Whether 6 ÷ 2(1 + 2) = 1 or 6 ÷ 2(1 + 2) = 9 depends on….

Subjective Intent in Mathematics.

January 5th, 2013

Whether 6 ÷ 2(1 + 2) = 1 or 6 ÷ 2(1 + 2) = 9 depends on who is asking and why.  Ultimately, the answer depends on the subjective intent of the person who wrote the equation.  Subjective intent in mathematics is something we obviously don’t hear very often, especially when speaking of mathematical equations and mathematical operators. 

For the various arguments involved as to whether the answer is nine (9) or one (1), the best place to look is Ask a Mathematician / Ask a Physicist at http://www.askamathematician.com/2011/04/q-how-do-you-calculate-6212-or-48293-whats-the-deal-with-this-orders-of-operation-business/.   Also, Wikipedia has a good synopsis on the order of operations in mathematics which seems to be correct, located at http://en.wikipedia.org/wiki/Order_of_operations.  By any reader of this blog entry reviewing the arguments at those other sites listed above saves me the trouble of having to repeat it all here, by the way.  :)  Nevertheless, as we can see, this matter appears as a heated debate among the internet mathematicians. 

A.  The ultimate answer depends on who is asking, why they are asking, and who or what is performing the mathematical operations.

Starting in reverse order:

1.  The answer is dependant on who or what is performing the mathematical operations represented by the equation.  As in the real world we mostly have been taught to clear the parentheses first and then proceed on from there - additionally, it is likely that a second set of parentheses is implied surrounding the two (2) multiplying the quantity of one plus two, ie: 6 ÷ (2 (1+2)).  This would yield an answer of one (1).  But a computer program would likely proceed from left to right and would divide six (6) by two (2) and then multiply by three (3, or 2 + 1 as given in the equation) which would then yield an answer of nine (9).  :)   But then again, a computer program would likely need a mathematical operator to be inserted between the two (2) and the parenthetical sum of two plus one (2 + 1).  Also, the operation represented by the division sign would likely be an issue for a computer program as well - as most programming languages use a slash for the division operator.

2.  Then we have to look at why someone is asking this question regarding the numerical answer of this poorly written equation and in light of the confusing notation of this equation as well.  Are they asking because they have a genuine need to decipher the poorly constructed equation or are they asking because it’s a trick?  Most likely they are asking because it is all a trick and therefore the answer they are seeking would probably be nine (9).  Because as I said above, the typical answer in the real world to humans would probably be one (1).  So if one were being asked by a jokester or trickster, the trickster would likely be looking for the answer of nine (9).

3.  Ultimately, the answer is dependent on who is asking or who wrote this equation because it all depends on the subjective intent of the individual who wrote or transcribed the equation.  What did they intend to be the order of the operations when they wrote the equation?  As I mentioned above, in the human world, such notation probably intends an answer of one (1).

But this all begs the question that in math, there can only be one right answer.  Right?  If math is done properly, shouldn’t we all get the same answer?  Well, maybe, but maybe not – as displayed by this equation in this matter/blog.

So, in this blogger’s mathematical world, the answer could be one (1) or nine (9).  But most likely to us humans the answer would normally be one (1).  That is to say, if a human wrote this poorly clarified equation, he/she probably was looking for an answer of one (1), unless they are a trickster as explained in paragraph A.2. above.  But if a computer displayed this equation, regardless of the syntax errors for the typical computer program, the answer could be nine (9) as contrasted in paragraph A.1. above. 

The answer is particularly and ultimately dependent on the subjective intent of the creator of the equation, as discussed in paragraph A.3. above.   So, to make an analogy for those who were told there was no math involved in blog reading, it’s sort of like the use of certain punctuation (and wording) in grammar.  With such an analogy being, when is it proper to use a comma, when is it not, and when is it up to the discretion of the writer as to use of the comma (or colon, or question mark).     

Therefore and as such, the answer is:  It depends.  Start at the top of this blog and reiterate through the paragraphs herein again, if this answer bothers you.  If so, it will probably only bother you more as you repeat any iterations of this blog.  :) 

AVT

6 ÷ 2(1 + 2)
6 / 2(1 + 2)

Invocation of Law

 Oct 22nd, 2102

With all due respect, I think one of the issues that many have with the invocation of Law is the apparently varied and often conflicting interpretations of any given law – and contradictions and varied interpretations seem to apply to almost every single law.  As it is, it would appear that such invocation should be a matter of the black and white text which brings the Law forward – or so it would seem to those who have a background somewhere other than law. And, as such, it would seem that less room for interpretation would exist rather than any room for such wide variances as is often displayed by the legal systems applying the laws.

AVT

Equity Begets Equity

Equity Begets Equity.

If one is not equitable, they will not be given equity.

AVT (September, 2012)

From:   http://dictionary.reference.com/browse/equity?s=t

eq·ui·ty, [ek-wi-tee], noun, plural eq·ui·ties.

1.         the quality of being fair or impartial; fairness; impartiality: the equity of Solomon. Synonyms: disinterest, equitableness, impartiality, fair-mindedness, fairness, justness, evenhandedness, objectivity; justice, probity. Antonyms: bias, discrimination, inequity, injustice, partiality, partisanship, prejudice, unfairness, unreasonableness; injustice.

2.         something that is fair and just: the equities of our criminal-justice system.

3.         Law.

a.         Also called chancery, the application of the dictates of conscience or the principles of natural justice to the settlement of controversies.

b.         Also called chancery, a system of jurisprudence or a body of doctrines and rules developed in England and followed in the U.S., serving to supplement and remedy the limitations and the inflexibility of the common law.

c.         an equitable right or claim.

d.         equity of redemption.

eq·ui·ta·ble, [ek-wi-tuh-buhl], adjective

1.         characterized by equity or fairness; just and right; fair; reasonable: equitable treatment of all citizens.

2.         Law.

a.         pertaining to or valid in equity.

b.         pertaining to the system of equity, as distinguished

from the common law.

Also posted at:

http://poetrybyadamvernontrotter.blogspot.com/2012/09/equity-begets-equity.html

Rain on the Scarecrow…, Collapse of Family Farms and the Great Depression(s).

August 21^st, 2012

As I sit in one of my favorite Indiana towns for the evening, the following correlation and analogy occurred to me:  Just as it was said that the collapse of the agriculture industry in the ten years prior to the Great Depression of the 1930s foretold of the nation’s prior Great Depression; so can it apparently be argued that the threatened near-total collapse of the family-run segment of the farming industry during the last few decades may have also foretold of the ongoing Great Depression of the New Millennium – of which the nation is currently embroiled (CY2007+).

Adam Trotter

//
Maybe I'm merely stating the obvious here, though. And, whether the family farm industry managed to pull itself out of the mire is somewhat irrelevant to my point in that the industry appeared to be in dire straights at times and I ask whether such may have amounted to a foreshadowing of the economic difficulties that subsequently appeared across the nation.
// 

See:

The Great Depression of the New Millennium

http://poetrybyadamvernontrotter.blogspot.com/2011/03/great-depression-of-new-millennium.html

See also:

John Mellencamp - Rain On The Scarecrow

http://www.youtube.com/watch?v=joNzRzZhR2Y

Executive Core Qualifications (ECQs): Building Coalitions

1. Building Coalitions: This core qualification involves the ability to build coalitions internally and with other federal agencies, State and local governments, nonprofit and private sector organizations, foreign governments, or international organizations to achieve common goals. Competencies: Partnering, Political Savvy, Influencing/Negotiating.

August 12th, 2012
For anyone that who might be interested, here was my answer(s).  I wrote this at the end of last May.

Partnering – Partnering is likely the best and most feasible alternative to achieve mutually beneficial goals when faced with shortages of resources and expertise.  Partnering allows for the development of relationships and alliances.  If partnering will allow for success of workplace endeavors, it will often do so at significantly reduced costs.  Successful partnering also provides for other positive externalities as well.  I truly enjoy having the opportunity to work with new people and other entities.  I enjoy meeting others from different organizations and being allowed to have the opportunity to meet new individuals.

Political Savvy – To survive in the modern governmental workplace setting, one must be aware of on-going politics from within and outside of the organization.  In order to succeed, one must be aware of available options and display good judgment as to which ‘battles’ one chooses to fight.  To be successful, one must be able to properly assess when to take steadfast issue to resolve any given difficulty and when it is best to not to do so and let the matter best resolve itself.  I believe that I have a talent for reading political landscapes.  I enjoy interacting with behemoth and bureaucratic organizations to uncover where the matter lies and with whom one must ultimately deal to resolve issues.  From my early days at the University of Maryland in College Park to my days of interacting with a multitude of ____ entities, I enjoy meeting new individuals and uncovering where the real decision maker rests and how to court this individual to view an issue through my perspective.

Influencing/Negotiating – I believe that nearly any difficult or potentially adverse situation can be resolved with a ‘win-win’ outcome for all stakeholders.  To properly influence or negotiate with others, respect and empathy cannot be downplayed.  When the other party becomes aware that the first party is also concerned for the others welfare, the other party then becomes more giving and willing to deal.  Politeness and respect for others also can go a long way in this regard.  When I worked aboard ____ Vessels, my peers seemed constantly amazed at how willing the sailors were to help me with my endeavors, as the sailors did not always do so for my engineering peers.  No matter what the task at hand, the sailors were always willing to help and did help to complete my required efforts.  Though my engineering peers seemed flabbergasted, the matter was simply this:  I was always respectful and pleasant to the sailors, consequently the sailors were always willing and happy to help with my efforts.  

Adam Trotter

 

Executive Core Qualifications (ECQs): Business Acumen

1. Business Acumen: This core qualification involves the ability to manage human, financial, and information resources strategically. Competencies: Financial Management, Human Capital Management, Technology Management.

August 12th, 2012
For anyone that who might be interested, here was my answer(s).  I wrote this at the end of last May.

Financial Management – Financial and budgetary processes are important to a successful organization.  Procurement and contracting are extremely important as well.  A proper return on investment is a major concern to most organizations, but maybe not always the sole concern.  Nevertheless, an organization that cannot properly manage its funds has significant issues.  Insufficient budgetary funds also can present unique challenges.  However, justification for budgetary decisions should be based on fairness and with an eye toward any opportunities presented.  I have a long history of productively interacting with financial support personnel.  In fact, many of my co-workers were so despised by members of the procurement department that these engineers would often ask me to author their procurement documents and present the documents to purchasing as if the documents were for my projects.  This was because I maintained such a good relationship with the buyers that buyers would often process my purchase requests with priority over all other requests in their queue. 

Human Capital Management – An organization’s people and employees are the true measure of any business.  Not allowing for employees to flourish and grow surely equates to a death knell for an organization.  However, while an organization should be concerned for the well-being of its employees, the employees should reciprocate with like sentiment for the organization.  And, while the common law may say that employment contracts do not necessarily require ‘good faith’ contracting efforts, I would disagree.  Furthermore, employee performance problems require proper investigation, communication, and problem solving approaches as does any other problem.  Typically, if difficult employment/employee-related problems have been properly addressed, many will resolve themselves.  It is a personal maxim that employees should be enabled to rise to their highest potential.

Technology Management – Modern technology continually provides for improved tools and methods to aid in workplace endeavors.  Not keeping abreast of technological opportunities displays a potentially inept organization.  As always, new risks might also be inherent along with any new opportunities, technological or otherwise.  Therefore it is important to maintain one’s knowledge base regarding technology that is available to an organization.   

Adam Trotter

Executive Core Qualifications (ECQs): Results Driven

1. Results Driven: This core qualification involves the ability to achieve organizational goals and customer expectations. Inherent to this ECQ is the ability to make decisions that produce high-quality results by applying technical knowledge, analyzing problems, and calculating risks. Competencies: Accountability, Customer Service, Decisiveness, Entrepreneurship, Problem Solving, Technical Credibility.

August 12th, 2012
For anyone that who might be interested, here was my answer(s).  I wrote this at the end of last May.

Accountability – While extenuating circumstances might often be apparent, one needs to set goals and strive for the attainment of such.  Should errors in judgment arise, all should recognize their mistakes and do their best to remedy any unwanted results.  Errors can often allow for learning opportunities but not if the parties are unaware of the mistakes.  Workplace efforts should be properly delegated and competently completed.  Mistakes should be acknowledged and remedied as part of furthering the knowledge base, if not merely to make things right.  Furthermore, accepted processes and rules require compliance and cavalier and unilateral actions can prove detrimental to proper workplace functions.  Failure to acknowledge mistakes and improper behavior allows for the proliferation of such unwanted behavior.  I am a believer of the ‘buck stops here’ mentality, though I am aware such an attitude may not always be the predominant attitude in the government workplace.  Nevertheless, mistakes inevitably happen. Blame should be irrelevant as should fear of accountability.

Customer Service – Meeting the needs of customers is absolutely necessary to display the value potential of an organization.  The continued inability of an entity to meet customer’s needs displays an entity that is no longer required.  Customer’s needs should be clearly determined through proper communication and negotiations.  Again, mistakes can happen, but output must be continually improved to meet the general norm of value required by the customer.  Every effort undertaken during my career has been customer oriented.  From my ____ Department experience to my entrepreneurial efforts, all my efforts are geared to help the customer better their situation.

Decisiveness – Impact and consequences of decisions must be reviewed to ensure goals are met.  Decisions should be made in accordance with the mission and vision of the organization.  Again, mistakes can occur but such also allows for learning opportunities to do better in the future.  Nevertheless, I do not fear making decisions.  I always strive to make well-informed decisions. 

Entrepreneurship – To maintain the ability to capitalize on new opportunities allows for the legacy and continuation of a worthwhile organization.  Without the ability to properly ascertain risks and benefits while acting in a profitable and timely manner reduces an organization to a relic of by-gone days.  I enjoy making workplace-related decisions particularly when such decisions are in pursuit of new opportunities.

Problem Solving – Efficient problem solving is a talent as well as a practiced art.  Technical competency to properly identify and analyze problems is crucial to the success of an organization in the modern era.  The ability to properly arrive at perceived solutions in light of the predominate variables and with regard to any given situation should be required of all managers in the modern workplace.  I pride myself upon developing processes to yield proper solutions and recommended courses of actions.  I view the problem-solving process as I would any collegiate engineering physical problem:  determine which are the crucial variables and which of these variables is unknown and needs to be determined or controlled. 

Technical Credibility – Technical credibility is a major link in the problem-solving chain.  Obviously, if one has no specialized experience or qualifications relevant to the subject matter, that individual should not be making uninformed decisions on the subject. I believe I have the required technical credibility on a wide range of subjects.  From engineering to economics to dealing with others, I prefer to deal from a position of knowledge and never from a position of ignorance.  

Adam Trotter