On Wed, Feb 11, 2015 at 12:08 AM, Bruno Marchal <[email protected]> wrote:
> > On 10 Feb 2015, at 08:21, Samiya Illias wrote: > > > > On Tue, Feb 10, 2015 at 12:50 AM, Bruno Marchal <[email protected]> wrote: > >> >> On 08 Feb 2015, at 05:07, Samiya Illias wrote: >> >> >> >> On Thu, Feb 5, 2015 at 8:27 PM, Bruno Marchal <[email protected]> wrote: >> >>> >>> On 04 Feb 2015, at 17:14, Samiya Illias wrote: >>> >>> >>> >>> On Wed, Feb 4, 2015 at 5:49 PM, Bruno Marchal <[email protected]> wrote: >>> >>>> >>>> On 04 Feb 2015, at 06:02, Samiya Illias wrote: >>>> >>>> >>>> >>>> On 04-Feb-2015, at 12:01 am, Bruno Marchal <[email protected]> wrote: >>>> >>>> >>>> >>>> >>>>> >>>>> Then reason shows that arithmetic is already full of life, indeed full >>>>> of an infinity of universal machines competing to provide your infinitely >>>>> many relatively consistent continuations. >>>>> >>>>> Incompleteness imposes, at least formally, a soul (a first person), an >>>>> observer (a first person plural), a "god" (an independent simple but deep >>>>> truth) to any machine believing in the RA axioms together with enough >>>>> induction axioms. I know you believe in them. >>>>> >>>>> The lexicon is >>>>> p truth God >>>>> []p provable Intelligible (modal logic, G and G*) >>>>> []p & p the soul (modal logic, S4Grz) >>>>> []p & <>t intelligible matter (with p sigma_1) (modal logic, Z1, >>>>> Z1*) >>>>> []p & sensible matter (with p sigma_1) (modal logic, X1, X1*) >>>>> >>>>> You need to study some math, >>>>> >>>> >>>> I have been wanting to but it seems such an uphill task. Yet, its a >>>> mountain I would like to climb :) >>>> >>>> >>>> 7 + 0 = 7. You are OK with this? Tell me. >>>> >>>> >>>> OK >>>> >>>> >>>> Are you OK with the generalisation? For all numbers n, n + 0 = n. >>>> Right? >>>> >>>> >>>> Right :) >>>> You suggest I begin with Set Theory? >>>> >>>> >>>> No need of set theory, as I have never been able to really prefer one >>>> theory or another. It is too much powerful, not fundamental. At some point >>>> naive set theory will be used, but just for making thing easier: it will >>>> never be part of the fundamental assumptions. >>>> >>>> I use only elementary arithmetic, so you need only to understand the >>>> following statements (and some other later): >>>> >>> Please see if my assumptions/interpretations below are correct: >>> >>>> >>>> x + 0 = x >>>> >>> if x=1, then >>> 1+0=1 >>> >>>> >>>> x + successor(y) = successor(x + y) >>>> >>> 1 + 2 = (1+2) = 3 >>> >>> >>> I agree, but you don't show the use of the axiom: x + successor(y) = >>> successor(x + y), or x +s(y) = s(x + y). >>> >> >> I didn't use the axioms. I just substituted the axioms variables with the >> natural numbers. >> >> >> And use your common intuition. Good. >> >> The idea now will be to see if the axioms given capture that intuition, >> fully, or in part. >> >> >> >> >> >>> >>>> Are you OK? To avoid notational difficulties, I represent the numbers >>>> by their degree of parenthood (so to speak) with 0. Abbreviating s for >>>> successor: >>>> >>>> 0, s(0), s(s(0)), s(s(s(0))), ... >>>> >>> If the sequence represents 0, 1, 2, 3, ... >>> >>> >>> We can use 0, 1, 2, 3, ... as abbreviation for 0, s(0), s(s(0)), >>> s(s(s(0))), ... >>> >>> >>> >>> >>>> Can you derive that s(s(0)) + s(0) = s(s(s(0))) with the statements >>>> just above? >>>> >>> then 2 + 1 = 3 >>> >>> >>> Hmm... s(s(0)) + s(0) = s(s(s(0))) is another writing for 2 + 1 = 3, but >>> it is not clear if you proved it using the two axioms: >>> >>> 1) x + 0 = x >>> 2) x + s(y)) = s(x + y) >>> >>> Let me show you: >>> >>> We must compute: >>> >>> s(s(0)) + s(0) >>> >>> The axiom "2)" says that x + s(y) = s(x + y), for all x and y. >>> We see that s(s(0)) + s(0) matches x + s(y), with x = s(s(0)), and y = >>> 0. OK? >>> So we can apply the axiom 2, and we get, by replacing x (= s(s(0))) and >>> y (= 0) in the axiom "2)". This gives >>> >>> s(s(0)) + s(0) = s( s(s(0)) + 0 ) OK? (this is a simple substitution, >>> suggested by the axiom 2) >>> >>> But then by axiom 1, we know that s(s(0)) + 0 = s(s(0)), so the right >>> side becomes s( s(s(0)) +0 ) = s( s(s(0)) ) >>> >>> So we have proved s(s(0)) + s(0) = s(s(s(0))) >>> >>> OK? >>> >> >> Yes, thanks! >> >> >> You are welcome. >> >> >> >> >>> Can you guess how many times you need to use the axiom "2)" in case I >>> would ask you to prove 1 + 8 = 9. You might do it for training purpose. >>> >> >> 1+8=9 >> Translating in successor terms: >> s(0) + s(s(s(s(s(s(s(s(0)))))))) = s(s(s(s(s(s(s(s(s(0))))))))) >> Applying Axiom 2 by substituting x=8 or s(s(s(s(s(s(s(s(0)))))))), and >> y=0, >> s(s(s(s(s(s(s(s(0)))))))) + s(0) = s( s(s(s(s(s(s(s(s(0)))))))) + 0) >> Applying axiom 1 to the right side: >> s(0) + s(s(s(s(s(s(s(s(0)))))))) = s(s(s(s(s(s(s(s(s(0))))))))) >> 1+8=9 >> >> Is the above the correct method to arrive at the proof? I only used axiom >> 2 once. Am I missing some basic point? >> >> >> Let me see. Axiom 2 says: x + s(y)) = s(x + y). Well, if x = 8, and y >> = 0, we get 8 + 1, and your computation/proofs is correct, in that case. >> >> So you would have been correct if I was asking you to prove/compute that >> 8 + 1 = 9. >> >> Unfortunately I asked to prove/compute that 1 + 8 = 9. >> >> I think that you have (consciously?) use the fact that 1 + 8 = 8 + 1, >> which speeds the computation. >> >> Well, later I ill show you that the idea that for all x and y x + y = y + >> x, is NOT provable with the axioms given (despite that theorey will be >> shown to be already Turing Universal. >> >> No worry. Your move was clever, but you need to put yourself in the mind >> of a very "stupid machine" which understand only the axioms given. >> > > I understand > > > > OK. > > > > >> Can you show that 1 + 8 = 9. Better, tell me how many times you will >> need to use the second axioms? >> > > Nine times. Here: > > 1+8=9 > > Prove: s(0)+s(s(s(s(s(s(s(s(0))))))))= s(s(s(s(s(s(s(s(s(0))))))))) > > For x=s(0) > > Using axiom 2, > > Rewriting for y=(s(s(s(s(s(s(s(0)))))))=7 > > Step 1: s(0)+s(s(s(s(s(s(s(s(0)))))))) = s{s(0)+s(s(s(s(s(s(s(0)))))))} > > Simplifying the bracket on the right side, for y=(s(s(s(s(s(s(0))))))=6 > > Step 2: s(0)+s(s(s(s(s(s(s(s(0)))))))) = s[s{s(0)+s(s(s(s(s(s(0))))))}] > > Simplifying the bracket on the right side, for y=(s(s(s(s(s(0)))))=5 > > Step 3: s(0)+s(s(s(s(s(s(s(s(0)))))))) = s[s[s{s(0)+s(s(s(s(s(0)))))}]] > > Simplifying the bracket on the right side, for y=(s(s(s(s(0))))=4 > > Step 4: s(0)+s(s(s(s(s(s(s(s(0)))))))) = s[s[s[s{s(0)+s(s(s(s(0))))}]]] > > Simplifying the bracket on the right side, for y=(s(s(s(0)))=3 > > Step 5: s(0)+s(s(s(s(s(s(s(s(0)))))))) = s[s[s[s[s{s(0)+s(s(s(0)))}]]]] > > Simplifying the bracket on the right side, for y=s(s(0))=2 > > Step 6: s(0)+s(s(s(s(s(s(s(s(0)))))))) = s[s[s[s[s[s{s(0)+s(s(0))}]]]]] > > Simplifying the bracket on the right side, for y=s(0)=1 > > Step 7: s(0)+s(s(s(s(s(s(s(s(0)))))))) = s[s[s[s[s[s[s{s(0)+s(0)}]]]]]] > > Simplifying the bracket on the right side, for y=0 > > Step 8: s(0)+s(s(s(s(s(s(s(s(0)))))))) = s[s[s[s[s[s[s[s{s(0)+0}]]]]]]] > > Using axiom 1 > > Step 9: s(0)+s(s(s(s(s(s(s(s(0)))))))) = s[s[s[s[s[s[s[s{s(0)}]]]]]]] > > Rewriting with round brackets > Step 10: s(0)+s(s(s(s(s(s(s(s(0)))))))) = s(s(s(s(s(s(s(s(s(0))))))))) > > > > OK. (get the feeling you use axiom 2 only 8 times, but that is a > detail). > Yes, its eight times. > > >> >>> Let me ask you this. Are you OK with the two following multiplicative >>> axioms: >>> >>> 3) x * 0 = 0 >>> 4) x * s(y) = x + (x * y) >>> >> >> Yes, they hold true when substituted with natural numbers. >> >> >> >> Really? >> >> Have you verified for all numbers? >> > > Generalisation ? > > > Well, I explain to you the type of axioms we need to be able to prove such > generalization. P(n) means P is some formula of arithmetic (made using only > the logical symbols and the arithmetical symbols: they are s, 0, + and * > (together with "(", ")", and as I said the logical symbol: we can use only > "->" (and define ~A by A -> (0 = 1)). > So that we are speaking the same language, please see if the following are as you mean them: s = successor 0 = zero + = plus / and ‘* = times / multiply -> = implies that ~ = all / everything / negation ? (0=1) ??? P = prove n = natural numbers > > To prove "for all n P(n)", you will need to prove > > P(0) > for all n P(n) -> P(n + 1) (P(s(n)) > > But to extract from this that for all n P(n), we need to explicitly accept > the infinity of induction axioms, for all formula F that we can express in > the arithmetical language. > > {F(0) & (for all n F(n) -> F(n + 1)} -> For all n F(n) > Can you please write this in English as well, so that I can learn to read your arithmetical sentences correctly instead of guessing parts of it? > > > > > >> Are you convinced that 768953 * 7999580012 = 768953 + (768953 >> * 7999580012) ? >> > > If (768953 * 799958001*2*) is corrected to (768953 * 799958001*1*) :) > > > > Excellent :) > > > > > >> >> >> >> >> >> >>> Can you prove that s(s(s(0))) * s(s(0)) = s(s(s(s(s(s(0)))))) ? This is >>> of course much longer, and you need all axioms 1), 2), 3) and 4). >>> >> >> I've tried two approaches, but I am getting stuck at the last step. >> Please see: >> >> Approach 1: >> Prove s(s(s(0))) * s(s(0)) = s(s(s(s(s(s(0)))))) >> for x=s(s(s(0))) and y=s(0) >> Applying axiom 4 >> Step 1: s(s(s(0))) * s(s(0)) = s(s(s(0))) + (s(s(s(0))) * s(0)) >> >> >> OK. With the usual notation, you proved that 3 * 2 = 3 + (3 * 1) >> >> >> >> Simplifying the bracket on the right side, again using axiom 4, assuming >> x=s(s(s(0))) and y=0 >> x * s(y)= x + (x*y) >> Step 2: s(s(s(0))) * s(0) = s(s(s(0))) + (s(s(s(0))) * 0) >> >> >> 3 * 1 = 3 + (3 * 0) >> >> >> >> Applying axiom 3 >> Step 3: s(s(s(0))) * s(0) = s(s(s(0))) >> >> >> 3 * 1 = 3 >> >> >> Replacing the value in Step 1: >> s(s(s(0))) * s(s(0)) = s(s(s(0))) + s(s(s(0))) >> In number terms, this translates to 3 * 2 = 3 + 3 which is correct but I >> do not know how to proceed with the proof. >> >> >> You are just forgetting the axioms 1 and 2. s(s(s(0))) + s(s(s(0))) >> matches axiom 2: x + s(y) = s(x + y). >> >> OK? >> > > Step 4: s(s(s(0))) * s(s(0))= s(s(s(0))) + s(s(s(0))) > > Using axiom 2, > > Simplifying the the right side of the equation, for y=s(s(0))=2 > > Step 5: s(s(s(0))) * s(s(0)) =s[s(s(s(0))) + s(s(0))] > > Simplifying the the right side of the equation, for y=s(0)=1 > > Step 6: s(s(s(0))) * s(s(0)) =s[s[s(s(s(0))) + s(0)]] > > Simplifying the the right side of the equation, for y=0 > > Step 7: s(s(s(0))) * s(s(0)) =s[s[s[s(s(s(0))) + 0]]] > > Using axiom 1, > > Step 8: s(s(s(0))) * s(s(0)) =s[s[s[s(s(s(0)))]]] > > Rewriting with round brackets > Step 9: s(s(s(0))) * s(s(0)) =s(s(s(s(s(s(0)))))) > > > > OK. > > > > > > >> >> >> >> >> >> >> >> Approach 2: >> Prove s(s(s(0))) * s(s(0)) = s(s(s(s(s(s(0)))))) >> for x=s(s(s(0))) and y=0 >> >> >> y = 0 ? >> >> >> Using the distributive property of multiplication (or whatever is the >> correct term for the following), >> Step 1: s(s(s(0))) * s(s(0)) = {s(s(s(0))) * 0} + {s(s(s(0))) * s(0)} + >> {s(s(s(0))) * s(0)} >> >> >> This is a bit weird, and besides, I will show that the distributive law >> is also NOT provable in this theory. >> >> To prove such generalization, we will later need a quite powerful >> collection of axioms: the induction axioms. They made the difference >> between "just Turing universal", and "Löbian". >> >> >> >> Using axiom 3 to simplify the first {} on the right side, >> Step 2: s(s(s(0))) * s(s(0)) = {0} + {s(s(s(0))) * s(0)} + {s(s(s(0))) * >> s(0)} >> Using axiom 4 to simplify the second and third {} on the right side, >> Step 3: s(s(s(0))) * s(s(0)) = {0} + {s(s(s(0))) + [s(s(s(0))) * 0]} + >> {s(s(s(0))) + [s(s(s(0))) * 0]} >> Using axiom 3 to simplify the second and third {} on the right side, >> Step 4: s(s(s(0))) * s(s(0)) = {0} + {s(s(s(0))) + 0} + {s(s(s(0))) + 0} >> Using axiom 1 to simplify the second and third {} on the right side, >> Step 5: s(s(s(0))) * s(s(0)) = {0} + {s(s(s(0))) + {s(s(s(0)))} >> Removing {}, >> Step 6: s(s(s(0))) * s(s(0)) = s(s(s(0))) + s(s(s(0))) >> which again translates to 3 * 2 = 3 + 3 which is correct but I do not >> know how to proceed with the proof. >> >> >> >> See above. >> >> Tell me if you are OK with my remarks, and we will proceed (as long as it >> is OK with you, of course). >> > > Very OK! Yes, please and thank you! > > > All right. > > > > > > > >> The problem with computer science and mathematical logic is that there is >> a long and tedious part to do at the beginning, almost like making empty a >> sea with a tea spoon. >> > > I've studied a bit of programming/scripting several years ago, so yes I > understand the need to be explicit with all steps. > > > OK. We have the same need when we translate statement about machine in > arithmetic. That this could be done was illustrated by Gödel, and can be > used to distinguish what is true about a machine (or even more general > creatures) and what the machine (or general creature) can justify, guess, > observe, feel ... about that, admitting some definition of those terms. > I get the drift > > Have you followed my posts on Cantor diagonalization, and Kleene > diagonalization? Do you know what the phi_i are? And the W_i? > No > > > I might need also you opinion about how much you conceive that a brain > might be a "natural" machine: which means something between will you accept > digital teleportation in case of some urgent travel? > Yes, I do think the brain is a natural machine, specialised to do its role as all other organs, so transplanting could be a possibility. You propose a digital teleportation where the brain is to be cut and pasted, while the organic material of the body is to be destroyed at source, and new organic material used at reconstitution level. This assumes that the brain contains all the information of the self. How can we be sure of that? > > The question is not a question "in practice", but in theory. Later on we > can prove that no correct machine can determined in a 100% justifiable way > its substitution level, that's why it asks for some explicit act of faith > (which really means: *cannot* be imposed to someone). > I suppose so, at least till it can be practically demonstrated to be possible and safe. Theoretically, I think more work needs to be done on the nature of consciousness and whether the mind is a part of the organic body or not, and if it is only located in the brain. > > > >> In particular, there are still little other "obvious" idea that you have >> used, and which have not made explicit into axioms, so we will need some >> refinement. >> > > Please guide. Thanks! > > May be after. > > The way I proceed makes it possible to avoid wishful thinking, > That’s the scientific approach! > and, although I find what is there absolutely fabulous, > Look forward to discovering it :) > I have learned that somehow many are not so much interested in that kind > of "possible truth". > Wonder why? Isn’t that what seeking knowledge is all about? > This seems confirmed by the fact that few like taking salvia twice, and > somehow, I can understand. > I wouldn’t be willing to take it even once. Other than the fact that the Book clearly guides against the use of intoxicants (as the sin is greater than the benefit), the use of a mind-altering drug just seems wrong. Also, I googled salvia inspired images, and they seem to be quite similar to images in polytheistic traditions. Perhaps its a parallel world you experience under its influence, and though I do believe in the existence of parallel worlds (of angels, and dJinns, and God knows what else), I also know that they have been hidden from normal human vision for a purpose. > It is really stuff for those having a passion in theology. > Passion in theology can be satisfied through the use of reason as well. Isn’t that what your comp represents? > Have you an opinion on Everett's formulation of quantum mechanics? > >From what I’ve read and understand of his theory, it seems like the logical deduction from possible quantum outcomes, in the absence of an outside force collapsing all other outcomes except one. However, intuitively, there seems something amiss. > > Are you OK with meeting another Samiya Illias? > Interesting idea! Ask me after I meet her :) > > I am not pretending that anything I say is true, > Good > but I do say that it can be derived from computationalism (there is a > level of brain/body description where consciousness is invariant for the > functional digital substitution), and even constructively for "classical > computationalism" (comp + Theaetetus, from the point of view of PA). > Need to study this before I can comment upon it. > > Jews, christians, and muslims were more open to, if not more aware of, the > Platonist way to conceive/search God in their earlier periods, but > eventually the mainstream continues to stick on the Aristotelian dogma, > like notably, the existence of some primitively physical beings. > I believe in [1] Allah, [2] His Angels, [3] His Books, [4] His Messengers, [5] The Latter Day (of destruction and re-creation), [6] Predestination (all fate, good or otherwise, is from Allah, the Most High), [7] Resurrection after Death. I believe in it just like I believe I’m alive in the present moment and that I will be dead at some future moment. > > To progress in the fundamental, we have to progress in doubting *almost* > everything. OK? > I am willing to doubt reason and logic and all other constructs of human intellect including my own. I am willing to question your theory and assumptions and proofs, in an effort to arrive at the possible truth. However, I am not willing to sacrifice faith on the altar of doubt. I do not believe that science has the ability to conceive God but I’m a believer in science’ ability to reason the existence of God, without presuming the existence of God. I think your comp represents the latter approach. That is why it interests me. Samiya > > Bruno > > > > > > > Samiya > > >> >> In case of doubt, please feel free to ask what is the point of all this. >> >> Bruno >> >> >> >> >> Samiya >> >> >> >>> If you can do this, Allah already knows that you are Turing universal >>> (in some large sense). You can know that too, once we have a definition of >>> Turing universal. >>> >>> With computationalism, except for some purely logical axioms, we have >>> already the "theory of everything". You can see that it has very few >>> assumptions. It does not assume matter or god, nor consciousness. The link >>> with consciousness, and Allah, can be made at some metalevel, by accepting >>> the idea that the brain or the body is Turing emulable. But for this we >>> need to work a little bit more. >>> >>> Bruno >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> Samiya >>> >>>> >>>> Bruno >>>> >>>> >>>> >>>> Samiya >>>> >>>> >>>> >>>> >>>> >>>> >>>>> to see that this give eight quite different view the universal >>>>> machines develop on themselves. >>>>> >>>> >>>> Reminds me of this verse [http://quran.com/69/17 ]: >>>> *And the angels are at its edges. And there will bear the Throne of >>>> your Lord above them, that Day, eight [of them]. * >>>> >>>> >>>> It is like that: The four first (plotinian) hypostases live >>>> harmonically in the arithmetical heaven: >>>> >>>> >>>> God >>>> >>>> Terrestrial Intelligible Divine Intelligible >>>> >>>> Universal Soul >>>> >>>> >>>> >>>> But then the Universal Soul falls, and you get the (four) matters, and >>>> the "bastard calculus": >>>> >>>> >>>> Intelligible terrestrial matter Intelligible Divine >>>> matter >>>> >>>> Sensible terrestrial matter Sensible Divine matter >>>> >>>> >>>> >>>> Here divine means mainly what is true about the machine/number and not >>>> justifiable by the numbers. >>>> >>>> >>>> >>>> >>>> >>>> >>>> It provides a universal person, with a soul, consistent extensions, >>>>> beliefs, and some proximity (or not) to God (which is the "ultimate" >>>>> semantic that the machine cannot entirely figure out by herself (hence the >>>>> faith). >>>>> >>>> >>>> Interesting! >>>> >>>> >>>> All universal machine looking inward discover an inexhaustible reality, >>>> with absolute and relative aspects. >>>> >>>> Babbage discovered the universal machine, (and understood its >>>> universality). The universal machine, the mathematical concept, will be >>>> (re)discovered and made more precise by a bunch of mathematical logicians, >>>> like Turing, Post, Church, Kleene. >>>> >>>> You are using such a universal system right now, even plausibly two of >>>> them: your brain and your computer. They are a key concept in computer >>>> science. They suffer a big prize for their universality, as it makes them >>>> possible to crash, be lied, be lost, be deluded. They can know that they >>>> are universal, and so they can know the consequences. >>>> >>>> The religion which recognizes the universal machine and her classical >>>> theology might be the one which will spread easily in the galaxy in the >>>> forthcoming millenaries. (Independently of being true or false, actually). >>>> >>>> Bruno >>>> >>>> >>>> >>>> >>>> >>>> Samiya >>>> >>>>> >>>>> If you want to convince me, you have to first convince the universal >>>>> person associated to the Löbian machine, I'm afraid. >>>>> >>>>> I am not pretending that the machine theology applies to us, but it is >>>>> a good etalon to compare the theologies/religions/reality-conceptions. The >>>>> problem is that we have to backtrack to Plato, where what we see is only >>>>> the border of something, that we can't see, but yet can intuit and talk >>>>> about (a bit like mathematics or music) >>>>> >>>>> Bruno >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> -- >>>>> You received this message because you are subscribed to the Google >>>>> Groups "Everything List" group. >>>>> To unsubscribe from this group and stop receiving emails from it, send >>>>> an email to [email protected]. >>>>> To post to this group, send email to [email protected]. >>>>> Visit this group at http://groups.google.com/group/everything-list. >>>>> For more options, visit https://groups.google.com/d/optout. >>>>> >>>>> >>>>> -- >>>>> You received this message because you are subscribed to the Google >>>>> Groups "Everything List" group. >>>>> To unsubscribe from this group and stop receiving emails from it, send >>>>> an email to [email protected]. >>>>> To post to this group, send email to [email protected]. >>>>> Visit this group at http://groups.google.com/group/everything-list. >>>>> For more options, visit https://groups.google.com/d/optout. >>>>> >>>>> >>>>> http://iridia.ulb.ac.be/~marchal/ >>>>> >>>>> >>>>> >>>>> >>>>> -- >>>>> You received this message because you are subscribed to the Google >>>>> Groups "Everything List" group. >>>>> To unsubscribe from this group and stop receiving emails from it, send >>>>> an email to [email protected]. >>>>> To post to this group, send email to [email protected]. >>>>> Visit this group at http://groups.google.com/group/everything-list. >>>>> For more options, visit https://groups.google.com/d/optout. >>>>> >>>> >>>> >>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups "Everything List" group. >>>> To unsubscribe from this group and stop receiving emails from it, send >>>> an email to [email protected]. >>>> To post to this group, send email to [email protected]. >>>> Visit this group at http://groups.google.com/group/everything-list. >>>> For more options, visit https://groups.google.com/d/optout. >>>> >>>> >>>> http://iridia.ulb.ac.be/~marchal/ >>>> >>>> >>>> >>>> >>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups "Everything List" group. >>>> To unsubscribe from this group and stop receiving emails from it, send >>>> an email to [email protected]. >>>> To post to this group, send email to [email protected]. >>>> Visit this group at http://groups.google.com/group/everything-list. >>>> For more options, visit https://groups.google.com/d/optout. >>>> >>>> >>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups "Everything List" group. >>>> To unsubscribe from this group and stop receiving emails from it, send >>>> an email to [email protected]. >>>> To post to this group, send email to [email protected]. >>>> Visit this group at http://groups.google.com/group/everything-list. >>>> For more options, visit https://groups.google.com/d/optout. >>>> >>>> >>>> http://iridia.ulb.ac.be/~marchal/ >>>> >>>> >>>> >>>> >>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups "Everything List" group. >>>> To unsubscribe from this group and stop receiving emails from it, send >>>> an email to [email protected]. >>>> To post to this group, send email to [email protected]. >>>> Visit this group at http://groups.google.com/group/everything-list. >>>> For more options, visit https://groups.google.com/d/optout. >>>> >>> >>> >>> -- >>> You received this message because you are subscribed to the Google >>> Groups "Everything List" group. >>> To unsubscribe from this group and stop receiving emails from it, send >>> an email to [email protected]. >>> To post to this group, send email to [email protected]. >>> Visit this group at http://groups.google.com/group/everything-list. >>> For more options, visit https://groups.google.com/d/optout. >>> >>> >>> http://iridia.ulb.ac.be/~marchal/ >>> >>> >>> >>> >>> -- >>> You received this message because you are subscribed to the Google >>> Groups "Everything List" group. >>> To unsubscribe from this group and stop receiving emails from it, send >>> an email to [email protected]. >>> To post to this group, send email to [email protected]. >>> Visit this group at http://groups.google.com/group/everything-list. >>> For more options, visit https://groups.google.com/d/optout. >>> >> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at http://groups.google.com/group/everything-list. >> For more options, visit https://groups.google.com/d/optout. >> >> >> http://iridia.ulb.ac.be/~marchal/ >> >> >> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at http://groups.google.com/group/everything-list. >> For more options, visit https://groups.google.com/d/optout. >> > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
