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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, s...

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...

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 ...

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...

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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 http://braintenance.blogspot.com/2011/09/asymptotes-closer-but-never.html , 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 ma...

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 inc...