Re: Radioactive Decay States

[Brent Meeker]

On 6/22/2018 3:13 PM, agrayson2...@gmail.com wrote:
*I've been struggling lately with how to interpret a superposition of 
states when it is ostensibly unintelligible, e.g., a cat alive and 
dead simultaneously, or a radioactive source decayed and undecayed 
simultaneously. If we go back to the vector space consisting of those 
"little pointing things", it follows that any vector which is a sum of 
other vectors, simultaneously shares the properties of the components 
in its sum. This is simple and obvious. I therefore surmise that since 
a Hilbert space is a linear vector space, this interpretation took 
hold as a natural interpretation of superpositions in quantum 
mechanics, and led to Schroedinger's cat paradox. I don't accept the 
explanation of decoherence theory, that we never see these 
unintelligible superpositions because of virtually instantaneous 
entanglements with the environment. Decoherence doesn't explain why 
certain bases are stable; others not, even though, apriori, all bases 
in a linear vector space are equivalent. These considerations lead me 
to the conclusion that a quantum superposition of states is just a 
calculational tool, and when the superposition consists of orthogonal 
component states, it allows us to calculate the probabilities of the 
measured system transitioning to the state of any component. In this 
interpretation, essentially the CI, there remains the unsolved problem 
of providing a mechanism for the transition from the SWE, to the 
collapse to one of the eigenfunctions when the the measurement occurs. 
I prefer to leave that as an unsolved problem, than accept the 
extravagance of the MWI, or decoherence theory, which IMO doesn't 
explain the paradoxes referred to above, but rather executes what 
amounts to a punt, claiming the paradoxes exist for short times so can 
be viewed as nonexistent, or solved. AG. *


If you're willing to take QM as simply a calculational tool, then QBism 
solve the problem of wf collapse.


Brent

--
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Primary matter

[Brent Meeker]

On 6/22/2018 4:41 AM, Bruno Marchal wrote:

This does not mean that a conscious machine is necessarily more efficacious on 
all task,

What is the added undecideable sentence implied by consciousness?

“I am conscious”.


What does that speed up?  Does the speed up from adding an undeciable 
sentence suffer from Goodheart's curse?


Brent

--
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Fwd: "Finally, A Problem That Only Quantum Computers Will Ev

[Lawrence Crowell]

The upshot is that with forrelation equivalent to the BPQ problem a match 
occurs with few oracles that with PH. An oracle is a sort of hypercomputing 
system outside the Church-Turing thesis or λ-calculus. If BPQ requires 
fewer oracle inputs it means it is a closer approximation to a hyper-Turing 
machine or the Löbian machine. This is a different domain in the theory of 
computation.

LC

On Thursday, June 21, 2018 at 8:20:35 PM UTC-5, cdemorsella wrote:
>
> The birth of a fundamentally distinct new class of problems.
>
> BQP has carved out a realm of its own... beyond the reach of the combined 
> set  PH =  {P, NP} 
>
> Chris
>
> On Thu, Jun 21, 2018 at 3:52 PM, Brent Meeker
> > wrote:
>
>
>
>  Forwarded Message 
>
>
>
> https://www.quantamagazine.org/finally-a-problem-that-only-quantum-computers-will-ever-be-able-to-solve-20180621/
> ref: https://eccc.weizmann.ac.il/report/2018/107/
> ...
>
> *Here’s the problem. Imagine you have two random number generators, each 
> producing a sequence of digits. The question for your computer is this: Are 
> the two sequences completely independent from each other, or are they 
> related in a hidden way (where one sequence is the “Fourier transform” of 
> the other)? Aaronson introduced this “forrelation” problem in 2009 and 
> proved that it belongs to BQP. That left the harder, second step — to prove 
> that forrelation is not in PH.*
>
> *Which is what Raz and Tal have done, in a particular sense. Their paper 
> achieves what is called “oracle” (or “black box”) separation between BQP 
> and PH. This is a common kind of result in computer science and one that 
> researchers resort to when the thing they’d really like to prove is beyond 
> their reach.*
>
> *The actual best way to distinguish between complexity classes like BQP 
> and PH is to measure the computational time required to solve a problem in 
> each. But computer scientists “don’t have a very sophisticated 
> understanding of, or ability to measure, actual computation time,” said 
> Henry Yuen, a computer scientist at the University of Toronto.*
>
> *So instead, computer scientists measure something else that they hope 
> will provide insight into the computation times they can’t measure: They 
> work out the number of times a computer needs to consult an “oracle” in 
> order to come back with an answer. An oracle is like a hint-giver. You 
> don’t know how it comes up with its hints, but you do know they’re 
> reliable.*
>
> *If your problem is to figure out whether two random number generators are 
> secretly related, you can ask the oracle questions such as “What’s the 
> sixth number from each generator?” Then you compare computational power 
> based on the number of hints each type of computer needs to solve the 
> problem. The computer that needs more hints is slower.*
>
> *“In some sense we understand this model much better. It talks more about 
> information than computation,” said Tal.*
>
> *The new paper by Raz and Tal proves that a quantum computer needs far 
> fewer hints than a classical computer to solve the forrelation problem. In 
> fact, a quantum computer needs just one hint, while even with unlimited 
> hints, there’s no algorithm in PH that can solve the problem. “This means 
> there is a very efficient quantum algorithm that solves that problem,” said 
> Raz. “But if you only consider classical algorithms, even if you go to very 
> high classes of classical algorithms, they cannot.” This establishes that 
> with an oracle, forrelation is a problem that is in BQP but not in PH.*
>
> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to everything-li...@googlegroups.com .
> To post to this group, send email to everyth...@googlegroups.com 
> .
> Visit this group at https://groups.google.com/group/everything-list.
> For more options, visit https://groups.google.com/d/optout.
>
>

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Fwd: "Finally, A Problem That Only Quantum Computers Will Ev

['Chris de Morsella' via Everything List]

True, but as you mentioned, and we are in agreement this is a fundamentally new 
class of problem. Whether it turns out to be of practical utility or remains as 
an interesting oddball is yet to be determined.Chris

Sent from Yahoo Mail on Android 
 
  On Fri, Jun 22, 2018 at 1:42 PM, John Clark wrote:   On 
Thu, Jun 21, 2018 at 9:20 PM, 'Chris de Morsella' via Everything List 
 wrote:


​> ​The birth of a fundamentally distinct new class of problems.BQP has carved 
out a realm of its own... beyond the reach of the combined set  PH =  {P, NP} 

This new result does not prove a quantum computer could solve all 
nondeterministic polynomial time problem s  in polynomial time but it does 
prove that even if P=NP and even if we had an algorithm that could solve NP 
problems on a conventional computer in polynomial time there would still be a 
class of problems a conventional computer couldn’t solve efficiently but a 
quantum computer could.  This class of very exotic problems may be of 
fundamental interest in themselves or they may be interesting for no reason 
other than that a conventional computer can’t solve them.​ 
 John K Clark​



-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
  

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Radioactive Decay States

[agrayson2000]

On Friday, June 22, 2018 at 10:13:37 AM UTC, Lawrence Crowell wrote:
>
> On Thursday, June 21, 2018 at 6:48:53 PM UTC-5, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, June 21, 2018 at 11:18:25 PM UTC, Lawrence Crowell wrote:
>>>
>>> The emergent nuclear interaction occurs on a time scale of 
>>> 10^{-22}seconds. The superposition of a decayed and nondecayed nucleus 
>>> occurs in that time before decoherence.
>>>
>>
>> Is that calculated / postulated if the radioactive source interacts with 
>> its environment? Can't it be isolated for a longer duration? If so, what 
>> does that imply about being in the pure states mentioned above? AG 
>>
>
> Quantum physics experiments on nonlocality are done usually with optical 
> and IR energy photons. The reason is that techniques exist for making these 
> sort of measurements and materials are such that one can pass photons 
> through beam splitters or hold photons in entanglements in mirrored 
> cavities and the rest. At higher energy up into the X-ray domain such 
> physics becomes very difficult. At intermediate energy where you have 
> nuclear physics of nucleons and mesons and further at higher energy of 
> elementary particles things become impossible. This is why in QFT there are 
> procedures for constructing operators that have nontrivial commutations on 
> and in the light cone so nonlocal physics does not intrude into 
> phenomenology. Such physics is relevant on a tiny scale compared to the 
> geometry of your detectors.
>
> LC
>

*I've been struggling lately with how to interpret a superposition of 
states when it is ostensibly unintelligible, e.g., a cat alive and dead 
simultaneously, or a radioactive source decayed and undecayed 
simultaneously. If we go back to the vector space consisting of those 
"little pointing things", it follows that any vector which is a sum of 
other vectors, simultaneously shares the properties of the components in 
its sum. This is simple and obvious. I therefore surmise that since a 
Hilbert space is a linear vector space, this interpretation took hold as a 
natural interpretation of superpositions in quantum mechanics, and led to 
Schroedinger's cat paradox. I don't accept the explanation of decoherence 
theory, that we never see these unintelligible superpositions because of 
virtually instantaneous entanglements with the environment. Decoherence 
doesn't explain why certain bases are stable; others not, even though, 
apriori, all bases in a linear vector space are equivalent. These 
considerations lead me to the conclusion that a quantum superposition of 
states is just a calculational tool, and when the superposition consists of 
orthogonal component states, it allows us to calculate the probabilities of 
the measured system transitioning to the state of any component. In this 
interpretation, essentially the CI, there remains the unsolved problem of 
providing a mechanism for the transition from the SWE, to the collapse to 
one of the eigenfunctions when the the measurement occurs. I prefer to 
leave that as an unsolved problem, than accept the extravagance of the MWI, 
or decoherence theory, which IMO doesn't explain the paradoxes referred to 
above, but rather executes what amounts to a punt, claiming the paradoxes 
exist for short times so can be viewed as nonexistent, or solved. AG. *

>  
>
>>
>>> LC
>>>
>>> On Thursday, June 21, 2018 at 5:50:12 PM UTC-5, agrays...@gmail.com 
>>> wrote:

 Why don't we observe the pure states, decayed + undecayed, or decayed - 
 undecayed? TIA, AG

>>>

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Fwd: "Finally, A Problem That Only Quantum Computers Will Ev

[John Clark]

On Thu, Jun 21, 2018 at 9:20 PM, 'Chris de Morsella' via Everything List <
everything-list@googlegroups.com> wrote:

​> ​
> The birth of a fundamentally distinct new class of problems.
> BQP has carved out a realm of its own... beyond the reach of the combined
> set  PH =  {P, NP}
>

This new result does not prove a quantum computer could solve all
nondeterministic polynomial time problem s  in polynomial time but it does
prove that even if P=NP and even if we had an algorithm that could solve NP
problems on a conventional computer in polynomial time there would still be
a class of problems a conventional computer couldn’t solve efficiently but
a quantum computer could.  This class of very exotic problems may be of
fundamental interest in themselves or they may be interesting for no reason
other than that a conventional computer can’t solve them.
​

 John K Clark​

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Do we live within a Diophantine equation?

[John Clark]

On Thu, Jun 21, 2018 at 5:09 PM, Jason Resch  wrote:

​>* ​*
> *The only thing I am asking is:*
> *1) Physics -> Brains, Cars, Atoms, Etc.*
> *2) ??? -> Physics -> Brains, Cars, Atoms, Etc.*
> *Do we have enough information to decide between the above two theories?
> Have we really ruled out anything sitting below physics?*
>

If I define physics as the thing that can tell the difference between a
correct computation and a incorrect computation and between a corrupted
memory and a uncorrupted memory, and as long as we're at this philosophic
meta level that's not a  b ad definition, then I don't think anything
is below physics.


> ​>>​
>> Then why is brain damage a big deal? Why do I need my brain to think?
>>
>
> ​>* ​*
> *The base computations that implement your brain may be sub-routines of a
> larger computation,*
>

If true then that is an example of something physics can do but mathematics
can not. And I have to say that is a mighty damn important sub-routine!

> ​>>​
>> Without physics 2+2=3 would work just as well as 2+2=4 and insisting the
>> answer is 4 would just be an arbitrary convention of no more profundity
>> than the rules that tell us when to say "who" and when to say "whom".
>>
>> ​> ​
> *For any computation to make sense, you need to be working under some
> definitions of integers and relations between them. *
>

​Definitions are made for our convenience, they do not create physical
objects. And there are an infinite number of ways integers and
the relations between them could have been defined, so why did
mathematicians pick the specific definition that they did? Because that's
the only one that conforms with the physical world, and thats why
mathematics is the best language to describe physics.


> * ​> ​Without that, you can't even define what a Turing machine or what a
> computation is.*
>

​I don't need to describe either one because I've got something much much
better than definitions, examples.​

*​>​I can imagine a computation without a physical universe. *
>

​I can't.​


​>* ​*
> *I can't imagine a computation without some form of arithmetical law.*
>

​I can. A Turing Machine will just keep on doing what its doing regardless
of the English words or mathematical equations you use to describe its
operation.

> ​>>​
>> As far as simulation is concerned in some circumstances we could figure
>> out that we live in a virtual reality, assuming the computer that is
>> simulating us does not have finite capacity we might devise experiments
>> that stretch it to its limits and we'd start to see glitches. Or the
>> beings doing the simulating could simply tell us, as they have complete
>> control over everything in our world so they would certainly be able
>> to convince us they’re telling the truth.
>>
>>
> ​>​
> T
> *hey could convince us something strange is going on, but they couldn't
> convince us they weren't lying about whatever they might be telling us
> about the architecture that is running the simulation.​ ​This follows
> directly from the Church-Turing thesis. The Church-Turing thesis says any
> program or Turing Machine can be executed/emulated by any computer.
> Therefore, no program or machine can determine whether it is being computed
> by or emulated by any particular Turing machine vs. any other that might be
> emulating it.*
>

​OK, they could prove they're simulating us but they couldn't prove the
logical hardware architecture of their machine worked the way they said it
did, however in some circumstances they could provide some pretty
compelling evidence that they were telling the truth. For example suppose
they found out how to solve all non-deterministic polynomial time problems
in polynomial time and that's how they were able to make a computer
powerful enough to simulate our universe. And they said they themselves
were being simulated and their simulators told them how to do this and now
they are passing the secret on to us. We try it and pretty soon we have
made our own simulated universe with intelligent, and presumably conscious,
beings in it. After that I’d tend to believe what they said.

​>>​
>> It was discovered more than 30 years ago that if Quarks didn't exist
>> inside protons then high speed electrons would scatter off protons
>> differently than the way they are observed to scatter. If you assume Quarks
>> don't exist then there are consequences, those high speed electrons will
>> behave in ways that surprise you. In other words physics told you that your
>> assumption was incorrect.
>>
>
> *​>​Okay. So you do accept relations between mathematical objects can
> support your consciousness?*
>

​A mathematical object is just something that has been defined in the
language of mathematics, J K Rowling defined Hogwarts Castle in the
language of English but that doesn't mean either of them must exist. There
are an infinite number of ways mathematicians could have defined a quark
but they picked the one that physics told them to, the one that scattered
elec

Re: Do we live within a Diophantine equation?

[smitra]

On 21-06-2018 23:46, Brent Meeker wrote:

On 6/21/2018 6:33 AM, smitra wrote:

On 21-06-2018 05:01, Brent Meeker wrote:

On 6/20/2018 6:30 PM, smitra wrote:

On 19-06-2018 23:22, Brent Meeker wrote:

On 6/18/2018 6:03 PM, smitra wrote:

On 17-06-2018 22:42, Jason Resch wrote:

Hi Lawrence,

Is the evolution of states of the wave function computable? If so 
then

the result of MRDP implies it is Diophantine.

Jason


Or you could try to see if QM could be a meta-theory that arises 
when you try to give a statistical description of the set of all 
these Diophantine sets. I tried to do something similar with the 
set of algorithms a few years ago, getting a half-baked result, 
some hints at how quantum field theory could arise from this.


You want to compute the probability that an observer that's 
encoded by some mathematical structure has some given information 
content. So, if you observe the outcome of an experiment, that's 
information in your brain.


Which is the QBism interpretation of QM.  If you take the view that 
QM
is about predicting and explaining what one will see, there's no 
point

in going further...the rest is metaphysics.

Brent



QM should then emerge as an effective theory and the correct 
interpretation should also follow.


?? QBism is an interpretation.

Brent


If we derive QM from a more fundamental principle then that is likely 
to single out one particular interpretation of QM as the correct one. 
So, which interpretation is correct is then no longer a philosophical 
or metaphysical question, it's something that can be probed 
experimentally by testing the underlying theory from which QM is 
derived.


So you're considering finding a more fundamental theory such that QM
will be a consequence or effective theory.   Of course that may
involve questions of interpretation of the more fundamental theory.

Brent


Yes, and there are good reasons to believe that even if the MWI is the 
correct interpretation that it is unlikely to be the last word. There is 
a problem with deriving the Born rule, also simply interpreting the 
meaning of probability from within the MWI is problematic. Also, if 
another sort of a multiverse exists besides the quantum multiverse, then 
in any physics experiment you're going to measure the totality of all 
the effects of all multiverses in which you have exact copies. The 
effects of these other multiverses e.g. as provided by inflation theory 
cannot necessarily be dismissed as trivial (e.g. by saying that it leads 
to uncertainty of the quantum state, the effects of which can be 
absorbed in a density matrix), as counting states with the restriction 
that the same observer is present per my argument in the previous 
posting, also leads to quantum-like laws.


Saibal

--
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Primary matter

[Bruno Marchal]

> On 21 Jun 2018, at 12:55, Telmo Menezes  wrote:
> 
> On 21 June 2018 at 00:53, Brent Meeker  wrote:
>> 
>> 
>> On 6/20/2018 4:51 AM, Telmo Menezes wrote:
>>> 
>>> Hi Bruno,
>>> 
> I follow your reasoning, from one of your recent articles. This leaves
> me dissatisfied, but if I try to verbalize this dissatisfaction I feel
> stuck in a loop. Perhaps this illustrates your point.
 
 
 We might need to do some detour about what it would mean to explain
 consciousness, or matter.
 I might ask myself if you are not asking too much, perhaps. Eventually,
 something has to remain unexplainable for reason of self-consisteny. I
 suspect it will be just where our intuition of numbers or combinators, or 
 of
 the distinction finite/infinite comes from (assuming mechanism), or just 
 why
 we trust the doctor!
>>> 
>>> I thought about it for some time. It seems that at a meta level, we
>>> are always stuck in this situation of "give me one miracle for free
>>> and everything else becomes explainable". The miracle can be matter,
>>> or consciousness, or arithmetic.
>> 
>> 
>> Do you see that is just another form of my circle of virtuous explanation.
>> Start wherever you understand or accept the starting point and then you can
>> go around the circle and get to everything else.
> 
> I see your point and even concede that it might be the wise approach
> for many things, but I don't think one can "get to everything else"
> this way.
> 
> The problem with my analogy with heliocentrism/geocentrism is that
> these are, in the end, compatible -- but the same doesn't seem to
> apply to materialism/computationalism. I think that Bruno proves
> convincingly that the two are incompatible. I'm not sure if you are
> convinced by the UDA argument or not. Are you?
> 
> If one takes this incompatibility seriously, things become a bit more
> tricky. In this case, and to expand on what I was suggesting:
> 
> - There is a set of beliefs M that are consistent with materialism;
> - There is a set of beliefs C that are consistent with computationalism;
> - The intersection between M and C, let's call it A, is non-empty but;
> - There are justified true beliefs that belong to C if one starts from
> comp, but not to A, let's say C*
> - There are justified true beliefs that belong to M if one starts from
> materialism, but not to A, let's say M*
> - Furthermore, there is empirical data that fits C* and not M*, and 
> vice-versa.

I might miss something. Empirical data fits with C*, and might fit M*, but only 
by abandoning M (although consistent with M’s appearance).

Bruno



> 
> Most people nowadays live only within A. It used to be the case that
> people lived with A + R (R is some set of religious beliefs), and that
> is more or less what enabled us to build civilization. R might be
> wrong, but it is clearly useful (and also has a very dark side, of
> course). A-only-living is the domain of mid-life crisis, existential
> despair, hating Mondays and scientific utilitarianism. M* is the
> domain of the emergentist project of neuroscience, and I would argue
> is the proto-religion of many contemporary scientists, and especially
> militant atheists. C* is the domain of neoplatonism. Not surprisingly,
> it irritates M* people, and vice-versa.
> 
> On a practical level, it makes sense to operate in M* while performing
> surgery, but it does not make sense to restrict oneself to M* when
> trying to answer fundamental questions. I think that's the point where
> it becomes religious dogmatism - R*.
> 
> Telmo.
> 
>> Brent
>> 
>> --
>> You received this message because you are subscribed to the Google Groups
>> "Everything List" group.
>> To unsubscribe from this group and stop receiving emails from it, send an
>> email to everything-list+unsubscr...@googlegroups.com.
>> To post to this group, send email to everything-list@googlegroups.com.
>> Visit this group at https://groups.google.com/group/everything-list.
>> For more options, visit https://groups.google.com/d/optout.
> 
> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to everything-list+unsubscr...@googlegroups.com.
> To post to this group, send email to everything-list@googlegroups.com.
> Visit this group at https://groups.google.com/group/everything-list.
> For more options, visit https://groups.google.com/d/optout.

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Primary matter

[Bruno Marchal]

> On 21 Jun 2018, at 06:44, Brent Meeker  wrote:
> 
> 
> 
> On 6/11/2018 8:32 AM, Bruno Marchal wrote:
>> Hi Telmo,
>> 
>> 
>>> On 11 Jun 2018, at 13:53, Telmo Menezes  wrote:
>>> 
>>> Hi Bruno,
>>> 
>>> Sorry for the delay, had a friend visiting.
>> 
>> No problem. From tomorrow (Tuesday) to Friday, I have many oral exams (+ a 
>> conference in Nivelles, a city nearby). So take your time to comment and 
>> express the dissatisfaction.
>> 
>> 
>> 
>> 
>>> 
 Ah! Let me try to answer.Keep in mind that I assume elementary arithmetic 
 and thus computations, etc.
 (I am not sure I need YD here, but it can help).
 
 
> - Why does consciousness even exist?
 Consciousness is somehow the doubt between consistency and truth (<>p v p).
 
 All universal number self introspecting meet this, and it is felt as 
 immediately obvious, and thus true, and undoubtable, yet non rationally 
 justifiable, and even non definable.
>>> I follow your reasoning, from one of your recent articles. This leaves
>>> me dissatisfied, but if I try to verbalize this dissatisfaction I feel
>>> stuck in a loop. Perhaps this illustrates your point.
>> 
>> We might need to do some detour about what it would mean to explain 
>> consciousness, or matter.
>> I might ask myself if you are not asking too much, perhaps. Eventually, 
>> something has to remain unexplainable for reason of self-consisteny. I 
>> suspect it will be just where our intuition of numbers or combinators, or of 
>> the distinction finite/infinite comes from (assuming mechanism), or just why 
>> we trust the doctor!
>> 
>> 
>> 
 It goes from the rough dissociated universal consciousness of Q to the 
 elaborate self-consciousness of PA or ZF, or us.
 
 
 
 
 
> Darwinism does not seem to require it.
 It does. When the machine opts for <>p in the doubt between p and <>p, if 
 it let it go, in some sense, it transforms itself into a more speedy and 
 more efficacious machine, with respect to its most probable history.
 So, consciousness brings a self-speedable ability, which is quite handy 
 for self-moving being living in between a prey and a predator.
>>> I'm not convinced. Consider a simple computer simulation where agents
>>> are controlled by evolving rules. Agents can eat blue or red pills.
>>> 90% of the time blue pills give them energy and red pills cause
>>> damage. 10% of the time the opposite happens. It is not possible to
>>> know before eating a pill. Let's say the rule system evolves to make
>>> the agents always eat blue pills and never red pills. Most of the time
>>> this helps the agents, precisely because it assumes the most probable
>>> histories. This is a simplified version of the sort of "decisions"
>>> that evolution makes, and I would say that it is reasonable to assume
>>> that our own evolutionary story consists of the accumulation of a
>>> great number of such decisions. I still don't see how consciousness
>>> makes a difference in such a mechanism.
>> The reason why consciousness makes the difference is not related to the 
>> environment, but is intrinsic to the machine itself.
>> 
>> I am aware to be quick on this, but the reason is a bit mathematically 
>> involved, and again, depends crucially of a discovery made by Gödel, and 
>> exposed in his paper “the length of proof”.
>> 
>> Gödel discovered the existence that if you have some essentially undecidable 
>> theory, like RA, PA, ZF, there are always undecidable sentences, like <>RA 
>> in RA, of <>ZF in ZF, etc, then if you add an undecidable sentence (in the 
>> theory T, say) to T, you get a theory which not only will prove infinitely 
>> more sentence than T, but that infinitely many proofs will be arbitrarily 
>> shorter in T+the undecidable sentence than the proof of it in T, making 
>> “somehow” T+the undecidable sentence much faster than T.
>> 
>> Even if the added sentence is false, we get that speeding-up
> 
> ?? What does it mean that it is false?  I thought "true" was undefinable. 

True about the machine M is not definable by the machine M, but can be defined 
by some cognitively richer machine. Arithmetical truth is definable in set 
theory, analysis, etc.
Here true meant “satisfied by the standard model of arithmetic, i.e. the usual 
structure (N, 0, +, *).



> Do you mean it contradicts some theorem of T? 

No. I mean false, not inconsistent. Take the sentence "PA proves '0=1’ ”. It is 
false, but by incompleteness you cannot prove it in PA. (PA cannot prove it). 
So, you can add the sentence “PA proves 0=1” to PA, and you still have a 
consistent (yet unsound) theory. And the speed-up will still apply. 


> But in that case it would make T+the undecidable (false) sentence speed up 
> the proof of every sentence.

T + the undecidable sentence remains consistent. The arithmetical []f -> f is 
not provable, and indeed the modal []p -> p not a theorem of G. It is a theorem 
of G*, and only

Re: Primary matter

[Bruno Marchal]

> On 20 Jun 2018, at 13:51, Telmo Menezes  wrote:
> 
> Hi Bruno,
> 
>>> I follow your reasoning, from one of your recent articles. This leaves
>>> me dissatisfied, but if I try to verbalize this dissatisfaction I feel
>>> stuck in a loop. Perhaps this illustrates your point.
>> 
>> 
>> We might need to do some detour about what it would mean to explain 
>> consciousness, or matter.
>> I might ask myself if you are not asking too much, perhaps. Eventually, 
>> something has to remain unexplainable for reason of self-consisteny. I 
>> suspect it will be just where our intuition of numbers or combinators, or of 
>> the distinction finite/infinite comes from (assuming mechanism), or just why 
>> we trust the doctor!
> 
> I thought about it for some time. It seems that at a meta level, we
> are always stuck in this situation of "give me one miracle for free
> and everything else becomes explainable". The miracle can be matter,
> or consciousness, or arithmetic. I believe I have to accept this state
> of affairs for the reason of self-consistency that you express above,
> but I'm human and I still feel the curiosity. Epistemic limits are
> hard to accept.
> 
> Could it even be that it doesn't make sense to say that materialism is
> true or false, or that idealism is true or false and so on? I mean in
> the same sense that the sun is not really the center of the solar
> system (the center is just a human mental model), but assuming it
> makes it simpler to describe the orbits. Perhaps assuming materialism
> makes it easier to describe certain aspects of nature, while assuming
> comp makes it easier to describe others, but in the end we always have
> to sacrifice something. Model realism at the meta level…


We have to sacrifice something. But the point is that if the Brain or the body 
is Turing emulable, then we have to sacrifice materialism. 
FAPP we lost nothing, unless we lose the appearance of matter, in which case 
the observation of matter refutes comp, but up to now we don’t loss them, and 
at least we have a rather simple explanation of consciousness, which has to be 
sacrificed if we want to keep matter in the ontology, but then I am still 
waiting for any non mechanist theory of consciousness (beyond the fairy tales).




> 
 It goes from the rough dissociated universal consciousness of Q to the 
 elaborate self-consciousness of PA or ZF, or us.
 
 
 
 
 
> Darwinism does not seem to require it.
 
 It does. When the machine opts for <>p in the doubt between p and <>p, if 
 it let it go, in some sense, it transforms itself into a more speedy and 
 more efficacious machine, with respect to its most probable history.
 So, consciousness brings a self-speedable ability, which is quite handy 
 for self-moving being living in between a prey and a predator.
>>> 
>>> I'm not convinced. Consider a simple computer simulation where agents
>>> are controlled by evolving rules. Agents can eat blue or red pills.
>>> 90% of the time blue pills give them energy and red pills cause
>>> damage. 10% of the time the opposite happens. It is not possible to
>>> know before eating a pill. Let's say the rule system evolves to make
>>> the agents always eat blue pills and never red pills. Most of the time
>>> this helps the agents, precisely because it assumes the most probable
>>> histories. This is a simplified version of the sort of "decisions"
>>> that evolution makes, and I would say that it is reasonable to assume
>>> that our own evolutionary story consists of the accumulation of a
>>> great number of such decisions. I still don't see how consciousness
>>> makes a difference in such a mechanism.
>> 
>> The reason why consciousness makes the difference is not related to the 
>> environment, but is intrinsic to the machine itself.
>> 
>> I am aware to be quick on this, but the reason is a bit mathematically 
>> involved, and again, depends crucially of a discovery made by Gödel, and 
>> exposed in his paper “the length of proof”.
>> 
>> Gödel discovered the existence that if you have some essentially undecidable 
>> theory, like RA, PA, ZF, there are always undecidable sentences, like <>RA 
>> in RA, of <>ZF in ZF, etc, then if you add an undecidable sentence (in the 
>> theory T, say) to T, you get a theory which not only will prove infinitely 
>> more sentence than T, but that infinitely many proofs will be arbitrarily 
>> shorter in T+the undecidable sentence than the proof of it in T, making 
>> “somehow” T+the undecidable sentence much faster than T.
>> 
>> Even if the added sentence is false, we get that speeding-up (even for 
>> interesting sentences as Eric Vandenbussche convinced me (He thought that 
>> this was false, but eventually he proved that statement true).
>> 
>> Blum has got a similar result in computer science, and eventually Blum & 
>> Marquez characterised the spedable machine/set (he used the w_i instead of 
>> the phi_i), and he obtained the 

Re: Do we live within a Diophantine equation?

[Bruno Marchal]

> On 21 Jun 2018, at 23:46, Brent Meeker  wrote:
> 
> 
> 
> On 6/21/2018 6:33 AM, smitra wrote:
>> On 21-06-2018 05:01, Brent Meeker wrote:
>>> On 6/20/2018 6:30 PM, smitra wrote:
 On 19-06-2018 23:22, Brent Meeker wrote:
> On 6/18/2018 6:03 PM, smitra wrote:
>> On 17-06-2018 22:42, Jason Resch wrote:
>>> Hi Lawrence,
>>> 
>>> Is the evolution of states of the wave function computable? If so then
>>> the result of MRDP implies it is Diophantine.
>>> 
>>> Jason
>> 
>> Or you could try to see if QM could be a meta-theory that arises when 
>> you try to give a statistical description of the set of all these 
>> Diophantine sets. I tried to do something similar with the set of 
>> algorithms a few years ago, getting a half-baked result, some hints at 
>> how quantum field theory could arise from this.
>> 
>> You want to compute the probability that an observer that's encoded by 
>> some mathematical structure has some given information content. So, if 
>> you observe the outcome of an experiment, that's information in your 
>> brain.
> 
> Which is the QBism interpretation of QM.  If you take the view that QM
> is about predicting and explaining what one will see, there's no point
> in going further...the rest is metaphysics.
> 
> Brent
> 
 
 QM should then emerge as an effective theory and the correct 
 interpretation should also follow.
>>> 
>>> ?? QBism is an interpretation.
>>> 
>>> Brent
>> 
>> If we derive QM from a more fundamental principle then that is likely to 
>> single out one particular interpretation of QM as the correct one. So, which 
>> interpretation is correct is then no longer a philosophical or metaphysical 
>> question, it's something that can be probed experimentally by testing the 
>> underlying theory from which QM is derived.
> 
> So you're considering finding a more fundamental theory such that QM will be 
> a consequence or effective theory.   Of course that may involve questions of 
> interpretation of the more fundamental theory.

Not if you start from the interpretation, which is reasonable for elementary 
arithmetic. Of course, if you start from the combinators, that might be more 
difficult, but has still been solved (by set theoretical model, with the work 
of Dana Scott, notably).

In logic, interpretation is part of the mathematics, and with mechanism, it is 
part of the arithmetic reality. You need only weak version of the excluded 
middle.

Bruno



> 
> Brent
> 
> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to everything-list+unsubscr...@googlegroups.com.
> To post to this group, send email to everything-list@googlegroups.com.
> Visit this group at https://groups.google.com/group/everything-list.
> For more options, visit https://groups.google.com/d/optout.

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Do we live within a Diophantine equation?

[Bruno Marchal]

> On 21 Jun 2018, at 21:49, John Clark  wrote:
> 
> 
> 
> On Thu, Jun 21, 2018 at 1:32 PM, Jason Resch  > wrote:
> 
> ​> ​We can use physical analogies to reason about mathematics,
> We can't reason about ANYTHING without physics, that's why  our  physical 
> brain is so handy.
> 
> 

Because we are material, but that makes not matter primitive. There is a 
“begging the question” here.



>  
> ​> ​but doing so cannot prove that physical things are more fundamental than 
> mathematical things.
> 
> Then why is brain damage a big deal? Why do I need my brain to think?

You don’t. You need only an apparent stable brain to think in an apparent 
stable physical realities,




>  
> ​> ​Accept for one second that a platonic computation could be conscious. 
> I'll be damned if I understand how a unique platonic computation could even 
> exist much less be conscious. I don't see any way to tell the difference 
> between the one correct platonic computation from the infinite number of 
> incorrect ones. Without physics 2+2=3 would work just as well as 2+2=4 and 
> insisting the answer is 4 would just be an arbitrary convention of no more 
> profundity than the rules that tell us when to say "who" and when to say 
> "whom". 
> 
> 

That makes no sense. Without a physical universe, 2+2=3 would still contradict 
RA or PA, or the arithmetical reality.




>  
> ​> ​(we can debate this later)  Accepting this premise, do you agree that the 
> conscious computation cannot determine whether it is running on a platonic 
> computer vs. a physical computer? 
> To answer that question I'd have to have at least some understanding about 
> how a platonic computer could work, and I have absolutely no idea.
> 

Because when I give your reference where this explained, you answer that books 
cannot think, indeed of looking to the books to see why thinking, with 
Mechanism, involves only the additive and multiplicative assumptions, and 
nothing physical needs to be referred through. The physical is needed only for 
our human communication, but that does not make it primary, like physicalism 
demands.



> As far as simulation is concerned in some circumstances we could figure out 
> that we live in a virtual reality, assuming the computer that is simulating 
> us does not have finite capacity we might devise experiments that stretch it 
> to its limits and we'd start to see glitches. Or the beings doing the 
> simulating could simply tell us, as they have complete control over 
> everything in our world so they would certainly be able to convince us 
> they’re telling the truth. 
> 
> ​> ​If I run software, any software, it can never perform any computation 
> that can reveal to it anything about what is ultimately executing it.  I 
> might run a Nintendo game,
> If I'm a intelligent being living in that Nintendo game I could figure out 
> that my enviroment was unbounded but finite and consisted of 57,344 cells 
> arranged in a 256 by 224 grid with each cell having a finite number of 
> states, and from that figure out the minimum size memory the simulating 
> computer  would have to have. People have done something similar with our own 
> observable universe and figure that the computer simulating its running on 
> must have between 10^122 and 10^124 bits of memory.  
> 
> The only thing I know about how the hardware of this universe simulating 
> computer works is that it must have some way of telling the difference 
> between a correct computation and a incorrect computation and between a 
> corrupted memory and a uncorrupted memory. Actually that might not be a bad 
> definition of "physics".
> 
> ​> ​You are willing to accept that relations between quarks and electrons can 
> implement and support your consciousness.
> 
> ​Yes,​ 
> 
> ​> ​Quarks and electrons are fundamentally mathematical objects (they can't 
> be described in terms of anything simpler than their mathematical 
> properties). 
> 
> It was discovered more than 30 years ago that if Quarks didn't exist inside 
> protons then high speed electrons would scatter off protons differently than 
> the way they are observed to scatter. If you assume Quarks don't exist then 
> there are consequences, those high speed electrons will behave in ways that 
> surprise you. In other words physics told you that your assumption was 
> incorrect.
>  
> ​>​Integers are also mathematical objects (they can't be described in terms 
> of anything simpler than their mathematical properties).
> Why do you think that the only mathematical objects that can sustain 
> computation are quarks and electrons?
> 
> ​Because Platonic integers can be arranged in any way but quarks and 
> electrons can not be, when they can not we call that "wrong"; when the wings 
> of your airplane fall off that is physics telling you that one of your 
> calculations was wrong. Without physics Platonic integers are never wrong, 
> 2+2=3, 2+2=4, 2+2=5 its all fine, one relation is as 

Re: Do we live within a Diophantine equation?

[Bruno Marchal]

> On 21 Jun 2018, at 19:11, John Clark  wrote:
> 
> On Wed, Jun 20, 2018 at 9:00 PM, Jason Resch  > wrote:
> 
> ​>> ​If mathematics was more fundamental than physics then Intel would be a 
> ridiculously unnecessary company and would have gone  bankrupt decades ago, 
> but physics can clearly do things that mathematics can't and so the company 
> is thriving 
> 
> ​> ​That doesn't follow.​ ​It could be that:
> Number relations -> Platonic computations -> Conscious Computations ->​ [...]
> 
> No that could not be because it doesn't conform with what we observe. When 
> the matter in our brains changes our consciousness changes and when our 
> consciousness changes the matter in our brain changes; that wouldn't be the 
> case if consciousness were created by some sort of mystical Platonic heebie 
> jeebie that did not involve matter or the laws of physics.

That is false, but you need to get through step 3, so I will not insist, 
especially you are invalid below.



> 
> ​>>​If neither matter nor physics existed but "1+1 =2" did then "1+1 =3" 
> would exist too, one of those statement is fiction and one id nonfiction but 
> the only difference between the 2 is the way physics treats matter, for 
> example 2 merged hydrogen atoms behave differently in a gravitational field 
> than 3 do.
> 
> ​>​Is "1", "2", and "3" have any meaning, then "1+1 ~= 3".
> 
> I agree, but if not even one physical thing existed then the consequences of 
> 1+1 ~= 3 would be exactly the same as 1+1=3

That is simply invalid, even before step 3. But I guess Jason will tell you 
this.

Bruno



> and that would be none at all because the concepts "1","2","3", "equal", and 
> even "not" would have no meaning. In the final analysis you always need 
> physics to tell you the difference between fiction and nonfiction; if your 
> bridge falls down then some idea you employed in building that bridge was a 
> fiction. If physics did not exist then falsehood would work just as well as 
> truth because neither would have any consequences.
>  
> ​>​You understand that we could be in a matrix type of simulation.
> 
> ​Yes, but some *thing* must be performing all those calculations needed for 
> the simulation, and that couldn't be done if there were no things.
>  
> ​> ​If you accept the Church-Turing Thesis, then you know no program can ever 
> determine what machine is executing it. 
> I'm not exactly sure what "it" in the above refers to, but I accept that, 
> ignoring the speed difference, if a Turing Machine can do something then the 
> human brain can do it and if the  Human brain can do it then a properly 
> programed Turing Machine can do it.  
> 
> ​> ​If you accept multiple-realizability (which I think you do) you 
> understand that computers can be made of anything, so long as it preserves 
> the necessary relations. 
> Yes, but preserving the necessary relations means rejecting an infinite 
> number of incorrect relations. There are an infinite number of relations 
> between the numbers 1, 2, and 3 but only one of them is consistent with the 
> addition operation and only physics can tell you which one that is. If "one" 
> hydrogen atom combines with "two" hydrogen atoms and if it is falling in a 
> gravitational field it will have "three" times the momentum and energy that 
> "one" hydrogen atom would have; if you build a wall and figure it will stop 
> the atoms because you think 1+2=2 and the wall is strong enough to withstand 
> twice the energy of one hydrogen atom then there will be consequences for 
> your erroneous belief that you didn’t expect.  But without physique there are 
> no consequences. 
> 
> 
> ​ John K Clark​
> 
> 
> 
> 
> 
> 
> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to everything-list+unsubscr...@googlegroups.com 
> .
> To post to this group, send email to everything-list@googlegroups.com 
> .
> Visit this group at https://groups.google.com/group/everything-list 
> .
> For more options, visit https://groups.google.com/d/optout 
> .

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Do we live within a Diophantine equation?

[Bruno Marchal]

> On 20 Jun 2018, at 17:56, John Clark  wrote:
> 
> On Wed, Jun 20, 2018 at 1:06 AM, Jason Resch  > wrote:
> 
> ​> ​I am not sure I am seeing  the relevance of your comments to what I 
> said.​ ​Are you disputing that computational relations are embodied by 
> statements concerning solutions to certain polynomial equations?
> 
> No I'm not disputing that, but computational relations couldn't exist without 
> computations, and computations couldn't exist without matter that obeys the 
> laws of physics. 


Could the number 17 exists without matter?


>  
> ​>​ Do you believe "7 is prime" was true before any human mathematician 
> considered the question?
> 
> ​Yes, but if there was ever a time when not even one thing existed, much less 
> seven things, then you could assume 7 is prime and it would produce no 
> contradictions or you could assume 7 is not prime and it would produce no 
> contradictions either because the concept of “seven" would be meaningless as 
> would the concept of “prime". Well... you could assume that except that if 
> nothing existed then you wouldn't either so you couldn't assume anything nor 
> could anybody else.​ 

I don’t think that this is valid. If you agree that “7 is prime” independently 
of matter, you will have to believe that “John believes that 17 is prime” is 
itself independent of matter, once you assume computationalism.

Bruno



> 
> John K Clark​
> 
> 
> 
> 
> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to everything-list+unsubscr...@googlegroups.com 
> .
> To post to this group, send email to everything-list@googlegroups.com 
> .
> Visit this group at https://groups.google.com/group/everything-list 
> .
> For more options, visit https://groups.google.com/d/optout 
> .

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Do we live within a Diophantine equation?

[Bruno Marchal]

> On 20 Jun 2018, at 14:55, Jason Resch  wrote:
> 
> 
> 
> On Tue, Jun 19, 2018 at 11:36 AM, Bruno Marchal  > wrote:
> 
>> On 17 Jun 2018, at 02:18, Jason Resch > > wrote:
>> 
>> In solving Hilbert's 10th problem 
>>  in the negative, 
>> the work of Martin Davis, Yuri Matiyasevich, Hilary Putnam and Julia 
>> Robinson culminated in 1970 with the MRDP theorem 
>>  which 
>> concludes:
>> 
>> Every computably enumerable set has a representation as a Diophantine 
>> equation  (an equation 
>> involving only integer coefficients and variables).
>> 
>> This shocked number theorists, because it meant simple equations involving 
>> nothing more than a few integer variables have the full power of Turing 
>> machines.  In fact, it was shown by Yuri Matiyasevich that a universal 
>> Diophantine equation can be made with as few as 9 unknowns.
>> 
>> Some examples:
>> k is even if there exists a solution to: k - 2x = 0
>> k is a perfect square if there exists a solution to: k - x^2 = 0
>> k is a Fibonacci number if there exists a solution to: k^4 - k^2*x^2 - x^4 - 
>> 1 = 0
>> (k+2) is a prime number if there exists a solution to the sum of: (these 14 
>> equations )
>> k is a LISP program having output n, if the equation having variables: k, n, 
>> x1, x2, x3 ... x2 (a polynomial having ~20,000 variables 
>> ) has a solution.
>> The universality of Diophantine equations means there are polynomial 
>> equations that compute things quite surprising, such as polynomials that 
>> have solutions of 0, IFF:
>> One of the variables "k" is a valid MP3 file.
>> One of the variables "k" is a JPEG image containing the image of a cat 
>> (where the equation implements the same computation as a neural network 
>> trained to recognize images of cats)
>> For two of the variables "y" and "x", "y" equals a state of a chess board 
>> after deep blue makes a move given a chess board with a state of "x".
>> For two of the variables "y" and "x", "y" equals the state of the Universal 
>> Dovetailer after performing "n" steps of execution.
>> 
>> The last example seems to suggest to me, that pure arithmetical truth, 
>> concerning the solutions to equations, is identical to computation.  That is 
>> to say, certain mathematical statements carry with them (effectively) Turing 
>> machines, and their executions.
> 
> Matiyazevic results is indeed quite impressive. It finishes an inquiry begun 
> by Davis and Putnam with important progress by Julia Robinson, and eventually 
> Matiyazevic got the proof, and its solved the 10th problem of Hilbert: there 
> is no mechanical procedure to tell if a diophantine polynomial equation has a 
> solution or not. (Assuming Church’s thesis, as Matiyzevic explains well in a 
> ten page section in his book).
> 
> 
> 
> 
>> 
>> Just as all solutions to the deep-blue implementing equation is equivalent 
>> to the computations that Deep blue makes when evaluating the board, and all 
>> solutions to the cat recognizing equation are equivalent to the processing 
>> done by the trained neural network, all solutions to the LISP equation are 
>> equivalent to the execution of every possible LISP program (including the 
>> UD).
>> 
>> Does this our conscious experience might be a direct consequence of 
>> Diophantine equations?
> 
> Yes. Although you could *equivalently* say that our conscious experience is a 
> direct consequence of the combinators laws Kxy = x and Sxyz = xz(yz).
> 
> 
> Do you have some references that you would recommend for someone wanting to 
> learn more about combinator laws and how they lead to universality?

I would simply recommend Smullyan’s book “How to mock a mocking bird?”, which 
proves in details the Turing universality of the combinators.




> Is the above the same thing as a Y-combinator, or some more specific equation 
> in lamda calculus or combinatorial logic? I wish to lean more.

The Y combinator is the fixed point of Yx = x(Yx). All fixed point equation can 
be solved in combinatory logic. The Y combinator can be used to program the 
“definition by primitive recursion”, but, as Smullyan shows well, you can 
easily start from scratch and use the Dxyz = T(xx)yz trick. You need to be able 
to eliminate variables from combinations, but this too is well explained by 
Smullyan. His last book “A Beginner’s Further Guide to Mathematical Logic” 
contains a rather detailed summary of his book “How to Mock a Mocking Bird”. 
I have some rare text by Rosser, in French, on the combinators, which are very 
good, but uneasy to find, but maybe in second hand bookshop, notably his “Deux 
Esquisses de Logique”.
The classical treatise is the North Holland book 

Re: Radioactive Decay States

[Lawrence Crowell]

On Thursday, June 21, 2018 at 6:48:53 PM UTC-5, agrays...@gmail.com wrote:
>
>
>
> On Thursday, June 21, 2018 at 11:18:25 PM UTC, Lawrence Crowell wrote:
>>
>> The emergent nuclear interaction occurs on a time scale of 
>> 10^{-22}seconds. The superposition of a decayed and nondecayed nucleus 
>> occurs in that time before decoherence.
>>
>
> Is that calculated / postulated if the radioactive source interacts with 
> its environment? Can't it be isolated for a longer duration? If so, what 
> does that imply about being in the pure states mentioned above? AG 
>

Quantum physics experiments on nonlocality are done usually with optical 
and IR energy photons. The reason is that techniques exist for making these 
sort of measurements and materials are such that one can pass photons 
through beam splitters or hold photons in entanglements in mirrored 
cavities and the rest. At higher energy up into the X-ray domain such 
physics becomes very difficult. At intermediate energy where you have 
nuclear physics of nucleons and mesons and further at higher energy of 
elementary particles things become impossible. This is why in QFT there are 
procedures for constructing operators that have nontrivial commutations on 
and in the light cone so nonlocal physics does not intrude into 
phenomenology. Such physics is relevant on a tiny scale compared to the 
geometry of your detectors.

LC
 

>
>> LC
>>
>> On Thursday, June 21, 2018 at 5:50:12 PM UTC-5, agrays...@gmail.com 
>> wrote:
>>>
>>> Why don't we observe the pure states, decayed + undecayed, or decayed - 
>>> undecayed? TIA, AG
>>>
>>

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Do we live within a Diophantine equation?

[Bruno Marchal]

> On 20 Jun 2018, at 04:02, John Clark  wrote:
> 
> On Sun, Jun 17, 2018 at 9:27 AM, Jason Resch  > wrote:
> 
> ​>​Below is some Python code...[blah blah] John Clark often tells Bruno 
> mathematical truth won't put Intel out of business
> 
> ​Yes, I have been known to say that from time to time.​ 
>  
> ​>​ but
> 
> ​But?! This code can *can" put Intel out of business without even being run 
> on a computer? ​ 
>  
> ​> ​this case, (more than any other I have seen), leads me to believe that 
> mathematical truth does embody computation.  No physical computer is 
> necessary for these computations to exist, only for us to access it. 
> 
> ​Computations are required even to access an item on a list,

A physical computation is required for a physical observer to get a result, but 
that remains true when the physical computation + the observer are themselves 
the product of a computation, and that one can be arithmetical or diophantine, 
without the observer being able to notice that.



> of course a Intel microchip is not the only thing that can do calculations, 
> the human brain can too, but they both have one thing in common, they are 
> both made of atoms that obey the laws of physics.​ ​

Yes, but you are talking about physical computation. But with mechanism, the 
physical computations emerges from the first person indeterminacy on all 
(relative) computations. What you say remains true for the physical 
computations, but there are not a primitive notion. No need for atoms or 
physical laws, as those are emerging patterns in the first person (plural) 
observables.

Bruno



> 
> John K Clark​
> 
> 
> 
> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to everything-list+unsubscr...@googlegroups.com 
> .
> To post to this group, send email to everything-list@googlegroups.com 
> .
> Visit this group at https://groups.google.com/group/everything-list 
> .
> For more options, visit https://groups.google.com/d/optout 
> .

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Schrodinger's Cat vs Decoherence Theory

[Bruno Marchal]

> On 19 Jun 2018, at 19:07, Brent Meeker  wrote:
> 
> 
> 
> On 6/18/2018 10:21 PM, Bruce Kellett wrote:
>> From: Brent Meeker mailto:meeke...@verizon.net>
>>> On 6/17/2018 10:41 PM, Bruce Kellett wrote:
> But the lens doesn't send one color to one photoreceptor and another 
> color to a different photorecptor.  It focuses a spot of light on several 
> photorecptors and the one with the right pigment fires its neuron.  So it 
> is energy detection.
 
 But if you use a different position basis the lens will no longer focus 
 point objects to points on the retina.
 
>> I don't know enough about the physics of calorimeters as used in HEP to 
>> comment here. But if temperature changes are measured by bimetals or 
>> strain gauges, position comes into it in an essential way.
> 
> Most work by measuring a voltage.  But you miss the point.  Those 
> position measurements are not essential in the QM sense.  They are just 
> changing one classical value into another.  Temperature is the first 
> classical level.
 
 Fair enough. I suppose I am just very conscious of the fact that in a 
 different position basis all of this physics will be very different. The 
 classical universe will not look the same at all.
>>> 
>>> I guess I don't understand your idea of "position basis".  My understanding 
>>> of linear algebra is that any basis that spans the space can be used to 
>>> represent any relation between structures.  Why should choosing a different 
>>> basis make any difference to the physics aside from the simplicity of its 
>>> representation.  It's just a coordinate basis in Hilbert space.  Or are you 
>>> thinking of bases different from position, e.g. momentum, energy, 
>>> live/dead,...
>> 
>> Yes, there does seem to be a degree of miscommunication. I am not think of 
>> different variables such as energy, momentum, or the like. These are not 
>> different bases, they are different variables and they inhabit different 
>> Hilbert spaces. So a change of base in one Hilbert space does not take you 
>> to another space.

?


>> 
>> No, what I am considering is the possibility of different bases in a single 
>> space, such as position space. If you assume an eignevector interpretation 
>> of a set of basis vectors, then a different basis will correspond to the 
>> eigenvalues of some different operator. It still acts in the same, position, 
>> space, so it must be regarded as a position operator, but it will have quite 
>> different physical properties from the usual position operator that we use 
>> from classical mechanics, where the eigenvectors are delta functions along 
>> the real line.
>> 
>> Because this will be a different operator, it will correspond to different 
>> physics. For instance, if the position eigenvalues are superpositions of 
>> delta functions, corresponding to superpositions of different points, the 
>> point interactions of particles that we assume in constructing the 
>> interaction Hamiltonian will be replaced by some set of interactions between 
>> superpositions of points. This why I suggest that the physics will be 
>> different. If the physics is the same under this basis change, why is there 
>> any question about the preferred basis? The point is that a change of basis 
>> does not mean that we simply go to measure some other variable. I think 
>> Schlosshauer makes this mistake, if I remember correctly; he seems to 
>> suggest that the basis choice is between position or energy in most cases. 
>> That is just wrong.
> 
> I think you're wrong about position operators.

I agree. The Hilbert space is always the same. 


> Sure, we usually think of dividing space into little bins and a position 
> operator has eigenvectors that are 1 in some bin and zero in the other.  But 
> we could do the same analysis in the Fourier transform of that space and the 
> delta function locations would be integrals over the wave numbers.  It would 
> be the same physics. 

Yes.


> There would still be localized interactions.  The Hamiltonian would be 
> written as an interaction of a superposition of points, except they would all 
> destructive interfere except at one location.  So the physics would be the 
> same.
> 
> Consider the paradigmatic two slit experiment.  The pattern you get on the 
> screen, which is predicted by the Schroedinger equation, is described in your 
> idea of position space by a lot of little bins that have different degrees of 
> probability, so if you put a detector there you get a certain count rate.  
> But that pattern on the screen is a certain wavelet and if you transformed 
> the Schroedinger equation to wavelet space that whole pattern would be just 
> one point in the space and it would be the eigenvector of the two slit 
> experiment.
> 
> The problem of the preferred basis arises in trying to explain why we measure 
> position of needles but not momentum or energy and why we don't se