Creativity relies on intuition, on a sixth sense, where you just absolutely know 'somehow' that something has to be so, even if you can't explain it in a satisfactory logical way.
You just sense it!
It can best be described as some sort of energy, an overwhelming desire or passion, that is taking you over and on which you have almost no control. You just get obsessed by one idea that totally overpowers you and you have no peace until you put into action.
There is something quite mystical and magical about the whole creativity process. It is almost as if you were becoming a medium and something supernatural was happening through you... almost possessing you. It is almost as if some unformed entity that wanted to be born into reality had come to inhabit you so that you could give it birth. And like the process of giving birth and bringing a new life into this world, it is not always entirely sure to succeed or be 100% risk-free.
The creative process is all about taking risks, about trying out new and unknown things just to see what may or may not happen. You just gotta try even if you may fail or if what you create might not turn out quite exactly as expected.
On the other hand, the analytical mind is purely scientific. The whole concept of scientific observation is that a theory has to be proven by supporting experiences which are carefully and meticulously analyzed before the underlying theory can be accepted as a fact.
The analytical scientific mind relies solely on knowledge and experience. It doesn't sense things, it just know things are so by comparing it with past experience or learned knowledge (which is the sum of experiences accumulated by past generation which have then been passed on to us to benefit from).
The analytical mind excels in things that are known to be so, hence its inherent limitation in judging things that are so new that they are not even existing yet. If no one ever gathered data on a particular subject before or conducted any type of previous experience, that subject is totally out of its scope and will be rejected as non-existent or irrelevant. The analytical mind doesn't take risk, it only accept and embraces what it fully knows and can comprehend.
For the anecdote, it was apparently stated by some scientist of the early 20th century that according to the laws of aerodynamics of the time, the bumble bee was actually not supposed to fly. Now, could the bumble bee have been designed by someone with a very creative mind who wasn't really bothered by the 'knowledge' of the era which deemed that feat impossible? Well, more seriously... Later on, when aerodynamics science progressed some more and learned new facts, it discovered and accepted new laws that explained why the bumble bees was in fact flying, which is much the same way that helicopters can move in the air rather than the classical way airplanes fly.
That early 20th century myth illustrates the limitation of the analytical scientific mind which relies strictly on what it knows at a given time while it is almost as if the creative mind was able to time travel in the future and intuitively sense possibilities that will one day be accepted as common knowledge, even if it is not yet quite capable of presenting them in an articulate logical scientific fashion. And that is why it is ultimately able to create incredible things that were previously thought impossible or simply useless.
All this to say that in the early stages of the creativity process, it is usually important to momentarily suppress our (or someone else's) analytical mind and not trust the impossibilities and objections it hurls at our new project, which we must initially keep under a protective cocoon. Later on, once the baby has been born and the analytical mind has accepted it in the family and has realized that it does indeed belong to reality and that it cannot deny its existence anymore, that same analytical mind can then play a very important role in the refining and polishing stage. By using its vast experience and knowledge it can contribute to sand the rough hedges, and will help perfect the new creation to the completion stage.
So... trust in your inspiration and go for it!