Hi Bruno Marchal

1) Yes, numbers float in a sea of universal mind (the One).  

2) Here's a thought. If the universe acts like a gigantic
homunculus, with the supreme monad or One as its mind,
then could there be a solipsism to our universe such that
other multiverse versions of oiur universe could not access
(the mind of) ours ? Would this be a problem for multiverse
theories ?

Roger Clough, rclo...@verizon.net 
"Forever is a long time, especially near the end." -Woody Allen 

----- Receiving the following content -----  
From: Bruno Marchal  
Receiver: everything-list  
Time: 2012-10-30, 12:38:34 
Subject: Re: Numbers in the Platonic Realm 

On 30 Oct 2012, at 14:23, Stephen P. King wrote: 

On 10/30/2012 7:30 AM, Bruno Marchal wrote: 

On 29 Oct 2012, at 22:38, Stephen P. King wrote: 

On 10/29/2012 1:08 PM, Bruno Marchal wrote: 

On 29 Oct 2012, at 14:36, Stephen P. King wrote:  

[Bruno Marchal wrote:] So numbers are universal and can be treated 
mathematically as always.  

    I agree, but the concept of numbers has no meaning prior to the existence 
of objects that can be counted. To think otherwise is equivalent to claiming 
that unspecified statements are true or false even in the absence of the 
possibility of discovering the fact.  

Dear Bruno 

I think you confuse numbers, and the concept of numbers.  

    No, I do not. My claim is that Numbers are objects in the mind of conscious 

This contradicts what you said before. It contradicts comp immediately, as comp 
needs the understanding of what a computer can do, even in absence of any 
conscious observer.  

Dear Bruno, 

    It contradicts your version of comp, yes, but not mine, as I see minds and 
numbers as co-existing simultaneously, there is no ontological priority between 
them in my version.  

Comp is only the assumption that the brain is a machine, to be short. Then it 
is proved that the TOE is arithmetic (or recursively equivalent). Matter and 
mind arise from the numbers (and + and *). If you reintroduce a mind 
assumption, mind will be epiphenomenal. It you reintroduce matter, it will be 

If there does not exist worlds where entities to whom numbers are concepts then 
there is no such thing as a concept of numbers in such worlds.  

But with comp, a conscious observer is explained by number relations. We 
explain the concept of numbers, and of human understanding of numbers, by 
number relations (computations). 

    Sure, but we should be able to 'go the other way' as well! You seem to 
insist on a well founded relation where as I do not! 

I derive proposition. I suggest nothing, nor do I insist on nothing, except on 
reasoning validly. I am not a philosopher. you must understand the technical 
result before philosophising on it. It is subtle as comp makes a part of 
philosophy of mind into a branch of science (indeed, arithmetic/computer 

My argument is that concepts of truth and provability of theorems apply only to 
the concepts of numbers and their constructions, not to numbers themselves. 

Truth applies to proposition, or sentences representing them for some 
machine/numbers. If not, comp does not even makes sense. 

    Your version, yes. 

Not my version. "My" version is just a technically more precise that the 
version used in some literature. Comp is the same for everybody. "My" Version 
implies all other one, as it is a very weaker version (because it does not 
depend on which level of substitution we use). 

And then your argument is not valid, as with numbers, the miracle is that we 
can specify the concept of numbers, as this result in defining some 
arithmetical sigma_1 complete theory in terms of 0, s(0), ... and the laws of 
addition and multiplication, that everybody understands (unless philosophers?). 

    I am a philosopher! My argument rests only on the fact that the 'miracle' 
is exactly as you state it here: we exist and have a concept of numbers and can 
ascertain the truth of arithmetic statements. My claim is that truth valuations 
supervene on the ability of consciousness to form concepts of numbers. 

That is idealism, if not solipsism. In comp plotinus term, you confuse the 
outer God (the objective ultimate truth) and the inner God, or the sould of the 
individual inquirer. 

    No, Idealism is that only the mind exists, i.e. idealism takes the mind as 
ontologically primitive. Solipsism is the condition of a mind such that it can 
only interact with some version of itself. 

Given that matter comes from the numbers, if the number comes from the human 
mind, everything comes from the human mind. This is a version of (collective) 

I question the entire idea of numbers existing as separate Platonic entities. 
In the absence of consciousness, there is no such thing as a concept! 

Again, we need only the relation between the numbers, not the concept of 
numbers, which with comp will be explained by computation occurring in the 
brain of some machine/number. 

    Let me ask you: Do numbers have "concepts" of each other" YES! Godel 
numbers are a way for one number to have a concept of another.  

You can't be serious. A Godel number is a coding of something, which can indeed 
be a number. For a concept you need a thinking universal number; not just a 
faithful coding. Some numbers can be said having concept of other number, but 
just because some numbers implement sophisticated person relatively to their 
most probable computations. 

No? If they do not have something equivalent to concepts, how can they dream?  

Yes, the universal numbers can have concept.  

This is just to show that your idea implicitly considers that concepts are 
'mental' and that if numbers can be coherently said to have minds then their 
concepts supervene on their minds. But what are numbers as themselves - as 

We don't ever know that. But we don't need to know that, as we agree on the 
axioms, and reason from that. It is not philosophy.  

    What can know the 'in-it-self-ness' of a number such that that 
'in-it-self-ness' is not a concept? 


PS BTW, from a computer scientist perspective, your use of NP never succeed to 
make sense. I don't dare to ask you to elaborate, as I am afraid you might 
aggravate your case. The NP question is fundamental and has many interesting 
feature, but it concerns a local tractability issue, and is a priori, unless 
justification, not relevant for the arithmetical body issue, nor number's 
theology (including physics) issue, etc.  

    It is the argument is sound and is the same kind of argument as what Kripke 
used to discuss the idea of possible worlds. In 
http://en.wikipedia.org/wiki/Possible_world we read: 

    "There is a close relation between propositions and possible worlds. We 
note that every proposition is either true or false at any given possible 
world; then the modal status of a proposition is understood in terms of the 
worlds in which it is true and worlds in which it is false."  

All this presuppose numbers at the outset. World in Kripke are only elements of 
any set having a binary relation. You must study the math, not use the naive 
interpretation based on the use of common terms. 

    Please, you are not addressing my critique, but some straw man. You are 
smarter than to do that! 

Rephrase your critics. You lost me, as I don't even see the critics. 

    Solutions to equations or computations are not available until after they 
are actually solved.  

That is constructive thinking, again incompatible with comp, although retrieved 
and explain for the subject. This is akin to your solipsism above. 

    Where am I claiming that only my thoughts exist? Could you define what 
solipsism is and how I am being such above? 

Because you seem to think that a solution of an equation exists only if we have 
found the solution. I think that arithmetic is boolean, and so a solution exist 
or does not exist independently of me and you. 

Of course it is hard to guess what you think as long as you don't propose a 

    Oh, so its OK that you do not think that you propose a theory, but it is a 
crime is someone else does that. You are being a hypocrite with that claim! How 
childish! Stop trying to evade my critique. 

I am trying hard to get it, and don't succeed, and point that this fact might 
come by my unability to see what are your assumption. 

My solution to this is to not go so far as you do in Step 8.  

You can't make the conclusion of a reasoning false by stopping the reasoning. 
This will only make you ignorant of a conclusion.  

    blah blah blah... 


Let me try to be more explicit: 

>From your paper 
>http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.pdf :  

"Instead of linking [the pain I feel] at space-time (x,t) to [a machine state] 
at space-time  
(x,t), we are obliged  to associate  [the pain  I  feel at  space-time  (x,t)]  
to a  type or a  sheaf of  
computations  (existing  forever  in  the arithmetical  Platonia  which  is  
accepted  as  existing  
independently of  our  selves  with  arithmetical  realism). " 

Yes. That is already true in a concrete robust physical universe (robust = own 
a non stopping  UD). 

    OK, so how does it remain true when there is no physical universe? How can 
actions be defined on entities that are, by definition, static and eternally 
fixed? You result is self-stultifying here - not self-contradictory. If we take 
step 8 to be correct then there is no possibility of a means to communicate the 
meaningfulness of comp to anything other than the mind of Bruno Marchal, since 
his chalkboard can be, do be consistent not a "physical object" and thus is at 
best a "dream".  

? The chalk seems to be obviously a physical object. But comp explains where it 
comes from.  

Whose dream? Dreams of Numbers. What makes how are the dreams of numbers more 
"special' than the dreams of Pink Unicorns or Purple Ponys? 

If you have a theory of Pink Unicorns precise enough to be proved Turing 
universal, it is OK.  
The laws of both mind and matter are totally independent of the initial objects 
you assume, be them numbers or combinators, or Pink Unicorn. Just give me the 
axioms you assume on Pink Unicorns. 

    We have discussed how concepts and objects are not the same thing, so what 
is the object aspect of a number?  

We don't need to know that. We need only to agree on the axioms: 

x + 0 = x   
x + s(y) = s(x + y)  

 x *0 = 0 
 x*s(y) = x*y + x   

together with some axioms on equality. 

How does a number demonstrate its nature other than through concepts? It 

It can. Read any textbook in mathematical logic, or theoretical computer 
science. Or G?el original papers. It is coneptually not so difficult, just long 
and tedious, as it it an implementation of high level notion (concept of 
number) in low level notion numbers, addition and multiplication. 

    I am pointing out that the idea of computations "existing independently of 
our selves" is wrong in that it conflates the meaning and truth valuation of 
numbers with the existence of numbers as Platonic objects.  

You seem to ignore that this conflation is not us, but the doing of the 
(universal) numbers themselves, and this independently of me, you, or 

    OK, then this very independents prevents any meaning from being associated 
with its existence and thus the ability for "this sentence is true" to refer to 
itself vanishes (as it would for any Godel Numbering that does exactly the same 
thing or any derivative thing).  

Why would meaning disappear? I guess you are again violating comp. The meaning 
and consciousness is preserved in the digital (arithmetical) emulation. 

Independence isolates and cuts off connections, so do not claim that the 
results of those connections remain once independence is claimed.  

Then you say no to the doctor. 

There is no such thing as "running" or "implementing" or "meaning" or anything 
that is anything derivative of an action if step 8 is correct as you state it 
therefore AUDA is steaming rubbish if you insist on it. Why? Because AUDA (and 
all the argument about G and G* and Z and  Z*, etc) is "independent' of 
physical implementation and that independence goes both ways - it independence 
is applied coherently. 

? All statements referred to in AUDA are theorems in PA. (the theory above + 
the induction axioms). And the theory above proves that already, as it emulates 
(but is different from) PA. 

    If A and B are independent then they have nothing to do with each other at 
all, unless their is some C that is prior to A and B. If A and B are 
independent of the physical and timeless, there is nothing prior to them 
therefore no relation or prior to them can be used to infer any relation what 
so ever between them.  

You might be correct here, and that is why it is a good thing that the 
*primitive* physical universe does not exist, as it would be indeed totally 
independent of any mind, and would be an epinomenon. 

Even the common naming conversion, A and B, is treachery as it tacitly assumes 
that there are two objects that can be simultaneously known and distinguished 
both between each other and some common background vanishes is they are 
independent and timeless. Your concept of Platonism is deeply flawed. 

But here you lost me again. 

        You should spend some time studying philosophy if you are going to 
pretend to make philosophical arguments. 

I do not. That's the point.  

It is absurd to refer to the claim that the truth of "17  is prime" depends on 
any one person or entity, but the claim that the truth of "17 is prime" is 
knowable by any person is not absurd.  

It is absurd with comp, as knowing, despite NON arithmetical in the logical 
sense, is still defined in purely arithmetical terms. If not, you will not 
surive with an artificial brain, even concrete. 

    No, it is not absurd, except for you that allows concepts of actions, such 
as "implements" and "runs", to exist when they cannot be coherently defined. 

But they can. I already define them once (or twice). read any textbook in 
theoretical computer science. running, implementation, etc. are purely 
mathematical notion. It just happens that we can approximate them through a 
physical reality, and that is what make comp possible. But the the physical 
reality appears to be necessarily emerging from the numbers and their mind (or 
the mind associated to person associated to the arithmetical relations, to be 
more precise). 

If we stipulate that the content of knowledge exists somehow prior to that 
which knowledge supervenes upon, we are being absurd.  

This is just realism. The semantical content of knowledge as to exist 
independently of you if you don't want to fall into solipsism.  

    How is it related to the word "real" at all? You are only showing us the 
mathematical theory of a consistent solipsist  

Not at all. On the contrary I ascribe mind to numbers (in relation with opther 
numbers). It is the contrary of solipsism. 

and, as a consistent solipsist you are unable to conceptualize that you are 
wrong, after all "it is absurd that anything contradict the solipsist as only 
it exists and its existence is only possible if it is consistent". 

    Some thing is "real" only is that reality is common for many, thus 
solipsism and realism are mutually exclusive. 

Of course. 

The content of knowledge and the ability of knowledge occur simultaneously or 
not at all. 

With comp they "occur" as consequence of + and * laws. 

    No. There is no "occurance" in your comp.  

The machine 678 on argument 456 stop after less than 456789 steps. That is a 
statement which if true can be proved in arithmetic, and you can defined many 
notion of occurrence from it. 

Nothing can possibly "occur".  

An infinity of emulation of the collision of the Milky way and Andromeda occurs 
in arithmetic.  

In your result these is only "is".  

In GR too. In physics you can always replace a dynamical phenomenon by a higher 
dimensional statical structure. With comp we get the higher structure at the 
start. Dynamics arise in the internal inside views. 

X is Y, not any X occurs iff Y. There are no coherent concept of actions in 
your comp. 

There are many. 

You really seems to lack even just the computer science intuition. Please study 
the book by Mendelson, or ask precise question, but most of it have already 
been explained. 

    Absent the "concept" of numbers there is no such thing as valuations of 

Then 17 is prime only since humans exist on the planet? or since insects use 
this to regulate mating? 
This is solipsism/idealism. 

    You fail to read temporarily or is it OK to attack straw men? Read further 
of my post.  

The fact is that your current posts makes me doubt about your position on "17 
is prime independently of us". 

because the notion of Platonic objects considers objects as existing 
independently as some singular "perfect" version that is then plurally 
projected somehow into the physical realm, as we see in the Allegory of the 
Cave. This is a one-to-many mapping, not a one-to-one mapping.  

? (so you postulate conscious observer *and* physical universes?). Your theory 
looks more and more like Craig's non comp theory. 

    They are very similar, I admit that. You have no idea what Craig's idea is 
as demonstrated by your inability to describe it accurately as anything other 
than rubbish or noise. 

I have great respect for Craig's attempt to defend a non comp theory. But you 
seem to want both comp and a Craig-like theory, and then that is what I have 
shown inconsistent. Craig's theory is consistent, as it assumes non-comp. But 
your "theory", as far as I understand it, is not. Now Craig is not consistent 
in most of his argument against comp, as his conversation with Stathis 
illustrates, but that is another point. 

    How exactly is a "type" or "sheaf" a singular and "perfect" version of each 
and every computation and yet be something that has individuated valuations? 
Individual valuations of computations are only those that occur as physical 
instantiations of computations  

"physical instantiation of computations" is something in needed to be 
explaiend, not assumed, if we want to understand something (not just comp). 
Computation evaluation is a too fuzzy terming for me. 

    A physical instance of a computation is the existence of a physical system 
that can "run" a universal turing machine.  

Trivially true. The whole point is that such a physical existence will no more 
be primary.  

It can do so, among other things, because it uses resources of time and/or 
memory to transform through some set of states such that it reproduces the 
functions of the UTM.  

Agains that is true for the physical universal machine. But not for all 
universal machine, and the physical emerges from the work of all universal 

Straight forward idea that we see in texts on computers. Nothing new or 

because computers are thought as physical, since we build them. but the 
mathematical notion preceded it, and does not rely on physical notion of 
resource, but on mathematical notion of "enough memory". 

and thus they do not "exist" in Platonia. 

Then Church thesis has no more meaning. 

    To you, perhaps. What a pity! 

To everyone. If arithmetical realism is excluded, you can no more explain the 
consistency of Church thesis by the diagonalization. You need to believe that 
for all i and j, either phi_i(j) stops or phi_i(j) does not stop, independently 
of you. 

The Many exist in the physical worlds, no? 

Primitive one? 

    No. Not primitive, derivative. No different from how numbers are derivative 
in my thinking and that of most natural philosophers.  


Your mistake is in assuming strict ontological well foundedness;  

? Comp makes this possible. 

the idea that there has to be a irreducible ontological primitive that has 
innate properties. If you would read Bertrand Russell's discussions of neutral 
monism then you might see his explanation of what I am proposing and not have 
the straw man of my terrible writing to use as a shield of your unwillingness 
to try to understand what I am trying to communicate to you. 

You are quite unfair as I try hard. 

    Irreducible objects, in the ontological sense, cannot have a particular set 
of properties as such is to exclude all other possible properties without 
justification. To claim that numbers can be ontologically primitive and yet 
have valuations and abilities is to deny their irreducibility, as values and 
abilities are derivative, not fundamental or innate. 

Give me the entire quote of Russell. keep in mind that Russell philosophy has 
been refuted by G?el, also. But the very existence of principia mathematica 
makes me doubt that Russell ever defended an ontology with object who 
irreducibility prevents them to have properties; such an ontology would be by 
construction not amenable to scientific analysis.  

    I propose a rephrasing of your statement above: We identify the 1p qualia 
to a sheaf of computations (as bisimilar Boolean Algebras) that is dual to 
physical machine states at diffeomorphically equivalent space-time coordinates 
(x, y, z, t). This is a restatement of the Stone duality into COMP-like terms. 

That does not make sense to me. Sorry. 

    Read some more books on philosophy, such as The Problems of Philosophy 

I read it, and it does not say one word related to the paragraph above. 

it might make sense in some non comp analogical theory of mind, with mind and 
matter explicitly defined in term of non computable diffeomorphism. But this 
looks to me like making the mind-body problem more complex just for fun. 

    No, I am trying to show you how to solve the 'arithmetic body' problem. 

You have just to see if the arithemtical quantization defines the measure, as 
it seems to promise up to now. If not, then comp + (theatetus definition) is 
All what I have done is a translation of the arithmetic body problem in 
arithpmetic. The solution can only be technical, although some variability 
exists due to the use of the classical theory of knowledge. It is already a 
mircale that the Theaetus definition of knowledge gives rise to the classical 
theory of knowledge. Without G?el and L?, that would be impossible. 

(The idea of diffeomorphic equivalence is discussed in detail here: 
http://plato.stanford.edu/entries/spacetime-holearg/Leibniz_Equivalence.html ) 

When you say:  


    Yes, this is the Pre-Established Harmony, but as I have argued before this 
concept is deeply flawed because it tries to claim that the solution to NP-Hard 
problem (of choosing the best possible world) is somehow accessible (for the 
creation of the monads by God) prior to the availability of resources with 
which to actually perform the computation of the solution. One cannot know the 
content of a solution before one computes it, even if one is omniscient!  


I don't find any sense. 

    How is this so difficult for you to comprehend? The Platonic Realm is 
defined as timeless, everything in it just 'exists', no?  

Only in the sense that if some proposition P(n) is true independently of me, 
then ExP(x) is true independently of me.  

    But you are not the only entity involved in the truth of P(n)!  

I am not involved at all. 

You pretend that it is possible for something to be so absurd! P(n) is true 
only because it is possible to implement some version of P(n) and verify that 
indeed P(n) is true.  

Then arithmetic is no more boolean, and both "yes doctor" and "church's thesis" 
have no more meaning.  

The mere Platonic existence of P(n)  

P(n) does not exist. 
n exist, and P is true or false about it. 

is insufficient for truth as truth is a derivative evaluation.  

Not at all. truth is a matter of fact. 

It cannot be ontologically irreducible. 

Truth is is the easiest notion to conceive as irreducible, for a platonist.  

Therefore any argument that shows that "if A does not exist then neither does B 
if B requires A to exist" is true in Platonia as well, (we stipulate the 
existence of Platonia as defined for the sake of this statement). If a solution 
to a computation cannot exist until the computation is run then if the 
resources required to run the computation do not exist then there does not 
exist a solution to the computation!  

So you cannot compute 10^1000 + 10^1000, and your theory is ultrafinitist (and 
so non-comp). 

    False. Straw man argument. 

Then why do you say that a computation has to be run to assert the existence of 
its solution. And run by who, and where? 

    I propose that we can easily resolve this conundrum by stating 
Computational universality as: "A computation is universal if and only if it is 
independent of any particular physical implementation."  

Universal applies to finite entity (numbers, humans, machines, language). Not 
to computations, although the running of a universal dovetailer can be said 
universal in some context, but only by abuse of language. 

    So? How does that contradict my definition of universality? 

The computation of 2+2 will not depend on any particular implementation, yet it 
is not universal. 

This allows for the existence of physical implementations,  

Comp allows this too; without the need of assuming physical realities. 

    Rubbish. You must assume the a priori possibility of physical reality to 
even have a coherent notion of comp or else it is, at least, not communicable. 

I have already explain why this is a confusion of level. 

even those that are themselves defined by correlations between sheaves for 
computations. This sets up a relation between computations - as abstract or 
immaterial objects - and physical systems that seems consistent with "COMP 
minus Step 8". We can recover the picture of step 8,  

Step 8 is a consequence of comp, like all steps in the UDA.   'Comp minus step 
8' implies that  0 = 1. 

    LOL, no. It only means "'Comp minus step 8' implies that  0 = 1."  for a 
consistent solipsist. 

Then you have to find a flaw. 

in a way that is truly neutral ontologically, by changing its single directed 
arrow to a pair of oppositely directed arrows, but this one that occurs only in 
the ultimate sense of the elaboration of all possible physical worlds 
consistent with Pratt's idea. 


    Straw Man. 

Then you have to elaborate. 

    This idea, BTW, is consistent with the concept of Indra's Net, as an 
inversion of the idea that every Jewel reflects all others: Every jewel is a 
physical world that is defined by all computations of it. Note also that this 
naturally includes self-computation as jewels also reflect themselves. ;-) 

I have no more any understanding by what you mean by "physical world". It seems 
like a God-of-the-Gap. 

    I define a physical world as the set of mutually non-contradictory 1p for 
some set of non-solipsistic entities that have certain properties that at least 
allow for some coherent notion of communication between those entities. 

Then the physical reality emerges from the 1p. Like in comp. why do you take so 
much time to criticize comp for not assuming a physical reality. And how do you 
define 1p, without using physics or notions of resources. 

I hope you don't mind my frankness. I wouldn't say this if I did not respect 
some intuition of yours. But math and formalism can't be a pretext for not 
doing the elementary reasoning in the philosophy of mind. If you use math, you 
have to be clearer on the link with philosophy or theology. To be 
understandable by others.  

    I am trying to be clear. I will correct and rephrase my verbiage until you 
understand it.  

It would help to tell us what you assume at the start. from what I understand 
it is just contradictory. Pratt assumes more than arithmetic. All paper you 
refer too assumes more than arithmetic. Your notion of consciousness and of 
physical universe seems to be very fuzzy and clearly not comp-compatible. 

    My point is that you are not "just assuming" arithmetic. You assume, 
additionally, at least that there is qualia.  

In UDA. No more in AUDA. They are defined and explain in arithmetic, as UDA 
eventually forces us to do. 

I reject the idea of an entity, 'God', whose total purpose is to "observe" the 
Reality of the Universe!  

Comp too. Comp rejects also the primitive reality of a physical universe. 

    So do I. I reject as ontologically primitive anything that is not property 

This makes no sense. It must be nuetral with respect to mind and body. Not 
neutral to any properties, as your theory will be unable to derive anything. 

If we accept the idea that numbers exist in our complete absence, then it 
follows that an entity like us cannot exist just to observe the existence of 
numbers (or anything else).  

? ? ? 

Why postulate the existence of a special entity that does what we collectively 
are already doing? 

Why postulate physical computations, and comp, when comp explains how physical 
computations emerges in our mind through the existence of the computations in 

    No, it does not do so alone. Comp requires the implementation of a physical 
symbolic representation of the idea for it to be even evaluated and thus 
implicitly requires something physical even if that "physicality" is derivative 
and not ontologically primitive.  

Then I don't see why you critics the consequence of comp, as it shows exactly 

Read Russell's book ad stop using straw amn arguments about my pitiful attempt 
to help you solve a problem that you ackowledge exists in comp. 

The existence of that problem is the main result (UDA) 
Then I transform it into a problem in arithmetic (AUDA). 

    It is our collective consciousness that Constitutes the Platonic Realm, 
IMHO. A theory that there is some independently existing realm is a gross 
violation of Occam. 

But you do it for the physical computations, like in this post, despite you 
often pretend the contrary in other posts. 



    Stop using logical fallacious statements. 

Which one. How is it fallacious? I might have been wrong, but you have to 
elaborate on the clarity of your statements. 



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