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Landstead Ternary Symbols and Their Meanings

This page is part of the resources for Turn-of-the-Century Toughs, a cycle of alternate history series about adults and youths on the margins of society, and the people who love them. Set in the nineteenth and twentieth centuries, the novels and stories take place in an alternative version of America that was settled by inhabitants of the Old World in ancient times. As a result, the New World retains certain classical and medieval customs.

Sections below:
* Table of symbols.
* What the ternary system means in the Dozen Landsteads.
* What the circle means in the Dozen Landsteads.
* Telecommunication, computer language, and different ways to represent Carr's name.
* Which parts of all this occur in our own world.

Updated October 2015.

Table of symbols

stead ternary symbols (ancient form)
Landstead ternary symbols (heliograph) Numbers (in the number symbolism of our world) Alphabet (in the alphabet symbolism of our world) Landstead Calendar: Months Landstead Calendar: Weeks Gregor-
ian Cal-
endar (in our world)
--- Red Red Red
N Spring End Spring Waning (beginning of spring term) Jan.
--0 Red Red Blue -12 O Spring Illness Jan.
--+ Red Red Green -11 P Spring Dying Jan.-
-0- Red Blue Red -10 Q Spring Middle Spring Death Feb.
-00 Red Blue Blue -9 R Spring Transformation (Approximate date of the Masters' Spring Festival; High Masters' council meets; end of spring term) Feb.-
-0+ Red Blue Green -8 S Spring Rebirth March
-+- Red Green Red -7 T Spring Beginning Spring Childhood March-
-+0 Red Green Blue -6 U Spring Youth April
-++ Red Green Green -5 V Spring Manhood April
-- Red Red -4 W Summer End Summer Waning (beginning of summer term) May
-0 Red Blue -3 X Summer Illness May
-+ Red Green -2 Y Summer Dying May-
- Red -1 Z Summer Middle Summer Death June No.
0 Blue 0 ~ Summer Transformation (New Year; High Masters' council meets; end of summer term) June-
False and/or True.
+ Green 1 A Summer Rebirth July Yes.
+- Green Red 2 B Summer Beginning Summer Childhood July-
+0 Green Blue 3 C Summer Youth Aug.
++ Green Green 4 D Summer Manhood Aug.
+-- Green Red Red 5 E Autumn End Autumn Waning (beginning of autumn term) Sept.
+-0 Green Red Blue 6 F Autumn Illness Sept.
+-+ Green Red Green 7 G Autumn Dying Sept.-
+0- Green Blue Red 8 H Autumn Middle Autumn Death Oct.
+00 Green Blue Blue 9 I Autumn Transformation (Approximate date of the Slaves' Autumn Festival; High Masters' council meets; end of autumn term) Oct.-
+0+ Green Blue Green 10 J Autumn Rebirth  Nov.
++- Green Green Red 11 K Autumn Beginning Autumn Childhood Nov.-
++0 Green Green Blue 12 L Autumn Youth Dec.
+++ Green Green Green 13 M Autumn Manhood Dec.

What the ternary system means in the Dozen Landsteads

Historians cannot agree whether the Dozen Landsteads' ternary (base 3) system grew out of the Landsteaders' traditional three-field agricultural system, or whether instead it was inspired by the three primary tenets of the Landstead faith: death, transformation, and rebirth. In any case, a large proportion of Landstead concepts are grouped into threes or multiples of threes.

The Dozen Landsteads' tri-years are divided into three planetary circuits around the sun (Fallow, Barley, and Clover), its sun-circuits are divided into three seasons, and its seasons are divided into three months of three weeks, for a total of 27 weeks (3 x 3 x 3).

For more about the Dozen Landsteads' calendar, see: Old Calendar.

The Dozen Landsteads' number/letter system is a ternary system, using three digits (-, 0, and +), in the same way that we use ten digits (0, 1,  2, 3, 4, 5, 6, 7, 8, and 9) and most computers in our world use two digits (0 and 1). As can be seen below, this system of numbers/letters was extended by Landsteaders into the realm of long-distance communications and computing. Thus it is no coincidence that the Dozen Landsteads' equivalent of a computer byte (2 x 2 x 2 = 8 digits) is a tryte (3 x 3 x 3 = 27 digits).

What the circle means in the Dozen Landsteads

The most striking way in which the Landstead ternary system differs from our own system of numbers and letters is that it is based on a circle rather than a straight line. (This can be seen most clearly from the fact that the alphabet wraps around on itself.) In our world, only time (the clock and calendar) is usually represented in circles, while increasingly that circular representation is being abandoned in favor of linear representation (for example, the digital clock). Likewise, our alphabet is almost invariably represented on a straight line rather than on the perimeter of a circle. And though we do acknowledge the existence of negative and positive numbers, we don't think of them as circling back on each other. This way of thinking clearly arises out of the Landstead belief that death (the end) is followed by transformation (the middle) and rebirth (the beginning). That belief may have been influenced by the seasonal cycle of the sun-circuit.

Telecommunication, computer language, and different ways to represent Carr's name

The English language is considered to be a particularly rich language because its words often have many different meanings which resonate at different levels. (Ancient Greek is an even more striking example of this phenomenon.) Similarly, Landstead ternary symbols have so many different meanings that any single word is practically a work of poetry in itself, regardless of its base meaning.

As an example of the way in which this pervasive use of the ternary system provides rich layers of meaning to the symbols, let's look at the name "Carr." Its base meaning is "from the wetlands." However, the word would have many other meanings to a Landsteader, simply because of how it was represented in the Landstead ternary sytem.

Carr's name appears as follows in the ancient Landstead alphabet. (The modern alphabet, not shown here, is simply a cursive form of the ancient alphabet.)

C =  +0
A =   +
R = –00
R = –00

The symbols of the alphabet also represent numbers, so Carr's name (much to the delight of numerologists) has a numeric equivalent:

C =  +0 =  3
A =   + =  1
R = –00 = –9
R = –00 = –9

The three digits of the ternary system (– and 0 and +, named hyphen and circle and cross) can be represented by colors:

– = Red
0 = Blue
+ = Green

These colors became vitally important in the development of telecommunication in the Dozen Landsteads, because the colors became the basis for the Landsteaders' code systems.

The original means of long-distance communication in the Dozen Landsteads was the heliograph, invented in the 1870s, which flashed beams of sunlight, moonlight, or limelight through colored filters. The heliograph code used in the Dozen Landsteads was ternary, using successive flashings of red, blue, and green lights to represent letters/numbers.

In the First Landstead, this was succeeded (upon that territory's precociously early invention of fiber optics and lasers in the 1930s) by the optic telegraph, which used the same color symbols as the heliograph. The heliograph and optic telegraph symbols for Carr's name are as follows:

C =  +0 = Green Blue
A =   + = Green
R = –00 = Red Blue Blue
R = –00 = Red Blue Blue

The telegraph symbols later became the basis of the code developed in the First Landstead for use in that territory's optical computers. Computer trits (computer ternary digits) consist of red, blue, and green lasers, which are flashed in succession, just as the earlier telegraph codes were. The most common trytes (a group of 27 trits) are based on the telegraph symbols, but with blues (zeros) added at the beginning of each tryte to fill up all the spaces until nine trits are reached. The trytes for Carr's name are as follows:

C = Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue.

A = Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green.

R = Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue.

R = Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue.

A more compact and easily memorable way for the name to be displayed by a computer to humans is through the use of a Landstead calendar circle. Calendar circles are divided into 27 parts to show the 27 weeks of the year, the 27 letters of the alphabet, and the 27 basic numbers that appear in the multiplication tables (-13 through 13).

These calendars are extensively used in Landstead primary schools to teach the calendar, the alphabet, and the number system. Thus any Landsteader immediately knows that a light just to the left of the bottom of a calendar circle represents the Landstead equivalent of the letter A.

Therefore, Carr's name could be shown by a computer through the successive flashing of four pie-segmented lights in a circle, corresponding to these four weeks:

C = Summer Youth (3 weeks after midsummer)
A = Summer Rebirth (1 week after midsummer)
R = Spring Transformation (9 weeks before midsummer)
R = Spring Transformation (9 weeks before midsummer)

The week positions simply represent visually the numbers that Carr's name corresponds to:

 3 = C =  +0 = Green Blue
 1 = A =   + = Green
-9 = R = –00 = Red Blue Blue
-9 = R = –00 = Red Blue Blue

. . . which brings us (appropriately) full circle back to where this discussion began.

Which parts of all this occur in our own world

Ternary (base 3) numbering systems really exist. The one used in the chart above is a system called balanced ternary notation. Balanced ternary allows for easy arithmetic operations. Unlike the binary code used in computers, balanced trinary has an built-in system for showing negatives.

One of the earliest mechanical calculators, built in 1840 by Thomas Fowler, did ternary calculations. In the 1950s, a Moscow State University scientist designed a computer, Setun, which used balanced ternary. In 1970, a successor, Setun 70, used trits and trytes (though they weren't the same size as the trits and trytes I cite above).

In the late 1960s, two optical computers were invented: the IBM 1360 Photo-Digital Storage System (also known as Photostore) and the FM 390 (designed by Foto-Mem). The FM 390 was intended to use lasers to record information on standard microfiche cards, but it was never built. The IBM 1360, which placed data on film through use of an electron gun, became the world's first storage device to hold a terabit of data (approximately 160 gigabytes). More recently, our world is in the process of developing optical computers using lasers, though, as far as I know, they all use the binary system.

Heliographs (using white light) were invented in our world in the 1870s and were used by the British and American armies to transmit Morse code. Morse code, which was developed in the 1830s, used dots, dashes, and space to represent numbers and letters.

Similarly, braille (invented in 1824) uses dots and spaces to represent letters and numbers. In braille, as in Ancient Greek and Hebrew, letters double as numbers.

The number of seasons, months, and weeks have varied in our world according to which calendar system is used. The Roman calendar, which originally had ten months, included months whose names corresponded to their numbers: September (seventh month), October (eighth month), November (ninth month), and December (tenth month).

Red, blue, and green are the primary additive colors: that is, the primary colors that can be combined to make up white light. In our world, two primary additive colors (red and green), along with their mixture (yellow), are used in traffic signs to designate Stop, Caution, and Go.

Ternary logic in our world has three values. In the balanced ternary sytem, they look like this:

– = False
0 = False or True
+ = True

The "fallow, barley, clover" definitions mentioned above refer to the three-field farming system used in the Middle Ages: one field was planted with grain such as barley, one field was planted with legumes such as clover (which restored the soil), and one field was allowed to rest by remaining fallow. The fields' crops (or lack of crops) were rotated annually.

The religious symbolism of death, followed by transformation and rebirth, is of course quite common in our world, and it has affected how we keep our calendars; for example, celebrations of death and rebirth commonly occur on the winter and summer solstices.

The fact that our alphabet is only one letter short of the 27-digit number/alphabet system of the Dozen Landsteads is pure coincidence. I'm not averse to taking advantage of coincidences.

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