The A3 vision on the mechanism of mind

The A3 approach proceeds from a vision on the process of formation of mind content,

treated as a network consisting of mental entities. Also, the formation of this network is

treated as „weaving“ rather than „creation of a whole“ because this process is perpetual and

it never ends during the lifetime of mind. Since the term „formation“ is too general to reflect

the specifics of this process, and „weaving“ is not a convenient word to serve as a term, I

will use the term „synthesis“ for such formation of mind content. Currently, there exist a

large number of different types of networks used in research and technology – neural

networks, semantic networks, Petri nets, and other types. Mind content is a new type of

network.

Synthesis unfolds in steps and for a natural (i.e. not „artificial“) mind, probably, a large

number of mental entities is created at one step. In order to simplify the analysis, in this

paper I will limit to only one atomic mental entity created at one step of the mind content

synthesis.

Since the mind content synthesis is regarded as perpetual and never ending during the

lifetime of mind, it always encreases in size and, even though the mental entities are more

abstract than sensual data, the mind content is always a realistic „film of the reality“ - a

„conceptual film“. I am not interested here in the dynamic aspect of mind content which

determined me to assimilate it with a „conceptual film“. The dynamic aspect only shows

that mind content is an „open world“, i.e. a changing object. I am interested in mind content

as a „history“ or „memory“ of the synthesis process reflecting the „structure“ or „form“ of

the mind content. The Figure 1 below illustrates the „mathematics of brain“ and serves as a

roadmap to further material.

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Fig. 1. Brain Mathematics

Earlier (Drugus, 2007), I treated the synthesis of mind content without the part-whole

aspect. I explained that such synthesis is done by alternative involvement of each of the two

hemispheres of brain at one step of synthesis, and with each involvement, it does exactly

one operation whereby it creates an entity. For right-handed people, I substanciated that the

left hemisphere is specialized on the association operation whereby it produces a new entity

also called association, while the right hemisphere is specialized on the aggregation operation

whereby it produces a new entity also called aggregation. In this paper, I will additionally

treat the part-whole aspect, which became possible due to finding a better explaination of

the part-whole aspect, dealt with by the third component of brain – the bridge between two

hemispheres called corpus callosum. I assume this component to be specialized on the

operation of atomification of the A3 approach.

The mind content obtained in result of a perpetual synthesis can serve only as a basis for

intelligence, which alongside accumulation of conceptual experience as mind content,

manifests via other activities, including the logical activity. But the mind content synthesis

unfolds on a level which serves as a basis for higher levels of intelligence. The level

immediately above it allows to cut on this wealth of conceptual data and can be said to be

the level of identification. The identification allows to regard many mental entities as „the

same“. Because these two layers are sufficient for the discipline of Universics, in this paper,

I will focus only on the level of mind content synthesis and on the level of identification.

To summarize the account of the A3 approach vision on brain mathematics, I will say, that

at one step of mind content synthesis, the brain applies exactly one of the three operations,

said to be A3 operations, for creating a new entity:

- Aggregation operation for creating an entity also called aggregation – an entity type

generalizing the notion of set of set theory, and the notions of class, container and

collection of Semantic Web,

- Association operation for creating an entity also called association – an entity type

generalizing the notion of ordered pair of set theory, and the notion of property of

Semantic Web,

- Atomification operation for creating an entity also called atomification – an entity

type generalizing the notion of atom (also said to be ur-element) of set theory and

Universics - a Common Formalization Framework for Brain and Web 59

the notion of ‚whole’ of mereology, science of „parthood“ or of „part-whole“

relationship (and for which there is no corresponding notion in Semantic Web).

To clarify the above, it should be added that the entities are either untyped or typed, and if an

entity is typed, then it can have one of the three types above, which I will refer to as the A3

types. Each of the terms aggregation, association, atomification, will serve as a name both for the

operation and for its result, and we will distinguish between them by specifying to which of

the two we refer. So, we will use expressions like „an aggregation“, „entity of type

aggregation “, or „aggregation operation“ and similar expressions for „association“ and

„atomification“.

In the most general case, I am treating the term operation as a many-to-many

correspondence. So, even though A3 operations are not yet completely defined, they should

be treated as many-to-many correspondences or, how they are called elsewhere – „manyvalued

functions“. The notion of property in Semantic Web corresponds to the notion of set

theoretic relationship and of „functional property“ as it is said to be there. This is why to

avoid term collision, I will not say a many-to-many correspondence to be a function - I will

say it to be operation.

One of the greatest difficulties in guessing how the mind content is synthesized is to find

out how the representations of different objects can be retrieved at a later time. This is a

general problem for any kind of networks. Also in philosophy the process of discriminating

separate entities in the „material network“ of the Universe has been a problem since ancient

times – a problem, which has not been solved up to date.

I would have preferred the term „domain of integrity“ for the representation of an object in

the network of mind content, because this would have better reflected the idea of dealing

with the „wholeness“ treated here as a synonym for „integrity“. But „integrity“ has a special

meaning in English, and I will use the term „integral domain“, which though is good due to

being shorter. I consider the integral domains, as representations of objects, to appear in

mind due to the atomification operation.

Fig. 2. A piece of mind content

The figure 2 above illustrates the mind content obtained in result of a synthesis process,

which is a directed process: in this figure, we consider that mind content „grows“ upwards.

The results of applications of both the aggregation and association operation are represented

as nodes of the network. In order to simplify the picture, the distinction between the entity

types aggregation and association is not indicated in the figure and all the aggregations in

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this figure are deemed to be two-element aggregations – same number of arguments as of

the association operation. The colored areas are said to be integral domains. These pieces of

mind content are „production“ of the atomification operation, which can be thought to act in

a dimension, different from the dimensions where act association and aggregation. The

results of applications of the atomification operation can be imagined to lie in space above

the 2D space of the picture. This is why, to represent the integral domains as new entities

not lying in the plane and to be able to discriminate between them, they are represented in

different colors. The bottom of each integral domain is represented by the atoms (indivisible

constituents) of the represented object. This botom is „dented“ because in the synthesis

process the representations of the atoms appear at different times. The top of each integral

domain is represented by exactly one entity which we regard as the unity of this integral

domain. The first intuitive idea about the manner how an integral domain can be extracted

from the mind content is by imagining that such a domain is “carved out” from the mind

content taking into account the two boundaries - top boundary represented only by the

unity, and bottom boundary represented by many atoms.

Notice that in the Universe of matter, one body B is part of another body C, if B is spatially

“inside” C. The universe of mind differs from the Universe of matter and the

representations of B and C in mind look totally different. Namely, the unity of B becomes an

atom of C, so that in a graphical representation as that of Figure 2, the representation of B

would be beneath (and not inside) the representation of C.