Pyhton In CaboosE (ICE) [ Non Zero-C Production ]

 Team. The CABOOSE System found in the text, JAVA in CABOOSE, by Abraham Vati James, has been ported. The companion Rosetta CABOOSE web history is currently working on rendering this simple product in fourteen different languages. Within the past week, an instance of this general-purpose controller (GPC) written in von Rossum's Python was provided. It is called Python ICE. This should not be confused with the product by Zero C. It contains a very simple-minded code-generator for use with its architectural control language (ACL) file containing the CABOOSE Logic.

This also can be found on GitHub.

Notoriously "Bad" English Skills - The Oracle Effect

 Team. An "oracle's" response is considered infallible. We might formulate our next query upon it, but we do not question its validity. Unfortunately, the modern computer and the software tools which it provides are seen a "oracles". We do not doubt a "fact" found on the WWW anymore than we would an output provided by a modern Texas Instrument's calculator given the problem "3+4". Yet, computers can produce "erroneous" output. 

As of this decade, 2020, modern computers have not passed the Turing Test proposed by the computing visionary Alan Turing nearly a century ago. In this test, he felt that, if the responses made by a computer could not be distinguished from those that a human would make, a software program could be deemed "fully" intelligent. And, in this era of International Business Machine's Deep Blue which bested the chess Grand Master Kasparov on numerous occasions, one might feel that a computer's intelligence greatly exceeds that of the average human. This simply is not the case.

There is a "universal law of cognitive limitation" governing modern computers or thinking machines. They cannot reason beyond the capacity of their creators. In essence, their "intelligence" could never exceed the "weakest" link in the chain of humans who programmed them. Nascently, computers are "mindless" automatons. They can perform logical functions at "lightening" speed that dazzles the mind. Yet, although modern processors can perform "billions" of commands per second, they cannot reason beyond their design limitations and can only do what they are told. Unless they are told how, they cannot innovate, learn from experience, or decide what "skills" or "knowledge" that they will acquire next.

And sadly, in this WWW-era, most humans deem computers unquestionable. This is ever so true in the use of modern languages. The author of this weblog is a native "Amurican" English-speaker. Notice that was not spelt American. And, he has found that many of the on-line resources describing the rules of a language he learnt throughout grammar school differ from his what he was taught by his grade school instructors.

Firstly, the orientation is "backward". In Ms. Tschetter's kindergarten class in 1975, the author learnt that English was read from the natural "right" side of the page as the eye scans the page "leftward". This orientation was based upon the top and bottom of the page with it experiencing an anthropomorphization that arises during "natural" communication. Arabic and Hebrew were deemed read from the "left-side".

Secondly, future years in grammar school taught the presence of irregular verbs in the English language. Some were used earlier in this passage.

Thirdly, the word "who" should be "whom" when it is an indirect or direct object in a sentence or follows certain prepositions.

Sadly, as computers grow increasing "brighter", humans become exponentially "duller" it seems. Many modern English speakers cannot understand passages with inverted word order. Which is an acceptable language construction. While, in graduate school at the University of Texas, the fact that most of the student body could not read English became apparent. And, most were Americans.

It seemed that they processed the words of a sentence in sequential order starting on what they called the "left" of the page or console. If the structuring of the sentence was not "super" simple and non-inverted, extremely confused they would become. Many of these students, despite their "poor" command of written language, earnt doctoral degree in computing with honors. Remember our "law of universal cognitive limitations" and our tacit acceptance of a computer's response as an oracle speaking.

Truth be told, in this Grammarly-Spellchecker era, written language lacks many of the idioms and mellifluous transitions and segues in speech that makes it interesting. And, this limited written usage affects the words which we speak. We become highly technical dullards, in light of this.

This phenomenon was first described in the 1980s by a high-school German teacher whom the author has know for many years. She stated that many of her students could not tell time based upon the quarter hour in English, since the relied upon their digital watches. They would read 3:45 P.M. as "three forty-five" and not "a quarter of four". They had forgotten the lessons which they had learnt about telling time on analog clocks in first and second grade. And, seeing that they did not understand and could not grasp this concept in their mother tongue, she had difficulty teaching them German.

And, this morning produced a shocker when the author was searching on Google for information on "intrest" rates which is a valid financial term. Yet, he was told that he should be searching for "interest rates" instead. In actuality, the author was interested in finding information on the intrest paid based upon an annual percentage rate for certain savings accounts.

And, this was not a "Google glitch". Other on-line references, such as www.dictionary.com, did not contain the term intrest, indicating a percentage of a financial principle charged or paid on a recurring periodic basis. And, it is wondered whether this language "snafu" has spread throughout the pages of the Motley Fool and CNBC with their expert on-line financial commentary.

And, seeing that we will forget certain facts over the years, we must refresh our memories, like a processor's cache. And, it has escaped the author whether the choice of an article such as "a or an" should be based upon the first noun that follows it or the word that it immediately proceeds. The rules governing articles and vowels plus the soft "h", such as the one found in "humor" properly pronounced (oomor), are well-remembered. 

Yet, where might might one find a "reliable" on-line grammar reference outline the language rules that he long since forgat.

Is this simply a phenomenon occurring with English, the world's third most widely spoken language, or is it present in others used on-line such a Mandarin Chinese and Spanish which are both more prevalent in world-wide use? And, will this ever cease?

Faithful Viewer

CABOOSE Team. We have a handful of "faithful" viewers who reside on various continents.This one is for you.  One of the projects which was mentioned earlier in this web history, that spans a few years, has been "revived". It is the Code Rosetta Stone project. Its goal is creating small "meaningful" code projects in various popular modern high-level computing languages. It was started in 2016, placed on pause that Fall, and restarted this summer. It comprises less than fifteen total post at this time. The web history currently outlines the developer of a CABOOSE-like controller kernel in fourteen "different" languages. With that said, some of the languages are "related", such as JAVA, Groovy, and Clojure or Node.js and Typescript. Best of all, the author has supplied an archive containing all of the source code implementations.

Hunt. Peck. Think. Happy Coding!

Art of Programming - [ PTQ ] == [IPO]

During this modern era of technology, many are seeking computing skills. One of the most prized of those skills is computer programming.

The author had his first experiences programming a computer during his fourth grade summer. This was with the BASIC language. And, that was during 1979. The wisdom of a hoary head and decades of coursework plus professional software development experiences has taught three simple concepts: PTQ or equivalently IPO.

From his early days, in formal computing courses at Vanderbilt among the dorms in the freshman quadrangle during the Spring of 1989, he saw something simple. intrinsic, and fundamental in the construction of all computer programs.

These primitive and fundamental parts were P, the preconditioned input, T, the transformations on the input that occur in the internal portions of the program, and Q, the post-conditioned output. In fact, during those days of his Pascal course, well-taught by a female graduate students whose name he has long forgotten, he penned some notes in his primary red Mead notebook, intended for his prose fiction course, concerning this.

He noticed that programs have three basic parts, I - input, P - processing, and O - output. The input can be null or the output can be null. But, some form of "processing" or "work" must be done, otherwise one would not make use of the computer program.

The first program that most students of software development learn is "Hello, World!". It is a program which will simply place this output on the computer's, tablet's, or phone's screen.

Once a student has learnt how one places output on the console, he has mastered one of the three abstract and primary skills which he must have in his toolkit for a career as a successful software developer.

The second skill one must learn is how one reads in input. Every computing language has numerous means for reading input. This could be from the console, from a file on the computer's file system, or a source on the computer's network such as a web-page. The mechanisms for doing so are similar within a language. Usually, most students first learn how one reads input from the computer screen, the console.

So, the second step in writing a "standard" program is reading input from the screen and simply outputting it again. This might be a program that reads in a person name, such as "Millicent", and printing a message, such as "Hello, Millicent! We are keeping up appearances!"

Yet, simply reading in data and echoing it on the screen, even if it has some interesting textual annotation, is not highly useful.

In comes the process. Processing takes the input which has been supplied and transforms this data so it is in a meaningful form. Then, this altered data, in the form of new, relevant information, is output.

So, when one is faced with writing a program, he must ask himself treat basic questions first.

1. What is the input and where can it be obtained from the console, a file, the network, or etc?
2. What information should be output once the input data is obtained?
3. Finally, how must the input data be processed and transformed so it produces accurate and useful output information?

Input. Process. Output [ IPO ]

So, this answers some questions about the art of programming, but what is this PTQ acronym.

The P stands for precondition. For most, if not all programs, the supplied input must be in a valid range of values. If a teacher were entering grades in a program which will determine a semester's average, a input grade less than zero or greater than one hundred would be out of range. Plus, this input should be numeric and not alphabetic. If creating a well-written and robust program that most likely will not crash while processing, one should check any input and make sure that it is in an acceptable range for any internal computation which will be done.

Yet, one "got-ya" exists with checking preconditions. They require more programming instructions. And, these commands which validate the input by checking its range might be erroneously written.

The T in PTQ is a synonym for the P in IPO. It is simply the internal computations which one uses when working with the input and producing the output. These transformations can be drawn from the pool of commands built-in a computer programming language or the many libraries and packages of commands composed from various combinations of these built-in instructions which are available with these "built-ins" in all modern programming languages.

Finally, the Q is a symbol commonly used in logic courses for post-conditions when discussion proofs about reasoning. So, we use it here, since a program is an instance of logical reasoning represented in a language which a computer can understand. After we have produced output, we can verify that it is in a valid range of acceptable and expected values. So, in the example of a teacher entering assessment scores from the semester, the final grade for the term should be between zero and hundred.

Checking these conditions, both on the "entry" and "exit" of a computing routine when validating input and verifying output, is a crucial part of producing robust programs.

So, after one asks himself the three questions about IPO above, he should ask himself the following questions.

1. What are the valid ranges of values for the inputs?
2. Will the chosen processing transform the input properly and produce the expected output?
3. Is the output produced in an acceptable range of values and reasonable based upon the input and chosen transformations?

And, with a hand-waving summary including a flourish of wild gesticulations, that is basically the general abstraction at the center of the art of computer programming.

Sionese Zugzwang

This web-history speaks most frequently about concepts in mathematics and computing. They will be discussed in the midst of some other concepts, concerning political science. We have not been posting content as frequently as we were a year or so ago, seeing that we have been busied with numerous projects in computer science education. Yet, those have slowed some in light of COVID-19. So, the author thought that he would pick up this writing project again.

In the text, the Emperor of Ocean Park by Stephen L. Carter, the protagonist is an African American male and law professor who is a chess-fanatic. He is nicknamed after a great Russian Grand Master, Mischa. As such, during his life’s situations depicted in the text, the strategic concept of “zugzwang” is presented.

It, in itself, as shown in this text, is the “chess-playing” situation were a player is facing an imminent checkmate and any move which he makes will simply sink him, weakening his position and further solidifying the situation of the impending checkmate.

This became a blatant fact of life, as the author was streaming news in his quarantined community, on yesterday evening, a couple of days after April 1^st. It seems that during the current state of world affairs and the “raging” health pandemic, the government of the United States of America blindly has accepted healthcare equipment from countries with which it has had a bittersweet relationship for numerous decades. This includes the government that spearheaded the former Soviet Union and China.

This is a humbling experience, where the mightiest and greatest nation in the world must ask for help from others. Otherwise, it might collapse. And, this “help” must come from those who its propaganda machine says are untrustworthy.  Yet, if these countries are truly foes, what will stop them from shipping masks, some of which are tainted with COVID-19 or other harmful biological agents.

In this war, which every country is currently fighting, the healthcare workers are a front-line of defense. If their numbers are decimated by contaminated mask and respirators which cannot be sanitized, who will America have for defense.

https://www.cbsnews.com/news/coronavirus-news-putin-sends-military-plane-us-supplies-after-talking-donald-trump/

https://www.cbsnews.com/news/coronavirus-covid-19-robert-kraft-new-england-patriots-plane-flying-medical-masks-to-boston-from-china/

With this as the case, the battle of dominance as a super-power becomes one of the numbers. As the author’s high school American government instructor named Jack would say, “the country with the most citizen’s wins”, if the number of denizens lost in the battle remains fairly uniform between combatants.

Below is a list of the largest countries in the world based upon an approximate population:

Rank       Country               Population

1              China                  1,426,279,708

2              India                   1,338,558,742

3              United States      327,527,107

4              Indonesia            263,564,697

5              Brazil                  210,193,253

6              Pakistan              194,749,053

7              Nigeria                185,313,910

8              Bangladesh         165,552,994

9              Russia                 144,154,086

10           Mexico                 129,132,150

11           Japan                    127,962,410

Number one is larger than numbers three through seven combined.

Also, in that, the author has a close relative who has a small business that manufactures personal protective equipment kit, he is aware of the fact that the “best priced” wholesale masks, gowns, and nitrile gloves come from mainland China. And, they likely are the largest supplier of such. If that nation takes advantage of this “opportunity” while the United States and its other adversaries are weakened and vulnerable, it could decimate much of the world’s non-Chinese inhabitants.

Is this cause for alarm? Most likely, it is not. China could place the Trump-Pence team and the rest of the inhabitants in the world’s most eminent and well-known super-power with military installations on every continent in “zugzwang”. Although such a situation would likely not happen, it would not be a new strategy as far as the United States military is concerned. It is a well-known fact of history that while smallpox was ravaging the population of true indigenous Americans along with the rest of the European settlers during America's early years, the US Army provided those whom they were displacing from the land with the “gift” of blankets infected with that very same disease. In short, one should always be cautious when offered a “gift”, especially if it is offered for free by an adversary when one is desperate for help.

Yet, the leadership in China and the former Soviet Union likely are above doing such. China simply would not put America’s leadership in such a “zugzwang”. In fact, the world leadership likely operates much like organized crime syndicates in a single region, such as a city. They are simultaneously “friends” and “foes” who have mutual “best” interest. They agree upon the boundaries of each other’s operations and help each other keep their individual regions under control. 

Consider the vacuum that would be created in the world’s sociopolitical and economic systems, if America fell over the course of the next few decades. It would be much like the chaos that one currently sees in the East and Africa after the removal some of its pivotal and powerful leaders such as Hussein and Khadafi. And, it might take a century or more before the reverberations of such a move settles down. That is more instability than anyone is interested in seeing. Such a political tidal current could wash away many of the world’s current super-powers.

Yet, all of this had been said so the author might set the stage for a simple postulate about human behavior and hand-wave through a couple of mathematical suppositions.

“Humans see and perceive what they choose and what they find pleasing and comfortable, although the contrary might be painfully obvious.”

As a martyr and the leader of a peaceful insurrection many centuries ago said while discussing an ancient prophesy…

“[Mat 13:14-15 KJV] 14 And in them is fulfilled the prophecy of Esaias, which saith, By hearing ye shall hear, and shall not understand; and seeing ye shall see, and shall not perceive: 15 For this people's heart is waxed gross, and [their] ears are dull of hearing, and their eyes they have closed; lest at any time they should see with [their] eyes, and hear with [their] ears, and should understand with [their] heart, and should be converted, and I should heal them.”

Yet, men of learning often discount what this leader said as platitudes and emotional opiates for those of a weak, feeble, and untrained mind.

Well, those of great learning, especially, in mathematics, let us discuss what is truly irrational. This incredibly “simple” paradox in modern mathematics, which could result in a dissertation for more than a pair of docs, has been mentioned before in this web history.

When examining the number sets that we have available, such as the integral and rational numbers, we have accepted that some numbers with which we work do not have a rational representation. Yet, is such true without the removal and banishment of at least one key integer from the “primitive set” of integral values? We, as mathematicians, both professional and amateur, accept that values such a π and e have expansions which are never-ending and do not repeat. These are called “irrational” numbers. It is “accepted” that such cannot be formed from a ratio of other numbers. It can therefore be determined that any integers which one can place in a ratio will produce an expansion that eventually terminates or repeats indefinitely. This repetition of the terminal digits of such an expression is signaled with the vinculum, a bar drawn above the final repeating digits of the ratio’s written expansion.

Yet, what if we make use of this symbol, or an equivalent one, on the opposite side of the decimal, when working with the number 10. What is the largest possible power of ten? 10…., one followed by a non-terminating sequence of zeros. Although one could never render such a number, it can and should exist based upon the rules of the basic numbering system. And, it would be an integer, by definition. Plus, it would be less than infinity, because it is less than 9…, or the number which is a never-ending sequence of nines. And, what if we take this “largest” power of ten, LPT, and multiply if by π or e. Thus, we would have the non-repeating, non-terminating integers Z^π and Z^e formed from (π * LPT) and (e * LPT). Then, what if we divide Z^π and Z^e both by LPT? We will have π = (Z^π / LPT) and e = (Z^e / LPT), if the LPT aka “the big honking ten” does exist. And, the irrational becomes rational. At least, for those who will open their eyes, unstop their ears, and soften their hearts. Yet, if men will not do such over the trivial, trifling, and niggerling issues found in numeric manipulation, will they do so over the weightier matters?

And, those great men of learning in academics might explain away how such a misrepresentation concerning the foundations of mathematics has persisted over the centuries and undergirds much of the work done this day is modern STEM fields which will be establishing the technological infrastructure that this world has for any future millennia that mankind might see.

And, as for i, it is the “sloppiest little mathematical bugger” but also is the basis for establishing the set of complex numbers. Yet, alone, it remains a reckless contraction of mathematical information. The great geometers, such as Pythagoras and Euclid, would fast faint at the structuring of such a myopic mathematical misfit. In that, the value i, represents the root of a square area, it, in essence, is the measure of at least a pair of the sides of such a shape. A square of area nine has four sides of length three or negative three, if examining their measures in the first and third quadrants of the Cartesian plane. So, the true square root of 9 is the n-tuple (3,3,3,3) or (-3,-3,-3,-3). That is exact and might be safely condensed becoming (3,3) and (-3,-3) in light of its complex counterpart and the fact that an area is number with a pair of factors. What is the square root of a square with an area of -9? Considering its geometric representation when centered at the origin, starting from that point, and working clockwise, it would be the n-tuples (-3,3,-3,3) and (3,-3,3,-3). This might be safely condensed producing (-3,3) and (3,-3) or 3*(-1,1) and 3*(1,-1) instead of 3i. So, i must truly and simultaneously be (-1,1) and (1,-1).

Does this remind anyone of the superpositions found in quantum mechanics? Well said. The author loves hearing what you are thinking.

Notice the information concerning orientation and direction lost when one simply uses the complex number, i. Doing so, hides the geometric nature of square roots which can be vital when they represent concepts within the worlds of physics and chemistry and not simply those wafting in the miasma of mathematical reasoning.

So, write your i s as (-1,1) and (1,-1), if not (-1,1,-1,1) and (1,-1,1,-1). Then, see what marvelous insights arise.

In a summarized conclusion, this day we find that, in mathematics, as in life and political situations, the irrational just is rational and the complex simply is overly simplified.

Off Topic | Yet On | The Limits of Computing and Heueristics

Team. Numerous textbook have been written that describe the limits of computing. One was written by one of the author's college mentor and instructor while he studied for a year at a well-ranked liberal arts college in the American heartland. The textbook describes some of the bounds established within the 1970s and 1980s.

Also, classic textbooks in the theory of computation from this time describe the notions spanning between computability and intractability. Yet, a brief overview of Michael Sisper's work, which is more conceptual and qualitative and less quantitative might make one question some of the results in the "well-established" traditional works.

When working with mathematical concepts, one must keep an architectural view, the big picture, while working in the details of the equations, or, in the case of computing, the imperatives of the system under development. One can become so mired in the numbers that he loses his path along the way, seeing the trees and forgetting that he is in Sherwood forest. And, the eagle-eye view lets one see the start of the trail, the finish, and the possible routes in-betwixt these.

And, this is ever so true in the field of algorithms and their analysis. Cormen, Leirson, Rivest, and Stein wrote a classic comprehensive text on the subject. Yet, it presents heuristics as computational problems for which algorithms which are efficient in space and time cannot be found.These are place in the class of "nondeterministically" polynomially-complete problems, or NP-complete problems.

In terms of algorithm analysis, a procedure is said that it is efficient if the amount of steps required in solving it is a polynomial function of its input and the number of memory space required for performing the computation is also the same class of function of its input.

In practice, it is best that this be a quadratic polynomial or better, such as a logarithmic or linear function of the input. In other words, the number of computations required for processing the input should grows as one of these functions as the size of the input increases.

Yet, as taught, these problems were presented as part of an early doctoral dissertation in the earlier years of graduate computer science program. Seeing that the oldest computer science program in the states was established at Carnegie Mellon around 1968, these programs are rather new. And, absolutely nothing novel presented among the theses and dissertations prepared during these early years of computing has stood the test of time. For one, it is said that one should never be a respecter of personages; anyone is fallible. As such, one should not be in awe of program names such as Cambridge, Oxford, Harvard, Princeton, Brown, Princeton, Harvey Mudd, Stanford, Yale, MIT, or CalTech. Furthermore, the greats in computing have limitations, human foibles, and weakness in the midst of their mistakes. So, simply because Lamport, Berners-Lee, Turing, Gosling, VonNeumann, Cerf, Diffe, Hillman, Goldwasser, Naur, Kay, Karp, Hopcroft, Tarjan, Hilbert, Dirac, Nash, or any other "heavy" in computing and mathematics states it as such, it might not be the case.

Professor Stephen Cook is quite famous for his work with "heuristics"; yet, the connotation for this term in computer science is suggestive of "a problem which does not have an efficient optimal solution, one that must be solved approximately". Yet, as we excel in certain areas, we often have deficiencies, minor and gross, in others.Most mathematicians and computer scientist are not know for the strength of their vocabulary, on average, although they are quite "bright". They simply do not focus on such topics. One cannot excel in all areas. And, finding a student, even at the graduate-level who will check every reference in a research paper which they are reading or define every term in a problem specification is exceedingly rare. Most students simply "fill-in" meaning from the context. At time, this might misrepresent the actual meaning of the passage and occasionally present an opposite semantic. And, in some languages, such as English which can have quite a spin on it at times, word with similar sounds might be antonyms, such as timority and temerity.

And, on the topic of computing and heuristics, the following are three of the traditional definitions of the term.

from: www.dictionary.com

heuristic
[ hyoo-ris-tik or, often, yoo- ]
adjective
serving to indicate or point out; stimulating interest as a means of furthering investigation.
encouraging a person to learn, discover, understand, or solve problems on his or her own, as by experimenting, evaluating possible answers or solutions, or by trial and error: a heuristic teaching method.
of, relating to, or based on experimentation, evaluation, or trial-and-error methods.
Computers, Mathematics. pertaining to a trial-and-error method of problem solving used when an algorithmic approach is impractical.
noun
a heuristic method of argument.
the study of heuristic procedure.
Origin of heuristic
1815–25; < New Latin heuristicus, equivalent to Greek heur(ískein) to find out, discover + Latin -isticus -istic

from:the Webster's Collegiate New World Dictionary

heuristic
adjective

    The definition of heuristic refers to techniques, activities or lessons that allow someone to discover something for himself or by finding solutions through experiments or loosely defined rules.

    A process whereby you are asked questions to discover answers on your own and learn more about yourself on your own is an example of a process that would be described as heuristic.

noun

    Heuristics are defined as ways of finding out the answer to a question.

    An example of heuristics are common sense and trial-and-error.

Heuristic. (n.d.).

from: the Merriam-Webster Dictionary

heuristic

helping to discover or learn; specif., designating a method of education or of computer programming in which the pupil or machine proceeds along empirical lines, using rules of thumb, to find solutions or answers

Origin of heuristic
from German heuristisch from Classical Greek heuriskein, to invent, discover: see eureka

heuristic adjective
heu·​ris·​tic | \ hyu̇-ˈri-stik

Definition of heuristic(Entry 1 of 2)

: involving or serving as an aid to learning, discovery, or problem-solving by experimental and especially trial-and-error methods heuristic techniques a heuristic assumption also : of or relating to exploratory problem-solving techniques that utilize self-educating techniques (such as the evaluation of feedback) to improve performance a heuristic computer program

heuristic noun
heu·​ris·​tic | \ hyu̇-ˈri-stik

Definition of heuristic (Entry 2 of 2)
1 : the study or practice of heuristic (see heuristic entry 1) procedure
2 : heuristic (see heuristic entry 1) argument
3 : a heuristic (see heuristic entry 1) method or procedure

German heuristisch, from New Latin heuristicus, from Greek heuriskein to discover; akin to Old Irish fo-fúair he found

So, as the above three definitions show, a teaching heuristics is a learning aid that lets the student investigate a challenging problem developing a method of solution without direct guidance and "hand-holding" from an instructor. It should result in a "Eureka!" moment when one solves the problem.

As such, by definition, heuristics are solvable. Yet, let us examine this "popular" connotative and not denotative definition from Wikipedia:

A heuristic technique (/hjʊəˈrɪstɪk/; Ancient Greek: εὑρίσκω, "find" or "discover"), often called simply a heuristic, is any approach to problem solving or self-discovery that employs a practical method, not guaranteed to be optimal, perfect, or rational, but instead sufficient for reaching an immediate goal. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision.[1]:94 Examples that employ heuristics include using a rule of thumb, an educated guess, an intuitive judgment, a guesstimate, profiling, or common sense.

Yet, often those who excel in computing and mathematics do not do the same in language arts.

However, one does not say "Eureka!" when he is near gold, but when he has it in hand.

In term of the NP-Complete problems, it was Professor Cook who is credited with determining that they are mutual reducible. In other words, one problem in the class NP can be cast in the light of another. They are convertible.

So, what might be a procedure for resolving a an NP-Complete problem. One such class of problem is that of the subset-sum. This problem says that given a set of costs find a subset whose total cost equals a certain amount.

Consider the following set cost where we want a subset of cost 15:

S = { 3, 5, 7, 11, 13 } C = 15

Try solving the problem with a Diophantine Equation.

 C = 15

 F(a,b,c,d,e) = 3a + 5b + 7c + 11d + 13e = 15

 where {a,b,c,d,e,f} are in [0..1] for example.

This can be solved by inspection; however, such is unsatisfactory in the general case of the problem.

Yet, let us use Miller-Kovarik's Secondary Method.

G(a,b,c,d,e) = F(a,b,c,d,e)-15 = 0

0 = H(a,b,c,d,e) = G(a,b,c,d,e)^2

0 = ( 3a + 5b + 7c + 11d + 13e - 15 )^2=H(a,b,c,d,e)

The root of G(a,b,c,d,e) and H(a,b,c,d,e) coincide; yet, H is a near parabolic-surface. The Miller-Kovarik Secondary Method which is also described in these notes will address this multidimensional case of a root- or minimum-finding problem.

The solution and minimum of the surface composed with a parabola would be at (1,1,1,0,0)

In fact, such a minimum finding procedure is effective in factoring integers of arbitrary size when one realizes that for every odd composite, N:

N = (2x+1)(2y+1)
N = 4xy + 2x + 2y + 1
N = 2( 2xy + x + y ) +1
N = 2C+ 1, where C = 2xy + x + y
C= (N-1)/2 and F(x,y) = (N-1)/2 = 2xy + x + y
G(x,y) = F(x,y) - (N-1)/2 = 2xy + x + y - (N-1)/2 = 0
H(x,y) = G(x,y)^2 = (2xy + x + y - (N-1)/2)^2 = 0

This is also an application of Sundaram's Theorem. This does not bode well for "eft" and "https" which each use public-key ciphering systems and the traditional Diffie-Hillman key exchange. It also suggests that a block-chain might be vulnerable and corruptible if each "node" were attacked concurrently.

Yet, on the topic of NP-Completeness, based upon the work of Stephen Cook, if one problem falls then they all do. However, it has been taught that some ciphering protocols depend upon these problems which often result in a combinatoric, factorial, or exponential growth in the number of steps or memory locations required in their solution when solved naively.

Polynomial-time algorithms exists for the solution of the clique problem, which is resolvable using unique prime numbers mapped with each node, the highest common factor algorithm of Euclid, and an iterative pairwise comparison of the adjacency list in graphs until new maximal sub-cliques are not found. It should be noted that these sub-cliques might overlap.

During the Spring of 1987, when the procedure known as the Miller-Kovarik Secondary Method was first jotted down in the author's recreational math textbook, he shared this ideas with his trigonometry teacher for whom it is named. She shared this with the enrichment mathematics teacher who had just hosted a mathematics seminar where a blind student surnamed Miller presented a poster that inspired the approach, about a month earlier. Attending this seminar were a couple of United States naval intelligence officers. The enrichment mathematics teacher stated that the United States military network had been securing the non-public Internet at the time with the difficult problem of factoring large integers, yet they had recently decided that they would secure it with other "secret" Diophantine equations. For, if the equation for public-key exchange is known, then the network is breach-able.

Yet, given a public key K and the knowledge that it might have three parts, A, B, and C. The equation
F(A,B,C) = LA+MB+NC+OAB+PAC+QAB+RABC = K and an application of the Miller-Kovarik would produce candidate private keys. If these private keys do not change over time, the application of F(A,B,C) and Miller-Kovarik on a series of public keys exchanged betwixt the same computing node would result in differing sets of potential private keys (A,BC). It would be the aggregate intersection of these sets that would produce the actual (A,B,C).

Yet, it would be unfortunate if the key exchange were actually this weak; if so, this would justify the old joke that states military intelligence is an oxymoron. Otherwise, our goose is Cooked.

OPEN-VM | General-Purpose Protocol Handler-Interpretor As a Kernel | Houston Embryo

Team. It seems the plenty of interest was shown in the post describing OPEN-VM, a pattern for an actionable overlay that will "open-up" any set of language libraries provided an OPEN-VM is written for such a language. The author should mention that he has written a simple general-purpose protocol handler that uses reflection and dynamic invocation. This basic system for handling protocol message might also process language imperatives (commands). The source might be found on this page of the NuevoArchitect www-site .