On 07 Jul 2011, at 03:12, B Soroud wrote:
" If reality = a physical universe"
Personally, I don't believe that. Here is the catch, I don't believe
its antithesis or any alternative.
Well the idea is to search for a theory.
"My point is that if we assume mechanism"
Unfortunately, since I am new to this... I don't know what you mean
by mechanism.
The idea that the body is a sort of machine, including the brain. So
that you can in principle survive with another body, coming from the
first by local functional substitution. I coin this into saying "yes
doctor" to a surgeon proposing you an artifical digital brain. But the
reasoning does not depend on the size of the brain, it might even be
the entire universe, which in that case is supposed to behave like a
machine.
The conclusion is an explanation how the laws of physics emerges in
the mind of the universal machine, or number (the digitality makes
them analog to numbers). This needs some amount of work to be familiar
with.
"physical reality emerges from something else"
Perchance, but what exactly is this "something else"... and where do
"we" fit into all of "this".
That something else is arithmetical truth. You have been taught this
at school:
1+1 = 2
1+2 = 3
etc.
Since Gödel, we suspect we know really nothing about just that. Here,
simplicity is a delusion.
"I want nothing. I am just pointing on the fact that mechanism is
not compatible with materialism, and I suggest or illustrate that we
can remain cold on those questions, and improve the clarity so that
the question mechanism versus materialism leads to testable empiric
consequences."
Fair enough. But unfortunately I can't fully follow you as we don't
have the same intellectual background in the sciences... we have
studied a different body of literature. I am not entirely sure what
you mean by mechanism versus materialism..... and I don't see why it
has to be a either/or. How about neither/nor?
I *assume* I am a machine, and I show that the "real" laws of
prediction of anything I can observe are given by a measure on an
infinity of computations going through my states. I worked a little
bit the math of this, enough to get interesting comparison with
physics. The point is that the theory suggest an explanation between
the observable and the "feelable" but non communicable, etc.
If you are anti soulless and vulgar materialism... and propose a
more spiritually fair and philosophically sophisticated position...
what exactly is that position? a species of Monadology? neo-
objective idealism?
yeah ... you can call that neo-objective rational idealism. But the
ideas are very elementary, just the natural numbers with addition and
multiplication.
There is something compelling in Objective Idealism... but what does
it mean to me beyond just an interesting speculative idea...
Well, no more once you accept the digital transplant. You can already
understand that *you* are immaterial. You might be able to change your
body every morning, or to travel through the web, useful to go back
and forth Earth and Mars. But then the delicate point to show, is that
such immateriality of you is contagious on your environment, and
testably so below your substitution level.
and why do I have the creeping suspicion that our notions of reality
are all too heavily dependent on our whim and fancy and conceptual
contingencies.... furthermore.... why do I have sufficient reasons
to be very skeptical and critical of human psychology and its
manifestations in every domain of action and thought? read:
Nietzsche, the Will to Power.
It is because I am an ultra skeptical that eventually I realize that I
might only believe in natural numbers and addition and multiplication.
I can't really doubt that 6 is even, and I need no more to explain why
some numbers develop stable believes in monstruous deep and complex
histories.
"OK. At least it looks like we share some anti-dogmatism."
We share more, I just don't follow your branch and line of thought,
and the system you've built... from my standpoint of ignorance
perhaps I completely misconstrue you, but it all strikes me as kind
of a computerscientists/mathematicians dream-baby. How could I
possibly approach your branch of thought, what are the background
readings and building blocks?
Hmm... You might read the book Mind's I, which is rather good (the
closer to the line I followed). For UDA you need just to trust your
reasoning ability, and you can take some point for granted, even if
for coming later to them. Yu have to train yourself on the ability of
reasoning from an assumption (with the knowledge that we cannot know
if the assumption is true or not). It is not that difficult, even if
the result seems scary. I called comp "terrifying thinking" once. Let
us pray that comp is false if it is to much scary, or that someone
will find a flaw in the argument.
"if comp is correct then you are stuck in "consciousness" for ever"
forever? forever ever? does forever even exist?
We don't know that, but it follows from comp, which assume
arithmetical truth, which is already very big.
How can you prove infinite time or eternal duration exists.... last
time I checked, you can't. Infinity is at best a mathematicians
symbolic fiction, he misconstrues it, it is pure imagination/pure
theory... if you ask me.
That is why I put it in the hypothesis. I accept that the independent
truth of 1+1=2, 1+2=3, 2+7= 9, etc.
That's not more than most scientists. In fact it is much less than
most scientist. To be sure, I will need more at the meta-level to
descrive the views and behavior of the numbers themselves.
But anyways, I'll give you the benefit of the doubt.... but read
Kant's critique of Infinity... its similar to the Kabalistic
critique... i.e. imagining expanding a circle until it reaches a
point of termination (its limit) beyond which you can imagine no
further, in other words... infinity is inconceivable.
I think for me to properly understand you guys I need background
reading and building blocks.... you guys abbreviate words and assume
a common body of knowledge and a certain proficiency in mathematics
and theoretical computer science/cutting edge cogni-sci etc. (for
example, I haven't even read Godel).. So what do you recommend I
read to learn about "comp"?
You might read GPodel, Escher, Bach from Hofstadter. Raymond Smullyan
wrote many puzzle book to get the idea of Gödel's theorem, I will
think about that question, but the field is a bit technical. The old
Anderson's "Mind and Machine" is not bad. Well, in this list we are a
bit in advance :)
"The discovery of the universal machine, by Post, Turing, Church,
etc. shed a lot of light on the mind body problem, if only to
explain it, and to show that it is not yet solved."
Okay, I know nothing about this... never read any of these guys...
any recommended readings... should I read them? I know not a thing
about universal machine.
It is the basic of theoretical computer science. I have often try to
explain a bit, but it is hard to give a course on mail. There is a
shortcut from Cantor diagonal to Kleene diagonal to Gödel diagonal,
etc. But it is real math.
"Now, you are right: some tradition develop clerical habits, and
some period can see the religion used to manipulate gullible people.
But that happens everywhere, even in academies."
I am surprised by your sympathy towards religious tradition, it is a
very unusual position that I am not used to. I mean I am sympathetic
to certain aspects of some... like how the Jewish tradition has a
very sophisticated argumentative tradition.... rife with debate and
open to it.... and it seems generally no one thinks they have the
final word or that things are one-dimensionally straight forward.
Yes, that is the point. taoists and some budhist have also allow rich
period of discussion. Then there is the theological trap: the
authoritative argument. But if you allow it in religion, you allow it
in science. Religion is the truth, and science is the tool. The truth
is alway the truth we search, and never the one we know, except in the
particular study of qualia (by definition).
"Without humans, no human will state "galaxies have many stars", but
the galaxies does not need the humans to have many stars."
Bruno, the funny thing is, I question that.... I seriously do. I
seriously seriously do. I believe our understanding of galaxies is
uniquely our understanding of galaxies... and if we didn't exist
there would be no such cognition as the one we have... and our
cognition = the galaxy in so far as we are concerned. It is our
cognition... one point of view on the matter... I don't believe
there is an objective and disembodied point of view on the matter.
And there is a point where we can agree, because I agree with you
about this, but you might have to replace "we, the humans", by "we the
universal machine".
So the way in which we understand this system of many stars is the
way in which we understand it... and if we go, the meaning,
perception, concept, formation or formulation, and cognition goes.
We see it in light of our own relative position and limitations...
we see our own form of "it"... which has no independent objective
existence in so far as anyone can conceive in actuality. That's my
view.
Yes, but then you want to share the view with someone else, and you
have to agree on some principle. If not it will be only an insight.
I firmly believe this is an undercontemplated and subtle insight:
""Man is the measure of all things: of things which are, that they
are, and of things which are not, that they are not".
Exactly. When you interpret "man" in the sense of the arithmetical
interpretation of Plotinus (it is the (Löbian) machine).
"Likewise, the truth (not its human expression) of Ex(x=x) might not
depend on the humans."
It might not, but... I wonder.... because it seems to be a
disembodied abstraction... what does it point to, where does it find
concrete actuality or particularity? In other words, what is it
really saying, what is it really pointing to or pointing out? It
might just be a simple statement of fact, a kind of pointless duh
that isn't actually independent of concrete phenomena, of concrete
particulars. Perhaps it is just a funny symbolical and generalistic
way to speak or view actual particulars...
Not really because the number reality behaves in way which never stop
to surprise those who study it. It kicks back, a lot. may be you
should read Derbyshire on the prime numbers.
I don't really buy logical truths in the abstract sense (I think
they are getting lost in our ability for abstract thought)....
We cannot derive the numbers from logic. They already escape logic,
and give a sort of very concrete reality, which appears to be more
complex than anything we might have imagine.
I don't think they exist in and of themselves... i think they are
human constructs... many have thought this.... in fact, you know I
haven't really read much on logic, not even one book.... because I
have always felt while reading it and learning about it.... that it
was illogical! I honestly feel a lot of logic is illogical or
somehow meaningless and artificial!
I like to say the english humor consists in taking classical logic
seriously. It never works, and so it is alway funny!
Deustch or constructive logic always works: and so is never funny. But
then pot is legal ;)
"I have evidence that the moon was the moon before life appeared on
the planet"
It may have been.... but it was not the moon as it appears to us...
We have our own particular point of view on the moon... and we can't
know the moon apart from that... not in a literal and actual
sense... or a truly objective one if that even exists.
" and I have evidence that 17 was already prime a long time before
the first human realized it is the case that 17 is prime."
well I don't want to push this point or dwell on this.... but I
personally see it as either a) irrelevant b) not absolutely apriori
c) kind of how do I say.... fake... meaning.... it works in a
certain system of axioms rules and truths and definitions, but not a
system that exists apriori in some cosmic sense and that has any
real value. I don't believe its like a absolute of the demiurge or
has any objective existence from its own side or any pre-human use
or conscious existence or self-transcendental reality.
We might differ on this, but I am not sure. that might be playwords.
Anyway, the axiom of elementary arithmetic are part of the comp
theory. You need it to just give comp any meaning.
"lol, Bruno, lets not argue... we will eternally disagree.
The fun is when we disagree. Nothing is more boring than a
conversation between people who agree. If we disagree eternally, we
will have fun eternally. Cool :)"
Yeah, don't you feel that thought is inherently dialectical? like
how it most go on and on and is in a sense dynamic radical and
endless? Once thought becomes static and crystallized... it becomes
dogma, creed, system... perhaps that is some forms of religion?
The real religion cannot be dogmatic. Dogma and terror is used by
those who does not trust their God.
"With (N,+,*)"
frankly, no clue what this means, nor do I know what universal
numbers are. nor was I aware I was one.
N is the collection of the non negative integers: 0, 1, 2, ...
+ is addition
* is multiplication
And a number is universal when it has some universal relation without
other numbers, and that would be too log to describe just here.
basically a universal number is the code or local description of a
computer, or a brain. Something which transform numbers or programs
into behavior. With comp we have or are such sort of numbers, even if
they are extremely variable.
" But we can relate to realities that we feel non temporal. This
happens when we listen to music, do love, do drugs, and, formidably,
when we do mathematics. Sometimes we can feel that eternity in
anything, even driving a car, or paying taxes"
see here I don't follow you.... I don't see how anything human could
truly be eternal. Mathematics serves humans, it is at least in part
our invention, no?
No. The words are invention, but math is really in the discovery of
what those words implied.
Mathematics would have value to no one else but us humans on this
earth. And I don't think we or this earth will be here forever.
Mathematics is useful everywhere, even outside the universe. Some
mathematical truth can take many different shapes according to the
view you take on it. Arithmetical truth is full of life and
catastrophes. After Gödel, we know that even in Heaven there are
typhoons!
If you are wishful driven, abandon comp!
Plus if the realm of independent truth has to be approached through
math.... that seems like a pretty dry and weird realm...
Not at all. They can't make math illegal, so they make it boring (a
bit like the Deutsch do with cannabis). But math is the biggest
reservoirs of big surprises that we can play with here.
it doesn't hold up to our aesthetical needs... like music and nature
and color does.... our emotional aesthetics needs of fulfillment. we
crave form and color and sound and diversity. Math is heartless. and
math is too cold and disembodied.
It is, but this is due to contingent cultural reason. I think. I know
a successful jazzman who quit jazz for math, and when someone asked
him why, he said that only math was able to satisfy its needs of
beauty and freedom. But math is also used to select people, and
mathematician often develop a feeling of superiority which can disgust
some other to go on the road. math is very rich, there is part for all
sort of taste. It needs work, but doing music too.
"Since Gödel, we know that simple truth really hide an unimaginable
amount of complexity. An object like the Mandelbrot illustrates that
too, and the notion of computer per se can help to understand where
the complexity come from: they do some mess in Platonia, a mess
which was unexpected by them, although intuited (see the chapter on
Numbers by Plotinus, for example). At least we comp we can explain
ho we related to them, because our bodies and mind result from an
infinite competition among them. The higher reality is both simpler
than us, and more complex than us. It is amazing, but explainable by
the distinction between the points of view, and those distinction
are not human made, they are universal machine made. This extends
Everett relativity to arithmetic. There is no much choice in the
matter, beside abandoning comp for taste prejudice."
I lost you here.... you are obviously coming from another field of
thought then me.......
This higher reality you speak of, is it aware of us,
Open problem. I would say no. Only recently I think it is aware, but
not really aware of us. Through us, it becomes aware of us, somehow.
does it think of us and hypothesize about us?
Yes. In a sense.
Does it desire and feel?
No.
Does it love and appreciate aesthetic phenomena?
No.
Does it plan for us?
No. (I use the comp theory + classical knowledge. I don't know what is
true, 'course).
Because if it is not as conscious as us, if it does not have our
same ability to think and understand and feel and love....
Indeed.
if it does not have higher faculties or powers then us... then I
wouldn't call it higher.
It is just vaster than the physical universe. It is not so big from
outside, but uncomputably big from inside.
I can't see how there could be a "higher" reality then the one we
are aware of or a higher being then us...
It is amazing but machines looking inward can get the idea of
something bigger than themselves.
But your Platonia strikes me as empty.... it feels like a heartless
world devoid of flesh and blood.
From outside. But the party proceeds inside.
"You just don't know, especially as a scientist.
If human continue to feel superior, God might invest on a more
humble creature"
I say we are the most "advanced" or the "highest" because we are the
one here doing all this thinking,
Who? You? This is partially an illusion. man has a big debt vis-à-vis
all living creatures. If man disappear right now, life continues. If
Bacteria disappear, life disappear. We have our role, but the whole
thinking has deep roots, and not just in our histories, also in that
abstract realm.
all this creative imaginative thinking and reasoning and
understanding and debating... it is our play and our enjoyment... I
am not aware of anyone else doing this....
No doubt that man thinks a lot. But the dinosaur could have said this
about their monumental physical forces. We might think too much, or
not enough.
and in so far as I am aware of them it is my thought or thinking
that makes me aware of hte possibility of concept of "them".....
therefore I see everything depending on my or our thinking....
thinking brings everything into being in a certain sense....
But you go close to solipsism. At some point we have to share
hypothesis on something we bet is not obviously us.
thinking plays the god of creator and destroyer (in a certain
sense).... and I just can't seriously conceive of a being of my
conception being superior to me (the one who conceives this being
and argues about it). What evidence? Just the endless play of thought.
In matter of competence (not intelligence) it can be shown that there
is something uncomputably more complex than a machine: two machines.
From the feeling you give me, I think that you would have love math
and computers, if they were appearing in some other way than in your
school or youth.
But if you like music, it is about the same, except for the
applications.
"Only, the phenomenal world is not all what is."
I don't follow you here. To me the phenomenal world is the main
event, the whole point. and I can't conceive of some other world...
yes, that might be your problem. And math is a tool for conceiving
other worlds and realities.
"I assume digital mechanism, then I explain why consciousness
preceded matter, in some sense."
But this must be practically indemonstrable, right?
Digital mechanism, like $any* theory cannot be proved, but my point is
that it is experimentally testable.
Even if it was true... and there is some notion of some form of pre-
terrestrial consciousness..... does it still exist... in the here-
and-now.... and what relevance does it have to us as mortal
beings... as ordinary human beings.
It might be relevant when we die, or before birth. Things appears more
complex than materialist want to believe.
And what of this "consciousness" what its destiny or teleology, what
its purpose or place.... and how does it explain the "scheme of
things" and the point of our being?
We might have to teach math and physics to our descendants so that
they will come back and save our souls, before the galaxy collide, but
there might be shortcut and exit door already nearby. The point of our
being is a difficult question. We start from 'to eat or being eaten',
to 'to be or not to be'. It is a bit like what is the use of a baby.
But then we get attached to them, and want to set them free, and hope
they will go farer. Comp does not answer everything, but usually can
justify why he remains silent on some question.
"From inside we confuse temporal evolution and the logical
deduction. That is why I do follow Pratt, and King, on the dualism
between set (3-person in Pratt) and boolean Algebra. It is already a
sort of points of view distinction in math (mathematically hard, or
not, to directly apply in the comp frame, for technical reason).
I think that stable measure makes us very rare in reality branches,
and the branches being very numerous, in at least an intuitive
rendering of the measure problem. But that is a good and important
question which we have to work on."
I lost you here Brun's
OK. I was alluding to years of conversation. Sorry.
"I love you Pseudonymous. You confirm so well my feeling that
materialists are religious about this. So I sin? So just proposing a
theory is a sin?"
Those son-of-a-bitches are religious about this.... but I am -not- a
materialist..... I am a agnostic/quarter Nietzschean....
I am a super agnostic too. I don't believe in God, nor in Matter. And
I don't believe in their inexistence as well. But then I show that if
we assume comp, much light on those kind of things is given. It is
free, and not yet taxed.
but I find materialism 75% compelling and 25% problematic or
perplexing and dissatisfactory. At the same time I find eternalists
highly suspect.
"That's an idolatry of nature. I do give her just a more solid base:
the natural numbers. Pun included."
Once again, frankly, i am unable to follow you.
p.s. I do believe in spiritual forces, or at least a more rarefied
and psychical variety of forces not spoken about by present day
physics. Or at least I think I do.
That is not so incoherent for someone who find materialism 75%
compelling. I am open to the idea that we can discover new force, but
spirituality is already some exploding just from the number relation,
that I find it not necessary to hypothesize more than necessary.
"I "resurrect" it from what any universal computer (including you)"
Surely you can think of a more romantic metaphor for my identity
then universal computer....
The point is that when you say yes to the doctor, it is no more a
metaphor. And personally I can imagine romance.
Also, I find this "looking inward" to be a form of psychic
confusion.... I don't believe in an actual inward, especially in
terms of inside the physical body.... nor do I believe in a actual
"inner space" or "mind-space"?
Me neither, literally. But it makes sense it term of the information
you can discover.
I think to "look inward" is to become confused, incredibly
confused.... it is an enigma.
That is an excellent start.
I think the majority of what we "see" when we "look inward" is the
figment of our imagination.
We can see that, but that's not all. That is why mediation technic ask
for some amount of calming down the thoughts.
Perhaps "inward" is something we imagine... I am very convinced of
this.
"we can already listen to the machines."
not sure what you mean here again... unfortunately. I don't know if
its my fault or your fault or both our fault.
Or the fault of someone else.
p.s. what is this UDA that you speak of which doesn't need math or
compsci and has 7 steps?
It is an argument which shows that if we are machine (comp) then
physics has to be derived from computer science or number theory, even
from number's theology (the truth about number, as opposed to what the
number can prove). If you want we can do each step one by one.
Actually I promised this in another forum, so I can give you a link
(here I have done it many times, and I think we need just to verify
one or two things for the step 8).
" It is a bit like the effect of drug, and there too, some headache
can happen."
I hope you don't take too many of these drugs Bruno!
You mean the legal one? Yes that is very nasty (toxic, addictive,
inefficacious, expensive).
I have taken them but I am skeptical of them. I prefer the
"analytical meditation" of the Buddhists as giving a more clear and
sharp and undeluded awareness.
yes, but many buddhist confuse the samadhi (total peaceful mind) and
enlightenment ("big sudden shift or perspective").
"and I look on the origin of physics "in the head" of the universal
machine (the key computer science object), as the thought
experiences/experiment (the 1 and 3 views) suggests"
eww... I am warry of thought-experiments....
But in the comp frame, they allow to skip hundred pages of math. you
have just to check the validity of the reasoning, hoping that the
definition and assumption are clear enough to proceed. It is really
the main tool to reason in the field.
It seems to me that you are on the cutting edge of super-theoretical
comp sci.... I want to emphasize super-theoretical. But that's cool
I guess.
"You might take a look to zooms on the Mandelbrot set. Here too, a
very simple relation z_n+1 := z_n^2 + 1, in the "complex number"
leads to a super-fractal, which is not just similar, but more and
intricate and complex."
lol, lost you again.... I guess Plato was right..... I am doomed to
not understand you unless I learn all the stuff you know. But we can
still argue in other ways.....
yeah, but as you can guess, my point is that comp can make many things
more precise, so that is is testable (but then it is also technical,
and needs work).
"Soroud, but you will become a mathematician if you enter.
And if comp is correct, you already entered, so strictly speaking we
have just to remind you of some things and different things."
good lord!
And the worst is that I meant it ...
"To be frank, you look a little bit like you forget that WE KNOW
NEXT TO NOTHING. If you agree you know next to nothing, how can you
be so quick in evaluating the works of the others, especially in a
complex if not taboo fields?"
Because I have struggled to grasp those guys..... and I have found
them ultimately lacking, just like everything else I've studied.
They didn't bring me any consolation of understanding or edification.
Not sure that science can give that, although I tend to believe it
does, in some long run (but that is just optimism).
DESIGN QUESTION: why would the "fundamental reality" be outside of
human experience.... what is the point of that?
But it is not. Arithmetical truth is not entirely outside you. It is
just big, but then the apparent cosmos too. Look at the filamentous
trails of galaxies ...
Human can play the big role, but they can also put the big mess. This
is not yet decided, from our perspectives.
We are the only ones that care or concern about it, hey it might
even be a figment of our imagination.... so why should it be so
utterly elusive and transcendent and out of reach and a reversal of
naturalism? That seems ridiculous.
It is counter-intuitive.
"But it needs observable feature to be a reality, at least a human
reality"
how observe?
By interaction in sharable histories/computations.
"The more correct we are on our probable universal environment, the
more we get free of it, and free to explore many dimensions of
reality."
Ah ha, now this is where you get real and get interesting.... so you
talk about exploring many dimensions of reality.... how so? what
dimensions? where? what for? how long? etc. etc. etc.
That is the whole point of reasoning. To fit the pieces of the puzzle,
we need something simple, but big. Arithmetical truth from inside is
¨very big*. This list is based in part of the work on Everett in
Quantum Mechanics, which shows that if we read QM literally, there are
infinities of parallel universes. I show that a priori, if we
similarly take just arithmetic seriously and literally, there are many
more dreams, and realities emerges from gluing property of dreams.
Reality is beyond fiction, always.
"It seems like any reality is assumed to not be us and we are assumed
to be related to it... therefore it is separate and either conceived
of as blind and inferior to us, our super conscious and superior to
us.
and why are we seemingly superior to this other...
And are we?"
doesn't it feel that way..... as far as I know this is all a figment
of our imagination.... all these thoughts we are having are
historically conditioned and of a historical moment...... If there
is anything outside this bodily awareness system..... especially any
superior intelligence.... why are we the ones philosophizing about
it, and in search of it. it seems that we are the creators here. I
haven't found any superior intelligence... and personally I am
amazed and impressed by our intellectual creativity and
sophistication.... so that is why I say we are. Its like even when
people talk about God as a force.... it seems to me that it is a
blind force, an impersonal force..... While we are the hyper aware
thinking beings making various evaluations and affirmations and
negations and giving everything its name and label.
By a sort of chance, locally, we might be, but universal machine will
be "terrible children", especially if we take time to recognize
ourself in there. But don't worry, I am thinking in geological times.
Universal numbers are universal babies, and without education they can
put a lot of troubles.
"It might depend on which One."
this is funny.... many One's?-------
lol. I meant many conceptions of One.
"You say that you know nothing, why don't you do a bit of research
and reflexion?"
okay, let me see if I can try, If I have an affinity for it, If i
find it not boring, dry, trivial, far-fetched etc.
so you are saying I can just read your paper without a extensive
background in math and cog-sci and comp-sci and physics and symbolic
logic etc.? Is your paper what you are referring me to research or
something else, like some other papers, articles, books or somehting?
Jason referred to Tegmark, but Tegmark is naive on math and still very
physicalist. In particular he uses the identity mind-brain. sane04
leads quickly to the understanding that such an identity cannot work.
Yes, I am biased of course, but I think the sane04 paper is a
shortcut. But the reading of Mind's I should help. And for the long
run with Gödel, Hofstadter's book is rather good (but long).
Hmm ... I have many nice books, but today books are quickly out-of-
print. I will think.
Bruno
http://iridia.ulb.ac.be/~marchal/
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