Suppose a small alien craft lands in, I dunno, Istanbul, and a group of ETs gets out. They have a translator and say, in essence: “We weren’t really sure what you’d be like, but we’re happy to see you’re reasonably intelligent and advanced. However, we’re not prepared to make any kind of alliance or treaty. We will report back and send a proper delegation in about 25-30 years.”
How long would it be before people didn’t think about the visit every day?
At least until people felt they’d figured out (by parsing their words to death) whose years they meant. 
Even if the aliens came, rounded up two billion people and told us we were all food, there would still be people who claimed that was a conspiracy and a lie and who wanted to go with the aliens because they had to be better than us because they’re so advanced.
And I don’t think they’d ask for an alliance, since we’re nowhere near FTL tech, plus we (as a species) absolutely do not have our shit together.
More like “When you’re ready to talk to us, send a ship to (wherever). We’ll be waiting.”
It’s very hard to answer this question, in part because it depends on a lot of social factors.
As a quick example, 2000 years ago, a Jewish carpenter was crucified. Quick, which one am I thinking of? And a very large percentage of the population still think about Him every single day in one way or another, even the ones who don’t believe it happened. Meanwhile, the guy who was crucified the week before or the week after? Totally forgotten, probably within days.
Aliens landing is at least newsworthy enough to capture everyone’s attention immediately and for a few months, probably. Where it goes from there is purely guesswork, though. Are alien T-shirts a thing? Are there thousands sold, or millions? Do people demonstrate in the streets demanding additional SETI funding? Does someone found a religion about the aliens? Is an annual “Alien Visitation Day” declared a federal holiday? Do we put aliens on the next $20 bill? All of these things will affect how many people are thinking about this on a daily basis, and for how long.
An alien visit would have planetary-level consequences far beyond any event in human history. You can count on on a massive increase in R&D spending by private corporations, new spending space exploration by almost every government, and vast new military spending across the board. Property values in Istanbul would skyrocket and the specific site of visitation would be the focus of an enormous effort by many different parties to exert influence. Alien life would raise existential and religious questions that would be debated and discussed for centuries.
Even a mere “just saying hello” visit like the one you posit has the potential for cataclysmic violence and would permanently change life in ways that we can’t even comprehend.
Depends. Is anal probing involved?
I think it depends a lot on the extent to which their visit is accepted as fact. If they hang around long enough that every news network in the world can get helicopters there, or if they leave permanent and inarguable physical evidence behind, then it changes EVERYTHING, more than we can possibly predict.
If there are a dozen witnesses with cell phones and one local Turkish station gets a cameraman there, and all that is left is some blast marks, then we spend a LOT of time arguing bout whether it was a hoax or not.
Interesting question, however.
I like the idea of them landing in Turkey far better than the idea of them landing in, say, New Mexico. Outside Ho Chi Minh City would be even better. Somewhere that doesn’t get a lot of attention normally.
It might actually help solve conflicts here on Earth. When you’ve seen pictures of an alien on CNN, the differences between, say, Christians and Muslims will seem much less important. Our tribalism instincts will be able to classify “humanity” as “my tribe”.
This.
There are vast forces out there amongst the humans which would be very threatened by this event. So they will have a very strong tendency to not believe it, try to claim it never occurred, or claim that it’s a hoax.
Consider how many entities are totally against believing that (A)GW is true. And we have lots more evidence for that than just a few minutes or hours of recorded video.
I agree with this. It would mean fundamental changes in how we view ourselves; from thinking we might be the only intelligent species in the galaxy or universe to knowing for sure that we are not. And some people will find their religious beliefs challenged.
Anthropogenic global warming?
OP:
I guess most people would cease thinking about it *every day *after a few weeks since it wouldn’t impact their immediate concerns much and the 24/7 news cycle would quickly enough create saturation.
A sizable minority would think about it every day for months or years as it would have a new religious importance to them.
A small minority wouldn’t care.
I think it would soon simply become background info.
Look at how little we now consider the fact, utterly bizzare to our ancestors, that humans have weapons that likely could destroy humanity itself.
People think about it from time to time … but in the meantime, there are celebrity scandals on TV to watch.
I should explain the background behind this question: On another board I was having a discussion re: the alien invasion in the first Avengers film and the fact that it’s barely mentioned on Daredevil. My argument was that while an alien visit/repelled invasion is important and newsworthy, the day-to-day life of people would not change to any great degree, and that since the even happened 3 years ago it wouldn’t be a topic of everyday conversation. The other fellow contended that it would be such a huge sea change that he’s puzzled that there’s still people fighting over territory in Hell’s Kitchen.
And I picked Istanbul both because it’s a city I like and I’m tired of aliens visiting the USA first.
Leave out the part about their return, and I could see folks going back to normal. But if we know they’re coming back in 25-30 years, that basically sets a clock running. I think we humans would still bicker like fuck, because that’s what we do, but a tremendous amount of our bickering would be about how to prepare for their visit. Do we assume that they’re coming back with military might and we need to be ready? Do we try to build a one-world government? Do we try to make our own country the most alien-friendly country so they’ll strike an agreement with us? Do we assume that they’ll give us enough advanced technology that we don’t need to worry about global warming’s long-term effects? Do we interpret their visit as a sign from Revelations (don’t ask me how, everything gets interpreted as a sign from Revelations)?
I think a lot of folks would think about it all the goddamned time.
As for the Avengers and Daredevil, I duno. Folks do talk about it some on Daredevil, but the event wasn’t such a sea change for those earthlings, I think, given widespread knowledge of Iron Man and Thor in that universe.
There’d be a lot of running message board jokes and memes.
“Aliens, wait.”
Several cults will form to await their return. At best people will lose interest in 12.5 to 15 years before the countdown to the return begins. Plenty of “aliens were a hoax” CT will happen also (there’s a twist).
Get over an alien visit?
We haven’t even gotten over Macho Grande.
sploosh
No anal probing for you!
Yes but like I told you the last time, it’s going to cost you extra. 
You picked the wrong week to stop sniffing glue.