What we would like is some development of mathematics by which the equations could be made to cease to have meaning outside the range of numerical magnitude in which the physical concepts themselves have meaning. In other words, the problem is to make our equations correspond more closely to the physical experience back of them; it evidently needs some sort of new invention to accomplish this. We return later, in discussing Lorentz's equations of electrodynamics, to the disadvantages arising from the present undiscriminating character of mathematics. In the meantime, we must recognize that there are very important advantages here, as well as disadvantages. All experience justifies the expectation that the laws of nature with which we are already familiar hold at least approximately and without violent change in the unexplored regions immediately beyond our present reach. By assuming an unlimited validity for the laws as we now know them, mathematics enables us to penetrate the twilight zone, and make predictions which may be later verified. It is only when we are carried too far afield that we must deprecate this characteristic of our mathematics. There is another aspect of the use of mathematics in describing nature that is often lost sight of; namely, that any system of equations can contain only a very small part of the actual physical situation; there is behind the equations an enormous descriptive background through which the equations make connection with nature. This background includes a description of all the physical operations by which the data are obtained which enter the equations. For instance, when Einstein formulates the behavior of the universe in terms of the world lines of events, the events as they enter the equations are entirely colorless things, merely 3 space and 1 time coördinate. To make connection with experience there must be a descriptive background giving the physical contents of the events; for example, there may be the statement that some of the events are light signals. This descriptive background is supposed to remain fixed, unaffected by any operations to which the equations themselves are subject. If, for example, the frame of reference of the equations is altered by changing its velocity, the physical significance of the descriptive background is supposed to remain unaltered, or rather no mention is usually made of this question at all. It would seem, however, that this matter needs some discussion. The descriptive background gets its meaning only in terms of certain physical operations. If the descriptive background remains unaltered when the uniform velocity of the frame of reference is changed, for instance, this means that the motion of the frame of reference does not at all affect the possibility of carrying out certain operations. This is pretty close to the restricted principle of relativity itself, which states that the form of natural laws is not affected by uniform velocity.