World is a number of entities E.

Society is a number of subjects S.

Any subject has a number of C channels of perception (color, taste, etc.).

Each E could be considered as a vector of values based on all possible C.

Strictly speaking, value of each C for each E appears as probability distribution of certain value range. Let us consider the mean of distribution to be single value for vector.

Indeed, value ranges for different C differs. Let us consider we know all channels range beforehand, and normalize all values to 0-1 range.

World is a bidimensional function of appearance of each E within each C A(E,C). Function A(E,C) is "ideal world".

Each S has it's own perception P(C,S) of world. This is a function of how each C is detected by each S.

Strictly speaking, perception of different C could depend оn certain E. In this case we have to deal with P(C,S,E). This case is not considered below.

Outer W reflects into inner image of world I for any given S as I(S,E,C)=A(E,C)*P(C,S) , where * is multiplication or convolution.

That is, cognition works as: World Appearance -> Perception -> Inner world.

That is, we have three basic functions below.

A(E,C) - Objective appearance of world entities.

P(C,S) - Subjective perception by channels.

I(S,E,C) - Subjective image of world by society of subjects.

Let us fix variables of basic functions and perform generalization on those variables. This way, we come to number of different particular functions below:

A(C)_{e -} characteristic of given abstract ideal E

A(E)_{c -} characteristic of given C

I(C)_se - subjective image of given E by certain S

I(S)_ce - "social" characteristic of given E within certain C

I(E)_cs - subjective characteristic of given C for certain S

I(E,S)_{c -} "social" characteristic of given C

I(C,E)_{s -} characteristic of given S

I(S,C)_{e -} "social" knowledge regarding E

P(C)_{s -} characteristic of subjective perception

P(S)_{c -} "social" characteristic of perception channel

Finally, we have a number of functions. We are able to build a number of solutions depends on what we are looking for exactly.

Applications:

The subject's mind is a process of how does subject sense the world. This process could be expressed as

P(C)s or P(C,E)s to be exact.

So we have

I(E,C)s=A(E,C)*P(C,E)s

Let us imagine that ideal world A(E,C) is known.

Let us consider that I(E,C)s is evaluated as subject's knowledge.

Than we are able to obtain P(C,E)s by I(E,C)s and A(E,C).

That is a question - how to obtain I(E,C)s?

• Asking subject directly;
• Considering subject as just one entity among others. This way, channel values for each subject are it's relations to another entities. That means, we are able to look about how does E of this S present in entire world - independently on it's own perception.

So we have separated the subject's mind P(C,E)s and the subject's knowledge I(E,C)s. P(C,E)s is "process" and I(E,C)s is "data". At the same time, it is not easy task to find a boundary between them. This fact requires additional considerations.