"Man lies at the heart of a web ... extending through the starry reaches of sidereal space, as well as backward into the dark reaches of prehistory.... Like the orb spider, man lies at the heart of it, listening. Knowledge has given him the memory of earth's history before the time of his emergence.... [O]ne can see him reaching forward into time with new machines...until elements of the shadowy future will also compose part of the invisible web he fingers." Anthropologist Loren EisleyA June, 1994, Fortune Magazine heralded changes in the "work-style" of production workers. The old style has been a hierarchical chain-of-command. (This is mathematically equivalent to the lattice which I describe in a "mathtivity" for preschool children, Pecking Order. It is still the work-style of most of the military services. But The Commandant of the Marines is introducing it into the Marines!)
The new work-style of production workers is the web, wherein worker-power derives from connections to others who provide information and assistance, while disseminating and advancing the worker's ideas and achievements.
Management expert, Peter Drucker, in The New Realities (1989), wrote similarly about "knowledge workers" in the "information-based organization", composing "task-focused teams" working toward common goals.
This parallels my educational ideas, which developed independently from lifelong yearning for knowledge. After a B. S. in physics from Columbia University (with equivalents of a mathematics major, a chemistry minor) and an M. S. in mathematics at New York University, I completed all doctoral course work, culminating in 103 mathematics credits. Then my real education began. As the great quality control expert C. Edwards Deming said, an academic degree is like a driver's permit -- a permit to learn more. (Deming also said, "Cooperate with your fellow workers; compete with yourself".)
When I completed my academic work, I felt very incompletely educated. But I had learned two important things. I knew, more than ever, that I wanted an education. And I had learned how to study.
I've never met most of my teachers -- only their papers and books. My greatest teacher is Charlotte. You know Charlotte. Of course, you do! the spider in E. B. White's delightful, Charlotte's Web. I've told students, "To mean is to weave a web of connections about a term". I often say, "Charlotte struck again!", regarding "a great idea". Or, "Charlotte, please weave connections between these strands."
Two blessings sustain me. Often, putting my head to the pillow at night, I can murmur, "How ignorant I was this morning!" And, when a "teacher" explicates math or physics puzzles, often I can say, "Thanks to Charlotte's connections, I know more about that than this other teacher."
For example, in the 1970s, I read about the deveopment, in the1960's, of "multisets". Once I understand their structure and use, I realized, thanks to my Charlotte connection, that they resembled o-sets which I first wrote about in 1957. (This was in connection with lectures I gave on "The Foundations of Mathematics" in the first National Science Foundation Institute to take place in Puerto Rico -- which I organized.) . Whereas multisets hybridly map sets into integers, my o-sets are type-degree extensions of type-only sets. And Charlotte wove for me unique o-set webbings to factor and distributive lattices (adult versions of my afore-mention mathtivity for preschool kids, Pecking Order). I call these "unique webbings" because you cannot derive these connections from multisets as formulated in the literature.
As a second example, I also learned in the 1960s about the development in the 1970s of fuzzy logic and fuzzy sets, which hybridly map from logic or sets to decimal fractions less than or equal to 1. When I understood these, I realized, thanks to my Charlotte Connection, that these resemble my 1957 probability-interpretations of type-only indicators (binary "truth tables") extended to type-degree indicators. Again Charlotte wove for me unique webbings to factor and distributive lattices.
As a third example, in the 1980s, I encountered a book by Z. A. Melzak, which taught me about about the bypass pattern, which I describe in ab associated file. This same Melzak book also explained to me the origins, in the18th century of basic hypergeometric functions. Charlotte showed me that their q-nomial forms spin from the same generating functions I derived as partorial combinatorics, described elsewhere. My partorials extend the familiar binomial combinatorics. (I labeled them "partorial" because the nth partorial distribution canonically partitions the permutations derived from the (n+1)-binomial.) I derived partorials in 1969 for my o-sets and they enjoy those webbings I've described.
These, and more, I owe to Charlotte's web education.
So? Well, likely you learned about "hypotheticals" from watching the "O. J. Trial" on TV or reading about it in the newspaper. I'll explain my point by putting a hypothetical to you.
Suppose I were your financial adviser. And suppose you found out that I know about many very-low-risk, high-payoff investments. "Chances are" that even the most marginal investor can make a significant investment and expect a rewarding rise in the value of her or his investment, and the many possible marginal investments will drive up the value of your own investment. If you can "stay in the market", the payoff after several years can be spectacular. But --as the critical supposition! -- I do not advise you or any other investor about these "goodies". What kind of a financial adviser would I be? What would you want to do about my negligence?
I'm not being hypothetical regarding many educational "goodies" which require only the most pedestrian learning efforts. Yet they pay off big in our high-tech economy. And extensive effort, could put you on the frontier of modern physical science, ready to benfit from its advances. Yet representatives of the educational institution, the National Science Foundation, corporations, the media, and American parents ignore these "goodies". I know, because I've spent more than 30 years pleading for support from all of these groups. "Web education" articulates my terms: "connek", "loconnek", "hiconnek". ("Hiconnek for HiTech! Loconnek for The People!") In my financial analogy, a connek is an "average" investment; a loconnek is a marginal investment; a hiconneck is a big investment with big pay-off. But I'll translate this from financial terminology into web terminology.
"Raw" loconneks spin conneks, thereby changing history. Magnified into "subjects", conneks spin hiconneks. And learning to spin connek into hiconnek gains you creative potential.
In web terminology, an orb spider's web-center represents the loconnek. A center-strand to web-edge is a particular connek. (Usually, correlative conneks emanate from loconnek center-strands, with side-strands to other correlative conneks.) Finally, the web is the hiconnek -- what the spider (expert) sees when the web is spun and appraised.
My educational program then becomes: (1) Seek crucial conneks in elementary curricula. (2) Trace these conneks to ancestral loconneks. (3) Ensure that children spin from these conneks to loconneks of preschool education. (For, in terms of my distinction between proto-education and education, THE CHILDREN DON'T KNOW THAT THEY KNOW!) (4) If associated hiconneks exist, teach these conneks so that "strands are anchored" for "extending the connections that weave into" those hiconneks.
Otherwise, fragmented education shifts this "spade-work" from teachers to learners! Only a loconnek¬connek-hiconnek educational "unit" is complete!
To deal with all the drugs available, their benign- and side-effects, what treatments they've been tested in, etc., the physician references a voluminous Pharmacopoeia.
Realizing this, I applied, in 1962, for a grant from the National Science Foundation to work with colleagues in assembling a Methodocopoeia of all the different ways of teaching counting, adding, subtracting, etc. (The request was ignored. But nothing like this yet exists.)
Here's an illustration of the need for diversity of methodology. In 1967, while on sabbatical leave from my university, I did volunteer tutoring at Yorkville Settlement House in New York City with six boys having trouble with fractions, decimals, and percentages. To communicate effectively, it required a different mix of methods for each student! Then I consulted their teacher, who was not using either of two methods in their textbook. I then taught the boys how to translate their correct homework so their teacher could understand.
The Methodocopoeia should also deal with problems arising from a particular teaching method, such as I discuss in IATROGENIC MATH. "Different ways" connotes tactics. The Methodocopoeia could also reference many mathematical strategies, such as I discuss in associated files on strategy. .
The Methodocopoeia could support myMathematics Appreciation files for adults, engendering the enthusiatic participation now enjoyed by art appreciation and music appreciation courses, workshops, and seminars.
The Methdocopoeia could reference learning dysfunctions, such as acalculia and dyscalculia, disorders in calculation, comparable to dyslexia in reading.
The Methodocopoeia could occupy a database in a laptop computer for the teacher-on-the-line. Laptops can network with a larger school computer, with public and university libraries, with PCs in student homes. Networks and internets are information webs, "trapping flies of knowledge".
For web education, as in the associated file on "African Violet Education", let conek (l; c; h) list, in The Methodocopoeia, the number (l) of loconneks of this given conek; the number (c) of its correlative conneks, and the number (h) of its hiconneks -- with references for each parameter.
And this, in turn, suggests several strategies. In teaching an algorithm or concept, choose that method invoking the most loconneks, hiconneks, correlative connecks. Or the most loconnecks for a given conneck. Or the most correlative conneks for .... Or the most hiconnecks for .... Etc. The Methocopoeia could advise the teacher-on-the-line about the nature and advantages and disadvantages of these and other strategies.
Given such tools, teachers and students, by spinning web education under The Charlotte Connection, could become web workers.
Do you think, as actors, you can teach WEBWORKING. If so, then you can be of great value to the BUAINESS WORLD.
FULFILL BY FILLING SOCIETY'S NEEDS. Happy teaching!