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Creation
- Thread starter Wedjat
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Naraoia
Apprentice Biologist
You can start by understanding what spontaneous generation is.
Then perhaps continue by explaining how the heck we got from the RNA world to "natural proteins"*, and what any of this has to do with the original point I made.
(Which I'll repeat in case you forgot: the truth of evolution doesn't depend on the manner of life's origin.)
*What does that even mean? Every protein that living cells make is natural, and not racemic. There's your proof. Perhaps you meant non-biogenic? (In which case, can you explain where abiogenesis requires such proteins? The RNA world scenario certainly doesn't. In the RNA world scenario, IIRC small peptides play a role in the origin of ribosomes, but proteins proper are only ever made by living things.)
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Zaius137
Real science and faith are compatible.
Put together all the essential DNA components in the proper concentrations and orientations and refresh them continuously. Provide wet and dry cycles and seed the mixture with tiny RNA and Protein segments catalyzed by enzymes. Provide a elemental sugar for fuel and expose the mixture to all wavelengths of light and polarizing radiation. Incubate it and cool it at regular intervals any way you like. Simulate great stretches of time by varying all the necessary parameters.
AND….. !no life will come fourth! Why? Because the science specifies the probability of life well below the universal bound. Simply (probability of life<< universal bound).
AND….. !no life will come fourth! Why? Because the science specifies the probability of life well below the universal bound. Simply (probability of life<< universal bound).
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Naraoia
Apprentice Biologist
Lies, Damned Lies, Statistics, and Probability of Abiogenesis Calculations
In any case, how do you propose we simulate great stretches of time*? What are "all the necessary parameters"? Should we put test tubes of RNA in time warps or what? This whole idea has the smell of cluelessness all about it...
By the way, even without "simulating great stretches of time", some clever folks have managed to come up with a generalist RNA polymerase made of RNA using in vitro evolution and a bit of engineering. Can you give me a reason why millions of years of natural experimentation on a planetary scale shouldn't be able to trump the efforts of a few labs over a few measly years?
You also might want to check out the Szostak lab's work on protocells. Here is cdk007's neat rendition.
*And space, for that matter. The earth is, from the point of view of ancient organic molecules, "vastly, hugely, mind-bogglingly big". It's certainly much bigger than the sum total of all test tubes in all laboratories engaged in abiogenesis research over the whole history of the field.
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Zaius137
Real science and faith are compatible.
Summary:
1. How close are scientists to creating life in the laboratory?
Scientists have not even begun to scratch the surface of the origin of life problem. It appears to be intractable.
2. Best estimates of the probability that life arose spontaneously on the earth.
All calculations for the spontaneous origin of life give essentially zero chance, even in 10^9yrs.
3. Understand the problems
no such thing as a "simple" form of life
monomers cannot be synthesized under prebiotic conditions
origin of chemical chirality
origin of genetic information
proteins/DNA/RNA - irreducible complexity
4. Other naturalistic theories to explain life on earth?
Crick, Hoyle - panspermia or life seeded from outer space
(would brilliant scientists propose this if there was any hope at all for spontaneous generation?)
entirely different chemistry that evolved into the chemistry of life that exists today?
5. SETI / life on Mars?
naturalism - earth cannot be unique in the universe, therefore life must exist elsewhere
Origin of Life
1. How close are scientists to creating life in the laboratory?
Scientists have not even begun to scratch the surface of the origin of life problem. It appears to be intractable.
2. Best estimates of the probability that life arose spontaneously on the earth.
All calculations for the spontaneous origin of life give essentially zero chance, even in 10^9yrs.
3. Understand the problems
no such thing as a "simple" form of life
monomers cannot be synthesized under prebiotic conditions
origin of chemical chirality
origin of genetic information
proteins/DNA/RNA - irreducible complexity
4. Other naturalistic theories to explain life on earth?
Crick, Hoyle - panspermia or life seeded from outer space
(would brilliant scientists propose this if there was any hope at all for spontaneous generation?)
entirely different chemistry that evolved into the chemistry of life that exists today?
5. SETI / life on Mars?
naturalism - earth cannot be unique in the universe, therefore life must exist elsewhere
Origin of Life
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Naraoia
Apprentice Biologist
What, in your eyes, would constitute "scratching the surface on the origin of life problem"?
Clearly, somehow creating growing, replicating lipid bubbles that can take up spontaneously self-replicating nucleic acids doesn't... Alternatively, you don't know what the "problem" actually entails.
I highly advise you to read the TalkOrigins article. Right now, it doesn't sound like you have.
Also, please show your maths. Big numbers out of thin air ain't gonna impress me.
You would do well to...
Um... wut?
Monomers of what? Amino acids can. RNA bases can, IIRC. Adenine definitely, I think cytosine is a bit of a problem. Sugars can, though I seem to recall ribose is not the easiest to get. (But then, there are several possible alternatives to RNA as the first genetic material)
Far as I know, this is the biggest actual problem in your list. Unsurprisingly, we are not completely in the dark about possible solutions...
Define "genetic information".
Irreducible complexity is an empty buzzword, and this is sheer waffle.
Irreducible complexity evolves. It is expected to evolve. It has been expected to evolve for nearly 100 years. Again, TalkOrigins has a nice rundown with citations.
To save you the trouble of actually reading it, I'll quote the gist of it - how IC evolves in the general sense.
Douglas Theobald said:
There.
As for proteins, DNA and RNA?
This question plainly shows that you are not familiar with abiogenesis theories at all. Because the way out of that conundrum was suggested several decades ago.
You do know that every single protein molecule in your body is still synthesised by a ribozyme right?
(Do speak up if you don't know what ribozymes are... at this point I wouldn't be surprised)
Stop confusing spontaneous generation with abiogenesis. After correcting your wording: the answer is yes. Brilliant scientists are allowed to have nutsy ideas, you know.
Such as?
What on earth is wrong with that as a hypothesis? And what bearing does that have on abiogenesis?
Holy ribosome, so none of the above "points" are even your own. I love how that page is still stuck in the mid-20th century with Miller-Urey. I love how they never bothered to update their information on RNA replication with, I don't know, this neat pair of indefinitely cross-replicating ribozymes, or this even neater one that can copy an arbitrary template up to 95 nucleotides long. (And I'm sure that number will increase further in the near future. It went from 14 to 95 in a decade...)
I know molecular biology progresses at a truly breakneck pace, but perhaps such significant advances should have made it into any critical article on abiogenesis, huh?
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Zaius137
Real science and faith are compatible.
The clay has recently shown the tendency to spontaneously self assemble into Green Gumbys
Children in the San Francisco area have reported instances of creatures springing fourth from green Play-Doh containers; the creatures exhibit a tendency to break windows and steal cigarettes. Checking for evidence and finding strange unexplained phenomena, Police contacted Evolutionary scientists. Top scientists in the field were able to identify the first evidence of Spontaneous Biogenesis. Professor Dawkins dubbed the new creature Evil Green Gumby or (EGG). He further stated that evolution guarantees the existence of an evil Blue Gumby and evil Yellow Gumby. Some biological scientists remain skeptical of his assertions. They argue that Play-Doh shows no tendency to auto assemble into life. Dawkins argues in light of extraordinary new scientific evidence; (EGG) must be accepted and expected on evolutionary face value.
Dr. Zveegee, et. Al.; http://en.wikipedia.org/wiki/Gumby
Children in the San Francisco area have reported instances of creatures springing fourth from green Play-Doh containers; the creatures exhibit a tendency to break windows and steal cigarettes. Checking for evidence and finding strange unexplained phenomena, Police contacted Evolutionary scientists. Top scientists in the field were able to identify the first evidence of Spontaneous Biogenesis. Professor Dawkins dubbed the new creature Evil Green Gumby or (EGG). He further stated that evolution guarantees the existence of an evil Blue Gumby and evil Yellow Gumby. Some biological scientists remain skeptical of his assertions. They argue that Play-Doh shows no tendency to auto assemble into life. Dawkins argues in light of extraordinary new scientific evidence; (EGG) must be accepted and expected on evolutionary face value.
Dr. Zveegee, et. Al.; http://en.wikipedia.org/wiki/Gumby
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Zaius137
Real science and faith are compatible.
RMKQLEEKVYELLSKVACLEYEVARLKKVGE
“The probability of generating this is successive random trials is (1/20)^32 or 1 chance in 4.29x10^40. This is much ,much more probable than the 1 in 2.04x10^390 of the standard creationist” generating carboxypeptidase by chance” scenario, but still seems absurdly low.”
Let’s make it lower Ian…
Ian is not correct with the 4.29x10^40 nonsense.
His figure of 1/20^32 seems a bit optimistic since he is assuming only 20 amino acids to start with, actually there is more than 500 known natural amino acids. So the first correction that needs to be made is 1/500^32. The author still does not include the odds of forming the correct configuration of those amino acids (I will not include those either); the odds would be greatly decreased if you consider it. So the real calculation of the author must approach (1/500)^32=4.3^-87.
Does Ian really want to trivialize statistics?
Fair coin toss:
Now the probability of 4 heads in a row is is (1/2)4or 1 chance in 16: do we have to do 16 trials to get 4 heads (HHHH)? No, in successive experiments I got 11, 10, 6, 16, 1, 5, and 3 trials before HHHH turned up.
Probability predicts that over a field of possible outcomes there is a desirable outcome. Ian’s example seems simple enough, but here is some perspective on outcomes and universal bounds. Let’s, use one white marble and 15 black marbles (same odds as Ian’s). What are the odds of picking that one white marble out of a bag of 16 marbles and just one being white? Of course 1/16 right? That does not mean you can not pick the white marble the first time but only it is not the most likely outcome. Simply stated that out of 16 trials you are likely to pick the white marble (on average) once every 16 tries. Now let’s see the odds of picking the white marble 16 times in a row. That is (.0625)^16 or 1/5.42x10^-20 (very small). Now let’s look at really small possibilities, say picking a white marble out of a bag with 10^80 marbles, one being white. According to Borel that event would never happen, why? I will not go into his justification for Borel’s upper limit but I will try and put some perspective on it. In the observed universe it is estimated there are only 10^80 atoms. Say you could mark one atom ant throw it into the vastness of space. Now if you could pick from anywhere in the universe what are the odds of picking that marble the first time? 1 in 10^80th right. OK say you could pick one atom every second for several billion years longer than the age of the universe. How many atoms are left? Well about 10^80. In other words you did not discard enough atoms to affect the overall amount. So the last single choice would be for a volume of about 10^80th atoms or 1 chance in ten to the 80th. Sound reasonable? Well by Borel’s upper limit states that choice would not produce that single marked atom (no chance at all). I would have to agree with that conclusion. Where would you pick from? Maybe a hydrogen atom in the Crab Nebula?
You see Ian’s simplistic example does not consider a universal probability bound Borel’s or Dembski’s.
http://www.talkorigins.org/faqs/abioprob/abioprob.html
http://en.wikipedia.org/wiki/Universal_probability_bound
“The probability of generating this is successive random trials is (1/20)^32 or 1 chance in 4.29x10^40. This is much ,much more probable than the 1 in 2.04x10^390 of the standard creationist” generating carboxypeptidase by chance” scenario, but still seems absurdly low.”
Let’s make it lower Ian…
Ian is not correct with the 4.29x10^40 nonsense.
His figure of 1/20^32 seems a bit optimistic since he is assuming only 20 amino acids to start with, actually there is more than 500 known natural amino acids. So the first correction that needs to be made is 1/500^32. The author still does not include the odds of forming the correct configuration of those amino acids (I will not include those either); the odds would be greatly decreased if you consider it. So the real calculation of the author must approach (1/500)^32=4.3^-87.
Does Ian really want to trivialize statistics?
Fair coin toss:
Now the probability of 4 heads in a row is is (1/2)4or 1 chance in 16: do we have to do 16 trials to get 4 heads (HHHH)? No, in successive experiments I got 11, 10, 6, 16, 1, 5, and 3 trials before HHHH turned up.
Probability predicts that over a field of possible outcomes there is a desirable outcome. Ian’s example seems simple enough, but here is some perspective on outcomes and universal bounds. Let’s, use one white marble and 15 black marbles (same odds as Ian’s). What are the odds of picking that one white marble out of a bag of 16 marbles and just one being white? Of course 1/16 right? That does not mean you can not pick the white marble the first time but only it is not the most likely outcome. Simply stated that out of 16 trials you are likely to pick the white marble (on average) once every 16 tries. Now let’s see the odds of picking the white marble 16 times in a row. That is (.0625)^16 or 1/5.42x10^-20 (very small). Now let’s look at really small possibilities, say picking a white marble out of a bag with 10^80 marbles, one being white. According to Borel that event would never happen, why? I will not go into his justification for Borel’s upper limit but I will try and put some perspective on it. In the observed universe it is estimated there are only 10^80 atoms. Say you could mark one atom ant throw it into the vastness of space. Now if you could pick from anywhere in the universe what are the odds of picking that marble the first time? 1 in 10^80th right. OK say you could pick one atom every second for several billion years longer than the age of the universe. How many atoms are left? Well about 10^80. In other words you did not discard enough atoms to affect the overall amount. So the last single choice would be for a volume of about 10^80th atoms or 1 chance in ten to the 80th. Sound reasonable? Well by Borel’s upper limit states that choice would not produce that single marked atom (no chance at all). I would have to agree with that conclusion. Where would you pick from? Maybe a hydrogen atom in the Crab Nebula?
You see Ian’s simplistic example does not consider a universal probability bound Borel’s or Dembski’s.
http://www.talkorigins.org/faqs/abioprob/abioprob.html
http://en.wikipedia.org/wiki/Universal_probability_bound
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Naraoia
Apprentice Biologist
That IS the odds of the correct configuration.
1/a is the probability that a given position will hold the "correct" amino acid out of a choice of a amino acids. Since the identity of each amino acid is (assumed to be) independent of the previous one, the probability of getting a particular string of n amino acids is just (1/a)[sup]n[/sup].
It's worth noting that this is just one peptide, which "Ian" - is calling him by his first name a "clever" attempt at disrespect? - picked because it happens to be self-replicating. Nowhere is it written in stone that there is only one such peptide, let alone organic molecule. In fact, he cites several other examples of self-replicating molecules in that very article.
Since we have no real grasp on how common self-replicating peptides, RNAs or other molecules are, we cannot put a number on the probability of self-replicators appearing - but given that there's definitely more than 1 of them, it's certainly going to be higher than the probability of the Ghadiri peptide appearing.
Still rather greater than whatever times ten to the power of 390, and well within Dembski's nonsensical universal probability bound.*
Also, how many of the hundreds of naturally occurring amino acids can form stable polypeptides? I gather some of them just break the chain if they get incorporated. Furthermore, how many of the "naturally occurring" amino acids are "naturally occurring" in the sense of "synthesised by organisms", versus "would have been there on prebiotic Earth"? If you really want to get technical, perhaps the number 500 also needs some adjustment...
I don't know, but you certainly seem to trivialise him...
What is the relevance of this wall of text?
I know what the relevance of Ian Musgrave's example was, and it flew straight over your head. (Hint: the whole point was that this:
doesn't mean as much as people think it does. In fact, in the majority of his trials, he got four heads in less than half the expected number of trials.you said:
You see, he doesn't consider it because it's utterly irrelevant. You, on the other hand, didn't seem to consider this:
TalkOrigins said:
and the following paragraphs. (Feel free to point out the errors. Even feel free to redo the calculations with your "adjusted" probability.)
And, of course, you completely ignored the fact that there's many more than one possible self-replicator even in the size range of "relatively small". Oh, and quite possibly many more than one habitable planet...
***
*Why nonsensical? Well, according to the Wikipedia article, it's derived from the number of "events" that could have happened over the lifetime of the universe.
So if a certain event actually has a 10[sup]-150[/sup] chance of occurring, wouldn't that mean its chance of having occurred in the lifetime of the universe approaches 1??? Anything with that chance or higher has almost certainly occurred since the universe began. Out of Dembski and myself, one of us really doesn't get probability...
Now, that is a huge oversimplification, since not all events have an equal chance of occurring over the whole lifetime of the universe. Peptides, for example, can only start forming once heavy elements have dispersed into space and assembled into amino acids.
And that tells you why the magic number is completely meaningless - you're not looking at the probability of anything relevant, you're just lumping all possible subatomic level "events" under one big umbrella. You are not accounting for the way many of these events are not independent and certainly not equiprobable. For example, once hydrogen and oxygen form in a universe like ours, their probability of reacting to form water might be damn close to one. (For that matter, hydrogen and oxygen don't really form by chance, except in the sense that quantum mechanics is inherently probabilistic. But given the amount of material in the universe and the laws of physics, these elements NOT appearing is the event with the vanishingly small probability.)
(By the way, Dembski got the Planck time wrong...)
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Zaius137
Real science and faith are compatible.
What planet do you live on?
“That IS the odds of the correct configuration.
1/a is the probability that a given position will hold the "correct" amino acid out of a choice of a amino acids. Since the identity of each amino acid is (assumed to be) independent of the previous one, the probability of getting a particular string of n amino acids is just (1/a)n.”
You keep proving you know nothing about probability. If you had the given amino 32 acids combined the probability of the order would be 32 ! = 2.63130837 × 10^35. My calculation for Ian’s mess is correct and concedes all possible allowances.
Do you really think that it is reasonable to assume that a collection of these 20 particular proteins are just floating around in a primordial soup?
“Originally Posted by TalkOrigins
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].
and the following paragraphs. (Feel free to point out the errors. Even feel free to redo the calculations with your "adjusted" probability.)
And, of course, you completely ignored the fact that there's many more than one possible self-replicator even in the size range of "relatively small". Oh, and quite possibly many more than one habitable planet...”
That is one of the most fanciful, ridiculous postulations I have ever heard of. The only proteins formed would be racemic junk and stuck in a hopeless equilibrium from mass action.
Evolution knows nothing of natural chemistry…
“That IS the odds of the correct configuration.
1/a is the probability that a given position will hold the "correct" amino acid out of a choice of a amino acids. Since the identity of each amino acid is (assumed to be) independent of the previous one, the probability of getting a particular string of n amino acids is just (1/a)n.”
You keep proving you know nothing about probability. If you had the given amino 32 acids combined the probability of the order would be 32 ! = 2.63130837 × 10^35. My calculation for Ian’s mess is correct and concedes all possible allowances.
Do you really think that it is reasonable to assume that a collection of these 20 particular proteins are just floating around in a primordial soup?
“Originally Posted by TalkOrigins
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].
and the following paragraphs. (Feel free to point out the errors. Even feel free to redo the calculations with your "adjusted" probability.)
And, of course, you completely ignored the fact that there's many more than one possible self-replicator even in the size range of "relatively small". Oh, and quite possibly many more than one habitable planet...”
That is one of the most fanciful, ridiculous postulations I have ever heard of. The only proteins formed would be racemic junk and stuck in a hopeless equilibrium from mass action.
Evolution knows nothing of natural chemistry…
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Naraoia
Apprentice Biologist
Last time I checked, it was earth...
Excuse me, but where the hell did you get that number?
Look. I can't make it any simpler than that.
Assume you are building a 32-AA peptide amino acid by amino acid.
First, you pick a random amino acid to start from. You have 1/a chance, where a is the number of different amino acids, to pick any particular amino acid. That means you have a 1/a chance of picking the one you wanted.*
Second, you pick the second amino acid. Again, chances of getting the correct one are 1/a.
And so on for the rest of the 32. That multiplies up to (1/a)[sup]32[/sup]
This method considers the peptide position by position. Order is taken into account. Your use of that factorial would only make sense if we counted combinations to begin with, and we didn't.
*Simplifications apply, of course - this assumes that all AAs are present at equal concentrations, which likely wouldn't have been the case in the primordial ocean. E.g. being smaller and simpler, glycine is much easier to synthesise than, say, tryptophan.
A significant subset of them probably would. But that's not really the question, isn't it? The Ghadiri peptide was taken as a concrete example to illustrate a principle (i.e. that the creationist probability calculations are calculating the wrong thing), and it just happens to be a replicator. But there is nothing to say that you need all 20 amino acids to get a replicating peptide, and in fact, peptides are probably irrelevant to the origin of self-replication anyway. (Try doing the numbers for the hexanucleotide replicator mentioned in the same article.)
"That" being...?
It probably "knows" more than you do... I for one have no idea what you mean by "stuck in hopeless equilibrium from mass action". Maybe I didn't study enough chemistry, after all, I quit it after high school. Please explain?
Also, note that this FAQ was never meant to deal with the homochirality problem. If you want to debate homochirality, here's the stuff to criticise.
(And no, "that's nonsense, I don't think that works" is not a valid criticism.)
But honestly, if you are worried about D-amino acids, multiply the number of choices by 2, not accounting for amino acids (read: glycine) that don't have enantiomers. Here: (1/40)[sup]32[/sup] = 5.42*10[sup]-52[/sup] and (1/1000)[sup]32[/sup] = 10[sup]-96[/sup]. That is still nowhere near Dembski's magic number, let alone the 10[sup]-390[/sup] or whatever nonsense creationists came up with. Besides, it's still just the extremely oversimplified probability of obtaining ONE PARTICULAR self-replicating peptide in a SINGLE TRIAL given equal amino acid concentrations and equal propensities to form peptide chains.
"Earth did lots of parallel trials" was the second biggest point of the whole article after "you're calculating the wrong thing".
(Speaking of, you never answered my questions about how many of the "naturally occurring" amino acids are (1) synthesised by abiotic means, (2) capable of forming stable peptides.)
And again, bear in mind that Musgrave's probability calculations are for a peptide. Self-replication probably didn't start with peptides, or if it did, no evidence of that stage survives that I know of.
Let's see how your probability calculations change when you're working with nucleotides rather than amino acids. You are dealing with (1) fewer possibilities and (2) molecules that are potentially capable of Watson-Crick or non-canonical base pairing, which is a straightforward mechanism for self-replication.
I think Jack Szostak's team had self-replicating oligonucleotides that weren't specially engineered for that purpose, but I'd have to go back to their papers to know for sure. They certainly published something on replicating oligonucleotides in their lovely protocell system. Also, that cute little palindromic hexanucleotide the FAQ mentions? If you're going to tell me 4[sup]6[/sup] is unbelievably high odds, a lolcat is all I can give you...
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Zaius137
Real science and faith are compatible.
Sorry I have a quick correction…
I will cover all your reply latter.
First of all about the universal bound. Supposed I asked you to pick a number between 1 and 5. There is an almost an infinite amount of numbers between 1 and 5, say I picked 2.00009 or 4.1287. A bound on the numbers must exist to make the choice meaningful, say to actually define a probability of 1 in 5, you would place a restriction of whole numbers. The very same thing must be done with a limit that restricts probability that can actually happen within our know universe and time. Face it; if you cannot accept the universal bound just throw out probability all together. Because some probability just has no chance of ever coming up (that is just fact).
Here is my new probability for Ian….
RMKQLEEKVYELLSKVACLEYEVARLKKVGE
Probability for order: (31!)/ (5!) (5!) (6!) (4!) (2!) (2!) = 8.2x10^33/1x10^8= 8.2x10^24
Probability of formation: 500 natural amino acids and both a dextrorotation and levorotation configuration gives (1000)^31 or 1 in 1.0x 10^93. This event will never happen given Borel’s upper limit.
10^93 is approximately 100,000,000,000,000x greater than the total number of estimated atoms in the universe.
I will cover all your reply latter.
First of all about the universal bound. Supposed I asked you to pick a number between 1 and 5. There is an almost an infinite amount of numbers between 1 and 5, say I picked 2.00009 or 4.1287. A bound on the numbers must exist to make the choice meaningful, say to actually define a probability of 1 in 5, you would place a restriction of whole numbers. The very same thing must be done with a limit that restricts probability that can actually happen within our know universe and time. Face it; if you cannot accept the universal bound just throw out probability all together. Because some probability just has no chance of ever coming up (that is just fact).
Here is my new probability for Ian….
RMKQLEEKVYELLSKVACLEYEVARLKKVGE
Probability for order: (31!)/ (5!) (5!) (6!) (4!) (2!) (2!) = 8.2x10^33/1x10^8= 8.2x10^24
Probability of formation: 500 natural amino acids and both a dextrorotation and levorotation configuration gives (1000)^31 or 1 in 1.0x 10^93. This event will never happen given Borel’s upper limit.
10^93 is approximately 100,000,000,000,000x greater than the total number of estimated atoms in the universe.
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Naraoia
Apprentice Biologist
There is exactly an infinite (uncountably infinite, to be precise) number of numbers between 1 and 5. And what you're doing by limiting the choice to whole numbers is making the probability of picking any one number using an unbiased method finite, not making the choice meaningful. It also fails to relate to the concept of a universal probability bound in any way I can see. Are you saying that the universe has an infinite number of choices unless we arbitrarily limit the possibilities we consider? Because that's what your analogy says...
No, that is diametrically opposite to the whole concept of chance (i.e. you can never be certain about it). More to the point:
Let's pick whole numbers between 1 and 5, then. If I have n opportunities to pick, what's my chance of picking 5 somewhere along the line?
Since the chance of not picking 5 in any one trial is 1-(1/5) = 4/5, my chance of not picking 5 in n trials is (4/5)[sup]n[/sup]. The chance of picking 5 at least once out of n trials is therefore 1-((4/5)[sup]n[/sup]). If I'm given 5 attempts, same as the number of possibilities, that comes to about 2/3 (not close to 1 as I'd guessed). If I have to pick one number out of 10 rather than 5, and have 10 attempts to pick, my probability of bagging the right number decreases slightly, to about 65%. However, as I increase the number of choices, the probability seems to converge to somewhere around 63%. Unfortunately, I have no calculators capable of handling stupidly small numbers, so I couldn't actually get anywhere near 10[sup]80[/sup] choices.
Now, maths was a long time ago, so if anyone can confirm or refute that this probability converges rather than going to zero with an ever decreasing slope, I would be immensely grateful. Thus far, it seems that a 1 in [universal bound] event would have a very reasonable chance of occurring in this universe, if the universal bound represents the number of events that could have occurred.
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