Theories are compelled to pass more and more from the inductive to the deductive method, even though the most important demand to be made of every scientific theory will always remain: that it must fit the facts.

We now reach the difficult task of giving to the reader an idea of the methods used in the mathematical construction which leads to Einstein's general theory of relativity and to the Space Quantum Field Theory.

The general problem is: Which are the simplest formal structures that can be attributed to a four-dimensional continuum and which are the simplest laws that may be conceived to govern these structures? We then look for the mathematical expression of the physical fields in these formal structures and for the field laws of physics - already known to a certain approximation from earlier researches - in the simplest laws governing this structure.

The conceptions which are used in this connection can be explained just as well in a two-dimensional continuum (a surface) as in the four-dimensional continuum of space and time. Imagine a piece of paper ruled in millimeter squares. What does it mean if I say that the printed surface is two-dimensional? If any point P is marked on the paper, one can define its position by using two numbers. Thus, starting from the bottom left-hand corner, move a pointer toward the right until the lower end of the vertical through the point P is reached. Suppose that in doing this one has passed the lower ends of X vertical (millimeter) lines. Then move the pointer up to the point P passing Y horizontal lines. The point P is then described without ambiguity by the numbers X Y (coordinates). If one had used, instead of ruled millimeter paper, a piece which had been stretched or deformed the same determination could still be carried out: but in this case the lines passed would no longer be horizontal or vertical or even straight lines. The same point would then, of course, yield different numbers, but the possibility of determining a point by means of two numbers (Gaussian coordinates) still remains. Moreover, if P and Q are two points which lie very close to one another, then their coordinates differ only very slightly. When a point can be described by two numbers in this way, we speak of a two-dimensional continuum (surface).

The general relativity theory that brought together the metric and gravitation would have been completely satisfactory of the world had only gravitational fields and no electro-magnetic fields were taken into consideration. But it is not true that the latter can be included within the general theory of relativity by taking over and appropriately modifying Maxwell's equations of the electro-magnetic field. The gravitational fields have a structural property of the space - time continuum and is logically of an independent construction. The two types of field can not be causally linked in this theory or fused to an identity. It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds, and it is natural to suspect that this only appears to be so because the structure of the physical continuum is not completely described by the Riemannian metric.

The new Space Quantum Expanding Field Theory removes this fault by displaying both types of field as manifestations of one comprehensive type of spatial structure in the space-time continuum. The stimulus to the new theory arose from the discovery that space is quantized and in a state of expansion. My opinion is that our space-time continuum has a structure of the kind vastly different than the one now contemplated.