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Geometric Symbols of Progress
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except along the wire; and no mode of expressing statements about distance, except on the paper. They have a vague, dawning consciousness of movement in the up and down direction, and of distance from the paper. In some, this consciousness of up and down is very much more developed than in others. In some it is so weak that they believe it to be mere illusion; in others so strong that they fancy all other modes of movement are illusion. But (we suppose) none can make definite statements about motion, except by reference to the lines on the paper. Progress upwards, therefore, is, for all of them, non-statable except in so far as it is connected with motion across the surface of the paper.

A group of them have climbed round a half-coil, beginning at the northern extremity of the longer axis; and have now arrived at its southern extremity. Their actual progress has been upwards, and amounts to half the distance between two coils; their expressed and apparent progress is the length of the longer axis of the shadow-ellipse on the paper. Whether any individual will be most conscious of his actual or of his recorded progress will depend on the condition of his individual consciousness. The condition common to them all is this:—Such progress as is actual is not recorded; and that which is recorded and registered is not actual nor permanent.

Every part of the progress which is registered will have to be unmade soon after it is made. Only that which is not registered is permanent. The particular group of creatures under our consideration first made some progress in a direction partly southward, but