Does the physical world exist independent from a conscious observer?
This is not at all obvious. Maybe it is like in the computer-game Minecraft, so that the world is only generated once we move towards that part of the world. That would even open for the possibility that the new parts of the world are generated based about our expectations what to find there.

And more than that, this concept is not necessarily only about world-locations.
What if there are countless thinkable "truths" which "physically" manifest themselves only once we think about them?

Just think about the revolutionary theories of Albert Einstein, no doubt that they are true.
But on the other side they are kind of "remote" in a sense that they are not something we encounter in the daily life, so the major part was really to think about these things, that kind of brought these truths into existence. Same thing with the incompleteness-theorem of Kurt Gödel, just to start thinking about such a unthougt thought (if a logical system can prove itself to be either incomplete or contradictory) was the major step.

So it is really fantasy and imagination which are the prerequisite in finding new truths, it is not sufficient to "keep the eyes open".

And it is up to us to discover those truths which we want to discover, so the choice what we think about is really an important choice; it is unlikely to make progress with "good things" when thinking about "bad things", and vice versa.

We hear a lot of dangerous ideologies, dangerous religions, dangerous movements, which turn people into psychopathic idiots. But I think this is not the whole truth, I think also that there are just psychopathic idiots around with dark intentions, and they use and abuse ideologies, religions and movements by holding them up in front of them, as reason for what they do, but the simple truth is that they are just psychopaths which need some kind of explanation for their idiotic actions.
It is just by chance if such a persons shows up in one radical group or in another radical group with the opposite ideology, it does not really matter for them.
They do not deserve to be identified with an ideology or religion - this is what they want. They deserve to be seen as what they are - psychopathic idiots.

I am really a supporter of the guideline "getting far with small steps".
However, there are situations and problems which can not be solved that way.

If you learn how to ride a bike, you will not succeed when being to cautious to steer hard enough.
There is no way to learn this by first steering a little bit only, and then increasing this in small steps.

I did a simulation today of a random chaotic system, trying to find system parameters where this system would do what I wanted. I did not succeed first, only after I substantially increased the mutation size of the parameters the system would snap over from the chaotic behavior to the stable behavior.

Can this be generalized somehow?
Well, looks like making small steps is good to find a solution only in certain environments, in other environments it is necessary to make big steps.
This is not as trivial as it may sound in the first place.