the appearances for all possible states of uniform motion of the observer. The result was to add another dimension to the world, making it four-dimensional. Next the synthesis was extended to include all possible variable motions of the observer. The process of adding dimensions stopped, but the world became non-Euclidean; a new geometry called Riemannian geometry was adopted. Finally the points of view of observers varying in size in any way were added; and the result was to replace the Riemannian geometry by a still more general geometry described in the last chapter.
The search for physical reality is not necessarily utilitarian, but it has been by no means profitless. As the geometry became more complex, the physics became simpler; until finally it almost appears that the physics has been absorbed into the geometry. We did not consciously set out to construct a geometrical theory of the world; we were seeking physical reality by approved methods, and this is what has happened.
Is the point now reached the ultimate goal? Have the points of view of all conceivable observers now been absorbed? We do not assert that they have. But it seems as though a definite task has been rounded off, and a natural halting-place reached. So far as we know, the different possible impersonal points of view have been exhausted—those for which the observer can be regarded as a mechanical automaton, and can be replaced by scientific measuring-appliances. A variety of more personal points of view may indeed be needed for an ultimate reality; but they can scarcely be incorporated in a real world of physics. There is thus justification for stopping at this point but not for stopping earlier.
It may be asked whether it is necessary to take into account all conceivable observers, many of whom, we suspect, have no existence. Is not the real world that which comprehends the appearances to all real observers? Whether or not it is a tenable hypothesis that that which no one observes does not exist, science uncompromisingly rejects it. If we deny the rights of extra-terrestrial observers, we must take the side of the Inquisition against Galileo. And if extra-terrestrial observers are admitted, the other observers, whose results are here combined, cannot be excluded.
