To try to put it succintly, it's reasonable to be agnostic about alien contact ten years from now, but not ten minutes from now. — RogueAI

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.

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. — PhilosophyRunner

Well, what about ten thousand years?

I'm afraid I don't know!

Well, then you're agnostic!

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%"

I think it does, but I'm curious what other people think. I'm getting out a little beyond my skis!

To try to put it succintly, it's reasonable to be agnostic about alien contact ten years from now, but not ten minutes from now. But I can't see what's driving that intuition. — RogueAI

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.

There's a subjective component to probability. If I say there's a 20% chance of Trump winning the next elections what exactly do I mean?

If I say there's a 20% chance of Trump winning the next elections what exactly do I mean? — Agent Smith

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 $\frac{A}{B}$ where

A = the # of outcomes that satisfy the desired event.
B = the total # of possible outcomes.

@Agent Smith I could have a go. But I'm not interested in aliens. I'm only vaguely interested in Trump's form at the bookies. I'm interested in distinguishing sensible from non-sensible talk about probability and I've done some reasonably heavy lifting on that question.

Where there's uncertainty (we've been discussing that all along), there's (mathematical) probability. I thought that was the rule. You seem to disagree and I kinda get where you're coming from. It's not impossible, but it's hard to find a foolish mathematician (an oxymoron some would say). That said the subject we're discussing isn't a simple game of cards, dice, or coins.

That said the subject we're discussing isn't a simple game of cards, dice, or coins — Agent Smith

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.

Nor will counting Earth-like planets help. The answer we get will be exactly in accordance to the prior assumptions we put in.

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.

Where are those damn aliens? :groan:

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?

:up:



What about the famous Drake Equation?

So if we had data we could derive more accurate probabilities from them? — Agent Smith

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

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. — SETI

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.

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. — SETI

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.

I recommend this article:

https://www.americanscientist.org/article/misuse-of-models

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 code—or 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? — American Scientist

If we had data we might be able to estimate probabilities rather than dressing up our speculations in mathematic — Cuthbert

: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).

I'm stating - not insinuating - that mathematical models will produce only speculative results when only speculative data are entered. Even when data are not merely speculative, sensitivity to assumptions remains an issue for many models.

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.

Now I think you're on a wee wind-up. From someone's believing that something is baloney it does not follow either that that thing is baloney or that the person thinks other things are baloney. That's why I put "it's my prejudice" in brackets and why I said nothing about casinos.

Well, the two are logically connected mon ami (they're both possibility mathematized i.e. probability). Granted that casino games of chance are relatively easy to tackle for a mathematician, but probabilities about alien life and visits from our galactic neighbors are just more complex, not a case of comparing apples to oranges.

OK - by 'the whole thing is baloney' I meant 'it's my hunch that there's no extraterrestrial life and we are wasting time looking for it'. I did not mean that mathematical models and probability theory are baloney. I hope that was clear from context. So, back to your question:

How do you explain the fact that someone who understands mathematical probability can win casino games?

Things that have a low probability can and do happen. It's only things with zero probability that never happen.

Is that baloney?

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.

:up:

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?

Why would you be prejudiced against probability? Don't you wanna fix that or are you happy (with yourself)? — Agent Smith

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.

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 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.

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 — Cuthbert

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:

$P(A) = \frac{A}{B}$. 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).

but there's more (I think). — Agent Smith

There are more things in heaven and earth, Horatio, / Than are dreamt of in your philosophy

:yawn: