Re: Tao and Physics

[spudboy100 via Everything List]

Some see The Flying Nun, and others see a C-130 Cargo plane adapted by the 
military, to fire vulcun minigun 30mm rounds! Now, which is the most 
spiritual??? Only the observer, or Schrodinger, can say. 



-Original Message-
From: Philip Thrift 
To: Everything List 
Sent: Wed, Oct 3, 2018 3:58 pm
Subject: Re: Tao and Physics





On Wednesday, October 3, 2018 at 11:45:25 AM UTC-5, spudb...@aol.com wrote:
Here is the 3 letter ascii symbol for God
   ¯\_(ツ)_/¯



Flying nun


/‾‾(ツ)‾‾\ 


- pt





-Original Message-
From: John Clark 
To: everything-list 
Sent: Wed, Oct 3, 2018 12:10 pm
Subject: Re: Tao and Physics



On Wed, Oct 3, 2018 at 11:27 AM Bruno Marchal  wrote:


 



> Please read Plotinus or Proclus




Not a snowball's chance in hell!!  I'd learn more science and mathematics from 
reading Mother Goose.




 >>So there is not one God there are an infiniti of them





>No, there is only one. The reason why you are here is the same as the reason 
>why any universal number exist. I did not say that any machine is god.



You said "Consider any digital machine. It corresponds to some number k [...] 
The theology of the machine k is define by the set of all true sentence about 
k".  And all true statements about digital machine k are not the same as all 
true statements about digital machine k+1. And if theology is the study of God 
then there are a infinity of Gods. And not one of those Gods is as smart as a 
sea slug. 


I said it before I'll say it again, you've abandoned the idea of God but refuse 
to abandon the 3 character ASCII sequence G-O-D.


John K Clark 







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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 10/4/2018 12:06 AM, Bruno Marchal wrote:
You need a universal machinery. Very elementary arithmetic (like Peano 
without induction) determines such a universal machinery (the phi_i), 
then, you get all the universal number u (such that phi_u(x,y) = 
phi_x(y), and each u defines its own universal machinerery: phi_u(0, 
_), phi_u(0, _), phi_u(1, _), phi_u(2, _), …


All universal “thing” mimic all universal “thing”, but they have 
special statistical relation, and different personal beliefs. They 
determine (in the arithmetical reality) the “consciousness flux”, 
which determine the (unique!) physical reality, which is a sort of 
multiverse/multi-dreams.







What would be the programs and languages (π,λ) that could be defined?




All of them, but with their different relative measure. They are 
mathematically determined by the G* logic (self-referential truth).


What is the measure on universal machines in arithmetic?

Brent

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Thursday, October 4, 2018 at 2:06:30 AM UTC-5, Bruno Marchal wrote:
>
>
> On 3 Oct 2018, at 22:07, Philip Thrift > 
> wrote:
>
>
> Suppose one starts with the PLTOS template:
>
> PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a language λ 
> that is transformed via a compiler/assembler τ into an output object ο that 
> executes in a computing substrate Σ.
>
>
> Suppose Σ = *UniversalNumbers* 
>
>
> That is, the computing substrate is the actual Universal Numbers 
> (arithmetic reality).
>
>
> You need a universal machinery. Very elementary arithmetic (like Peano 
> without induction) determines such a universal machinery (the phi_i), then, 
> you get all the universal number u (such that phi_u(x,y) = phi_x(y), and 
> each u defines its own universal machinerery: phi_u(0, _), phi_u(0, _), 
> phi_u(1, _), phi_u(2, _), …
>
> All universal “thing” mimic all universal “thing”, but they have special 
> statistical relation, and different personal beliefs. They determine (in 
> the arithmetical reality) the “consciousness flux”, which determine the 
> (unique!) physical reality, which is a sort of multiverse/multi-dreams.
>
>
> What would be the programs and languages (π,λ) that could be defined?
>
>
> All of them, but with their different relative measure. They are 
> mathematically determined by the G* logic (self-referential truth).
>
> Bruno
>
>
>


Approaching this with a *PLTOS* template identifies the parts  π,λ,τ,ο,Σ. 
What is the compiler/assembler τ for example?

(PLTOS is a bit of a play-on-words: It looks like PLT Operating System.)

In PLT (programming language theory), one part of comprehending the whole 
shebang is in terms of semantics, specifically its denotational vs 
operational semantics 
[ http://courses.cs.vt.edu/~cs3304/Spring04/notes/Chapter-3b ].

In the case of "real" hardware Σ (is there a CPU or a GPU or a TPU - 
Google's NN chip?) then the operational semantics are significant.

In the case of Σ = UniversalNumbers/UniversalMachine it is a bit difficult 
to see what the operational semantics would be.

- pt



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Re: Combinator 5 (Numbers errata)

[Bruno Marchal]

Hi, 

The next combinator thread (“combinator 6”) will be the proof of the 
(Turing/Church) universality.

Here, I correct the typo error, which was that I forgot the predecessor P in 
the last formula. See below.

It is time to revise, and to ask any question if anything remains unclear.

After the Turing universality, I will give the definition of the first and 
third person “pronouns”, and go toward the notion of Löbian combinator or 
Löbian number, and explain the Curry-Löb paradox. That will be the thread 
Combinator 7.

The main results will be the first and second recursion theorems (or fixed-pint 
theorem):

1) For any combinator F there is a combinator X such that FX = X.
2) For any combinator F there is a combinator X such that F’X' = X.

‘X’ will be a Gödel numbering, or code, of the combinator X.

Bruno




> On 16 Sep 2018, at 12:05, Bruno Marchal  wrote:
> 
> Hi, 
> 
> We will implement the numbers with the combinators. In particular we will 
> emulate Robinson Arithmetic(*) with the combinators. 
> 
> Robinson arithmetic is classical logic +
> 
> 1) 0 ≠ s(x)   0 is not a successor of any number x
> 2) s(x) = s(y) -> x = y   Different numbers have different 
> successors
> 3) x = 0 v Ey(x = s(y))   Each number has a predecessor
> 4) x+0 = xAdding nothing keep a number invariant
> 5) x+s(y) = s(x+y)Recursion equation of addition
> 6) x*0=0  Multiplying by 0 gives 0
> 7) x*s(y)=(x*y)+x Recursion equation of multiplication
> 
> On the right I have put the intended intuitive semantic.
> 
> Usually I use the "Church numerals”, but I will use those of Barendrecht. 
> Smullyan’s book convinced me of their elegance, and it gives a nice 
> opportunity to use our new recursion tools, as they strikes the eyes in line 
> “5)” and “7)”. Isn’t it? “+” is defined from itself. “*” also. 
> 
> 
> Barendrecht's Numerals
> 
> Definitions.
> 
> The number 0 is defined by I, that is SKK, but I will abbreviate it by I.
> The successeur function is defined by the combinator Vf. V is the Vireo,
> Vxyz = zxy. f is KI. We have seen that V = BTC (and that B = S(KS)K, …). I 
> mean V is a combinator (a combination of K and S), and it does what it does 
> (that circular permutation of its argument). Reread previous post if 
> necessary.
> 
> f is the “logical” abbreviation for false, that is KI, i.e. K(SKK), as 
> defined  in the logical interlude.
> 
> Does it work? 
> 
> We have that 
> 
> 0 = I
> 1 = VfI   which remains stable, as V has not enough of its 
> “arguments”.
> 2 = Vf(VfI)   idem
> 3) = Vf(Vf(VfI)   It looks everything is fine and (by induction) will 
> remain fine.
> Etc.
> 
> So a number n, which is defined by s(s(s(s(…(0))…), with n “s“ in, or by, 
> Robinson Arithmetic is defined, or represented by 
> 
>   Vf(Vf(Vf(Vf( …(I))…)with n “Vf”.
> 
> It will be handy to have a predecessor. 
> You might try to find one by yourself before reading what follows, but there 
> is no obligation. What is obligatory is to verify that it works. Barendrecht 
> proposes Tf. (Where T is the “trush”: Txy = yx).
> 
> OK, but does it works? We need to verify this. So let us try it on 0, just to 
> see!
> 
> TfI = If = f. 
> 
> Well, that is OK. All we need is that it does not give some number, and 
> giving f is not so bad, almost an “error message” :)
> 
> I will abbreviate Vf(Vf(Vf(Vf( …(I))…) by n (hoping the underline will not 
> disappear).
> 
> We have tested the predecessor Tf on 0, now we must test it on some 
> successor, that is some Vfn 
> 
> Tf(Vfn)
> Vfnf  (Vfn)f  for the beginners
> ffn   f is KI, KIxy = y, revise the preceding posts if needed)
> n
> 
> It works!
> 
> Now, to implement “x + y” we need an ability to distinguish between a null 
> and a non null number, to decide between using axiom “4)” or “5)”.
> 
> So we need a combinator Z which answer truth, i.e t, that is K, when given 0, 
> that is I,  and gives KI when given a non null n. 
> 
> We want Z0 = ZI = K, and Zn = KI in case n is different from 0.
> 
> Barendregt's solution: Z = Tt.
> 
> We have already met Tt. It played the role of the “OR” in logic, and works 
> very well also to test if a number is null or not:
> 
> TtI = It = t
> Tt(Vfn) = Vfnt = tfn = f.
> 
> Let me sum up:
> 
>  t = K
>  f = KI
> 
> 0 = I
> s = Vf   (successor)
> p = Tf(predecessor)
> 
> Z = testing “nullness” = Tt.
> 
> And I recall that, thanks to t = K and f = KI, we have that 
> 
>   if A then B else C
> 
> becomes simply ABC, as tBC = B, and fBC = C.
> 
> ===
> 
> ADDITION
> 
> 
> Now, we have all we need to program addition. 
> 
> Addition is defined by its recursive equation (cf above)
> 
> 4) x+0 = xAdding nothing keep a number invariant
> 5) x+s(y) = s(x+y)Recursion equation of 

Re: Tao and Physics

[Bruno Marchal]

> On 3 Oct 2018, at 23:49, Chris J  wrote:
> 
> Question: If God is the 3-character ASCII sequence G-O-D, does that require 
> God to be American?
> 
> If not, then what, Unicode? UTF-8? ISO/IEC 10646? 


God, the notion, (not a special theory) is defined by whatever is responsible 
for us to exist, with perhaps a body, but certainly consciousness.

With the Mechanist hypothesis, God can be defined by the arithmetical truth, 
that you can represent as the set of (Model number) or the true arithmetical 
proposition.

By Tarski theorem, that set is not definable in arithmetic. 
By Gödel’s theorem, that set is highly not computable.

So, we get a common theological point (common to many traditions) which is that 
God is not a nameable thing. The term “god” is a substantiva pointing to the 
notion, but is not a definition per se (of course).




> 
> Same for Bruno, I am also curious about this question for notation for the 
> Löbian Machine.

A Lôban machine is a universal machine which knows that she is universal. 
Typical example is any (sound) machine believing in addition and multiplication 
of natural numbers, + the induction axioms, like PA, ZF, ...



> And if not for this very instant, then I ask what encoding standard should be 
> preferred in its future implementation?

In the arithmetical reality, to derive physics, we need to take all encodings. 




> 
> I know this query sounds absurd but if any of these things are to become real 
> (assuming they are not already), then will they not require definition not 
> merely of notation but of the substructure of that very notation?

The structure arise from the laws of addition and multiplication, only.
Or from abstraction and application, if you start from the lambda terms, or the 
combinators.
You can take the game of life patterns, … Any universal system would do 
(universal in the sense of Turing, Church, …).



> 
> Or if these are not notations and exist only in the mind (of 1p? of 3?) then 
> is that not already self-referential proof?

It exists in the arithmetical reality, a bit like the complex distribution of 
prime numbers is determined by the arithmetical axioms.

Nothing more than arithmetic is assumed (with mechanism at the meta-level to 
make the relation with consciousness).

The shorter and smallest theory I use often is the two axioms Kxy = x, and Sxyz 
=xz(yz). See the combinators recent thread(s).



> 
> Do my letters have any weight in this argument or are John Clark and Bruno 
> Marchal the same symbol talking to itself?


We are the same person, yes. But that identity will belong to G* \ G, so I have 
not the right to say this, actually.
But the body is different. The body is just a word. The physical body is the 
word which arise from the sum on all computations, below our substitution 
level. It is word written in the biochemical language, apparently.

Bruno



> 
> 
> 
> On Wednesday, October 3, 2018 at 12:10:53 PM UTC-4, John Clark wrote:
> On Wed, Oct 3, 2018 at 11:27 AM Bruno Marchal  > wrote:
>  
> > Please read Plotinus or Proclus
> 
> Not a snowball's chance in hell!!  I'd learn more science and mathematics 
> from reading Mother Goose.
> 
>  >>So there is not one God there are an infiniti of them
> 
> >No, there is only one. The reason why you are here is the same as the reason 
> >why any universal number exist. I did not say that any machine is god.
> 
> You said "Consider any digital machine. It corresponds to some number k [...] 
> The theology of the machine k is define by the set of all true sentence about 
> k".  And all true statements about digital machine k are not the same as all 
> true statements about digital machine k+1. And if theology is the study of 
> God then there are a infinity of Gods. And not one of those Gods is as smart 
> as a sea slug. 
> 
> I said it before I'll say it again, you've abandoned the idea of God but 
> refuse to abandon the 3 character ASCII sequence G-O-D.
> 
> John K Clark 
> 
> 
> 
>  
> 
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Re: Tao and Physics

[Bruno Marchal]

> On 3 Oct 2018, at 21:51, Brent Meeker  wrote:
> 
> 
> 
> On 10/3/2018 1:10 AM, Bruno Marchal wrote:
>> Consider any digital machine. It corresponds to some number k (such that 
>> phi_k(x) = y describes the behaviour of the machine k) (digital machine are 
>> recursively enumerable).
>> 
>> The theology of the machine k is define by the set of all true sentence 
>> about k. That includes the sentences that k is able to prove (relatively to 
>> the base phi_i) *and* the sentences which are true about k, but that k 
>> cannot prove.
>> 
>> With mechanism, you can define theology by the difference between computer 
>> science and computer’s computer science.
>> 
>> You can define it by Tarski’s notion of truth minus Gödel’s notion of 
>> probability.
>> 
> 
> I assume you meant "provability”.

You are right. Typo error. Sorry.

Bruno



> 
> Brent
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 3 Oct 2018, at 22:07, Philip Thrift  wrote:
> 
> 
> 
> On Wednesday, October 3, 2018 at 2:54:46 AM UTC-5, Bruno Marchal wrote:
> 
>> On 2 Oct 2018, at 17:11, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> On Tuesday, October 2, 2018 at 9:25:17 AM UTC-5, Bruno Marchal wrote:
>> 
>>> On 2 Oct 2018, at 09:53, Philip Thrift > wrote:
>>> 
>>> 
>>> 
>>> On Tuesday, October 2, 2018 at 2:20:10 AM UTC-5, Bruno Marchal wrote:
>>> 
 On 1 Oct 2018, at 14:20, agrays...@gmail.com <> wrote:
 
 
 
 On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:
 
> On 30 Sep 2018, at 16:30, Philip Thrift > wrote:
> 
> 
> 
> On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:
> [Re:] forcing theory in set theories with classes. 
> 
> 
> Bruno
> 
> 
> 
> Do you follow the work of Joel David Hamkins (forcing applied to 
> set-theoretic "multiverse", etc.)
> 
> (I have a basic idea of a type-theoretic parallel to this.)
> 
> The set-theoretic multiverse
> 
> https://arxiv.org/abs/1108.4223 
> 
> Joel David Hamkins
> @JDHamkins
> Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow 
> in Philosophy, University College Oxford. Formerly of New York.
> http://jdh.hamkins.org 
> 
 
 The math is interesting, and could be of some use, but it is a priori far 
 too much Aristotelian to be coherent with the mechanist hypothesis. That 
 should follow “easily” from the result described in most of my papers on 
 this subject. The author does not seem aware of the mind-body problem, 
 which put extreme constraints on what the physical reality can come from. 
 Even Peano arithmetic, although integral part of the notion of observer, 
 is too much rich for the ontology, where not only the axiom of infinity is 
 too strong,
 
 Since you want to banish the concept of infinity from mathematics, how 
 would you define, say, the limit of an "infinite" series? How would you 
 even discuss this series in the context of finite mathematics? AG
>>> 
>>> 
>>> Good question.
>>> 
>>> The answer is not simple technically. The point is that using only the 
>>> theory Q (Robinson Arithmetic) or SK (the combinators), I can define the 
>>> universal (Turing, Church) machine, and the concept of infinity will be a 
>>> tool used by them in their mathematics.
>>> 
>>> I do not ban anything from mathematics, nor from physics. I ban only 
>>> infinity from the ontological terms. I ban only infinity in the 
>>> metaphysics/theology. (Even God is not ontological, like in Proclus or 
>>> Plotinus theology).
>>> 
>>> Have you understand the post on Church’s thesis. You might tell me as this 
>>> will help me to see how to proceed to make you grasp all this.
>>> 
>>> Bruno
>>> 
>>> 
>>> 
>>> 
>>> What do you think of bounded arithmetic and other "finitist" approaches?
>>> 
>>> https://en.wikipedia.org/wiki/Bounded_arithmetic 
>>> 
>>> see bibliography: 
>>> http://jeanpaulvanbendegem.be/home/papers/strict-finitism/ 
>>> 
>> 
>> I wrote a paper on this, in a book in honour to Jean-paul Vanbendegem. But 
>> its approach is more than finitist, and a bit less than ultra-finitism. It 
>> does not fit the study of the “theology” of the machine, and is thus useless 
>> for deriving physics. That does not mean it is not interesting 
>> pragmatically, on the contrary, it is well fitted with the goal to make 
>> usable programs. I do think that mathematically, it is also a restriction of 
>> Post creativity (Turing universality in set theoretical terms) to sub 
>> creativity. There is no possible universal machine there.
>> 
>> 
>> 
>> 
>>> 
>>> Computable real analysis (one can teach computable calculus instead of 
>>> "conventional" calculus) is essentially finitist:
>>> https://en.wikipedia.org/wiki/Computable_analysis 
>>> 
>>> 
>>> One can formulate the Axiom of Infinity [ 
>>> https://en.wikipedia.org/wiki/Axiom_of_infinity 
>>>  ] in a type of bounded 
>>> set theory (Jan Mycielski [ https://en.wikipedia.org/wiki/Jan_Mycielski 
>>>  ], described in 
>>> https://books.google.com/books/about/Understanding_the_Infinite.html?id=GvGqRYifGpMC
>>>  
>>> 
>>>  ]. What results is an "ontology" of bigger and bigger finite sets of 
>>> numbers with gaps in them.
>> 
>> 
>> Yes, and that is interesting. But not so much for the mind-body problem, 
>> where we cannot bound anything, except by omega. 
>> 
>> The weaker theory known from which my approach can work, is the