Second, it's always missing the second part: and then what? One can recognize an optical illusion as one, but that knowledge doesn't make it fade away. I mean, it can help to know, but it seems there's step missing between that and feeling serene.
Meditation forces a meta-examination of that stream and recognize that it isn't the one flowing river that you normally feel it to be. Meditation allows you to exercise other levels of your consciousness that can recognize, observe, and even control those other parallel threads of consciousness.
I have read that there are possible pitfalls for people already suffering from paranoid schizophrenic-ish disorders. I think they're already dealing with an out-of-control sense of not having a single stream of consciousness that they always recognize as themselves.
I can only speak for myself, but I don't find the sensation of a multi-threaded "me" all that alarming. YMMV
Once the feeling is no longer something that automatically 'happens to you', one can start to explore it - at a safe distance, no rush. Why am I feeling in this way? Is there a good reason? If yes, what could I do about it? What would happen if I would just dismiss the feeling without doing anything? What would happen if I embrace this feeling/act it out? Once an idea of what strategy is most likely to give a good outcome, one makes the choice.
Its kinda like having a person with an outsider perspective help you analyze the situation in a calm and thoughtful manner. Just with much higher bandwidth, less communication challenges and the person is always there for you.
In fact, I should really say you operate from a place which is 'before thought', since 'beyond' suggests something after the thinking process. Actually it can almost feel like thinking is a strenuous burden in this state, which suggests you're 'before' the thinking process.
Observing thoughts while still operating from "within your mind", which it sounds like you're describing, doesn't necessarily lead to that experience.
It's a shift in perception to something that lets you view thoughts without getting caught up in them. So countering one thought with another isn't it because then you're still in thoughts. However...
The reason this is tricky is because a logical process can be used to reach this realisation - indeed I experienced this state while working with the koan "Who am I?" on a Zen retreat. As I continued to ask myself that question I "took myself apart". I deduced that "I" wasn't my body (because when I sleep my body remains but "I" don't), that I wasn't my thoughts (because I can observe them), nor the other "aggregates" as they're called in Buddhism. The one that I'd struggled with was my awareness, but I realised "I" wasn't even that.
Through this process of logical deduction I realised on some deeper level that I just fundamentally didn't need to pay any attention at all to my thoughts. They became as insignificant as if someone had left a radio on. Note that this is different to just the usual meditative technique of observing thoughts. At this stage, there is no technique involved, it's just how you operate at that time.
So then what? I just ignored them! Totally. I didn't try to shut them off, I literally didn't care if they were there, and I didn't pay any attention to them. In doing so I just felt so at peace. I didn't need to do anything to reach step 2. There is no step 2 :-D.
This is called "non-doing" in Taoism, and this serenity is claimed to be our "natural" state - that's to say if you view our continual pandering to thoughts as "unnatural", which it did strike me as. More like a big, habitual mistake to be honest. I guess this is also called "transcending the ego".
So I'd stand around at this farm where the retreat was happening. I didn't care that there were sheep in the field, but there were. I didn't care when it rained or if it didn't. At meal times I could see when something needed doing, and I did it, but I didn't care for it. I just felt deeply contented.
So it's very different from recognising an optical illusion, unless it's at a level where the recognition goes to your core and causes you to absolutely ignore your thinking mind, and not feed thoughts on any level (even sub-vocally).
Now the tricky part is it's so habitual to fall back into listening to your mind. I haven't experienced that state since the retreat (although it did last for a couple of weeks). However, it proved to me beyond doubt that it exists. It also has made me re-evaluate my life, why I do what I do, and what's important to me.