ecl@hocsj.UUCP (11/09/84)
I have been giving some thought to the process of the first development
of life and this morning I realized that I had been leaving out an
important step. I had been more or less thinking of it as a process
with two major steps. One is the creation of life from amino acids on a
micro-level, the other is the evolution of that life into an intelligent
being. Both are very low probability events and each model must be
repeated mega-many times before intelligent life can come about on a
planet. Because of this, I find it highly unlikely that any two
intelligent races will ever meet in the universe. There may be more
than one intelligent, race but the probability of them being close
enough to find each other is very low, in my estimation. (Not to
mention the low probability that they would recognize each other as
intelligent.) The first step, I am told is not quite as amazing as I
thought because the constituents of life as we know it, the amino acids,
are more common than we may have thought in the past.
That was my thinking up to this morning. Now it strikes me that I have
been glossing over a pretty complex step, one which is likely to have a
lower probability than either of the ones mentioned above. That is the
step of going from something that is merely alive to a self-reproducing
(SR) cell. This, it seems to me, is the biggest step of the three. It
is one thing for the amino acids to form something that in some abstract
sense is alive, it is quite another for this thing to be an SR organism.
I have never looked into the mathematics of SR automata, but my guess is
that it is pretty complex. In the evolution of life on a planet, it is
not sufficient that life come about, but also that it can outlive the
single organism. Even assuming that lightning strikes the right amino
acids and they start squirming, that is a long way from the organism
created actually being SR. Of the three probabilities:
P(life forming)
P(new organism is SR given that it is alive)
P(SR, living organism evolves into an intelligent form of life)
I judge the second to be the lowest. It is hard to judge the first
which seem almost mystical, but I can accept that it is a matter of
amino acids forming and adding electricity as was whimsically described
in the Julia Child Primordial Soup film some of you might have seen.
The tide of opinion in articles (and films) seems to be that it might
not be such a low probability event. I have come to accept that the
third probability is not all that low. Nobody talks much about it that
I have heard, but the second probability it seems to me could well be
the smallest of the three. Any comments?
[Incidentally, anyone wishing to build up brownie points with their
personal deity by claiming credit for Him/Her/It for having done it all,
you can send these comments to me directly by writing them into
/dev/null. I don't rule out the possibility, of course, but it all
comes down to faith and has little place in a scientific discussion.
Usually the arguments come down to say I should read what some person
said in a book rather than going out to nature and looking at the
evidence that the deity, if there is one, created with His/Her/Its own
hand. It is another whole farble, of course, but if someone believes in
a God, then they should believe the fossil record was created by that
God much more directly than any book ever printed.]
(Evelyn C. Leeper for)
Mark R. Leeper
...ihnp4!lznv!mrlprins@cornell.UUCP (Jan Prins) (11/10/84)
Evelyn/Mark Leeper write: > >[The] step of going from something that is merely alive to a self-reproducing >(SR) cell ... seems to me, is the biggest step of the three. It >is one thing for the amino acids to form something that in some abstract >sense is alive, it is quite another for this thing to be an SR organism. > This statement seems turned around to me. I find the creation of complex self- replicating molecules much less problematic than labelling them 'life-like'. Richard Dawkins feels 'survival of the fittest' can apply at a molecular level: If a large supply of 'parts' is available in the organic soup, then a simple self-replicating molecule (one that, in the presence of the right components incorporates them into one or more self-similar structures) will eventually become the most prevalent molecule in the soup. Unless, of course, there are several such molecules, in which case the 'fittest' (i.e. making use of more readily available parts, or having a higher probability of replication succes) will become the more numerous, by definition (the problem with these evolutionary theories is that they're dangerously close to being tautologies!). I take the sequence of events leading to ever-more complex self-replicating structures to be not unplausible. That it should proceed inexorably in the direction of 'intelligence' I find more unlikely and mysterious. "We started small" cornell!prins
ian@loral.UUCP (Ian Kaplan) (11/12/84)
The question raised in the original posting is so complex that it defies
any sort of simple answer, so I will keep my note brief (also this is
going to multiple news groups, and doubtless cluttering up other wise
useful disk space).
o There seems to be a fair amount of controversy regarding the
probability of live arising out of the primevil soup. The best that
can probably be said is that the probability is unknown.
o In the last issue of Scientific American there was an article on
Prions. Prions are infectious particles which seem to reproduce.
They have, as yet, been unable to find any DNA or RNA associated with
Prions. If it is indeed finally shown that Prions do not contain DNA
or RNA, it suggests that a Prion like form might have been the step
between the primeval protiens and a more complex organisum with genetic
memory.
o Intellegence has survival value, so I do not think that it is a valid
assumption that intellegence is rare.
o Intellegent life could have arisen many millions of years ago and
either progressed on to something else or wiped itself out.
o While you are thinking about questions like the origin of life think
of this:
There is a theory that the universe is cyclic. It arose from the
primal monoblock (something like a huge black hole, which contained
the entire universe) and will eventually contract into another primal
monoblock. From there it will explode again, creating yet another
universe. If this creation of new universes goes on without end all
things will happen, since there is an infinity of time. Not only
will all things happen in this infinity, but they will happen an
infinite number of times. This means that even though the
possibility of you existing again is infinitely small, in an infinity
of time it will happen.
I did not want you to run out of philosophical questions to ponder.
Ian Kaplanlab@qubix.UUCP (Q-Bick) (11/12/84)
An excellent book on this is A.E. Wilder Smith's _The Natural Sciences
Know Nothing of Evolution_. He discusses the problem in detail**2. (I.e.
he concentrates on the key points and works them to death.) It can be
understood with an elementary background in biology and chemistry,
although *really appreciating* would require a background in organic
chemistry (more than what I have).
--
The Ice Floe of Larry Bickford
{amd,decwrl,sun,idi,ittvax}!qubix!lab
You can't settle the issue until you've settled how to settle the issue.carter@gatech.UUCP (Carter Bullard) (11/13/84)
Indeed, it is an extremely complex thing. However, the probability of
complex living organisms evolving ( coming into existence ) is actually very
high, say 1, since it has occured, for whatever reason.
--
Carter Bullard
ICS, Georgia Institute of Technology, Atlanta GA 30332
CSNet:Carter @ Gatech ARPA:Carter.Gatech @ CSNet-relay.arpa
uucp:...!{akgua,allegra,amd,ihnp4,hplabs,seismo,ut-ngp}!gatech!carteremigh@ecsvax.UUCP (11/13/84)
<> carter@gatech says: > Indeed, it is an extremely complex thing. However, the probability of > complex living organisms evolving ( coming into existence ) is actually very > high, say 1, since it has occured, for whatever reason. In the same manner, let me toss a coin. As you can see, it is 'heads'. Does this mean that since heads has occurred the probability of obtaining heads is 'actually high, say 1'? An event occurring does not alter the probability that it would have occurred--however it may alter our perception (estimation) of the probability that it will occur. -- Ted H. Emigh Genetics and Statistics, North Carolina State U, Raleigh NC USENET: {akgua decvax duke ihnp4 unc}!mcnc!ecsvax!emigh ARPA: decvax!mcnc!ecsvax!emigh@BERKELEY
wapd@houxj.UUCP (Bill Dietrich) (11/14/84)
Is the mechanism of DNA/RNA reproduction understood well enough that someone could create other molecules with similar reproduction abilities ? Has someone at least determined that similar molecules can be built from other elements ? I assume that actually building such a big molecule from scratch is beyond present-day capabilities. Bill Dietrich houxj!wapd
chuck@dartvax.UUCP (Chuck Simmons) (11/14/84)
<mexican jumping bean --> (-:) > > Indeed, it is an extremely complex thing. However, the probability of > complex living organisms evolving ( coming into existence ) is actually very > high, say 1, since it has occured, for whatever reason. > > Carter Bullard Perhaps, then, we should ask "what percentage of solar systems in the universe (galaxy/within 500 light years of our sun/etc) will develop 'complex living organisms' (whatever *they* are)?" Now and then I hear estimates from people like Carl Sagan and people who enjoy speculating about UFO's suggesting that the galaxy is teeming with intelligent life. I always wonder where these estimates come from. How do experts decide whether or not a star is capable of supporting life? (And not just life but 'interesting life'.) How close to the star does a planet have to be to support life? How far away? Do you need the planet? How likely is it that a planet is in this range? What sort of an atmosphere does the planet need? Is an oversize moon necessary? Unfortunately, I think we will only be able to guess at these answers until we meet our first alien civilization, and I don't see that happening in the forseeable future. By the by... I hear rumours that some secret government agency has actually found pieces of a wrecked spaceship and alien bodies and everything! I don't suppose any of you out there in netland work for this government agency and would like to spill some beans? (:-) dartvax!chuck
lambert@mcvax.UUCP (Lambert Meertens) (11/14/84)
: > Indeed, it is an extremely complex thing. However, the probability of > complex living organisms evolving ( coming into existence ) is actually very > high, say 1, since it has occured, for whatever reason. The probability of a continent coming into existence, shaped exactly like North-America, is very high too, since it HAS occurred, for whatever reason. The probability of such a continent existing elsewhere in the universe (especially if we define the Twin Towers etc. to be part of the shape) is not that high. If life on Earth counts, the probability of living organisms having evolved is 1 and not less. If we try to estimate the probability of life evolving elsewhere, the information that it happened here (once) does not increase that probability one bit. Lambert Meertens ...!{seismo,philabs,decvax}!lambert@mcvax.UUCP CWI (Centre for Mathematics and Computer Science), Amsterdam -- Lambert Meertens ...!{seismo,philabs,decvax}!lambert@mcvax.UUCP CWI (Centre for Mathematics and Computer Science), Amsterdam
friesen@psivax.UUCP (Stanley Friesen) (11/15/84)
<> > I have been giving some thought to the process of the first development > of life and this morning I realized that I had been leaving out an > important step. I had been more or less thinking of it as a process > with two major steps. One is the creation of life from amino acids on a > micro-level, the other is the evolution of that life into an intelligent > being. Both are very low probability events and each model must be > repeated mega-many times before intelligent life can come about on a > planet. The evolution of "intelligent" life has little to do with "probability". The prime controlling factor in evolution is *biological selection* NOT chance, thus if the right combination of ecological circumstances occurs then "intelligent" life WILL evolve. It is a recognized principle of evolutionary science that similar circumstances produce similar organisms. Witness the similarity between the marsupial wolf and the timber wolf, which are only distantly related; or the similarity between the rat kangaroos and kangaroo rats. And it is a principle of ecological science that similar climates produce similar ecologies, often with completely different organisms. Witness the occurance of "chaparral" type scrublands in California, Chile, Southern Europe, and Southern Australia, all with completely unique species of plants. Thus a planet with a similar climatic history to Earth has a HIGH probability of eventually evolving "intelligent" life. > That was my thinking up to this morning. Now it strikes me that I have > been glossing over a pretty complex step, one which is likely to have a > lower probability than either of the ones mentioned above. That is the > step of going from something that is merely alive to a self-reproducing > (SR) cell. This, it seems to me, is the biggest step of the three. It is not a *seperate* step, most biologists consider self-reproduction to be a necessary(but not sufficient) condition for life, thus something that is not SR is not alive, by definition. Thus instead of: > P(life forming) > P(new organism is SR given that it is alive) > P(SR, living organism evolves into an intelligent form of life) we have: P(life forming) P(evolution of "intelligent") life) Of these the first is very high, perhaps even 1.0 given a planet with liquid water and a high carbon content in the atmosphere. That is on the right sort of planet the formation of life may be almost certain, due to the structure of the universe. The second is probably somewhat lower because chance does play a small role in evolution - because there is usually more than one evolutionary solution to any given problem - BUT it is still a fairly large probability. Sarima Noolendur sdcrdcf!psivax!friesen
johnston@spp1.UUCP (11/15/84)
> Indeed, it is an extremely complex thing. However, the probability of > complex living organisms evolving ( coming into existence ) is actually very > high, say 1, since it has occured, for whatever reason. > > -- > Carter Bullard I don't know what to say exactly to this statement. Am I missing some logic link or can you really state the probability of something coming into existence by a certain method soley on the fact it is in existence? I guess I can now advance my pet theory about the grand canyon coming into existence by a prehistoric giant urinating on arizona because, indeed, the grand canyon exists. Mike Johnston
carter@gatech.UUCP (Carter Bullard) (11/16/84)
> <> > carter@gatech says: > > Indeed, it is an extremely complex thing. However, the probability of > > complex living organisms evolving ( coming into existence ) is actually very > > high, say 1, since it has occured, for whatever reason. > and Ted Emigh retorts: > In the same manner, let me toss a coin. As you can see, it is 'heads'. > Does this mean that since heads has occurred the probability of > obtaining heads is 'actually high, say 1'? An event occurring does not > alter the probability that it would have occurred--however it may > alter our perception (estimation) of the probability that it will occur. > What I would like to say is that it is difficult to talk about the probability of a past event having occured. If I toss a coin x number of times, the probability that a specific sequence will occur is a simple concept. But if after obtaining a sequence, I then ask the question, what is the probability that that sequence of coin tosses did just now occur, I believe the only real answer is 1. You are absolutely correct in saying that the calculation of the probability of a future event is not affected by any subsequent occurence of the event( assuming a random process ). But, I believe that statistics provides for a sensation of confidence over events whose determinates are not completely known, a kind of blind but very educated quess. If one utilizes the appropriate approximation of distributions or chooses the appropriate model, then the statistic can give reasonable approximations for the confidence of a specific occurence. But when one looks back in retrospect at an event that has already occured, the temptations that "causality" allow spring to mind and suggest, " if we had only known everything that was involved in the process, then possibly we could have calculated that its occurence was indeed inevitable ." If you would rather suggest that statistics is involved with the analysis of potentiality, instead, then in the specific case of the current disscusion "living organisms and their evolution", I think that you would be hard pressed to suggest that any other possibility for either molecular or cellular organization is available. The biochemical and physiological basis for "living organisms" is so consistent among all, and I mean all, the samplings that are available on this planet that it is very difficult to suggest that we represent one of a set of survivable random configurations. Although the apparent level of complexity in the evolution of "living organisms" is quite high, there is no reason to suspect that on that path there were any other possible routes than the specific one that was taken. And without the demonstrated occurence of other potential states, the discussion of what the probability of any specific stage should be, is quite premature. Let's not reduce the discussion of evolution to the scenario of a coin toss. The popular concept of genetics and evolution is extremely outdated, being similar to the theories of people who had never dreamed of DNA and the biochemical processes involved in self- replication, and their attitudes were that randomness played a great role in the construction and direction of evolutionary development. These ideas I feel give randomness too high of a hand in the game. I would rather think it was much more deterministic than they would have had us believe. -- Carter Bullard ICS, Georgia Institute of Technology, Atlanta GA 30332 CSNet:Carter @ Gatech ARPA:Carter.Gatech @ CSNet-relay.arpa uucp:...!{akgua,allegra,amd,ihnp4,hplabs,seismo,ut-ngp}!gatech!carter
jfw@mit-eddie.UUCP (John Woods) (11/16/84)
A.E.Wilder-Smith -- I watched him and Dr. Jerome Lettvin debate at MIT some time ago. Dr. Philip Morrison was the moderator. Dr. Wilder-Smith made several statements which incoming MIT Freshlings not majoring in biology or chemistry know better than to make, regarding those topics. If his book is more of what I saw in that debate, I would not use the book for wrapping fish with. -- John Woods, Charles River Data Systems decvax!frog!john, mit-eddie!jfw, JFW%mit-ccc@MIT-XX When your puppy goes off in another room, is it because of the explosive charge?
woods@hao.UUCP (Greg "Bucket" Woods) (11/17/84)
I think the concept that everyone is trying to get at here is this:
If an event has a probability of occuring that is greater than zero, and there
are an infinite number of attempts at it, then the probability that it will
eventually occur is indeed 1, no matter how small the probability that it will
happen on a given attempt. The only assumption needed here is that time
goes on forever (and I'm not going to debate that here, I take that as a given).
--Greg
--
{ucbvax!hplabs | allegra!nbires | decvax!stcvax | harpo!seismo | ihnp4!stcvax}
!hao!woods
"...once in a while you can get shown the light
in the strangest of places if you look at it right..."friesen@psivax.UUCP (Stanley Friesen) (11/19/84)
<> After my earlier posting on this subject I recieved a request to explain my reasoning behind concluding that the probability of life evolving on an Earth-like planet was "very" high, given enough time. The following seems to express it very well: > If you would rather suggest that statistics is involved with the analysis > of potentiality, instead, then in the specific case of the current disscusion > living organisms and their evolution, I think that you would be hard pressed > to suggest that any other possibility for either molecular or cellular > organization is available. The biochemical and physiological basis for > "living organisms" is so consistent among all, and I mean all, the samplings > that are available on this planet that it is very difficult to suggest that > we represent one of a set of survivable random configurations. Although > the apparent level of complexity in the evolution of "living organisms" is > quite high, there is no reason to suspect that on that path there were any > other possible routes than the specific one that was taken. And without > the demonstrated occurence of other potential states, the discussion of > what the probability of any specific stage should be, is quite premature. > > .... and their attitudes > were that randomness played a great role in the construction and direction > of evolutionary development. These ideas I feel give randomness too high of > a hand in the game. I would rather think it was much more deterministic > than they would have had us believe. >-- >Carter Bullard >ICS, Georgia Institute of Technology, Atlanta GA 30332 >CSNet:Carter @ Gatech ARPA:Carter.Gatech @ CSNet-relay.arpa >uucp:...!{akgua,allegra,amd,ihnp4,hplabs,seismo,ut-ngp}!gatech!carter However, I would like to add some additonal evidence that the deterministic concept that Mr. Bullard presents is reasonable. First there is the evidence of widespread existance of organic compounds in interstellar space, clearly of no-biological origin. Then there is the great ease with which Dr. Urey and others like him have created *complex* organic systems in the lab from non-biological sources with relatively crude methods. These organic systems include poly-nucleic acids, polypeptides, and closed membrane systems resembling living cells. All this in only about 20 years. This indicates, first that organic compounds *are* present everywhere the conditions are right, and secondly that the chemistry of organic compounds tends towards producing life-like systems under Earth-like conditions. In other words, at least the earliest stages of the origin of life are deterministic and inevetible, and the later stages may be reasonably concluded to be equally deterministic. This is especially true since a crude form of "natural selection" may well apply to proto-biotic systems. Stanley Friesen P.S.: My qualifications in this area include a B.S in Biology with emphasis on Systematics and Evolutionary Theory.
mmt@dciem.UUCP (Martin Taylor) (11/20/84)
==============
Is the mechanism of DNA/RNA reproduction understood well
enough that someone could create other molecules with
similar reproduction abilities ? Has someone at least
determined that similar molecules can be built from other
elements ? I assume that actually building such a big
molecule from scratch is beyond present-day capabilities.
==============
Logically, it isn't necessary that molecules reproduce themselves.
What is required is that in their presence (or presence in the recent
past) the likelihood of finding another such molecule increases.
Surface catalysis might lead to such conditions. Imagine a scenario
involving something rather like a crystal (viruses can form crystals,
so they are not limited to just non-living material). On this surface
molecules of another kind can form by selective adsorption or some
such mechanism. These other molecules can themselves seed new crystals.
Or again, think of the clay-surface catalysis that has been proposed
for construction of complex molecules. If there happened to develop
a molecule whose presence on the surface slightly improved the catalysis
for making more of the same, the result would be sufficient to permit
evolution of better self-replicating systems.
Whatever happened, it's a pretty good bet that catalysis of one kind
or another was involved.
--
Martin Taylor
{allegra,linus,ihnp4,floyd,ubc-vision}!utzoo!dciem!mmt
{uw-beaver,qucis,watmath}!utcsrgv!dciem!mmtdubois@uwmacc.UUCP (Paul DuBois) (11/20/84)
> > I think the concept that everyone is trying to get at here is this: > > If an event has a probability of occuring that is greater than zero, and there > are an infinite number of attempts at it, then the probability that it will > eventually occur is indeed 1, no matter how small the probability that it will > happen on a given attempt. The only assumption needed here is that time > goes on forever (and I'm not going to debate that here, I take that as a given). This argument is an example of the gambler's fallacy: if I lose *this* time, then it's more likely I'll win *next* time. The outcome of event i does not affect the outcome of event j in any way, for independent events. (If the events are not independent, then the above argument doesn't apply anyway.) The event could occur the first time; it might never occur. -- Paul DuBois {allegra,ihnp4,seismo}!uwvax!uwmacc!dubois
jlg@lanl.ARPA (11/21/84)
> > > > I think the concept that everyone is trying to get at here is this: > > > > If an event has a probability of occuring that is greater than zero, and there > > are an infinite number of attempts at it, then the probability that it will > > eventually occur is indeed 1, no matter how small the probability that it will > > happen on a given attempt. The only assumption needed here is that time > > goes on forever (and I'm not going to debate that here, I take that as a given). > > This argument is an example of the gambler's fallacy: if I lose > *this* time, then it's more likely I'll win *next* time. The outcome > of event i does not affect the outcome of event j in any way, for > independent events. (If the events are not independent, then the > above argument doesn't apply anyway.) > > The event could occur the first time; it might never occur. Neither one of these are quite right (neither is really wrong either). If the probability of an event is 'p' per try (0<p<1) then the probability that the event will NOT occur in 'n' tries is: n q = (1-p) The probability that the event will occur in the 'n' tries is '1-q'. The limit of 'q' as 'n' approaches infinity is clearly zero, so in an infinite number of tries, the event has probability 1 of occuring. However, at any given time that you check the experiment for results, an infinite number of tries has not yet occured. Therefore, the probability of success is not quite 1. If the event has not occured at time 't' then future time evaluation must be done as if the counter 'n' were reset to zero at 't' - that's what the independence of trials implies.
ethan@utastro.UUCP (Ethan Vishniac) (11/21/84)
>> I think the concept that everyone is trying to get at here is this: >> >>If an event has a probability of occuring that is greater than zero, and there >>are an infinite number of attempts at it, then the probability that it will >>eventually occur is indeed 1, no matter how small the probability that it will >>happen on a given attempt. The only assumption needed here is that time >>goes on forever (and I'm not going to debate that here, I take that as a given). >This argument is an example of the gambler's fallacy: if I lose >*this* time, then it's more likely I'll win *next* time. The outcome >of event i does not affect the outcome of event j in any way, for >independent events. (If the events are not independent, then the >above argument doesn't apply anyway.) >The event could occur the first time; it might never occur. >-- >Paul DuBois {allegra,ihnp4,seismo}!uwvax!uwmacc!dubois No it is not an example of the gambler's fallacy. The assertion being made is that if one has N cases and the probability of the desired outcome is some small, but finite number, then as N goes to infinity the probability that the desired outcome is obtained *in at least one of the cases* goes to unity. The probability that the desired outcome is obtained in any single case remains small. "I can't help it if my Ethan Vishniac knee jerks" {charm,ut-sally,ut-ngp,noao}!utastro!ethan Department of Astronomy University of Texas Austin, Texas 78712
crs@lanl.ARPA (11/21/84)
> If an event has a probability of occuring that is greater than zero, and there > are an infinite number of attempts at it, then the probability that it will > eventually occur is indeed 1, no matter how small the probability that it will > happen on a given attempt. I'm not sure I'm convinced of this. As I recall from the little probability that I've had, *if* an event has a probability associated with it, that probability is unaffected by the number of attempts that have occurred. The rather mundane example of the coin toss comes to mind. With a fair coin the the probability of tossing heads is 0.5 *with each toss* so that if I have tossed the coin n - 1 times, the probability of tossing heads on the n-th toss is *still* 0.5. It seems to me that this applies to the discussion about the probability of life forming. Perhaps there is a probability expert out there who can elaborate. Charlie Sorsby ...!lanl-a!crs crs@lanl Cc: crs@lanl
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (11/21/84)
The fallacy was in attempting to lump the concepts "has occurred during the past N years" and "has a probability P of occurring in N years" together to decide that P = 1. Probability in its technical sense has properties somewhat different from its everyday usage. The attempt to estimate probabilities for rare events is fraught with difficulty. A recent example is the attampt to determine nuclear reactor safety: How does one estimate the probability of a specific class of failure that has never yet been observed? What are the odds for a reactor having a catastrophic meltdown? What are the odds of a Three-Mile Island class disaster (1 has been observed in N reactor- years; is the correct answer "1/N reactors per year"?)? Sampling theory tells us that the relative error of a mean value computed from N samples is 1/sqrt(N - 1). When N is 0 or 1, what is the expected error of the estimate?
crs@lanl.ARPA (11/21/84)
> The fallacy was in attempting to lump the concepts "has occurred during > the past N years" and "has a probability P of occurring in N years" > together to decide that P = 1. Probability in its technical sense has > properties somewhat different from its everyday usage. > > The attempt to estimate probabilities for rare events is fraught with > difficulty. A recent example is the attampt to determine nuclear > reactor safety: How does one estimate the probability of a specific > class of failure that has never yet been observed? What are the odds > for a reactor having a catastrophic meltdown? What are the odds of > a Three-Mile Island class disaster (1 has been observed in N reactor- > years; is the correct answer "1/N reactors per year"?)? > For some interesting reading in this area try _The_Cult_Of_The_Atom_ by (I believe) Daniel Ford.
ward@hao.UUCP (Mike Ward) (11/24/84)
> I think the concept that everyone is trying to get at here is this: > >If an event has a probability of occuring that is greater than zero, and there >are an infinite number of attempts at it, then the probability that it will >eventually occur is indeed 1, no matter how small the probability that it will >happen on a given attempt. The only assumption needed here is that time >goes on forever (and I'm not going to debate that here, I take that as a given). The relevence of this argument to the question at hand rests with the assumption that time goes on forever. Since there is no evidence that this is so, to make such an assumption is little more than a religious belief. Even if one were to assume that time goes on forever, there is no evidence that an infinite amount of time has already passed, and so the argument as a proof that the probability of life arising by this point in the life of a universe is invalid. -- "The number of arguments is unimportant unless some of them are correct." Michael Ward, NCAR/SCD UUCP: {hplabs,nbires,brl-bmd,seismo,menlo70,stcvax}!hao!ward ARPA: hplabs!hao!sa!ward@Berkeley BELL: 303-497-1252 USPS: POB 3000, Boulder, CO 80307
friesen@psivax.UUCP (Stanley Friesen) (11/26/84)
>> >> I think the concept that everyone is trying to get at here is this: >> >> If an event has a probability of occuring that is greater than zero, and there >> are an infinite number of attempts at it, then the probability that it will >> eventually occur is indeed 1,no matter how small the probability that it will >> happen on a given attempt. The only assumption needed here is that time >> goes on forever (and I'm not going to debate that here, I take that as a >> given). > > This argument is an example of the gambler's fallacy: if I lose > *this* time, then it's more likely I'll win *next* time. The outcome > of event i does not affect the outcome of event j in any way, for > independent events. (If the events are not independent, then the > above argument doesn't apply anyway.) > > The event could occur the first time; it might never occur. > -- > Paul DuBois {allegra,ihnp4,seismo}!uwvax!uwmacc!dubois I am sorry but the original statement *is* correct, it is *not* the gamblers fallacy. The confusion arises because it *sounds* like an increase in probability is being invoked, when it is not. It is true that the outcome of event j doesn't affect the probability of event i, but that has nothing to do with the limit as n approaches infinity of P(at least one success in n trials), which is what the original statement was talking about. The mathematical result is that given any *finite* sequence of trials there is a positive probability of 0 successes, but that probability approaches 0 asymptotically as n approaches infinity. My qualifcations in this area include a Master's Degree in Biostatistics. Stanley Friesen
gino@voder.UUCP (Gino Bloch) (11/27/84)
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