Remarkably astute observation. Are you suggesting that increasing the number of planets beyond 50 billion (towards infinity) actually makes it MORE likely that there are no other planets with life? Because that’s sure what this sounds like
No it isn’t. This is a total non-sequitur.
You mean the way you have done multiple times, with statements like"You seem to be arguing that we should ignore the information provided by theories relevant to the origin of life."?
That sort of pejoratively assigning statements to others?
In that case I have no idea why you quoted me, because I have never addressed that issue nor do i have any interest in it.
If you wish to introduce new arguments then by all means do so, but don’t do it after quoting me, as though it has some relevance to what I have posted.
Had you bothered to read the thread, you would know that they have indeed argued that:
The fact that there are ideas at all (most of which do not run on – cosmically speaking – all that implausible assumptions)** is already some indication that things needn’t be all that unlikely** – otherwise, it’d be highly implausible given the short time we’ve been thinking about this stuff that we should’ve come up with anything much at all.
That is a direct quote. The poster is arguing explressely that the fact that ideas exist is an indication that events are more probable. Not that our ability to calculate probabilities alters, but that the actual event is more probable.
So you seriously believe that life is more likely to exist now than in 1986?
No, that is not the point.
The point is whether the existence of multiple ideas indicates that events are more likely. Thatis the only point that I havebeen discussing. Once again, if you wnat to discuss some other point then I thank oyu not to quiteme before doing so.
Utterly incorrect. The argument is that the existence of ideas is indicative that events are more probable. Not that ideas aid in guessing probabilities, but that they actual indicate that probabilities have increased. The claim was that more ideas indicates increased probabilty.
If the argument had been that theories are relevant information to use when guessing a probability, then more ideas could just as easily lead to a decrease in probability.
Or do you perhaps believe that new ideas can never lead to a downward revision of likelihood?
[quote]
A theory as to the origin of life does not make it more likely for life to arise in some absolute sense, but – if the theory is plausible – it gives us some reason to reevaluate our estimate of the probability of life arising.
And why could that revision not be a revision downward? Why is that impossible?
Absolutely not what has been claimed my arse. Please have the courtesy to read the thread before making such claims.
I doesn’t make it more likely. It makes it a certainty. At an infinite sample size the probability of *any *event approaches unity. It doesn’t matter whether the event is life or no life, it become infinitely close to unity. And according to the participants in this thread the distinction between something that never occurs and something that occurs at infinitely low probabilities is effectively non-existent.
Wait – no, I wouldn’t agree with that (although the second sentence is strictly speaking true; if the probability that no other life exists is one then with probability one there will be no life elsewhere in the universe – that’s begging the question). I wonder if we have suffered from a disconnect in our notation. Taking p > 0 to be the probability that life has arisen on a given planet, I argued that as the sample size increases – as we allow the number of planets to grow without bound – the probability that life exists elsewhere in the universe approaches one almost surely. The “infinite” sample will include both an infinite number of planets with life and an infinite number of planets without life.
If instead p refers to the probability that life exists elsewhere in the observable universe, and each observation is a particular realization of the observable universe, then the probability that life exists elsewhere in the observable universe does not change as the sample size increases. As we let the number of sampled universes grow to infinity, we have an infinite number of universes with life-beyond-earth and an infinite number of universes without life-beyond-earth, with respective probability p and 1 - p.
Assuming we’re in the framework of an infinite universe in which the probability that life arises on a given planet is a fixed p > 0, yes.
If the probability that life exists on a given planet is p, then the probability that the first planet we sample supports life is p. If I’m misinterpreting your notation please advise.
See the previous question.
Even if the probability of finding life on a particular planet were zero, it could still be the case that the probability of picking a planet with life is nonzero. This is the nature of infinity. Consider a standard normal random variable inversely weighted by n = 1, 2, … to infinity. The probability of drawing zero is zero for any member of the sequence, but is one in the limit.
So, with 50 billion planets being considered, we would expect 5 billion planets to have life, but if we extend it to an infinite number of planets, we would expect no planets to have life.
[sub]
Pssst… If you have an infinite number of planets, you can have infinite planets with life AND infinite planets without life. [/sub]
And your claim is that if the probability that other life exists is one then with probability one there will be life elsewhere in the universe – that’s not begging the question?
You are not misinterpreting it, you are not in any way addressing the question I asked.
Assume the number of planets within no life is infinite. What is the probability of the first planet we sample supporting life? Don’t worry about the probability that life exists on a given planet. That is the conclusion we are trying to reach, not a given.
So, once again, if the number of planets within no life is infinite, what is the probability of the first planet we sample supporting life?
What is the probability of the second planet we sample supporting life?
And that the probability of the nth planet we sample supporting life?
Which once again was not the question. The question was: do you agree that regardless of how many planets we sample, the chances of finding one that supports life is infinitely small?
Let’s not worry about what might happen if that is true until we resolve *that *it is true.
Do you agree *that *it is true?
Let me get this straight. I devise a theory as to why the egg may break; it survives several rounds of peer review; I subject it to tests and fail to falsify it; the brightest minds agree that my egg breakage theory is highly plausible. Are you arguing that someone who wishes to guess whether or not the egg may break should ignore my theory? Should they claim complete ignorance of whether the egg shall break?
What? That wasn’t pejorative; it genuinely seemed that you were arguing that we shouldn’t use information from theories on the origin of life to reassess our estimate of the probability that life arises. Am I wrong here?
What? No, I believe that our assessment of the likelihood of life should be different today than in 1986. Just like our assessment of the probability that, say, it is possible to build mechanical flying machines might have been adjusted with developments in physics and engineering. This is not the bizarre idiosyncratic ranting of the Time Cube guy.
You quote this statement as an indication of why I’ve misinterpreted others in this thread:
But this supports my contention! He’s arguing that the existence of plausible theories is important information for probability assessment. In other words, if no plausible theories existed at all – despite many bright minds working on the problem – then this is some indication that (our estimate of) the probability should be lower. Please note the phrases he used: “some indication”, “highly implausible”; these indicate that he is speaking subjectively and not contending that devising a theory changes the fabric of reality.
Of course not. But I’m not arguing in favor or against your other interlocutors – I’m merely claiming that they’re not completely retarded madmen, as they would be if your characterizations were true. It is by no means misguided or silly to make use of theories when estimating a probability.
Exactly. And what is the probability of selecting the desired result out of a sample that contains an infinite number of undesirables?
If I have a universe that contains an infinite number of lifeless planets, how many planets do you need to sample before your chances of finding one with life is not infintesimally small? At what sample size does x/infinity not produce a result that approaches infinitely small?
Infinity is not a number, it is a concept. There are more lifeless planets in our universe than planets with life. So if we have an infinite number of each there must also be infinitely more lifeless planets. As a result the chances of any planet supporting life must be infinitely small.
And as we all agree, “x never occurs” and “x only occurs with infinitesimally small probability” are colloquially the same statement.
But that wasn’t my claim; my claim was that, if p > 0 is the probability that life exists on any given planet, then life exists with probability one in a universe with an infinite number of planets however small p might be. See my request for clarification on your notation, which was asked in good faith (and responded to with snark).
And how, pray tell, am I suposed to ignore that? You’re asking me to assume that there are an infinite number of planets without life, but by disallowing any assumptions about the number of planets with life you make your questions unanswerable. If there are only a finite number of planets with life, then the answer to each of your questions is 0 – but that’s begging the question – so we’re no closer to answering the question of how likely it is for life to arise elsewhere.
(What does “infinitely small” mean? For someone who berates others for not understanding probability, you’re clearly comfortable being fast and loose with the relevant terminology.) Again, your question cannot be answered without more information.
The concept doesn’t really work this way. If you have an infinite number of each, they can be in any proportion, 1 life to 10 lifeless or 1 life to 100000 lifeless, or any other proportion. While there may be infinitely more lifeless planets, the likelihood of finding a planet with life stays at exactly p (the probability of life on a planet).
Increasing the number of planets to infinity does not make it harder to find a planet with life, because the number of planets with life increases at the same rate as the number of planets without life.
If there are an infinite number of planets with life and an infinite number of planets without life, then you can’t make any a priori statement about the likelihood of drawing one kind of another without some idea of the proportion. Either you’re misreading Cheesesteak or you have incorrect ideas about asymptotic probability theory.
No, of course not. It is the tests that you have carried out that make it useful in gauging probability. Not the conception, as you originally contended.
Yes, you are wrong. I have said so several times now.
Then you do not dispute my position that the the existence of more ideas doe snot automatically indicates that the probability of an event is increased. And you agree that when various posters said that the existence of more ideas about the origin of life makes the origin of life more likely, that is also incorrect.
As such I fail to see why you quoted me.
No he isn’t and no it does not support ant such contention. He never even uses the words “probability assessment” or anything remotely like that. He says clearly and expressly that he existence of ideas increases the likelihood of the event occurring. Not that it can modify the “probability assessment” either up or down, butthat it always increases the probability.
Simple question. Do you agree with this statement:
The fact that there are multiple ideas indicates that things connected to those ideas are are more likely?
No, they don’t.
My characterisations are true, and what that may make them is not the subject of this thread.
Once again, if you wish to discuss some position that I have never commented on I would thank you not to quote me prior to doing so. It gives myself and others the impression what you post has some bearing on my own posts.
Once again, I ask you to refrain from quoting me prior to making statements on positions that I have never commented on. If you wish to make such posts then by all means do so, and I will cheerfully ignore them. But quoting me prior to doing so gives a deliberately misleading impression that they are relevant to my own posts.
You can say so all you like, but – without support for your contention – I nevertheless believe that my interpretation is correct.
He says that because he is speaking informally. Nowhere has anyone made a statement that the very conception of an idea changes whether an event occurs, which would be utterly bizarre. However: We are all intuitive Bayesians. “I now believe that x is more likely than I believed before” is just what it means to say “the probability of x has increased.”
No. But I do believe that multiple plausible ideas can, all things equal, give some indication of how likely something is.
I am arguing that your contentions are wrong. I quote your contentions to show that they are wrong. It is possible that I misunderstand you, and if so then you have my apologies, but I never quoted with the intention of misrepresenting you.
In fact, as the discussion clearly isn’t being approached with a rational temper by all involved parties, I’m done with this avenue of discussion (the interpretation of other posters vis-a-vis the existence of theories and probabilities). From here on I shall only respond to comments in the other subthread (asymptotic probabilities).
IOW he comes in here, spouts a lot of nonsense, misrepresents me and then slinks away.
Classy. :rolleyes:
I lean toward the we are not alones.
In 1955-6, when I was 12 or 13 years old, I and a friend were walking out my parents front door. We both noticed a vehicle driving very fast about 2 blocks to the right. One of us said, man that guy is hauling ass. It came very fast and quietly down the street. When it got close to where we were, it swooped up in the air and climbed steeply quickly shot off getting smaller and smaller.
I ran to the picture window and neither of my parents were in the living room, so they did not see it. We ran out to the sidewalk and looked around for someone to say," did you see that"? Nobody was on the street. We knew we had to say nothing. Who would have believed a couple kids? So we barely mentioned it again, unless we were alone.
I mentioned this one time on the board. Some guy who was not even born then ,took the time to explain to me I did not see what I thought I did. That I did not understand what it was.
That is why people don’t talk about it.
Going against my own better judgement here, but this provides a very instructive example of how everyday intuition can be very misleading when dealing with concepts decidedly non-everyday, like infinity.
Think about the following two sets: the natural numbers, and the natural numbers divisible by seven. Clearly, for any finite interval, there are more natural numbers than there are numbers divisible by seven. So one might think that, going ‘to infinity’, there ought to be ‘infinitely more’ natural numbers than those divisible by seven; however, one would be wrong. In fact, there are exactly as many numbers divisible by seven as there are natural numbers proper. Why? Because one can pair them one-to-one: n -> 7n, and thus, associate to every natural number a number divisible by seven, and vice versa. But then, this means there must be equally many of each.
This even works if one set actually does contain ‘infinitely more’ members than the other in some sense: between any two distinct natural numbers, there are infinitely many rational ones; yet once again, one can find an isomorphism pairing up each rational number with a natural one. (This isn’t necessary, however: there are actually more real numbers than there are natural ones.)
Similar things happen with probability. Think about a fair coin: in the limit of infinitely many coin throws, both sides will appear equally often. This is a statement of certainty, not a probabilistic one – it is indeed how ‘probability 1/2’ (or any other probability) is defined (eq. 2). It’s true that there are admissible ‘histories’ – i.e. infinite series of throws – in which this is violated, such as ‘heads infinitely often’, but those form what’s called a measure-zero set, whereas the histories where both outcomes appear according to their relative probabilities form a measure-one set. What this means, roughly, is that if you were given a bag full of all possible histories of coin throws, and drew randomly from it, you’d never draw a history in which the relative probabilities are violated, and you’d always draw a history in which both heads and tails appear equally often. And I do mean ‘never’ and ‘always’: there is no number of draws such that you are expected to have drawn a probability-violating history at least once; you could draw for however long you liked, and that would never happen.
The reason why that isn’t contradictory is simply the failure of intuition at infinity: just as it is possible for there to be ‘more’ natural numbers than numbers divisible by seven for any finite amount of numbers, while as infinite sets, both are of equal cardinality, it’s possible that while for every finite amount of options, every option occurs at least some of the time, for an infinite amount of options, some never do (‘never’ here having the precise meaning that for any amount of trials, the expected number of times that option manifests remains at zero).
Thus, for any given possibility with finite probability, it is indeed the case that in infinitely many trials, it manifests infinitely often – and the relative frequency of its occurrence is exactly equal to its probability. So if the probability of life occurring is one in ten to the googol, then every ten to the googolth planet will have life in an infinite universe.
Great take on the subject. Few people think about the time synch factor.
There’s something delightfully meta about that particular response coming twenty-eight months after the post to which it’s responding.
If I may add something that came to me a while ago…
I think that one “missing consideration” in the Drake equation might be that it’s extremely rare to have a planet with both esposed landmass and liquid ocean like ours; e.g., most planets end up being almost barren or “waterworlds” since it doesn’t take much more to cover a sphere completely if water (or some liquid) is present on the sphere at all.
The “waterworld” poses a problem for radio wave receipt or emission since it’s such a great attenuator for signals - so much so that hypothetical Dolphin Aliens may not even discover their existence. As well as developing physical extraplanetary exploration that requires concentrated energy sources like fire.
Whereas the barren “desert world” may not be able to sponsor enough reaction sites for the beginning of life to come about so it ends up being millenia of lot of dust howling in the wind.
Certainly this can be addressed by knocking a healthy few orders of magnitude off the “suitable for intelligent life” factor and we still have millions of civilizations in principle, but it’s well possible that “life that’ll contact us is rare” is actually “life that’ll contact us is actually unbelievable mind-numbing rare like-winning-Powerball-every-day-of-your-life-rare.”