Apparently you are the only person to respond to my post. I do not know if that means that no one has a criticism or that they all think it is not worth responding to. I know you are very open to the idea of working with a specific definition so I really didn't expect any criticism to speak of from you. Thanks for responding anyway.
However, I'm still curious as to what that has to do with preparing oneself to solve a problem. Are you saying you are justified in assuming that every problem can be expressed in a rational way?
Fundamentally I am! I guess what the issue is here is the existence of the problem itself. I think I would say that, if you cannot express the problem in a rational way, you don't know what the problem is. But maybe someday someone will understand the problem you are having a problem with and then what I have to say will be applicable. This is a matter of opinion, not fact. All I can do is lay out my thoughts.
I suppose not, I suppose you actually mean that only those problems you have to think about can be expressed in a rational way. Am I correct? There's still a whole lot of problems out there which cannot be solved rationally, and for which we rely on intuition or commonsense.
Now this goes exactly to my comment "So I guess this tirade has to do with the fact that you all expect too much!" I am of the opinion that, when one goes to think something out, the moment they take a step which they cannot defend well, anything concluded down the line is suspect. As Harv points out, we cannot think about things without presuming our present understandings are correct. It follows that all of our thoughts are highly suspect (and it's even worse then Harv thinks it is).
Thus it is that I propose we let our subconscious solve those problems. Certainly our subconscious can do a much better job than we can even conceive of doing on a conscious level. The best and most dependable authority you will ever come in contact with is what you are calling your intuition. And all the "problems" you can conceive of are beyond your ability to solve "in a rational way" except for a precious few. The most rational thing you can do is to see the world around you as a playground created by your subconscious to keep you busy while it handles the big problems which I am afraid are far beyond your capabilities.
So my advice? Relax and enjoy life; it could be a lot worse. And think a little when you get around to it, it's fun.
Still, your paper seems to deal with a very specific rational problem, not a generic one.
No, my paper deals with the generic one. My discovery deals with a very specific problem. As I say, "you guys expect far too much!"
The problem, in my understanding, concerns the probability of observing a particular pattern given a finite sample. I would hardly call that a generic problem, but perhaps I'm going too far ahead. I'll wait and see what others have to say.
Yeh, I think you are getting ahead; but if you are going to wait and see what the others have to say, we might as well go home to our wives. There are some problems there which are far beyond my comprehension which I nonetheless enjoy exploring.
Have fun -- Dick