[Footnote 2: The relativity theory does not suggest that there is such a thing in nature as a four-dimensional space. The whole object of the recognition of the four-dimensional world is to eliminate the harassing frame of space.] [Footnote 3: The inclination must not exceed a certain limit. This limiting angle may be regarded as a fundamental constant of the world-structure, and owing to its fundamental character it appears in many kinds of phenomena; for example, it determines the velocity of propagation of light. The instant on the sun which is simultaneous with a given instant on the earth is indeterminate (varying according to the space and time frame employed) but only within a range of 16 minutes. Any event on the sun happening before this 16 minutes is _absolutely_ in the past, all observers agreeing on this point; in fact it would be possible for us to have already received a wireless message announcing its occurrence. Events after the 16 minutes are in the _absolute_ future. The neutral zone which is (absolutely) neither past nor future becomes proportionately wider as the distance increases; at the nearest fixed star it extends to 8 years, and at the most distant stars yet known it reaches 400,000 years.] [Footnote 4: The three events must not be at the same place since that would give a time-_line_ not a triangle. The clock must move so that the two events whose time-distance is to be determined both happen where it is, just as the scale must be directed so that the two points fall on it. You are not allowed to 'bend' the clock, i. e. apply force so as to make it move with other than uniform velocity, any more than you are allowed to bend the scale by applying force.] [Footnote 5: Of course, it is not true that _any_ two sides are less than the third side. A clock, unlike a scale, can only measure in one direction, viz. from past to future, so that the sides _AB_ + _BC_ and _AC_ can be chosen in only one way.] [Footnote 6: This involves only a comparatively trifling generalization of Euclidean geometry, not to be confused with the 'non-Euclidean' geometry introduced later in the lecture.]