1921 .] 
Farr.—Relativity. 
243 
this idea clear to you simply because we have not been given the faculty 
of perceiving it, any more than the circle had been given the power to 
perceive height. Up to the time the sphere came and lifted him out 
of the flat plane which had been to him the universe, it (height) had 
been altogether outside his experience. But, though he had not experienced 
it, there was nothing to prevent him (he being a highly.organized individual 
of many sides)—there was nothing to prevent him thinking about it, and 
even working out problems about it. And that is just what Minkowski 
and other mathematicians have been doing. They have asked themselves, 
“ Suppose events were to happen in such a world of four dimensions, and 
suppose these events were to be watched by a being who lived in three- 
dimensional space, and who had no mental consciousness of the fourth, 
what would this three-dimensional being see ? ” And Minkowski has 
shown that the bodies moving in such four-dimensional space would seem 
to perform the most extraordinary antics to the three-dimensional looker- 
on. The lengths of bodies would seem to depend upon the speed and 
directions in which they moved through dimensional space. Their masses 
would alter, and all the things that we have seen that we must believe 
to be happening, if we are to explain the universe on a scheme of 
three dimensions, would also seem to be happening. And this is true 
not only in “ character ” of the extraordinary happenings, but also in 
their “ magnitude. 55 Thus, if we consider with Minkowski that the universe 
is in reality a four-dimensional manifold, or continuum, or entity, whereas 
we ordinary mundane beings are compelled to be conscious of only three, 
the conspiracy of silence which we seemed to invariably come across in 
all our efforts to determine the speed of the earth through the ether 
disappears. And, as I have said, this fourth dimension is a kind of time, 
though not time as we know it. In the now most famous words of 
Minkowski, if these things should prove from the experiments and measure¬ 
ments to be so, then, “ Henceforth space and time in themselves vanish 
as shadows, and only a kind of union of the two preserve an independent 
existence.” For as we can, and do, choose any one of the three directions 
that we know so well in this world of appearance and call it height, or 
length, or breadth, as the case may be, and as the three are, and must be, of 
the same nature, so in Minkowski’s more complicated and unfamiliar space 
we could choose any direction and call it a “ sort of time,” or a length, as 
we pleased. There is nothing to distinguish the one from the other. 
Now, whilst we have seen that this four-dimensional space of Minkowski 
is capable of giving a natural explanation of the extraordinary lengthenings 
and shortenings of bodies, and the not less puzzling shortenings and 
lengthenings of times which have to be imposed upon the duration of 
■events, which Fitzgerald, Lorentz, Larmor, and others have shown would be 
necessary if we are to explain things by reference to the three-dimensional 
space that we know—while, I say, we get a more 4 ‘ natural ” explanation 
in this way, yet we must not fall into the much too common error of 
saying, “ It may be so, and therefore it is.” We must not accept such 
an hypothesis, however elegant and satisfying the explanation by means of 
it may be, without exhausting all available means of securing a direct check. 
A scientific man has no brief for any explanation except the right one, and 
he recognizes that any explanation he may give, and which may com¬ 
pletely cover the facts known to-day, may require alteration and amend¬ 
ment to-morrow when new facts are very possibly by its aid discovered. 
A touch here and an improvement there to bring it into line with recent 
discoveries, and he hopes by this means to approach truth asymptotically, 
