This the Special Theory of Relativity does. It accepts Postulates I and II above; their consequences it deduces and interprets. For extensive demonstration of these I lack space, and this has been satisfactorily done by others so it is not my chief duty; but clearly they will be startling. For the very ray of light which refuses to recognize our relative motion is the medium through which I must observe your system and you mine. It turns out that I get different values for lengths and time intervals in your system than you get, and vice versa. And we are both right! For me to accept your "correction" were for me to admit that you are at absolute rest and I in absolute motion, that your measure of light velocity is right and mine wrong: admissions barred by the postulates. We have nothing to correct; we can only recognize the reason for the discrepancy; and knowing our relative velocity, each can calculate from his own results what the other's will be. We find, of course, that at ordinary velocities the discrepancy is many times too small for detection; but at relative velocities at all comparable with that of light it rises above the observational horizon. To inquire the "true" length is meaningless. Chicago is east of Denver, west of Pittsburgh, south of Milwaukee; we do not consider this contradictory, or demand the "true" direction of Chicago. Einstein finds that the concept of length, between points in space or events in time, does not as we had supposed represent an intrinsic property of the points or the events. Like direction, it is merely a relation between these and the observer--a relation whose value changes with the observer's velocity relative to the object. If our ideas of the part played in the world by time and space do not permit us to believe this, we must alter these ideas. Let us see how we may do this. A WORLD OF POINTS To deal with points in a plane the mathematician draws two perpendicular lines, and locates any point, as $P$, by measuring its distances, $X$ and $Y$, from these "coordinate axes." The directions of his axes acquire for him a peculiar significance, standing out above other directions; he is apt to measure the distances $X-x$ and $Y-y$ between the points $P$ and $Q$ in these directions, instead of measuring the single distance $PQ$. We do the same thing when we say that the railroad station is five blocks north and two east. The mathematician visualizes himself as an observer, located on his coordinate framework. For another observer on another framework, the horizontal and vertical distances $X'-x'$ and $Y'-y'$ between $P$ and $Q$ are different. But for both, the distance from $P$ direct to $Q$ is the same. In each case the right triangle tells us that: $$PQ = \sqrt{(X-x)^2 + (Y-y)^2} = \sqrt{(X'-x')^2 + (Y'-y')^2}$$