SENSATION AND PERCEPTION 123 



comes from muscular activities : The measurement of the 

 diameter of a fixed star involves the adjustment of scales in the 

 astronomer's apparatus and this is no different in principle than 

 the muscular activities and adjustments in the optical axes of the 

 eyes when we look at more or less distant objects. 



And all cosmic spatial estimates are also based on bodily move- 

 ments. All such estimates make start from a terrestrial " base- 

 line " which is only a distance along which a man can walk in 

 an hour or so. It is true that the distance is measured with 

 extraordinary accuracy — far more so than could be attained merely 

 by " stepping-off " the base-line. The standard of distance is 

 a " made " thing which we take as unchangeable. Just as the 

 standard duration is that, between two successive transits of a 

 fixed star so the standard distance is that of a metal rod 

 ('* corrected " for temperature). Two or more of these rods are 

 laid end to end and their " ends " are not placed in contact but 

 are laid near to each other and the distances between them are 

 measured by a microscope. We obtain these latter space-intervals 

 again by the adjustment of scales, that is by bodily muscular 

 activities. The rods are put end to end in a " straight line " 

 between the extremities of the base-line and the straightness is 

 that of the ray of light passing between telescopes at the ends 

 of the base-line. The ends of the rods are adjusted (by screws, 

 scales, etc.) so as to lie in this straight line. All further trigono- 

 metrical and celestial space-estimates involve the use of this base- 

 line and the adjustments, by bodily muscular activities of apparatus 

 that are really artificial receptors. 



43/. The " Forms " of Space and Time. The mathematical 

 space (of the Newtonian period) was 3-dimensional. There was 

 motion in space from side to side along the axis — x < — o — > + x 

 (parallel to the lower margin of this page), motion in space, up 

 and down, along the axis — y < — — > + y (parallel to the 

 right-hand margin of this page) and motion in space backwards 

 and forwards, along the axis — z < — — > + ^ (perpendicular 

 to the page). Mathematical expressions involving these motions 

 were the same in form irrespective of the -|- ve and — ve signs 

 (except when negative quantities might become positive ones 

 by squaring). Thus mathematical space, or extension, was 

 *' isotropic," or the same in any direction. 



