The line between "visible disability" and "invisible disability" is a shifting one. Often hard to pin down. For example, my disabilities are really invisible - if you looked at me while I was sitting up you'd appear to see a normal healthy 26 year old woman. But if you saw me when I was going out I'd be in a wheelchair with somebody pushing it! - That's not invisible at all. And from experience I can tell you that attitudes differ immensely between when I'm invisibly disabled and when I'm visibly disabled.
But apart from people's part-time wheelchair use, are there actual disabilities which vary between visibility and invisiblity while still being disabling all the while? The answer is a resounding "Yes!".
For example psoriasis usually manifests itself as a very visible skin rash where the skin grows thick and scaly. This is the visible side of the disability, but up to 1/3 of people with this condition also have psoaratic arthritis - very painful joint problems - which may manifest even when their skin is clear. Arthritic joints may not be as visible as a skin condition but they can be far more disabling. So psoriasis can be both an invisible and a visible disability!
Another specific disability which can change from visible to invisible (but still be disabling in both states) and back again is Multiple Sclerosis. A friend of mine has at one point had weakness of the legs requiring her to use a cane or crutches - making her MS very visible. At other times these symptoms have gone into remission and she has had invisible symptoms such as vertigo, memory loss and bladder problems - equally severe and very disabling, but invisible symptoms.
A person with a prosthetic leg may experience something similar on a short term basis where they look normal while standing still (assuming the wearing of long pants) but are noticably disabled with a limp or abnormal walking action once they start to move. But they're still as disabled whether they're standing still or moving.
Anybody who watches knows that if you have a visible disability, people go out of their way to help you. They will hold doors open for you, make sure you get a place in the elevator, lift things from high shelves, help you not have to wait in queues. Anything to make life a little easier. This is just one of society's gentlenesses at the moment.
But society hasn't progressed to knowing that invisible disabilities are out there in the community yet. Some people take a walking stick or crutch or cane they don't quite need, just to make their disability more visible and therefore receive the special treatment that visible disabilities rightly command. In a society that accepts visible disabilities and ignores invisible ones, it's the only sensible thing to do, really.
