Teaching, Systematically

Yoann Trellu

06.10.2021

By means of quotes, an essay arguing for a unified and systematic method for education and documentation.

Le choix n’est donc pas entre le savoir particulier, précis, limité, et l’idée générale abstraite. Il est entre le Deuil et la recherche d’une méthode qui puisse articuler ce qui est séparé et relier ce qui est disjoint.

Divide and Rule

When a thing accepts many descriptions, this leaves agency when communicating. And this can be used to either mislead or enlighten, as examplified by Bernays

Recently the word Bolshevik has performed a similar service for persons who wished to frighten the public away from a line of action.

And not only an impulsive public, but also individuals. And in fields known for their rigor, here by the mathematician Bellman

My first task was to find a name for multistage decision processes. (…). We had a very interesting gentleman in Washington named Wilson. He was Secretary of Defence, and he actually had a pathological fear and hatred of the word, research. (…). You can imagine how he felt, then, about the term, mathematical. (…) Let’s take a word which has an absolutely precise meaning, namely dynamic, in the classical physical sense. (…) Try thinking of some combination which will possibly give it a pejorative meaning. It’s impossible. Thus, I thought dynamic programming was a good name. It was something not even a Congressman could object to. So I used it as an umbrella for my activities.

Many descriptions for one thing not only enable misleadings, but also distantiates disciplines. A prime example being that of a medical researcher rediscovering integration and getting a high number of citations

A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves

When looking at the current state of higher education, we may have a cynical view and understand the explosion of disciplines and terms as a by-product of academia politics.

Divide and rule, because dividing produces specialists, invariably needing rulers.

Yet an optimistic view could be that consolidating disciplines requires abstraction tools and models we do not yet possess.

Unite and Build

Teaching without a system makes learning difficult

And what if a thing had a ‘canonical’ description? What if there was a systematic, standardized approach for describing processes, and anything people build?

And from Rosenblueth and Wiener, how about focusing on purposes?

It is apparent from these considerations that although the definition of purposeful behavior is relatively vague, and hence operationally largely meaningless, the concept of purpose is useful and should, therefore, be retained.

What about cross-pollination?

Fischer’s intellectual formation was instead in physics and mathematics, and his success in finance came from applying the methods of astrophysics. Lacking the ability to run controlled experiments on the stars, the astrophysist relies on careful observation and then imagination to find the simplicity underlying apparent complexity. In Fischer’s hands, the same habits of research turned out to be effective for producing new knowledge in finance.

And adapting the language and words used, as abstractions become apparent?

Therefore, value, just as information, in its general form can be defined as entropy, given that they are the same mathematically. In the following we will discuss the properties of this simple analytical theory of value as scarcity.

And most of all, how great would it be if descriptions of engineered systems could be rigorously defined in a unique way?

One of our goals in this book is to relate the following diverse topics:

• a generalization of finite group theory which includes finite semi- groups and finite state automata;

• a reasonable, precise and useful definition of complexity of organ- isms and machines;

• a mathematical theory of physics and/or biology for the case in which models are applicable with nonlinear but finite phase spaces. Our theory will give rise to the following: relations between the Darwinian theory of evolution, the complexity of the evolved or- ganisms and the Mendelian genetics;

• a definition of a global (generalized) Lagrangian from which the philosophy of Thom’s program for studying morphogenesis (i.e., the origin, development, and evolution of biological structures) via the topological methods of the theory of structural stability (`a la Smale, Thom, etc.) might begin;

• a Mendeleev type table for the classification of biological reactions (e.g., bacterial intermediary metabolism) isomorphic to the classifi- cation scheme (`a la Dickson, Chevalley, Thompson, etc.) for simple non-abelian groups (SNAGs);

• a mathematical theory of personality including a definition of emo- tion which synthesizes the ideas of S. Freud and R. D. Laing;

• a theory of complexity for certain games (in the sense of von Neu- mann) which includes Chess, Checkers, Go, etc.

Unite and build, because this bonds people together, building towards the same purpose.

Bibliography