The stream of knowledge is heading towards a non-mechanical reality; the universe begins to look more like a great thought than like a machine. Mind no longer appears to be an accidental intruder into the realm of matter...we ought rather hail it as the creator and governor of the realm of matter.

Kant, discussing the various modes of perception by which the human mind apprehends nature, concluded that it is specially prone to see nature through mathematical spectacles. Just as a man wearing blue spectacles would see only a blue world, so Kant thought that, with our mental bias, we tend to see only a mathematical world.

...nature seems very conversant with the rules of pure mathematics, as our own mathematicians have formulated them in their studies, out of their own inner consciousness and without drawing to any appreciable extent on their experience of the outer world.

All discussion of the ultimate nature of things must necessarily be barren unless we have some extraneous standards against which to compare them.

The stream of knowledge is heading towards a non-mechanical reality; the universe begins to look more like a great thought than like a machine. Mind no longer appears to be an accidental intruder into the realm of matter...we ought rather hail it as the creator and governor of the realm of matter.

In real science a hypothesis can never be proved true...A science which confines itself to correlating phenomena can never learn anything about the reality underlying the phenomena, while a science which goes further than this and introduces hypotheses about reality, can never acquire certain knowledge of a positive kind about reality; in whatever way we proceed, this is forever denied us.

Sciences usually advances by a succession of small steps, through a fog in which even the most keen-sighted explorer can seldom see more than a few paces ahead. Occasionally the fog lifts, an eminence is gained, and a wider stretch of territory can be surveyed-sometimes with startling results. A whole science may then seem to undergo a kaleidoscopic rearrangement, fragments of knowledge sometimes being found to fit together in a hitherto unsuspected manner. Sometimes the shock of readjustment may spread to other sciences; sometimes it may divert the whole current of human thought.