bodner088

Several observations -- and do not look at your watch because you will be wasting valuable, irreplaceable time by the act of tracking it! Since you've been kind enough to stay with me for this length of time, I will attempt to add some "party conversation starting quotation" value to this post, with a quote from my closest associate, Mr. Douglas E. Castle : "Prepare for the future, because the present moment becomes history all too quickly." More Quotes follow, invoking paradoxes or infinitely self-recursive statements which provoke deeper and more expansive thought. The Human Mind, when challenged by a concept that warrants analysis (actually "validation" or acceptable analogy). "You cannot make up for lost time. No matter how expediently and ambitiously you accelerate the pace of your work, the unproductive present moment is permanently gone, except for its persistence in memory." "You cannot change the speed of the passage of time ...

We can all safely admit (even to ourselves, if we are not in a confessional or a crowded subway car ) that doing arithmetic computations with eyes closed, from memory and using sheer brain power is a challenge, but one that is a worthwhile undertaking. Here are the answers, as well as some observations, regarding the last posting . That makes this post, which are reading, a post-post posting. Or worse, it could be considered a commentary on a past posting . Alliteration and irony combined tend to produce an excess of spittle...an effect which I enjoy witnessing in others but which I try to avoid inadvertantly engaging in myself. --------------- The following embedded image (although the subject appears wide awake), exemplifies irony: It's now back to the exercise with some answers in RED . Here's a new set of operations to work on in the same manner as you did on the previous set, except that now we will use multiplication and division. Never mind about your third-grade teac...

Image via Wikipedia  In our last thrill-packed episode of Braintenance , we discussed the benefits of doing arithmetic calculations ("chain calculations") without the assistance of computers or any extrasensorial visual aids. The problem in the re-posting of the last show, yielded an answer of 28 [or at least it should have]. Most people's biggest challenges are not the arithmetic at all -- the challenges are 1 ) memorizing a string of data, and 2 ) recalling the string in "pieces" ("fractional recall") when going back to check or reaffirm our computations . One hint which might prove helpful is to visualize the entire string as if it were placed at the top of your mental blackboard for reference, and to do the individual calculations below. In this way, you can trick your mind into having a source of embedded reference to go back to. By doing this, you'll have less problems worrying about 'losing your place,' during the computational pro...

When we utilize computers and other visual aids to do arithmetic calculations, several of our cognitive and computational abilities atrophy. We must exercise them in order to keep them strong. The simple process of doing arithmetic in your head allows you to visualize and to memorize. Many studies have shown that this rather simple exercise is one of the best ways to delay the onset of dementia and a number of other physiological manifestations of diminished mental capacity . Do the following example in your head...no using fingers to draw in the air, or using of any other external physical processes (especially whispering the numbers to yourself0. I'll get you your answer tomorrow. Go ahead. Try this simple one [by the way, you'll actually find it confusing to look at the numbers on this page at the same time you visualize the computations in your head. With practice, this problem can be eliminated by simply taking a mental "photograph" of the numbers, closing your ...

Our challenge of several days ago was to use intellectual "brute force" (very rapid, iterative trial-and-error ) to find out which arithmetic operations were being performed on the numbers in the equations which follow. Instead of using the common symbols, I had substituted the letter "n" for any operation. Let's crack the code, Oh Braintenancers . Find the missing signs which are all represented below as the letter "n" in the following simple equations. I'll have answers for you within the next two days. You have plenty of time. Put away the crossword and Sudoku , and give this exercise a whack. Have at it, then. Answers are posted in red . A ) 9 n 3 n 3 = 30  The first n is multiplication, and the second n is addition . B ) 7 n 5 n 3 = 9  The first n is addition, and the second n is subtraction . C ) 12 n 3 n 1 = 5  The first n is division , and the second is addition . Have fun. By the way, are you doing mathematics, arithmetic or something el...