Self-knowledge--and the new science is full of self-knowledge--is a great liberator: if perhaps it imposes some retrenchment, essentially it revives courage. Then at last we see what we are and what we can do. The spirit can abandon its vain commitments and false pretensions, like a young man free at last to throw off his clothes and run naked along the sands. Intelligence is never gayer, never surer, than when it is strictly formal, satisfied with the evidence of its materials, as with the lights of jewels, and filled with mounting speculations, as with a sort of laughter. If all the arts aspire to the condition of music, all the sciences aspire to the condition of mathematics. Their logic is their spontaneous and intelligible side: and while they differ from mathematics and from one another in being directed in the first instance upon various unintelligible existing objects, yet as they advance, they unite: because they are everywhere striving to discover in those miscellaneous objects some intelligible order and method. And as the emotion of the pure artist, whatever may be his materials, lies in finding in them some formal harmony or imposing it upon them, so the interest of the scientific mind, in so far as it is free and purely intellectual, lies in tracing their formal pattern. The mathematician can afford to leave to his clients, the engineers, or perhaps the popular philosophers, the emotion of belief: for himself he keeps the lyrical pleasure of metre and of evolving equations: and it is a pleasant surprise to him, and an added problem, if he finds that the arts can use his calculations, or that the senses can verify them; much as if a composer found that the sailors could heave better when singing his songs.