~~ 
J.—PSYCHOLOGY. 183 
attitudes and beliefs which were in vogue among physicists of that time. 
No physicists would then have dared, as now, to cast doubt on the sole 
sway of determinism in the physical world. None of them would then 
have suggested, as now, the impossibility of predicting what any individual 
atom (or still smaller individual entity) will do next. None would have 
questioned, as now, the universal truth of the second law of thermo- 
dynamics or of the principle of conservation of energy. None would have 
ventured, as now, to suppose that electrons change in the very act of 
becoming known to us, and that therefore the mental factor is ultimately 
inseparable from physical investigations. None would then have dared, 
as now, to conjecture that particles of matter correspond in their properties 
to certain growp waves of the ether, the constituent waves of which, 
travelling at an enormous speed, * guide’ and ‘direct’ the group waves 
without any energy of their own. 
In those days one of the most distinguished physicists refused to 
accept a theory unless he could make a mechanical model of it ; whereas 
to-day we are asked to believe, e.g. in an inconceivable space or ether of 
ten dimensions in order that the theory of wave mechanics may describe 
in the simplest terms what happens when three electrons meet one another. 
In those days it was urged that ‘ nothing can be more fatal to progress 
than a too confident reliance on mathematical symbols; for the student is 
only too apt... . to consider the formula and not the fact as the physical 
reality.” But to-day (whether rightly or wrongly) we have passed far 
beyond the study of mere ‘ physical realities.’ At first called in as a 
servant, the mathematician has now come ‘ to assert himself as master.’ 
“He does not ask permission from Nature when he wishes to vary or 
generalise the original premises. . . . In geometry . . . he has forgotten 
that there ever was a physical subject of the same name, and even resents 
the application of the name to anything but his network of abstract 
mathematics.’* The mathematician is not primarily interested in the 
physical significance of the variables that he is discussing. His particular 
interests lie in mathematical operations and in numbers and figures for 
their own sake. | 
Psychology has been similarly bereft of ‘reality’ by the operations 
of mathematicians, present and past. The earliest example of this was 
the derivation by Fechner of the ‘law’ which now bears his name, that 
the intensity of a sensation is proportional to the logarithm of the magni- 
tude of its stimulus. This statement was deduced by purely mathematical 
procedure from Weber’s law that just appreciable differences between 
sensations depend on a constant ratio between the magnitudes of their 
respective stimuli. Weber’s law, however, was based on direct observation 
and experiment; whereas Fechner’s ‘law’ was the outcome of purely 
mathematical calculations which not only neglected a constant appeal to 
the ‘ reality ’ of experience, but ran actually counter to it—neglectful, for 
example, of the ‘facts’ (i) that Weber’s law holds for only moderate 
_ magnitudes of stimuli ; (ii) that from the standpoint of conscious experi- 
1 Treatise on Natural Philosophy, by W. Thomson and P.G. Tait. Oxford, 1867, 
vol. i, p. viii. 
“s The Nature of the Physical World, by A. S. Eddington. Cambridge, 1929, 
pp. 161, 162. 
