TOWARDS A MATHMETICAL MODEL OF CONSCIOUSNESS

Consciousness is a function. Its output is awareness.

Awareness = Consciousness( … )

Consciousness may produce different awarenesses qualitatively or quantitatively depending on time. For example the awareness of self may change at different moments of the day. Consciousness depends on time.

Awareness = Consciousness( time, … )

Consciousness changes for different subjects. A person may be more cost aware while an other does not. Also we can talk about the consciousnesses of a single person or a group of person. For example, human rights consciousness of a country or nation.

Awareness = Consciousness( time, subject, … )

Consciousness may change based on the context. Different contexts may cause the consciousness function to produce different awarenesses. Seeing a piano carried may make you think the weight of it while listening a performance may make you think about the instrument quality of it. Consciousness depends on context.

Awareness = Consciousness( time, subject, context, … )

Consciousness may change according to the experience of the person it belongs to. An experienced engineer may handle a problem and estimate its difficulty much different than a novice. Experience helps form the consciousness indirectly and as part of the background. A collection of past awarenesses may help form the experience. Experience is more than a collection of awarenesses but it also includes their interactions with each other and with knowledge as a whole.

Awareness = Consciousness( time, subject, context, experience, … )

Consciousness may change according to the amount and quality of knowledge it belongs to.

Awareness = Consciousness( time, subject, context, experience, knowledge, … )

Consciousness is a function or a process. The outcome is awareness. Awareness must be calculated from the input parameters, time, subject, context, experience, knowledge and the last parameter. This calculation may be done with an algorithm. Actually this algorithm can be defined as Consciousness itself… This brings us to the conclusion that Conciousness is
somewhat recursive.

Awareness = Consciousness( time, subject, context, experience, knowledge, Consciousness(…) )

Thinking of the development process of a child, and taking consciousness function as a constant such as sleeping vs being awake, the formula given above can explain the accumulation of experience and knowledge.

The problem with this approach is Consciousness function itself is not constant even during a day and also it changes gradually through a longer period of time. Consciousness learns and improves itself. This can be seen in artificial neuralworks with a learning mechanism.
If we make a change according to this point, a final formula could be:

Awareness = Consciousness( time, subject, context,
experience, knowledge, algorithm )
algoritm = Neural Network (previous Consciousnesses())

I admit that this may look quite subjective for some but it is possible to reduce this assertion to concrete examples and narrow the subjectivity to the point of objectivity.

For example, if we design a system which checks numbers in its input, and senses a sequence that increases by two, the context becomes absolute. Experience may be formulated as past sequences that comply with the increase by two rule. Knowledge becomes the mathmetical calculation. The biggest difficulty is simulating the evolution from experience to knowledge. Knowledge may be limited first as sensing a regular increase, than sensing a regular increase of two. Neural Network algorithm and its learning ability may be used to teach this to the system.

Again, the key thing here is application. This model may be useful, if only applied in a specific domain to handle a specific problem.

On the Nature of Decision Making

The difficulty of making decisions can be made easier by choosing the right decision process. The approach, the epistemology of decision making has to be correctly chosen to make a difficult decision.

We have developed various techniques for making difficult decisions. Partial decisions, delayed decisions, temporary decisions, imperfact decisions, incomplete decisions, reduced decisions, extended decisions.. When studied closely each of these make decision taking easier.

Partial decisions may be implemented in many ways. The basic principle is dividing a difficult task to smaller pieces. The decision may be taken as an aggregate of decisions made on various parts of the main task. The sub divisions may even be given by different individuals. A decision may be divided to subdecisions which are spreaded through time. This may be useful for time dependent tasks. Flight Plan Processing uses this tecnique for ensuring the safe surveillence of air craft.

Delayed decisions also help to clarify complex situations and minimize risk. Air traffic controllers try to delay their decisions as much as possible to avoid unnecessary moves and reduce risk.

Temporary decisions are used when nothing is clear but something has to be done. The chances are your choice may be correct. It is used emergency situations. Temporary decisions are used by companies when they do not have the ability to see the economic situation or the situation of their operations.

Imperfact decisions are made when the ability of the workers or company is not enough. An imperfact decision is taken nevertheless to continue working and improve it ASAP.

An incomplete decision is not an imperfact decision. You make an incomplete decision with open options to be selected later on. It is used when flexibility is required.

Reduced decisions are logically reduced from the required decisions. They are not necessarily the same as the original decision but its results give the linearly independent items of the original decision.

Extended decisions may make things easier by enhancing the results area of the original decision.

It is not enough to educate and train students who can just think excellently. Students of mentally demanding professions should be trained to develop skills and habits of how they can reduce their load of thinking.

A Mathematical Model of Abstraction

Soyutlamanın Matematiksel Bir Modeli
A Mathematical Model of Abstraction

Soyutlamalar = { [a1 .. ai] a is a name and i € ( 1… N+) }
Abstractions = { [a1 .. ai] a bir isim ve i € ( 1… N+) }

ai = { name, [item1 .. itemj] name is the name of ith abstraction, item is the name of any object, j € ( 1… N+)}
ai = { isim, [şey1 .. şeyj] isim i. Soyutlamanın ismi, şey herhangi bir nesnenin ismi, j € ( 1… N+)}

Abstraction is realized by selecting a unifying attribute of a certain group of objects. The later use of this abstraction is done through looking up the existing abstractions list. As a first step the existing abstractions list is defined for this reason. Large systems require the frequent use of many terms, abbreviations, and acronyms. Each item of these is a list of abstractions of the problem domain.

Soyutlama belirli bir grup nesnenin ortak özellikleri seçilip buna bir isim vererek gerçekleşir. Bu soyutlamanın daha sonraki kullanımları ise ‘Soyutlamalar’ adlı varolanlar listesine bakarak gerçekleşir. Bu nedenle ilk olarak bir var olan soyutlamalar listesi tanımlanmıştır. Büyük sistemler çok sayıda kısaltma ve teknik deyim kullanımını gerektirir. Bunlara ilişkin sözlüklerin herbiri aslında birer varolan ‘soyutlamalar’ listesidir.

Indeed all airplanes form a single group. But if we view them from the point of passenger count or power they may be grouped otherwise. As seen in the second formula abstraction is grouping. Abstraction can be made up of any group of items. These items may also be abstract things. Thus an abstraction may be a grouping of other abstractions. For example, airplanes may be grouped as jets, propeller planes, an abstraction of two other abstractions.

İkinci formulde görüldüğü gibi soyutlamak gruplamaktır. Soyutlama herhangi bir nesneler grubundan oluşabilir.Bu nesneler soyut nesneler de olabilir. Yani bir soyutlama diğer soyutlamaların gruplaması olabilir. Örneğin uçaklar Jet uçakları, pervaneli uçaklar diye iki soyutlamadan oluşur. Bu iki grupta yolcu ve özel uçaklardan… Ama hepsi kanatlıdır ve motorludur. Eğer bu açıdan bakarsak uçaklar tek bir soyut gruptur. Eğer yolcu sayısı ve
kullanım açısından bakarsak uçaklar farklı alt gruplardan oluşur.

The flexibility of abstraction gives us the ability to approach different problems from different point of views.
Soyutlamadaki esneklik farklı sorunlara çeşitli açılardan yaklaşma imkanını verir.

Soyutlamanın Nesne Yönelimli Tanımı
An Object Oriented Definition of Abstraction

public abstract class AbstAbstraction {

ABSTRACTION IS GROUPING

ABSTRACTION IS GROUPING
SOYUTLAMAK GRUPLAMAKTIR

Miller(1956) has stated that human attention can focus on seven plus/minus two things at the same time.

Miller(1956) insan ilgisinin aynı anda yedi artı/eksi iki şey üzerinde yoğunlaşabileceğini ileri sürdü.

Abstraction enables us to handle more than nine things at the same time. Abstraction reduces things to one of their attributes. This eleveates the burden of handling the unnecessary mental load of treating a whole thing. For example, a ticket seller treats his customers as simple buyers nothing else.

Soyutlama bizeaynı anda dokuzdan daha çok şeyi idare etmemizi sağlar. Soyutlama şeyleri yalnızca bir özelliklerine indirger. Bu bizi şeyin tümünü ele almanın gereksiz yükünden kurtarır. Örneğin, bilet satan kişi müşterilerinin yalnız bilet almasıyla ilgilidir.

Abstraction is grouping. You can reduce five apples and ten peares (of different types) to two by handling them as just apples and peares. You can even reduce that to one by treating them as just fruits.

Soyutlamak gruplamaktır. Çeşitli tipte beş elma ve yine çeşitli on armutu yalnızca elma ve armuta indirgeyebilirsiniz. Hatta tümünü meyva olarak ele alıp tek bir gruba indirgeyebilirsiniz.

ABSTRACT (1)

ABSTRACT

1 a : disassociated from any specific instance
b : difficult to understand : ABSTRUSE
c : insufficiently factual : FORMAL

2: expressing a quality apart from an object

3 a : dealing with a subject in its abstract aspects : THEORETICAL
b : IMPERSONAL, DETACHED

4: having only intrinsic form with little or no attempt at pictorial representation or narrative content


TO ABSTRACT
1: REMOVE, SEPARATE

2: to consider apart from application to or association with a particular instance

3: to make an abstract of : SUMMARIZE

4: to draw away the attention of

Origin:
Medieval Latin abstractus, from Latin, past participle of abstrahere to drag away, from abs-, ab- + trahere to pull, draw

First Known Use: 14th century

Source: Merriam - Webster Online
http://www.merriam-webster.com/dictionary/abstract

The Effect of Feelings on Concentration - II

What is forgetting? Anything which has remained a minimum period of time in our memory gets written in our long term memory. Anything which considerably gains our attention cannot be forgotten at all. There are limits to the quality of remembering though. A healthy person cannot forget his/her parents’ names for example. It is a fact that we have increasing difficulty to remember the details of the past as time proceeds. This should not make you think that you have forgotten everything. You lose the means to reach the memories not the memories themselves. Many times has a person got astonished at how many details he remember when he enters the same classroom he has gone to primary school.

What is temporary forgetting? Indeed all forgetting is temporary as we do not forget anything in our long term memory. I mean short term forgetting with temporary. For example when you are eating your favorite meal you forget the rest of the world. When you are studying for a critical exam you forget the rest of the world. When you go to shopping you forget to buy the most needed item.

Air Traffic Controllers do forget also. After solving a critical situation, it is not rare that they forget they have to handle a secondary one. The large system controllers’ brains blank out or forget some critical data sometimes. I remember an airplane accident, in which the pilots socialized with some small talk and forget to enter a route point to the flight computer …

Concentration causes forgetting. It focuses the attention on a certain subject area and considers only things related to this area. This causes the loss of access to the secondary areas and hence the temporary forgetting of them. Situation awareness concept is developed to handle this problem. Situation awareness requires continuous tracing of system variables whenever possible.

Concentrating is good when absolute concentration on a single thing is needed. When a partial attention is required for a specific task besides the task of general surveillance of others it is not good to concentrate too much. Divided attention requires not too much concentration on only one of specific tasks. Concentration causes masking.

Everybody remembers a student who forgets her line when reading a poem from her memory in primary school. Excitement, strong feelings cause memory retrieval failures also. In this situation, concentration
is not the culprit. Concentration is required and obtained. The required mental resources are ready.
What is the thing that makes the child forget while reading the poem from her memory?

Another similar situation can be observed when you are walking down the apartment stairs. If you look at each step and each stair you step on, you tumble… If you get excited and afraid you get stiff your muscles harden. If you ‘let it go’, ‘let it lose’ a little bit and walk with confidence (to something out of your control) you walk down the stairs easily…

If you concentrate too much, more than necessary and increase the stiffness of your posture, you increase your brain’s cognitive section’s control. On the other hand, remembering requires the functioning of your subconscious. You do not remember things with using your logic. You give hints, keys and then your subconscious finds and brings them to your conscious. Remembering requires a fine balance between conscious and subconscious entities. So, the primary school student who stiffens and gets excited does not give a chance to her subconscious to retrieve the lines. She fails.

Tonus – posture, In fact, there is more to the problem than stiffening or hardening the muscles… Yes, when concentration increases cognitive abilities increase and they use most of the brain resources but how does this happen? How is the balance obtained between different functional parts of the brain?
How does a professional theater actor remember thousands of lines without any mistake? What does a pianist learn in many years of education that she does not forget in the concert?

A professional learns to orchestrate his brains functional parts through education and professional practice. Choosing the right thinking speed sets the right timeframes to enable the brain to activate its right functional part itself. Excessive concentration hurts memory retrieval not only because of the muscle stiffening and hardened posture but also because of the thinking speed cognition reaches. Cognition can reach thinking speeds that feelings use by the help of high concentration. This may hurt the overall functioning of the brain and may be the subconscious (I have a few more words on that for the future articles).

There are many implications of the thinking speed. But, I will note here only, you must select the right timeframe and hence the right thinking speed in order to be successful in any task. Be careful feelings are the fastest processing brain activity, emergency processes(programmed), automatic processes (thinks you do by memorizing) are the second, cognitive processes the third, safety related risk sensing(the slowest). So, next time you lock the door of your house, do not behave as if you are typing on your computer. Last but not the least, the speed of cognition can be controlled by concentration. Some of the emergency processes such as fear etc. are built-in feelings, I indicate learned processes as emergency processes.

It is vital to select the right posture and muscle tonus which will give the correct message to our brain at first. Then one must set the right salience, the right time frame and thinking speed and then increase the concentration to the required level, nothing more nothing less… One can set himself the right mood to do a task by using his education and PERSONALITY. Each person is a different solution and each profession requires a specific mental set of human mind.

The Effect of Feelings on Concentration

This is about the effect of feelings on focused attention and concentration. There is a difference between focused attention and high concentration. Focused attention requires the use of attention resources for a very limited area or task. Concentration is different from focused attention. Concentration does not exclude whole areas of interest unless they can be linked to the subject at one or other level of abstraction. That’s why we talk about deep concentration but not deep focusing.

The effect of feelings, namely getting sentimental or a certain affective mood during a task may have certain effects to the quality of the work done. These effects may be positive in the short term as increasing motivation under /against too much load. They may be negative as the effect of an airplane accident on the air traffic controllers who must still continue to control the remaining hundreds of aircrafts in the air.

Feelings control the thinking speed hence control the depth and establish the context of thinking. Thinking speed is a commonly used term but diffrent hormones effect different parts of the brain and may cause working speeds in those regions. It may not be wise to use thinking speed in place of a global brain speed performance as in CPU speeds of the computers. I refer to the cognitive processing speed of the brain when I mention thinking speed. It is also interesting to question what exactly thinking speed means. Is it the propagation speed of signals in the neural networks via chemical reactions? Or is it the inverse of the resolution duration of a minimal decision taking in the neural networks?

There certainly exist time frames in the brain processing which establish time limits for the propagation of signals in the neural networks. These time limits may be set by hormones which control the chemical conditions that in turn control the propagation conditions in these networks. Feelings effect the hormon production and flow in the body. Hence feelings effect our cognitive abilities, namely decisions.

Speaking of thinking speed, one must not forget the dynamic character and differentiate between minimal and major variations. The effect of minimal variations may be positive on the thinking performance while the reverse on major variations. Also, one must consider the gradual and sudden changes. The effect of gradual changes may create complex situations such as the loss of the situational awareness in pilots while making smalltalk with colleagues. The effect of sudden changes may be good when the operator is well trained and can control the extra influx of the hormones to increase his performance in emergencies.

Last but not the least, the feeling of taste is the key to understanding feelings as much as seeing for understanding cognition. Tasting sets the way to feeling and seeing to thinking, developmentally and evolutionarily.