Re: Measuring a system in a superposition of states vs in a mixed state

[agrayson2000]

On Monday, November 19, 2018 at 3:52:37 PM UTC, Bruno Marchal wrote:
>
>
> On 18 Nov 2018, at 14:00, agrays...@gmail.com  wrote:
>
>
>
> On Sunday, November 18, 2018 at 12:19:20 PM UTC, Bruno Marchal wrote:
>>
>>
>> On 16 Nov 2018, at 15:38, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, November 16, 2018 at 10:14:32 AM UTC, scerir wrote:
>>>
>>>
>>> Il 16 novembre 2018 alle 10.19 agrays...@gmail.com ha scritto: 
>>>
>>>
>>>
>>> On Thursday, November 15, 2018 at 2:14:48 PM UTC, scerir wrote:
>>>
>>>
>>> Il 15 novembre 2018 alle 14.29 agrays...@gmail.com ha scritto: 
>>>
>>>
>>>
>>> On Thursday, November 15, 2018 at 8:04:53 AM UTC, scerir wrote:
>>>
>>> Imagine a spin-1/2 particle described by the state psi = sqrt(1/2) 
>>> [(s+)_z + (s-)_z] .
>>>
>>> If the x-component of spin is measured by passing the spin-1/2 particle 
>>> through a Stern-Gerlach with its field oriented along the x-axis, the 
>>> particle will ALWAYS emerge 'up'.
>>>
>>>
>>> *Why?  Won't the measured value be along the x axis in both directions, 
>>> in effect Up or Dn? AG*
>>>
>>> "Hence we must conclude that the system described by the |+>x state is 
>>> not the
>>> same as a mixture of atoms in the |+> and !-> states. This means that 
>>> each atom in the
>>> beam is in a state that itself is a combination of the |+> and |-> 
>>> states. A superposition
>>> state is often called a coherent superposition since the relative phase 
>>> of the two terms is
>>> important."
>>>
>>> .see pages 18-19 here *https://tinyurl.com/ybm56whu 
>>> *
>>>
>>>
>>> *Try answering in your own words. When the SG device is oriented along 
>>> the x axis, now effectively the z-axix IIUC, and we're dealing with 
>>> superpositions, the outcomes will be 50-50 plus and minus. Therefore, 
>>> unless I am making some error, what you stated above is incorrect. AG *
>>>
>>> sqrt(1/2) [(s+)_z +(s-)_z]  is a superposition, but since sqrt(1/2) 
>>> [(s+)_z +(s-)_z]  =  (s+)_x the particle will always emerge 'up'
>>>
>>
>> I'll probably get back to on the foregoing. In the meantime, consider 
>> this; I claim one can never MEASURE Up + Dn or Up - Dn with a SG apparatus 
>> regardless of how many other instruments one uses to create a composite 
>> measuring apparatus (Bruno's claim IIUC). The reason is simple. We know 
>> that the spin operator 
>>
>>
>> Which one? 
>>
>
> *Good question. AG*
>
> There are spin operator for each direction in space. The superposition of 
>> up and down is a precise pure state, with precise eigenvalues, when 
>> measuring state in the complementary directions.
>>
>
> *As I wrote earlier, based on scerir's superpositions on different axes, 
> and simulation, I now think that Up + Dn and Up - Dn can be measured along 
> the x axis but not along the z axis (which I was focused on). *
>
>
> All you need to do is a change of base. The operator will be defined 
> clearly by the Eigen value on the diagonal in the corresponding base. You 
> can prepare any state, and measure them “in any base”. 
>


*I'll get back to this issue in my next post. AG *

> *You were probably correct about x axis measurements, but perhaps were not 
> clear enough. You were not explicit that measurements along the x axis is a 
> different SG experiment from along z axis.*
>
>
> OK. Sorry. 
>
> * I thought you meant do them in succession, not as separate experiments.*
>
>
> Ah? OK.
>
>
> * Also introducing an infinity of universes seems extraneous and confusing 
> for a solution to this problem. AG *
>
> I are probably different on this. I don’t take the word “universe” too 
> much seriously, as with mechanism we know at the start that there is 
> “physical universe” at all, just the natural numbers with the laws of 
> addition and multiplication. Both the computational and the quantum state 
> are relative, and high level, pertaining to what is “observable” for some 
> the point of view of some locally finite subject, run by some computation.
>
> The empirical point, though, is that to predict correctly an event in 
> quantum mechanics, we have to take into account may simultaneous 
> “incompatible path”, like going through each hole in a plane. Quantum 
> computations, for example, exploits that seemingly parallelism. 
>

*I don't like this approach -- in fact I abhor it -- since it implies 
simultaneous interference among a multitude of paths to the same point on 
the detection screen. This adds an unnecessary mystery to QM. In the 
Hilbert Space representation, the wf is what it is, but can be represented 
in a multitude of different bases. It is therefore misleading to claim the 
system being analyzed is in a multitude of states; rather it is in one 
state, which due to linear algebra, has many representations. AG *

> has exactly two eigenstates, each with probability of .5. We can write 
>> them down. We also know that every quantum measurement gives up an 
>> eigenvalue of some eigenstate. Therefore, if there existed an Up + 

Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

[Philip Thrift]

On Wednesday, November 21, 2018 at 3:48:31 AM UTC-6, Bruno Marchal wrote:
>
>
> Matter plays a fundamental role in sensibility, but that is a theorem in 
> Mechanism, and that “matter” is phenomenological. It does not exist in the 
> base ontology. Or f it does, then how could it play a non mechanist role? 
> No problem with rejecting computationalism, if you want matter or other 
> god to play a role, but why not testing this before complicating the 
> cognitive science for … what?
>
> Bruno
>
>


If the starting point is

   *There are no such things as numbers* [ or - in general terms - 
*mathematical 
entities* ],

then one is left with something (assuming there is something) and something 
is matter.

There is no evidence in any scientific sense that mathematical entities 
exist.

Mathematics is fiction (in the sense of mathematical fictionalism). That 
applies to computation, if computation is viewed as a branch of mathematics.

But matter that has intrinsic experientiality can be that something that 
does exist for both behavioral (information) and phenomenological 
(experience, consciousness) aspects of the universe.

- pt

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Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

[Bruno Marchal]

> On 19 Nov 2018, at 21:50, Philip Thrift  wrote:
> 
> 
> 
> On Monday, November 19, 2018 at 4:54:47 AM UTC-6, Bruno Marchal wrote:
> 
>> On 16 Nov 2018, at 19:55, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> On Friday, November 16, 2018 at 11:05:51 AM UTC-6, Bruno Marchal wrote:
>> 
>>> On 15 Nov 2018, at 18:13, Philip Thrift > wrote:
>>> 
>>> 
>>> 
>>> On Thursday, November 15, 2018 at 5:15:39 AM UTC-6, Bruno Marchal wrote:
>>> 
 On 13 Nov 2018, at 11:06, Philip Thrift > wrote:
 
 
 
 On Monday, November 12, 2018 at 8:35:23 PM UTC-6, Bruno Marchal wrote:
 
 A model is a model of a theory. The notion of model of a model can make 
 sense, by considering non axiomatisable theory, but that can lead to 
 confusion, so it is better to avoid this. When a model is seen as a 
 theory, if it contains arithmetic, the theory cannot be axiomatised, 
 proofs cannot be checked, the set of theorems is not recursively 
 enumerable, etc.
 
 
 Bruno
 
 
 
 This is why some have mathematical theories (alternatives to ZF) that have 
 finite (i.e. Only a finite number of numbers needed!) models (e.g. Jan 
 Mycielski, "Locally Finite Theories" [https://www.jstor.org/stable/2273942 
  ]). In this approach quantifiers 
 are effectively replaced by typed quantifiers, where the type says "this 
 quantifier ranges over some finite set".  
 
 Another approach is to nominalize physical theories theories (Hartry 
 Field, Science Without Numbers, summary [ 
 http://www.nyu.edu/projects/dorr/teaching/objectivity/Handout.5.10.pdf 
  
 ]). In this approach the model of the theory is a finite set of 
 (references to) physical objects.
 
 This is the best point-of-view to have: The set of natural numbers simply 
 doesn't exist!
>>> 
>>> 
>>> I agree. It is actually a consequence of mechanism. The set of natural 
>>> numbers does not exist, nor any infinite set. But that does not make a 
>>> physical universe into something existing. Analysis, physics, sets, … 
>>> belongs to the numbers “dreams” (a highly structured set, which has no 
>>> ontology, but a rich and complex phenomenological accounts). 
>>> 
>>> I gave my axioms (Arithmetic, or Kxy = x, Sxyz = xz(yz)). As you can see, 
>>> there is no axiom of infinity.
>>> 
>>> Bruno
>>> 
>>> PS Sorry for the delay.
>>> 
>>> 
>>> 
>>> 
>>> The "highest" programming may be higher-type (or higher-order) programming:
>>> 
>>> http://www.cs.bham.ac.uk/~mhe/papers/introduction-to-higher-order-computation-NLS-2017.pdf
>>>  
>>> 
>>> examples @ http://www.cs.bham.ac.uk/~mhe/ 
>>> 
>>> 
>>> "Higher-order [programming involves] infinite objects, such as infinite 
>>> strings, real numbers, and even functions themselves, etc. [which 
>>> themselves] are computable. And, more importantly, how to compute them. In 
>>> practice, computation with infinite objects often takes place in languages 
>>> such as ML, Haskell, Agda etc. In theory, some canonical systems are 
>>> Godel’s system T, Platek-Scott-Plotkin PCF, Martin-Lof’s dependent type 
>>> theory, among many others. But how can we (or a computer) compute with 
>>> infinite objects, given that we have a finite amount of time and a finite 
>>> amount of memory and a finite amount of any resource? Topology comes to the 
>>> rescue [revolving] around the [finite vs. infinite dichotomy], mediated by 
>>> topology. We can say that topology is precisely about the relation between 
>>> finiteness and infiniteness that is relevant to computation."
>>> 
>>> 
>>> 
>>> But there is a new biochemical programming language:
>>> 
>>> CRN++: Molecular Programming Language
>>> (Submitted on 19 Sep 2018)
>>> https://arxiv.org/abs/1809.07430  
>>> "We present its syntax and semantics, and build a compiler translating 
>>> CRN++ programs into chemical reactions...laying the foundation of a 
>>> comprehensive framework for molecular programming."
>>> 
>>> A programming language whose purpose is to create bugs!
>>> 
>>> So the question becomes: Is bioprogramming > programming? (if biomatter has 
>>> experiential qualities in addition to informational quantities)
>> 
>> Assuming some primary matter, and some non mechanist theory, why not. That 
>> seems to quite speculative, though, and adding difficulties to a subject 
>> which is already difficult when assuming the “simplifying” assumption of 
>> Mechanism. With mechanism, the mind-body problem reduced into justifying the 
>> existence of a canonical measure on all computations “seen from inside” 
>> (which admits a number of modes, imposed by incompleteness). In case the 
>> physics in the head of the universal machine/number 

Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

[Bruno Marchal]

> On 20 Nov 2018, at 00:44, John Clark  wrote:
> 
> On Mon, Nov 19, 2018 at 6:24 AM Bruno Marchal  > wrote:
>  
> > The notion of model “modelises” the notion of reality.
> 
> I see. No I take that back I don't see. What does that mean, how would things 
> look different if it were the other way around, what if the notion of reality 
> realizes the notion of model?


In logic, a model is a reality. I will use “reality” instead of “model”, 
because physicists use “model” for theory.

A reality is anything which satisfies a theory (i.e. each axioms, and all 
theorems).

A theory is sound means that what we prove in the theory will be true in all 
models of the theory.
A theory is complete if what is true in all models is proved in the theory.

All first order theories are complete in that sense. A corollary is that a 
theory is consistent if and only if the theory has a model.





>  
> >> that is like using English to talk about the English word "cat". Whenever 
> >> mathematics tries to model something that is not itself, like something 
> >> physical,
> 
> > Which might be part of mathematics. 
> 
> If so  you could make a calculation without the use of matter that obeys the 
> laws of physics and you would be the richest man who ever lived.


By definition of computations, all computations are done without primary 
matter. The appearance of matter is explained by the way some computations are 
seen from inside. 

If you believe in some primary, non deductible matter, and that such primary 
matter has a role for consciousness, it is up to you to explain how that matter 
can select computation(s) in arithmetic. But either
A) that matter role is not Turing emulable, but then mechanism is false. Or,
B) that matter role is Turing emulable, but then it occurs in arithmetic (in 
all models of arithmetic), en you failed.





>  
> > Unless you assume [...]
> 
> What I assume is you are NOT the richest man who ever lived.
>  
> >> But, I hear you say, the numbers 11 and 13 are prime and that fact is 
> >> unchanging and eternal!  Well yes, but the English words "cat" and "bat" 
> >> rhyme and that fact is also unchanging and eternal.
> 
> > Not in the same sense, and if you make things precise, for mechanism, a 
> > theory with bat and cat rhyming can be Turing universal,
> 
> If both English and mathematics are Turing universal then both are just 
> languages and everything mathematics can do English can do, although perhaps 
> a little less eloquently.   

Neither English nor mathematics are defined precisely enough to assert that 
there are Turing universal. It can or cannot make sense without further 
precisions.



> 
> >> Mathematics can't even identify all true sentences about arithmetic much 
> >> less become the master of physical reality. We know  the sentence "the 4th 
> >> Busy Beaver number is 107" belongs in the set of true sentences, but what 
> >> about "the 5th Busy Beaver number is 47,176,870"?  It's either true or its 
> >> not but will you or I anybody or anything ever know which one?  Nobody 
> >> knows and nobody knows if we'll ever know, but we do know that nothing 
> >> will ever know what the 8000th Busy Beaver number is even though its well 
> >> defined and finite.
>  
> > You make my point. The value of the busy beaver function is arithmetical 
> > well defined, but not computable, which illustrates that the arithmetical 
> > reality kicks back,
> 
> Arithmetical reality "kicked back" by saying "I can NOT identify all true 
> sentences in arithmetic", and many many centuries before Godel or Turing 
> Arithmetical reality "kicked back" by saying "I can only predict 
> approximately what a physical system will do”

Gödel’s theorem says nothing about the physical, and does not assume anything 
in physics, nor metaphysics. But this changes when we assume Mechanism; physics 
becomes a first person plural statistics on computation, and indeed quantum 
mechanics is recovered in the extraction of physics in arithmetic “seen from 
inside”.





> and with the more recent development of Quantum Mechanics the approximations 
> have become even more approximate. And that is exactly what you'd expect to 
> happen if mathematics was the model and physics was the real thing because 
> models are always simpler and less complete than the thing they're modeling.  
>   

Model in the physicist sense. OK. But that is provably true for the 
arithmetical reality, which is provably infinitely more complex than any 
theories (model in the physicist sense) of arithmetic, by incompleteness.



> 
> > your argument needs your ontological commitment in some primary matter, for 
> > which there is no evidence found yet.
> 
> You've been saying shit like that for years and I still have no idea what 
> you're talking about. What exactly would you consider relevant evidence of 
> the existence of "primary matter"? I don't think you even know what "primary 
> matter" means.

That is a