite amount of 
information. A stupid program that just toggles between two states 
endlessly requires a single qubit. A Rabi oscillation of a two state atom 
in a cavity fits the bill, and if it can run forever then in this case as 
there is no input energy needed. Now if you want a program and runs forever 
and that does not come back to the same state except for a finite number of 
times (or if it does return an infinite number of times it is a small 
measure), then you will require an infinite number of states available. 
Entropy of information is S = -k sum_{n=1}^NP_n log(P_n), and an elementary 
case of an infinite number of states, say N → ∞, are states with p_n = 1/N 
and 

S = -k sum_{n=1}^N(1/N) log(1/N) = k sum_{n=1}^N(1/N) log(N) = log(N)

and for N → ∞ this is infinite.

This gets to the heart of a whether nature is discrete or continuous, or 
finite or infinite. We are always faced with a discomfort either way we 
think about this. If things are finite, then we always sense there is 
“more,” and if things are infinite then we run into difficulties 
quantifying that. Infinity is not really a number, but an odd cardinality 
of a set. James Carse wrote a book *Infinite and Finite Games*, which 
compares games of some bounded level of knowability or complexity with 
those unbounded. We have then the notion of finite games as having some 
envelope that defines a “perfect game play,” such as what one can do with 
the game blackjack. Quantum games make even finite games with a known bound 
on a perfect game less knowable, and in some cases unknowable. In fact it 
would take an infinite amount of processing to find the perfect game and 
what the percentage of winning a game is.

Whether space is discrete or continuous is potentially a sort of duality. 
Any causal system must fit in a convex system, such as a bounded region of 
a space, a set or a polytope. Convex systems describe L^p normed spaces 
such that |X|_p = (sum_n x_n^p)^{1/p}. Quantum mechanics is an L^2 system 
such that a sum of probabilities sum_P_n = sum_n|a_n|^2, which is a sort of 
square of a distance in Hilbert space.  The dual of an L^p system according 
to convex sets is an L^q system with 1/p + 1/q = 1 so the dual system is 
also L^2. This is also a metric space system, and it is spacetime. A pure 
stochastic system is a sum of probabilities and is an L^1 system.  The dual 
convex set is a system L^∞, which corresponds to the singular collapse of a 
metric space. This is a completely deterministic system, which can include 
classical mechanics or deterministic Turing machines etc. 

For stochastic systems we have entropy measures. The standard on is the 
Shannon entropy S = -sum_n p_n log(p_n). and there is the relative entropy 
measure S = -sum_n p_n log(p_n/q_n). This is useful for looking at 
conditional entropy, such as S(p|p + dp). It is not hard to see that this 
leads to a metric’

S(P|P+dP) = -½sum_n dp_n^2/p_n

This spans the set of problems with subadditivity. We can generalize this 
with something called the Rényi entropy 

S = 1/(1 – q) ln(sum_n=1^∞p_n^q),

Where this gives the subadditivity rule

S(P + Q) = S(P) + S(Q) + (1 – q)S(P)S(Q).,

where for q = 1 there is no subadditivity. It is also possible to show that 
for q = 1 this gives the Shannon entropy. To do this the limit q → 1 with 
the Rényi entropy and using l’Hospital’s rule. For q = 2 this recovers the 
metric space measure or distance. 

So we can interpolate between these measures. The relationship between 
infinity and finiteness is then evident here. A pure stochastic system is 
difficult to define, but we have a sense that pure randomness is something 
that is not finitely described. In some ways it is not computable, as seen 
with random number generators that give more the appearance of randomness. 
A perfectly random sequence of integers can’t be data compressed beyond 
some measure, and we might be tempted to say they can’t be compressed at 
all. However, even the most random of sequences will contain repeats of 
integers that are compressible. What is this limit? Zurek demonstrated that 
it is not possible to determine if a data compression algorithm is really 
minimal or not. If I compress some data, I can never know whether I have 
the absolutely minimal compression. This is a form of the no-halting 
decision problem, and as this is connected to Cantor diagonalization is 
also ultimately tied to infinity.

However, we have Hawking’s results that the entropy of a black hole is S = 
A/4ℓ_p^2 = N or the number of Planck areas of a black hole horizon. This 
means a discrete structure to spacetime eliminates any infinite content to 
spacetime. So within that setting have some uncertainty on whether it makes 
sense to talk about a continuum of spacetime or whether there really exist 
random numbers in the universe. If the Hilbert spacetime of the universe is 
finite, then in this duality 

Re: Dark energy-powered devices

[John Clark]

In 1972 Bennet  showed that a universal Turing machine could be made both
logically and thermodynamically reversible,[7]
 and
therefore able in principle to perform arbitrarily much computation per
unit of physical energy dissipated, in the limit of zero speed. In 1982 Edward
Fredkin  and Tommaso Toffoli
 proposed the Billiard ball
computer , a
mechanism using classical hard spheres to do reversible computations at
finite speed with zero dissipation, but requiring perfect initial alignment
of the balls' trajectories, and Bennett's review[8]
 compared
these "Brownian" and "ballistic" paradigms for reversible computation.






On Sun, Apr 7, 2019 at 3:21 AM Bruno Marchal  wrote:

> *To sum up: an infinite physical computation does not require an infinite
> amount of energy*


If you want to perform an infinite number of calculations and you don't
have infinite energy available then you'd better have infinite time
available. In 1972 Bennet showed that a reversible Turing Machine could
make a calculation with an arbitrarily small amount of energy but at the
cost of speed; the less energy used the slower the calculation. And if
we're headed for a Big Rip you will not have infinite time.

 John K Clark

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Re: Dark energy-powered devices

[Bruno Marchal]

> On 3 Apr 2019, at 01:36, John Clark  wrote:
> 
> On Tue, Apr 2, 2019 at 5:23 PM Mason Green  > wrote:
> 
> > It appears as though it would indeed be possible to build a device powered 
> > by dark energy. Such a device could keep running forever (as long as the 
> > universe keeps expanding forever and vacuum decay doesn’t occur) and be 
> > able to survive (or prevent) the heat death of the universe. Even proton 
> > decay would not present a problem; new protons could always be created from 
> > the energy generated.
> 
> I agree. 
>  
> > As far as I know, neither of these devices has been proposed before in the 
> > literature; I might have been the first person to come up with them.
> 
> 
> Well... on August 4 2012 I sent this to Fabric Of Reality List: 
>  
> "Could we still extract an infinite amount of energy from the real universe 
> and thus perform an infinite number of calculations? Perhaps.
> 
> Suppose you had 2 spools of string connected together by an axle and you 
> extended the 2 strings to cosmological distances 180 degrees apart from each 
> other. As long as the Dark Energy force between the atoms in the string that 
> were trying to force them apart was not stronger than the attractive 
> electromagnetic force holding the atoms of the string together the string 
> would not expand as the universe expanded, so there would be a tension on the 
> strings, so there would be torque on the spool, so the axle would rotate. The 
> axle could be connected to an electric generator and it seems to me you'd get 
> useful work out of it. Of course you'd have to constantly add more 
> mass-energy in the form of more string to keep it operating, but the amount 
> of mass per unit length of string would remain constant, however because the 
> universe is accelerating the amount of energy per unit length of string you'd 
> get out of it would not remain constant but would increase asymptotically to 
> infinity. If the theories about the Big Rip turn out to be true and the 
> acceleration of the universe is itself accelerating then it should be even 
> easier to extract infinite energy out of the universe; it would just be a 
> simple matter of cosmological engineering. What could go wrong? 
> 
> If you have infinite energy then you can perform an infinite number of 
> calculations, so you could have an infinite number of thoughts, so you would 
> have no last thought (the definition of death), so subjectively you would 
> live forever. Of course the objective universe might have a different opinion 
> on the matter and insist that everything including you had come to an end, 
> but that hardly matters, subjectivity is far more important than objectivity; 
> at least I think so.”  


Doing a physical computation does not require energy, except for the external 
read and write. It is enough to never erase any information. As Landauer found: 
only erasing information requires energy, and as Hao Wang already discovered (I 
think around 1950), but also Church (Lambda-I calculus), there are 
Turing-universal model of computation where no information is ever discarded.

With the combinators, this is illustrated by Turing universal base of 
combinators with no “eliminators”, without kestrel of similar. The kestrel K 
eliminates information (Kxy = x), like a projection, it is not reversible. 

K = [x][y] x (= in Church notation : lambda x lambda y . x). But Church forbade 
using lambda for a variable absent in the core, which is the same as forbid 
elimination of information. Note that quantum computation has to be reversible, 
and never eliminate information (except at some final measurement possible). So 
an infinite physical computation requires only a finite amount of energy. The 
universal dovetailing, which generate and execute all computation, can be 
physically implemented so as using only a finite amount of energy.

But this concerns physical computation. Gödel implicitly and Turing, Post, 
Church and many others will show that the tiny partial computable part of the 
arithmetical reality already implement all computations, including all the 
approximation of all physical computations, and with mechanism, the “real 
physical computation” have to emerge from those computation emulated by the 
arithmetical reality.

This already generates a doubt that physical computation exist, and indeed no 
universal machine can subjectively distinguish a physical computations from a 
purely combinatorical one, or from a purely arithmetical one, or any purely 
mathematical one. But they can detect a difference by doing some measurement, 
given that the physical laws are constrained by Mechanism. That would still be 
undistinguishable from a computation + some special Oracle. No such detection 
have been currently found, and, (finite) machines, although they can suspect 
some oracle (or magic) to be at play, no certainty can be obtained because a 
machine cannot distinguish an