A New Era of Thought

by Charles Howard Hinton

where a stands for Arctos, c for Cuspis, d for Dos, and o for Ops, and the other letters for the four axes in space. a, c, d, o are the axes of the tessaract, and can take up different directions in space with regard to us.

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Let us now take a smaller four-dimensional set. Of the 81 Set let us take the following:—

Z	X	Y	W
a	c	d	o

Second Block.
Second Floor.	-		Ocrea Mala	Tessera Mala
			Cardo Mala	Cudo Mala
First Floor.	-		Crates Mala	Cura Mala
			Thyrsus Mala	Vitta Mala
First Block.
Second Floor.	-		Uncus Mala	Pallor Mala
			Ostrum Mala	Bidens Mala
First Floor.	-		Frenum Mala	Plebs Mala
			Urna Mala	Moles Mala

Let the First Block be put up before us in Z X Y, (Urna Corvus is at the junction of our axes Z X Y). The Second Block is now one inch distant in the unknown direction; and, if we suppose the tessaractic Set to move through our space at the rate of one inch a minute, the Second will enter in one minute, and replace the first. But, instead of this, let us suppose the tessaracts to turn so that Ops, which now goes W, shall go -X. Then we can see in our space that cubic side of each tessaract which is contained by the lines Arctos, Dos, and Ops, the cube Vesper; and we shall no longer have the Mala sides but the Vesper sides of the tessaractic Set in our space. We will now build it up in its Vesper view (as we built up the cubic Block in its Alvus view). Take the Gold cube, which now means Urna Vesper, and place it on the left hand of its former position as Urna Mala, that is, in the octant Z X Y. Thyrsus Vesper, which previously lay just beyond Urna Vesper in the unknown direction, will now lie just beyond it in the -X direction, that is, to the left of it. The tessaractic Set is now in the position Za Xō Yd Wc (the minus sign over the o meaning that Ops runs in the negative direction), and its Vespers lie in the following order:—

Second Block.
Second Floor.	-		Tessara	Pallor
			Cudo	Bidens
First Floor.	-		Cura	Plebs
			Vitta	Moles
First Block.
Second Floor.	-		Ocrea	Uncus
			Cardo	Ostrum
First Floor.	-		Crates	Frenum
			Thyrsus	Urna

The name Vesper is left out in the above list for the sake of brevity, but should be used in studying the positions.

Fig. 20.