2nd instalment - the plot thickens! (scroll down if you have read the
first instalment)
The Amoeba’s Secret
Bruno Marchal
May 19 2000
English version by K. Jones
To the memory of my parents
Contents
1. Introduction
2. The Amoeba’s Secret (1961→1971)
3. Goedel’s Diagonal (1971→1973)
4. Blacker than you thought [I] (1973→1977)
To be cont.
Chapter 1
Introduction
The mind returns to itself like a glove – Buddhist proverb
Mr Edgar Morin, president of the jury on Le Monde 1998’s University
Research Prize, commended the laureates, I amongst them, seeing the
happy fortune of our doctoral theses published chez Grasset, that we
should have no hesitation in adopting a presentation bearing full
witness to the human and personal aspect - all of which decided me to
relate it’s entire history.
I should recognise the somewhat special character of the result, but
also, and perhaps especially, because of the nature of the path
undertaken. I brought up the question of the work’s basis for the
first time in 1963, at a school in Brussels. I was eight years old: I
do not know if I was particularly precocious or merely highly-strung.
In effect the motivation for this work and, for the research toward it
commencing in infancy, has always been linked to a fear of death.
There are other more fundamental reasons for my describing this
unfolding path, an essential part of which is situated in my earliest
infancy:
1. The work is essentially multidisciplinary. It is situated at
the intersection of numerous disciplines – theology, psychology,
biology, chemistry, physics, mathematics, information technology –
and, suddenly, it is difficult to know with what to begin. Bearing
this in mind, the way of kids’ questions is particularly fit for the
purpose.
2. I questioned myself, but rapidly began wondering where the
questions came from; a good part of the thesis rests on a process of
self-observation. We will see how the thesis is naturally self-
explanatory, how it explains its own genesis. An aspect made clearer
if one follows, even if only briefly, the path of the kiddies’
questions. I myself profited thereby and ended up with a more polished
version of the principal argument. There is no attempt at dumbing-down
and the reader can skip any passages judged too technical.
3. The opportunity to do justice and homage to the great authors
and books that stake out my quest, amongst them: G. Ames & R. Wyler,
James Watson, Linus Pauling, Michel-Yves Bernard, Lewis Carroll, E.
Nagel & J.R. Newman, Jean Ladrière, S.C. Kleene, Bernard d’Espagnat.
4. …and to recount a Belgian in the best, or universal story in
the worst of cases, nothing at all of which is very funny. This story
explains why I defended my thesis in 1998 in France. I shall recount
these events without hatred or spirit of revenge.
I will tell you in several words even now, the principal result. To
begin with, the work presents a proof, which is to say a deductive or,
to use heavier terminology, a hypothetico-deductive argument. This
signifies there is a hypothesis as much as a “thesis”, in the more
technical sense of what is demonstrated from this hypothesis.
By way of proof, I expect that if the reader is not fully convinced of
the result after study of the work, he should put up either a non-
justified proposition or an error. Note that, concerning deductive
work, conclusions never officially carry over to reality. Scientific
proofs operate inside the frame of a postulated theory. Science is
thus always modest on the subject of its applicability to or its
approximation to the real.
The hypothesis is that of Mechanism: the idea that we could be digital
machines, in a sense that will be rendered more clearly in due course.
Grossly speaking, we would be machines in the precise sense that no
parts of our bodies are privileged with respect to an eventual
functional substitution: this says that we can survive a heart
substitution by the transplant of an artificial heart, or of a kidney
by an artificial kidney, etc., inasmuch as the substitution is carried
out at a sufficiently fine level. Neither can there be any constraints
imposed on the level of substitution chosen. It’s important to
remember that I am not going to defend the hypothesis of Mechanism. I
only want to pose this hypothesis at the outset. It constitutes the
predefined frame of the work1 [footnote 1]
[Footnote 1: Note that the idea of taking Mechanism or
Computationalism as a hypothesis seems to be, rather curiously,
original. Since Descartes (and even before, notably among the Hindu
logicians), there is a staggering amount of literature surrounding the
question of Mechanism and the mind, but it is always a question of
arguments in favour of Mechanism or arguments against it. Many also
think that Mechanism is by itself a solution to the mind-body problem.
This, I hope is a strong suit of the current work, to show that
Mechanism does not automatically resolve the mind-body problem. On the
contrary, it necessitates a reformulation of the problem taking the
form of a necessary justification of belief in the appearance of a
material world, physical or substantial (to anticipate in one phrase
the principal result of the work.)]
The discovery described here is that in this case, that with this
hypothesis of Mechanism, physics becomes reducible to the psychology
of machines. The “of” should be interpreted in both the transitive
and intransitive senses: clearly it is a question of psychology
concerning machines as much as psychology inferred or postulated
correctly (by definition) by the machines themselves. We will be able,
with a little information theory, to define this psychology in the
wider sense of the machines’ “self-referentially correct”
discourse. Such a psychology appears non-normative: we will see that
it makes of us beings vastly less well known to ourselves than we had
ever imagined. It constitutes a sort of “vaccine” against the
numerous forms of reductionism of human psychology.
The reduction of physics to psychology happens also at the
epistemological level: physics effectively becomes a branch of
psychology – the science of observable machines – as it does at the
ontological level: matter or the appearance of matter emerges from
consciousness, from the mind or the mental or even as we will see, of
“possible gambles” made by all digital machines.
It seems that what I have succeeded in demonstrating is that to truly
take seriously the hypothesis that we are digitalisable machines, is
to be forced to recognise a reversal of the naturalist or materialist
idea, quite widespread among philosophers, physicians and the man in
the street, that physics is the fundamental science to which all the
other natural and human sciences - at least ontologically and thus in
principle - should be reducible. I summarise this theorem by:
comp ⇒ reversal
where comp designates “computationalism”, a name often given to
“Digital Mechanism” and reversal designates the reversal of
psychology with physics. What results is not a primitive matter with
consciousness emerging from the organisation of the matter but the
reverse: consciousness is now the more primitive and matter, or rather
the appearance of material organisation, emerges from all the possible
experiences of all the possible consciousnesses; and this in a
sufficiently precise sense that derives physics (science of matter)
from psychology (viewed as a very general science of conscious
experience, or more positively, of stable discourses by the machines
themselves: physics, but not geography2, belonging necessarily to this
self-referential discourse, which I will demonstrate.)
[Footnote 2: Physics becomes the study of what is a priori observable
by every observer. The moon’s existence is not (in all truthfulness)
a physical law. By now one might fear that the physical laws lead only
to trivial truths, but we will see that the constraints of Mechanism
detrivialise this introspective physics.]
At this stage, anyone who for any good reason were to be persuaded
of the veracity of contemporary materialism3, can always surmise that
the present work constitutes a rejection of Mechanism. This will
nevertheless pose a problem since Mechanism is, implicitly or
explicitly, the philosophy adopted by the majority of materialists.
[Footnote 3: Throughout this work, “materialism” will be taken in
the weak sense of the philosophical doctrine that postulates the
existence of a substantial universe (a fact of things obeying laws
independent of us).]
Concerning my own position on this I remain silent. My philosophical
opinions rest and will remain private. In the more technical part of
the thesis I nevertheless show that one can already extract enough
qualitative and quantitative givens from physics once this is shown to
be derivable from machine psychology. We can then confront the results
with the usual empirical and modern physical theories – notably
quantum mechanics – to start to see an empirical confirmation of this
psychology and thus confirmation of the reversal.
By illuminating problems in the interpretation of (quantum) physical
facts, this thesis vehiculates a de facto judgement: the judgement
that the reversal and Mechanism, its reasoning logic, are plausible.
A final observation concerns rationalism and interdisciplinarity.
This work pleads as “rationalist”. Like Karl Popper, I appreciate
the match between rationalism and elitism. Rationalism is a form of
hope concerning the reasoning powers of others. It is the hope that
the other will have the courtesy to listen to you and accept your
results or to indicate to you your errors, or to say to you at the
very least that the subject is of no interest to him. Popper writes:
Faith4 in reason is not only a faith in our own reason but also – and
even more – in that of others.
[Footnote 4: French translation of Popper quote suppressed.]
Thus a rationalist, even if he believes himself to be intellectually
superior to others, will reject all claims to authority since he is
aware that, if his intelligence is superior to that of others (which
is hard for him to judge), it is only insofar as he is capable of
learning from his own and other peoples’ mistakes, and that one can
learn in this sense only if one takes others and their arguments
seriously. Rationalism is therefore bound up with the idea that the
other fellow has the right to be heard, and to defend his arguments.
(Karl R. Popper5)
[Footnote 5: The Open Society and Its Enemies. London, Hutchinson, 1950]
I feel in particular, that reason is a universal and, universally
profitable. Nothing else like science exists that is clearly separate
to all other human endeavours. I merely believe that there are those
possessed of a scientific attitude, which is no more than a form of
modesty and honesty with themselves and with others. This attitude
does not depend on any particular domain. I have a ready-made slogan:
Some gardeners are more scientific than astronomers
And, I might have said astrologers in place of gardeners6.
[Footnote 6: One can consult a fine book by Suzanne Blackmore In
Search of the Light for an example of a scientific contribution to
parapsychology, albeit somewhat negative.]
Today a kind of artificial chasm is maintained between the human
sciences and the exact sciences. To combat the so-called elitist usage
of mathematics, a minister of politics7 was struck by the notion of
suppressing numerous hours devoted to maths in diverse sections of
secondary teaching.
[Footnote 7: This idea was defended by Claude Allègre, explored in his
book The Defeat of Plato (Fayard, Paris, 1995) and applied when he
ascended to the post of Education minister.)]
In the same way, more and more hours of maths teaching are being taken
away from the human sciences. This can only finish by discouraging
teachers from teaching by demonstration – meaning explanations – of
formulas in mathematics courses. One would presumably do the opposite,
short of teaching other mathematics in the human sections.
The prohibition on the generalised use of deductive or interrogative
reason, and on mathematics itself, contributes not only to rendering
the human sciences less exact and the exact sciences less human, but
also especially to rendering the human sciences less human and the
exact sciences less exact, as should be clear from a reading of the
present work.
Note that I do not claim that reason is everything, or that it is a
kind of universal panacea. I only say that reason, properly
considered, should stand as the first rung of courtesy, permitting
evolution and progress in the research of knowledge. Short of making
courageous “backflips” from time to time, as in revising one’s
beliefs or abandoning a prejudice, this is how things should be.
Reason is not sufficient for progress in knowledge. There must also be
inspiration, attention, imagination, bravery etc. While reason is not
of itself sufficient, it is necessary to communicate results to others.
Again concerning interdisciplinarity, I often like to cite Descartes.
He wrote:
One must therefore be convinced that all the sciences are so linked
together that it is easier to learn them all at the same time, than to
isolate each from the other.
I hope that the present contribution will illustrate to what extent
Descartes was inspired on this point. As with the collaborations on
quantum mechanics of Einstein, Podolski and Rosen on the one hand, and
of Bell on the other, this work should also illustrate the artificial
character of the frontier between science and philosophy, or even
between science and theology. We will return to this point.
Any traces of eventual frontiers existing between the sciences and the
philosophies rest ultimately on philosophical postulates, avowed or not.
The advantage in my briefly recounting to you the pathways taken by my
still-young thoughts, lies in the fact that children are naturally
interdisciplinary: they have not yet submitted to that form of
brainwashing known as “academic specialisation”. Children will
always pose questions without fear of where they might be putting
their feet.
Chapter 2
The Amoeba’s Secret
(1961 → 1971)
what am I doing here in these miasmas
tiny little Lilliputian
seized by terror, sometimes by asthma
before these tonnes of thingumajigs
Gaston Compère, “Geometrie de l’absence”
What follows evidently constitutes a partial view of the past. I am
not telling my life-story, merely those sparse events that illustrate
the threading of the ideas and questions that together form the origin
of the discovery.
Certain paediatricians claim that the first metaphysical crisis, or
the first anxious moments concerning death, occur in children around
age 4. Perhaps. I remember well the terror that invaded my mind day
and night, and I demanded all manner of assurances from my parents
that I would wake up the following morning.
With the well-intentioned care of silencing any woes in children,
parents are apt to tell stories. As I was born in Germany, a nanny
would regularly read to me in German many folk-tales, mainly those of
the brothers Grimm, although I am not so certain that these offered me
any appeasement concerning my worries.
It must have been at around the age of 5 or 6 when as I remember,
doubtless by a sort of absent-mindedness or simply out of fatigue
since I assailed him with questions remorselessly, that my father
informed me that Saint Nicholas did not exist.
“And Father Christmas?”
“Him neither” my father replied, sadly noting my incredulous and
king-hit countenance. Thus collapsed my first theory – or ontology,
mythology, theology, belief, dream…call it what you will; at this
age, any precision on my part had been premature.
“And the fairies?” I pleaded.
“Them neither”
“But, come on – the angels and all that…?”
Here I could see that I had come once again to pose my father an
embarrassing question. After a long drawn-out sigh, he explained to me
that really he believed in none of it – in angels or in God, but that
my cousins and uncles and aunts believed it all. This astonished me
all the more in that fairies were for me no more than female angels
equipped with magic wands. I liked fairies and angels because they
could fly (had I gone on to develop this tendency I might have become
an aviator), but in the main because fairies and angels were immortals.
By now I had realised that adults could have differing beliefs. I
found this profoundly shocking. If my cousins could believe in angels,
was it not my right to also believe in them, as well as in fairies?
My father explained to me that it was surely my right after a certain
fashion, to believe in whatever I wanted to believe, but that it was
by no means evident that to do so would be in my best interest.
To believe in false propositions is to invite deception and
disappointment. I found entirely pathetic the notion of believing in
the false, and the whole thing gave me the shudders. From this moment
on, I would try to adhere to the rule: avoid at any price belief in
falsity.
The truth, evidently, can give rise to fear. In particular the idea
that I was a mere mortal seemed to me to be at the very limits of the
acceptable. But the idea of believing in falsity out of fear of the
truth worried me all the more. I therefore made promise to myself to
always search for the true, fearsome as this may well turn out to be.
To know would seem even better.
To know is better: agreed. But is this even possible? Surely it cannot
be easy.
To start with, I observed that during nightly dreams I was able to
believe in just about any falsity. In addition, I suffered sleep
problems, like many kids, something confirmed by
electroencephalography. My dreams were abnormally realistic. This
hyperrealism was fine in the case of lovely and pleasant dreams, but
it became truly worrisome in the case of strange dreams and
nightmares. Doubts arising from dreams, even concerning the
possibility of knowing truth, will play a role in the story that
occupies us here. There is nothing original in any of this; the
metaphysical role of dreams appeared with the Hindu idealists, Plato,
Descartes, Berkeley, as I would learn later on.
There followed the problem of a divergence of opinion between my
father and my uncle. Before, everything was simple: a proposal was
true if and only if my father asserted it1.
[Footnote 1: I express myself here in adult language; at the time I
would have been hard-pressed to formulate such a proposal in this way.]
Since he had evinced several seconds of doubt over the existence of
angels and told me that my uncle himself believed in them, I truly
wondered just whom I should believe over this.
I asked my uncle why he believed in angels. He replied, inasmuch as I
can recall with any precision, that his belief was based in the fact
that his parents believed in them, also his grandparents, etc. I found
his reply frankly troubling. In effect, if his ancestor had been
mistaken, this mistake would be propagated from generation to
generation. I came to admire my father’s placing in doubt his own
parents’ beliefs, and I decided to never believe in a proposition
under simple pretext that it had been announced by a trusted person or
family-member. I had hit upon what one now calls the principle of
Independent will, a founding principle of the Independent University
of Brussels, the university where my father concluded his juristic
studies after a learning spell with the Jesuits. I have no doubt that
he may have influenced me.
I asked my father why he did not believe in angels and fairies (I
could not have cared less about St Nicholas and Father Christmas
because to my mind they were not even immortals). He responded by
saying that having thoroughly searched everywhere, no one had
encountered them anywhere. There followed a deluge of revelations: we
live on a ball suspended in space, we have already orbited it etc. It
seemed like no place existed for fairies and angels.
In order to not run the risk of believing falsity, my interest in
imaginary beings slid over to a pronounced interest in animals, for
whose existence nobody had even the slightest doubt. Returning to
Belgium from Germany, my parents bought a small hobby-farm in the
country to which we would go during vacations and on the weekend. I
passed a lot of time observing swallows, butterflies, ants etc. When
observing an animal, for example, a butterfly, I identified body and
soul with this butterfly. If it flew, it was I who flew, if it
gathered pollen, it was I who gathered pollen and it was I who became
intoxicated by the multiple nectars of the flowers of the fields.
One day, I pointed to a white butterfly and exclaimed to my sister and
brother “Look! This butterfly, I recognise it, it’s me; I have been
this butterfly for several weeks now.” And they, with a delicacy well
known amongst siblings, broke the news to me that this was not
possible “because butterflies only live for one day.”
This came as quite a shock. It reminded me that if swallows and
butterflies flew, like angels, they were none the less mortal for it,
like me. They did seem though, to live a much shorter life than I,
which I found disturbing.
At this time, whenever I identified with an animal, the identification
took place in real time: I did not yet imagine from the butterfly’s
point of view that one day could appear very long. Thus, if a
butterfly truly lived but one day, due to my identification with it, I
also lived but one day and no longer. And this was no laughing matter.
I became maniacally obsessed with the maximum life spans of animals.
Every time I heard of a new animal I would ask about its longevity. I
was rather disappointed to discover that, on the whole, large animals
lived longer than the small ones with which I had been identifying
almost exclusively since I myself was of small stature at this time.
It was then that I made an authentic and revolutionary discovery. I
had a canine companion in whom I confided my metaphysical concerns, my
partner in the quest for truth. One fine day, I tried to show him a
tiny red spider (in fact a tiny garden acarina), without managing to
attract his attention. I concluded that the acarina was too tiny for
my dog to see and suddenly, I found myself identifying with my dog. It
thus came into my mind that the fairies and angels were perhaps just
that little bit too miniscule for us to be able to perceive them.
As quickly as I could, I presented my theory to my father. I was
particularly serene, not only in view of a proof of the existence of
fairies, but also of the proof that my father could not be sure of
their non-existence. I played devil’s advocate not because I wanted
to contradict my father at any price, but rather to show that my
cousins and uncle were perhaps not entirely in the wrong.
“Even if you searched everywhere on Earth for angels and didn’t
find any, that proves nothing” I said. “Perhaps angels and fairies
are simply too small for us to see them?” I explained to him the
experience with my dog. My father, who had an answer to hand for
everything, enlightened me that the search had included the direction
of the tiny as well. He spoke to me of the microscope and – and in
fact it was this that surprised me the most - he explained that the
effective discovery of a multitude of tiny animals invisible to the
naked eye had thereby been made. He then took a piece of paper and
drew a sketch of an amoeba. I fell headlong in love with this tiny and
adorable creature, multiform and so easy to draw.
And so to the fundamental question of the moment: how long might an
amoeba expect to live?
Considering my belief that the smaller an animal was, the less time it
could live, I hardly had any illusions. It must be that my tiny amoeba
could not possibly live very long at all.
On this question of the lifetime of an amoeba, my father, with
infinite wisdom, contented himself to explain that having eaten their
fill of even tinier (!) creatures during a day, rather than merely
dying like any ordinary beast such as a butterfly, it divided itself
instead into two. Instead of dying and disappearing, an amoeba would
divide itself and give birth to two amoebas. This was practically the
reverse of death itself.
“So they’re immortal, then?”
This time, my father made no response.
I requested, of my elder brother and sister notably, that they bring
back from school as many documents as they could find on amoebas,
which they very kindly did. I thus started to write (more exactly, to
scribble in just about every sense) a book: The Invisible World. My
idea was that if invisible worlds existed – and the existence of the
amoeba proved the existence of such worlds – one could no longer
enjoy any form of certainty over whatever the case might be. In the
final analysis, my uncle may well have been right on the subject of
angels. The amoeba was surely a tangible piece of evidence that at
least certain animals could be immortal. I killed time by annoying my
parents with the demand for a microscope of my own. When the
microscope inevitably arrived, I looked for amoebas. I discovered
euglenas and especially paramecia, and when they divided themselves
into two, I divided into two also. The question now was to know
whether the paramecium had survived its division.
What exactly was going on?
I arrived at my first public seminar on amoebas. Even though I may be
driven by self-imposed questions, I have always had an immense
enthusiasm for giving oral exposés, even delivering classes and
seminars on subjects at a considerable distance from those that
preoccupy me directly. Thus, I had already given several verbal
exposés, notably on minerals, but, in 1963, at the age of 8, people
were urging me to deliver a seminar on microbes.
Entitled Amoeba, Euglena and Paramecium, I have managed to rediscover
my succinct resumé in an old notebook:
My friends let me tell you, in this room, we are not 24 in number, but
several million2.
[Footnote 2: I already liked paradoxical propositions; true but
slightly astonishing statements, so to speak. “We” to my mind,
evidently designated the students of the class with the teacher and
the microbes in the class. The “million” would have had to be a
much higher number in reality, if one had wanted to be more exact.]
Does the elephant see the tiny red spider? Could living beings exist
who are so tiny that to us they would be invisible? Could there be an
invisible world and a tunnel through which to explore it? As
incredible as this may sound: yes. The microscope is the tunnel and
the microbes are the discovery. Amoeba, euglena, paramecia,
vorticellae, stentor, bacteria, ovum and spermatozoa, the protozoa
among us! Nutrition, digestion, excretion, diverse sensibilities (the
euglena’s eye), and …. reproduction.
Question: How long can an amoeba live? One day or forever? If it lives
two days it lives every day… forever. (Robert Catteau public
secondary school, in the presence of Prof. Verschaeve)
I would become more and more obsessed by this question of the
immortality of the amoeba. For the following two full years, I would
pass half my free time on walks gathering every possible kind of water
(sewerage, liquid manure, pond water, estuarine, puddles of every
sort) and the other half observing these waters under the microscope.
As usual, I always identified completely with the microorganisms I was
observing and attempted to somehow sense whatever was going on at the
moment of their division. I scaffolded an unimaginable number of
theories illustrating the immortal character of unicellular creatures
without arriving at a stage of conviction over any of them. The
consistent effort to go from fairies to amoebas had been kick-started
by my fear of believing in non-existent things and I did not at any
price want to believe that amoebas were immortal if they in fact were
not.
Yet, certitude had come through: IF an amoeba lives two days THEN it
lives every day3
[Footnote 3: In fact the common amoeba divides on average every 50
hours approximately, but for the sake of simplicity I will continue to
speak as though its divisions occur every 24 hours.]
It remained to demonstrate that for an amoeba to be immortal, it only
needed to survive one division.
An example of a theory heading in this direction was what I called
“The Principle of the Inspector”:
NO CORPSE means NO MURDER
According to the inspector, when the amoeba divides, it leaves behind
no corpse, so no “body” dies in the act of division, therefore an
amoeba survives its division. But this reasoning is invalid. When a
hydra eats an amoeba, it gets digested and neither is any corpse left
behind. The difficulty lies in believing that it survives the process
of digestion. The “Principle of the Inspector” collapsed.
My basic theory or argument in favour of the immortality of the amoeba
or paramecium had been directly linked to the experiment of swapping
places with a concrete paramecium and keenly observing it through a
microscope. Evidently I had come up against a problem of scale. It
seems that I go from one to two but how is this possible? Which is the
original paramecium between the two new ones? Both or only one of
them? Which one?
In particular, if I become one of the two paramecia, how could I
convince the other, given that it could just as easily make the claim
of being me?
Completely gobsmacked by this, given over to a sort of semi-ecstatic
vertigo I realised something just as extraordinary and incommunicable.
My feeling had been that the amoeba survived its division (and thus
every division, meaning that it was immortal) but as it had become
two, each of the two resulting amoebas were unable to convince the
other that it had survived, where “it” referred to the original
amoeba. From whence arose the incommunicability.
If an amoeba could not bring any of its copies to accept its survival
or its immortality, how much more difficult might it be to convince a
human being?
How difficult might it be for me to convince another human of the
immortality of an amoeba even if immortality were an accepted notion?
The more I reflected on this, the more it seemed to me that this
immortality, if immortality it was, must be condemned to remain
forever secret. This explained to my satisfaction the prudent silence
of my father.
A spectacular confirmation would arrive when I was given The Marvels
of Life, the very fine book by Ames & Wyler with a preface by Jean
Rostand and superb illustrations by Charles Harper – it was also the
first book I ever took to bed and slept with!
This book contained an entire chapter consecrated to the amoeba.
Distraught by the toll of new information it contained, I initially
believed that it would not get down to the question of the immortality
of protozoa, but one day, I fell upon the photo of a paramecium for
which the legend was “Is the paramecium immortal?” I quickly felt
relieved because I could see that one could at least pose this
question. Soon thereafter I felt astonished: “here, finally is a book
that addresses an enormous number of questions and is content to pose
the question”. This astonishment was given legs by the confirmation
that the immortality of the paramecium, if immortality exists, could
be no more than a necessary interrogation: a wager on uncommunicable
success.
Ames and Wyler were just as prudent as my dad. I wondered if I was
going to succeed at being just as prudent as them. What rotten luck
all the same: I discover a fundamental truth and it seems forbidden to
communicate it. I would have to wait until 1971 to get out of this
impasse and to weigh up the communicable as per the uncommunicable
parts of the amoeba’s secret.
It is noteworthy that up until this time, I had never asked what an
amoeba was made of, or what I myself was made of. It seemed to me that
the question did not truly depend on whatever things were made of. I
did not imagine myself as made of something(s). The problem of
immortality seemed to me to be more a question of biology, or of
psychology, or of theology - not a question of physics. The matter did
not rest there either in that I demanded to know how an amoeba managed
to divide itself into two. Moreover, the argument in favour of the
amoeba’s immortality on one hand and especially the incommunicability
of this immortality by the amoeba on the other hand, depended
crucially on the fact that after the division, the two resulting
amoebas were rigorously identical, since only in this case did the two
amoebas seem to contradict one another in claiming to have survived,
one, each!
The reading of Ames & Wyler, accompanied by books of Jean Rostand
passed to me by my father as well as some excellent manuals of Jean-
Pierre Vanden Eeckhoudt – teacher at the Robert Catteau Public School
– would drive me from astonishment to astonishment. There, I learnt
the magic words that described the principal phases of cellular
division: prophase, metaphase, anaphase, telophase; as well as their
significance in chromosomal terms. I learnt especially that I am
myself constituted from a colony of social amoebas! Our pluricellular
organic quality posed me problems: how could I as a society of amoebas
still identify with an individual amoeba? Unless an amoeba itself were
in turn a colony of sub-microbes, and so on and so forth? I was thus
led naturally to an interest in chemistry and to atomic physics.
On the subject of matter, I would pose myself a question that would
prevent me from truly taking seriously the idea of the atom, to say
nothing of the very notion of matter itself. Initially, I imagined
atoms to be ultra-smooth and ultra-hard spheres; next I learnt that
atoms were in fact constituted of electrons spinning around a nucleus
of protons and neutrons that I imagined were in their turn, like ultra-
smooth and ultra-hard spheres. It seemed that you could always divide
matter and that research to find the ultimate particle was all in
vain. At the same time however, if one were to find an ultimate
particle, it seemed to me, what could it possibly be other than a
smooth and ultra-hard sphere once again, and what could such a sphere
be made of?
The very idea of matter seemed to me to be void of any explanatory
capacity? To me, the notion of matter seemed to bring out more
questions than it did answers and seemed to threaten perhaps, the
unity of the amoeba.
It was in the volume by Joël de Rosnay that I learnt of the existence
of DNA4, the gigantic molecule of deoxyribonucleic acid which is a
long chain in the form of a double helix “like the inside of a
certain castle of the Loire”, comprising the repetition of molecules
taken from the group {Adenine, Thymine, Cytosine, Guanine} resulting
in a very long “word” in the genre of AATGGCTATGGACCTCAG….and it
was in this book that I would learn how this word, seen as a suite of
triplets AAT GGC TAT GGA CCT CAG…. is translated into RNA, another
nucleic acid, itself translated into a “word”: proteins, comprising
tiny molecules, amino acids, chosen from the alphabet of 20 “amino
acids”. I would learn how these proteins and their enzymes coped with
the rest: from the synthesis of tiny molecules (amino acids,
nucleotides, sugars), even right up to the constitution of the cell.
[Footnote 4: Of course Ames & Wyler also speak of this, but I had no
real understanding of what was in question. More and more, my Ames &
Wyler opened automatically to the little chapter consecrated to the
amoeba!]
All the same, this gave oxygen to more questions. How did we know
all this? What, indeed is a molecule?
In fact my “Joël de Rosnay” and the review Science & Life, was a
springboard for the book destined to become my basic bible for the
following years (1968 and thereafter): the French edition, edited by
François Gros and prefaced by François Jacob of James D. Watson’s
The Molecular Biology of the Gene. In this book, I would gain a
glimpse of the incredible molecular dance that goes on, not only with
the amoeba, but also with an even tinier creature: the bacterium
Escherichia Coli.
My “Watson” was so biblical that in my vocabulary, the very word
“Watson” had become synonymous with THE Bible. In retrospect, my
“Ames & Wyler” had been my first Watson, but at the age at which I
read it, I believe that I did not pose questions in the genre of
knowing who might have written a book.
Even though The Molecular Biology of the Gene enjoyed pride of place
as the Watson, another Watson rapidly outflanked it: General Chemistry
by Linus Pauling, and this augmented a bitter conflict in my mind,
destined also to endure through the years to come.
On the one hand, my Watson gave me the impression of a wonderful
molecular dance perfectly encoded by RNA and decoded by the cell. This
allowed me to see the essential machinery, wherein each molecule’s
identity made no contribution to the identity of the whole organism.
All of this being accounted for, it now made sense to say that the
amoeba, repeating in a fashion much more complicated, though in
principle similar to the molecular dance of bacteria, reproduced
itself mechanically. I was able to observe, through molecular
genetics, an implementation5 of a solution to the problem of knowing
how an amoeba could manufacture another amoeba identical to itself.
[Footnote 5: a representation in terms of data; also known as an
“implantation”]
Concerning the lifetime of an amoeba, this proceeded in the direction
of an amoeba’s survival of its duplication (a high-fidelity
reproduction). Thus, given the “basic theory” investigated in
19636, an amoeba is immortal.
[Footnote 6: An amoeba lives one day or every day. Otherwise put: if
an amoeba lives for two days it lives forever. Or again: if an amoeba
survives one of its cellular divisions, it survives every one of its
cellular divisions.]
This is truly independent of the fact that the amoeba cannot
communicate this, and just as independent of the fact that “I”
cannot communicate it either.
My Linus Pauling was a kind of concrete proof that I was somehow
forbidden to relate the truth about the amoeba’s immortality. Watson
said, “Cells obey the laws of chemistry”. To be sure of the truly
“machine-like” - discretely causal if you will (I had yet no
concept of the digital or the numerical) - character of self-
reproduction, it was imperative that I assure myself of the discrete
and machine-like profile of the activity of molecules themselves.
Now, if Linus Pauling abounded along the lines of the discrete aspect,
with quantification by nature’s chemical properties, including atoms
and distinct energy levels – all seemed to rest on mathematics,
perhaps even on the real numbers; on the continuous, the differential
equations. How about that! What was I dealing with?
The conflict between Linus Pauling and Watson was for me a truly
palpable war of ideas, which took on major proportions at the onset of
the student vacation. As always, and to my lasting joy, we headed off
to the countryside, and the question loomed: do I take Watson or do I
take Pauling? I knew full well that if I took both I would pass the
entire vacation vacillating between them. As it was during the school
year, I would dissipate my time by continually flicking pages in the
one and in the other without deciding on anything and remaining stuck
in an abyss of perplexities.
This progressed to the point of reading other authors’ works, the
“non-Watson” literary genre, in a range comprising the diaries of
Tintin and Spirou on which I was fixated, whodunnits, Freud, Young,
Ionesco, Borgès. There was even a certain Alice in Wonderland with
which I became bored to death and though I gave up on it halfway, I
would nevertheless return to it later on.
During this whole time, I had kept my taste for oral exposés. In
Biology class at high school, I constructed an exposé on “the
lactose operon” (results due to Jacob and Monod in bacterial
genetics). Though I had not finished my talk, the teacher let me
continue the following hour and again the following hour etc. In the
end, he allowed me to have my say during several weeks. One day, the
teacher summarised my exposé. This had evolved into a small
introduction to molecular biology and during this, he committed a
negligible error. Always careful vis-à-vis the truth, I discreetly
informed one of my classmates but one of them (the traitor) pushed me
up against the speaker’s platform saying “Sir! Marchal wants to
tell you something.” I was thoroughly annoyed by this and with
infinite politesse let the teacher know about the error in his
summary. He remained silent for a while, deciding ultimately to put
all the students straight on his mistake. He was never the type to
hold out on me and we developed a relationship based on mutual
respect. In fact I have an enormous respect for those who can
recognise and correct their errors. Recall how much I admired my own
father for changing his opinion. With Camus, I opine that perhaps the
only eternally persisting thing is stubbornness.
I fretted also over the choice of university studies even though this
still seemed a long way off. I was nevertheless extremely impatient to
get to uni if only to be in a position to pose all those questions
that both excited and oppressed me. Would I do biology or chemistry? I
asked myself this question practically every day.
By then, I would have the luck to be able to frequent the Molecular
Biology Laboratory of ULB at Rhodes-St-Gènese, thanks to the kindness
of Jean Rommelaere, whose mother was a friend of my own mother. There,
I would meet Jean Brachet who was director of radiobiological services
and I especially got the opportunity to meet and chat with René Thomas
who directed the bacterial and viral genetics service – Escherichia
Coli and the lambda phagias. What an opportune encounter! René Thomas
was the biologist who discovered the formal logic in Lewis Carroll’s
book The Game of Logic. This was a wonderful book the French edition
of which contained magnificent illustrations by Max Ernst, including a
drawing of a marvellous planarian worm. Most interesting in René
Thomas’ work was his showing how logic circuits could be simulated in
bacteria by means of genetic monitoring of the genome of the bacteria;
thereby corroborating my intuitive reading of Jacob and Monod’s
article to whit life was a matter of encoded dialogues. We promised
each other to meet up again; I still had 2 or 3 years of high school
to go. This encounter unleashed my impatience to get to university.
I continued however, to pursue my interest in chemistry and in the
question of the amoeba’s constitution. From Linus Pauling I would
move on to my next Watson. A real tiny masterpiece came my way: none
other than Michel-Yves Bernard’s book Introduction to Quantum
Mechanics and Statistical Physics. It was a rare introduction to
quantum mechanics written for secondary school students.
Finally, I fell back on the question “what is matter?” Organisms
are societies of cells, cells are societies of molecules, molecules
appear to be societies of elementary particles, but the relation
between the particles seems to necessitate a science of the
continuous. But – what IS the continuous? What, in addition, would
the relevant advanced mathematics bring to the issue?
To summarise, biology and molecular genetics presented strong clues
that we are machines. Our biological identity seemed to me to be
defined by the encoded information and essentially independent of the
material involved, this being continually replaced. In this case, the
amoeba faithfully reproduces itself and must be immortal since its
identity resides in its form and activity and not in its substance.
Hidden behind this, chemistry and mathematics throw a shadow of doubt
on this mechanist conception. Even in Newton’s “mechanics”,
objects - often identified as “material points” - seem to act at a
distance by means of scalar fields in space and described by a
mathematics causing the intervention of the mysterious continuum. With
quantum mechanics, this aspect of things seems pushed to extremes:
even an isolated particle or an atom are described by functions that
only cancel out at infinity. It wasn’t at all evident to me how,
under such conditions, the amoeba could make identical self-
reproductions, or even how it might otherwise self-replicate. With
quantum mechanics and the continuous, it seemed that a filament might
always subsist between the two apparent amoebas and that in reality,
there existed but one amoeba making a good impression of seeming self-
division.
In 1971, on the eve of a scholastic voyage to London, the spiritual
conflict between biology and chemistry hit its apogee.
Above and beyond the immortality of the amoeba on one hand, it seemed
that the explanatory power of molecular genetics resided entirely in
digitalism. This permits the use of encodings and an explanation in
quasi-psychological terms: of memory and its transformation and
interpretation. With hindsight, the article of Jacob and Monod on the
Lactose operon - rehashed by Taylor7 – represents my first discovery
of the formal explanation of “IF...THEN...ELSE” of logicians and
computer scientists.
On the other hand, this quasi-psychological explanation of the
functioning of the cell seemed vastly incomplete without a
clarification of the nature of matter.
[Footnote 7: Taylor J.H., Selected Papers on Molecular Genetics,
Academic Press, New York & London 1965]
It sufficed not simply to say that there are things obeying laws; one
must also explain what these things are, where they come from, why
they obey laws and where the laws themselves come from.
“Cells obey the laws of chemistry,” said Watson. We shall see.
Might it even be that chemistry obeys the laws of cells, as though
chemistry were the product of an amoeba’s dreaming...
Chapter 3
Gödel’s Diagonal
(1971 → 1973)
If DA gives AA; and DB, BB; and DC, CC; what gives DD?
In 1970 I enrolled in “Poetry”. This is the penultimate year of
secondary school. The final year is called “Rhetoric”. My
impatience to get to uni was such that I put myself down for the
central jury examinations with the idea of leaping over my last two
years of high school. Ultimately I did not pursue this enterprise, a
largely paradoxical affair. In effect, not only was I in a constant
state of hesitation between biology and chemistry, but my doubts had
also enlarged to the point where I could now see myself opting for
philosophical studies.
As an independent student, I would attend different classes at
university by cutting a few hours of classes at school. In particular
I attended the exciting chemistry classes of Lucia de Brouckère from
whom I gained the opportunity to briefly go over my hesitancy, but
also to chat with in a spirit of free enquiry. Lucia de Brouckère was
a towering figure of secularity and freedom of thought in Brussels. I
continued to go to the Molecular Biology Laboratory at Rhodes-St-
Gènese, although now I only bothered with its library.
Irritated by my hesitancy as I said earlier, I ended up reading all
sorts of books, most found at random during a walk through a bookshop.
It was through a reading of Gilles Deleuze’s book Logic of Sense that
my mind was finally opened to Lewis Carroll and especially his book
Sylvie and Bruno that I read several times in quick succession. I
again took up Alice in Wonderland and also The Game of Logic. I still
- even today - manage to maintain the claim that English humour is
built on the taking seriously of classical logic; this never works –
which explains the inherent laughter-value. As a result, I started to
take an active interest in logic and in paradoxes of ensemble theory.
Besides, I knew that chemistry brought advanced mathematics into the
picture, and I had to admit that I took great pleasure in maths
classes at school.
During my scholar’s voyage to London the year before, and in
Amsterdam, I recall buying only (Anglo Saxon) books on genetics and
chemistry including William Hayes’ fine book on bacterial genetics
and their viruses1, as well as the Taylor2 that contained the article
by Jacob and Monod. I penned an enthusiastic letter to Bill Hayes who
responded with fervent sympathy. That year, now in “Poetry”, I was
going to London3. The conflict between chemistry and biology was at
its maximum and in Foyles’ Bookshop, I fled this internal quarrel by
giving myself over almost entirely to the range of Lewis Carrolls as
much as to the mathematics and logic sections of the store.
[Footnote 1: The Genetics of Bacteria and Their Viruses, Blackwell
Scientific Publications, Oxford and Edinburgh, 1964, 2nd 1970.]
[Footnote 2: Taylor J.H., Selected Papers on Molecular Genetics,
Academic Press, New York & London 1965]
[Footnote 3: I so appreciated London and Oxford for their scientific
booksellers - and Lewis Carroll - that from that date on, I would go
to England every year, notably to Oxford for what I called my
“Carolien Pilgrimage”.]
It was there that I came across the little red book Gödel’s Proof by
Nagel and Newman. I had no idea who Gödel was and with what his proof
was concerned, but in browsing this book I took it that the work
presented a proof on the subject of the existence or the inexistence
of a proof. I was intrigued. I next understood that this state of
affairs had been achieved by means of an encoding. The resemblance to
biological encodings literally leapt off the page to my eyes.
Without necessarily believing in it too much, I progressively realised
that this piece of work proposed a general means with which to
construct formal expressions4 capable of referring to themselves. I
was surprised to discover that these expressions were perfectly well
defined by the signs and symbols that represented them, in much the
same way as the amoeba seemed to be by the molecules and atoms of
which it was constituted.
[Footnote 4: collection of signs lending themselves to interpretation
at the core of a formal theory, like logical statements, or capable of
interpretation by a machine, like a software program. At this time,
none of this was anything like a clear notion for me.]
I had a good idea of how the amoeba or Escherichia Coli self-divided,
which is to say, I had a quasi-visual model of reproduction at the
molecular scale. I thus had to hand a sort of proof that the amoeba
could clone itself; but as it turned out, this model (as I have
already mentioned) rested on the manner by which the molecules
interacted. Because of this, I could not be sure that the amoeba had
even replicated – either by itself or with an exact clone resulting.
The amoeba’s genome or its genetic encoding had been seemingly
replicated identically, but this capacity for identical replication
rested to all extents and appearances on the laws of chemistry, which
in turn seemed founded on the continuous.
I wondered whether it truly was the amoeba – this tiny and discrete
unit with which I identified since my earliest childhood – that
divided itself, or indeed whether it was the very universe – which I
conceived of as a gigantic and unknowable continuum – that divided
the amoeba.
With Nagel & Newman in hand, I started to understand that it was
possible to envisage self-reproducing entities having a priori no
links with chemistry or with the continuous, or even apparently with
the universe of physicists or chemists. I discovered a new sort of
abstract amoeba that may well be infinitely easier to interrogate than
the tiny, concrete beastie inhabiting the waters of the neighbourhood.
Practically speaking, “Gödel’s Proof” seemed to turn the key in
the hesitancy-lockup between chemistry and biology. This was a
veritable triumph for biology, all the more so in that its
transformation into an abstract biology of formal beings - concerning
whose nature I yet lacked complete clarity - might be in order.
(The dilemma of knowing whether or not, in this case, I could still
identify with the amoeba had yet to fully surface. At this stage
however, I was so happy to have discovered a totally new kind of
amoeba that I relegated this question to the future.)
There were other things about Nagel & Newman! Not so much in Gödel’s
proof – where apparently self- reproductive or self-referential
entities appeared – but in the result, in theorem, specifically, in
his second incompleteness theorem, published in 1931. In effect, and
in rather crude terms, it seemed that there actually existed, say,
“whatsit-names” (Fr: machins) with the capacity to communicate true
propositions (me – in love with the true! 5), capable in addition of
communicating apparently true propositions concerning themselves, but
(it would seem) directly because of this, incapable of communicating
or of demonstrating6 certain truths about themselves.
[Footnote 5: Or the idea of the true. Rest assured that I make no
claim to having a privileged relationship with the truth. I very much
like to propose poetic definitions of the “truth”. For example: the
truth is a queen who wins every war minus an army. Or even: the truth
is a goddess that no god could ever completely undress. Truth is
something you will never read in any newspaper, not even something you
might divine for yourself by comparing two independent newspaper
articles, or that you might divine even better by comparing three etc.
Truth is the source of doubt: the more you know, the more you don’t
know; so said Socrates and Jean Gabin.
Truth is nothing more than the hope of our conscience.]
[Footnote 6: I will always use the term “communicate” in the sense
of honest or scientific affirmation. I identify or model, here and
further on, this type of communication with a formal (or the formalism
of a) proof.]
Just like the amoeba, these whatsit names seemed to be intrinsically
incapable of affirming certain propositions, certain truths concerning
themselves.
What truths? The consistent quality of the self. The fact that one
will not communicate the false.
Here is an honest entity that, due to its honesty, is completely
unable to assert that it is honest. Thus, among honest thingamajigs,
those who assert that they are honest are by definition dishonest.
Following this realisation, I developed an irresistible attraction for
these whatever-they-are. I found them amusing and pertinent. This
time, it was no longer a question of abstract biology, but frankly of
abstract psychology, and this psychology concerned incommunicable
truths, similar to the amoeba’s secret. The most wonderful of all, if
I may dare to anticipate Nagel & Newman, is that these entities seem
able to prove that if they are honest, then they are incapable of
communicating the fact; just as my amoeba seen under the microscope in
the act of self-division “told” me that it could not possibly make
any claim to having survived. Each of its siblings asserted it
implicitly by pointing a pseudopodium at the other amoeba! If one of
them was another one of them, they could very well be others – both
of them.
Gödel’s theorem and his proof showed me the existence of (self-)
reproductive entities; of abstract amoebas as much as the existence of
whatever-you-likes incapable of asserting certain self-referential
truths such as the consistent nature of self. This was exactly what I
had been looking for. The whatever-you-likes in question were formal
theories like Peano arithmetic or the principia mathematica of Russell
and Whitehead. No longer in any doubt, I resolved to become a
mathematician and to specialise in mathematical logic.
Note that at this time, I was suffering from an immense handicap: I
had not yet heard any talk of Church’s thesis or of the computer. The
term “computer” (Fr: ordinateur or “calculating device”) evoked
in me visions of the immense and rigid refrigerator lookalikes used by
bankers. I had no idea that a century earlier, Babbage had dreamed of
a device calculating the positions of heavenly bodies. I had no
inkling of a “Turing machine”. I did not yet truly know what I was
up to or what I was conjuring with in terms of informatics, much like
Jourdain with prose. Grossly speaking, Church’s thesis says that:
All thing(amajig)s are machines
(Tous les machins sont des machines)
Or, better: anything formally calculable (and relatively communicable)
can be calculated (and relatively asserted) by computers (relative to
a formalised theory).
I still had no idea that machines were actually thingamibobs (the
reverse of Church’s thesis) or that universal machines – computers
– were at one and the same time close matches to formal theories and
very likely candidates for self-reproducing entities. I only realised
this much, much later. (In any case, information technology was not
yet an entirely new branch of study at university, merely an option
for mathematicians or engineers.)
(to be cont.)
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Received on Sat Mar 07 2009 - 01:22:15 PST