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This post will review 2 of the major difficulties faced by studies in naturalistic abiogenesis (undesigned origin of life).
No experimental evidence
Those arguing that naturalistic abiogenesis is the best explanation--or the most promising avenue of research--for the origin of life must assume that naturalistic abiogenesis is possible. If it isn't possible, none of the other arguments are going to matter.
Many hypotheses have been put forward, but none have found support through experimental evidence. No conditions--whether intelligently designed by scientists or naturally occurring--have ever been observed to yield life from non-life. Belief in life coming from non-life is supported by exactly the same amount of experimental evidence as belief in unicorns.
In any other scientific discipline, a hypothesis that is not supported by evidence would not be considered a leading theory.
It is, of course, possible to test a naturalistic hypothesis through methodological naturalism, and withhold judgment until compelling evidence is available. A scientist employing this method could not truly claim to believe in naturalistic abiogenesis (due to the absence of experimental evidence), but can still rationally continue to run tests by exercising faith in methodological naturalism (because it has been a useful experimental technique in the past). Furthermore, each time a hypothesis is designed, tested, and fails to produce results, one could genuinely call this progress in the OOL field.
Another common approach seen in OOL discussions is not methodological naturalism (a means of conducting an experiment), but metaphysical naturalism, a non-scientific philosophical worldview. Any argument for naturalistic abiogenesis which presupposes metaphysical naturalism is circular. Those taking this approach can claim to believe in naturalistic abiogenesis, but that belief would be based on something other than evidence.
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Probability
If a naturalistic means for the origin of life were discovered, would this resolve the question of the origin of life on this earth? No. (though this wouldn't stop less-scrupulous individuals from making millions on books which proclaimed "God is dead" to less-discerning audiences).
Even after discovering a naturalistic means for life to originate (which we haven't done--see above), one would still have to argue that the naturalistic mechanism in question was the mechanism by which life originated (as opposed to design or some other, as yet undiscovered naturalistic process). The argument from probability would still have to be faced.
Doug Axe famously argued that the sequence space for protein folds is too vast for successful innovation by chance, indicating through extensive testing that only approx. 1 in 10^78 possible DNA variations is viable.
The odds of a DNA strand generating 1 successful protein fold through random accident are prohibitively low, let alone a full DNA sequence (even for a simple single-celled organism) producing many functional proteins. And this comes even before the problem, already noted by NigelJ, that for continuation of life, this miraculous strand of information must also self-replicate.
Let's use a more accessible example: computer code. Let's consider a very, very simple computer function, which is made up of code containing just 1,000 characters. These 1,000 characters could be arranged 4.02 × 10^2567 different ways, almost all of which would be gibberish. A miniscule portion of these combinations would actually compile, and only a fraction of those which compiled would actually produce a functional program.
If we encounter:
While it is possible the computer function resulted from the machine's random process, we would rationally conclude that this code--like all other computer programs we've ever encountered--came from a programmer (or a program designed by a programmer, if we want to be picky), not from the wildly improbable random combinations.
Thus, even if there were a naturalistic process that transformed non-life into life, the level of design in DNA--far more complex than any computer program--would still provide a formidable obstacle to a rational belief in naturalistic abiogenesis.
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Conclusion
Does Dave Farina have a point when he points to a tremendous amount of OOL research publications that seem to indicate that we are NOT clueless?
Clueless is a harsh term. We aren't clueless about how cells function or how they replicate. But it is that very knowledge of cells that demonstrates the canyon-sized-gaps in hypotheses of naturalistic abiogenesis.
Is James Tour correct when he dismisses all these publications as "hyped"?
Hype sells, and there is indeed plenty of it. But there also appear to be methodologically consistent scientists working on the OOL problem along the lines described in paragraph 4 of the "no experimental evidence" section. Any time they test a hypothesis and find it doesn't work, that is progress in the Edison sense--we've ruled out another possibility. It is my observation that such disciplined scientific inquiry gets much less attention than those who make sensational claims in order to turn a tidy profit.
What are examples of major (and perhaps unsurmountable) obstacles that OOL research is facing right now?
Naturalistic abiogenesis is supported by 0 experimental evidence, which evidence (if obtained) would only be an entrance fee to compete with teleological arguments.
The teleological argument from biological specified complexity is an argument for an intelligent mind behind the creation of life, and is a formidable objection to chance-based hypotheses.
Re comments
Identifying the characteristics of that "something alive" is outside the scope of this post. Those seeking to review more detailed teleological arguments for God's existence (since that's not really the focus of the OP here) are encouraged to review the existing teleological questions on this site, or post a fresh question on the matter if the existing questions are inadequate.
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Anyone who has a reasonable understanding of molecular biochemistry can see that any attempt to produce the truly immense complexity of the organic chemistry of life from non-living (that is to say 'inorganic') material is doomed to failure from its inception.
Take, for example, the Krebs cycle, which I have seen postered on the wall of just about every Organic Chemistry Laboratory and every Biochemistry Laboratory I have ever visited (and I have visited many in the days when I marketed Spectrophotometers and Chromatographs throughout the Southern half of England).
In order to make energy, the cell (that is to say every cell of cellular life on planet Earth) converts ADP to ATP and stores it, then uses the ATP to release a phosphate and also release energy.
Just this one aspect of cellular existence requires scores of organic components which are only found in cells (and nowhere else). They do not survive outside the cell.
Then take DNA and RNA which both need to be already in the cell for the cell to procreate. These are the most complex molecules found in nature and they occur only in cells.
Then consider proteins, which have a specific three-dimensional structure necessary to grasp one component, then another component, then (once both are grasped) to twist themselves such that both components come together and react. Proteins are catalysts and they provide the chemistry which combines components into usable artefacts.
Of which proteins we have something like 20,000 in our cells, which are produced (individually) by 20,000 different genes in our DNA. Proteins, also, are only found in cells. They do not occur elsewhere. They do not survive outside the cell.
This staggering array of organic activity must exist first.
Then it must live.
Then it can be active and it can generate energy and it can procreate.
The idea that this staggeringly complex mechanism can be composited from inorganic materials, by chance . . . . . is just beyond my own belief.
I speak, in this answer, as a Chemist.
And just as a Chemist.
As a Chemist, I simply cannot believe that the production of cellular life is possible other than by a Divine and Wise and Masterful Deity, by immediate, independent, purposeful, knowledgeable and constructive ability.
I just cannot believe it.
Yes, we are (I say 'we' meaning scientists) utterly clueless as to how life could possibly have begun from inert, inorganic materials. Because it simply could not have done so.
That is why Inorganic Chemistry and Organic Chemistry are totally different branches of study and speciality.
Because one does not, and - indeed - cannot, produce the other.