Probability Question
Let H = "indisputable contact with advanced aliens will happen in ten years".
Let E = "there has been no indisputable contact with advanced aliens so far"
Let's assume we're agnostic about H, and assign it a .5 value.
Pr(H) = .5
Pr(E/H) is where I'm having trouble. Given indisputable contact with advanced aliens will happen in ten years is E really surprising? If the given alien contact happens through, say, gravitational waves, wouldn't it be unsurprising that there has been no contact so far? After all we've only been detecting gravitational waves for a very short amount of time. There are other hypotheses that also explain why aliens would contact us in the next ten years, but remain silent for all the years we've been searching.
I'm also having similar problems with Pr(E). Since we know so little about aliens and the odds of abiogenesis, I can't justify anything for Pr(E) other than .5.
Let E = "there has been no indisputable contact with advanced aliens so far"
Let's assume we're agnostic about H, and assign it a .5 value.
Pr(H) = .5
Pr(E/H) is where I'm having trouble. Given indisputable contact with advanced aliens will happen in ten years is E really surprising? If the given alien contact happens through, say, gravitational waves, wouldn't it be unsurprising that there has been no contact so far? After all we've only been detecting gravitational waves for a very short amount of time. There are other hypotheses that also explain why aliens would contact us in the next ten years, but remain silent for all the years we've been searching.
I'm also having similar problems with Pr(E). Since we know so little about aliens and the odds of abiogenesis, I can't justify anything for Pr(E) other than .5.
Comments (62)
[math]P(H/E) = \frac{P(E/H) \times P(H)}{P(E)}[/math]
Do we know anything about aliens?
They're illegal, I think.
P=1
(ask Gov. Abbott)
That's one of the fundamental problems with probability. How to assign values to probabilities. It's easy for simple stuff like coin tosses and dice throws, but the real world is a different story altogether.
[quote=Morpheus]Welcome to the real world, Neo.[/quote]
Yes. One thing. That we don't know anything about them.
We immediately jump into the conclusion that they must be human-like, except more intelligent, less sexy, and peace-loving or else warmongers, but never in-between.
Whereas aliens have reached our planet, in the form of protein formation, maybe not exactly viruses, but simple proteins such as amino acids. Travelling on meteorites and other space debris that fall to earth on Earth. I don't know if this is still just theory or it's proven.
So what we know about aliens that reached the Earth is that they are simple organic compounds.
Watch the tabloids next week. "GOD ON WEBSITE SPAKE: ALIENS THAT REACHED THE EARTH ARE REAL AND THE PENTAGON KNOWS ABOUT IT."
I think you are running ahead too fast. Before we think about conditional probability we need to think about probability. For the kind of calculation you have in mind, probability is one number on top of another to make a proportion. The number on the top is (let's suppose) the number of times that aliens are seen in the next ten years. That number can be 1 to begin with, for example, because that's the least that we're interested in; later, we would be interested in whether aliens are seen more than once. Now how about the denominator on the bottom? We want to know whether we see aliens exactly once out of ..... what? Well, I suppose, out of all the times we don't see aliens plus all the times we do - that makes all the times we see or we don't see aliens. OK, how do we count that number of times? Take today, for example. How many times have I seen aliens? That's easy: it's zero. Now how many times have I not seen aliens? The question doesn't seem to make sense. But until we can make sense of that denominator and so hypothesise a proportion, then we cannot even talk about probability, let alone conditional probability.
The problem is that you are not talking about probability in a mathematical sense at all. You are talking about plausibility. That is, do we think it's credible that we might see aliens, given that we've never seen them before? Well, that depends partly upon whether there are aliens.
H = Aliens will contact us in the next 10 years
E = Aliens have never contacted us in the past
[math]P(E/H) = \frac{P(H \land E)}{P(H)}[/math] (i)
Consider.
1. Do aliens have favorites?
If they don't, E and H are dependent on each other. They might not want to visit a place they've already been to. P(E/H) decreases.
If they do, E and H are still dependent on each other. May be they like the place and want to see it again even if what they liked about earth is long gone. P(E/H) increases.
---
Refreshing me memory ...
[math]P(H/E) = \frac{P(H \land E)}{P(E)}[/math] (ii)
From (i) and (ii)
[math]P(E/H) \times P(H) = P(H/E) \times P(E)[/math]
[math]P(E/H) = \frac{P(H/E) \times P(E)}{P(H)}[/math]
The odds of abiogenesis occurring are 1. Because here we are talking about it lol.
As for the odds of abiogenesis occurring multiple times? A little bit trickier. We could assume our planet and its conditions are an extremely rare phenomenon.
However, sun's are extremely common. In the trillions. 400 billion alone in our own galaxy. Solar systems are almost just as common if not as. Let's say 100 trillion for arguments sake.
Then if we take earth to be in a goldilocks zone that's not too close not too far. And that is around 1-1.5 astronomical units, the entire solar system being around 40 Au thats about 3% of the span of a basic solar system give or take thats ripe for life "as we know it".
So out of trillions we can cut it down by a factor of 97% which is 3 trillion.
2 of the four solid planets in our system have magnetic fields. If that runs true in general that's 50% and if they have magnetic fields they're likely to have both liquid water and an atmosphere.
That's 1.5 trillion planets.
Other variables need to be considered but as you can see, even with Conservative estimates the basic conditions for life appear to be pretty common given the massive quantities involved.
If life is a natural progression of the laws of physics and some probabilities of them interacting in the right way. Then abiogensis is almost a certainty.
If life was created by a creator. Which seems to have an obsession with just earth out of all of the universe, then multiple life sustaining planets is unlikely.
Mathematical probabilities are calculated. Empirical probabilities can at times be theoretically estimated based on looking at the actual world. Probabilities of fictional events are meaningless.
One issue with empirical theoretical estimates is that they require biased philosophical presuppositions prior to any personal experience or possible futuristic scientific observations. Another is that cosmological speculations require cosmological presuppositions, not fictional ones.
To my estimate, even if there ever was any extraterrestrial intelligence, their signals will never cross our timelines, therefore whether there are or ever were aliens out there we remain thankfully alone and free forever.
Yep, some presuppositions are made.
We've reached an absurdity.
[math]P(E/H) = \frac{P(E) \times P(H/E)}{P(H)}[/math]
Each one of these probabilities (use the variable p) can be such that
1. p = 50% (agnostic)
2. p < 50% (unlikely)
3. p > 50% (likely)
Note that [math]0\% \leq p \leq 100\%[/math]
There are 3 values to consider [p is P(E) or P(H/E) or P(H)] to calculate P(E/H) and so there should be [math]3^3 = 27[/math] possibilities to calculate. Lemme calculate two of these possibilities (vide infra)
1. P(E) = 50%; P(H/E) = 50%; P(H) = 50%
[math]P(E/H) = \frac{50\% \times 50\%}{50\%} = 50\%[/math] i.e. we have to be agnostic about it.
2. P(E) = 50%; P(H/E) < 50% (let's say it's 40%); P(H) = 50%
[math]P(E/H) = \frac{50\% \times 40\%}{50\%} = 40\%[/math] i.e. its unlikely.
So on and so forth ...
For different time frames e.g. in the next 10,000 years, in the next microsecond, etc. we can scale up/down the probability we assign to P(H) = aliens will contact us in the next 10 years. For example the suppose P(H) = 20%. Then the probability that aliens will contact us in the next 5 years will be 10% [5 years is half of 10 years; I'm assuming that the probability of contact increases with time].
N. B. Scaling up can sometimes lead to percentage probabilities > 100%. These should all be made = 100%.
For example, given that the probability of contact within the next 10 years is 70%, what is the probability of contact in the next 100 years? 70% × 10 = 700%. Probabilities can't be > 100%. You'll have to go with 100%.
Quoting RogueAI
I don't get this. There is a 100% chance that we've had indisputable contact with aliens. For each item of evidence, it is disputed.
Quoting Agent Smith
You're assumption is twofold: (1) there are aliens and (2) the probability of contact with them increases with time.
Once you've assumed #1, you've got your proof of aliens, with or without contact.
Consider these 2 questions:
1. What is the likelihood we'll send a man to Mars in 10 years?
2. What is the likelihood we'll find bigfoot in 10 years?
#1 is something we can compute because it doesn't assume an unsupportable fact. There are men, spacecraft, and Mars.
#2 is asking the chances that something occur for something that may not even exist.
You can't assume this! In order to assume it, you would have to know that aliens, in fact, exist, and will contact us at some point in the future.
:chin: Then we have to factor that into our calculations:
What is the probability that aliens have contacted us in the past given that aliens exist & Aliens will contact us in the next 10 years?
This turns the whole conversation into probababble. :roll:
Why?
E = aliens exist
V = aliens will visit us in the next 10 years
C = aliens have visited earth
[math]P(C/(E \land V)) = \frac{P(E \land ~ V) \land P(C)}{P(E \land V)}[/math]
Because the hypotheses are nonsense. You're just playing with math equations.
But if it pleases you to do so by all means continue.
Hypotheses -> Conclusion
The old CS adage, garbage in = garbage out.
G'nite :smile:
There's nothing wrong with the hypotheses. RogueAI is asking an interesting question. What are the chances that aliens have visited us given they will in the next 10 years. Basically, if we make contact, is it the first time for planet earth or is it not? Preliminary examination of the question shows that the two (contact in the next x years and past contact) are dependent events (check my posts where I explain why).
@Hanover then kindly pointed out I'm making an unfounded assumption assumptiom (aliens exist). I then tried to include that into the formula and you (resident mathematician) declare me analysis "probabble" :snicker:
What is the probability of this happening to a guy like me? :lol:
Because a probability (in maths) is a proportion and a proportion has a numerator and denominator. In the case of the OP the denominator is not defined. https://thephilosophyforum.com/discussion/comment/766026
No defined denominator -> no measure of probability.
No measure of probability -> no conditional probability.
Quoting Agent Smith
50% means, for example, 1 out of 2 or 500 out of 1,000. '1' and '500' would perhaps refer to the number of times an alien is spotted. What does '2' refer to? Impossible to say. You are trying to fit a non-mathematical concept of probability into mathematical terms.
About the only one of your probabilities I could attempt is P(E), which as an above poster said is 100%. Every potential contact with aliens so far has been disputed, so the probability that there has been no undisputed contact with aliens so far is 100%.
If by agnostic your mean p=0.5 (as you said in your OP), I would disagree that it is reasonable to think that there is a 50 percent chance that we will have alien contact in the next 10 years.
Then again I have no idea what would be reasonable - anything would be a stab in the dark for me.
Well, what about ten thousand years?
I'm afraid I don't know!
True!
But I'm not sure that corresponds to a p=0.5, as you suggested in the OP.
I don't think the following two mean the same thing:
1) "I don't know the probability of that happening"
2) "The probability of that happening is 50%"
Now I can suggest the hiding denominator. We're thinking about probability, not (yet) conditional probability.
What are the chances of you catching a cold some time in the next two years? Pretty high. What are the chances of you catching a cold today or in the next week? Still something, but much lower. That's the intuition we have and it's largely correct.
It works like this.
Suppose the chance of catching a cold today is one in one thousand, as calculated from the known incidence of common cold (made up for this example). Then the chance of not catching a cold today is 999/1000, that is, a tiny bit less than 1. Now, the chance of you not catching a cold today and also not catching one tomorrow is 999/1000 x 999/1000. Each day that passes, the total is multiplied by 1-less-a-tiny-bit. So the probability of not catching cold goes down gradually, You can work out how long it would take for the chances of getting a cold at some time as 1/2 or 50%. It works out to be a little less than two years, meaning that in a two year period you've got about an evens chance of getting a cold. There are some assumptions, for example, it is assumed that being cold-free for a while does not in itself alter your chances of getting a cold.
Now, the whole calculation depends upon a reasonably good estimate of the incidence of the common cold and on independence of events. How does that translate to observation of aliens? Not great. If we go by past experience then the number of days on which aliens have been observed is zero. That's the numerator. The number of days we choose as our denominator can be as big or as small as we like. The resulting proportion will still be zero. The estimated probability of not seeing an alien is therefore 1. So, assuming that our past observations are a good measure of the probability of seeing an alien, then we would predict that the chances of not seeing an alien in the next ten years is 1 x 1 x 1 x 1.... for 3,650 times, which still equals one. In common language: no-one's ever seen an alien and we've no reason to think they ever will.
That is as far as mathematical probability will get us, when we measure it as a number of outcomes (days when aliens are seen) divided by a number of events (total days, whether aliens seen or not).
But that doesn't give an answer to the OP. There are other concepts of probability. For example, there was no written European record of black swans before 1700. So what was the probability of someone recording a sighting of a black swan? By the argument above, the probability was zero. But clearly the probability was not zero. Someone saw a black swan and made a written record of it and now there are many such records. Black swans existed, Europeans travelled, saw them, wrote down their experience. We are no longer discussing mathematical probability. We are discussing the plausibility of a set of events such that some hitherto non-existent outcome will come to exist.
There may be a place for conditional probability in this question. But so far we have only progressed to a measure of mathematical probability which yields the answer zero. If we want to invoke conditional probability then we need (at least) to begin with some measure that is between zero and one and is not zero and is not one. And by 'measure' I mean a proportion with a numerator and denominator that are both countable items.
You might just mean that you'd be willing to lay a bet against Trump winning, without being able to say why you'd be willing to do that.
But you might have studied his form, like a bookie. He's only run one race, so you need other data. E.g. you could look at his weight and health records, how similar horses from the same stable of similar levels of fitness have fared in the past, which jockey is going to ride Trump in the race etc etc. You'd have to take account of the risk that he would be nobbled by the Chinese or given illegal performance enhancing drugs by the Russians. Aliens visiting is a similar question. We have no observational data. But we can look at (for example) how many similar planets to Earth there are in the galaxies we know about. We can quantify our assumptions. Then, and only then, can we begin to think about mathematical probability, let alone conditional probability.
Now translate all that you said into [math]\frac{A}{B}[/math] where
A = the # of outcomes that satisfy the desired event.
B = the total # of possible outcomes.
True. If you want to quantify probability then you need to compare one thing with another. One way to quantify a comparison is to express it as a proportion. So you can quantify the probability that we'll see aliens in the next ten years just as you can quantify the probability that you'll catch a cold in the next two years. The difference is that in one case you have some data to start with. In the other you have just speculation. The answer you get out will depend entirely on the assumptions you put in.
Let's say that there's a 50% chance that aliens will be observed on some day in the next ten years. You can work backwards from the calculation I gave above and work out the probability that, on any given day, aliens will be observed. That calculation is fine. But you will have made the whole thing up. The 50%, the ten years, and therefore the daily probability will be entirely speculative. It might be 50% in ten years or in fifty or a hundred.
It's like this with the aliens:
The probability that on a given day we'll see aliens is p. 0 < p < q.
The entirely made-up probability that we'll see them in the next ten years is 50%. It could be 30% in fifty years or 90% in five hundred. We are just guessing. But let's stick with 50% in ten years. It's nothing to do with equilibrium and agnosticism, because the choice of the number of years, ten, twenty or a hundred, will affect the calculation and we can be as agnostic about five hundred years as about five years.
There are roughly 3,650 days in ten years.
Now, the probability that we won't see aliens is 1 - p.
So the probability that we won't see aliens on any day in ten years is (1 - p) ^ 3,650.
Now, we've decided arbitrarily that (1 - p) ^ 3,650 is 50%, that is, it's as likely that we'll see aliens as not in ten years.
What is the probability that we'll see aliens on at least one day? Answer: about 0.00019.
Note: that figure, 0.00019, is entirely the result of an arbitrary choice about how long we must wait for us to have even chances of seeing or not seeing aliens. It has nothing to do with the likelihood of seeing aliens. It has proceeded entirely from our speculation.
We have no data. And we can make up data. But we cannot then say anything about the probability of any event.
So, yes, mathematical probability can be assigned to any supposed event. But in the absence of data, we are just assigning whatever value we want. It's fantasy and fiction and not to be confused with truth in any way whatsoever.
We need to know the probability of intelligent life evolving in an Earth-like environment. We've got a way of estimating this. We've counted (let's suppose) the Earth-like planets - the denominator. We also have a numerator: it's one, Earth. Let's suppose it's 1 in 10^10 (I have no idea about the number of Earth-like planets). But the probability might be higher. There might be life on other planets. So our estimate could be too low. Then let's make it a higher estimate. Let's say the probability is actually 100 in 10^10. Now we are ready to do some maths. If the probability of an event is 100 in 10^10, then what are the chances that in fact we see exactly 1 event out of 10^10? That is, how likely is it that we are alone and that Earth is unique? Now, this sounds hopeful. But it's not hopeful at all. We can do the maths. But we already assumed a hundred-fold increase in the probability over what we observe. All we have done is to take our speculation and dress it up with arithmetic: "Look, in all those similar planets, there must be intelligent life in hundreds more, not just ours!"
So then we drill down further. We look at chemical reactions necessary for the creation of life and assign probabilities to these. And so on. At each stage we are working with one data point - Earth - and speculating what would happen in similar circumstances. We might do slightly better than pure speculation if we can set up comparisons (on Earth) of chemical reactions that go towards creating life. But at each stage of comparing Earth with other planets we will get out the assumptions we put in.
The whole project suffers from lack of data. The maths is fine but it relies on assumptions that are crucial to the result. It's circular. It's a waste of time in terms of estimating the probability of seeing aliens. But it's useful in terms of understanding how to calculate probabilities.
I get what you mean. We'll have to assign values to crucial probabilities arbitrarily. So if we had data we could derive more accurate probabilities from them?
What about the famous Drake Equation?
Almost right. If we had data we might be able to estimate probabilities rather than dressing up our speculations in mathematical terms.
The Drake equation is an example of results depending entirely upon assumptions. We are tempted to think it can provide an estimate of probability, but it cannot and it does not claim to do so. It is a description of a method for estimating probability, if we had data about the variables. E.g., we have no ways of estimating these from observation:
f_l = fraction of life-supporting planets that develop life
f_i = fraction of planets with life where life develops intelligence
f_c = fraction of intelligent civilizations that develop communication
[quote=SETI]At the time of the meeting, essentially none of the seven factors in the equation was known excepting the first, the production rate of stars. Nonetheless, the attendees bandied about their best guesses for the other terms, concluding that the freshman rate was on the order of one. In other words, new transmitting societies appear once a year somewhere in the Milky Way. All that remains is to multiply this by the lifetime of such a broadcasting civilization.[/quote] https://www.seti.org/drake-equation-index
This is the process. We make 'best guesses'. We don't know whether a guess is good or not or how to evaluate one guess as better than another. But it's all we've got. We plug the results into the equation. We get a result. Now we have a number. We imagine that this number means something in relation to the question we posed - conveniently forgetting that it is the result of guesses of completely unknown quality. "All that remains" is not to multiply the result by some other number. What remains is the task of finding some data to put into the equation in the first place.
The Drake equation is useful as a statement of (some of) the kind of data we would need to make an estimate.
[quote=SETI]It has been sixty years since the Drake Equation was conceived. Have we nailed down more of the terms than the single one known in 1961? Sadly, no........There are 100 scientists at the SETI Institute, working on nearly 100 research questions. But each of these topics can be related to one of the terms in the Drake Equation.[/quote]
The problem is that we can be bewitched by mathematical models due to the ease with which we can get quantitative answers - forgetting that we do not have reliable data as input. It is a problem generally in science, not just in the search for extraterrestrial life. 'Sensitivity analysis' is useful - changing the assumptions to observe how the results change - but where there are no data at all and we have only assumptions then we do not even have parameters for sensitivity.
One danger of the process is that a single quantitative answer may be seized upon and widely communicated and become a 'factoid', again forgetting that it is only mathematical cosplay for our guesses.
https://www.americanscientist.org/article/misuse-of-models
[quote=American Scientist]With modern computers, it is now possible for a graduate student or a practicing engineer to acquire a very complex computer code, hundreds of thousands of lines long, worked over by several preceding generations of scientists, with a complexity so great that no single individual actually understands either the underlying physical principles or the behavior of the computer codeor the degree to which it actually represents the phenomenon of interest. These codes are accompanied by manuals explaining how to set them up and how to run them, often with a very long list of "default" parameters. Sometimes they represent the coupling of two or more submodels, each of which appears well understood, but whose interaction can lead to completely unexpected behavior (as when a simple pendulum is hung on the end of another simple pendulum). One hundred years in the future, who will be able to reconstruct the assumptions and details of these calculations?[/quote]
:up:
So, I wanna know the probability that aliens exist. What kinda data should I be collecting?
P. S. Are you trying to insinuate that math is witchcraft? :grin: Astrologer = Astronomer = Mathematician (factoid).
As for what data you need to collect - I think Drake led the way on that and the SETI institute page that I quoted from at length seems very sensible to me. It says quite frankly that the results are guesses and that no progress has been made on establishing data to put into the Drake equation. Personally, I think the whole thing is baloney (that's just my prejudice) but SETI's page has refreshing honesty.
How do you explain the fact that someone who understands mathematical probability can win casino games? Is that baloney? There's nothing wrong, prima facie, with the math.
Things that have a low probability can and do happen. It's only things with zero probability that never happen.
No, it's not baloney. People win jackpots. Every week someone wins the lottery jackpot, and also there is a very low probability of any particular person winning it. And it could turn out that aliens will visit next week. Then my 'best guess' of zero probability will turn out - from the accumulation of new data - to have been wrong. That's why I put "it's my prejudice" in brackets. It's my prejudice and in the absence of data it's as good as anyone else's equally uninformed prejudice. And by 'as good as' I mean equally valueless as science, which depends upon data.
Why would you be prejudiced against probability? Don't you wanna fix that or are you happy (with yourself)?
You never actually answered my question on what sort of data I should be collecting to estimate the probabilities in re aliens. You did say data will improve our guess, oui?
I'm quite happy with it as regards extraterrestrial life. Other people are prejudiced in favour of the possibility and would assign a 'best guess' of greater than zero. I'm happy with them doing that. We're both ignorant and both speculating. Neither of us knows anything. Neither of us is crazy. Either of us could turn out to be right or wrong. The speculation would last about a pint and then it's my round I guess. I mean, it's idle talk but not hopelessly vain or damaging idle talk.
I quoted three examples of data we might collect, drawn from Drake's work, and I linked to the SETI site which enlarges upon these and has assigned a hundred scientists to look for said data. SETI's refreshingly honest point is that, despite sixty years of looking for data, we have not found any that will improve upon our initial 'freshman' guesses. I'm doing the heavy lifting here. C'mon.
But the details, mon ami, go into the details. It's hard for me to make sense of someone who, on the one hand, claims probabilities in re aliens are nothing more than wild guesses, and on the other hand, also asserts relevant data could help and then doesn't show how his story all hangs together.
Let me give you a nice place to start:
[math]P(A) = \frac{A}{B}[/math]. You already seem to know what A and B are. P(A) = probability aliens exist.
You seem to on the right track mon ami as far as me tiny cerebrum can tell, but there's more (I think).
:yawn:
[math]N = R_* \cdot f_p \cdot n_e \cdot f_l \cdot f_i \cdot f_c \cdot L [/math]
N = number of civilizations in our galaxy we could come into contact with
R[sub]*[/sub] = rate of star formation = 3/year (in our galaxy)
f[sub]p[/sub] = fraction of stars that have planets = 25% (unlikely)
n[sub]e[/sub] = the average number of planets per star that can support life = 1 (from our own solar system)
f[sub]l[/sub] = fraction of planets that could support life and have evolved life = 25% (unlikely)
f[sub]i[/sub] = fraction of planets with life that develop intelligent life = 25% (unlikely)
f[sub]c[/sub] = fraction of planets that have intelligent life and develop civilizations that emit detectable signals = 25% (unlikely)
L = the length of time for which civilizations emit detectable signals = 99 years (earth estimate, radio broadcasting began in 1923)
N (for our galaxy) = [math]3 \cdot 25\% \cdot 1 \cdot 25\% \times 25\% \times 25\% \times 99 \approx 1[/math]
We should have found ET. We're not trying hard enough!
What do you know of subjective probability? We use words like "likely", "unlikely" and I've been trying to map those words onto actual numerical values. I intuit the following where P stands for probability.
Certain: P = 100%
Highly likely: [math]100\% > P \geq 75\%[/math]
Likely: [math] 75\% > P > 50\%[/math]
Neither likely nor unlikely (50/50): P = 50%
Unlikely: [math]50\% > P > 25\%[/math]
Highly unlikely; [math]25\% \geq P > 0\%[/math]
Impossible: P = 0%
Are these reasonable numerical values we can assign to these notions?