Let's consider the numeral 5 as an object of awareness.

AW: 5 = 5. Awareness of 5 is 5.

Our awareness of Roman numerals should follow the same pattern.

AW:V = V

As an example, this is the question that needs to be answered: How does our AW:V get "equated" to our AW:5?

We can describe 5 as a representation of some number that we call "five"

5; A NUMBER --> "5" represents a number.

How is our awareness of 5 different than our awareness of 5 as A NUMBER or 5 as A SYMBOL?

AW:5 = 5

AW:(5; A NUMBER) = (5; A NUMBER)

AW:(5; A SYMBOL) = (5; A SYMBOL)

Clearly (5; A SYMBOL) is not the same as (5; A NUMBER). Or in english, 5 as a symbol is not the same as 5 as a number. But both 5 as a symbol and 5 as a number are both 5.

How do we show this?

AW:5 = 5

5 = 5; "A NUMBER"

(5; "A NUMBER") = AW:(5; "A NUMBER")

5; "A NUMBER" = "A NUMBER"

AW:"A NUMBER" = "A NUMBER"

Through this series of steps we modeled how the awareness of "5" is associated to "5" as "a number". And how "5" itself is equivalent to "5" as "a number". And that "number" is the same as awareness of that "number". The " are for clarity, but are they necessary?

For the association of 5 as a symbol, we can show this shift in awareness with a single string of identities, associations, and equivalence.

reading left to right or right to left:

AW:5 = 5 = (5;A SYMBOL) = AW:(5; A SYMBOL) = (5; A SYMBOL) = A SYMBOL = AW:A SYMBOL

We have three objects of awareness. 5, 5 as a symbol, and a symbol. And through association and equivalence we can see a path or connection between the three.

We know that objects are the same as objects of awareness. And we also know from experience that representations occur. So how do different objects relate to each other? They relate to each other by being representationally equivalent.

To ask again: How does our AW:V get "equated" to our AW:5?

reading left to right:

AW:V = V = (V;NUMBER FIVE) = AW:(V;NUMBER FIVE) = (V;NUMBER FIVE) = NUMBER FIVE = AW:NUMBER FIVE = NUMBER FIVE = (A NUMBER FIVE;5) = AW:(NUMBER FIVE;5) = (NUMBER FIVE;5) = 5 = AW:5

note that NUMBER FIVE refers to the mathematical concept of the number or quantity we call five.

in english:

awareness of roman numeral five is the same as roman numeral five which is equivalent to roman numeral five as the number five. Roman numeral five as the number five is the same as the awareness of roman numeral five as the number five. the awareness of roman numeral five as the number five is the same as roman numeral five as the number five which is equivalent to the number five. The number five is identical to the awareness of the number five. The awareness of the number five is identical to the number five which is equivalent to the number five as the english numeral five. the number five as the english numeral five is identical to the awareness of the number five as the english numeral five. The awareness of the number five as the english numeral five is the same as the number five as the english numeral five which is equivalent to the numeral five. the numeral five is the same as the awareness of the numeral five.

Once we learn this association from V to number five to 5 we can make a new association. V;5. Once a string of associations are made in awareness, we often make direct associations to the things at the end of those strings. thus:

AW:V = V = (V;5) = AW(V;5) = (V;5) = 5 = AW:5

we see at the center of this string of equality and equivalence the awareness of the association of V to 5. And for most people, once they have learned Roman numerals, they no longer make the association of "V" to the number five and then to the english symbol for 5 but associate "V" directly to "5". It's not that the association of "V" to the number 5 disappears, but it is no longer needed for "translation". A new association is made because of the associative or representational equivalence.

What is critical here is that all the associations or representations must exist in awareness. If the associations between objects do not exist in awareness, the association does not exist*. What is being connected through representational equivalence are different objects of awareness. It is because they are objects of awareness that we know they are objects and that they have associations.

*note: associations of objects must be associations of objects of awareness. there are not objects that exist apart from awareness, and there are not representations (which are objects) that exists apart from awareness. In practice, this must mean that representational objects must be local to the subject or shared among subjects.

In our ordinary way of speaking or writing we could leave out the steps of awareness and model the associations and equivalence like so:

V = V;NUMBER FIVE = NUMBER FIVE = NUMBER FIVE; 5 = 5 showing the long connection or

V = V;5 = 5 showing the short connection to the ends of the longer associative string. Once a longer string is made, the shorter one can be made creating 6 objects: V, 5, NUMBER 5, V;NUMBER FIVE, NUMBER FIVE;5, V;5

But V;5, and V;NUMBER FIVE, and NUMBER FIVE; 5 all must be objects of awareness to connect the concept V, 5 to the mathematical idea of five . We often speak about associations or representations as being external to awareness, but representations must be objects of awareness.

Representational objects may not be considered objects of direct experience.

We may not think of representational objects as being objects of direct awareness, or experienced directly, because we experience some objects only in representational ways. Names of objects often demonstrate the problem of direct experience or representational experience. And we can flit between the sense of a name being a thing itself, and being a stand-in for something else.

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We can add representation to the awareness because representation is part of experience itself we can show how objects relate to various representations of objects. This function has two "sides" to it. The awareness side (AW:X) and the non-awareness side (X).

The simple form of representation is some object X as some other object Y. Say a flower is object X. and Red Flower is object Y. so X = X;Y A flower is the equivalent to a flower in the form of a red flower. the semi-colon can be expressed as "in the form of" or simply "as".

I'm using the symbol for equivalence, but this may be a conceit. On the awareness side of the equation, it's not the same. But on the non-awareness side of the equation it is. We are aware of the difference between a flower versus a flower as a red flower.

If the representation were somehow separate from our awareness of it, there may not be a difference between a flower and a flower as a red flower. The representational shift seems to occur on the awareness side of the function. But the there is an identity on the non-awareness side between a thing and the thing in a form.

We can ordinarily say this (read ";" with "as" or "as a" or "in the form of")

flower = flower;(red flower) = (red flower)

In the ordinary way, we say a flower is a red flower.

But on the awareness side we should say this: AW:(flower) = AW:(flower;(red flower)) = AW:(red flower)

We must distinguish the object and the object as a representation on the awareness side because awareness of a flower, awareness of a red flower, and awareness of a flower as a red flower are three different instances of awareness. And so on the awareness side, the different awarenesses are not identical, but they are equivalent.

Now lets put these three parts together.

I am aware of a flower:

AW:flower

which is the same as the flower:

AW:flower = flower

A flower is the same as a red flower:

flower = flower;(red flower)

Which is the same as awareness of a flower in the form of a red flower:

flower;(red flower) = AW:(flower;(red flower))

And an awareness of a flower in the form a red flower is equivalent to an awareness of a red flower;

AW:(flower;(red flower)) = AW:(red flower)

This can be shorthanded to:

AW:flower = flower = flower;(red flower) = (red flower) = AW:(red flower).

I use the = because I'm skipping the AW:(flower;(red flower) portion. The equivalence indicates the awareness is implied.

It can be shorthanded even more using variables below:

AW:X = X;Y = AW:Y

Alternatively, if it makes you feel better you could say: AW:(flower) = AW:(flower;(red flower)) = AW:(red flower)

This all 'awareness side' relationship is true. But showing how representation is taking place on the non-awareness side of the equation will be useful later in explaining how to code for changes in experience. Because, the awareness has to shift as the objects of experience shift.

The awareness function is an identity. That produce changes in awareness that match the changes of objects. The changes flow both ways. It's important that changes "in the world" correspond to "changes in awareness". This mystical notion that "changes in awareness" correspond to changes "in the world" is important, because it will let us model and explain experience that would be impossible to model otherwise. The awareness function is a two-way street between the awareness side (AW:X) and the non-awareness side (X) of the function.