I believe what you're getting at is the Ludic Fallacy, which could probably apply here. That said, whether it's a fallacy in the science or in the reporting, it's hard to say. I have a degree in statistics, and I'd say I spent half the time learning stats, and half the time learning to use language precisely to avoid overgeneralizing stats.
There's a really great TED talk about how even very educated people get it wrong when talking about stats: https://www.ted.com/talks/peter_donnelly_shows_how_stats_foo...
Does this single observation tell you anything about reality? I would argue that it does - it should strongly suggest to you that you're in the "every car is ARW 357" reality. Similarly, if you draw a ball from an urn and it's red, and you know you've drawn either from the "urn of red balls", or the "urn of one million green balls and one red one" you should be pretty confident you've drawn from the "urn of red balls".
If one theory can explain your observations but the explanation is highly unlikely, and another theory explains your observations and the explanation is likely, the second theory is more likely to be correct all else equal.
I think this scenario is incoherent after thinking about it for a minute. You say "there is equal probability that either explanation is true" but you imply that you, the storyteller, know something about license plates. Probability is a description of incomplete knowledge, so whose knowledge are we talking about, yours or mine?
I see no reason (in my hypothetical ignorance) to exclude the possibility you know I will see "ARW 357" next even if all license plates are different.
Instead, consider the example with the urns. I think that's a lot more realistic and illustrates the problem.
In both cases you do not have enough information to make any conclusions.
That's why the field of statistics exists in the first place.
However, are we able to reduce down our understanding of "which universe we're in" in such simple terms? I think I'd understand better if I knew how long we've been capable of detecting oumuamuas.
There's no evidence it is aliens. Obviously it could be, and it's unlikely there are not such things in our universe.
It just seems more appropriate to say "there's no evidence it is related to alien tech." Everyone having to say "it's NOT aliens" seems like some sort of cultural phenomenon.
Most theories on physics are evaluated this way. "We theorize that light is a particle, which would explain these properties of light, and means we should expect to see these other properties of light if we test them." If further observation of light matches those properties you predicted then that's pretty good evidence that your theory is on the right track.
If your ancient aliens theory didn't actually predict "Stonehenge", but predicted that the aliens would have left "all sorts of cool weird stuff", and then you point at Stonehenge and say "see, that's the sort of cool stuff I mean", then I'm no longer impressed by the predictive power of your ancient aliens theory.
Predictions have to be precise for a theory to be supported by them: they can't be vague generalities. cf. astrologers, who "predict" the future by predicting nothing.
My theory is wrong, but it assigns higher likelihood to Stonehenge than yours. That’s why I don’t like the license plate example.
A theory that is wrong will sometimes predict correct things by accident. That's unavoidable, but we a) have statistical methods for modelling how often things go right by chance, and b) have a philosophy of science in which theories are forever tentatively held: your aliens theory might beat any theory which says Stonehenge is impossible, but will soon be replaced by a theory which explains Stonehenge more economically.
We can suggest that there are N classes of objects in space, we picked one at random, and it happens to be Oumuamua belonging to the class of Oumuamua-like. To one of N classes. The more some class is common, the more probability for us to see element from this class. Here we can use Bayes' theorem and conclude that the fact of observation of Oumuamua is a weak evidence that the class of Oumuamua-like is more common in the interstellar space than any other class.
It is a weak evidence, and I dont know how much is it. But the point is this evidence points to an ordinariness of objects like Oumuamua not to a rareness.
You start monitoring it. Year 1, the thing happens. Which is more likely:
1. You've encountered a 1/1,000,000 event
2. Your prior is incorrect and the thing happens more often than once every million years?
Without more information we can't actually answer this question with certainty, but "re-evaluate your priors" would absolutely be a thing one might suggest in response to this event.
https://en.m.wikipedia.org/wiki/List_of_gravitational_wave_o...
[1] https://en.m.wikipedia.org/wiki/Observable_universe
[2] https://www.livescience.com/56634-how-many-stars-are-in-the-...
You press the button. The light bulb turns green. There's no windows to check for rain or internet to check for winning numbers. You have no further information beyond the fact that the light bulb turned green.
Which is more likely to be the case: That you're now a millionaire, or that you should grab an umbrella as you leave?
We know we saw 'Oumuamua (the green light). We now can construct many models for why we might see such results. The probability that we would see the results given the model (lotteries or rain) can be used to infer what the true model most likely is.
1) Somebody starts flipping a coin they claim is fair. You're not sure whether or not that's true. It comes up with 10 heads in a row.
2) Somebody tells you there's a 1 in 10,000 chance of something happening each day. You're not sure whether or not this is true. It happens tomorrow.
Which, if either, do you think has reasonable evidence to begin to doubt the claimed odds are the real odds? Which do you think is better evidence of the proposed claim being false?
With the logic you expressed in your post you might suggest the first is better evidence of a false claim, but it's not. The odds a fair coin going 10 heads in a row is 1 in 2^10, or 1 in 1024. Even though it's 10 'events', it's ultimately just a 1 in 1024 happening if we assume a fair coin. By contrast the second event is about an order of magnitude less likely to have happened by chance. So even though the second event is only one happening, it's more likely that that event is not a 1 in 10,000 event than it is that the coin is not fair.
But to answer your question more generally: you start with some model, with one or more parameters for which you don't know the value. e.g. "the galaxy contains N uniformly spread out interstellar objects that are big enough to see if they happen to come within 1 AU of Earth."
Then we start watching the sky, and after 10 years we see 1 such object.
Then for each possible value of N, you could calculate the probability of observing exactly 1 such object during a decade. One particular value of N is going to give us the highest likelihood of getting that result. We call that value the "maximum likelihood estimate" for N.
http://www.thebigalientheory.com
Certainly, any new information is going to radically adjust the posterior probabilities, but you can still make some tentative inferences.
This was worked out in WW II for estimating tank production.
In fact, an argument that it's more likely to have come from somewhere nearby holds even if it was sent by design. Conscious beings are more likely to want to explore the stuff they can reach sooner, and they are more likely to succeed at reaching nearby things. But without knowing their engineering constraints and their preferences, we can't quantify that like we can the random ejection scenario.
It seems far more likely that objects like 'Oumuamua are relatively rare, and that means it likely came from someplace close by (if it came from farther away, the odds are even lower we'd ever see one).
I'd rather look at the density of Oumuamua-like objects in space. First, it seems like these objects rarer than some things but dense enough for us to have seen them.
Their "terminal density" comes when their rate of production managers to equal their rate of consumption. Who knows how they're produced but I'd assume they are consumed when they are gravitationally captured by a solar system - actually flying into a sun is much less likely I'd assume. Such gravitational capture is more likely if these objects are moving at a similar speed to the solar system they encounter.
The one thing we know about Oumuamua is it seemed to speed up as it left the solar system. This factor might imply that the chances of capture wind-up very low. Now, the rate of production could be low and thus life-span could be high. A high lifespan implies this came from far away. I could be wrong on the consumption chances. But still, I think arguments about how far these travel would do better with such life span analysis than with the quote argument, whose implications are foggy imo.
As to whether the thing is a product of alien intelligence? If the very low density analysis is correct, if such a thing could behave as Oumuamua did, then that too might be a good spacecraft design. Which is to say, the amount of information we have is low that making absolute answer seems pretty hard here.
- observe this thing at all
- accurately measure it's velocity and acceleration
- understand that it's velocity and acceleration were unusual?
A number that I saw quoted earlier was that it is expected that around 3 of these things go through the solar system every day. This one just happened to be the one caught by the survey, which itself required a bunch of coincidences since it means catching multiple pictures of the same object in different locations so as to establish a trajectory, so an ability to detect is not just resolution, but also timing and orbital trajectory.
We've been observing space 'forever'. Pre-telescope observers had quite accurate star maps (of the naked-eye stars, obviously) and were fully aware of the complex movements of the planets. Their models of the movements were good enough for predictions even if the underlying explanatory causal models were sometimes wrong.
Ok, it's on my list of things to do this year to actually learn how statistics work, but my naive reaction to this supposition, which I read is "the fact that we have encountered Oumuamua means that it's likely it didn't come from far away, because if it did, it's less likely we would have encountered it," is: We did encounter it. Just this one, ever. How can we draw any statistical information from that? Either we encountered it, or didn't, how does that have any bearing on the statistical probability of seeing it?