See also:  [(art) Concepts]

                  [Philosophical Concepts]
                  [Games]
                  [Maths (the representation problem)]
                  [Computation]

On this page: 

APPENDICIES
                         {Intro to Data types & operations}
                         {Operations}
                         {Data Types}
                  

Coding

The coding problem

consequences of Goedel numbers in finite universe



Coding Within semi-infinite libraries

coding representations & Borges' Library of babel
"" "" "" -- infinite library

link to computation


Appendices


Intro to Data & Operations

Things that look the same are not always the same. Thus,
we might in a computer langauge write something like this:

     Name = "Sam";
     Be       ="I am";

     Sentence = Name + Be;
     Print Sentence;
     End

>RUN
      Sam I am
>

We are used to seeing this sort of thing. What about this:

     A = 5;
     B = 10;

     Print A+B
>RUN
      10
>

I introduce (in a naive way) the ideas of different kinds of data,
and operations that we can perform on the data.

ADDTIION -- add numbers together,

subtraction, multiplication, division -- other NUMERICAL operations

CONCATENATION -- take TEXT and string it together to form
                                     new STRINGS.

NUMBER -- a number; eg, 1, 21,   1.2424208203980280238,
                                              1/7th, pi, the square root of 2, etc.
                     A collecrtion of DIGITS.

DIGIT --  A thing like  "1"  "2" "3" "4" etc

STRING -- a collection of CHARACTERS

CHARACTER -- A think like "A"  "4"  "J"  ";"

Notice that we already of an ambiguity:  "4"  and "4" -- which
do I mean?  The number 4 (which is "pretty much the same as"        
                                             4.0
or                                         4.00000000000000000000000000

or the typed character "4" (as it appears on the screen or paper)?

In computer programming"> it is v. important
to always distinguish this.  In the area of logic known as 
semiotics it is VITAL to make our
meaning clear.

In computation, we restrict the KINDS of things
that can be done. But, in the ever-changing nature of the matrix, this
too can change. (As Old Eclesiastes sed, "The only constant is change").

There are two basic types of data:

Numbers and synbols.   We use the symbol "1" to represent
the concept of a ONE.  The word ONE is a symbol for the 
concept of a thing which has just one thing in it (or is a
kind of "one-ness".  No matter how, hard we try, we can
not escape the self-referential paradox. So, we have to
just get on with it as best we can

The word "uno" is a set of symbols (made up of the characters
"u", "n", and "o" which are CONCATENATED (without spaces)
to form a word which:   MEANS "1" in LATIN

UNO means "1" in SPANISH.

This is a statement. (see logic (statements)

It is also a SENTENCE (written in a HUMAN LANGUAGE, called ENGLISH).

(see Human language)

You can see how confusing things get.  (And we haven't even
gotten to the under-lying science that can treat the way that
we "talk" in maths, or in "english", or ...)  Semiotics
-- Things *really* get out of hand. 

The coding problem depends upon being able to STORE (or
represent) information in the form of numbers, text, pictures,
etc.

It would not make any sense to ADD one IMAGE (picture) to another.

Or to take the word "orange" and ADD it to the NUMBER "7"

Now, note that we can actually DO those things, if we define the
operation in the right way. (In this case what DO we mean when
we say:

   ADD the IMAGE "x" to the NUMBER "z".

Where "x" might be a scanned image of the Mona Lisa
and      "z" might be 3.1416 (an approximation of the number pi)

You might want to skip the next section (I have so far ;)

Advanced Stuff
operations can "overload" data types -- this leads to 
confusion; the "generic" problem



Operations

There are as many TYPES of data (things) as we want to define.

NUMBERS:   1,  12.5    -40-degrees-celcius

CHARACTERS  'x'   "Z"   '"'    "?"

TEXT-STRING (or just STRING)    "how are you?"


In geernal, a number has different "flavors" (see below). Which
because of COMPUTATION, have to be treated differently. And
in addition (no pun intended) create problems in the representation
of the RESULT.

For example, if we take a cheap calculator and punch in 1 divide by 0
we might get 0.

On a scientific calulator, would probably get an ---E--- display,
but in some cases, computer scientists creates systems that
can keep track of the "infinite" value. And use it. A bit off the
topic, so I'll handle it here:    Infinity


Data Types>/h2>