Thought Laboratory

Its been a while.  My last actual post was in August, though (as you’ll see shortly), I did have another post partially written in October that I never actually finished.  Although I doubt there is a large readership out there wondering what happened, I at least want to record - if only for myself - what has stopped the flow of writing. 

In mid-September, my role as manager of the Coating engineering department at Goodrich came to an uneasy end.  The initial reorganization of that department into separate Engineering and Operations departments, and their separation over directorates, had been a matter of contention within the upper management of the Company.  I myself had never assumed that my position as Coating Engineering Manager would last more than a few years - long enough to change the direction of the department’s technical staff, and raise a successor.  This plan was interrupted - permanently - by mounting pressures and insecurities within the senior management team, which lead to a complete reversal of the original reorganization.

What followed was a month or two of re-inventing my role at Goodrich, turning back to my engineering career, and expanding in new directions.  In this I have succeeded, and I have emerged onto a new path of exciting activity, finally engaging some technical interests of mine that I’ve been trying to bring to bear within Goodrich for the past 20 years.

This settled down just in time for a much more significant life event - the birth of my son Aaron, on December 13th.  Aaron has a great disposition, as have all of my children, but the first months of life certainly require a re-adjustment of life style.  Any available excess energy is needed just to support the proper functioning of the home, and writing comes rather far down on the list of priorities.

And then, along came this little surprise.  A hernia that had been “repaired” back in 1999 apparently recurred within a year of that operation.  At a physical late last month, my general physician went into a bit of a panic when she noticed the lump in my stomach.  Now this lump has been there for the past 8 years, and I had dismissed it as scar tissue from the surgery - certainly this physician had seen the lump at least 8 times in the past.  Nonetheless, off I went to the surgeon (same as in 1999), and he confirmed that the hernia had recurred.  And so, this Monday (March 10th), it was repaired for a second time.

The result is that I’ve been confined to bed since then.  And yesterday, I learned that the surgical site is infected, which means I’ll remain in bed for the next several days.  And that gives me an opportunity to catch up a bit on both reading, and writing.

(This post was started sometime in October, 2007.  I’ve completed it in March, 2008, but altered the timestamp to indicate its approximate date of conception). 

I’ve just finished reading Charles Darwin’s first major book, Voyage of the Beagle.  This is an account of a 5 year surveying voyage aboard the HMS Beagle, circumnavigating the globe, which Darwin joined as an observer.  I had been interested in reading Darwin’s evolutionary work - Origin of Species, Descent of Man - and had acquired a comprehensive volume of four of his books published recently as “From the Simplest of Beginnings”.  It is one of my odd characteristics to insist on reading such things from cover to cover, and the first of the works in this collection was the Beagle. 

I approached this book figuring it could be a very dry account of a naturalist on an exploring expedition, filled with descriptions of flora and fauna, using terminology with which I would be unfamiliar (not at all having an interest or education in biology), loaded with Latin categorization.  I was very wrong in this prejudgement.  Although there is plenty of description of flora and fauna, Latin species and genera are used, and familiarity assumed, Darwin focuses this work more on anthropology than biology.  There is also a fair bit of geology - in fact, the only original theory stated in this work is on the formation of coral islands and barrier reefs, having to do with the rising and falling of land masses.

Another surprise was in the specific geographical focus on South America.  The mission of the Beagle was to survey the coasts of this continent, and they spent about 3-1/2 years of the 5 year voyage sailing from point to point along its coasts.  I had expected more coverage of areas farther from European influence - Pacific islands, southeast Asia, Africa - but indeed the Beagle visited no location that had not previously been explored, and Darwin’s account dwells upon the colonized areas much more than those predominantly aboriginal.  There are no exciting discoveries revealed, no strange new species found (plenty of new species, but not particularly unusual), and little in the way of drama portrayed.

Nonetheless, it is in his descriptions of the people and societies that he encounters that I found the most thought-provoking material.  One encounter in particular is worthy of discussion. 

The Beagle visited Tierra del Fuego, at the southern tip of South America.  The native inhabitants of Tierra del Fuego were the Yamana Indians, living in one of the least hospitable areas on Earth, in a stone age society.  This area of South America has a high annual temmperature near 50 degrees (F), and only a handful of days without precipitation.  The Yamanas were strictly a hunter/gatherer tribe, attempting no agriculture, and commonly went through periods of starvation, during which they resorted to cannibalism (of the older women in the tribe) to survive.  It is to be noted that they remained in the Tierra del Fuego area, for apparently thousands of years, despite being only a few hundred miles south of the much more temperate areas supporting advanced civilization.

On a previous visit to the area, the Beagle had taken four of the natives on board and returned with them to England, where they became well-known “celebrities”, and visited with the King and Queen.  The youngest of these captives, whom the British called Jemmy Button, was educated in Britain, and acquired a limited understanding of the English language.  During Darwin’s voyage on the Beagle, Jemmy and two other surviving captives were returned to Tierra del Fuego.  The Beagle returned to the area after a few months, to find Jemmy reverted completely to his native condition - naked and emaciated.  A small party of Europeans remained in the area while the Beagle continued its explorations.  Upon the return of the Beagle after a couple more months, it was found that the Yamanas, led by Jemmy, had attacked the small campsite, stealing food and various other items.  Twenty years later, a missionary group was similarly attacked and massacred, again by a party of Yamanas lead by Jemmy.

I find this story of interest in several ways.  What struck Darwin was the fact that these were human beings of the same species as Europeans, and in his commentary he wonders if and how this can really be the case.  What I find fascinating is that this stone age tribe, when exposed to civilizations providing modes of living clearly superior to their own, not only failed to acquire any of the advantages of that interaction, but clearly could not understand the advantages, and actively chose to ignore them.  In this, I am not merely referencing the Jemmy Button story, but returning to the observation that Tierra del Fuego is close enough to Patagonia to expect that some Fuegians must have wandered into these regions and returned home to tell of this land of plenty located only a few hundred miles to the north.  Recalling that the Yamanas had been in this region for perhaps as long as 10000 years prior to the Beagle’s visit, I find it fascinating that this pocket of stone age humans persisted for so long when the surrounding humans advanced into civilization.

There are other cases of stone age peoples surviving far into the 20th century, but the ones I recall have all been islanders, separated from civilization by thousands of miles of ocean, or Africans, in which the majority of the continent until very recently had been living in pre-historic conditions.

I further wonder about the mentality of the Tierra del Fuegians.  Returning to a consideration of the bicameral mind theory of Jaynes (which I may not have discussed in this blog - I apologize, but will refer the reader elsewhere instead of going through this here), I wonder if these latter stone age peoples are not still bicameral.  If so, there may be a case for declaring them to be of another species than human, in answer to Darwin’s contemplations.

When I started my career some 21 years ago as a junior engineer at a technology company located in Connecticut, the standard work attire consisted of a button-down shirt, dress slacks, shined leather shoes, and a tie.  Most of the employees wore an undershirt beneath the dress shirt.  Managers and businessmen always wore suits, upper managers wore 3-piece suits.  If there was any official dress code “policy”, no one ever bothered to point it out.  I was considered a bit radical when summer ended and I continued to wear short sleeve shirts (I can’t stand having my forearms covered).

A few years later, the company was split up, and we were purchased by a California-based company.  After a couple of years, a new policy was announced - “casual Friday”.  Every Friday, we were allowed - even encouraged - to dress in casual clothes - defined as jeans or cotton slacks, knit shirts, comfortable shoes, and (definitely) no tie.  The reasoning was to allow a level of “relaxation” for the final day of the work week, as well as to match the trend in California.

After a few more years, and yet another corporate buy-out, “casual Friday” had gradually expanded into casual every-day, and the quality of clothing being worn had slowly devolved to the point where the company needed to reinforce a proper dress code policy.  We were again encouraged to wear casual clothes, but more carefully defined, though the restriction to one day a week vanished. 

At that time, a definite separation of dress behavior occurred.  More managers and businessmen returned to wearing formal attire, though the suit had largely disappeared.  Most engineers embraced the casual wear, and rather quickly began the slow degradation of what was considered casual.  Older engineers, and (though not universally) the more capable engineers continued wearing formal clothes.

That was about 10 years ago.  Today, the collapse of the dress code is just about complete.  Almost all engineers, almost all managers and businessmen, even our senior managers, can be found most days wearing at best the old “casual” standard; at worst, jeans and a tee-shirt.  Ties (for all but unusual days) have vanished from the building.  The dress code has begun to merge with the sexual harassment policy (no shorts, no short skirts, no muscle shirts, no offensive slogan tee shirts). 

I still wear a button-down shirt, dress slacks, shined leather shoes, and a tie.  I have embraced casual Friday, and I did give up the tie for about the last 6 months, but I have put the tie back on, and its staying on. In a building of 500 employees, with about 300 engineers and managers, I am now one of perhaps 5 employees (and very possibly the only one) wearing a tie when not visiting with a Customer (many of whom, incidentally, do not arrive at our facility wearing ties).

So - do the clothes worn affect our professional behavior?

Absolutely.

The choice of clothing worn represents to others an individual’s emotional frame of mind, or attitude.  It is not representative of the exact emotional state of the person, as this can change throughout the day without requiring continual changes in clothes; rather, it portrays the individual’s expectation of what their emotional state shall be, or should be for that day.  Hence the practice of wearing black for mourning, bright colors for gayiety, wrinkled or loose clothing for relaxation, and pressed clothing with plain or simple pattern in muted colors for seriousness.  Of course, there are exceptions in which clothing may be chosen for practical reasons separated from attitude - low cost, high durability clothing for occupations involving hard physical labor; damaged or even dirty clothing for hard labor performed at home.  The use of uniforms is indicative of occupations in which emotion is not considered a proper component to one’s job activities.

It should be emphasized again that the selection of clothing may be not one’s actual expectation of emotional state, but what one believes others expect that state to be.  It is this that explains in part the spread of changes in my company’s dress code.  The company sends a message by “relaxing” the dress code - don’t take the job so seriously.  Loosen up.  This is accepted by some as a command, by others as an affirmation of their actual attitude toward work, and by others, over time, by what they see as a change in the Company’s attitude, as reflected in the clothing, and indeed the resulting behavior, of their peers.  Once this dynamic starts, most will not resist the trend toward greater and greater expectations of relaxation.  The Company’s former productivity cannot be recovered easily.

As I saw after the Company attempted - temporarily - to stop the decline, there was a subpopulation of employees who saw what was happening (perhaps without fully understanding), and resisted the loss of seriousness, focus, concentration in the larger population, by holding on to the “old ways”.  Interestingly, I myself discovered during this time that by continuing to wear a tie (the most visible of the clothing elements to generally disappear), my presumed status in the Company rose in situations where my actual achievements were not well known.  I have joked that “he who wears the tie runs the meeting” - but by and large this became increasingly true.

As I stated above, I did give up the tie for several months recently - perhaps the peer pressure finally began to affect me as well.  But I found that I indeed “feel” more appropriate in a tie when at work.  It has been through introspecting on this “feeling” that I have been led to understand the role of clothing in the portrayal of attitude, and its effect on the wearer and those with which he interacts.

This is a phrase I’ve heard with increasing frequency in my career as an optical engineer, usually coming from the mouth of a manager with an engineering background.  The context is typically either the beginning of an investigation into the cause of a significant anomaly, or near the completion of the development of a new technique of manufacture or verification testing.  My reaction has always been one of disgust, followed by confusion.  The phrase is used almost as an apology, as the real intent of the manager is actually to do some limited experimentation, but is used to indicate that a strong limit is to be set on the extent of the experiments.  My confusion stems from not at all understanding what the manager means by the term “science project”, and why such a person would be using “science” as a derogatory term.  I now believe I have an answer to my confusion.

Engineering is the practical application of scientific knowledge to produce material items of value for Man’s use.  Engineering presumes the existence of science, and each engineering field relies upon the existence of one or more fields of science containing an understanding of the phenomena which the engineers will create and control to Man’s advantage. Most engineers have a respect for the science upon which their careers rely, though most would admit to either not having the depth of knowledge, or the interest, in pursuing a scientific career.

What would cause an engineer to have a disinterest in science?  One aspect of the difference typically between an engineer and a scientist is the level of education completed.  The term “scientist” almost always applies only to individuals who have obtained a doctorate; most engineers are not doctorates.  Although the resulting inequality in academic background can cause arrogance on the part of the scientist, and a latent envy in the engineer, I do not think this is the primary source of the engineer’s disinterest in most cases. 

Rather, there appears to be a prevalent attitude that scientists are overly “theoretical”, and are therefore somehow removed from the “practical” concerns of the engineer.  Rephrasing this, engineers may see scientists as Rationalists whose analytical constructions do not fully apply to the “real world”.  Scientists may conversely see engineers as Pragmatists who fail to fully understand the science underlying their empirical experimentation and tinkerings. (Of course, I am speaking in gross generalizations here - not all scientists and engineers relate in this manner - but I do believe this is the general trend). 

And so, what we see here is yet another manifestation of the analytic / synthetic dichotomy originally promoted by Kant.  The engineer who has implicitly accepted the division of knowledge along these lines sees Science (and more fervently scientists) as impractical, and believes only in what he can observe through experiment.  Analysis is generally rejected as insufficient “proof” (truth obtained by reason alone can contain no knowledge of “things-in-themselves”), and the engineer seeks confirmation in direct experience.  However, he then faces the problem of empirical uncertainty (truth obtained by observation alone can never be certain).  Experimentation can never be sufficient to establish certainty - there always seems to be another test that could be (should be?) done. 

It is the engineering manager that needs to confront and solve this apparent paradox.  The epistemology he has come to accept creates the paradox - he fails to see the certainty that comes (and can only come) from a proper union of the use of theory and experiment - the use of the Scientific Method.  What is needed in this situation is precisely a “science project”, because only a project based in Scientific Method can lead to an understanding of the phenomenon under consideration, and can avoid an infinite progression of meaningless experimentation.  Instead of declaring this need, the manager makes an irrational appeal to limit the effort arbitarily.  Far too often, the results are at best exuberantly wasteful, and at worst insufficiently misleading.

The tools I discussed in my earlier post on this topic only attempt to deal with the storage of information.  Organization of knowledge, attempts to integrate various facts or propositions, relies upon the human entirely.  The tools are designed to improve the efficiency with which information can be organized, while allowing for changes in the organizational structure.   As previously noted, I have not found a viable solution yet which handles that challenge well.

 Another of my long-term fascinations has been in the area of what is conventionally called “Artificial Intelligence”.  For years, this interest was centered on the possibility - which fueled the majority of AI research - that a machine could actually attain “intelligence”, and even consciousness.  After a great many years of attempting to integrate this possibility with the tenets of Objectivism - and this only after becoming a serious student of Objectivism - it became clear to me that such a machine can indeed never exist.  Specifically, it is impossible for a machine to attain a rational conciousness, as this requires a reasoning faculty, aware of its surroundings, operating with free will, performing goal-directed actions.  Free will is impossible to devise in a machine, therefore values cannot be held by a machine (that connection requires additional comment, but not tonight), therefore goals cannot be developed, and consciousness cannot occur.

I’ll leave that direction of thought for a later discussion.  My purpose tonight is to discuss my search for a thinking assistant using AI concepts.  What can be achieved by a machine is a repository of information, combined with a logic processor.  There are two approaches to combining these elements which AI research has developed to a level of sophistication sufficient to be considered as a possible route to eventually creating a useful tool for storage and maintenance of structured information.  In this, and an ensuing post, I’ll discuss each in turn.

The first approach of interest is in the development of declarative programming languages.  These languages, of which Prolog is the flagship, rely upon an interpreter in which is contained a generalized logic processor.  This processor can determine the truth or falsity of statements of symbolic logic [the Objectivist reader cringes], once the truth-state of the parameters used by a symbolic logic statement are determined.  The language harnesses this logic processor through definition of a grammar which allows a programmer to state a set of “facts”, and then construct a complex logical statement using these facts, which the logic processor will attempt to “prove”.  In the process of solving the logical problem posed, the system achieves the programmer’s desired goal through various “side effects” generated as the system traverses the logical statement and facts in the quest for all possible “solutions” to the problem.

If this sounds like a simply bizarre way to create a software program, let me assure you, as a standard procedural programmer, I found this approach almost laughably alien to grasp.  As a general-purpose programming language, the power of this approach is in the ability to create extraordinarily complex computational flows indirectly through the use of clever logical statements and a firm understanding of the algorithm underlying the logic processor.  I reached the point of “seeing” this power, but certainly have not mastered the art of harnessing it effectively. 

That being said, the underlying combination of a database of “facts” combined with a logical processor remains intriguing.  A common “text book” use of Prolog is to create an expert system.  An expert system is a set of encoded facts, which can be asked an encoded question (or series of questions) to receive an encoded answer.  In the most trivial of expert systems, the question posed will have a True or False answer, and the system will respond with “True” or “False”.  Slightly more advanced is a system structured as a diagnostic tool, which asks the user a series of questions, starting from the most general to increasingly specific, with the questions selected by the system based upon the previous answers of the user.  Most of us have undoubtably dealt with various automated help systems that are poor implementations of this form of expert system.

Can one use such a declarative language system to encode a body of knowledge, and then examine its internal consistency?  Or ask a question and receive an answer?  The trick here is in the encoding, as is the case in any attempt to reduce knowledge to a symbolic logical form.  Each “term” in the system needs to be exhaustively defined, along with all of its inter-relationships with other terms.  A key problem is setting boundaries on the universe of terms introduced to the system - there will always be a practical limit to the number of terms and relationships that the system can manage, and the problem of precise definition of the terms themselves, and of all actual connections between terms rapidly becomes overwhelming.  It is indeed quite likely that the task of creating a sufficient database of encoded facts is always impossible to accomplish.

I recall seeing one attempt to examine the possibilities of using such a system in this manner.  In fact, the author of the software attempted to use Objectivism-based concepts as the terms in several of his examples.  I have no idea if this system is still available, but if I find it on the Internet, I’ll be sure to post a link for interested parties.  My recollection was that I could not at all understand the encoding scheme he was attempting to use, and made little or no headway in creating my own examples.

I’ve owned a copy of Immanuel Kant’s Critique of Pure Reason for probably 20 years now.  After an initial attempt at reading this, it has sat on my various bookshelves - usually far away from the Objectivist shelf - and tempted me with its evil.  Finally, I picked it up a couple weeks ago and began trying to comprehend its pages, under the motivation of knowing one’s enemy.  I am reading Kant gradually, as a challenge to my understanding of Objectivism, as an exercise in learning through contrast. 

The basic premises of Kant are easily dismissed - this entire work rests on the false dichotomy of Analytic versus Synthetic propositions, further supported by the presumption that the human mind comes pre-formed with a-priori knowledge.  Nonetheless, it is equally important to resolve each of his detailed arguments into the categories of the completely incorrect in premise and argument, vs. the correct, but argued from erroneous assumptions.  Where possible, I would like to be able to counter his erroneous conclusions with more than merely a negative evaluation, and provide a positive explanation of an alternative conclusion.

In the opening sections of Kant’s text, after revealing his overall thesis in a lengthy introduction, he begins building evidence for the existence of a-priori synthetic knowledge by considering the concepts of Space and Time.  The concept of space, he declares, is not arrived at through experience of the senses.  The observation of individualized entities, separated in location, pre-supposes and invokes the concept of space.  He places emphasis on the fact that while we can visualize objects being in space, we can also accept that space may exist devoid of objects.  Because we can understand space in the absence of entities, we must therefore not need entities - and their observation - in order to comprehend the properties of space.  Therefore, we must be able to intuit space without requiring experience.  Space is then an a-priori synthetic concept.

Against this description, I offer the following.  The newly born infant fails to comprehend the concept of space.  His very first observations of the world through his sensory apparatus will not result immediately in an understanding of individuality of entities.  All is a continuous blur of light, sound, smell, and touch. 

In the very first moments of life, the infant begins the learning process.  His limbs move about and make contact with objects.  The brain begins to form connections between the motor movements of his various muscles and the sensations of touch from epidermal nerves.  His other senses are also immediately active. The eyes at first are unfocussed.  Through a rapid process of learning, the brain associates clarity of sight with levels of ciliary muscle contraction (the muscles controlling focus of the eye’s lens) for various content of his visual field.  Both the sequence and magnitude of motor movements associated with various sensations of touch and sight, and the training of the focussing mechanism of the eye form the first yardsticks by which the concept of distance, and therefore of space, is learned.  A third distance and orientation measuring sensation is hearing, which learns distance from the magnitude of a sound, and direction from the differential timing of the reception of sound between the two ears.  (The use of differential timing to determine orientation is well-documented in neuroscience - I found this to be an amazing fact).

After a very short period of time - as little as a few hours, at most a day - the human infant will begin formulating an understanding of space from these sensual observations.  The brain will accumulate remembered - trained - connections between motor movements and sensations.  Space will be understood and measured by the muscular motions required to reach a nearby object.  Sight and hearing will at first be secondary checks on the measurement of distance and orientation.  As the space intuition matures, over weeks and months, sight and hearing will become increasingly the dominant source of spatial information.  Finally, over a period of years, the spatial intuition will become increasingly generalized to account for distances beyond the child’s immediate experience.

As evidence that spatial intuition is gained through experience, and that the process of internalizing and learning the concept of space can last years, if not a lifetime, consider the following examples.  A young child will only begin to understand the distance to a specific destination after having repeatedly travelled to that destination using the same means of transport.  Say I walk my 2 year old daughter to the end of our driveway repeatedly (a distance of about 400 ft), and then on other days walk her to a nearby park (a distance of about 1/4 mile).  She will soon understand the relative length of time it takes us to cover these two distances, and since the mode of transportation is constant, she will begin to grasp the relative distances involved.  If I then drive her past the end of the driveway, and past the park, and on into town (about 4 miles away), she will similarly begin to grasp those relative distances.  Notably,  there can result some confusion at first - specifically about the distance to the park - it will simultaneously seem far away at walking speed, and close at hand at driving speed.  (As you can guess, I’ve heard this confusion in the form of a complaint - “Why does it take so long to get to the park, Dad?” “Because we’re walking there”).

In later years, it remains true that until an individual travels a given distance, or farther, it is hard to grasp that distance.  Even though my geography is rather accurate, I didn’t fully understand the size of the United States until I flew from New York to San Diego a few years ago (and properly integrating that experience is definitely complicated by the changing of time zones - even though I abstractly understand the effect, I still “feel” that flying from California to New York takes more time than flying from New York to California).  Saying that the Moon is 380,000 miles from Earth does not communicate its distance completely.  Watching men travel on a spacecraft which travels 100 miles to reach a low Earth orbit in 30 minutes, for over three days to reach the Moon brings clarity to the meaning of that distance (though this is a confused example physically, due to deceleration along the way, these flights still improved our understanding of the distance).  Similarly, it is undoubtably true that no one can claim an understanding of the distance to the nearest star, let alone the sizes of galaxies or distances between them.

I’ve just spent the past hour going through all of the posts and mapping them to appropriate Categories.  In emphasizing that this space should not be read as a Blog, but as a collection of ideas, I recommend making use of the Category list found on the lower right side of this page, if you are not merely bringing yourself up to date on my latest additions to Thought Laboratory.

I also completed (I hope) removing those dang A-hat characters that magically appeared in some of the older posts.  If you find any remaining, please post a comment so I can remove them.

The reader may notice that I have become rather disorganized in the order in which I am creating and expanding topics.  This is in line with the nature of my desire for the use of this “blog” (a term I dislike using to describe this space).  Thought Laboratory is meant to be primarily a storage location for my ideas.  The fact that others can read and comment on these ideas is merely a bonus (one that I am guessing is not very often being exercised). 

When I mark a topic as “Part I” etc, this is an indication to myself that the topic is incomplete. In some cases, I merely ran out of time or energy to complete an existing thought.  In other cases, I recognize the topic as incompletely formed, and yet I have not yet thought through the additional components of the topic that I wish to visit.  The patient reader may or may not find additional parts forthcoming.

One general comment, which I might try to add to the banner of the site:  Unlike “blogs” (ugh), this collection is not meant to be read in any particular order, nor is the content meant to be “timely”, but quite the opposite - “timeless”.  The organization of the material itself is indeed an example of my most recent post on the problem of organizing information (Quest for a Thinking Assistant: Part I).  This archive is clearly not the best solution, but at least allows a persistent storage location for my thoughts as they occur.

I’ll try to examine the features of this environment (e.g. keywords and categories) to see if these can be of use in at least coarsely structuring the material for the reader.

Throughout my career, both as an engineer and as a lifelong student on a large host of topics, I have repeatedly faced the problem of how best to organize information in an external representation to reflect and aid in my internal understanding of a field of study.  By “external representation” I mean anything from a simple handwritten notebook to an online database of facts.  I have tried a great variety of methods (and have succeeded in gaining a greater variety of knowledge) over the years, but none have been sufficient to allow me to refer back to them at a future date to efficiently recall and recover my internal knowledge to a level I deem acceptable.

A spiral-bound notebook was generally the first method to which folks of my generation were introduced.  While reading a text, or listening to a lecture series, notes are taken in a serial manner by hand.  The structure of the serial notebook is static, editing is difficult to impossible, so any later effort to reorganize the material to better represent the abstractions and relationships arrived at through contemplation of material requires a reproduction of the material in a new notebook.  Folding in a second source of material - merging notes from a lecture with notes from a text, for example - is equally difficult. A small step up is the loose bound notebook, which at least allows insertion of later material, but the other serious problems of static text remain.

And then personal computers arrived.  Static text was no longer a problem, though the process of collection of material remained handwriting, or required reading, or listening to recorded lectures, in front of a terminal.  I used a rather slick word processor (ChiWriter), which allowed the use of mathematical symbols (my main interest in that period being mathematics of dynamic systems), but I rapidly found the process of creating and organizing a large electronic notebook daunting.  The structure of the notebook was generally dictated by the first large text I read on a topic.  Then subsequent material had to be manually merged into this structure until it became evident that the structure was imperfect and needed a different hierarchy.  Dealing with the mess of reorganization in a flat word processor made the whole thing terribly arduous and distracted mightly from the process of learning.

Next came Think Tank, a DOS program which was really no more than an outlining program.  This was marginally better in principle, as larger sections of text could be manipulated in a collapsable grouping, but the program was not really intended to hold large bodies of text, and - with my interests still primarily requiring mathematical notation - lack of anything other than ASCII input made the tool fairly useless.

More recently, I have examined the use of “mind mapping” software systems (MindManager by MindJet is a commercial product, though FreeMind and CMaps are equivalent or even better freeware systems).  At first, these looked more interesting, by allowing a more general mapping of concepts and relationships in a not-necessarily hierarchial order.  However, these tools fail on two counts.  First, there remains the clumsiness of dealing with large amounts of detail in a pictoral representation (there are offered solutions to this, but they consist of mere hyperlinks to documents).  But the more fundamental failure is that knowledge is hierarchial, and allowing for freeform relationships between concepts leads to a much more confusing, and ultimately non-rational, representation of the data to be organized. 

One of the most fundamental principles within mathematics is randomness.   The study of random processes is the direct subject matter of probability and statistics, from which a broad assortment of additional fields arise, including game theory, and the theory of stochastic processes.  Applied mathematics is heavily populated with applications of statistics, in finance - from market dynamics to insurance models, in physics - from thermodynamics to quantum mechanics, and throughout engineering in the form of error budgeting, tolerancing, safety factoring, and risk analysis.

What, precisely, is meant by randomness?  A common definition is that a process is random if no order can be discerned in its manifestation.  A more mathematical definition may include the necessity of unpredictability, a lack of bias or correlation to other processes, and may require that though “random”, the process output must follow a particular probability distribution.  In a higher-order of randomness, which has been referred to as an “arbitrary” process, no probability distribution in particular applies to the process output.  A more philosophically-oriented description may assume a-causality and non-determinism in the events depicted as “random”.  

In the quest for the proper philosophical foundations for the fields of mathematics arising from the concept of randomness, two main questions require consideration:

1) What form of randomness exists in Reality?
2) What is the relationship between the philosophical understanding of randomness, and the nature of randomness required by the fields of probability and statistics?

It is an axiomatic, self-evident truth that all physical events are caused by prior events.  The Law of Causality therefore forbids the existence of random physical processes exhibiting a-causal and non-determined behavior.  On the other hand, there can exist causal, but unpredictable behavior. 

Unpredictability can take two forms.  What I will term “soft” unpredictability arises from a lack of knowledge on the part of the entity attempting a prediction.  Soft unpredictability is not inherent in a process, but lies in the current state of the predictor.  By educating the predictor, the unpredictability can be removed. Hence, I cannot predict my company’s cafeteria’s lunch menu for tomorrow only because I am not in communication with the manager of the cafeteria service.  My ability to perform this prediction could be altered with an appropriate phone call (if I knew the name or number of the cafeteria manager).

By prediction, I mean specifically the ability to indicate the future state of a process at a time prior to the time at which the process will achieve that state (the prediction must also be for a particular future time).  This is an essential distinction to consider in the description of what I term “hard” unpredictability. 

There is a vast category of phenomena in which infinitesimal changes in starting conditions lead to exponentially divergent outcomes as the process evolves.  This is the (approximate) mathematical definition of a chaotic process.  For purposes of illustration, consider a simple mathematical series: x’=Gx(1-x), with G=3.7.  On each iteration, take x=x’ and repeat the calculation.  If we run two series A and B, with the first value in A being 0.1, and the first value in B being 0.100001, we get the following results:

Start            0.1                 0.100001
20 iterations 0.256724484   0.256693475
30 iterations 0.682868078   0.68171437
40 iterations 0.767514785   0.750851267
50 iterations 0.608389182   0.924135972

Beyond this point, the two series are completely uncorrelated (as will be very obvious if you plot the series).  In this example, an accurate prediction of the 50th iteration of the series requires knowledge of the starting point to better than 1 part in 100,000.  As the series progresses, the maximum allowable error of knowledge in the starting condition to allow accurate prediction decreases exponentially.  This characteristic of chaos is what I am terming “hard unpredictability”.

(There is much, much more that can be said about our example, which is known as the “logistic series”.  For the adventurous: run various examples varying the value of A from 0 to 4 to see a variety of behaviors, particularly right around A=3.57.  If you then think you’ve got a handle on it, try A=3.82.)
- To be continued