That's an interesting question, which simply answered is a plain yes or no.
If they use technology as we understand it, then presumably yes. Prime numbers are just a unique artifact of basic arithmetic. Our knowledge of prime numbers appears to date back to at least Ancient Egyptian times, so it's quite safe to assume an alien race capable of something as technologically adept as transmitting a signal with the purposeful intent of contacting another race would know what prime numbers are.
The issue is we're limited to our view point, we're exceptionally naive of anything different as we've never experienced it. So, is our technology the only way?
We're designing nanotechnology that could fabricate anything we could dream of, but what if an alien race ended up evolving a unique cell that could do it too. We have white blood cells, they have nanofab cells. Would they even comprehend math if they're just growing jet engines and rocket nozzles?
It's this latter, our unknowable unknowns that will broadside us. How do we relate to something that's unfathomably alien to us.
The good news is you and I likely won't be around to care when we find out what aliens are really like.
> The good news is you and I likely won't be around to care when we find out what aliens are really like
I've never understood this sentiment. I would most certainly like to be around if and when we find this out, for better or worse. Why wouldn't you want to be?
> Do you feel despair when you step on ants on the sidewalk?
Well no, but neither do I go out of my way to step on them. And I don't see that we'll be so very, very far behind these beings that they're not even capable of recognising we're sentient. Indeed, with all their technology, they should be even more aware of the potential sentience of life than we are.
In the last 100 years or so, humanity has made great strides towards its treatment of lesser animals - we have a long way to go, but it wouldn't be unreasonable to set a goal of zero intentional animal cruelty by 2100. I'd expect technologically advanced aliens to be similarly advanced ethically, or if they do wipe us out, it would at least be deliberate (eg 'the killing star' logic).
Most of the pessimistic alien-encounter scenarios involve the aliens' wiping us out for reasons of convenience. They need our resources, and we're either pointless or competitive to keep around.
Personally, I find that argument a little naive and anthropocentric. Who's to say they need our resources? Couldn't they find resources aplenty in asteroids, on planets closer to their home, or through artificial synthesis? It makes little economic or biological sense to go through the trouble of exploring vast, deep regions of space purely for the purposes of acquiring resources. (And that's even assuming they need the same resources we do, in the first place.)
In all likelihood, an alien intelligence that made itself deliberately known to us would be doing it for scientific or diplomatic reasons. If they want our planet, they could just take it. There'd be no need even to deal with us; they could just lob a few asteroid-sized objects at our planet, eradicate life on the surface, then come in and harvest away.
To your point: any sufficiently advanced intelligence that's going to bother interacting with us will probably have studied us well in advance. It will know as much as it can about us. It might (depending on its alien mindset) have a good understanding of our potential sentience, and a respect for sentience in general.
The real threat isn't from alien intelligence, but from alien AI. A dumb AI, at that, of the kind that mindlessly travels the galaxy, self-replicates, and harvests material without discrimination. But again: a race advanced enough to develop such technology would probably be aware of the consequences of letting it run amok. There would be checks against that scenario by design.
We're very quick to ascribe a bleak, law-of-the-jungle amorality to alien intelligence. But let's think about it. Such an intelligence had many "tests" to pass: a nuclear age (or some equivalent thereof), climate change (or some equivalent thereof), wars, and so forth. If it's far more advanced than we are, it probably passed and survived all those tests to get there. It's very hard to pass those tests in the absence of a complex, well-developed ethical system.
>The real threat isn't from alien intelligence, but from alien AI. A dumb AI, at that, of the kind that mindlessly travels the galaxy, self-replicates, and harvests material without discrimination. But again: a race advanced enough to develop such technology would probably be aware of the consequences of letting it run amok. There would be checks against that scenario by design.
Don't have too much confidence in that. If a civilization creates AI, it could possibly improve itself and become incredibly intelligent, but still keep the simple goals that it was originally programmed with. Thus endlessly self-replicating, consuming the universe to create bigger computers, or destroy threats to itself, or preserve it's existence as long as possible.
Its interesting to think how we would react if we encounter a superior alien race. It completely changes everything.
Frankly, I don't think it would end well at all (even if they are benign). We are too smart/proud to let someone set the rules for us, not after being at the top of the food chain for so long.
People do go out of their way to step on ants, because they are pests. If aliens see us as competition for resources or a potential threat in the distant future, it might be better to eliminate us now.
There is no such thing as "advanced ethics". Our human sense of morality evolved under our specific evolutionary conditions. Aliens would be completely different. Even worse, they could be taken over by Paperclip Maximizers (http://wiki.lesswrong.com/wiki/Paperclip_maximizer).
Further to your point about treatment of animals, I imagine that our best and brightest would be at the forefront of any equivalent transport and communication. And I think they'd be more likely to carefully consider their treatment of animals than the average person amongst us.
You're being naive. We mass produce animals for slaughter.
Those ants are pests, I pour boiling water down their holes and leave poison around my house because once in a while a few get on my counter, or they cover the sidewalk when they go to war with each other. I have a pet rabbit, vermin, but I put out mouse traps.
An alien species entire reason for making us extinct or pushing us back to the dark ages might be as petty as because we were a visual nuisance, or like Douglas Adams suggested: we got in the way of road construction.
If they were directing the design they would be pretty likely to have abstractions. If you are making designs utilizing abstractions you are probably trying to maximize their effectiveness, which sort of naturally leads to at least some math.
Yes. Prime numbers are fundamental features of the universe. Fundamental things that are global rather than local; Mathematics, the periodic table, physical constants, physics, chemistry, no doubt others that don't occur to me instantaneously. Things that might be local only include biology ....
On the other hand there might be the possibility of the existence of Kardashev type ≥0 civilizations that skipped our level of intelligence in their evolution and to which basic number theory is so trivial that it’s not worth mentioning, just like the concept of addition is trivial for us.
It's abstractly possible, but you have to tell one hell of a Just So story to get them there. Foreign life forms are embedded in the same physics we are, and most likely experienced the same basic life-and-death fight for every resource that our species did before our intelligence explosion. There's many ways they can be different than us, but there's a lot of ways that any intelligence embedded in the same universe as us must be the same, too. I think people get stars in their eyes and put way too much focus on the former quite often.
Possibly. We should keep in mind that our knowledge of number theory is very limited. They are probably not really interested because it's all really obvious to them -- and has been for quite a while. It's quite amusing to think about how they might laugh at our encryption systems relying on simple discrete logarithm-problems etc. Not unlike we laugh at Julius Ceasar for relying on simple substitution.
Julius Caesar didn't have number theory nor computers so his cypher was actually pretty sound.
We have a pretty good idea about the limits of encryption. I doubt advanced aliens would have much to laugh about our current state of our encryption systems.
Considering that most people couldn't even read regular text back then it was definitely pretty sound, but that's not really my point.
We do? Got any references for that? Take RSA -- it's not even proven that breaking it is equivalent with integer factorization. Even if it was, there are no proof that integer factorization needs to be time consuming at all, there might very well exist an algorithm with polynomial complexity.
I imagine they would at least recognize that it's a handy tool for communicating intelligence. "This signal is not an accident. Pay attention to this signal."
Ha! Of COURSE they do! Didn't you know? We got OUR interests in prime numbers from aliens, and they are still interested, e.g., still trying to find an algorithm to factor integers that runs in O(n) for an integer of n decimal digits. Why decimal? I know the answer, but there is no room in this post for me to write it down!
And for 'The Book', Paul Erdős, that was from aliens, too. Why? Sure, could there be any doubt, Erdős was one of them!
