A New Era of Thought

by Charles Howard Hinton

CHAPTER VIII.
REPRESENTATION OF FOUR-SPACE BY NAME. STUDY OF TESSARACTS.

We have now surveyed all the preliminary ground, and can study the masses of tessaracts without obscurity.

We require a scaffold or framework for this purpose, which in three dimensions will consist of eight cubic spaces or octants assembled round one point, as in two dimensions it consisted of four squares or quadrants round a point.

These eight octants lie between the three axes Z, X, Y, which intersect at the given point, and can be named according to their positions between the positive and negative directions of those axes. Thus the octant Z, X, Y, is that which is contained by the positive portions of all three axes; the octant Z, X, Y, that which is to the left of Z, X, Y, and between the positive parts of Z and Y and the negative of X. To illustrate this quite clearly, let us take the eight cubes—Urna, Moles, Plebs, Frenum, Uncus, Pallor, Bidens, Ostrum—and place them in the eight octants. Let them be placed round the point of intersection of the axes; Pallor Corvus, Plebs Ilex, etc., will be at that point. Their positions will then be:—

Urna	in the	Octant	Z	X	Y
Moles	„	„	Z	X	Y
Plebs	„	„	Z	X	Y
Frenum	„	„	Z	X	Y
Uncus	„	„	Z	X	Y
Pallor	„	„	Z	X	Y
Bidens	„	„	Z	X	Y
Ostrum	„	„	Z	X	Y

The names used for the cubes, as they are before us, are as follows:—

Third Block.
Third Floor.	-		Arcus Mala	Ovis Mala	Portio Mala
			Laurus Mala	Tigris Mala	Segmen Mala
			Axis Mala	Troja Mala	Aries Mala
Second Floor.	-		Postis Mala	Clipeus Mala	Tabula Mala
			Orcus Mala	Lacerta Mala	Testudo Mala
			Verbum Mala	Luctus Mala	Anguis Mala
First Floor.	-		Telum Mala	Nepos Mala	Angusta Mala
			Polus Mala	Penates Mala	Vulcan Mala
			Cervix Mala	Securis Mala	Vinculum Mala
Second Block.
Third Floor.	-		Ara Mala	Vomer Mala	Pluma Mala
			Praeda Mala	Sacerdos Mala	Hydra Mala
			Cortex Mala	Mica Mala	Flagellum Mala
Second Floor.	-		Pilum Mala	Glans Mala	Colus Mala
			Ocrea Mala	Tessera Mala	Domitor Mala
			Cardo Mala	Cudo Mala	Malleus Mala
First Floor.	-		Agmen Mala	Lacus Mala	Arvus Mala
			Crates Mala	Cura Mala	Limen Mala
			Thyrsus Mala	Vitta Mala	Sceptrum Mala
First Block.
Third Floor.	-		Mars Mala	Merces Mala	Tyro Mala
			Spicula Mala	Mora Mala	Oliva Mala
			Comes Mala	Tibicen Mala	Vestis Mala
Second Floor.	-		Ala Mala	Cortis Mala	Aer Mala
			Uncus Mala	Pallor Mala	Tergum Mala
			Ostrum Mala	Bidens Mala	Scena Mala
First Floor.	-		Sector Mala	Hama Mala	Remus Mala
			Frenum Mala	Plebs Mala	Sypho Mala
			Urna Mala	Moles Mala	Saltus Mala

Their colours can be found by reference to the Models 1, 9, 2, which correspond respectively to the First, Second, and Third Blocks. Thus, Urna Mala is Gold; Moles, Orange; Saltus, Fawn; Thyrsus, Stone; Cervix, Silver. The cubes whose colours are not shown in the Models, are Pallor Mala, Tessera Mala, and Lacerta Mala, which are equivalent to the interiors of the Model cubes, and are respectively Light-buff, Wooden, and Sage-green. These 81 cubes are the cubic sides and sections of the tessaracts of an 81 tessaractic Set, which measures three inches in every direction. We suppose it to pass through our space. Let us call the positive unknown direction Ana (i.e., +W) and the negative unknown direction Kata (-W). Then, as the whole tessaract moves Kata at the rate of an inch a minute, we see first the First Block of 27 cubes for one minute, then the Second, and lastly the Third, each lasting one minute.

Now, when the First Block stands in the normal position, the edges of the tessaract that run from the Corvus corner of Urna Mala, are: Arctos in Z, Cuspis in X, Dos in Y, Ops in W. Hence, we denote this position by the following symbol:—

Z	X	Y	W
a	c	d	o