How assumption and basic theory can be used to solve a problem (upon request from a friend, I wrote this, this just fits into a long discussion we had about assumption in social and scientific situations)
Lets say, we have a basic problem at hand. The problem is amenable to a solution based on basic theory. Its quite straight forward. We have a method of attacking the problem. We apply the method to find a solution. eg solve a quadratic equation, solve a trajectory problem using either classical mechanics or relativity theory.
There are basic theory for solving a problem and the scope of such theory is quite well defined. On the other hand while solving a problem where there is a basic theory but some of the parameters could be missing so as to get a specific solution we may need to make an assumption to get at a specific answer.
eg in quantum mechanics which gives rise to differential equations and boundary conditions one may encounter a situation where one has to assume a part of the solution and then reach a specific solution. If the solution is physical and consistent our assumption is valid or else, as you remark, we change our assumption a bit more, this assumption although, will need a lot of smart thinking.
Now this also occurs in experimental research where one assumes or hypothesize a process and inputs values already known for part of the process or a particular variable in the process. Then as a whole one solves the problem and may reach at one or more than one solutions. One may also find a bunch of process whose solution is quite different from the one in question. Our assumption is invalid for such processes and therefore leads to answer that are not physical. We may not even reach a solution where there is any physical significance.
So, you see, assumption could be very valuable in real world science. The last example I gave you directly cuts into my research. Sometimes it takes months or year to form a valid assumption. Assumption is not wishful thinking by the way. Thats the point I have been trying to get at.