Yet that is just what Haeckel has done.

With crystalline clearness he separates and reunites and arranges everything, from the primitive organic individual, that is not yet a true cell—the monera he had himself discovered—upward. Organic morphology begins with them as its first object, the first complete individuality, the first “form.” All that lies below it is beyond the province of morphology. The last conceivable organic individuality is, perhaps, the atom; and that is not the concern of morphology. We start from the organic. Above the pre-cellular individuals and the true cells the next form-unities are the organs. Above the organs, after a few subtle intermediate stages, are the “persons.” Thus a new word is given to what we have hitherto conventionally called an “individual,” when we wanted to denote a turtle, a bird, a man, or an higher animal as a whole. To this corresponds in the plant the sprout. The stage above the “person” is the “stock.” We might also call it the social individual; in the plant-world it is the tree, in the coral the coral-stock, in the human case the social combination of a number of men for common action.

We are reminded of Virchow’s speech, and how “consciousness” was dragged into the debate on the cell-state. What psychological perspectives are opened out by this doctrine of individuality! Each form-unity, each single individuality in the series, with a soul! Souls combining for common action, and forming higher psychic unities! There is no detail in Haeckel’s whole life-work in which he speaks more boldly and freely and philosophically than he does here. His lucid treatment raises to a higher stage a philosophic question that has occupied thinkers for ages.

That is the third book. The fourth takes up a different subject. Let us adopt in organic morphology this wonderful theory of individuality, the theory of stages within the form. Then let us turn to consider impartially the vast multitude of living forms. How can we now arrange this infinite confusion by merely looking at it? Artificial classification has attempted it a hundred times, and always without success. On this side there is only one way to proceed—the mathematical.

I study them with strictly mathematical figures. I determine their axes, and the mathematical aspects of their forms. Possibly that will give a practical result; the only kind of artificial system that can be accommodated with the Darwinian theory, and perhaps render it assistance by the sharpness of its lines. Does it answer? Take a crystal, a specimen from inorganic morphology. The description of it is susceptible of a strictly mathematical form. Now take a star-fish, a worm, a human being. We find that even these organic structures have a mysterious relation at bottom to certain mathematical, stereometric forms. We might almost say, to certain forms of human thought. Everything in the organic world is in a state of flux. But through the whole moving stream we can trace the outline of one stable element, something like a mathematical idea. A sort of Platonism of the living forms vaguely takes shape.

Haeckel speaks of lines, axes, circles, radii, and all kinds of rhythmic structures. It does seem that the countless individual forms of living things fit into a scheme of a limited number of mathematical forms. Strictly speaking this is not a real morphology of living things. We only find these clear and rigid forms schematically in the wild profusion of forms of the protists, plants, and animals. They are only a reminiscence of the laws of the purely inorganic, which the eye of the observer just detects as the lowest stratum. Hence Haeckel calls this section the “promorphology” of organisms.

It is true that this section, which essays to compress all living things into a very simple scheme, is the hardest to read in the whole work. A number of strange and difficult words have to be invented for this stereometric scheme to which he would reduce the animal and plant forms. Haeckel himself declared, twenty years afterwards (in the second part of the Monograph on the Radiolaria), that this stereometry of organic forms had found little favour in biology “especially on account of the difficult and complicated nomenclature.” But he had complete confidence as to the substance of it, even after so great a lapse of time.

In point of fact we have here, it seems to me, a gigantic preparatory work, not so much for the strict purpose of classification, as for a real philosophy of botany and zoology that will be founded some day. This recurrence of sharp stereometric structures, not only in the crystal, but also, if less clearly, in the biological world, will one day prove an important source of knowledge, in a sense that is not even clear in Haeckel himself.

We are already entering upon a period that has a glimpse of the truth that the deepest power of Beethoven’s music, or Goethe’s poetry, or Raphael’s painting, or Michael Angelo’s sculpture is a mysterious revelation of the most subtle mathematical relations and effects—produced without conscious perception of these relations, though a human mind is at work in them. In spite of all our “consciousness,” the obscure intuitive power at work in these human artistic achievements differs very little from the curious force with which a radiolarian builds up its little house in the deep-sea or a caseworm fits on its fine, rhythmic, snail-like coat. In both we have the same profound, crystal-like constructive power that brought forth the wings of the butterfly, the feathers of the bird, the bodily frame of all the animals and plants, that harmonises so well with strict mathematical forms. In Beethoven and Raphael it is not more conscious or unconscious, not clearer or vaguer, not more mystical or more natural, than in the poorest worm or the microscopically small radiolarian. The æsthetics of the twentieth century will take up these ideas.