Probability and life by Chance Alone

[cypress]

 

It's generally considered bad etiquette to ignore questions when you're making claims.

 

Agreed, I did look at that question again now. I didn't respond because I considered it answered in the explanation. You pointed out the error I made and I believe I revised my statement. If you want to continue with the discussion let me know.

 

 

As DJBruce points out, this is why limits exist. When we multiply by infinite, we get an undefined result; but when we increase the operand towards infinity, we can see the result also tends to infinity. So as the universe increases in size to infinitely large, the probability of life scales similarly.

 

Fair point. DJBruce, you needn't explain any further. The remaining issues with postulating infinite mass is that it lacks a real analog from uniform experience and it leads to illogical outcomes. I will continue to describe these issues next.

 

You again forget that the same inflationary model that can predict an infinite universe can also predict a finite universe, depending on observations. If you throw out the inflationary model because of issues, you are left with an assortment of finite or infinite models.

 

I have not forgotten. The assortment of infinite models all have issues according to Pemrose. He addresses nearly all of them and you have said nothing about his work. 2005 was when he published his latest summary.

 

And again Mr Skeptic's point about probability still stands. So long as there's a chance of the universe being infinite, his argument works.

 

Perhaps by the math edit: though I'm not convinced that this treatment of limits applies to independent chance events, for now I will stipulate this while I work it over a bit. I may come back to this :end edit

 

but I am not sure it works by reason. I will come back to this.

 

I'm a capable argumentative multitasker.

 

Yes you are.

Edited August 11, 2010 by cypress

[Mr Skeptic]

I'm not following this formula. Help me relate it to the probability equation relevant to the situation described by Mr. skeptic. I did give you a + for the translation.

 

For the formula:

[math] \lim_{n\to\infty} 1-\left(1-10^{-41000}\right)^{n}=1-0=1[/math]

 

Translation:

Suppose you want to find the probability that an event occurs at least once, given it has a probability of p per try to occur and n tries. As stated it is a nasty thing to calculate, but it turns out that it is really easy to calculate how likely it is for n events to occur in a row. The probability that your event does not occur is (1-p), and the probability that it does not occur n times in a row is (1-p)^n. This is the probability that the event did not occur given n tries, so to get the probability that it did occur, you subtract this from 1, for 1 - (1-p)^n. The limit part is formally necessary because infinity is not a number, but taking limits solves this. As it turns out, raising a number who's absolute value is less than 1 to a large power makes the number smaller and smaller, and the limit of this done infinitely many times is zero. The chance that it won't happen at least once is zero, which leaves the probability that it will happen at least once as 1.

 

For this formula:

[math] \lim_{n\to\infty} \left(10^{-41000}\right)\left(n\right)=\infty[/math]

 

Translation:

This formula is sometimes used by the lazy to approximate the value in the above formula, and works OK under certain constraints. So for example if you roll a 6 sided die once it has 1/6 chance of landing on 1 at least once, if you roll twice it is about 2/6 and three times about 3/6. You may be familiar with this formula in this context, and noticed it will give nonsensical results for certain values (such as rolling 7 times, or infinity). The proper thing to do in this case is to use the previous formula, which will give probabilities of 1/6, 11/36, 91/216, and as you can see will never give values above 1. The proper meaning of this formula is to give the expected average number of results, for example if you roll a dice 60 times you expect to get 10 1's.

 

I used both formulas, the first to give you the probability an event with probability of 10^-41,000 happening at least once in an infinite universe (it's 1), the second to give you the approximate number of such events (infinite).

 

As you say, whether the universe is infinite or not is currently speculation. That, however, does not mean that you can discount it because your argument depends on the premise that the universe is finite. So if you say that whether the universe is finite or not is speculation, congratulations, you have said your own argument consists of nothing more than speculation upon speculation. So unless you can prove that the probability of life forming entirely by chance is exactly zero, or that the probability of the universe being infinite is known to be less than 10^-41,000, this disproves your argument.

 

It goes without saying that the probabilities for life by the actually proposed mechanisms are much much higher than via pure chance, but that's not really relevant to my argument (just for the folks who are wondering why we're talking about 10^-41,000 -- it's because for this argument the actual probability isn't really relevant).

[Cap'n Refsmmat]

I have not forgotten. The assortment of infinite models all have issues according to Pemrose. He addresses nearly all of them and you have said nothing about his work. 2005 was when he published his latest summary.

I don't have Penrose's book, but I do have the paper from Annals of the New York Academy of Sciences that you say his work was an "outgrowth" of. Despite your claims to the contrary, it says nothing about infinite universes -- it refers to inflationary cosmology, which can have finite or infinite universes, and explores difficulties in the entire theory. It makes no specific claims about infinite universes that I know of.

 

Are there other peer-reviewed papers that he has published on the subject? Lorenzo and Sorbo (UC Davis physicists) characterize inflationary cosmology as having "survived extensive theoretical and observational scrutiny and has come to be seen as the leading theory of the origin of the universe (see for example [2])" as of 2008, while of course noting there are open questions -- which still may be solved.

 

But we'll see what you think about the chance of the universe being infinite when you get back later, apparently.

[cypress]

I don't have Penrose's book, but I do have the paper from Annals of the New York Academy of Sciences that you say his work was an "outgrowth" of. Despite your claims to the contrary, it says nothing about infinite universes -- it refers to inflationary cosmology, which can have finite or infinite universes, and explores difficulties in the entire theory. It makes no specific claims about infinite universes that I know of.

 

Right that is why I called it an outgrowth as opposed to a restatement.

 

Are there other peer-reviewed papers that he has published on the subject? Lorenzo and Sorbo (UC Davis physicists) characterize inflationary cosmology as having "survived extensive theoretical and observational scrutiny and has come to be seen as the leading theory of the origin of the universe (see for example [2])" as of 2008, while of course noting there are open questions -- which still may be solved.

 

But we'll see what you think about the chance of the universe being infinite when you get back later, apparently.

 

Yes, I have a couple diversions to work through. will be back to the other topics tonight or tomorrow. I don't know of any other articles Pemrose wrote on inflation and infinite universe ideas.

 

Returning to the probability equations I note again that zero probability is potential solution to the probability for life from non -life by chance alone. Since this is the case, it is not a certainty that the probability assuming an infinite universe approaches one. It is also possible that it is zero.

Edited August 12, 2010 by cypress

[DJBruce]

Returning to the probability equations I note again that zero probability is potential solution to the probability for life from non -life by chance alone. Since this is the case, it is not a certainty that the probability assuming an infinite universe approaches one. It is also possible that it is zero.

 

 

No zero probability is not an option if we assume that the number you keep supporting as the probability of life forming is [math] 10^{-41000}[/math].

[D H]

Why are all of you bandying this 10^-41,000 number about as if it is anything but fiction? cypress was asked to provide a reference multiple times; that reference was never given. I'll give a couple; there are plenty more out there.

 

 

"Lies, Damned Lies, Statistics, and Probability of Abiogenesis Calculations," http://www.talkorigins.org/faqs/abioprob/abioprob.html

Every so often, someone comes up with the statement "the formation of any enzyme by chance is nearly impossible, therefore abiogenesis is impossible". Often they cite an impressive looking calculation from the astrophysicist Fred Hoyle, or trot out something called "Borel's Law" to prove that life is statistically impossible. These people, including Fred, have committed one or more of the following errors. ...

 

"Hoyle’s fallacy," http://en.wikipedia.org/wiki/Hoyle%27s_fallacy

Hoyle's Fallacy, sometimes called the junkyard tornado, is a term for Fred Hoyle's flawed statistical analysis applied to evolutionary origins. Hoyle’s fallacy is a surprisingly easy mistake to make when one has not quite grasped how powerful a force natural selection can be. Hoyle's Fallacy predates Hoyle and has been found all the way back to Darwin's time.

[cypress]

DH, the fact that you are able to cite it as Hoyle's fallacy indicate that I did provide Hoyle as one of two references by the way. You simply don't accept his method of estimating life by chance alone and I am OK with that, because I note that nobody has offered a better estimate of the probability before considering resources. Skeptic chose to try to improve the odds by making an appeal to ignorance about what might extend beyond the observable universe. We continue to discuss that approach. It is interesting though that you and everyone else here seems to agree with Hoyle's conclusion.

 

Please answer these two questions:

 

If his method is incorrect then did he stumble into the correct conclusion by luck?

 

What is the correct method and result?

 

DJBruce, the formal estimate is that the combinatorial probability of life by chance alone not considering the resources available to act is less than 10^41000. If you have information that shows there is a probability floor above zero, I would like you to describe it and provide a reference.

[swansont]

Coming to the right conclusion is not a guarantee that you got there via valid means. So yeah, he got there by luck.

[cypress]

Fair enough. The answer to #107 is "no," because you misunderstood Mr Skeptic. Let me quote:

 

 

Mr Skeptic's hypothesis does not mean that if, for example, there is a minute chance that two people on Earth have the same DNA, the size of the universe alters that chance. It means that if an event has a probability of occurring, and the size of the universe alters how many chances that event has, the probability that it will occur at least once in the entire universe is increased when the size of the universe increases.

 

For example, if we are looking at the chance that life will occur by chance alone anywhere in the universe, it increases when the universe (and amount of matter, and number of habitable planets, and so on) increases in size. A large universe gives more opportunities for life to arise; an infinite universe gives infinite opportunities.

 

If we are looking at the chance that life will occur by chance alone at one specific location, the size of the universe is irrelevant. Only the age is.

 

So Skeptic's argument does not apply to the probability of life by chance alone on earth? Do I have that correct?

 

Coming to the right conclusion is not a guarantee that you got there via valid means. So yeah, he got there by luck.

 

 

Please demonstrate the valid mechanism.

[Mr Skeptic]

Skeptic chose to try to improve the odds by making an appeal to ignorance about what might extend beyond the observable universe.

 

Where did I make an appeal to ignorance?

 

So Skeptic's argument does not apply to the probability of life by chance alone on earth? Do I have that correct?

 

I said as much several times, including in the post you quoted to start this thread.

[D H]

It is interesting though that you and everyone else here seems to agree with Hoyle's conclusion.

We must be living in different universes. I see only one person who is agreeing with you, and that person is clueless about probabilities.

Please answer these two questions:

 

If his method is incorrect then did he stumble into the correct conclusion by luck?

Nice one, piling a fallacy on top of a fallacy. Should we call this cypress' fallacy?

 

His answer is wrong, as both of my links (there are several others) show.

 

 

What is the correct method and result?

The correct method is to say until we have more knowledge it is best to not to practice numerical proctology.

 

 

[swansont]

 

Please demonstrate the valid mechanism.

 

What is this, a trick question? The contention that life arose by chance alone is an inherently flawed proposition. Hence there is no valid mechanism for calculating such a probability. Which is why Hoyle's conclusion that life did not arise by random chance is correct, but for the wrong reason.

[cypress]

We must be living in different universes. I see only one person who is agreeing with you, and that person is clueless about probabilities.

 

Hoyle's conclusion is that life on earth did not arise by chance alone. I take it you disagree? I note that swansont, and Skeptic both clarified that they agree with this conclusion. Moontonman and Cap'n did quite a while ago.

 

 

Nice one, piling a fallacy on top of a fallacy. Should we call this cypress' fallacy?

 

His answer is wrong, as both of my links (there are several others) show.

 

Your links take exception to his method but both agree with his conclusion without offering a better method.

 

The correct method is to say until we have more knowledge it is best to not to practice numerical proctology.

 

I'm not sure this is the best practice. I will be looking for you to be consistent on this point going forward since you believe so.

[ydoaPs]

Hoyle's conclusion is that life on earth did not arise by chance alone. I take it you disagree? I note that swansont, and Skeptic both clarified that they agree with this conclusion. Moontonman and Cap'n did quite a while ago.

No, he's saying Hoyle got the answer by accident.

 

No scientist ANYWHERE says that life arose by chance alone. No scientist ANYWHERE says that all of the molecules necessary for life popped into existence all at once in the same place. No scientist ANYWHERE says that the first life was the same as what we have now. There's a reason it's called Hoyle's FALLACY.

[cypress]

What is this, a trick question?

 

No.

 

The contention that life arose by chance alone is an inherently flawed proposition. Hence there is no valid mechanism for calculating such a probability. Which is why Hoyle's conclusion that life did not arise by random chance is correct, but for the wrong reason.

 

It seems perfectly valid to develop a hypothesis (life on earth is a product of chance processes) then a prediction (if by chance alone, biological processes require that a minimal set of functional systems would first have to arise randomly, then these systems would generate the system plans for future life) then one could use reaction kinetics, chemical affinities and knowledge of what it means to be functional to derive a mathematical model that shows how this prediction is false and therefore how the hypothesis is false. Seems straightforward. As far as I know, nobody has provided a better demonstration and yet there must be one otherwise we have no basis for coming to a conclusion on this point. How did you arrive at your conclusion?

 

No, he's saying Hoyle got the answer by accident.

 

I get that, but thanks for the restatement.

 

No scientist ANYWHERE says that life arose by chance alone. No scientist ANYWHERE says that all of the molecules necessary for life popped into existence all at once in the same place. No scientist ANYWHERE says that the first life was the same as what we have now.

 

Hoyle is/was one of these scientists who agree with the others on your points. However, there are some prominent scientists who do still advocate for life by chance alone. I offered one name earlier.

[Cap'n Refsmmat]

Hoyle's conclusion is that life on earth did not arise by chance alone. I take it you disagree? I note that swansont, and Skeptic both clarified that they agree with this conclusion. Moontonman and Cap'n did quite a while ago.

The conclusion D H refers to is the number Hoyle got as a result.

[ydoaPs]

Hoyle is/was one of these scientists who agree with the others on your points. However, there are some prominent scientists who do still advocate for life by chance alone. I offered one name earlier.

If that one you named earlier is the one I think you're talking about, you're either deliberately misrepresenting him, or you're mistaken. The paper mentioned is freely available online and says no such thing.

[cypress]

The conclusion D H refers to is the number Hoyle got as a result.

 

Hmm, that's not what I took from his words. However if that is the case, and it is entirely possible that Hoyle's numbers are wrong. They are after all only estimates. Perhaps D H or you have better estimates. I would be grateful if you would please provide them. It seems silly to claim that someone's estimates are wrong if you are unable to offer better estimates.

[Cap'n Refsmmat]

Hmm, that's not what I took from his words. However if that is the case, and it is entirely possible that Hoyle's numbers are wrong. They are after all only estimates. Perhaps D H or you have better estimates. I would be grateful if you would please provide them. It seems silly to claim that someone's estimates are wrong if you are unable to offer better estimates.

I believe the entire point of the TalkOrigins article is that the mathematics is wrong, because of the numbers and methods of the calculation. e.g. "They calculate the probability of sequential trials, rather than simultaneous trials." "They assume that there is a fixed number of proteins, with fixed sequences for each protein, that are required for life." And so on.

 

I know that the number 32,104,893,252 factorial is not 7. Why do I need to know the correct answer to know that 7 is wrong?

[cypress]

If that one you named earlier is the one I think you're talking about, you're either deliberately misrepresenting him, or you're mistaken. The paper mentioned is freely available online and says no such thing.

 

Here is what Koonin says:

 

I argue that the “many worlds in one” version of the cosmological model of eternal inflation implies that emergence of replication and translation by chance, as opposed to biological evolution, is a realistic possibility. Under this model, any life history that does not violate physical laws is realized an infinite number of time in the infinite universe although the frequencies of different histories are vastly different. Thus, the complex system of coupled translation and replication that is required for the onset of biological evolution would emerge an infinite number of times by pure chance although the probability of its appearance in any given region of the universe is vanishingly small.

 

I believe the entire point of the TalkOrigins article is that the mathematics is wrong, because of the numbers and methods of the calculation. e.g. "They calculate the probability of sequential trials, rather than simultaneous trials." "They assume that there is a fixed number of proteins, with fixed sequences for each protein, that are required for life." And so on.

 

I find these argument vacuous and I responded to each one previously, but I don't think it is useful to go through them again. It would only be a diversion from the primary argument. For example the sequential vs. simultaneous issue is addressed once probabilistic resources are applied.

 

I know that the number 32,104,893,252 factorial is not 7. Why do I need to know the correct answer to know that 7 is wrong?

 

You need to have a basis to understand and demonstrate what it means to be wrong. We know that it is not 7 because we have experience with factorials of numbers, and that for numbers above 2, the solution is greater than the base number. So we have an idea of what it means to have a correct answer for factorials.

 

Are you not able to offer a better estimate? If Hoyle's supposed errors are known, then corrections can be made and a new estimate is possible. Perhaps the problem is that these supposed errors are nothing more than ignorance masquerading as a critique. But really does it even matter? Skeptic, you, swansont, moontonman and I are in agreement that life by chance alone on earth is and always was an unreasonable position. Should we not move on?

[Cap'n Refsmmat]

You need to have a basis to understand and demonstrate what it means to be wrong. We know that it is not 7 because we have experience with factorials of numbers, and that for numbers above 2, the solution is greater than the base number. So we have an idea of what it means to have a correct answer for factorials.

Likewise, we have an idea of what it means to calculate the probability of life occurring by chance. We know many of the factors involved. We just do not know all, nor do we know the exact values associated with each -- numbers of proteins, numbers of required chemicals, abundance of required chemicals, and so on. Hoyle violates much of what we do know.

 

Or, in short: Part of Hoyle's work is demonstrably wrong. The other parts are demonstrably unknown.

 

Are you not able to offer a better estimate? If Hoyle's supposed errors are known, then corrections can be made and a new estimate is possible.

No. If we do not, in fact, know the exact composition of the first self-replicating organism, we cannot calculate the odds of its existence. Likewise if we do not know the environment in which it existed, the means by which it reproduced, or the energy source it required. We also do not know of the other numerous possibilities for life-forms -- whether there are other simple self-replicators that could exist under different conditions.

 

It's quite possible for errors to be known without a correction being possible, and you should stop pretending otherwise. For example, there have been numerous occasions when I attempted a difficult math problem, arrived at an answer, and checked my answer in the original equation to find it was totally wrong. I did not have the knowledge to solve the problem, but I was absolutely certain that a given solution was incorrect. Is this so difficult to understand?

 

Perhaps the problem is that these supposed errors are nothing more than ignorance masquerading as a critique. But really does it even matter? Skeptic, you, swansont, moontonman and I are in agreement that life by chance alone on earth is and always was an unreasonable position. Should we not move on?

Ah, the old "I'm going to drop an insult but pretend it doesn't really matter" trick. Seeing as Hoyle's computation is the basis for this entire conversation, I think it's worthwhile to determine its veracity. Also, attempting to direct a conversation merely makes your adversaries more determined to discuss what you wish to avoid. Also, post #128 is waiting if you want something else to discuss.

[cypress]

It's quite possible for errors to be known without a correction being possible, and you should stop pretending otherwise. For example, there have been numerous occasions when I attempted a difficult math problem, arrived at an answer, and checked my answer in the original equation to find it was totally wrong. I did not have the knowledge to solve the problem, but I was absolutely certain that a given solution was incorrect. Is this so difficult to understand?

 

I understand and disagree. In my line of business, applied science, we don't have the luxury of throwing up our hands and giving up. Reasonable estimates that we know are not exactly correct but give us the correct conclusion are better than no estimates.

 

 

Ah, the old "I'm going to drop an insult but pretend it doesn't really matter" trick. Seeing as Hoyle's computation is the basis for this entire conversation, I think it's worthwhile to determine its veracity. Also, attempting to direct a conversation merely makes your adversaries more determined to discuss what you wish to avoid. Also, post #128 is waiting if you want something else to discuss.

 

I am a literalist. You are misreading me when you try to read into me between the lines.

[Cap'n Refsmmat]

I understand and disagree. In my line of business, applied science, we don't have the luxury of throwing up our hands and giving up. Reasonable estimates that we know are not exactly correct but give us the correct conclusion are better than no estimates.

How do you know if you get the correct conclusion when you have one estimate and no historical data to verify it against?

 

Why are estimates with known flaws "reasonable"? Why are estimates based on laughably incomplete data considered "reasonable"?

 

Who says anyone's giving up? All we're doing is stating that Hoyle's estimate is flawed and there is insufficient information to complete a new estimate. When further information is discovered, a new estimate can be created.

 

Why is giving up a problem? Whether or not we "give up" has no impact on the fallacies in Hoyle's Fallacy. It's still wrong, regardless of attempts to correct it.

[ydoaPs]

I understand and disagree. In my line of business, applied science, we don't have the luxury of throwing up our hands and giving up. Reasonable estimates that we know are not exactly correct but give us the correct conclusion are better than no estimates.

Remind me to never hire you. Going off of wild-assed guesses based on flawed methodology is a TERRIBLE idea.

[cypress]

How do you know if you get the correct conclusion when you have one estimate and no historical data to verify it against?

 

This was similar to a question I asked of swansont. Earlier I provided some new information by Douglas Axe that provided indication that Hoyle's estimates were reasonable. I believe there is more than one estimate and they are in the same range. I would like to hear how one comes to a conclusion without a basis.

 

Why are estimates with known flaws "reasonable"?

 

Because doing nothing is often not an option. If BP did not react to the debacle they created, because they had known flaws in their plans, oil would still be flowing today.

 

Who says anyone's giving up? All we're doing is stating that Hoyle's estimate is flawed and there is insufficient information to complete a new estimate. When further information is discovered, a new estimate can be created.

 

Then you can offer a better estimate given the corrections that have been made in Hoyle's analysis. Please do if you have not given up.

 

Why is giving up a problem? Whether or not we "give up" has no impact on the fallacies in Hoyle's Fallacy. It's still wrong, regardless of attempts to correct it.

 

I explained above why it is not good to give up.

 

I stated from the beginning that Hoyle's number is an estimate. Estimates are generally regarded as being subject to revisions. In other threads you have been quite comfortable with estimates that you know are wrong. Why not this thread? If you know it is wrong, improve on it. If you can't improve on it then it is the best one we have.