# Probability and life by Chance Alone

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In another post I offered an analysis by Fred Hoyle indicating life by chance alone was astronomically poor. In response Skeptic suggested life by change alone could be improved by bringing in resources from a hypothetical infinite universe. Since this discussion was not the primary purpose of the original post I offer this thread to explore the idea further. Here is Skeptic's explanation.

It is a rough estimate of the probability that the universe is infinite (we don't yet know). Given an infinite universe, now calculate the chance that at least one life form formed by a process with a probability to occur of 1 in 10^41,000 (your numbers): $Probability = 1 - (1 - 10^{-41,000})^{\infty} = 1 - 0 = 1$. On average you would expect there to be $10^{-41,000} \infty = \infty$ life forms forming by said method. So the probability that some life formed by such an unlikely method is the same as the probability that the universe is infinite -- which I estimated at ~50% -- and the number of such life that would exist in that case would be inifinte. Feel free to look up more accurate numbers, but know that they will be much closer to 50% than you will be comfortable with. The numbers may instead refer to the curvature of the universe; in that case the closed universe is finite and the flat and open are infinite.

The reason I would not expect to ever find such life forms is that our observable universe is quite finite due to the expansion of space, and in any case if we did find a life form it would most likely have been formed by a much more likely method, such as one of the current theories of abiogenesis.

I see at least three issues with this analysis.

First off it is not clear that an infinite universe is real or even possible. Even it it were possible and was real it is not clear that expansion would actually obscure any part of the universe from our vantage point even though one can create a mathematical model that does, it does not mean that the model is correct or even the only workable one.

Second, I am aware that if one assumes expansion, one can derive probabilities near 50% given the assumption. If one chooses other models compatible with General Relativity then the probability of a substantially larger universe than what is observable approaches 0. The choice of assumption is arbitrary and primarily based on metaphysical bias. Since the probability of an infinite universe is based on an arbitrary presumption, we can't say if the estimate is real or not. This seems more like putting an appeal to ignorance (about the extent of the universe) into a chance wrapper and claiming one has made a good point. It is creative though, I'll give you that.

Finally, it lacks causal adequacy since we have no experience of any material thing having a property that is infinite. On the other hand math has many known concepts with no real counterpart and thus it is possible that infinity is a mathematical construct alone.

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The universe has been expanding since it was created by the Big Bang billions of years ago, and it's going to keep expanding. In this way, the universe can be thought to be infinite.

Even though this is the correct way to estimate the probability, there are variables left out that must be there to give an absolute accurate estimate. With an infinite universe, the OP is saying that there would be infinite life forms, which makes sense. The 50% he mentions, is the probability that our universe is infinite. Because duh, it's either infinite or finite.

We shouldn't be looking at just the probability of a life form formed, but also the probability that that life form is found by us in any given way. If it hasn't been found by us, we cannot say that it ever existed in the first place.

Edited by Neco Vir
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If the formation of life was a completely random thing then the probability of life occurring would be infinitesimally small, almost but not quite impossible. Fortunately we now know it isn't a random chance, not only does order tend to arise from chaos but in the presence of excess energy chemistry tends to form more and more complex chemical structures.

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Using the very same laws of physics that we use to model a finite universe, we can likewise get an infinite universe. The only difference is a different matter density -- a higher matter density means that gravity will have a stronger influence. Both the finite and infinite universe have interesting properties that might make them attractive from a philosophical point of view. An alternative form of infinite universe is a cyclic universe, for example one that goes through infinite cycles of expansion and contraction -- this one is extra nice because then you don't have to describe how time starts or ends. Yet another way to get an infinite universe is the quantum multiverse nonsense.

The shape of our universe and finite/infinite

Cyclic universe

Multiverse/Parallel universes

Each of these three is a separate way in which the universe could be infinite. All three could be true, or none at all. The first one we may be able to measure definitively sometime soon. The second is a theory which could describe our universe (its still work in progress). The third can result from an interpretation of quantum mechanics, and so more or less outside the realm of science to say whether it is so or not (interpretations are like God, they are for "making sense" not "making predictions"). This particular option boils down to a matter of opinion. There are however other multiverse possibilities that would be within the realm of science, such as M-theory.

My estimate of 50% was only for the first option only, the only one that we can meaningfully estimate at this time. The current best estimate is that the universe is flat (infinite), with a 2% margin for error. Of course the slightest deviation would result in either an open (infinite) universe or a closed (finite) universe.

Another option that could also be is that the universe is finite but very very big (closed, but almost flat). For example the whole universe could have 10^41,000 times the volume of our observable universe.

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The universe has been expanding since it was created by the Big Bang billions of years ago, and it's going to keep expanding. In this way, the universe can be thought to be infinite.

A universe of fixed mass forever expanding outward does not improve probability the way Skeptic proposed because it does not and cannot add unobserved probabilistic resources for events that occurred in the past.

Even though this is the correct way to estimate the probability, there are variables left out that must be there to give an absolute accurate estimate. With an infinite universe, the OP is saying that there would be infinite life forms, which makes sense. The 50% he mentions, is the probability that our universe is infinite. Because duh, it's either infinite or finite.

As I indicated above it is not the correct way to estimate probability unless one knows that the mass of this universe (and therefore the amount of probabilistic resources) was infinite at the time that life occurred. Since we can only make assumptions about the mass of the universe beyond the observable horizon, if there is any universe beyond that and this is a huge if, we cannot know. As far as the probability of finite or infinite goes, it is not a 50-50 proposition. Since we don't have any experience with infinite material things, Occam's razor hacks away at the idea of infinity and leaves only finite.

We shouldn't be looking at just the probability of a life form formed, but also the probability that that life form is found by us in any given way. If it hasn't been found by us, we cannot say that it ever existed in the first place.

This is a topic for another thread. Start one if you wish.

If the formation of life was a completely random thing then the probability of life occurring would be infinitesimally small, almost but not quite impossible. Fortunately we now know it isn't a random chance, not only does order tend to arise from chaos but in the presence of excess energy chemistry tends to form more and more complex chemical structures.

We don't "fortunately know that order tends to rise from chaos". On the contrary the laws of thermodynamics ensure that forming order requires still higher order, and chemistry plus energy forms chemical structures of equal or lesser order. Deterministic repeating structure is not a lower entropy (and therefore higher order) system. Simple repeating patterns are not complex.

Although this is an interesting area of inquiry, bringing in non-random processes is off topic. consider starting a new thread if you wish to discuss this further.

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Could someone explain how time and an infinite universe effects probability? Because it doesn't.

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As I indicated above it is not the correct way to estimate probability unless one knows that the mass of this universe (and therefore the amount of probabilistic resources) was infinite at the time that life occurred. Since we can only make assumptions about the mass of the universe beyond the observable horizon, if there is any universe beyond that and this is a huge if, we cannot know. As far as the probability of finite or infinite goes, it is not a 50-50 proposition. Since we don't have any experience with infinite material things, Occam's razor hacks away at the idea of infinity and leaves only finite.

Occam's razor is a suggestion, not a logical rule. It is not a substitute for evidence.

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I disagree with your characterization. Are you suggesting that it is valid to make an appeal to ignorance and a less parsimonious explanation to prop up the idea of a past infinite mass in this universe? I am guessing you would not.

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I disagree with your characterization. Are you suggesting that it is valid to make an appeal to ignorance and a less parsimonious explanation to prop up the idea of a past infinite mass in this universe? I am guessing you would not.

I don't see where an appeal to ignorance enters into this. Models that give an infinite universe do exist, and some are supported by evidence.

To state "the universe is clearly infinite in size and mass" would be premature, but it is an option with some non-trivial evidence. It's worth consideration, along with other suggested and supported models.

An argument to ignorance would be "Well, anything could happen outside the observable part of the universe, so maybe there's a giant life factory out there!"

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Could someone explain how time and an infinite universe effects probability? Because it doesn't.

So, $\frac{1}{1000000}\times1000000\neq1$?

Edited by ydoaPs
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I don't see where an appeal to ignorance enters into this. Models that give an infinite universe do exist, and some are supported by evidence.

I might be wrong, but inventing a model that is molded to fit some limited number of observations (so one can claim it enjoys evidence) and also is molded to infer an infinite universe is not the same as finding observations that are directly consistent with and fit having infinite mass in this universe. I describe these kinds of models as metaphysics masquerading as science. It is a form of confirmation bias to my way of thinking.

Could someone explain how time and an infinite universe effects probability? Because it doesn't.

Good point. An infinite universe can only influence the outcome if the probabilistic resources from this hypothetical space can be brought to bear and act on the events in question. if these resources do not interact, they are isolated and irrelevant so you cannot multiply them since they are not dependent.

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I might be wrong, but inventing a model that is molded to fit some limited number of observations (so one can claim it enjoys evidence) and also is molded to infer an infinite universe is not the same as finding observations that are directly consistent with and fit having infinite mass in this universe. I describe these kinds of models as metaphysics masquerading as science. It is a form of confirmation bias to my way of thinking.

As far as I understand, the latter is what occurred, not the former. I also don't see the functional difference; science requires a model substantiated by evidence, and pays no attention to the mindset of the researcher who created it. Two independent models with independent evidence are considered equal, even if, say, one of the models was created by a Nazi to suit his evil purposes.

Good point. An infinite universe can only influence the outcome if the probabilistic resources from this hypothetical space can be brought to bear and act on the events in question. if these resources do not interact, they are isolated and irrelevant so you cannot multiply them since they are not dependent.

Why's that? If there's a million isolated independent sites where an event can occur, and the probability of that event occurring is fixed, there are now a million independent chances for that event to occur. The interaction of the sites isn't important.

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The universe, as we know it, is designed to make life more likely than pure chance. For example, life is mostly C, O, N, H which just so happen to be the small atoms even a first generation star can make, starting with only isotopes of hydrogen/helium. The two most abundant chemical molecules in the universe are H2 and H2O. The high level of H2O slants the odds for life in water. While the energy of life, as we know it, stems from the energy within reduced materials. The hydrogen molecule is an extremely abundant reducing agent; #1 molecule of the universe, which means NH3, CH4, etc. Small molecules like these, in the presence of the H2O (#2) and gravity, gives us weather, lightning and the formation of amino acids. The universe was designed to get the ball rolling since it most abundant things are what life also makes use of.

Metabolism is a process that lowers energy and increases entropy. All you really need is a metabolic pathway to develop and there is energy output and entropy increase to push faster than just random collisions without a metabolic push. Metabolism is modeled on fire, but metabolism burns under water. Depending on how hot our fire is and the fuel to terminal electron acceptor ratio, we can get a large variety of broken bonds and combustion products.

One thing that is always left out is water and its ability to direct. It is not coincidence that life molecules and water both use hydrogen bonding, with water doing the H-bond thing f first. For example, in liquid water, individual H2O molecules only exist for about 1 millisecond until the H switch O partners. What that means is the entropy of the aqueous hydrogen is moderately high. We get the pH effect as one constant example. The high entropy of H in water means the entropy of other hydrogen dissolved in water will see this entropy potential. The hydrogen bonding of life molecules, implies these hydrogen are closer to the H entropy of water; share, swap and mobilize. Water started this and life followed the lead from water as life conformed to the potential of the H.

Edited by pioneer
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We don't "fortunately know that order tends to rise from chaos". On the contrary the laws of thermodynamics ensure that forming order requires still higher order, and chemistry plus energy forms chemical structures of equal or lesser order. Deterministic repeating structure is not a lower entropy (and therefore higher order) system. Simple repeating patterns are not complex.

Although this is an interesting area of inquiry, bringing in non-random processes is off topic. consider starting a new thread if you wish to discuss this further.

First off the idea that life is random process is totally bogus, every bit as bogus as th idea that order cannot arise from chaos. You continuously stating other wise will not change reality, I did say that if indeed your premise was true then life would be unlikely to happen, of courts the fact that it did happen at least once is obvious. I was not trying to hijack your thread, I was trying to participate in the only way I know how by stating an observable truth, two in this case. Order does arise from chaos and that a build up of chemical energy can give rise to complexity. now I'm sorry if I misinterpreted your OP but i did not make claims that could not be backed up.

http://en.wikipedia.org/wiki/Chaos_theory

http://nirmukta.com/2009/11/13/complexity-explained-9-how-did-complex-molecules-like-proteins-and-dna-emerge-spontaneously/

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First off the idea that life is random process is totally bogus,

I agree, but others do not. this thread is intended to have a discussion with those who do not agree and this is why I suggested you start a new post. Not that you were trying to hijack the thread, I think this is another topic that is worthy of discussion on its own.

every bit as bogus as th idea that order cannot arise from chaos. You continuously stating other wise will not change reality,

Your link relies on a very precise and altogether different definition of "chaotic system" then what you described as "chaos". No sorry there is no objective evidence to suggest that order arises from disorder (what you called chaos). Entropy laws require that order requires equal or higher ordered sources. To claim otherwise is to thumb your nose at thermodynamics.

I did say that if indeed your premise was true then life would be unlikely to happen, of courts the fact that it did happen at least once is obvious.

Yes and how it happened is the question at hand. This thread is intended to investigate chance alone.

I was not trying to hijack your thread, I was trying to participate in the only way I know how by stating an observable truth, two in this case.

Yes I know you were not. I have read many of your posts and I find them always relevant. Sorry to imply otherwise. I simply thought your point was worthy of a thread on its own.

Order does arise from chaos and that a build up of chemical energy can give rise to complexity. now I'm sorry if I misinterpreted your OP but i did not make claims that could not be backed up.

http://en.wikipedia.org/wiki/Chaos_theory

http://nirmukta.com/2009/11/13/complexity-explained-9-how-did-complex-molecules-like-proteins-and-dna-emerge-spontaneously/

Ordered systems can be modified into equally ordered system by chaotic processes. This is what your link describes. HOwever, order does not arise from disorder by chaotic systems or by disorganized processes (chaos). Your second link is speculation. It does not provide any real observed examples of chemistry and energy generating complex systems like RNA or DNA. Ifs and ands, what-ifs and maybes.

By all means though please start a thread on life by deterministic processes if you like.

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I might be wrong, but inventing a model that is molded to fit some limited number of observations (so one can claim it enjoys evidence) and also is molded to infer an infinite universe is not the same as finding observations that are directly consistent with and fit having infinite mass in this universe. I describe these kinds of models as metaphysics masquerading as science. It is a form of confirmation bias to my way of thinking.

This only shows your ignorance about models of the universe. If you had read my earlier post #4 in this thread, you would know by now that it is the same model that is used to predict a finite universe, that predicts an infinite universe as well. The only difference is a variable in the very same equation -- and if you had followed the link, you would see that it is you who is choosing to disregard data to choose the finite universe. The current best estimate is a flat universe, which is infinite.

And on top of that, there are other, independent, models of the universe that could result in the universe being infinite in other ways. These increase the chance of the universe being infinite still further.

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Your link relies on a very precise and altogether different definition of "chaotic system" then what you described as "chaos". No sorry there is no objective evidence to suggest that order arises from disorder (what you called chaos). Entropy laws require that order requires equal or higher ordered sources. To claim otherwise is to thumb your nose at thermodynamics.

What thermodynamics requires for order to increase is simply an outside source of energy. We have one of those.

Yes and how it happened is the question at hand. This thread is intended to investigate chance alone.
Ok I get it, the point of this thread is to examine the likelihood of life occurring spontaneously as if natural chemical processes as they actually and conclusively occur weren't in play. Got it. So we're discussing a hypothetical alternate universe with different laws of physics. I understand. Erm... why?
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This only shows your ignorance about models of the universe. If you had read my earlier post #4 in this thread, you would know by now that it is the same model that is used to predict a finite universe, that predicts an infinite universe as well. The only difference is a variable in the very same equation -- and if you had followed the link, you would see that it is you who is choosing to disregard data to choose the finite universe. The current best estimate is a flat universe, which is infinite.

I read it, and I understood the claims. A flat universe is theoretically eternal (not the same as infinite) into the future, but it is not infinite in the past and is not infinite with respect to mass. Only the models that provide for infinite mass at the time of the event we are considering can influence outcomes. Please reread my posts where I made both of those distinctions.

And on top of that, there are other, independent, models of the universe that could result in the universe being infinite in other ways. These increase the chance of the universe being infinite still further.

The ability to invent independent models alone does not improve probability of past events.

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Why's that? If there's a million isolated independent sites where an event can occur, and the probability of that event occurring is fixed, there are now a million independent chances for that event to occur. The interaction of the sites isn't important.

So how would this effect the probability of an outcome?

If I gave 1 person a six sided die, and then told him to roll a six his odds of rolling a six is 1/6. If I then gave 1 billion people a six sided dice a told each to roll a six, the outcome for each person is still 1/6. That probability does not change just because more people are now rolling the dice or because more attempts are being made. The chances for each person is still exactly the same for rolling a six with a six sided die, as it is for one person... Whether it be many or be few... 1/6

Edited by Emilio Primo
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What thermodynamics requires for order to increase is simply an outside source of energy. We have one of those.

Thermal entropy indeed requires and outside source of thermal order (energy), molecular entropy requires an outside source of molecular order (coherent ordered systems), and information entropy requires an outside source of information. There is no indication that thermal energy is able to generate molecular or informational order.

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So how would this effect the probability of an outcome?

If I gave 1 person a six sided die, and then told him to roll a six his odds of rolling a six is 1/6. If I then gave 1 billion people a six sided dice a told each to roll a six, the outcome for each person is still 1/6. That probability does not change just because more people are now rolling the dice or because more attempts are being made. The chances for each person is still exactly the same for rolling a six with a six sided die, as it is for one person... Whether it be many or be few... 1/6

Right, but the chance of any person in that billion rolling a six is rather higher, since there are one billion independent dice rolls.

Likewise, in a large universe with many different possible sites for life, the chance for life occurring is higher than if there were only one possible site.

We are talking about chances of life evolving at all, and that requires consideration of all locations as a group.

Thermal entropy indeed requires and outside source of thermal order (energy), molecular entropy requires an outside source of molecular order (coherent ordered systems), and information entropy requires an outside source of information. There is no indication that thermal energy is able to generate molecular or informational order.

Wait, which laws of thermodynamics are you referring to?

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Right, but the chance of any person in that billion rolling a six is rather higher, since there are one billion independent dice rolls.

Likewise, in a large universe with many different possible sites for life, the chance for life occurring is higher than if there were only one possible site.

We are talking about chances of life evolving at all, and that requires consideration of all locations as a group.

Even still, this does nothing to effect the probability, the probability remains constant ALWAYS no matter how much time has past and no matter how many individual tries there are or chances you attempt. Then we are also talking pretty astronomical odds here. So if you take into account the OP, the chances are 1/10^41,000(So that is 1 chance in 10^41,000) (10^41,000 = 1 followed by 41 thousand zeros)

So each INDIVIDUAL chance has these odds. The fact that there may be billions of other attempts being made for life has no effect on these probabilities, it stays constant. So they are EACH faced with 1/10^41,000 odds...

Edited by Emilio Primo
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So how would this effect the probability of an outcome?

If I gave 1 person a six sided die, and then told him to roll a six his odds of rolling a six is 1/6. If I then gave 1 billion people a six sided dice a told each to roll a six, the outcome for each person is still 1/6. That probability does not change just because more people are now rolling the dice or because more attempts are being made. The chances for each person is still exactly the same for rolling a six with a six sided die, as it is for one person... Whether it be many or be few... 1/6

Right. Although mathematics allows us to construct combinatorial probabilities of independent events and although the results of the constructs of these model the combinations, the results of the these constructs are still artificial. So there is no analog in reality to suggest that non-interacting resources do influence the ability of improbable events to actually happen. As a point of fact, it is not clear that any real random events have outcomes with probabilities lower than what would be expected by applying just the resources directly acting on the event. This observation is consistent with what one can conclude from the laws of entropy.

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Even still, this does nothing to effect the probability, the probability remains constant ALWAYS no matter how much time has past and no matter how many individual tries there are or chances you attempt. Then we are also talking pretty astronomical odds here. So if you take into account the OP, the chances are 1/10^41,000(So that is 1 chance in 10^41,000. That is 1 followed by 41 thousand zeros)

So each INDIVIDUAL chance has these odds. The fact that there may be billions of other attempts being made for life has no effect on these probabilities, it stays constant. So they EACH faced with 1/10^41,000 odds...

Well, you need context for your odds. Are those odds saying that there is a [imath]\frac{1}{10^{41000}}[/imath] chance of life occurring ever, or do they refer to per planet, or per year, or per planet per year?

For example, suppose I calculated the odds per planet per year. The more planets there are, and the more years they exist for, the more likely it is that life will eventually arise.

So we have to examine just what our odds are saying.

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Even still, this does nothing to effect the probability, the probability remains constant ALWAYS no matter how much time has past and no matter how many individual tries there are or chances you attempt. Then we are also talking pretty astronomical odds here. So if you take into account the OP, the chances are 1/10^41,000(So that is 1 chance in 10^41,000) (10^41,000 = 1 followed by 41 thousand zeros)

So each INDIVIDUAL chance has these odds. The fact that there may be billions of other attempts being made for life has no effect on these probabilities, it stays constant. So they EACH faced with 1/10^41,000 odds...

You really misunderstanding probability here. I would suggest you take a look at this article it explains gives a good example to help you understand this. It also gives a good argument for why live would still be formed by chance.

So, if on our prebiotic earth we have a billion peptides growing simultaneously, that reduces the time taken to generate our replicator significantly.

Okay, you are looking at that number again, 1 chance in 4.29 x 1040, that's a big number, and although a billion starting molecules is a lot of molecules, could we ever get enough molecules to randomly assemble our first replicator in under half a billion years?

Yes, one kilogram of the amino acid arginine has 2.85 x 1024 molecules in it (that's well over a billion billion); a tonne of arginine has 2.85 x 1027 molecules. If you took a semi-trailer load of each amino acid and dumped it into a medium size lake, you would have enough molecules to generate our particular replicator in a few tens of years, given that you can make 55 amino acid long proteins in 1 to 2 weeks [14,16].

So how does this shape up with the prebiotic Earth? On the early Earth it is likely that the ocean had a volume of 1 x 1024 litres. Given an amino acid concentration of 1 x 10-6 M (a moderately dilute soup, see Chyba and Sagan 1992 [23]), then there are roughly 1 x 1050 potential starting chains, so that a fair number of efficent peptide ligases (about 1 x 1031) could be produced in a under a year, let alone a million years. The synthesis of primitive self-replicators could happen relatively rapidly, even given a probability of 1 chance in 4.29 x 1040 (and remember, our replicator could be synthesized on the very first trial).

Assume that it takes a week to generate a sequence [14,16]. Then the Ghadiri ligase could be generated in one week, and any cytochrome C sequence could be generated in a bit over a million years (along with about half of all possible 101 peptide sequences, a large proportion of which will be functional proteins of some sort).

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