A four-dimensional continuum described by the

"co-or-di-nates" $x_{1}$ , $x_{2}$ , $x_{3}$ , $x_{4}$ , was called "world" by

Minkowski, who also termed a point-event a "world-point."

From a "happening" in three-dimensional space, physics becomes, as it were, an "existence" in the four-dimensional "world."

This four-dimensional "world" bears a close similarity to the three-dimensional "space" of (Euclidean) analytical geometry. If we introduce into the latter a new Cartesian co-ordinate system $(x_{1}^{'}, x_{2}^{'}, x_{3}^{'})$ with the same origin, then $x_{1}^{'}$ , $x_{2}^{'}$ , $x_{3}^{'}$ , are linear homogeneous functions of $x_{1}$ , $x_{2}$ , $x_{3}$ , which identically satisfy the equation ${x_{1}^{'}}^{2} + {x_{2}^{'}}^{2} + {x_{3}^{'}}^{2} = {x_{1}}^{2} + {x_{2}}^{2} + {x_{3}}^{2} .$ The analogy with eqn:(12) is a complete one. We can regard Minkowski's "world" in a formal manner as a four-dimensional Euclidean space (with imaginary time co-ordinate); the Lorentz transformation corresponds to a "rotation" of the co-ordinate system in the

four-dimensional "world."

IIIThe Experimental Confirmation of the General Theory of Relativity

From a systematic theoretical point of view, we may imagine the process of evolution of an empirical science to be a continuous process of induction.

Theories are evolved and are expressed in short compass as statements of a large number of individual observations in the form of empirical laws,

from which the general laws can be ascertained by comparison. Regarded in this way, the development of a science bears some resemblance to the compilation of a classified catalogue. It is, as it were, a purely empirical enterprise.

But this point of view by no means embraces the whole of the actual process; for it slurs over the important part played by intuition and deductive thought in the

development of an exact science. As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms. We call such a

system of thought a theory. The theory finds the

justification for its existence in the fact that it correlates a large number of single observations, and it is just here that the "truth" of the theory lies.

Corresponding to the same complex of empirical data, there may be several theories, which differ from one another to a considerable extent. But as regards the deductions from the theories which are capable of being tested, the agreement between the theories may be so complete, that it becomes difficult to find such deductions in which the two theories differ from each other. As an example, a case of general interest is available in the province of biology, in the Darwinian