Bruno,
Does any or all forms of energy come from arithmetic?

On Wed, Nov 28, 2012 at 5:49 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:
>
> On 27 Nov 2012, at 19:52, Craig Weinberg wrote:
>
>
>
> On Tuesday, November 27, 2012 1:01:26 PM UTC-5, Bruno Marchal wrote:
>>
>>
>> On 26 Nov 2012, at 20:40, Craig Weinberg wrote:
>>
>>
>>
>> On Monday, November 26, 2012 1:46:53 PM UTC-5, Bruno Marchal wrote:
>>>
>>>
>>> On 26 Nov 2012, at 13:42, Craig Weinberg wrote:
>>>
>>>
>>>
>>> On Friday, November 23, 2012 11:54:57 AM UTC-5, Bruno Marchal wrote:
>>>>
>>>>
>>>> On 22 Nov 2012, at 18:38, Stephen P. King wrote:
>>>>
>>>>
>>>>
>>>>
>>>>     How exactly does the comparison occur?
>>>>
>>>>
>>>> By comparing the logic of the observable inferred from observation (the
>>>> quantum logic based on the algebra of the observable/linear positive
>>>> operators) and the logic obtained from the arithmetical quantization, which
>>>> exists already.
>>>> <snip>
>>>
>>>
>>> UDA refers to an argument. It is the argument showing that if we are
>>> machine (even physical machine) then in fine physics has to be justified by
>>> the arithmetical relations, and some internal views related to it.
>>
>>
>> Isn't an argument a logical construct though? I can't argue a piece of
>> iron into being magnetized. There has to be a plausible interface between
>> pure logic and anything tangible, doesn't there? It doesn't have to be
>> matter, even subjective experience is not conjured by logic alone. Can we
>> use logic to alone to deny that we see what we see or feel what we feel?
>>
>>
>> Of course not. Why would logic ever deny this?
>> On the contrary tangible things obeys some logic usually.
>
>
> The question though is how does that happen?
>
>
> Actually comp is better than physics here. in physics we don't know why and
> how electron obey the SWE. It is the ureasonable use of math in physics.
> With comp there is only math (arithmetic) and from this we can explain why
> numbers develop beliefs (axiomatically defined) and why they obey apparent
> laws
>
>
>
> How do tangible things interface with logic -
>
>
> I guess they would not tangible if they do not. tangibility ask for some
> amount of consistency.
>
>
>
> how do they know the logic is there, how do they 'obey' it, and through what
> capacity can they express that obedience?
>
>
> With comp this can be derived from the laws to  which the entities (actually
> 0, 1, 2, 3, ...) obeys.
>
> The number tree does not need to know anything for being able to divide 6,
> for example.
>
>
>
>>
>>
>>
>>
>>
>>
>>>
>>>
>>>
>>>
>>> Is your answer to 'what makes logic happen?' rooted in the presumption of
>>> logic?
>>>
>>>
>>> At the basic ontological level, I can limit the assumption in logic quite
>>> a lot.
>>
>>
>> I'm not sure why that changes anything at all. I think it makes it even
>> worse, because if you have a basic ontological level with very limited
>> logical assumptions, and everything is reducible to that, then what is it
>> that you are reducing it from?
>>
>>
>> ?
>
>
> If a roast pork loin is really a string of binary instructions,
>
>
> It can be that, but a string + a universal number can be decoded by a
> universal numbers into the apperance of a roast pork.
>
>
>
> then why isn't it a string of binary instructions? We do we need the pork
> loin?
>
>
> Worst, we cannot make sense of it in some absolute ontological sense, bu
> assuming comp, we can't avoid the delusion by the universal numbers about
> it.
>
>
>
> Why do binary instructions make themselves seem like pork (or shapes or
> anything other than what they actually are)?
>
>
> By the decoding process, like 100011011110 can be decoded into add 0 to the
> content of register 1000. Of course it is more involved in the "real case"
> of the "roasted pork smelly experiences".
>
>
>
>
>>
>>
>>
>>
>>
>>
>>>
>>> Actually we don't need logic at the base ontological level, only simple
>>> substitution rules and the +, * equality axioms.
>>
>>
>> Aren't rules and axioms the defining structures of logic? It sounds like
>> this:
>>
>> C: "How can you justify the existence of logic with logic alone?"
>>
>>
>> We can't. But we can derive the beliefs in logics in arithmetic.
>> (We can't derive arithmetic from logic alone, already).
>
>
> We can derive logic from sense though. All logic makes sense but not
> everything that makes sense is logical.
>
>
> You are right, even with comp. You need arithmetic above. At least, and with
> UDA: at most.
>
>
>
>
>>
>>
>>
>>
>>
>>
>> B: "Well, you don't need much logic. In fact you don't need any logic. All
>> you really need is logic."
>>
>>
>>
>> You need logic and arithmetic. Technically it can be shown that you don't
>> need so much logic (equality axioms are almost enough). The arithmetic (or
>> equivalent) part is more important. It is a technical detail.
>
>
> What does logic and arithmetic need?
>
>
> ?
> Nothing, I would say.
>
>
>
>
>>
>>
>>
>>
>>
>>>
>>> Only later we candefine an observer, in that ontology, as a
>>> machine/number  having bigger set of logical beliefs. But the existence of
>>> such machine does not require the belief or assumptions in that logic.
>>
>>
>> I'm not even bringing observers into it. I'm not talking about awareness
>> of participants, I'm talking about the emergence of the possibility of logic
>> at all.
>>
>>
>> Logic is defined by the minimum we assume like
>>
>> we will say that "p & q" is true, when p is true and q is true, and only
>> then.
>> We will accept that if we assume p and if we assume (p->q), then we cab
>> derive q from those assumption.
>> etc.
>> Logicians and computer scientist studies those kind of relations between
>> proposition. It is a branch of math, and it is not necessarily related to
>> foundations.
>
>
> So you are saying that logic comes from human teachings about how we can
> simplify the relations of ideas, not a universal primitive which is capable
> of animating matter or minds by itself.
>
>
> Yes.
>
>
>
>
>>
>>
>>
>>
>>
>>>
>>>
>>>
>>> That's ok with me, but you don't need any smoke or mirrors after that,
>>> you are pretty much committed to 'because maths' as the alpha and omega
>>> answer to all possible questions.
>>>
>>>
>>> On the contrary. The math is used to be precise, and then to realize that
>>> we don't have the answers at all, but we do have tools to make the questions
>>> clearer, and sometimes this can give already some shape of the answer, like
>>> seeing that comp bactracks to Plato's conception of reality (even
>>> Pythagorus).
>>> This is not much. Just a remind that science has not decided between
>>> Plato and Aristotle in theology.
>>
>>
>> How do we know that we aren't making the questions clearer by amputating
>> everything that doesn't fit our axioms?
>>
>>
>> If you believe some axioms is missing, you can add it.
>> If an axiom does not please to you, you can propose another theory.
>
>
> I start from the entire universe as a single indivisible axiom and refine
> focus from there.
>
>
>
> What entire universe? What is that, where does it come from? What is the
> relation with consciousness. You start from what I want to explain.
>
>
>
>
>>
>>
>>
>>
>>
>>
>>>
>>>
>>>
>>>
>>> when translated in arithmetic, makes a relative physical certainty into a
>>> true Sigma_1 sentence, which has to be provable, and consistent.
>>>
>>> Proof and consistency, again, are already features of logic. What makes
>>> things true? How does it actually happen?
>>>
>>>
>>> We assume some notion of arithmetical truth. I hope you can agree with
>>> proposition like "44 is a prime number or 44 is not a prime number".
>>
>>
>> What are the mechanics of that assumption though?
>>
>>
>> In comp we explains that mechanics with elementary arithmetic, universal
>> numbers, etc.
>>
>> We start from what we agree on, since high school.
>>
>> It is not more circular than a brain scientist using his brain.
>
>
> I agree it is no more circular than neuroscience, but I think the current
> neuroscientific approach to explaining consciousness is ultimately circular
> too. It might be a clue that the only way that we ourselves can disengage
> from circular thoughts is by using our will to consciously shift our
> attention from it.
>
>
> Or resolve the circularity. Computer science provides tools for doing that.
>
>
>
>
>>
>>
>>
>> The details of the propositions are not interesting to me, rather it is
>> the ontology of proposition itself. What is it?
>>
>>
>> That is a very interesting question, but out of topic. Logician model
>> often proposition by the set of worlds where those proposition are true, and
>> they often defined world by the set of propositions true in that world,
>> making eventually a proposition a set of set of worlds, and a world a set of
>> set of worlds, and there are interesting "galois like" connection, meaning
>> interesting mathematics.
>> It is an entire field of subject.
>>
>> With comp we don't need to go that far yet, although it is clearly on the
>> horizon.
>
>
> So comp is a proposition which has not yet proposed a theory of what a
> proposition is.
>
>
> Indeed. Proposition, as opposed to mere syntactical sentences, is as
> mysterious as consciousness, meaning, reality, etc. We need much more
> progress to handle that kind of things. But we can avoid the difficulties in
> comp by attaching proposition to couple "sentence" + "what a universal
> machine can do with the sentences". But this does not solve the riddle, but
> it can help.
> Keep in mind that all what I show in how complex the mind-body issue is with
> comp, if only because we must change our mind on the (currently
> aristotelian) physics.
>
>
>
>
>
>>
>>
>>
>>
>>
>>
>>
>> Who proposes?
>>
>>
>> Again, that is an interesting question too. here comp can answer, in the
>> 3p view, a number relatively to a bunch of numbers.
>
>
> Why and how does a number propose (undefined non-numbers?) to numerous other
> numbers?
>
>
> By virtue of the fact that they obeys the laws of addition and
> multiplication, which enable them to have complex computational relations
> with each others.
>
>
>
>
>>
>>
>>
>>
>>
>> How do they do it exactly?
>>
>>
>> By using their relations with each others. You need to study some books,
>> or follow my explanations on FOAR.
>
>
> What does it mean to use a relation though? It's sensory-motor metaphor.
>
>
> You can't redefined all term. I use relation in the usual (mathematical
> sense). A relation on a set A can be defined as a subset of AxA, for
> example.
>
>
>
>
> To use is to employ something as an object for a subjective motive.
>
>
> That's an higher level notion.
>
>
>
>
>>
>>
>>
>>
>>
>> That is the only magic that consciousness contains.
>>
>>
>> You make some jump here.
>
>
> Yes, it's only an editorial comment.
>
>
> Lol
>
>
>
>
>>
>>
>>
>> Beyond that, it's just mind-numbing patterns playing themselves out
>> forever. Participation is everything and no amount of interrogating
>> functions can conceivably synthesize that from logic. Logic does not
>> participate, it constrains and guides that which is participating as an
>> inert codex of blind axioms.
>>
>>>
>>> Not much is assumed, except for UDA, where you are asked if you are
>>> willing to accept a computer in place of your brain. The computer is
>>> supposed to be reconfigured at some level of course. We assume also Church
>>> thesis, although it is easy to avoid it, technically (but not so much
>>> "philosophically").
>>
>>
>> Church thesis is similarly reflexive logic. There is no reason to presume
>> that because anything that can be put into a Boolean box has other logical
>> commonalities that this (unquestionably important and worthwhile)
>> commonality extends to causally efficacious presence. An air conditioner
>> doesn't create air. Church assumes the air of sense making from the start
>> and then shows how all manner of air conditioners can be assembled from the
>> same fundamental blueprint. I'm not falling for it though. It's a sleight of
>> hand maneuver. While functionalism does card tricks with logic, the power
>> and reality of sense supplies the table, tablecloth, stage, lights,
>> audience, and girl to saw in half. Yes, I see, you pulled my card, King of
>> Diamonds, very impressive - truly, but how does it taste like chocolate and
>> dance Gangnam style?
>>
>>
>>
>> Comp explains why we cannot completely explain the sense, and this is
>> rather nice as it prevents reductionist theories of sense.
>>
>> On the contrary, by being open to sense in machine, comp is rather open in
>> matter of others consciousness.
>
>
> I don't see that explains the sense at all though. It explains how to use a
> certain kind of sense in a very powerful and extensible way, but it doesn't
> get to the hard problem.
>
>
> Indeed, comp does not solve it per se. You need the G/G* incompleteness to
> approach the explanation, which can be shown to be necessarily
> incompletable.
>
>
>
>
>>
>>
>>
>>
>>>
>>>
>>>
>>>
>>> So the observability with measure one is given by []p = Bp & Dt & p, with
>>> p arithmetical sigma_1 (this is coherent with the way the physical reality
>>> has to be redefined through UDA). Then the quantum logic is given by the
>>> quantization []<>p, thanks to the law p -> []<>p, and this makes possible to
>>> reverse the Goldblatt modal translation of quantum logic into arithmetic.
>>>
>>>
>>> Way over my head, but it sounds like logic proving logic again.
>>>
>>>
>>> It is not your fault. Nobody knows logic, except the professional
>>> logicians, who are not really aware of this.
>>>
>>>
>>>
>>> I talk about logic, the branch of math, not logic the adjective for all
>>> simple rational behavior that we all know. UDA does not use
>>> logic-branch-math, but of course it use the logic that you are necessarily
>>> using when sending a post to a list (implicitly).
>>> AUDA needs logic-the branch of math, due to the link between computer
>>> science and mathematical logic.
>>
>>
>> That's reasonable to me, but what I'm talking about is getting behind the
>> curtain of 'simple rational behavior that we all know', and what I find is
>> not a Platonic monoilith of idealism, but the ordinary experience of
>> discernment and participation. Logic supervenes on sense, but sense does not
>> supervene on logic.
>>
>>
>> You are right on this. Even with comp.
>> With comp sense supervene on logic and arithmetic though, in a testable
>> way as we get also physics.
>
>
> Comp bases that supervenience on its own amputated axioms though.
>
>
> Comp is the bet that we are machine (roughly speaking). This amputates
> nothing, unless you amputate machines from thinking, consciousness, but then
> it is your theory which amputates certain person.
>
>
>
> It says, 'whatever fits in this box also fits in every other box that is the
> same size'. It disqualifies everything out of its own box though.
>
>
> As a consequence we lost primitive matter, but then nobody has ever shown
> even one evidence for the existence of primitive matter, beyond the natural
> extrapolation of what we see (which proves nothing for the ontology).
>
>
>
> It has no theory of where logic and arithmetic emerge,
>
>
> We need to start from simple truth on which you can agree. If you doubt that
> 43 is prime, then I can explain nothing, indeed. But you seem to start from
> the entire universe, and sense, which nobody can really agree on. It is only
> recent that scientists approach the notion of sense, and the notion of
> physical universe is controversial.
>
>
>
> while it is clear to me that they emerge from sense.
>
>
> You are lucky.
>
>
>
>
> Counting is the intellectual act of making sense of a quantity
>
>
> OK, but how will you define quantity, then?
>
>
>
> - of naming experiences as an abstract collection.
>
>
> From what, on what?
>
>
>
>
>>
>>
>>
>>
>> Dreams prove that we are perfectly content to enjoy a universe without
>> logical consistency, but there is not any proof that I know of which
>> suggests that logic relies on qualia or matter. Therefore, it seems to me
>> that logic must either be a psychic phenomenon and therefore not primitive,
>> or that psychic phenomena is illogical and the universe which we think we
>> live in is impossible. I don't think the latter is plausible because it
>> would undermine our ability to have any kind of meaningful opinion about
>> anything real if that were the case.
>>
>>
>> It is unclear. Logic plays different role at many levels, and so do
>> algebra, statistics, arithmetic, computer science.
>
>
> It isn't clear that logic is the cause. To the contrary, I think it has to
> be an effect.
>
>
> No problem with this. I am a bit neutral on this issue.
>
>
>
>
>>
>>
>>
>>
>>
>>>
>>>
>>>
>>> Comparison is used in the everyday sense.
>>>
>>> Yes! Now that I understand. What's wrong with the 'everyday sense' being
>>> the reality
>>>
>>>
>>> That would cut all the funding in fundamental sciences, as this answer
>>> everything. It is a bit like "why do you waste your time trying to
>>> understanding the thermo-kinetics of car motor and how car moves? Why not
>>> just accept that car moves when we press on the pedal?"
>>
>>
>> I think just the opposite. My view says that thermo-kinetics is just the
>> beginning,
>>
>>
>> As a beginning it is fuzzy and assumes a priori much more. I do agree on
>> the importance of the concept of heat, we might all be some sort of steam
>> engine, but this is more a matter of implementation.
>>
>>
>>
>> we need to start studying what is the 'we' that presses the pedal also.
>> More funding for interdisciplinary science as well as fundamental.
>>
>>
>> I agree.
>>
>>
>>
>>
>>>
>>>
>>> The everyday sense is a part of reality, and I would understand it in
>>> term of the simplest assumption possible. Then my point is only that if comp
>>> is true (that is, roughly, if we are machine) then we can already refute the
>>> lasting current idea that there is a primitive physical universe. It gives
>>> at least another rational conception of reality, which gives the hope to get
>>> the origin of the physical laws, and the material patterns.
>>
>>
>> I don't see the advantage of a reality which is primitively arithmetic or
>> primitively physical.
>>
>>
>> I just show that if comp is correct, then it is enough, and adding
>> assumptions is cheating with respect to both mind and matter (and their
>> relation).
>
>
> Then I don't see the advantage of a reality which is comp or materialist.
>
>
> If you search advantages, then you let your mind open to wishful thinking,
> which is not a truth friendly attitude, even if the Löb formula seems to
> give a sort of role to a form of arithmetical placebo (see sane04 part 2).
>
>
>
>
>
>>
>>
>>
>>
>>
>>
>> Either way we are depersonalized and our lives are de-presented while
>> subterranean abstractions crank out automatism with ourselves as vestigial
>> deluded spectators, powerless in our inauthentic simulated worlds.
>>
>>
>> No. I'm just afraid you get some bad math teachers. Or you are unable to
>> understand that reductionism is provably dead about numbers and machines
>> already. You are the one who put the cold in some place.
>>
>
> It's hidden right in your words. "I'm just afraid you get some bad math
> teachers" is admission that the beauty and warmth of mathematics requires
> seeing them with the right eyes.
>
>
> Yes, OK.
>
>
>
> It's your sense of numbers which is wonderful - your sensitivity to them,
> not the numbers themselves.
>
>
> That is debatable. I have learn to appreciate the numbers because some
> people found amazing relations, and succeed in convincing me, and everyone
> taking the time to do the work,  about the truth of those relations.
>
>
>
>
> They are just unconscious, automatic fragments of mirror which will refelect
> whatever light is present.
>
>
> Yes.
>
>
>
> If your reason is particularly illuminating in the mathematical-logical band
> of sense, then it's like lighting up a fluorescent disco with a black light.
> If I go in there with only my FM radio to listen to, I don't hear much of
> anything.
>
>
>
> OK.
>
>
>
>
>
>>
>>
>>
>> If instead we look at what we are looking at, and see realism for the
>> sensory experience that it is, then arithmetic truth and Hermetic arts fall
>> out of it organically. Algebra and geometry coexist to serve an
>> experiential, theatrical agenda, not a functional one.
>>
>>
>> The sensory realism is 1p, and non communicable, and complex to describe
>> (you poetry, novel, movies, music, etc.), so we can't build on it. But it is
>> not because we build on 3p things, that we stop to ascribe consciousness to
>> them, and indeed comp ascribe consciousness to a much vaster set of entities
>> than any form of non comp.
>>
>> You just illustrate your reductionist conception of number and machine.
>
>
> Machine and number I think are as vast a universe as 1p experience, but in
> the impersonal 3p mode. From my view, it is functionalism which overstates
> 3p assumptions and compulsively assigns them to 1p, mainly out of a fear of
> personal realism.
>
>
> It assigns 1p to them, yes. Strong AI too. It is part of the assumption. The
> opposite assumption treats them as zombie. In case of doubt I think the
> attribution of consciousness to zombie is less damageable.
>
>
>
>
>>
>>
>>
>>
>>
>>>
>>>
>>>
>>>
>>>
>>> and the specialized logic being one category of specialized mechanisms
>>> within that?
>>>
>>>
>>> Logic is not fundamental at all, for UDA, you need only the everyday
>>> logic that you need to be able to do a pizza. Arithmetic is far more
>>> important, if only to understand how a computer functions.
>>
>>
>> Haha, you're still telling me that a little bit of shit in the tuna salad
>> doesn't count. If it tastes like logic, then I don't think you can use it to
>> prop up a primitive that supervenes on logic.
>>
>>
>> I never use the word logic. I use arithmetic which is infinitely richer
>> and stronger. Logic is just a very good tool, like algebra. I assume comp,
>> so it is normal that computer science plays some role, and many logics are
>> related to computer science.
>
>
> Isn't arithmetic a kind of logic though?
>
>
> Not really. (of course with "kind of" you might say that everything is a
> kind of something).
>
>
>
>
> Doesn't counting and addition require that an output is guided by logical
> transformations on an input?
>
>
> Not purely logical. It needs to assume some stuff, like 0 is a number, and
> that is not logical. The early 20th century logicians have tried to deduce
> "0 is a number" from logic, but they failed, and eventually we understand
> now what it has to fail (failure of logicism, discovery of the importance of
> intuition in math).
>
>
>
>
>
>
>>
>>
>>
>>
>>>
>>>
>>> Yet more advanced logic can help for two things, when doing reasoning:
>>>
>>> -showing that a proposition follows from other propositions (deduction)
>>> -showing that a proposition does not follow from other propositions
>>> (independence).
>>>
>>> Then, concerning the relation between mind, thinking, feeling, truth,
>>> etc. many result in logic put some light, and that is not astonishing once
>>> you bet on comp, even if temporarily for the sake of the argument.
>>>
>>> In logic, the branch of math, the beginning is the most difficult,
>>> because you have to understand what you have to not understand, like formal
>>> expressions.
>>>
>>> Logic is just like algebra, and those things imposes themselves once we
>>> tackle precise theories, and relations between theories. It helps for
>>> refuting them, or representing a theory in another, etc.
>>>
>>> I know that comp invites to math, and that this seems to be a problem for
>>> many.
>>
>>
>> To me the problem with comp is that it perfectly describes a universe that
>> we don't actually live in.
>>
>>
>> Not at all. Comp reformulate the problem into justifying what we live in
>> from arithmetic with the internal views. If this don't match we abandon
>> comp. Comp is just the assumption that we are machine emulable, at some
>> level.
>
>
> That assumption makes it so that all internal views are modeled in a way
> which automatically justifies them to comp. It is the yellow glasses that
> prove that everything is yellow.
>
>
> All theories are such glasses. You statement attacks science, not just the
> comp assumption. It criticize the act of doing assumption, it seems to me.
> Of course we can stop science and enjoy the view, and that can be a good
> philosophy of life, but it is not what scientists do.
>
>
>
>
>
>>
>>
>>
>>
>> In theory a formula could move my arm, because my arm could, in theory, be
>> nothing but data, but in fact, that isn't what we see. Most of our lives are
>> struggles for mathematically irrelevant resources - time, money, sex, more
>> money, more sex, etc. They aren't arithmetically interesting problems.
>>
>>
>> Don't confuse a tool and what humans do with it.
>
>
> Why not? What is a tool for humans other than some implement with which
> humans do things?
>
>
> So human can be guilty, not the tools. Guns are pacific, when human let them
> sleep in the closet.
>
>
>
>
>>
>>
>>
>>
>>
>> The universe which comp describes should be one of florid plasticity and
>> constant exploration,
>>
>>
>> I agree!
>>
>>
>>
>>
>> not struggle and frustration. How does a computer get frustrated? Why
>> would it?
>>
>>
>>
>> When he explores and got punished,
>
>
> I think that is an anthropomorphic projection. Is there any mathematical
> evidence which shows outcomes effected by punishment?
>
>
> As much as with human, by definition as humans are machine, by the comp
> assumption.
>
>
>
>
> Not talking about disadvantageous game conditions, but actual cruelty and
> intention to cause hurt feelings. Do computers care if you punish them?
>
>
> Yes. By definition of comp. I mean humans are computer and seems to care
> about punishment.
>
>
>
>
>
>>
>> when authoritative arguments abound, when the elders fear too much and the
>> youth not enough. The universal machine get frustrated when her universal
>> inspiration is constrained by the contingencies, despite they brought him
>> here also. That's life.
>
>
> That is life, but I don't think it's arithmetic.
>
>
> Yes, but that is due to your a priori that machines cannot think, be
> conscious, ...
>
>
>
>
>
>>
>> But we can suggest better way, and listening to the others is a good
>> heuristic, and when the other looks quite different, like with machine, we
>> might learn something.
>
>
> The way I see it, my way opens the door to a whole new universe of
> impersonal artifacts and beauty, while I think with comp, all we will end up
> doing is reinventing ourselves.
>
>
> Perhaps. There is a sense to say that the creation is what God can use to
> reivent himself all the time. But why would that prevent artifacts and
> beauty? Is not more beautiful? Well, that's personal taste of course, a
> priori independent of what is, or not.
>
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
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