Alone ... or lonely?

A lot of people think it odd that I choose to live alone, here in South America it seems to be expected that you are part of a big family and are amazed when they hear that I live alone. They assume that you must be very lonely, and try and involve you in things, but I want to choose the things I do, and not have to join in because people think I might need to be involved with others around me.
There is a world of difference between being "alone" and being "lonely". "Alone" is a physical state, no-one else around, and "lonely" is a mental state, when you feel bereft because no-one is around, though you can easily feel lonely in a crowd of people, or with loved ones, particularly if you feel that the others do not understand you.
I like being alone - I do not feel the need to have other people around me all the time, I do not feel the need to be part of a group or crowd, and, in fact, I avoid crowds whenever I can. Maybe it is because I was a very shy child, so was able to enjoy my own company - I could immerse myself in a book, or even watching a spider build a web, and didn't have to share that with anyone else to feel fulfilled. that doesn't mean that I do not enjoy the company of others, just that I now want that to be on my terms.
I used to work with guys who went out together in their free time, to the pub, to the cinema, to the disco, etc. and saw each other day in, day out, and I could not imagine anything worse - there was no spontaneity, no variety - if it was Wednesday it was disco night, Thursday was karaoke, and so on. When I lived in Mozambique we had a golf course in the village, and I used to go and play most afternoons - alone! Even if my friends were planning to play I would go out earlier, on my own, as I preferred it that way. I met up with them at the club most days, and we used to do things as a group, but I realise now I was always a bit aloof, and used to pass on some of the more dubious escapades!
I was married for 19 years, and living with my wife (now ex-wife) for some years before we tied the knot, and it was an enjoyable time for the most part. We used to do a lot together, and in fact I had very few interests outside family life, so married life was everything to me. After our divorce my daughter came to live with me, until she went away to University, so I had someone living with me for a few more years, but for the past 10 years or so I have lived alone - happily alone.
I can do what I want when I want, without anyone bothering me, and don't have to worry about my actions (in the home) affecting anyone else - I was, I think, a considerate house-mate while married, and would never dream of doing anything that might inconvenience anyone else - nor being bothered by the actions of anyone else. I have a large house in Brazil, and often I am asked why I don't rent out a room, or find a partner to share with - and basically there are 2 reasons, the main one being that I enjoy being alone and would feel uncomfortable working my life around anyone else (lodger or partner), and  the second one is that I am very independent and feel I could not afford to support a second person. OK, I am conveniently ignoring the fact that they might also contribute to the household - but the latter stages of my marriage this "partnership" fell apart due to loss of earnings from my wife (medical grounds) and my inability to support us alone, and do not want the stress of being in that situation again.
I now own two motorbikes, one in Brazil to run around town in (I do have a car there but use it only for long journeys), and one here for fishing and touring. I did consider buying a second-hand car here in Peru, but realised that this might solicit requests for lifts when I travel - so the bike allows me to travel alone at my own pace (even though not as comfortably as in a car!). I travel alone, stopping when I want for as long as I want, and generally in pretty remote spots (avoiding crowds!), and never feel lonely. If I have enough food in the house I can spend days without venturing beyond the boundary on my property, and if I do venture further I may just go for a ride along the coast (or down to the river in Brazil!) away from "civilisation", or here in Peru just a walk along the promenade and finding a quiet spot to watch the sea. I may not even say a word to anyone the whole time I am out. 
I suppose it would be nice to find a soul-mate, someone to share the remainder of my life with - and it could be a like-minded male just as easily as a female partner (though I rather hope the relationship would be different!) - but I do not feel a "need" for company, I am not looking for any sort of relationship, and am quite content being alone - but never lonely!