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It can easily be shown that the prior probability of the spontaneous formation of a living system is near zero. The same is true even for the prior probability of the spontaneous formation of a single macromolecule carrying biological information or

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This literature extract was gathered purely and subjective according the interests of the author (Manfred Bundschuh). Usually there were complete sentences from the srcinal transferred. Theres no guarantee for correctness.!iterature extract from"
Bernd Olaf Küppers: On the Prior Probability of the Existence of Life,
in" #igeren$er% #. &r'ger% !. Morgan% M. . (d.)" The *robabilistic +evolution ,-/,01" 2ynamics of cientific 2evelopment% 3ol. ,,,% *robability in modern ciences% Bradfond Boo4s% M5T *ress. 5t can easily be shown that the prior probability of the spontaneous formation of a living system is near $ero. The same is true even for the prior probability of the spontaneous formation of a single macromolecule carrying biological information or function. 5n view of such low probabilities of nucleation% three explanations of the srcin of life have been put forward% each laying a different emphasis upon the respective roles of chance and law in evolution" (,) the hypothesis of singular chance. (6) the hypothesis of the vitalistic forces% and (1) the molecular 2arwinian approach. 7n analysis based on algorithmic information theory shows that for fundamental reasons the chance hypothesis eannot be proven and that for fundamental reasons the vitalistic hypothesis cannot be disproven. 8nly the 2arwinian approach yields of epistemological standards. The problem/solving capacity of the 2arwinian approach is demonstrated with a game/theoretical model.
Introduction: he !olecular "oots of Li#in$ %ystems
The smallest catalytically active protein molecule of the living cell% such as the electron/transporting en$yme cytrochrome c% consists of at least , amino/acid residues. 7 protein chain of this length is already 6
&''
9 ,
&('
alternative se:uences. This ma4es it obvious that even the lowest stage of biologieal complexity opens up an almost unlimited multiplicity of possible structures. ;owever% the Brownian motion of the molecules interferes with the copying process% so that there is always a eertain probability that an error (a mutation) will appear. The genetie variability that results from such mutations is the souree of changes on the phenotypical level and is thus the target of natural selection.
Life )an Irreducible Phenomenon*
2o the laws of physics and chemistry cause biological macromolecules to arise spontaneouslyfrom their basic units% and to organi$e themselves into living systems< The first part of the :uestion belongs to the discipline 4nown as the prebiotic chemistry and can today be regardedas solved% at least in principle. The results of numerous experiments point to the conclusion that% under the conditions of the primeval earth% the two most important classes of biological macromolecules (proteins and nucleic acids) are able to form spontaneously in a non/instructed reaction from their basic ,
units (amino acids and nucleotides% respectively% which in turn emerge as a result of normal chemical reactions =. certainly constitutes a necessary condition for the srcin of living systems% but% as we shall now demonstrate% not a sufficient one. !et us first examine the phenotypic level. . >igner has estimated the prior probability of the existence of a self/reproducing molecular machinery using an approach based on :uantum theory. 7ssume that the state ?life? is completely given in the :uantum mechanical sense. 7ssume further that there is at least one state of the reservoir of nutrient that enables the organism to reproduce itself. The self/reproduction of a living system is then formally a specific inter/action between the organism and the nutrient that leads to a material copy. = the process of reproduction is described by the transformation <<< where is an unitary transformation matrix and is the state vector of the system after the reproduction. >e now replace ;ilbert space by a finite/dimensional space. 5n particular% the state space of the organism shall be of dimension @ and the state space of the metabolie products of dimension +% where @ and + are of course large numbers. That is%
there are @
6+
transformation e:uations but only (@A+A@+) un4nowns. ince @
+
+ is very much greater than (+A@A@+)% it is arbitrarily improbable that the transformation e:uations can be satisfied by the un4nowns. Thus as >igner correctly argued% the laws of :uantum mechanics lead to an arbitrarily low probability for the chance of a self/reproducing material system as a conse:uence of a gigantic fluctuation. 5f this is so% then the :uestion of the prior probability of the srcin of life must be formulated on the genotypic level" 5s it possible for biological information to arise pure chance% as a by/ product of the spontaneous and random synthesis of a 2@7 molecule < ven in the simple case of bacterial 2@7 (some million nucleotides) the number of alternative se:uences is almost inconceivable" ,
6%million
C Thus the prior probability of the chance appearance of a bacterial genome is so low that neither the entire space nor the age of the universe could suffice to ma4e the random synthesisof this information/carrying molecule even vagely probable /to say nothing of the exact conditions on the primitive earth. Thus traditional physics and chemistry leave the existence of living matter an unsolved riddle.ven so% physicists and chemists have continued to produce hypotheses about the srcin of life. D. Monod% for instance% believed that the existence of life must be considered as the result of a singular random event% which certainly has never been and will never be repeated anywhere in the universe. @. Bohr% on the other hand% had asserted many years earlier that lifemust be accepted as a fundamentally inexplicable
fact of biology =. >. lsasser and in moderate form also . >igner% went one step further and postulated% in the sense of critical neovitalism% the existence of life/specific natural laws that direct% and thus sustain% the processes of living matter% but that are not reducible to physical regularity.
Limitations of Obecti#e Kno-led$e in Biolo$y
6
The degree of incompressibility of a se:uence of symbols is indeed an ade:uate measure of the degree of its randomness. This fact is exploited in the following definition" 7 se:uence is defined as ?random? when the shortest algorithm needed to generate
it
contains about as manyinformation units as the se:uence itself. The smallest number of bits sufficient to specify a given se:uence is called the complexity of the se:uence. 8ne of the most important discoveries within the realm of algorithmic information theory is the theorem that the randomness of a particular se:uence can in practice never be proved. More precisely" 5n a formal system with n bits it is impossible to prove that a particular binarystring is of complexity greater that nAc% where c is a constant that is independent of the particular system employed. The theory of randomness is proved by formulating it as a halting problem for a universal Turing machine. The hypothesis of Monod that the blueprint of a living organism is the product of random synthesis% because there exists no detectable se:uence pattern% is not provable. 7 deeper analysis of his arguments shows that the chance hypothesis effectively negates the causality principle% in that the role of chance in the process of 2arwinian evolution is raised tothe ran4 of an antiteleological law% for which Monod tried to give a positive proof along the line indicated above. 7ll vitalistic hypotheses of the srcin of biological information are irrefutable. !et us recapitulate our conclusions so far" The chance hypothesis is fundamentally unprovable% while all vitalistic hypotheses are fundamentally irrefutable. Thus the theorem of Ehaitin% which is essentially an information/theoretical version of #Fdels theorem of the limitations of the axiomatic method% leads immediately to some important limitationsGof objective 4nowledge concerning the srcin of life.
he %emantic .spect Information
The statlstical problems that arise in connection with the phenomenon of the or,g,n of life appear to indicate that organisms are irreducable structures% whose scientific explanation transcends present/day physics and chemistry. Thus the laws of physics and chemistry cannot explain the srcin of those particular patterns that carry biological information. M. *olanyi argues that the nucleotide se:uence of 2@7 molecule must therefore be considered as an irreducible boundary condition under which the laws on nonliving nature are constrained to operate in the living system. 7 theory of the srcin of life must therefore necessarily include a theory of the srcin of semantic (i.e.% functional and not only structural) information. 7nd precisely here lies the fundamental difficulty confronting every scientific theory of the srcin of life. *hysics and chemistry% at least% have traditionally ignored semantic phenomena. 7gain% M. *olany has expressed this aspect the strongest way" ?7ll objects conveying information are irreducible to the terms of physics and chemistry.? =. The central :uestion of the srcin of lifeGtherefore 1
emerges as the :uestion of how far the semantic aspect of information can be formulated objectively and thus become an object of study in mechanistically oriented science such as molecular biology. The central statement of 2arwinian theory is that the generation of information follows the mechanism of evolution by natural selection. Thus the next :uestion is virtual,y forced upon us" is the principle of natural selection also valid at the molecular% apriori nonliving level% and% if so% can it explain the srcin of macro/molecules carrying biological information< 8rganismic biology has invariably denied this. ;owever% it has become clear% mainly through the wor4 of . piegelman and his cowor4ers% that natural selection is not a phenomenon restricted to autonomous living systems% but that it can also occur% under certain conditions% among biological macromolecules outside the living cell Hurthermore% proeeeding from the prere:uisites of piegelmans experiment (the system must be open% self/reproductive% and prone to mutation)% M. igen was able to demonstrate that natural selection follows inevitably as a physically derivable extremum principle and that natural selection is just as inevitable as property of nonliving matter as is the acceleration of a body acted on by a force. >e 4now that the nucleic acids fulfil all the material preconditions for the selective selforgani$ation. 7nd indeed% since the pioneering wor4 of piegelman% it has been shown in a number of experiments that selection in the 2arwinian sense ta4es place among nucleic acid molecules in the test tube% if they are put under selection pressure% and that this leads to environmentally adapted +@7 structures. The 8rigin of Biological 5nformation /a #ame/Theoretical 7pproach 5t remains for us to examine the :uestion of whether selection and evolution at the molecular level can solve the statistical problem described in section 6. 5 should li4e here to demonstratethe problem/solving capacity of the theory by appeal to a simple game/theoretical model. 5n the following example% prompted by an idea of M. igen% the generation of biological information is to be simulated on a computer">e ta4e a se:uence of letters that represents a particular information content @7TU+7!.!ET58@ >e shall start with a random initial se:uence% such as" 7E3I52*!8>+T58J7>e need at least K symbols to represent a letter of the alphabet in a binary code. (with K binarydigits% 6
K
?code words? can be produced% enough to encode 6L letters of the alphabet and some punctuation mar4s.) The , letters of the se:uence @7TU+7!.!ET58@ then represent a :uanitity of information amounting to -K bits. 7 se:uence of -K bits bits has 6
/0
N ,
6L
alternatives. ;owever% for the amplification process we introduce a selective assessment" every mutant se:uence that agrees one bit better with ?meaningful? of reference se:uence than its master copy will be allowed to reproduce more rapidly by a certain factor (the differential advantage). Thus as first the se:uences are reproduced% with occasional errors% at a eharaeteristic rate. >e
now allow the si$e of the overall population to grow up to , and then reduce it / by random choiee / to , copies. The total population is thus on average constant. By the restriction of growth we apply a eontinual selection pressure to the system. 5t can be shown that all se:uences whose reproduction rates lie below the average reproduction rate of the distributionare s:uee$ed out of the population and are thus excluded from further optimi$ation. This raises the average reproduetion rate% which risesGas the system evolves and which finally reaches an asymptotic maximum value. (mutation rate lOP differential advantage 6.) 5n the 1Kth generation% selection e:uilibrium has already been reached. 5t consists of (on average) K correct copies of the referenee se:uence and a stationary distribution of mutants arising from it. >e have thus% for this example% solved the statistieal problem raised in section 6. tarting from a random se:uence of symbols% we have arrived at a se:uence that is only of ,
6L
combinatorially possible alternatives% and whose prior probability was close to $ero. To generate this se:uence we needed neither a teleological nor a singular% random event.=. we started with a meaningful result (in our case the reference se:uence) and showed% loo4ing bac4ward% that the statistical problem can in principle be solved. 7 construction apriori% however% does not seem possible.There is a further aspect to consider. 8rganisms are themselves a part of their environment% and the environment changes in response to the evolution of the organisms =. 5n contrast to our computer experiment% the final structures called for by the environment are not defined until evolution is we5l under way. K

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