Dear Paul, dear Giovanni,
Paul, you developed and explained well my affirmation that "searching a TOE is no more "faith-based" than doing physics in general", and you provided in the mean time your own interesting view.
You said:
"The main problem with current searches for the Theory of Everything is that one must have a sufficient base of observational data to allow such a theory to be reasonably determined and at this time there still is a lack of adequate observational information and adequate interpretations of currently available information to allow man to adequately resolve the base structure to the degree necessary to find the base equations."
Let us say, for simplification, that we are trying to induce general laws from particular measurements of a system, for example to find how a quantity y depends on another quantity x. We draw some dots, representing (x1, y1), (x2, y2),..., (xn, yn) and then try to find a function f which connects them, so that yi=f(xi). Let's consider that our measurements are precise, and that the dependence of y on x is exact. In this case, there is a large set of possible functions f which fits through all the data, and each new data helps us eliminating them. But new data doesn't necessarily help us too much coming with an equation y=f(x).
What I mean is that we have too much data, not too little, and it is difficult, if not impossible for us to handle it in order to induce the fundamental laws. In time, we may try many sets of laws which fit this data. Any new observation will help us filtering the theories we proposed until that date. So, I see two stages (I am simplifying much the problem, to emphasize the idea):
1. find all possible functions f which fits all the data, let's say {f1, f2, ...fk}
2. conduct new experiments covering as much x data as possible, to eliminate some of the functions f, hopefully all but one.
The first point is difficult for us because of the complexity of the data. When we will have the first possible f, we can say we have a candidate unified theory. But it is impossible to have all. After that, if we have two or more such candidates, we go to the step 2, but we cannot cover all possible x data. We will make our choice by considering the predictions of the possible candidates so far: we conduct experiments for some x for which fi(x) and fj(x) are not equal. So I would replace 1 and 2 with
1'. find some possible functions f which fits all the data, let's say {f1, f2, ...fk}
2'. conduct new experiments covering some x data which can differentiate between the candidates proposed at 1'
with the mention that it is possible that the new data inspire us to add new candidates, so perhaps we will cycle between 1' and 2'.
I think that, if we don't have all the data available, we should, in principle, be able to create more unified theories. Our present data clearly is fitted by f0, the true set of laws. So, an intellect powerful enough (infinitely powerful?) should be able to find at least one candidate, f0, to which we may add some other possible candidates which fit the present data, but which can be invalidated in the future. It is even possible to have more than one f0 which fits our universe, but there is at least one.
Well, if we believe that the word is mathematical, we can find instead of f1, f2, ..., some classes F1, F2, ... containing all the f1, f2, .... On example is the class of all mathematical structures (Tegmark). Another one, more fitted to the physical theories, is defined in my World Theory. But these classes are too generic, they contain both structures which fit all the data we have, and structures which don't fit it, and we have no way of picking among the infinite number of such structures the good ones. Having such a way, will help us to realize at least the step 1, if not 1'.
Best regards,
Cristi