Today I was teaching Mathematics to my two younger brothers. We were working two-step reading problems.  The problems were something like the following example: 
         

           What is the cost of 1 1/4 lbs. of cheese at $2.16 per lb.

While working out examples for them on the blackboard, I somehow wandered from Arithmetic to Reasoning.  I have been giving much thought of late on the subject - particularly in the area of Apologetics.  Little wonder!  :)

I will replicate for you what my Math students turned their attention toward for the remaining twenty minutes of my class period. 

Problem:

            1 1/4 multiplied by $2.16 = ?

Circular Reasoning:
               
                1 1/4 multiplied by $2.16 = ?
 >             1 1/4 =  5/4 = 4 divided by 5 = 1 1/4
 >             1 1/4 multiplied by $2.16 = ?

We are left with the same premise/conclusion and data points that we began with when using this method of reasoning.  Remaining are also the same questions unanswered.  (In my class, I demonstrated this point by working the circle over again until they reacted.)

I am thinking namely of the presuppositional method of argumentation in apologizing for the existence of God, the inerrancy of scripture, etc.  The conclusion is essentially a restatement of the original data and/or thesis.  We are left with the problem unanswered.

 

I left the room briefly.  While I was away, my little opportunist took the liberty to take a sneak-peak at the teachers manual that lay open on my desk.  When I came back, he immediately informed me that he had the answer.  He did have the answer, but could give no rational defense for it.

So it is with the “confessional method” of argumentation.  If we do not subscribe to the “faith-without-reasoning” belief, we can not be satisfied with the answers that this argument gives.

To find a solution for our problem, we had to consider the mode of the numeral (i.e. decimal, improper faction, etc.).  We also had to take into account that we were working with two separate systems (monetary verses nominal). Had we neglected these factors, we would have ended with an alternate incorrect solution.   Alternate Solution:
                      1 1/4 times 2.16 =

    >              1.25 times 2.16 =
    >              368.00

Rather pricy?!  Pay if you will; I’ll bypass that method.

Correct Solution:

1 1/4 multiplied by $2.16 =

>              4 divided by 2.16 = .54
>              $2.16 + .54 =
>              $2.70

Above we have utilized in our correct solution both deduction and induction.  Moreover, we were able to come to the answer not by the given data solely, but also due to the fact that we could transfer one system of calculations over to another system, thus solving for inferred information.

We can be intelligent.  We can come to and give forth intelligent answers. After all, were we not created in the likeness of an intelligent Creator?  Whether we are discussing the weather or other things more important, let us not forget this fact.  :)

 

   

     

Musical Temperaments: Now and Then

Because music of the time is interrelated with the temperament of the time, historical developments are central to discussions of temperament. In 2500-2001 BC, the Chinese developed the five-note (pentatonic) scale. Two hundred to three hundred years later, we have record of five-tone and seven-tone scales in Babylonian music. We credit Pythagoras for his Pythagorean Temperament at approximately 550 BC, in which the chromatic scale was generated by tuning in perfect 5ths, using the circle of 5ths. He is said to have introduced the octave around this time.

Although we appreciate the concepts he promoted, we must recognize that his thoughts were imperfect. For example, when tuning in perfect 5ths, there is much to be desired with the 3rds. Moreover, although the Pythagorean temperament results in a scale with perfect 4ths and 5ths, at the last it ends in very poor dissonance. Due to this factor, we see the development of the Equal Temperament (ET) scale not but one hundred or so years after the invention of the Pythagorean Temperament. (If we were to tune by contracting each 5th by 23/12 cents, we would end up with exactly one octave and that is one way of tuning an ET scale.)

Since the introduction of the Pythagorean temperaments, all following temperament have been improvisions of the named temperament. Thus, we have the Meantone Temperament (MT), in which the 3rds were made just instead of the 5ths. I can see the sense in this idea because of the prominent role that 3rds play in certain music, especially during an age when music made greater use of 3rds. * The flaw presented by the MT is of a greater degree worse than that of its predecessor.

*{To illustrate, play a simple 4/4 timing song that changes chords only on new phrases. I noticed today, that as I played the tonic chord in my right hand [while still leaving the melody at top], and played the 3rd as the bass line for my left hand, it actually sounded more consistent in the Dorian mode. (When ending in the Dorian, I felt the need to play the tonic. I think perhaps that my ear is trained that way however, because it was not at all erratic to end on the 3rd.) Moreover, I played first in the Dorian mode, and without pausing switched to D Major to play the song anew. It was necessary to play the tonic in this key; and I would naturally have it no other way except for in passing tones, etc.}

Well Temperaments (WT) struck a compromise between Meantone and Pythagorean. Additionally, WT opened the door for not only good 3rds, but also good 5ths. It appears by Bach’s harmonies in his compositions that essentially all the details of tempering were already worked out by Bach’s time (before 1700). (Example: His "Well Tempered Clavier").

Over the past one-hundred years or so, ET has been the excepted temperament while the other temperaments are labeled "historical". The musical freedom presented by ET and our current trends toward increasing dissonance are two primary reasons for this preference. The advantages for the piano tuners are numerous. Moreover, ET reduces many lurking wolves that the various other temperaments allow to creep in with indiscretion. We do harm to the purity of intervals by providing security from these beasts by sacrificing the very motivation for chromatic scales (i.e. pure intervals).

I think that Bach would have us shed the muddy, tasteless water of ET for the pure, sweet tones of the WT. Yet what of the wolf tones? And what are we to do with the complexities of such the WT system? The quantry is age old. Unfortunately, I do not know much at all on this vast topic. Yet I would love to hear about you explorations and brainstormings on the topic...

Past thoughts concerning Halloween...

I wrote this to the editor of a local newspaper a few years back...  Publication: The Vandalia Leader;Date: Oct 13,2010 Section: Commentary;

Page: 2

  Dear Editor,
    I am writing in concern of your previous support and promotion of a holiday in which generations of Americans are embracing as traditional - Halloween. Some may find it shocking, however, that Halloween is a holiday of the Druids.  “Halloween had its origins in the festival of Samhain among the Celts”(Encyclopedia Britannica 2005)  In May 1977, the National Geographic wrote (pp.625-626),  “Halloween.  That was the eve of Samhain...firstborn children were sacrificed...Samhain eve was a night of dread and danger.”  Parents are deeming Halloween as harmless fun and fantasy, thus subtlety disarming their children of discernment of witches and the occult.  Its time to wake up!  More than 1.3 million proudly practicing witches exist in America today.  Is this any wonder when nearly every mother dresses her vulnerable little child in a witch costume thereby verifying to the child that the witches he/she saw on TV are “cool”?  Silver Raven Wolf, a witch who is the author of the book “Halloween: Customs, Recipes & Spells” says:  “Today, just about every little girl in our society, at one time or another, has chosen to costume herself as a witch...If you choose a witch’s costume this Halloween...Hold your hear up and wear your witch’s garb proudly in their honor.”  ...And some would say why not?  What inherent evil does witchcraft have?  If you are one who respects the bible, I would refer you to Lev. 20:6 which states that: “the soul that turneth after such as have familiar spirits, and after wizards, to go a whoring after them, I will even set my face against that soul.”  The original Halloween was a hellish night of Baal worship, child sacrifice and death!  A startling fact is that many of our current Halloween customs derived directly from ancient Baal worship (See “The American Book of Days” p.566).  “Baal is also a synonym for the devil.”  (Burns, Cathy.  “Masonic and Occult Symbols Illustrated” p.327)  As a Christian, you would know that you are to have no other gods before the great I AM.  According to the “Harper’s Encyclopedia of Mystical & Paranormal Experience,”  “They (Druids) sacrificed victims by shooting them with arrows, impaling them on stakes, stabbing them, slitting their throats over cauldrons and drinking their blood.”  “Since they are man-eaters...and since,further, they count it an honorable thing, when their fathers die, to devour them” (Strabo, Geography).  (Other activities described in this article are to explicit to discuss.)  For the unknowing sceptic, this is a taste of the evil behind such things.  Halloween is a “Witch’s New Year”, and does not deserve observation from any decent citizen of this God-fearing nation.  I must agree with the statement that Satanic High Priestess Blanche Barton made on The Church of Satan’s web site stating that “It [Halloween] gives even the most mundane people the opportunity to taste wickedness for one night.  They have a chance to dance with the Devil.”  That chance is given to the child by the parents of the child and is promoted by the society as a whole.  Granted, trick or treating, pumpkin carving and ornaments are not the “new rage” of this society.  The Druids had thought of that as well.  Instead of jolly masked children trick or treating, they were people who claimed “to be possessed by the supernatural being”, masked behind the gods of their time.  Jack-O-Lanterns, in that day, were severed human heads.  Bats were killed so that their blood could be used for spells, rather than the dull plastic figures American’s hang in their windows.  Black cats were “embodied demons”, not fury friends.  The skulls that some like to dress their bodies with were a symbol prominently of witchcraft and demon worship as a celebration of death.  (These disturbing facts may be found in “Masonic and Occult Symbols Illustrated”, p.388 written by Cathy Burns.)
    Why do we celebrate a “holiday” that promotes the decay of our society, as well as our very lives?!
                                                                        Respectfully,
                                                                   Evangeline Schultz

 

Vehicles: A medium

My foot pressed the acceleration petal as I drove the Interstate past a line of houses on the edge of a nearby small-time town.  I slowed, hastily stepping on the brakes when I noticed a little lump in the road ahead of me.  I approached the limp figure of a tiny Min Pin at a slowed pace, middling the car to pass over.

My mind flitted to our own vivacious Miniature Pinschers.  What a pity!  Someone had no doubt lost their beloved dog-friend.

The dog lay there dying, if not already dead.  I turned my head in time to see a girl of about ten years of age running down her short, broken cement walk.  The screen door slammed in her wake.  She ran toward the road with her eyes riveted upon the still animal that I was just ready to pass over.

As I did so, I looked at the child.  She stood there, a complete picture of despair and hurt.  My car was over the child’s companion by then, and her focus was forced to turn upon me.  She looked me full in the face then.  Her expression tore at me.  The river of tears that flowed from her eyes became a riptide that carried her accusations of blame upon me.  It washed over me, and my conscience could not escape it.  I, the driver of a vehicle, took the blame those eyes had hastily spoken.

A car had taken the dog from her.  As I drove by, she needed no further reason than that to lay upon my person the fault of that cruel circumstance. 

Her look haunted me as did the tender scene that I witness in my rear-view mirror.  I turned on the radio hoping to shift my mind from its current thoughts.

 

Obama was speaking.  He was addressing the recent school-shooting.  He spoke of the gun bans that he planned to impose, of the past harm done by such weapons, and of the damage that guns would cause in the future if laws were left unchanged. 

In his voice I heard the accusing eyes of that child that hated me for the loss of her play-mate.  The unspoken blame for my car’s cruelty to her friend was being cast by the President of our world’s leading nation as a legitimate judgment and response to the hurt and pain that we were feeling over the death of innocent, helpless playmates and family members.

If guns (or cars for that matter) are the cause for unfair deaths and unjustifiable behaviors, we need-no, we must seek a solution to be rid of such terrible and heartless destroyers.

But in thinking that way, we are approaching this topic with the anti-logic of a wounded and hasty child.  We need to be mature and sound enough in our reasoning to realize that guns are simply vehicles.  A car doesn’t drive itself; and a gun doesn’t discharge itself either.

When we focus the blame solely upon the weapon, we must ignore the good potential for it as well.  Was it not these objects that the American Revolutionists uncovered and utilized to buy the freedoms that we love and cling to today?

There is an evil behind the weapon.   This is the focus that our solution should be upon.  We cannot blame the trigger; we must understand the source of the problem.  Let us use our level heads on these issues.  Stop excepting the idiocy of unfounded arguments that result in more violence and the infringement of our costly freedoms.

A correct understanding of this issue will lead to the power of finding an adequate solution.

Homemaker - For Girls in the Prep Stage of Life PART 1

National Bible Bee Competition

National Bible Bee Competition

The Shelby Foundation began a scripture memory competition in 2007.  They desired through their non-profit organization to encourage youth to study the Word of God and to memorize it. 

I participated in it the year that it began as well as the following year, afterwards graduating out of the qualifying age category.

The first year I participated, we were given a booklet to memorize covering several topics, cards to memorize containing bible related questions and answers, and a list of 1200 verses of scripture to impress into our minds in those few summer months.  

The second year’s materials were similar, but were more family-oriented then the previous year.

Through extensive study and memorization of the scripture which was encouraged by the National Bible Bee Competition, I embedded a general reference of important scriptures into my knowledge as well as gained a better understanding of the Christian make-up which has provided wisdom on many critical issues in my personal life.  

Firstly, I would like to say thank you to all who volunteer their time and funds to promote this influential, God-honoring cause.  I have talked with youth nation-wide who have been positively affected by your efforts. Thank-you!

Secondly, I encourage parents and youth alike to get involved with this great opportunity to not only build a network of friendship with Christ-centered people, but more importantly to hide the Word of God in your hearts and minds. What holds more value?

Yo-Yo How-To

  Yo-yo How-To

Elegant southern styles are indeed fun to explore. From the complicated work of smocking to the simple task of making a yo-yo, you will find exemplified the ornate flair of beauty refined.

   What you will need:

• High-quality thread that harmonizes with fabric color
•   A needle of med. length and min. width
•   A pair of nippers or scissors
•   Fabric cut into 5 in. (diameter) circles* 

               *Note: Vary size of circle to increase or decrease size of yo-yo. I have seen it as small as 2 inches and as large as  14inches. 

Ready – Get set – Sew

Thread your needle, doubling the thread and knot the ends together. Insert needle approx. ¼ inch in from edge of fabric [as pictured (#1)]. Turn fabric edge over to create a lap (picture #2).  Begin sewing edge while letting fabric build on the needle [pictured (#3)]. When needle is full, pull through (picture #4) and tighten thread [also illustrated (#5)]. Repeat process until you have come full circle and are back at the beginning (otherwise known as the end). Pull the thread as tight as you can without breaking it (picture #7). Inset the needed in beginning pleats (#8) and tie as many knots as suits your fancy [pictured (#9)]. End by cutting the thread near the yo-yo (#10) and spreading it out in the desired form.