wield these enchanted weapons, the shape of space itself—the mind-shape. The child's plum-pudding brings before us the unreality of all the flats that Euclid deals in, showing us that there is no halfway house between nothing and the whole ball. I am reminded of another famous dogma in which the thundering adjectives roll to and fro, from One to Three, and back from Three to One. All unawares, perhaps, the mind that gave birth to that mighty inspiration was reasoning from One Space in Three Measures to One God in Three Persons. If it be not the creed of Athanasius it is the creed of Alexandria.

Perhaps the minds for whom the word One is the truest word in speech, whether they write it Monotheism or Monism, are shallower than they think they are.

IV

Those flats of Euclid's are eye shapes, and their power over the mind is owing, not wholly to the early man's belief in a flat earth, but in some measure to that enlargement of the eye nerves which makes

our brain, as it were, lopsided. We like to think in flats; our explanation is a map. And since the world is round, the map is false, and what we gain in clearness we lose in verihood.

Here we are at the heart of this two-thousandyear-old falsehood, these lengths without breadths, these flats without thickness, this whole denial, not merely of strength, but of reality. The science of Pure Earthmeasure is the science of Tidy Shapes. Whereas we know that real shapes are always ever so little untidy; the ball is not quite round, the face is not quite flat, the line is not quite straight, the point is not so fine as nothing, and it is not quite fixed. As soon as Pure Assurance undertakes to assure us of anything beyond its own purity, lo! the triangle is no longer equilateral, and the parallel lines run together, and we have to fall back upon the landsurveyor's chain, and use compasses of wood and brass. Alas! is even the purity of Pure Assurance free from scandal? Do we not hear of negligeable quantities being brushed aside, as Pure Physics brushes its scandals into the Ether? Is not the enchanted castle of Pure Earthmeasure haunted by a restless spirit that even the wizards cannot exorcise, a ghostly circle that will not be squared?

V

The study of Unreal Measure has been called for ages a training for the mind; as though the mind were some poor sickly plant that could not grow upward unless it were nailed to a dead stick. The healthy plant grows upward in search of light, because the light draws it upward, and because it needs and feeds on light. Pity for those that cannot bear the light, that creep and cling to their dead stick, and put forth their puny blossoms in the shade. Yet greater pity for those that pine and are denied the light, that climb and are forbidden, that bud and may not flower,-for the sound crucified to save the sick.

For my part when I stand outside the Roman forcing-house, and see the gardeners inside training the plants entrusted to their care; driving their nails, and turning on their Alexandrian gas-jets, and shutting out the day, I watch them with other feelings than reverence. I see the tired heads droop in the foul air; and I want to break open the door of the forcing-house, and draw forth the nails, and turn out the gas-jets, and let in the light of heaven.

Once when I was in Delft I visited the house where William the Silent was murdered by order of the

Catholic King. And looking out of a window into the courtyard I saw some flowers in pots standing in a corner over which the shadow of the wall had crept. And while I looked a girl came out into the courtyard, and took up the flowers, one after the other, and moved them out of the shadow into the sunshine again. Then I said to myself,-Lo! here I have seen the work of William the Silent: he saw the black shadow of Spain creep over his country, and he brought his countrymen out into the light of freedom again.

To me, while I looked, this also seemed to be a work of an idealist tendency.

TWELFTH HEAD

THE CIPHER

The Bottom of the Mind. 1. Pure Reason.

2. Burla Burla. 3. Perfect Certainty. - 4. The Leak. - 5. The Child's Prayer.

Pure Earthmeasure, instead of affording a true starting point, has turned out to be a mere balloon arising from the real earth. But there is another kind of measure which seems to come before earthmeasure, more truly than Euclid's point before his lines and flats. If measure be the handmaid of knowledge, number is the handmaid of measure. Here, surely, we touch bottom; if not the bottom of the All-Thing, at least the bottom of the mind, so often mistaken for the bottom of the All-Thing. Did not Pythagoras strive to build the All-Thing out of numbers? And did not the chief architect of the Roman school, Boethius, choose ciphering for his foundation stone; for the first tread of that curriculum which the imprisoned squirrels turned round so painfully in the Logical Age?