1 Language is on plane.
2 Plane has lattice inside.
3 Each lattice’s inside is called plate.
4 Plate is given for sentence.
5 Plate has lattice inside.
6 Lattice’s inside is called tile.
7 Tile is given for word.
8 Word, sentence and language are correspondent with tile, plate and plane.
9 Tile, plate and plane are all on Gauss’ plane.
10 Tile, plate and plane are all expressed by complex numbers.
11 Word, sentence and language are all expressed by set that consists of two coordinates of complex numbers.
12 Gauss’ plane is topologically transformed to torus.
13 Plate and tile are also transformed to toruses.
14 At the transformation, lattices are prepared to vertical two (upper and lower) arrange and the two-lattices are in a row.
15At first upper lattice is taken to make torus and next the right side lower lattice is taken to make torus. The third is again upper one and fourth is lower.
16 Lattices are connected to form a necklace-shape toruses chain.
17 The necklace has continuation but does not become topological manifold for two torus’ point of contact.
18 At the reverse necklace returns to plane, plate or tile.
19 Spatially plane shape is continuous but torus is discrete by the transformation.
20 Word-necklace is put in sentence-torus. Sentence-necklace is put in language-necklace. Language-necklace is put in universe-torus.
Refer to the following paper.
Nested Torus Theory Nested Torus Theory especially C13-20 Tokyo May 27, 2006
21 Universe-torus has nested toruses in itself.
22 From word to universe, all expression is expressed by one nested torus.
Tokyo June 19, 2006
Sekinan Research Field of Language
.www.sekinan.org
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