"A nation that produces nothing but advice and advisors will ultimately find itself without clients or an economy." - Douglas Castle

"A nation that produces nothing but advice and advisors will ultimately find itself without clients or an economy."- Douglas Castle

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Braintenance: Sorting Sand Into Two Containers (02.08.2010)

Dear Fellow Frenetic Self-Growth Enthusiasts:

The mission is to find the heights of each two containers, one which is cylindrical and one of which is conical such that each one can hold the same exact amount (volume) of sand. Each of the containers must have a floor area (which is a circular base, naturally) of three square feet.

Using some simple solid geometry and some simple algebra, this mission should be easy to accomplish. Good luck.

Faithfully,

Douglas Castle

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Braintenance - At Last! Some Answers to the post of 1/25/2010.

Dear Friends – Here are some answers to the problems posed in the BRAINTENANCE posting of January 25, 2010.

These problems are ridiculously simple. Or maybe not....
1) If you have started a savings account with $100,000.00 which accumulates interest at 4% compounded annually, after 10 years, what will be the accumulated sum in the account?

Solution:  Using the Compound Interest Calculator, the answer turns out to be $148,024.43. The principal amount was $100,000, the annual addition was $0.00, the years to grow were 10, the interest rate was 4%, and interest was compounded once annually.

2) Applying the same facts as in question #1, above, and assuming that inflation accumulates at a rate of 3% compounded per annum, how much would the accumulated sum in the account be worth (in the equivalent buying power of today's dollars) at the end of the ten-year period?

Solution: The simplest way to do it would be to use the same calculator as in the problem above, and find the total amount of “compounded inflation” which would occur on the same principal amount at 3% annually over the 10 – year period.

Doing this gives us a compounded value of $134,391.64…this means that the amount of compounded inflation on the account is $34,391.64. If we subtract $34,391.64 (the loss due to inflation) from the compounded total in the account of $148,024.43, we are left with $113,632.79. Inflation has taken its toll on our purchasing power!

3) Will the sum of an odd and an even number always turn out to be even or odd? (The smart answer "yes" is unacceptable).

Solution: Odd. Here’s the rule: The sum of an odd and an even number will always be odd; the sum of two even numbers will always be even; and the sum of two odd numbers will always be even, as well.

4) Will the product obtained by multiplying an odd and an even number always turn out to be even or odd? (Again, the smart answer "yes" is unacceptable).

Solution: Even. Here’s the rule: When an even and an odd number are multiplied together, the product will always be even; when two even numbers are multiplied, the product will always be even; and when two odd numbers are multiplied, the product will always be odd.

5) When people work together and combine their mental capabilities, the resulting "mind power" will be increased. If five collaborators are working together on the same project, what will the total mind power (expressed as a number) be if: a) the power is an arithmetic sum; b) the power is a geometric product; c) if the power is an exponential product???

Solution:

a) the power of five minds.
b) the power of 25 minds (5 x 5) or perhaps the power of 32 minds (2 x 2 x 2 x 2 x 2).
c) the power of 3,125 minds (5 x 5 x 5 x 5 x 5 x 5).

If you believe that this is the potential power which could be generated by a mere five people working together (with 100% efficiency/ telepathy and 100% cooperation/ active thought), and others feel similarly, why do you suppose that that potential (assuming that it could be accurately measured) would very seldom, if ever, be reached? This is an open question that leads us into areas of behavioral psychology and group dynamics, but it’s very worthwhile to ponder.

Faithfully,

Douglas Castle

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Braintenance: Answers to Most Recent Set of Problems? Comin' Up!

Dear Fellow Brainercizers, Cognitive Enhancers, Mind Expanders and Lingovistic Grandstanders:

Not to worry! I will be posting the answers to the last problem set within the next couple of days. I just sometimes get awfully busy writing about other things, and sometimes I feel obligated to share them with you here.

Answers are on their way.

Faithfully,

Douglas Castle

p.s. There is great growth potential in indulging and exploring the seemingly irrelevent. -- DC

Douglas Castle Explains the Economic "Boom" in the US

Douglas Castle Explains the Economic "Boom" in the US.

Dear Friends:

As a rule, I enjoy poking fun at the news, and people's interpretation of what it means. Especially when I read something like what follows in the New York Times:

Breaking News Alert
The New York Times
Fri, January 29, 2010 -- 8:48 AM ET
-----

U.S. Economy Grew at Annual Rate of 5.7% in Fourth Quarter, More Than Expected
The United States economy grew at its fastest pace in over
six years at the end of 2009, but a sluggish job market is
still souring economists on the sustainability of the
recovery.

Gross domestic product expanded at an annual rate of 5.7
percent in the fourth quarter, well above analysts'
expectations. It had grown at an annualized rate of 2.2
percent in the previous quarter.

Read More:
http://www.nytimes.com/2010/01/30/business/economy/30econ.html?emc=na
####

Folks... it sounds good, but what it might actually mean is that:

1. Businesses had run so low on stores of inventory, and that inventory prices (because of depressed demand) had actually fallen, so some businesses bought some things -- it's better than having empty showrooms and shelves.

2. Some business profit margins actually did grow (at least temporarily) because they had cut down on their costs -- often, by firing loads of "dispensible" employees. They might have lowered their cost profiles by tossing out some employees. Sadly, this contributes to growing unemployment, decreases disposable personal income, and diminishes consumerism, which ultimately destroys sales. It is rather like throwing the walls into the fireplace to heat the house - temporary.

3. Statistics are funny. Note that if my sales of last year were $50.0 million, and this year they were $52.5 million, my sales grew at a rate of 5% during the year. But what if (ooooooooooh.....) my sales had dropped to $25.0 million last year (and they had previously been at a pre-recession level of $50.0 million), and they had grown to $27.5million this year? That would appear to be an increase of 10%. Yet, despite the increase, my sales hadn't grown even close to earlier levels. In statistics, the smaller the selected starting number, the easier it is to evidence "growth."

In the words of a great American philosopher, "and that's all I've got to say about that."

Think about the implications behind the percentages, folks. And if you are just a tad mistrustful, think of the motives behind the sources presenting those statistics.

Global Futurists - I do not see a recovery in the United States economy for quite some time to come. I wish that I felt differently.

Faithfully,

Douglas Castle

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