This discussion is follow-up to a prior post, and is pertinent to my lead theories ‘Virtual Closed Systems’ (Does Life Violate The Second Law? Implications of Virtual Closed Systems, and ‘Indifferent Time’, as well as other discussions that I have initiated on my blog site. I note for reference my discussion of R. Pascall’s paper (2013) on Kinetic Stability Theory, as further relevant to basic questions about the validity of “molecular selection” as chemistry, and as meeting qualifications of scientific research, i.e. basic feasibility at a theoretical or experimental level. It begs the question, as to why this kind of “research” is valid for publication in so called “peer reviewed” magazines. I have already presented evidence, both theoretical and experimental, that such nonsensical science is no better than “perpetual energy”. These are not perpetual energy devices, but are claims of self-organizing, self-ordering matter, matter which they allege oppose laws of diffusion and heat-dissipation (fundamental to chemistry), and are equally dubious, and forbidden by the second law, as well as the first- as they are made without a single positive experiment or without any definition of what such a theory is in terms of how it would be disproven or negated. There are the absence of any test criteria or even a defined hypothesis. Yet these “molecular selection” and “maximal flow” theories, apparently, continue to be flogged in peer reviewed magazines. Ironically, unlike bogus perpetual energy claims, these theories as “molecular selection” get a free ride in the magazines, openly, with no resistance whatsoever from the scientific community. That does a great disservice to science, to those who adhere to scientific principals, and to the fair, pursuit of science now, and in the future. In other words, such pseudoscience promoted as “peer reviewed” does great harm which cannot be quantified. The reason I bring up these points is that they conflict with my lead theories, and that is the purpose of this discussion, and the reason I shall continue to bring up the errors shown in current papers relevant to Virtual Closed Systems theory and Indifferent Time.
*If the reader does
not have the time to read this entire article I would strongly suggest you skip
to the section “NOTES” at the bottom. This where I dissect the supposed
supportive references of molecular selection in detail.
The article I reference here appeared in Transactions A of the Royal Society Phil. Trans. R. Soc. A (2011) 369, 620–623 doi:10.1098/rsta.2010.0312 http://rsta.royalsocietypublishing.org/content/369/1936/620
I explore further into the enigma surrounding the so called
“molecular selection” and find only more ‘nothingness’, a critical void of
actual evidence to support it. Just more references from its proponents who
claim to have observed it, or rather that someone else observed it and reported
on it. And many of these cited in recent papers, “some of the first
observations of (molecular selection)” like Mills (1968) or Spiegelman (1967) are
almost 50 years ago. It is a term or at least the concept that it embodies,
that I’ve recently encountered in a number of locations, and heard it utilized first
hand as an explanation for molecular behavior. Molecular selection has a number
of aliases, self-organization, molecular evolution, and the like, but is also
now a foundation of so called ‘molecular paleobiology,’ Fournier G. et al.
(2015) http://www.ncbi.nlm.nih.gov/pubmed/25791872.
To start off, perhaps it should be noted that in the article
itself, de Duve references his previous work of virtually the same title but
almost two decades earlier: “Vital Dust: Life As Cosmic Imperative” (Vital
Books, NY 1995). de Duve also cites three of his other works in
his short review article, these are:
de Duve C. (1991)
Blueprint for a cell: the nature and origin of life (Neil Patterson Publishers,
Burlington, NC).
de Duve C. (2002) Life
evolving: molecules, mind, and meaning (Oxford University Press, New York, NY).
de Duve C. 2005 Singularities:
landmarks on the pathways of life. New York, NY Cambridge University Press
doi:10.1017/CBO9780511614736 (doi:10.1017/CBO9780511614736)CrossRef
On first “blush” it would almost appear as though de Duve
has simply re-published a scientific article here from his book, published
almost two decades prior. Does this qualify as new research for a published
scientific article? Apparently it does qualify , and de Duve explains:
“The title of this essay appeared, but without the question
mark, as the subtitle of my book Vital Dust [1]. In that book and in others
[2–4], I defended the view that life is an obligatory manifestation of matter,
written into the fabric of the universe, and that there must be many sites of
life, perhaps even intelligent life sometimes, in many parts of our galaxy and
in others..”
Biologists like de Duve are clearly aware that their theory
involving a chemical first or “bottom up” approach to the origins of life would
likely involve a great number of chemical optimization steps:
“The conclusion emerging from this summary analysis is that
the origin of Earth life, being dependent on deterministic chemical reactions
and on frequently optimizing selection processes, must have been close to
obligatory under the physical–chemical conditions that obtained at the site of
its birth. This contention is further supported by the fact that a very
large number of steps must have been involved.”
By “very large number of steps must have been involved” we
can presume that de Sousa and other proponents, are essentially claiming that
the chemical development of life, the precursor reactions, must have been
numerous, i.e. involving numerous reaction steps. And so their theory asserts
that life is a chemical reaction product, albeit a product that had an extremely
low probability of occurance.
Furthermore, the next part of the same paragraph strongly
suggests that de Duve, like other biologists, is fully aware of the argument
that a series of low probability events would, (S1…S2…S3…) if required to occur
in succession of each other, lead to a very unlikely probability of the final event,
as per normal probabilistic calculations would provide:
“For the final outcome to have a reasonable chance of taking
place, most of those steps must have had a ‘reasonably high probability’ ([12],
p. 1034) of occurring. Otherwise, the probability of the entire succession ever
coming to fruition tends to become vanishingly small [1,12].”
So, returning to the theoretical issues: what would be the
probability of a series of theoretical chemical steps, which lead up to a
complex molecule such as the first RNA? If some steps (1-3) leading to a
molecule were to occur only by chance alone, this would roughly be calculated
as the p(molecule occurring) = p(step 1) * p(step 2) * p(step 3) and so on, but
with each probability the frequency, or probability of its occurrence
decreases. The probability multiplies again, when we attempt to envision getting
three of those molecules, all by chance. This raises the fraction by a power of
3, making it even less likely an event, particularly if the fraction of
molecules ever achieving unlikely conformations, let alone remaining stable in
solution, becomes very remote if not theoretically prohibitive. And so the
claim that RNA or some precursor molecule came about exclusively by chance
“roll of the dice” is highly problematic since it may involve many possible
reactions or side reactions, but moreover, these are more theoretical
equilibriums, reactions that one can’t show normally in chemistry because they
are energetically disfavored. So it may be surprising, to some, that this
doesn’t sound at all like chemistry. But given the vanishingly low probability,
and the lack of steps with “reasonable high probability” it should be
surprising that this chemical pathway is considered feasible at all? No
reasonable, high probability steps are ever described. The purely probabilistic
“mechanism” we have just outlined here, has nothing to do with chemistry
proper, it is not relevant to mechanism; and in fact, assumes no mechanism as
such an assumption would mean that probability itself , chance, was not the
factor. (the probability of obtaining “heads” five times in a row, by simple
probability, isn’t calculable if there is higher probability of heads due to
some mechanical aberration.) The argument that chemistry involves species
reacting in more probable situations with more probable reactive species, is
not the same argument. [It is in fact,
the “propagating chemistry” I discuss HERE that I discuss as an alternative description
of the pre-life or pre-RNA chemistry they propose to self-assemble. The reason
is that the theoretical products they propose, to propagate and by chance,
interact in one reaction after another, again by chance, defies the second law,
as solutions do not behave in this way. Each microstate is reacting and
reaching a lower energy state simultaneously.] Furthermore, in my view, the
central assumption of their argument that there is a finite probability
of a reaction should be in question, as we find no physical examples of this in
nature. None on the bench. Their entire model of chemistry does not hold true
even in the most elementary bench chemical model. Their model of using chance
or probability is misrepresentative, since chemical reactions are actually
highly probable, not improbable. Otherwise chemistry would not be such a
precise science. The certainty by which these microstates reach their products,
precludes the notion that it is not certain, or has opened the door to “other
chemistry” they imply, i.e. the self-propagating chemistry of their model.
Nature does not advance by “mistake.” The idea that a flood
or storm occurred randomly is not the same as the mechanics behind the storm,
which did not impart a force by chance. And simply because molecules may end up
with other molecules in solution by chance, does not mean that the reaction
itself is driven by chance, by probability. So one has to consider thermodynamics
of what is driving the chemical reaction itself. It has to be a chemical
reaction. And yet a chemical reaction would involve certain reaction pathways,
i.e. S1…S2…S3 and so on, as well as the loss of useful energy, but this
obviates a purely chance scenario. The chance” dictated by the 2nd
law of thermodynamics preempts their model of self-propagating chemistry in
this case. Chemistry is mechanism driven, in theory. It is the model of the
hypothesis in question here, the framework, (not the specifics of what those
reactions actually are) since we should have doubts (based on their lack of
providing any chemical examples) that it’s even clear what it should be. We
realize that the question of “a chance of RNA” forming from n molecules, is a
distinct question from “what are the species or precursor reactions leading up
to RNA?” those are independent issues of one another. And I would argue, there
is no substantive basis to claim a reaction will occur if you cannot name what those
individual reaction components are. Otherwise, we could make all kinds of
ridiculous predictions, Pb could turn to Au for example, “by chance, even
despite it’s highly astronomically low frequency” and that claim is not
permitted.
There is also a chance, the bio-physicists will tell us that entropy (an event N) may proceed in
the opposite direction that it is favored, though extremely slight, and I explore HERE. That’s
the thinking of statistical mechanics with respect to this problem. But the
biologists and bio-physicists are likely keenly aware that there’s a bigger
problem, and that’s the thermodynamic barrier. RNA is much more organized, and
is a unique molecule, never found on asteroids or meteors. It isn’t lying
around, and that’s because it has been manufactured by an intelligent organism,
already containing DNA. To get around this dilemma, I believe that’s why they
argue so vehemently for the ability of matter to self-organize, and for some
kind of alleged “natural molecular selection” to be this force which can bridge
the thermodynamic divide, and help physics run in a direction it isn’t meant
to, if only for a short time. If you’re reasonably going to pursue that theory,
you have to weigh probability of many theoretical events, and it gets very
remote when these are stacked together, so selection is supposed to operate
here. Which brings us back to our discussion…about improbability of those steps
S1,S2,S3…n occurring! It has seemed relatively “easy” for biologists to say “an
organism will outcompete or eat a lesser organism, and thus a more “evolved”
complex organism will survive, but it’s not at all easy to envision that with inanimate
chemistry, with molecules. So this is, in my opinion a theater in which the self-selection
theory can be looked at very carefully, and if looked at too closely, it is
found to be grossly lacking in substance or evidence to support its basic
feasibility, that would be a single chemical experiment. Let us not raise the
bar too high. A single step from S1 to S2 showing a reversal in the tendency of
the second law would suffice to demonstrate this. Recall the statement that by
de Sousa and others, that there is “chemistry before selection”. Yes where, how
and when? I and other practitioners would be more than interested to see such
evidence of self-selecting molecules, but the fact that such chemistry would
have many useful implications to drug research also has a flip side- such
claims in this arena would need to be shown as distinct from the myriad other
chemistries already known. The obvious question that I raise here and elsewhere
(see comment I made in Quanta https://www.quantamagazine.org/20140122-a-new-physics-theory-of-life/
is that it is theory, a theory of chemistry, and yet there is no chemical
reaction for us to examine, not even in theory. But let us return again to the
probabilistic argument i.e for dissipative theory, the basis of their theory,
an example with links here https://www.quantamagazine.org/20140122-a-new-physics-theory-of-life/.
What de Sousa must also realize is that this same argument ,
i.e. the increasing improbability of a final event, gained by a series of
highly unlikely events, applies to selection
theory- not only for its alleged implications for bio-chemistry, but for
selection theory in general. However, what is very different about this
reference of de Sousa’s, or rather the context in which natural selection is
discussed, is that it is specifically regarding hypothetical environments,
chemical steps, which are not known. I don’t believe that it fully resolves
this issue. de Sousa means for the context of chemical natural selection to be
not that different from so called Darwinian Natural Selection, and in fact
teaches that molecules may be selected for in much the same way as Darwinian
Natural selection implies as he states
in the same paper:
“Originally formulated by Darwin as the mechanism of
evolution of reproducing living organisms, natural selection also affects
replicating molecules such as RNA, as first shown by Spiegelman [7]…. and since
repeated in a variety of ways by many investigators. In both cases, the essence
of the process lies in the imperfections of reproduction. For all sorts of
reasons, whenever entities are replicated, variants of the original model are
inevitably produced. Selection acts on those variants to automatically bring
out those that are most stable and, especially, most capable of producing
progeny, under the prevailing conditions. This process is inseparable from
replication itself and must have appeared at the same time as the first
replicating molecules in the development of life. “
The notion that life might be driven by what is “most
stable” shows a very striking misunderstanding of the chemistry underlying biological
systems. Many drugs cause their toxicities on bioorganisms for this very
reason, because they are the most stable binding to a specific site, or
energetically stable configuration, i.e with organism’s DNA, or an enzyme ,
which is more stabily binding to the natural molecule. Furthermore, many
examples of more stable formations are highly toxic to life, precipitation of
water (ice) is a lower energy form of water, but also the binding of metals to organism’enzymes,
Pb, Hg, and other toxic metals are only toxic because they bind more strongly,
than the more biologically desirable Ca or Mg ions. These thought experiments verify to us that the
arrangments of living chemistries are not the most stable that are possible,
but the stability is resisted. How? By infusion of energy by the organism. Consumption
of energy prevents water from freezing inside the cells, or tissues, it keeps chemical
gradients from reaching stable states. It is absurd to believe that it is a
function of a mere chemical reaction, even in theory, since the energy
component, is missing from their description. (These are factors I address in
my theory of VCS and elsewhere, in “indifferent time”.) They have omitted the
energy argument completely in “chemical selection”, and have ignored the opposing
forces , diffusion, exothermic drivers, and unavailability of free energy, that
oppose the very chemistry they propose.
Many are aware that similar arguments have been made against
natural selection theory, for a number of years at a theoretical if not
mathematical level. (For example, those
regarding the mathematical improbability of successive improbable events i.e
mutations in some tens of thousands of genes leading to positive forward
progress), BUT it is also well known these arguments have been rejected
vehemently by the core of evolutionary biology.
That it is not rejected here, but is in fact embraced as a
feasible mechanism, makes this admonition somewhat more surprising. If de Sousa
had made such an indictment of natural selection theory, in the non-chemical
sense and in the normal contexts of Darwinian Evolution or New Synthesis, i.e.
that natural selection of organisms allegedly operates by similar if not
analogous mechanisms that de Sousa himself discusses here and elsewhere, it
would be outright rejected as blasphemy against New Synthesis. In fact such
views likely would not see the light of day” in terms of peer-reviewed publications.
But the important aspect of this reference is that it clearly shows that
evolutionary biologists are fully aware that natural selection theory has the
same basic weaknesses as chemical natural selection.
Why the willingness to openly discuss the mathematical
improbabilities here in the case of chemical selection?” The clear articulation
of the theoretical issue of natural selection from a mathematical perspective,
the multiplication of probabilities” shows a keen awareness that this SHOULD be
a very critical issue in natural
selection theory proper. Here, a biologist clearly illustrates the very mathematical
probability issue that is denied as being irrelevant elsewhere. Does this show
that evo biologists are avoiding the discussion of contrary theoretical
evidence? Barring molecular sex, that is, the hypothetical sexual selection of
one “attractive” molecule for another sexy molecule, what are we to make of
this in terms of the selection theory? Let us review the quote: “…Otherwise,
the probability of the entire succession ever coming to fruition tends to
become vanishingly small” Would de Sousa agree that the probability that a theoretical
series of chance mutations (which are indifferent) also leads to events in
organisms i.e. forward “progress” would be viewed as “vanishingly small?”
What still remains to be understood, are highly ambiguous
(if not pseudoscientific) statements such as:
“Additional evidence
for [molecular selection] is provided by the growing number of instances of
evolutionary convergence ….There are reasons to believe that molecular selection may similarly come
close to optimization under sufficiently stringent constraints…”
in the article that are statements allegedly, about physical
phenomenon, completely without supporting chemical evidence or citation. Again,
it is impossible for us to determine what chemically, “evolutionary
convergence” might mean, let alone “evolution” in terms of chemistry. Does
water evolve? How about NaCl? If we are to believe for even a moment that this
“chemical selection” is based in science, these chemical distinctions must be
made clear by de Sousa and others of the “chemical evolution.” They must
provide clear examples of what reactions are chemical evolution and which are
not. That is the problem with evaluating any of their examples, such as nucleic
acid chemistry. They fail to realize that nucleic acids are merely polymers, no
different than the chemistry governing their monomers, these are the ubiquitous
rules governing chemistry. The formation of DNA complex, though much more
complex than simple atoms, is in principal energetically following the same
rules as any other chemical process in inanimate systems). Such terms as
“molecular selection”, “optimization” and “sufficiently stringent constraints”
have no physical meaning in chemistry or are not defined by the authors of
these kinds of claims, (i.e. where is a reaction NOT optimized?) but yet are
cited repeatedly and with emphasis by their peers in other publications as fact.
And as I have demonstrated here, the “optimization” of chemical processes, at
least non-manipulated, natural ones, tend towards disorder and lower energy,
but not with less available free energy than they had before, but essentially, the
same unavailable energy they had before. So they purport to discuss chemical
theoretical processes that are entirely imbalanced in their energy. And as I’ve
commented elsewhere in another essay, the molecular selectionists purport to
describe a kind of “perpetual energy mechanics”, alleged processes that
generate more freely available energy than they consume. The claims of
“molecular selection” are as vacuous and shaky in their evidence as they are in
their definitions. What reasons are there specifically, to believe that
“molecular selection” is a bona fide physical phenomenon, meaning one that is
actually different than any other chemistry involving molecular species? Or,
that there is anything resembling “optimization” in natural chemistry? They
must realize that “optimizing” could imply that their chemistry they propose,
in theory whatever it may be, will not ever occur as it is more “optimal” for
it not to. It is tiresome that they continue to wave their hands with nucleic
acid experiments, which are known to behave within the laws sof chemistry that
are applicable to all other molecules, and make certain claims without
specifying why a particular nucleic acid is unique, i.e. “evolving”. The term
“optimize” imbues the inanimate chemistry with properties it does not have. What
we do know, but what molecular selection proponents fail to acknowledge, is
that the optimization of all inanimate chemical reactions favors products with
less energy and energy of a form that is less available to do work, not the
opposite. de Sousa’s argument in this paper to equate molecular selection
principals with natural selection theory in general, i.e., Darwinian selection,
I believe raises new and important theoretical questions about selection theory
in general. But more importantly, it fails to address the problem of “chemistry
before natural selection” as it cannot account for imbalance in available
energy, a problem that my new theory of VCS, specifically addresses.
Addendum: (September 25,15) When I present my case to
reviewers for a new molecular species, say one that is releasing high nitric
oxide levels, I must present a reaction that involves two species A and B and
give justification for why those species will combine. These are fundamental to
chemistry. Furthermore, I must typically provide evidence of a product of A and
B, and not just A-B but presumably one that will release another by-product,
NO. That means that I now have presented both theoretical and empirical
evidence. The proponents of “molecular selection” intend for us to believe that
they have evidence of propogative reactions leading to simple nucleic acids.
Nucleic acids are far too complex a product , to be used as “evidence” for
their chemical arugment, and they have not examples of this in nature (outside
of those made my organisms). So, their burden instead, should be to provide
evidence of a much more simpler reaction, which gives a product that then
drives another. The question that I ask of this theoretical reaction they
provide, is thus: does this reaction oppose forces in solution? Does it oppose
diffusion, or of its own dissipation of energy, terminating in a few steps? If
they insist on maintaining their exemplary reaction is some kind of nucleic
acid I pose the same problem(s) for that reaction as well. It is identical.
There is no evidence that they provide here and yet it is published by various
peer reviewed publiications as though it is factual based chemistry. These
publications have not been held accountable fairly, to the same rules that are
applicable to other scientists working in chemistry.
NOTES
(*The so called
molecular seletion or “molecular evolution’ is chemistry that is proposed
without doing experimental controls or basic verification done in chemistry
Regarding the primary reference de Sousa quotes, recall one
of de Sousa’s central arguments: “Originally formulated by Darwin….natural
selection also affects replicating molecules such as RNA, as first shown by
Spiegelman [7]”
I looked specifically at
the citation, the key one, that is apparently cited by de Sousa as evidentiary
for “molecular selection”. If you look at a similar Spiegelman and Mills paper,
of the exact same year, which deals with in vitro RNA, and RNA viruses, you
will find that these are neither self-replicative molecules, nor are they
replicating in natural environments, that is, without assistance of RNA enzymes
extracted from an organism. There is absolutely no evidence to conclude that
reaction of these inanimate molecules will improve their odds of reacting
further in “successive” steps as proposed by molecular selection proponents. This
is a better reference to Spiegelman’s key work, and others (see below),
investigating, “natural selection” and also so called environmental selection
of the molecules of interest, which are RNA and also enzymes which process RNA
in vitro.
AN EXTRACELLULAR DARWINIAN EXPERIMENT WITH A
SELF-DUPLICATING NUCLEIC ACID MOLECULE*
BY D. R. MILLS,t R. L. PETERSON, AND S. SPIEGELMAN,
1967
It is interesting that
de Sousa and others have chosen these references for support of molecular selection, as there are much
better examples of the exact experiment Spiegelman and Mills performed, and
these are well known in a process called PCR invented by Kary Mullis.
Spiegelman states in his paper:
“The availability of a
molecule which has discarded large and unnecessary segments provides
an object with obvious experimental advantages for the analysis of
many aspects of the replicative process.”
That might have been inspiring to Spiegelman and Mills back
in 1967, but it is not in any way showing how RNA is “discarding large and
unnecessary segments”. Unnecessary to whom? Furthermore, it is hardly showing
Darwinian natural selection” as de Sousa claims it to be, and further, it is a
gross misinterpretation or at worse, a reading into, artificial non-real
desires or wants of molecules which don’t exist. And simply because it is in
print, in a cited reference ( citation=^170) doesn’t change these facts. It is
well known that small products of DNA are faster replicating than larger kb
sized strands, owing to the processing speed of the thermal stable polymerase,
typically TAQ polymerase. In fact it is well known that smaller lengths consume
nucleotides far better than longer DNA segments, an effect known as “noise” or
non-specific binding and one that DNA researchers attempt to avoid. I could say
much more about this, but what is relevant is that the reference is not what de
Sousa and others claim it to be. That is a fact. And simply because Spiegelman
invoked the words “natural selection” and believed with certainty that he’d
found evidence” for RNA segments, “discarding” unnecessary segments, he was
obviously reading into molecules, artificial wants or desires that do not
physically exist. If de Sousa really meant this to be a reference supporting
the “first demonstration” of self-replication, he’s truly traversing himself
here. The main gist of Speigelman appears to be taken out of context by de
Sousa, an investigation into how RNA virus operate, not to show
self-replication, AND critically, it is with RNA and enzymes which process RNA.
So it is yet another primary reference
which does not support or define “molecular selection” experimentally, at least
not in a non-teleological sense. The evidence we have for replicating RNA would
give no support for de Sousa’s statement that molecules “desire optimization”
or that some non-chemical phenomenon as chemical selection is occurring in
molecular broths in the sea, or hydrothermal vents or anywhere else..(see the
paragraph where de Sousa states “additional evidence…” above). What you
will find however, if de Sousa is willing to cite these references, is that RNA and the enzymes that process RNA, do
not exist or function outside the test tube for long. Why is that? Let us do a
thought experiment. Let us put large quantities of highly active DNA or RNA
along with enzymes, into a large vat of chemical amino acids and salts. After a
time t (sufficient), will we find the DNA or enzyme to be HIGHER in order? That
is, more reactive than it was at t=0? Consider that molecules in free
communication with adjacent molecules react with these, and reduce their energy
with a variety of irreversible chemical processes. What we expect to find is
that the molecules did select other species, but these are lower energy
species, to effectively dissipate stored energy or potential energy. In fact,
there is no evidence to lead us to believe that any other chemistry is
expected. This basic experiment would directly refute their claim of self-order
would it not? It’s merely an example of the kind of experiment that they should
run as a control, and explain why and how, their chemisty is or would be any
different. And it’s the exact question I would suspect that de Sousa and others
who support the delusion and pervasive myth surrounding “molecular selection”, would not want to answer.
- http://www.weizmann.ac.il/complex/tlusty/courses/landmark/Speigelman1967.pdf
- In Vitro Analysis of Self
Replicating Molecule, S Spiegelman 1967 http://www.jstor.org/stable/27836918?seq=1#page_scan_tab_contents
- Fournier GP1, Alm EJ.
(2015) Ancestral Reconstruction of a Pre-LUCA Aminoacyl-tRNA Synthetase
Ancestor Supports the Late Addition of Trp to the Genetic Code. J Mol
Evol. pr;80(3-4):171-85. doi: 10.1007/s00239-015-9672-1. Epub 2015 Mar 20.
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