Batek Binary and English Transformation Art

Embed Size (px)

Citation preview

  • 8/14/2019 Batek Binary and English Transformation Art

    1/6

    Batek Binary and English Transformation Art in Three Lessons

    copyright 2009 James R. Batek

    Lesson One

    English transformation art is the application, to a work of art, of a binary signalcode for numbers which the writer invented and to which he has given the nameBatek Binary. This lesson, lesson one, explains basically what Batek Binary is ingeneral. Lesson two explains how Batek Binary can encode English. Lesson threeexplains how English transformation art is constructed out of the code.

    Batek Binary is a signal system for numbers. How it encodes letters will becomeapparent later. The code uses a binary, or base two, sequence of zeros and onesto represent numbers in any number base, although the code itself is not anumber base.

    A number base is the way a set of numerals can represent a number by placevalues for each place in a series of places, each place occupied by a numeral andadding to the total value of the number the result of multiplying the numeraltimes its place value. The place values are all powers of the size of the set ofnumerals which can occupy places, and this size is called the base of the system.A power and a base go together to get another number. That number is, forpositive integer powers, the base multiplied by itself the power number of times.This is written, for example,

    23.

    2 is the base and 3 is the power, also called the exponent. This expression isevaluated as two multiplied by itself three times, or,

    2x2x2 = 8

    A number expressed in a number base system is evaluated as the sum of all thevalues gotten from multiplying place holding numerals by their respective placevalues. For whole numbers, these place values all have the same base--the baseof the number system being used, which is the same as the number of numeralswhich can be used in the places--and have exponents which start at zero andincrease by one every place beyond that. By convention the starting place is

    always at the right and the increasing place values are placed to its left.

    The exponents start at zero and are incremented by one each place to the left anddecremented by one to the right. This gives negative exponents to the right of thezero exponent and these are evaluated as fractions. Batek Binary does notrepresent fractions, only whole numbers, so these places will be ignored here. Thestarting place, whose exponent is zero, is set off by a point to its right and at the

    1

  • 8/14/2019 Batek Binary and English Transformation Art

    2/6

    bottom of the spaces to anchor all the place values. If a place is not needed tocontribute to the number it is filled by a zero. Zeros left of the greatest place thatdoes contribute are not necessary but can be given if the situation gains clarityfrom it.

    Any non-zero number to the zero power is defined as one, so every number starts

    its place values with the place value of one just to the left of the point.

    This writer sometimes uses a convention to give the base of a number.

    1111[100]

    represents a number in base four. The bracketed right subscript gives the baseand is always in base two. The value of the number, in this example, is found bymultiplying 1 by each of four different, ascending place values and adding. Thevalues of the exponents are zero, one, two and three, right to left. This isevaluated as

    ( 1 x 43 ) + ( 1 x 42 ) + ( 1 x 41 ) + ( 1 x 40 ) =

    64[1010] + 16[1010] + 4[1010] + 1[1010] =

    85[1010].

    A number which is a single digit does not need its base specified.

    Here is an example in base ten:

    9246[1010] =

    ( 9 x 10[1010]3 ) + ( 2 x 10[1010]2 ) + ( 4 x 10[1010]1 ) + ( 6 x 10[1010]0 ) =

    ( 9 x 1000[1010] ) + ( 2 x 100[1010] ) + ( 4 x 10[1010] ) + ( 6 x 1[1010] ) =

    9000[1010] + 200[1010] + 40[1010] + 6[1010] =

    9246[1010],

    which is somewhat trivial as base ten is the customary final form for all results.

    Now comes Batek Binary.

    Given any number base, having the base of n, Batek Binary associates with anynumeral in its set of numerals an uninterrupted sequence of ones the quantity ofwhich is the value of the numeral, all except the zero, which is associated with asequence of ones the quantity of which is the value of the base of the number

    2

  • 8/14/2019 Batek Binary and English Transformation Art

    3/6

    system, or n. By separating these sequences, or strings, with a single zero, anumber made up of any number of places can be formed. The longer a sample isthe more statistically probable it becomes that there is a largest string size, andthat is what an intelligent receiver will take to be representative of the zero.

    Thus, in base four, the number

    320[100]

    can be represented as

    11101101111

    in Batek Binary.

    Basically, that is the guts of the Batek Binary system.

    Lesson Two

    This lesson, lesson two, explains how Batek Binary can encode English.

    Knowing that any number base can be represented in a transmissible way, let's doit for base three. The three numerals of base three are:

    0, 1, 2.

    Translated into Batek Binary, these numerals are

    11101011.

    Returning to the number base system of representing numbers in base three, thestarting place of place values in base three has the exponent zero and the base ofthree, or

    30.

    The value of this place is one. The amount added to the number for this place isequal to the numeral in it times one, or just the same as the numeral. In basethree this place can be held by zero, one, or two with the contribution to the

    number being also zero, one, or two. The next place, to the left of the startingplace, has the exponent of one and the base of three, or

    31.

    The value of this number is three. The numerals which can occupy this place,again, are zero, one or two. Thus the contribution of this place to the value of the

    3

  • 8/14/2019 Batek Binary and English Transformation Art

    4/6

    number can be

    0 x 3 = 0, or1 x 3 = 3, or

    2 x 3 = 6.

    The next place has the exponent two and the base three, or

    32.

    The value of this number is 9. The numerals which can occupy this place are againzero, one, or two. The contribution of this place to the value of the number can be

    0 x 9 = 0, or1 x 9 = 9, or

    2 x 9 = 18[1010].

    If we have a three digit number in base three, it can have any value from

    000[11] = 0

    to

    222[11] =

    ( 2 x 9 ) + ( 2 x 3 ) + ( 2 x 1 ) =

    18[1010] + 6 + 2 = 26[1010].

    Thus these three places in base three are equivalent to a set of values from zeroto twenty-six. These are equivalent to the numerals of base twenty-seven.

    Now consider written English. A large portion of all English consists of strings ofletters plus a blank space which appears between words. If we think of the spaceas a numeral, the numeral zero that is, and the 26 letters as numerals, then wecan think of most of written English as sequences of numerals in base 27. Everysuch numeral can therefore be written as three numerals of base three, and anyseries of letters and spaces can be written as a concatenation of such triple digits.

    Here are the base three equivalents of the space plus the 26 letters of English:

    space000[11] I 100 R 200A 001[11] J 101 S 201B 002 K 102 T 202C 010 L 110 U 210D 011 M 111 V 211

    4

  • 8/14/2019 Batek Binary and English Transformation Art

    5/6

    E 012 N 112 W 212F 020 O 120 X 220G 021 P 121 Y 221H 022 Q 122 Z 222

    Now we transform these base three values into Batek Binary of base three:

    space11101110111 I 101110111 R 1101110111A 111011101 J 1011101 S 11011101B 1110111011 K 10111011 T 110111011C 111010111 L 1010111 U 11010111D 1110101 M 10101 V 110101E 11101011 N 101011 W 1101011F 1110110111 O 10110111 X 110110111G 11101101 P 101101 Y 1101101H 111011011 Q 1011011 Z 11011011

    This concludes lesson two.

    Lesson Three

    This lesson, lesson three, explains how English transformation art is constructedout of the Batek Binary code.

    The final step in creating English transformation art is to find a text both desirablefor its own sake and which fits as code into a pleasing rectangle made up ofcolored squares, one color representing a zero and another representing a one.

    The larger the body of bits in the desired code the smaller each bit will be in thefinal work, for a given size of work.

    Not all texts will make a nice rectangle, so before making the colored squares anyprospective text must be tested first, by calculation.

    Let us choose the text "goodness" as an example. Its Batek Binary code is:

    GOODNESS =

    11101101010110111010110111011101010101011011101011011011101011011

    101

    The total number of bits in the message is 68. The prime factors of 68 are 2, 2,and 17. These factors allow us two shapes of rectangle to fit the code into: 4 x 17,and 2 x 34. These are both quite oblong and so most folks would find such a workvery unaesthetic. We don't want to leave some locations in the rectangular gridunused because that too is quite unappealing.

    5

  • 8/14/2019 Batek Binary and English Transformation Art

    6/6

    Now let's try a different text. Let us try "yoga". Its Batek Binary code is:

    YOGA =

    11011010101101110111011010111011101

    This message has 35 bits. The prime factors of 35 are 5 and 7. A rectangle 5 bitsby 7 bits will contain this message perfectly and placed as a portrait view it willmake a nice piece of art.

    Note that at both ends of the string of zeros and ones for yoga the end bit is aone. Although this is the most basic end condition, it is acceptable as art to putanother zero on each end, increasing the size of the code in bits by two. This doesnot change the message encoded and it gives one additional bit count that couldpossibly make a nice rectangle. This tactic should be done on both ends of thewhole string, not just one, for art's sake. With either way of terminating ends

    accepted, it is generally one text out of every two that will make a nice rectangle.The artist and inventor of the code uses an aspect ratio (the ratio of height towidth in the rectangle of bits) of 1.6 as a somewhat arbitrary rule for accepting atext as art.

    All that remains is to select one color for the ones and another color for the zeros,make them a nice combination, pick a color for the border between squares (sincewhen the string of ones in one part of the message numbers two or three it isdesirable to show the string as composed of squares rather than a continuous bar,it is desirable for all the squares to be set off by a border of a third colorcontrasting with the colors of both zeros and ones), and basically that is how to

    compose English transformation art.

    This concludes the third and final lesson in Batek Binary and Englishtransformation art. Any questions or comments may be addressed to James Batekat [email protected].

    6