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I am an inventor. I find the process of inventing is an exercise in multiple streams of coexisting thoughts. For instance, first defining the problem is paramount. But after that I need to both understand existing solutions to see how they could be improved but also erase all existing solutions and imagine what solutions I can from scratch. Also, I need to imagine desired solutions with producible solutions. I need to pursue solutions but also periodically abandon them all and go back to square zero. I am trying to describe having multiple thought trains which, if not symultaneous, alternate in as complete a way as possible (where one disappears when the contrasting one is operating).
Whether a solution is an invention depends on if the solution is new or not. I may come up with something new to me which I discover someone else already came up with, thus it isn't offcially an invention. That's why I may use the word "solution" instead of "invention".
Then there is the wrinkle of whether a solution can be manufactured, whether as a one-off or in quantity. And the detail of whether materials exist to make it. And then the need to both take into account existing materials and also to try to think of "what if" there weren't that limitation. So often one can be self-limited by using known materials or processes. By thinking "There must be a way to…" or "Someone must know how to…" or "How hard can it be to…" can lead to dead ends or new solutions.
An interesting thing is using CAD to draw and a 3D printer to produce something. It is marvelous because I get to see it on-screen and to produce it effortlessly. I can make a change and then print it out without spending hours cutting, gluing and sanding. But at the same time I am limiting myself with what drawing skills I have (or the capabilities of the program) and by what the printer can produce. And then there is the maddening thing of also being haunted by what can be manufactured (3D printing and injection molding have distinctly different capabilities and limitations) which can limit me prematurely if I let it.
I sometimes try to transport myself back in time and try to imagine what I would have done when stone, bone and such were the materials to hand. As someone else noted, why work on an axeled wheel when no roads were available? A travois may actually be a better solution on that day. Or what would I imagine to be a problem that needed to be solved? What would improve the life I actually faced each day? How much of my life would be consumed with just learing how to do stuff that already existed? And how many inventions were the mavels of their day but then ceased to be preferred?
Oh, which leads to the topic of un-learning wrong information one has picked up. Or value judgements on what is good or bad.
And then there is the dual processes of imagining how something might work and actually making a prototype and seeing how it actually functions.
And then there is the aspect of whether something is truly new or is an improvement on an existing product. New products are difficult to introduce because they require educating users. Improvements may be too expensive for companies to justify. Either can canabalize sales of existing products yielding no net gain. So all the solutions cause problems for companies at the same time as they offer tantalizing new products.
And then there is the limitation of using words to describe solutions. Or of understanding of machines (basic ones like ramp, screw and so on). Knowledge is a blessing and a curse. A blessing in order to combine wjhat one knows, but a curse because it can fence one's thoughts in. A great example I used to use was how easy it was to spot an advertisment which had been created with Word…lots of text with boxes and so forth (generally looked terrible). Someone who used Quark Xpress or Illustrator would have a more flexible canvas to work on (and could produce more artistic or exotic stuff). But either way the tools and knowledge allowed for marvelous new things and limited one at the same time.
My point is how many counterposed or mutually exclusive thought trains are involved.
Oh and to answer your first wondering: yes, inventions are more ingenious than folks may suppose. That's why I am such an impressive guy. ;-)