An Attempt at A First Essay

The goal of this essay is to look at knowledge engineering from a theoretician’s perspective. More specifically, we would like to discuss the notion of a minimally competent theory to help ‘engineer’ practical solutions based on working with ‘knowledge’.

Our understanding of the world, and the way in which we maneuver in it, is based on a string of ideas and theories.

I will begin by describing a groundbreaking idea, and an uncommon occurrence. (This thread can be taken up again in a discussion of how to manufacture these uncommon occurrences.)

Albert Einstein had a remarkable theory: maybe light, in the presence of matter, does not travel in a straight line. In 1919, he gave credence to that theory. The scientific community, during the solar eclipse of that year, measured the deflection of stars erstwhile hidden by the intensity of emissions of the sun. The results gathered were inconsistent with the common notion that light travels in straight-line trajectories, erstwhile (and for hundreds of years) accepted. The world of physics was tilted off its axis. The rest of the world was content to buy the poster.

Theories can also come in smaller denominations.

My high school science teacher had a theory (though less original, I suspect): if we were to add equal parts vinegar and baking soda, we would produce carbon dioxide and water. She lent credence to this theory with the help of the class. In groups of two or three, we added various quantities of vinegar and baking soda, and attempted to measure the amounts of carbon dioxide and water produced. We found a spread of results, all of which, uncertainty included, convinced us that our teacher was right. The class might have been stunned, but likely was not, as it was accepted that our teacher would likely not mislead us.

Theories are, in fact, common occurrences.

Architects and builders are in the business of theories: they believe that they can plan the requisite steps in order to erect a house. This plan is multi-faceted and multi-layered. Included must be a structure whose walls will not fall, even if subjected to a wide variety of stresses, wiring that will provide future inhabitants with electricity and telephone use, pipes that will allow running water, etc. The spread of results for builders and architects must be of a much smaller range. The design and use of the structures may vary widely, but the buildings erected must be inhabitable and must abide by established safety regulations.

In the following dissertation, I would like to consider that which is involved in postulating a good theory.

First, let us dissect those theories stated above.

All three theories are postulated in a fashion understandable to members of the same academic or employment community.

Einstein formulated his theory of general relativity in the language of Mathematics. My high school science teacher expressed her theory in the symbols understood by beginner chemists. Builders and architects write their plans in charts and diagrams readable by other professionals. This is a description of the meta-theory of the individual theories.

The meta-theory consists of the components of the theory and the formalism. In a formulation of the meta-theory, should be included descriptions of that for which the theory (or family of theories) should be responsible and the language in which they should be expressed.

The above theories postulate something; they predict behavior or occurrence.

Albert Einstein postulated that light curves around matter. My third grade teacher predicted that two substances combine to produce foreseeable products. Architects and builders postulate that they can draft finite number of steps that, once completed, will lead to the creation of a house.

The theory itself should represent a predictor, usable and understandable to anyone in a general population. It should be expressed in the language decided upon in the meta-theory.

A theory should be, in some fashion, verifiable.

Einstein’s theory was satisfying because it was verifiable. He chose a phenomenon that could not be explained using contemporary theory, and he proposed a new theory. My science teacher directed our class to verify the result that she postulated in laboratory experiments. Architects and builders produce structures whose lasting existence proves that their theories are sound. Therefore, the above theories fit in a model of behavior.

The model is the situation in which the theory is evaluated. It is an application of the theory to a particular situation in which its prediction can be measured and its accuracy evaluated.

We will now treat another important theory that has existed in various forms for millennia.

My parents seem to have theorized that if I were subjected to between approximately fifteen and twenty-six years of education, then I would become a productive member of society. My community agrees; it is not socially acceptable to drop out of school before a given age. My country agrees as, in fact, it is not legal.

What is involved in this theory? More aptly put: what would be involved in constructing a theory of education?

Note that education is a good model with which to begin, because it is institutionalized in stages. Passing from one stage into another is dependent almost solely on passing a (standard) set of tests. Our model will thus not be artificial.

Therefore, in order to formulate an answer to the above questions, we will first consider the components of the theory. In other words, we will define the terms, and the manner in which we will proceed to talk about this theory of education.

The meta-theory:

If we were to postulate a good theory of education, then it would handle the following components. It would predict progress in increments (i.e. in years and semesters) and it would make long-term predictions. It would follow the learning cycles and curves of real students. It would treat a wide range of students, differentiated by intelligence, learning styles and capacity, and rates of maturity.

A good theory of education should be expressed in terms of intervals of semesters, intelligence, and maturity.

The theory:

A theory of education should predict the course content that would allow students to pass the tests required to pass to the next level of education. It should predict the difference in test scores of students given a range of intelligence and maturity. It should in fact predict the course of study and the student-type required to manufacture the next Albert Einstein or Mozart.

The model:

A theory of education may be evaluated within the framework of public education. We can evaluate a given grade ten course content administered to children who have demonstrated a grade nine competence level (i.e. monitor the spread of test scores at the end of the administration of the course.)

In order now to begin to maneuver inside our model, we will decide that which we would like to primarily accomplish. We will begin by formulating a minimal theory.

We would like to start with an educational policy that should translate into educational strategies. These educational strategies should translate into educational tactics. These educational tactics should finally be used to produce a curriculum (i.e. a course content for some particular course to satisfy some particular educational goal).

We will begin by imagining or modeling the behavior of a student. Our model is solipsist. We will therefore not represent any particular student, nor will we represent the average student. The behavior of the student that we imagine must have ‘something to do’ with the behavior of the students more generally. (Although in a more refined model, we would like to consider a wide spectrum of students in consideration of energy, motivation, intelligence, IQ scores, etc.)

We will initially place our student in grade ten. If he enters a grade ten level of education with a grade nine level competence (i.e. he passes the tests required of a student leaving the grade ten level), then we would like to know the requisite material that we must administer for the computer to pass the tests required by grade ten students.

We must now make some limiting assumptions. We will this student after one who is given only textbooks, and we will thus not consider the way in which material is presented. One important limiting argument is that the information must be presented in sentences, as it would be to a corresponding real student. Therefore, our computer model of a student must demonstrate the skill of sentence comprehension. The model student must also learn in a method comparable to corresponding real students. We will thus present material and test the model student in stages. Like corresponding real students, we do not expect perfect scores from our model student; in order to pass to the next stage in education, our computer model must merely pass the tests to which it is subject.

Testing for understanding, even in current educational practices, is a difficult matter with which educators contend. We will require that our model be cognitively competent. We don’t know whether our program truly understands what we are saying, but we are requiring for it to ‘fake it’ and to answer our questions correctly. We will thus require only that our computer model of a student have the skills necessary to ‘fake’ understanding on the tests to which we subject them, to act, within given constraints, as if they understand.

Our model should be parallel in measurement to the rules of evidence. Consider two students at the same starting position, both vested with the same information (i.e. in this example both given the same knowledge that yields grade nine competence). If we provide the students with different grade ten course contents, then one student should test higher on the tests to which both students are subject at the end of grade ten.

Now we must consider how to serialize this model. Our model should grow in accordance with real people. How did the student get to a grade nine competence level? This should work in the same manner in which a kindergarten student progresses; at the end of each step of educational training, the student should a possible cognitive competence of the corresponding child at the same level, following the same curriculum.

How can courses be evaluated? Clearly, if we were to evaluate the entire science curriculum in a school experience, or similarly, two years of physics in the high school level, we cannot isolate the physics from the other courses for which a corresponding real student would be responsible. Understanding the physics depends on a requisite amount of math and chemistry (for an adequate understanding of the core problems treated in the physics course) and English (for sentence comprehension and for communication skills.) Hence, if we would like to isolate courses, we must do so in the smallest possible increment.

Why is this a knowledge engineering problem? We should be able to optimize the curriculum content for a given course, by selecting and ordering the material and trying different sequences to maximize performance on the examinations. Optimization can take into consideration different entry qualifications, so that we can optimize across a known distribution of students, resulting in an optimal distribution of examination results.

The theory is verifiable since we can compare it to actual results.

The scope of the theory is limited, but fairly wide. Variants can be used to optimize instructions for complex products, operating equipment, learning new procedures and jobs. It applies where the instruction is explicit, in manuals or other verbal form. It can be evaluated where the performance can be measured.

The scope of the theory is limited, since it does not deal with collaborations, or with learning situations where the information is not presented in manuals but may be visual or is based on learning by doing.

How would the theory work? Since it is very complex, it will have to be computational rather than mathematical. In other words, the theory is represented by a computer software application for which the program or algorithms instantiate the theory in a model. The program behaves as the theory specifies it should behave.

What are the components of such a theory / model? There must be software algorithms and data that instantiate the knowledge and capabilities at any given stage. Rather than ‘dissecting’ the specimen, it should be possible to examine these algorithms and data. At the appropriate level of abstraction, the theory is represented. At a lower level of abstraction, the syntactic and mechanistic elements represent the notation and infrastructure for the theory, rather than the essential content of the theory.

How is such a theory/model used? For our grade ten example, the starting point must be a model /programme which can pass grade nine examinations. It must then be possible to feed in the grade ten curriculum materials – as textual material. It must then be possible to feed in grade ten examinations, and the system must be able to produce appropriate answers – not perfect, but sufficient to fake it as a student.

In conclusion, we hope that we have demonstrated how a competent theory would function, and what role it would play in dealing with knowledge engineering tasks.