Do the narrow interests of those with Aspergers give them peace? Are they a source of peace and calm as well as fascination?

"Are they a source of peace and calm as well as fascination?" Yes. Ohhh....wait. I guess you want more of an answer. Hell Yes. Interests are a soothing, somewhat escapist way to deal with stress. There is a reliability and sameness (predictability?) plus a definite feeling of competency.

I may be an atypical Aspie in this answer. My interests are not narrow. These include: Reading about anthropology, history, and travel. Writing fiction inspired by the above. Inventing Conlangs [CONstructed LANguages] as part of the books I write. Drawing and painting. Working out to build my muscles. Taking long bike treks because the roads are there. Listening to a wide variety of music. Friendships ... I do have a few of those. Answering on Quora, as I'm doing now. Why do I do these? Good question. Why did Rachmaninov compose symphonies? Do they make me happy? Yes ... except when they don't. Sometimes, I write badly. Sometimes, I cannot seem to draw/paint worth a damn. And then I'd rather be doing something else. But then I have the good days. One day I sat before an unfinished text, with no idea what to write. Then I asked myself why I did not write something about heresy ... and then, twelve hours later, I was done with the book I did not know if I could finish. And I don't really know how far I should go to be obsessive. But I do know that to accomplish anything takes dedication and discipline. And yes: my hobbies do make me happy. I don't think these are obsessions, though. But I may be the wrong person to ask about how obsessive I am.

Yes and no. Yes, the act of getting to focus on your interests without being interrupted is rewarding--the actual focus itself is rewarding. It puts bounds on the things you have to experience (most of us have a poor filter for stimuli) and bounds on what requires attention (less stuff to handle.) It's also inherently fascinating to get to learn at your own pace, on something you want to learn. No, in the sense that most of us are obsessive, and sometimes we think about things related to our interests in a way which prevents us from being able to manage the other tasks we have to do, which is super frustrating. If someone interrupts us and we have to tear our attention away from the thing we want to focus on, it's also really frustrating. And if we want to learn something and just can't (if, for instance, we're dyslexic or something of that kind), it's also a source of intense frustration. It's also frustrating when we can't get to the thing we want to focus on (because life keeps intruding.) Categorizing information is comforting. You have to understand, life is constant chaos--trying to manage multiple tasks, trying to figure out what is happening in a given circumstance, trying to figure out what other people want, trying to deal with sensory input which may or may not align correctly, trying to figure out what people are trying to do (the thing about people is that while they use categories of thought to make decisions, they use them inconsistently and in an overlapping fashion, so trying to figure out what they're doing means trying to figure out which schema is currently being used the most.) Finding a category is relieving: it allows us to close some thought processes for a little while, and there's always a LOT demanding our attention. Of course, despite all this I'm considered very high functioning, so it may be even worse for someone with more problems than I.

I hope the questioner isn't assuming that all people with Aspergers have only narrow interests. And I would like to know what he thinks is meant by narrow interests. My answer may not be typical because I'm on the high end of the spectrum. Unlike Mark Thorneycroft, my life doesn't depend on rituals or any of the other techniques that are more relevant to more severe Aspergers. And I don't speak about all people with Aspergers as if they were just like me. My interests cover a lot of ground. I'm obsessive about only specific topics, but in the same way any scholar or researcher would be. I want to understand how human beings work, but at a deeper level than that of simply making my way through the world. At the levels that concern me, knowledge is anything but peaceful or comforting.

If by "narrow interests" you mean a concern of one's own welfare, the Aspies are no different from you normal folk.  Their social means of achieving it are somewhat curtailed. if you are referring to the "obsessive" interests that Aspies sometimes have,  in a sense that is no more obsessive than a Normal who is interested in collecting stamps or coins or what have you.  The main difference is the Normal can turn it off and get back to doing the mundane necessities of daily life. An Aspie has to learn how to do that and it is sometimes difficult.  I am an Aspie, in my late seventies.  I have become well adapted to living with the Normal Folks (my wife of 57 years is one of them).  By hard work and focused effort I have learned to pass for human.

In my experience - trying to make sense of the world means that we have to predict what might happen next or cope with new situations using our past experience. We must also be able to understand how other people think and feel. People with autistic spectrum conditions have great difficulty in doing these things, as they tend to have problems with imagination. Instead they often rely on routines, or focus on special interests, to make sense of their world. These routines and interests can become elevated to the status of rituals that have to be followed down to the smallest detail.   Some people argue that these obsessive interests are relatively random and meaningless, whilst others argue that there is a focus on how things work rather than how people work. In my experience people with autism only tend to have one or two interests at any given time and they are usually linked in some way that is logical only to the person with autism. The combination of difficulties with social interaction and intense interests then often leads to unusual behaviour, for example talking at people about the interest without any of the usual social niceties – greeting people; understanding that others may not share their interest.   My point made, I have seen far more informed answers on Quora on these matters from people with autistic spectrum conditions. I anticipate that they will respond in due course.