Origins Thread

PlunkettsGhost

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Vox Day has been doing stellar work pointing out that biologists are mid-wits who can't do math or understand basic probability. (Jambo 50/50)

He has been promoting his MITTEMS concept quite a lot recently - the Mathematical Impossibility of The Theory of Evolution by Natural Selection.

This problem has been discussed within biological circles for decades btw:


the opening remarks from the chairman of the 1966 Philadelphia symposium on the mathematical challenges to Neo-Darwinism


A physicist chimes in with his support:

Your MITTENS Theorem is of course valid, and more precise and detailed than was possible for the physicists in 1966. You have also independently proposed the correct, and only possible alternative to Neo-Darwinism, what you termed IGM in your October 14, 2012 blog post. You should repost this mechanism, together with more discussion. This mechanism has been repeatedly rediscovered since the famous 19th century Harvard biologist Asa Gray first proposed it

 

PlunkettsGhost

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Here Vox breaks down how there simply hasn't been enough time to generate the required mutagenic changes necessary for speciation, based on observations within cellular cultures. Both observed science and math crush the underpinning time factor for natural selection to be valid. [Source: Sequencing of 19 whole genomes detected 25 mutations that were fixed in the 40,000 generations of the experiment.NATURE, 2009]

For example, based on the mainstream proposed averaged timeline for common ancestor to chimps/man (9 million years), the current observed rates of fixed mutation produces only 125 such fixations.

 

Fishalt

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Vox Day has been doing stellar work pointing out that biologists are mid-wits who can't do math or understand basic probability. (Jambo 50/50)

He has been promoting his MITTEMS concept quite a lot recently - the Mathematical Impossibility of The Theory of Evolution by Natural Selection.

This problem has been discussed within biological circles for decades btw:





A physicist chimes in with his support:



A classic anti-evolutionist argument now goes like this: A gene can be viewed as a sequence of DNA bases, typically represented by the letters A, C, G, and T. A gene can therefore be viewed as a sequence of letters, just as the outcomes of multiple coin tosses can be viewed as a sequence of Hs and Ts. If a specific gene is, say, 100 bases long, then the probability of getting just that sequence by random chance is 1/4 multiplied by itself 100 times. This is such a small number, the argument continues, that it could not possibly have been the outcome of a naturalistic process and must instead have arisen through intelligent design. Sometimes the argument refers to proteins (which can be viewed as sequences of amino acids) instead of genes, and sometimes additional biological details are invoked that in no way affect the logic of the argument. In various forms, this argument has long been a mainstay of creationist literature. For examples, have a look at Morris and Parker (1987, 97–100), Roth (1998, 69–70), and Foster (1999).

However, this argument is premised on the notion that genes and proteins evolve through a process analogous to tossing a coin multiple times. This is untrue because there is nothing analogous to natural selection when you are tossing coins. Natural selection is a non-random process, and this fundamentally affects the probability of evolving a particular gene.

To see why, suppose we toss 100 coins in the hopes of obtaining 100 heads. One approach is to throw all 100 coins at once, repeatedly, until all 100 happen to land heads at the same time. Of course, this is exceedingly unlikely to occur. An alternative approach is to flip all 100 coins, leave the ones that landed heads as they are, and then toss again only those that landed tails. We continue in this manner until all 100 coins show heads, which, under this procedure, will happen before too long. The creationist argument assumes that evolution must proceed in a manner comparable to the first approach, when really it has far more in common with the second.

The failure to consider the role of natural selection in evolution is really such a crass blunder that scientists rightly consider the persistence of such arguments among anti-evolutionists evidence of their fundamental lack of good faith. Modern proponents of intelligent design (ID) are usually too sophisticated to make such an error. Instead, they present a superficially more sophisticated probability-based argument. Their idea is best illustrated by example.

Let us return to coin-tossing. Suppose we toss a coin 100 times, thereby producing a chaotic jumble of heads and tails. It was very unlikely that just that sequence would appear, but we do not suspect trickery. After all, something had to happen. But now suppose we obtained 100 Hs or a perfect alternation of Hs and Ts. Now we probably would suspect trickery of some kind. Such sequences are not only improbable but also match a recognizable pattern. ID proponents argue that it is the combination of improbability and matching a pattern that makes them suspect that something other than chance or purely natural processes are at work. They use the phrase “complex, specified information” to capture this idea. In this context, “complex” just means “improbable,” and “specified” means “matches a pattern.”

As applied to biology, the argument goes like this: Consider a complex, biological adaptation such as the flagellum used by some bacteria to propel themselves through liquid. The flagellum is a machine constructed from numerous individual proteins working in concert. Finding this exact functional arrangement of proteins is extremely unlikely to happen by chance. Moreover, they continue, the structure of the flagellum is strongly analogous to the sort of outboard motor we might use to propel a boat. Therefore, the flagellum exhibits both complexity and specificity, and it therefore must be the product of intelligent design.

The most prominent defender of this argument is ID proponent William Dembski. He has presented it in numerous books and essays, most notably in his book No Free Lunch (Dembski 2002). Dembski presents his argument with a copious amount of mathematical notation and jargon. However, while his argument contributes some superficial sophistication, it is ultimately no improvement over what we have seen.

Let us address the issue of “specificity” first. There is a danger that saying that a flagellum looks like an outboard motor is comparable to saying that a fluffy, cumulus cloud looks like a dragon. We need to be able to distinguish the design-suggesting patterns from the ones we impose on nature through excessive imagination. Biologists say that natural selection produces functional structures as a matter of course. Thus, when we see a resemblance between a flagellum and a motor, are we seeing a design-suggesting pattern, or are we seeing something that is readily explained by natural selection?

In simplistic examples such as coin tossing, we have extensive background knowledge to help us with this problem. We know what usually happens when coins are tossed, and that enables us to distinguish design-suggesting patterns from what normally happens. Likewise for another example ID proponents use to illustrate specificity: Mt. Rushmore. We know what mountains look like when people do not carve faces into them, and this allows us to recognize Mt. Rushmore as the product of intelligent design. This sort of background knowledge is precisely what we lack in the case of evolution. When it comes to biological adaptations, we have no base of experience for distinguishing design-suggesting patterns from the ones explicable by natural processes.

The argument likewise founders on the question of complexity. According to ID proponents, establishing complexity requires carrying out a probability calculation, but we have no means for carrying out such a computation in this context. The evolutionary process is affected by so many variables that there is no hope of quantifying them for the purposes of evaluating such a probability.

In summary, any anti-evolutionist argument based on probability theory can simply be dismissed out of hand. There is no way to carry out a meaningful calculation, and adding “specificity” to the mix does nothing to improve the argument.
 

Fishalt

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Abiogenesis, not a word I had encountered before but it certainly moves the goalposts with regard to the spontaneous origin of life.

Like most of us I had been brought up to believe in the warm soup and lightening hypothesis, but just a few minutes browsing the above strips bare the the vulnerability of that theory to clinical examination.

I need to go away and read further.
Personally I think abiogenesis occurring in hydrothermal vents is the most probable theory at this stage.
 

Fishalt

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As I asked you some months ago Tiger, why the need to give the beast such a long neck in the first instance? Why not design it to eat stuff lower to the ground?

And why not put an eye above its arsehole so when bent down drinking water it'd be able to see the approach of a Lion from behind?
The only plausible argument from a creationist perspective that is coherent when it comes to this is that the creator designed life to fail--a kind of biological planned obsolescence type thing. From my perspective, I'd say that nature strives for equilibrium--which is why ecological overshoot is so interesting to me as a concept. Nature doesn't design organisms to be invincible, it designs them with interrelation and sometimes symbiosis in mind, subject to the laws of physics. A giraffe is by not a perfect design in terms of longevity, and if it were, this would actually be detrimental to the bioweb as a whole system. Nature isn't trying to make supermutants, it's making organisms well-enough to the point that they can send their genetic code into the future as an average in relation to every other organism operating in the environment. Ironically, a perfectly designed Giraffe is necessarily an imperfectly designed organism. We can see this arrangement repeating everywhere in the natural world.

It never ceases to amaze me how uninvolved with their local wildlife and plant life the average Christian ( or Muslim/Jewish) person is. I suspect this is because their holy texts teach them that plants and animals are simply here to serve mankind--a resource to be utilized, exploited and appropriated for our own ends and means. They never stop to consider that our continued existence is contingent upon the continuation of 'lower' lifeforms. For example, if Fungi disappeared from the Earth tomorrow so would plant life, and inevitably our species.
 
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Tiger

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The only plausible argument from a creationist perspective that is coherent when it comes to this is that the creator designed life to fail--a kind of biological planned obsolescence type thing. From my perspective, I'd say that nature strives for equilibrium--which is why ecological overshoot is so interesting to me as a concept. Nature doesn't design organisms to be invincible, it designs them with interrelation and sometimes symbiosis in mind, subject to the laws of physics. A giraffe is by not a perfect design in terms of longevity, and if it were, this would actually be detrimental to the bioweb as a whole system. Nature isn't trying to make supermutants, it's making organisms well-enough to the point that they can send their genetic code into the future as an average in relation to every other organism operating in the environment. Ironically, a perfectly designed Giraffe is necessarily an imperfectly designed organism. We can see this arrangement repeating everywhere in the natural world.

It never ceases to amaze me how uninvolved with their local wildlife and plant life the average Christian ( or Muslim/Jewish) person is. I suspect this is because their holy texts teach them that plants and animals are simply here to serve mankind--a resource to be utilized, exploited and appropriated for our own ends and means. They never stop to consider that our continued existence is contingent upon the continuation of 'lower' lifeforms. For example, if Fungi disappeared from the Earth tomorrow so would plant life, and inevitably our species.

Utter twaddle.

You seem to specialise in strawman arguments Fishalt. There’s no substance in any of what you wrote.
 

PlunkettsGhost

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Personally I think abiogenesis occurring in hydrothermal vents is the most probable theory at this stage.
Grand so, we look forward to your description of the mechanism at work here that brings a fully functional cell into being instantaneously, because that's what needs to happen.

Any newly formed cell not already capable of respiration, energy capture and absorption, and replication, to name but 3 necessary components of viability, won't survive more than a moment . Just the three necessary functions mentioned are all massively, biochemically complex processes btw.
 

PlunkettsGhost

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This is untrue because there is nothing analogous to natural selection when you are tossing coins. Natural selection is a non-random process, and this fundamentally affects the probability of evolving a particular gene.
I think you've missed the point. The proposed mechanism behind natural selection is genetic mutation with fixation. This something that can be observed and measured in cellular culture, over thousands of generations.

As such, it is now obvious that the rate of fixation is too slow to account for the theory of speciation (molecule to man)

And observed fixation today is also not creating new kinds of cells, just modifying the original .

The much vaunted fruit fly experiments didn't create new species of fly, just messed up versions of the original
 
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PlunkettsGhost

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In an attempt to make the subject easier for people to understand, a programmer ran MITTENS through ChatGPT, and despite the usual issues and very generous assumptions of tiny populations and high fixation probabilities, the results tend to demonstrate why biologists will have to avoid MITTENS as long as they possibly can in order to continue clinging to their outdated and disproven assumptions about the origin of the species. Somewhat amusingly, the AI did not provide a final answer in terms of the range of times required for fixation given its estimates and assumptions, but contented itself with saying that a population-wide fixation could perhaps happen eventually, in theory, given a sufficiently beneficial mutation.

 
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As Dawson has so amply pointed out from his rage-cage:

Evolutionists have no interested in the actual origins of life. Through the power of imagination, they accept the Norse tale of the lightning bolt as obvious fact, and simply move on. Until of course you point out there is no evidence of speciation via natural selection either. They then move on from that and hold onto the crumbling door-frames of micro-adaption as being evidence for macro-evolution. An obviously laughable, desperate situation.

It is interesting that unlike the Buddhists and the Mormons they do not simply believe that the Universe has always been here.
 

Fishalt

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I think you've missed the point. The proposed mechanism behind natural selection is genetic mutation with fixation. This something that can be observed and measured in cellular culture, over thousands of generations.

As such, it is now obvious that the rate of fixation is too slow to account for the theory of speciation (molecule to man)

And observed fixation today is also not creating new kinds of cells, just modifying the original .

The much vaunted fruit fly experiments didn't create new species of fly, just messed up versions of the original
The fruit fly experiments seem fairly awful prima facie TBH for several reasons. Firstly, it seems that fruit flies preference breeding on food consumption and what they eat affects mutational rates both:

Fruit fly larvae with a noted mitochondrial DNA (mtDNA) mutation showed a pronounced increase in development when eating high carbohydrate diet of banana, but stagnated on a high protein diet of passionfruit.

Conversely, fruit fly larvae without the mtDNA mutation thrived on the high protein diet, but dropped in frequency when put on carbohydrates.

UNSW School of Biotechnology & Biomolecular Sciences Professor Bill Ballard, who led the study, says the research is a rare demonstration of positive selection at work in evolution.

“What is unique about this study is we've identified one mutation in the mitochondrial genome, that when fed a specific diet is advantageous and causes the frequency of flies in a population cage to increase,” he says.

“Then when you swap the diet back to a high protein diet, the flies with the mutation go down in numbers and the other flies without the mutation go up.”


The second issue is that despite your protestations about people not being able to maths, you've somehow failed to consider the obvious fact that human beings--at least in the modern sense of what we mean by that term--have been around for at least 200K years. That's a lot more generations than what is produced by a decade of fruit fly breeding. To wit:

"OK, so if you get a new generation of fruit flies every other day, and you ran a 30 year long experiment, you would have 30 * 365 / 2 = 5475 generations of fruit flies. Human generations are generally taken at around 20-25 years. So, according to him, that's equivalent to about 136,875 years of human history.

Well, scientists generally think that modern humans have been around for about 200,000 years. That's just modern humans. The first members of the human family are estimated at 6-7 million years ago.

To put that in comparison, let's say each of these bars is 50,000 years:

||| 30 year fruit fly experiment
|||| Modern Humans
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| Total human time

Hmmm...those look just a BIT different!

But wait. Has anyone actually DONE a 30 year fruit fly mutation experiment?

Doing a quick check, the longest I've found mentioned for fruit fly mutation experiments that debunk evolution is a mere 600 generations. Equivalent to only a tiny 15,000 years. Less than 10% of the equivalent time modern humans have been around."


Finally, you still don't really understand how evolution works. You're still operating under the false premise that mutations happen, and they arrive perfect and complete or terrible and not suited to the environment and disappear from the gene pool, and that's not how it works. Evolution can happen very slowly or relatively fast., and the vast majority of the time, mutations are slight and provide virtually no survival advantage when they first arrive. Mutations are experiments tested by environmental conditions. It is these conditions that refine or discard them.

Bacteria?

Linksi has the longest running evolutionary experiment on bacteria and has observed major evolutionary change, and believes he has created a new species of bacteria.

 

Fishalt

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It is interesting that unlike the Buddhists and the Mormons they do not simply believe that the Universe has always been here.
I personally take a punt on that question. We don't really know enough. This is also the position Buddhists take on it. Kind of. They more or less just shrug and say, "We don't know. It just is. And it hardly matters, because you'll still have to live this life regardless of how it came into being".
 

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Do Organisms Have Goals and Purpose? - Amelia Lewis

[https://www.nas.org/academic-questi...ons/37/1/do-organisms-have-goals-and-purpose)

“Despite this, neo-Darwinism is not the only paradigm from which to interpret evolution and animal behavior. The Extended Evolutionary Synthesis (EES) is a non-creationist alternative to traditional neo-Darwinian thinking, and in this paper, from within the context of the EES, I will discuss how individuals not only respond to and manipulate their environment, but teleologically direct the course of their own evolution. However, they do so whilst embedded within a vast, complex system where each individual pursues its own goals. Thus, it is not only the genome which directs the course of life on Earth, any more than it is any one gene. From the cell, to the individual, to the population, to complex ecosystem function, the gene is a resource. It is not the ruler.”
 

Tiger

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A classic anti-evolutionist argument now goes like this: A gene can be viewed as a sequence of DNA bases, typically represented by the letters A, C, G, and T. A gene can therefore be viewed as a sequence of letters, just as the outcomes of multiple coin tosses can be viewed as a sequence of Hs and Ts. If a specific gene is, say, 100 bases long, then the probability of getting just that sequence by random chance is 1/4 multiplied by itself 100 times. This is such a small number, the argument continues, that it could not possibly have been the outcome of a naturalistic process and must instead have arisen through intelligent design. Sometimes the argument refers to proteins (which can be viewed as sequences of amino acids) instead of genes, and sometimes additional biological details are invoked that in no way affect the logic of the argument. In various forms, this argument has long been a mainstay of creationist literature. For examples, have a look at Morris and Parker (1987, 97–100), Roth (1998, 69–70), and Foster (1999).


?

Fishalt, it’s worth mentioning to the readers that what you posted above are not your own words, but that of Jason Rosenhouse. If you are quoting someone it’s customary to mention that.

Jason Rosenhouse has a misunderstanding of probability in complex systems.

Jason’s argument asserts that calculating the probability of a specific gene or protein sequence evolving naturally is fundamentally flawed due to the non-random nature of natural selection. However, this is grossly oversimplifying the problem. The calculation of probability does not merely concern the random assembly of sequences but also encompasses the likelihood of these sequences arising through the cumulative steps required by natural selection. Even with natural selection, the intermediate steps themselves need to be functional, which significantly limits the possible successful pathways, thus making the overall probability still extremely low.


This is William Dembski’s response to Rosenhouse’s article:

Rosenhouse’s Whoppers: Appealing to the Unwashed Middle
William A. Dembski

Before leaving academia for business, I used to lecture on intelligent design at colleges and universities, and often debate people on the Darwinian side. Michael Shermer and Michael Ruse were my most frequent debate partners. My philosophy at these debates was not to try to convince Darwinists that my views were correct. Nor was I particularly concerned about the intelligent design proponents — if they were proponents of ID, they had presumably put their necks on the chopping block and knew what was at stake, academically and culturally, in taking the side of ID. My challenge, rather, in these debates, was to win the unwashed middle — those who had not made up their minds — those who didn’t reside in the cloud cuckoo land of Darwinism. So this response is mainly directed at them.

Rosenhouse’s book is objectively bad. It purports to be a critique of mathematics as used by ID proponents and of my mathematical work in particular. Yet it betrays a lack of comprehension throughout. It makes a virtue of misrepresentation. Its aim is not to understand but to kill. In my review, I called Rosenhouse on his many failures in the book. It’s clear in his reply that he simply ignored the points I was able to score — points he made it easy for me to score because he did such a hack job. Read his book and read my review, and decide for yourself.

A New Dimension of Bad
His reply, however, adds a new dimension to the debate. The reply, too, is objectively bad in the same sense as his book. But it adds a level of delusion that in reading it made my jaw drop. I’m not writing this for rhetorical effect. In the reply, he lets loose with two whoppers that make me question what planet he’s been living on. Indeed, I have to seriously wonder about the degree to which Darwinists are in their right minds if they find in Rosenhouse a voice that speaks for them.

But before getting to the two whoppers, buried in his reply are two substantive points worth addressing. They came up in my review, received comment in the reply, and deserve some additional comment here. They concern (1) the connection between irreducible and specified complexity and (2) the role of the environment in supplying information to the Darwinian process.

Irreducible versus Specified Complexity
For Rosenhouse, irreducible and specified complexity are both bogus notions in that they purport to place some limitation on Darwinian natural selection when, of course, no such limitation can ever apply because of natural selection’s presumed wonder-working ability to build novel adaptations and transform one species into another. Yet, for Rosenhouse, specified complexity is the more bogus notion of the two.

Michael Behe, in introducing the concept of irreducible complexity, has argued that irreducibly complex systems could not evolve gradually. But once it’s known, or assumed, that these systems could not evolve gradually, what’s the point in doing a probability calculation, as is inherent in specified complexity, to show that these systems are unlikely to evolve? If something can’t happen or is assumed to be unable to happen, then it is improbable. What further need for a calculation? As Rosenhouse puts it in his reply, “It is really Michael Behe’s claims about irreducible complexity that are doing all the work. The probability calculations do nothing to strengthen the argument.”

I addressed this point in my review, but let’s have another go at it. Consider Sisyphus. As long as you can remember, he’s been rolling a rock up a hill, only to have it roll back down before it gets to the very top, which, let’s assume, is a stable equilibrium, so if he gets it to the very top, it will stay there (though he never does). What is the probability that Sisyphus will get the rock up to the very top? As a historical or inductive probability, it is quite low. All your life, you have been seeing him try to get the rock up there and somehow it never quite gets there.

That historical probability for Sisyphus is the same type of probability as inherent in Mike Behe’s assessment of Darwinian processes being unable to build irreducibly complex molecular machines. All the attempts by biologists to trace a detailed Darwinian pathway of how an irreducibly complex system might emerge from an evolutionary precursor performing a different function have failed.

Richard Lenski, for instance, has run tens of thousands of generations of E. coli, and produced no novel irreducibly complex system. The record of failure of evolutionary biologists in their inability to provide detailed Darwinian pathways for irreducibly complex systems is as complete as Sisyphus’s efforts to get the rock to the top of the hill. If you disagree, please provide an irreducibly complex system, its precursor system performing a different primary function, and then the step-by-step path of how to get from one to the other. Silence? Crickets?

The Nuts and Bolts
By contrast, specified complexity gets at the nuts and bolts of the probabilistic hurdles that render an evolutionary transition intractable. To continue with the Sisyphus analogy, specified complexity would look not at Sisyphus’s record of failure so much as the types of obstacles he faces in getting to the top and how those might render getting to the top improbable.

For instance, perhaps in rolling the rock up the hill, most of the path is clear and unproblematic, but at one point there’s a bump so that given his strength he just can’t get over the bump. Or perhaps, there are multiple bumps, where he’s got a positive probability of getting over each bump, but when all these probabilities get combined, he’s bound not to get over all the bumps. Or perhaps he gets tired, running out of steam as he moves up the hill, so that bumps lower on the hill would be no problem, but by the time he gets up the hill, they do become a problem, and his probability of getting over all of them approaches zero.

The point to appreciate is that such a probability analysis of Sisyphus adds to our understanding of his failure. His record of failure is enough to justify assigning a low historical probability to his being able to roll the rock to the very top of the hill. But an empirically based probability of his failure needs to look at the particularities of the probabilistic hurdles that he’s facing. The same holds for irreducible complexity. There’s a long record of failure by biologists to explain how these systems might evolve. Specified complexity attempts to understand the probabilistic particulars that could explain the record of failure.

But specified complexity is not merely a supplement to irreducible complexity. Not all biological systems are irreducibly complex. In consequence, specified complexity can assess the evolvability of biological systems that are not irreducibly complex. For instance, the beta-lactamase enzymatic system that Doug Axe examined (described at greater length in my review) is not in any clear sense irreducibly complex, but it is analyzable probabilistically and exhibits specified complexity.

Consider a Bridge
One more analogy to try to nail all this down. Again, I write for the unwashed middle and have no expectation of assuaging Rosenhouse. Consider a bridge. It’s stood for 100 years, faced all kinds of weather and hardship, and has remained imperturbable. And yet one day it suddenly collapses. Before its collapse, we might think that its probability of continuing to stand was quite high, and so the probability of collapse was quite low. Given its collapse, is it therefore safe to say that a highly improbable event happened?

 
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Tiger

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NO NATURALLY OCCURRING PROTOCELLS HAVE BEEN OBSERVED IN THE WILD

If even one of these 39 complex protein machines is missing or defective, cell division (reproduction) of the bacteria is impossible.

QUESTION: HOW WAS THE FIRST IMAGINARY CELL ABLE TO DEVELOP ALL THESE PROTEIN MACHINES DURING ITS SHORT LIFE?

Bacterial binary fission is a complex and highly coordinated process that involves at least 39 various protein machines and assistant proteins. Below is a comprehensive list of the necessary proteins categorized based on their roles in the different stages of bacterial cell replication...

4e04e403-37e3-40dd-90a6-f8479ef94f17.jpeg


Read more at: https://sciencerefutesevolution.blogspot.com/2024/05/if-even-one-of-these-complex-protein.html
 

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Bizarre bacteria defy textbooks by writing new genes - Ewen Callaway


Bacterial defensive systems scramble the standard workflow of life.

[“ bacterial version of reverse transcriptase reads RNA as a template to make completely new genes written in DNA. These genes are then transcribed back into RNA, which is translated into protective proteins when a bacterium is infected by a virus. By contrast, viral reverse transcriptases don’t make new genes; they merely transfer information from RNA to DNA.

“This is crazy molecular biology,” says Aude Bernheim, a bioinformatician at the Pasteur Institute in Paris, who was not involved in the research. “I would have never guessed this type of mechanism existed.”


Darwinism is becoming less relevant all the time.
 

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Are we not the same as most of the other Earthling's. Even the birds and fish - We're similar!!😊
 

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