Friday, September 30, 2011

Expand Your Mind: Pattern Recognition

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Your mental capacity, plasticity, memory, recall and deductive reasoning are all dramatically enhanced by your ability to recognize patterns and to extrapolate (or generalize) from them. In some cerebral circles, the NICs (nerds-in-charge) refer to this phenomenon as "learning a rule." This notion has great applicability in the world of artificial intelligence (AI), but it is the shining key to a means of improving our own intelligence as well as increasing the actual speed of thought. Imagine being able to think faster because you are able to make 'connections' more rapidly? This skill is valuable to cultivate. Not surprisingly, it is a skill that can be improved by simple exercise.

Pattern recognition skills are involved in every aspect of gaming, athletics, problem-solving and life.  The more different (and complex) patterns that we are able to recognize from prior exposure, the easier and faster it will be for us to recognize new patterns. By the way, simple analogies actually involve pattern recognition. To illustrate, in solving the analogy query that follows, an association between things (associations are the building blocks of patterns) is necessary for us to get the right answer:

Horrible but memorable analogy, with multiple choice possibilities:

Fahrenheit is to Temperature, as...

a) Tuna is to Fish;
b) Oral is to Rectal;
c) Length is to Height;
d) Celsius is to Cold;
e) Inches is to Length;
f) Pitney is to Bowes;
g) Antihistamine is to Allergy;
h) Wet is to Rain.

The correct answer, of course, is choice e) Inches is to Length. The reason is that Fahrenheit is a means of measuring Temperature, and Inches is (are) a means of measuring Length.

Perhaps it's time for some practice. If you'll complete the sequences below (i.e., find the next item in each of the series), I promise that I'll have the answers for you by Monday this coming. These don't involve word-based analogies -- they are simply series of numbers. Do these - they're as stimulating as they are beneficial...

Incidentally, I dedicate this post to Technorati 4F3BBD7YKWFZ.

A) 1, 3, 6, 10, 15, ?

B) 1, 1, 2, 3, 5, 8, 13, ?

C) 1000, 0100, 0010, 0001, 1000 ?

D) 1, 4, 9, 16, 25 ?

E)  200, 3000, 40000, 500000, ?

F)  1, 100, 2, 99, 3, 98, 4, ?

G)  1.21, 2.32, 3.43, 4.54, ?

That's all for now, fellow (and lady) Braintenance Buffs. We'll compare our answers on Monday. 

Douglas E Castle []

TechnoratiMedia -

Monday, September 26, 2011

Real Economics Lesson - Growth Rates

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Regardless of what we are always being told by the venerable Pantheon of pedigreed Economists out of Washington, DC, Wall Street, and academia (as well as by the seemingly cynical grumblings of self-professed "Main Street" economists -- I am one of those myself -- and I have growing misgivings regarding the utility of my undergraduate degree in Economics) regarding the state of the our sovereign finances, most of us develop a powerful "feel" for how well the machinery of monetary and fiscal policy are working by our own personal finances.

If my income is increasing, but at a lower annual rate than my ordinary living expenses (including my repayment of the debts which I incurred to either live beyond my means or to purchase investments that my neighbor (a smart fellow) said were "sure things") are increasing, I feel a decline in my sense of well-being. My finances are continuously getting tighter. This seems to make sense (except to people who don't have any ordinary concerns about income and expenses, and such dull pedestrian pastimes as "working for a living.").

This difference in rates of growth between income and expenditure are what wallop us in our respective wallets.

The Facts (which are actually fictional):

John Q. currently earns post-tax income (similar to actual cash inflows) of $80,000.00 per year. His post-tax income grows at a rate of 2% per year, compounded annually.

John Q. has annual expenditures (to cover his living expenses and to service payments on his mortgage and other debts) of $50,000.00 per year. His annual expenditures grow at a rate of 10% per year, compounded annually. He doesn't buy fancy new things, and replaces old, worn-out ones with their equivalents, as necessary. John Q. is a "middle class" sort of chap.


Initially, the difference between John Q's Income and Expenditures is $30,000 per year.

The growth rate difference between John Q's Income Growth and his Expenditures Growth is 8%.


What will be the effect on John Q's quality of life (i.e., his ability to cover his expenditure obligations with his income) over the next seven years?

Answer - Two Comparable Graphs:

Note: Special thanks to Kids' Zone Graph Creator (from Learning With NCES), at, for providing me with the tools to create these graphs. Haven't you noticed how much easier it is to explain things and to understand things by using graphs and charts?  Graphs and charts are wonderful learning tools -- we should use them more often. They engage more of our senses in the learning experience than just sitting about and listening to unsupported rhetoric.

Answer, In Ordinary Terms:

With each passing year, the margin between John Q's income and his expenditures decreases in real terms. By the end of year seven, John Q's "safety margin" has decreased from $30,000.00 per year to approximately $2,000.00 per year. Things are getting much tighter. John Q. is so worried that he is cutting back on his expenditures wherever possible (this hurts businesses, some of whom employ persons like John Q.) and is living in a state of growing desperation and fear.

Regardless, of what the experts say about recession, recovery, leading economic indicators, monetary policy, fiscal policy and different legislative packages, John is beginning to feel like he is a member of the "working poor." He cannot accumulate any significant savings, and can't find a new job -- it seems that fewer businesses are hiring, and more employees are worried about keeping their jobs.


The difference between growth rates (or price rates) is the chasm that economies fall into. The less the disparity between growth rates, the greater the grassroots perception of the economic picture. The problem is that some legislative policy makers, mainstream media sources and otherwise well-intended politicians either don't quite understand this arithmetic (let's call it "dangerously divergent rates of growth"), or, if they do they may present inaccurate or irrelevant statistics compiled by incompetent people.

I hope that you enjoyed this lesson in Real Economics, and that you'll forward this article to all of your friends, colleagues and elected officials. As always, thank you for reading me here at Braintenance.

Douglas E Castle

Friday, September 23, 2011

Updated List Of My Most Popular Blogs - 09.22.2011

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Is time merely an illusion? Then I can stay up as late as I want! - Douglas E. Castle

This article is an amended re-post. Previously, it was a combination of friendly self-promotion, news and some compost; that last ingredient is what is spontaneously generated when you try to do things in too much haste. This time, I have included hyperlinks embedded in each of the blue blog buttons (try saying that three times fast), which are hosted courtesy of CoolText, a wonderful graphics and design tool.

If you think that you've seen this post before, you actually haven't -- as they used to say on every package in every supermarket when I was a mere lad, this article is "NEW and IMPROVED!"

I've even added a picture to this article. The subject matter of the picture is irrelevant, but that doesn't make it any less entertaining - and entertainment, like education, is always welcome.

Please visit some of my most popular blogs, and feel free to comment on articles, to link to any of them (and I will reciprocate your backlink with an inbound link to your site), or to re-publish any of the content. You can re-publish without permission, provided that you republish any articles in their entirety, with all images and hyperlinks left fully intact and 'live,' and with attribution given to the author (that's me).

At the end of this post, you'll find a listing  of links to related articles that involve various aspects of  these search terms, categories, tags, keywords, labels and topics for your reference and use.

As always, I truly appreciate your reading me.

Thank you so much.

Douglas E Castle










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Question: Is time merely an illusion? If that's true, then I can stay up as late as I want! - DC

Thursday, September 22, 2011

Extreme Thinking: Increase Imaginative Capacity

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Your mind is a muscle. The more that you use it, the stronger it becomes. Also, as in a regimen of physical exercise, you must not only increase the resistance (the Braintenance analogical equivalent for lifting progressively heavier weights would be solving more complex problems), but you must "confuse" the muscle (the Braintenance analogical equivalent for this mixing up the order and nature of exercises, or avoidance of excessively predictable patterning, would be to engage in different kinds of thought using different processing skills). For example, instead of doing Sudoku or crossword puzzles every day, you might "mix in" algebra problems, memorization and recall exercises, perceptual challenges, creative multi-sensorial visualization, meditation, acquiring and using new knowledge (vocabulary, trivial facts, historical perspectives, math formulas), mechanical reasoning, cause-and-effect logic, extrapolation and other mental muscle-builders.

In caring for your mind, you must challenge it in diverse ways. The wonderful thing is that your mind will always expand to meet these tests -- and "it," separate and apart from your conscious awareness of its work [your mind actually thinks about itself, without your conscious knowledge or consent!] will hunger for more. Your mind will not, it will expand itself with amazing plasticity and capacity.

Today might just be a good day to challenge your imagination. Here are some thoughts to ponder. These conundrums all require Extreme Thinking -- the use of your critical faculties and your extrapolative imagination. Good luck. And now, ladies and gentlemen, start your engines, and you may use any research tools at your disposal as well:

1) Is there a difference between the absence of anything and the presence of nothing?

2) If I state that I am a liar, am I telling you the truth?

3) How far can a dog run into the woods?

4) If darkness is defined as 'the absence of light,' what would you call the absence of darkness?

5) If an individual believes that his fate is predetermined, why would he persist in trying to change the course of his life? What would be his incentive for socially responsible conduct, instead of just doing everything for instant gratification?

6) Can you explain to me why zero divided by infinity is zero, while infinity divided by zero is infinity?

7) Can you explain to me why if any number divided by itself equals one, my calculator tells me that when I divide zero by zero, the answer (the quotient) is zero? And how about that error message I see?

Think about these please. They all have answers. Don't all questions have answers, even if we do not know them or can't find or prove them?

Douglas E Castle

Saturday, September 17, 2011


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Increase Your IQ, Your Memory, Your Problem-Solving Skills and Your Creativity.  Ramp up your success. BRAINTENANCE -- because gray matters. 

Out of body experience[Image, "Astral Projection" via Wikipedia]We learn about how to measure things (and even about how to experience feelings) through a process of comparing and contrasting. Intelligence is, in large part, an associative or metaphorical process. Based upon experience or teaching, we recognize patterns and learn how to predict outcomes based upon information. This enables us to respond to changes in our environment, to solve problems...and to survive. Intelligence, when acted upon, is a wonderfully mysterious and exciting tool, although its absolute definition is still a bit elusive.

When it comes to perceptions of measurable things, like pleasure; pain, light; darkness, shallow; deep, too little; too much, how fast; how slow, and the like, we base our assessments (and even our interpretations of experiences -- one person's pleasure is another's pain...) upon what we have experienced. Everything we think or feel is relative, as well as subjective.

I refer to this means of measurement as Perceptual Relativity* (which is a Lingovation). Going a step further, it means that a person's reactions to and feelings about different things are going to be based upon his or her personal experiences, in his or her personal context. Context is very much the same as "frame of reference."

The compare and contrast components of context can be illustrated by these common examples:
  • You just don't appreciate your mother's cooking until you've spent some time in the military;
  • You don't know what pleasure is until you've experienced pain;
  • You can't appreciate the illuminating power of light until you've spent some time living in the darkness;
  • We often don't realize how fortunate we are to have someone or something until that someone or something is gone from our lives.
  • Your perception of the passage of time, and the length of time that something takes is very different from that of a person of two years of age if you have lived fifty years -- this really is 'experiential division' -- one year is half of a two year old's total lifetime of experience, while one year for you (old person, you) is representative of only two percent of your entire life's experience. Time seems to "speed up" as you've lived longer. A season can eventually seem like a moment...
In communicating with someone, it is extremely helpful to have some insight into that other person's context. Put simply, I don't talk to Millenials about the Watergate Scandal, The Kent State incident or Agent Orange -- I take care not to use these "ancient" references in illustrations. As a Baby Boomer, I have to take great pains to avoid using inappropriate (i.e., very dated), and obscure refences when speaking with those significantly younger. If I engage in conversation with someone from a very different culture than my own, I have to consciously calibrate my very American sense of humor.

Each of us, as a communicator, has to be conscious of our own context, as well as the context of the individual or group to whom we are imparting information. Part of smart communication involves using the other person's context in choosing and using our own metaphors and other illustrations. If we are not, then we render ourselves, and what we have say, irrelevant or unintelligible.

Douglas E. Castle

A fellow from Mongolia might not see the ironic humor in the above photo.
An excellent example of different contexts.

Tuesday, September 6, 2011

Asymptotes - Frustrating Problems With Unsatisfying Solutions.

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Illustration of the conditional convergence of...Image via Wikipedia

In our last posting, we discussed the notion of asymptotes, and I posed two problems for your consideration. One involved the eventual (but unreachable) sum of a convergent series of numbers, and the other involving a ever-more troubling fraction. You can quickly refresh your memory by clicking on, and by then hitting your browser's "BACK" button.

The answers are unsatisfying, but they were promised:

1) In adding the sum of the series 1 + 1/2 + 1/4 + 1/8....and so forth, the sum will eventually approach, but never quite reach a limit of 2.

2) In dividing (n-1)/n, as n increases, the value of the expression approaches, but never reaches 1.

There are examples of this type of complex conundrum in nature, in such things as trying to solve 22/7 (which is a never-ending decimal), and in determining the halflives of certain radioactive materials (isotopes), where one half of the material loses its radioactive potency over a certain period of time, but the residual amount keeps getting halved and never quite disappears.

I solemnly promise to offer you something more nifty in my next article. The idea is to tax your brain until it has to expand its capacity in order to solve increasingly complex problems.

Sadly (and speaking about interesting wordplay and punnery), taxing our brains , while making us brighter, still won't make up the federal deficit... Did I hear somebody groaning?

Douglas E Castle

Saturday, September 3, 2011

Asymptotes: Closer But Never QuiteTouching...

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Imagine trying to get to a finish line where with each leap you halve the distance remaining between you and your objective. Sounds good at first – but after a short period, you will realize that you can never actually get all the way there. You get closer and closer, halving the distance with each leap, but you won’t quite make it. Close, but no cigar. Your approach to the finish line is asymptotic. A mathematical limitation makes the intuitively simple task into the impossible conundrum.

No matter how assiduously you proceed, you can merely cut the distance in half – even after a (theoretically) infinite number of leaps you cannot bridge that gap. The early leaps are the most productive…however, with each successive leap, your dilemma becomes clearer, and you become more frustrated. You have come up against a limiting mathematical constraint.

The irony of this predicament is that although the objective is fixed, it might just as well be a moving target… retreating in smaller increments as you approach it.

This asymptote paradox is serious business, unlike when we were kids and we would (if there were only two of us) “each want the bigger half of the cake”; it was even more hysterical when there would be three or more of us each requesting an equal half of the cake. It wasn’t like the Miracle of the Loaves and the Fishes (in the New Testament); it was more like a rag-tag confederation of pre-pubescent imbeciles battling for territory with no concept of either the basic Laws of Physics or of rudimentary division or multiplication. As a youngster, I personally helped to put the “ass” in “asymptote.”

Here are two questions to ponder, with answers (I promise – I really do) to follow within the next three days.

A) In adding up the following series of numbers, what whole number (integer) will you ultimately approach asymptotically?

1 + ½ + ¼ + 1/8 + 1/16 + 1/32 + …. + 1/ 2* [where 2* represents 2 to the infinite power]

B) In performing the following arithmetic operation (looks like division) with an increasingly larger number substituted in for ‘N’, what number will you ultimately approach asymptotically?

(N-1) / N

Graphical Illustration Of Asymptotes - Vertical And Horizontal

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