Structuralism/Contents/Notes On Structuralism

SOME NOTES ON STRUCTURALISM

NOTE: This introduction, and others like it onsite, is written by the editor. It is not directly words, written or spoken, by any Guru.
Students have asked for explanations, and they have been given. This is what we think at this date, the best answer we can think of at the moment.
We may be wrong. If  it contradicts what the Gurus have said - tell us, and we will correct it.
A full discussion of structuralism exists in various parts of the Guru's work, among others in Contents/An Integrated Science of the Absolute/Introduction to Part 1, in the Shorter Works section and elsewhere; so we shall only touch briefly on the subject.

Nataraja Guru would say "My task in life is structuralism" or something similar on various occasions, so it is obvious that structuralism is the major part of his teaching.

One way of approaching structuralism is as follows:

1) All science, which means here all pursuit of correct knowledge, is a process of abstraction and generalization.
To take the classic (though fictional) case of Newton and the falling apple, the scientist takes one particular event at one time and in one place, (an apple with a particular mass gfalls to earth) and proceeds to make more and more general statements until he has a law  which applies to all objects which have mass, in all stuations.

2) Structuralism is abstraction and generalization taken to its limits.

3) Three hundred years ago, Descartes was the first to use what are still called the Cartesian Correlates - in other words, the principle of the graph. In the typical schoolroom exercise, you draw a vertical axis and a horizontal axis intersecting it - you call (for example) one axis "time" and the other "space", and from them you plot a line marking, say, the progress of a train travelling at so many kilometres and hour. This is used everywhere  and all the time in the modern world, and although it is just possible to imagine modern science without the use of the graph, it is difficult .

4) Descartes' correlates (the graph in other words) were a breakthrough in thinking because they used a new language to deal with ideas.
Before Descartes, people talked about ideas - things in the mind, or concepts - only by using verbal language - words, whether spoken or on paper. (This is what the Guru means by "Metalanguage.)
What Descartes discovered is that you can use other kinds of language - here the language of two-dimensional lines or shapes - to talk about ideas or concepts. (This is what the Guru means by "Protolanguage".)
For example - using lines for "time" or "distance" when we are talking about a moving car and plotting a line on the graph to find where it will be at a given time.
  
5) The three-dimensional structure used by Nataraja Guru provides a tool that can be used to revolutionize the non-physical sciences as Descartes' discovery did for the pysical sciences,

6) The  structure used by Nataraja Guru is three-dimensional while Descartes' is two dimensional.
For a specific example, see  Integrated Science of the Absolute/ Introduction to Part 1/ Colour Solid . This is a three-dimensional structure used to describe and define colours.
If you used a two-dimensional graph to help you define and relate colours, you would be limited to two variables - horizontal and vertical - the colour solid has three axes, the graph only two. A specific colour can be located at any point in the three-dimensional space defined by the two cones placed base to base.
What applies to physical phenomena like colour also applies to the sciences which do not directly involve physical  measurement but instead involve questions of "value" - such branches of human knowledge as metaphysics, ethics or economics.
A major difference between Descartes' correlates and the quaternion (four-limbed) three-dimensional structure used by Nataraja Guru is that the horizontal and vertical axes are not interchangeable.
 
In Descartes, (and also in the writings of many others on the subject since) you can swap horizontal and vertical around and it makes no difference.  In other words, in the example of the moving car above - it does not really matter whether you plot the kilometres along the horizontal axis and the hours on the vertical or vice-versa.

In the quaternion structure used by N. Guru this is not the case.
The most fundamental distinction that you have to make, if you want to understand what Nataraja Guru meant by structuralism is work out the difference between the horizontal and the vertical axes of the quaternion structure.
Once you understand this distinction, a lot of what the Guru wrote becomes clear.

Here are some definitions and examples:
(all the above are from Notes and are by Nataraja Guru, except when otherwise indicated)

Structuralism is the highest function of the human mind.

Marbles in reaction to one another are horizontal,
a lake inside a lake, a cup inside a cup are vertical

Horizontally viewed, one second can become a thousand years;
Vertically viewed, one thousand years can become one second.
(H.Bergson)

The vertical axis is happiness, the horizontal axis is suffering

The structure of woman reveals the structure of the negative aspect of man,
his psyche. Add the numerator to this feminine structure and you get the whole picture.

Transportation, e.g. a truck carrying a load of stones, is horizontal.
Transmission, e.g. of radio waves, is vertical.

Three causes and effects:
1. A billiard ball striking another is horizontal.
2. The unwinding of a clockwork gramophone is vertical
3. An explosion is horizontal
The fourth, which includes all these, is consciousness.

SOME EVIDENCE OF STRUCTURALISM
1) The Cartesian Correlates
2) Probability curves - curves on graphs
3) Multiplication, subtraction, addition and division form a quaternion structure.
4) The multiplication table of 9
5) The four forms of logic
6) What is "pi" ?
7) Fourier functions - sinus curves in electromagnetics
8) "Architectonique musicale"

The horizontal is multiple and the vertical is unitive in status.

Even within the scope of logic proper there are two main kinds,viz.:
one which recognizes contradiction and excludes the middle ground;
and that which is dialectical in approach,which proceeds by cancelling out thesis and antithesis into a central synthesis. 
The former moves horizontally,
the latter vertically. 

Vertically, existence prevails; and horizontally the breezes of phenomenal unreality,uncertainty or indeterminism blow, giving rise to an interplay of possibilites and probabilities.

The structure of woman reveals the structure of the negative aspect of man, his psyche. Add the numerator to this feminine structure and you get the whole picture.

THE FOUR LIMBS OF THE QUATERNION.

1. THE ACTUAL CHAIR in which the actual man can sit; this chair will exclude another chair, and occupies a particular space.
(Horizontal positive)

2. THE VIRTUAL CHAIR, in which a virtual man can sit; much like a mirror reflection.
(Horizontal negative)

3. THE ALPHA-POINT CHAIR, the form of the chair generalized, it excludes all other chairs.
This is the universal concrete version, it excludes horizontally but not vertically.
(Vertical negative)

4. THE OMEGA POINT CHAIR: the word "chair" in the dictionary, purely conceptual.
(Vertical  positive)
(From Eddington)

Schematise and you get the Absolute.

There are many more examples. In fact, almost any page of the G's writings could be used as an example.
The difference between horizontal and vertical is not complex, but is is very subtle.
By definition of course, it works at a higher level of abstraction and generalisation than verbal metalanguage, so it is impossible to describe it only using the words of metalanguage. Endless examples seem to hammer home the message by using analogy.

Another reason why it cannot be pinned down in words is that:
"There is a paradox at the core of the Absolute.
If you try to resolve the paradox, if you try and pin it down, you get a chair or a table; it does not dance.
We are dealing with a dynamism, not a static object." (NG)

Structuralism - to use structural language - has significance or value on three levels on the vertical axis (HP).

At the most negative level, it is the structure of the psyche.
In the central zone, it is the structure of the cosmos.
The positive pole,where purpose or meaning resides, is also structural.

However, structuralism can be approached from any number of directions. This is because the quaternion (four -limbed) structure is the structure of everything

This is just a first feeble attempt at clarifying this difficult subject.. Use the search button at the top right-hand corner of this page to learn more.

Best go to the actual words written by the Guru. If you have questions, comments or criticism, contact us.