INTUITION

Common sense, immersed in the mere business of living, knows no more about life than a fish knows about water.  The play of reason upon phenomena dissects life, and translates it in terms of inertia.  The pure logic of mathematics ignores life and disdains its limitations, leading away into cold, free regions of its own.  Now our desire for freedom is not to vibrate in a vacuum, but to live more abundantly. Intuition deals with life directly, and introduces us into life’s own domain:  it is related to reason as flame is related to heat.  All of the great discoveries in science, all of the great solutions in mathematics, have been the result of a flash of intuition, after long brooding in the mind. Intuition illumines.  Intuition is therefore the light which must guide us into that undiscovered country conceded by mathematics, questioned by science, denied by common sense—­The Fourth Dimension of Space.

OUR SENSE OF SPACE

Space has been defined as “room to move about.”  Let us accord to this definition the utmost liberty of interpretation.  Let us conceive of space not alone as room to move ponderable bodies in, but as room to think, to feel, to strike out in unimaginable directions, to overtake felicities and knowledges unguessed by experience and preposterous to common sense.  Space is not measurable:  we attribute dimensionality to space because such is the method of the mind; and that dimensionality we attribute to space is progressive because progression is a law of the mind.  The so-called dimensions of space are to space itself as the steps that a climber cuts in the face of a cliff are to the cliff itself.  They are not necessary to the cliff:  they are necessary only to the climber.  Dimensionality is the mind’s method of mounting to the idea of the infinity of space.  When we speak of the fourth dimension, what we mean is the fourth stage in the apprehension of that infinity.  We might as legitimately speak of a fifth dimension, but the profitlessness of any discussion of a fifth and higher stages lies in the fact that they can be intelligently approached only through the fourth, which is still largely unintelligible.  The case is like that of a man promised an increase of wages after he had worked a month, who asks for his second month’s pay before he is entitled to the first.

THE SUBJECTIVITY OF SPACE

Without going deep into the doctrine of the ideality—­that is, the purely subjective reality—­of space, it is easy to show that we have arrived at our conception of a space of three dimensions by an intellectual process.  The sphere of the senses is two-dimensional:  except for the slight aid afforded by binocular vision, sight gives us moving pictures on a plane, and touch contacts surfaces only.  What circumstances, we may ask, have compelled our intellect to conceive of solid space?  This question has been answered as follows: