Consider these technologies and innovations that had already been developed:
* Jacquard loom (http://en.wikipedia.org/wiki/Jacquard_loom)
* Player pianos (http://en.wikipedia.org/wiki/Player_piano)
* Widespread use of interchangeable parts (http://en.wikipedia.org/wiki/Interchangeable_parts#Late_19th...)
* Assembly lines (http://en.wikipedia.org/wiki/Assembly_line)
* Tabulating machine for the 1890 US Census (http://en.wikipedia.org/wiki/Tabulating_machine)
* Transoceanic telegraph networks (http://en.wikipedia.org/wiki/Electrical_telegraph)
* Use of humans for distributed computation (http://en.wikipedia.org/wiki/Human_computer)
Automated computation is an amazing concept, but--at the risk of historic bias--what we have now is merely an optimized and widely available form of what we had then.
What I imagine they'd have a really difficult time accepting is modern physics, particularly quantum theory. Then again, the vast majority of the public today (including me) struggles with it.
And culturally? Well, for one (U.S.-focused) example, there's that whole Civil War/end-of-slavery thing smack dab in the middle of it.
It's by no means clear to me that the changes of 1915 - 2015 somehow completely outstrip the changes of 1815 - 1915.
(I see that you agree with my general point, and with good illustration, too. I just wanted to point this out as well.)
The UK still had slums with limited indoor plumbing during the 1950s. It wasn't until the slum clearances of the 1960s that the standard became an indoor bathroom in a house with central heating.
The big change between 1915 and 2015 is that the technological GINI coefficient has shrunk so much.
Being rich gets you few technological perks. You can buy a supercar or a private jet, but that's a difference of degree, not a difference in absolute access.
Most people have cars, and almost everyone can afford to fly. And all but the very poorest have Internet and electronic media access.
Likewise for cultural differences. Sexual morality - at least as publicly presented - is completely different now.
Work culture is somewhat different. Politics and finance have probably changed least of all.
The point being that someone from 1915 may just about be able to understand the Internet and computing. But they're going to have a really tough time learning how to parse Buzzfeed or TechCrunch or Reddit. Never mind what happens when they find PornHub or Tinder.
There are three things to learn, not one. The first is what the technology does. The second is the vocabulary of new names and the new concepts used to describe. The last is the social scripting that defines appropriate and inappropriate behaviour.
Those last two will take longest and be hardest.
I'd expect similar challenges in 2115, with the difference that there's likely to be much more social and political change, and not less.
It would surprise me if the definition of "human" hadn't changed fundamentally by then, together with almost everything we think we know today about culture, politics, and economics.
Also, I didn't mean to imply full agreement with chaosfactor (https://news.ycombinator.com/item?id=9279631)'s "die from culture shock", which I think overstates it. I just meant to say that there's a wide gap between being told the facts (about anything profound, not just computers) and really coming to terms with their implications, and that I think that achieving the first is easy and the second hard.
Computers have changed our lives in many large and small ways. Great. Tell that to the traveler from 1915. Show them. They'll understand; they've witnessed the same phenomenon with the technological developments of their own time. They won't be used to our modern world, but their mind won't violently reject exposure to the concept.