Percentage Problems

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Problem with percentages.  These are not trick problems.  This kind of data and/or situations actually occur.  Maybe they are not so simple, however they do require some clarity of thought to resolve them.

• Jim make 75% of what Sally makes, and Mary makes 62% of what Jim makes.  However, it is known that Jim and Mary together make 1.5 times what Sally makes.  How much does each make?
  
  Answer: We do know that Mary makes 62% of 75% of what Sally makes, or in decimals 0.62 * 0.75 of Sally's salary.  But... This is an impossible problem as together Jim and Mary make (0.62 * 0.75+0.75) =1.215 of what Sally makes.  So, together they cannot make 1.5 what Sally makes.  In addition, we can never know how much each makes unless we know how much at least of the make.  There is the certain confusion of the percentages (62% and 75%) given and the factor 1.5.  Unless the student knows the 1.5 means 150%  he/she has little hope of solving the problem.
  
  Answer alternative:  What one student could say is that because we don't know what any of the three makes we cannot possibly know what all make.  This is a little superficial because the problems is missed completely - although the answer is correct.
  
  Curiously when multiplying percentages (of the same thing) the result is a percentage, not percentage-squared.  This is unlike the product of length measurements, where you do indeed get length * length = length-squared, or area.  You can also multiply area by length and get volume, as you know.  Yet, multiplying areas doesn't give much of anything, including areas-squared, which has no meaning.  No wonder kids have math problems with incredibly basic problems. They don't teach this, I think.
• From actual data...
  In 1961 71% of American men were married, when just last year 51% of American men were married.  So, the teacher said we have a drop of married men over this period of 21%. Sally Ann, from the last row said she thought is was more like 30%. Who is correct?
  
  Answer: In fact there is a 21% drop in the number of men actually married - in absolute quantities, but the drop in percentage is just like the drop in any quantities.  You take
  
  (previous - now)/previous * 100%
  to get the result, which is about 30%.  The confusion is with percentages and what they mean, and what "drop" means.
• At camp Wilderness, 45% of the campers got poison ivy while 70% had mosquito bites.  The teacher asked how many had mosquito bites and not poison ivy?   And how many had one or the other?  Bobby answered the first by subtracting to come of with 25%.  Karen answered the second by summing to come up with 115%.  Ken volunteered his ideas by saying both solutions are incorrect but gave no numbers.  Which answers are correct?
  
  Answer:  The issue here is with "number-banging," that is combining numbers in some fashion.  The tip off for Karen is that adding the percentages gives a result that is total unreal, i.e more than 100%.  The problem with Bobby is that he doesn't know how the populations of the mosquito and poison ivy folks interact.  Fundamentally, what we haven't considered is that the percentages are relative and not absolute. Ken is correct, and not giving the answers is correct - it cannot be done with the information at hand.
• Alternative...
  At camp Wilderness, 25% of the campers got poison ivy while 70% had mosquito bites.  The teacher asked how many had mosquito bites and not poison ivy?   And how many had one or the other?  Bobby answered the first by subtracting to come of with 45%.  Karen answered the second by summing to come up with 95%.  Ken volunteered his ideas by saying both solutions are incorrect but gave no numbers.  Whose is correct?
  Answer: The result is the same as above, but this time the sum of 25% and 70% being 95% result, is less a tip-off for a problem with the math.  Ken is again correct.  We definitely need to know how many had both mosquito bites and poison ivy. 
• In Mason City there are 1,000,000 TV sets.  What is known is that at a given time 44% of all TV's turned on were tuned to Channel 3.  It is also known that 56,000 TVs turned on were not tuned to Channel 3.  How many TV's were tuned to Channel 3?
  Answer:  The red herring here is the total number of TV's in Mason City.  This value is not needed.   So, we need to focus on the 56,000 TVs on but not turned to Channel 3.  Since this number is 56% (coincidence) of the number of TVs (i.e. 100%-44%), we know there must have been 100,000 TVs turned on.  Therefore, there were 44,000 TVs tuned to Channel 3.  What is the meaning of the 1,000,000 TVs?  It is to make the problem solvable.  See below.
  
  Alternate problem. In Mason City there are 75,000 TV sets.  What is known is that at a given time 44% of all TV's turned on were tuned to Channel 3.  It is also known that 56,000 TVs turned on were not tuned to Channel 3.  How many TV's were tuned to Channel 3?
  Answer:  This problem cannot be resolved because if there are 56,000 TVs turned to other channels, this represents a fraction of more than 56/75 TVs tuned to other channels, and this value exceeds 56% of the total.  Therefore, it is not possible that 44% of TVs turned on are tuned to Channel 3.   In this problem, we have inconsistent conditions given.

Why the Dozen?

Fact: 12, 24, 60, these are the big numbers of your everyday life.  These are surely different from the nickel, dime, quarter, and dollar.  Just why is that?

You may have questioned why do we, users of a base 10 system of numbers, seem so dedicated to the dozen (12), the 24 hour clock ( = 2 x 12), the minute (= 60 seconds), and the hour (= 60 minutes).  The answer lies in divisibility.

Clearly, a dozen (12) is divisible by 2, 3, 4, and 6.  This means you can ask for a quarter dozen, third of a dozen, half a dozen, etc.  The math is simple.  If the basic multiple were ten (10 = 2 x 5) we could only do a half or a fifth.  That would be it.

For the day (24 hours), we can divide it by 2, 3, 4, 6, 8, and 12.  This allows a half day, a third of a day (typical shift), a sixth of a day (= 4 hours which is the morning shift), and more.

For an hour (60 minutes) we can divide by 2, 3, 4, 6, 12, 20, 30.  This allows a half hour, a quarter hour, a third of an hour, and more.  The divisibility makes the calculation convenient and easy.  Imagine an hour of 100 minutes.  Then we could divide it into only half, fourth, fifth, tenth, twentieth, and a couple of others. There is less flexibility.

The ancient Babylonians used a base 60 system of enumeration for good reason.  Why? It's all in the divisibility.  Also, it made dealing with fractions a whole lot easier.   BTW, handling fractions were a problem for all the ancient civilizations.   Naturally, the multiplication tables were horrific.  But they had tricks to make calculations easy (well, easier than memorizing all products x times y for x and y in the range from 1 to 59).  Isn't it interesting that in the schools, the multiplication tables taught are for all products x times y for x and y in the range from 1 to 12.  There is that number, 12, once again. 

The year of 365 1/4 days, we can do nothing about.  It is what it is. But note, we have conveniently divided the year into 12 months.  Sure, the numbers of days differ a bit, but calculations are easy in this context.  On the other hand, imagine a year with ten months.  Divisibility is only possible into halves and fifths.  This is the same as if the basic multiple unit consisted of ten items, just like the discussion about the dozen.

Fingers and toes.  These are the basis of our monetary and measurement systems.  This means tens and twenties.  It is an apparent explanation of one system in contradistinction to the more facile base 12, 24, and 60 systems of everyday counting.  Go figure.

Paul Krugman

Paul Krugman has the Nobel Prize in economics, not an easy achievement. From Wikipedia, we learn the prize was given for Krugman's work explaining the patterns of international trade and the geographic concentration of wealth, by examining the effects of economies of scale and of consumer preferences for diverse goods and services.  This is hard to beat.  You cannot argue with the Nobel Prize, except possibly the Peace Prize. 

The Norwegians?  Being a descendent, even I question what are they thinking this nowadays. As a colleague in education recently stated, "What fruit is on the tree this week?"

From his own account, he is the 20th most widely cited economist in the world today and is ranked among the most influential academic thinkers in the USA.  He has written hundreds of articles on an array of topics.   This is impressive.

The prize in economics differs somewhat from the others, like physics, chemistry, and medicine, in that the awardees generally have created a model that fits extant data more-or-less correctly.  It is then generalized to the future, sans the model.  However, note that when such a model is created it profoundly affects the future, whose viewers take this into account to their own personal thinking, not to mention gain.  Basically, and perhaps a bit simplistic, if you have a model for making investments in stocks and it works, that is fine.  Make a bunch of money.  But if you publish it, the game changes.  The economic game is these days, partly econometrics, partly history, and partly political philosophy.  Opinion, logic, beliefs, intuition, and emotion are the rules of economics, now and always.  

Yet, in most cases, the work of a Nobel laureate, does change the game.  In the hard sciences, it refocuses and redirects research into new and possibly productive directions. 

You doubt this?  For every Keynsian, I can find at least one world renowned non-Keynsian.  For every supply-sider, I can find at least one world renowned non supply-sider. For every high taxation of the rich (ala Hollande in France) expert, I can find a low-taxation expert. Too many experts, each loaded with bushels of testimonials, each loaded with tons of data.   Powerlessness comes to mind. 

We live in an era of selected truths.  Watch the news - any channel you prefer.  You will see what they say; enjoy their comments, curse them, revile them.   Validate your own views.    To my mind, Krugman only examines a select points in the economic debate about which he makes his case.  Exactly this is the news model of our day.  

Krugman is the iconic representative of the Transference Effect, by which we mean that he transfers his unquestioned expertise in economics to whatever suits him at the moment.  See: http://used-ideas.blogspot.com/2012/10/transference-of-expertise.html.  He gains viewers and readers from all stripes; they listen to what he says with respectful obedience; they consider, reflect, and act upon his written word. My goodness, he publishes in the New York Times, wherein the motto is "All the News That's Fit to Print." What is better than that?

Professor Krugman, without the Nobel Prize, is just another, though prolific, liberal blogger.

On Memory - Part I, The Basics

On Memory - Part I, The Basics
Imagine your mind has a built in search engine, not unlike Bing or Google. Wouldn't that be great? You just set it to work and presto, up comes a number of hits on whatever you search. Guess what, it does!
The number of hits is small in most cases, larger in others, but significanly null in all too many, especially for searches distant in time. Like all search engines, your engine has limitations of capacity. This implies you have lots of information, carefully filed away in your brain, but essentially inaccessible. It has become unsearchable and unremembered. Google, et .al., can merely add more servers to increase capacity. You cannot. The question we pose here is: how can we find this "lost" information. The method we propose is called relational recall. Sounds mysterious?  It really isn't  This is something the search engines cannot do. They are digital, and limited to text searches. They cannot feel what you feel much less know what you feel or desire. They cannot reconstruct what you want to re-experience. Thank heaven. Happily, your brain is far more powerful - though profoundly flawed. Yet, how do we tap into these lost memories? This is our topic.
This piece is divided into three parts:

1. Your memory - basics of what and how, the categories and impressions of memory.
2. Relational recall - how to do it and the remarkable results.
3. Improving the memory - tricks exercises, games, venues.

We Humans like to Classify. We like to put things into a box, and if not one then several. Taking a great inductive leap from the philosophy of Emmanuel Kant, it is the way our brain works and thus how we function. It is how we store things important to us, important to remember, and important to recall. It is the way we know things. In a sense, the analysis of memory is a meta-application of this paradigm. Memory, therefore, also needs to be classified, boxed, and contained, as it has numerous independent facets. We construct here only a few of these containers.\

Memory includes the processes by which information is encoded, stored, and then retrieved within the human mind. Encoding can be either short-term or long-term, the latter being our focus. Storage involves the places in the mind where the information resides, and retrieval is about how we get it back. The latter point is indeed our point and direction here. The first two are substantially physiological, and while there is much evidence on these, they are substantially serious contemporary research topics - well beyond the scope of this short synopsis. On these, the philosophers must stand aside, and await some definitive information. What is needed right now is some glimmer of what human memory means; it is far more varied than might be imagined.
Below, we give some very broad strokes on types of memory and how we access it. In this catagorical delineation there is some overlap among them.

Types of Memory
Psychologists and neurologists have classified memory, ad nauseam. First of all, there is the declarative memory (knowing what) and procedural memory (knowing how). The former is simply remembering something, while the latter is procedural, the how of a process. For example, you may not remember the context of when you learned to ride a bicycle, but you do remember how to do it. The same may be true of reading, arithmetic, and swimming. Probably, we all remember both the declarative and procedural aspects of driving a car, a singular thrill in the life of most teenagers. Sub-categories of declaritive memory include episodic memory for events and experiences, while semantic memory includes facts and concepts.

Then comes the differentiation between recognition and recall. Recognition is merely the tag of a situation with something stored in memory, while recall is more like "dredging" up something from the past. If you see your picture from 30 years ago, you may recognize the events surrounding it, but if you want to recall how you and your grandfather faired together this may take some time and some effort. That is, if you can do it at all.

Next come flashbulb and topographic memories. From Wikipedia, we have "A flashbulb memory is a highly detailed, exceptionally vivid 'snapshot' of the moment and circumstances in which a piece of surprising and consequential (or emotionally arousing) news was heard." (http://en.wikipedia.org/wiki/Flashbulb_memory). You meet a long lost friend and "flash" you remember a sequence of events or situations that are fully connected. They are substantially autobiographic. Note the keyword emotional. Other examples may include the tragedy of 9/11, the assassination of John F. Kennedy, the hurricane Sandy, or the Challenger Space Shuttle disaster. These type of memories are not necessarily of the event but of what you were doing or where you were at the time of the event. Topographic memory is a recollection relating to a sense of space and what it implies in recalling or remembering something. Perhaps, it is the path to some location, or where in the store some item is located.

Remembering and recollection are two different attributes of memory. Remembering is merely the mind's interaction with the mind of some salient facts, say like the area of a rectangle or where you vacationed in 2010. However, recollection, which implies remembering, implies discovering some time line (forward or back) by which you can arrive at a desired memory. This was an important topic for Aristotle in his essay, On Memory and Recollection, where he carefully distinguishes the two, stating that persons with quick memory are quite different from those with quick recall. In the second part of this note, we take to task the methods of recall with specific ideas not quite like the general notions posited by Aristotle, who gave a rather general account, more of a practical and psychological rather than philosophical nature. The important idea of recollection involve mnemonics - the keys to unraveling what you are seeking. More on this later.

Retrospective and prospective memories are further slices and subslices of this memory pie. Retrospective memory basically refers to people, words, past events - roughly experiential. It can also involve "seeing" moments (episodes) from the past. On the other hand procedural memory includes remembering how to do something after a lapse of time. You remember how to bake a cake or shingle a roof - neither of which you do every day. This is akin to declarative and procedural memory, as above. Prospective memory is often tied to retrospective memories.

Temporal memory. This includes long-term and short-term memory. Often the aged seems to have excellent long-term memory, i.e. memory from the past, while they have diminished short-term memory. Short-term memory is more-or-less your working memory (an alternative term) , things you keep active, on the top of your head at one time. Usually, this is limited to about seven items. For example, the air traffic controller needs to have a wide-scale short-term memory to keep track of multiple events. Remembering names of a group of people at a party connects with short-term memory. Some are good at this; others poor (like me). Forgetting of these types of memories involve quite different processes.

Another memory type is usually called sensory memory. This is a brief, even very brief, recall of a sensory experience. Sensory memories may last only seconds. Two subcategories are the echoic memory - related to hearing, and iconic memory - related to vision. You hear a boom in the distance or see a for-sale sign on an attractive house. Both memories are gone in seconds. Indeed, you can associate memories with each of your senses, mostly specifically odor. You just can't retain these things in long-term memory; the risk of doing so would be to overload the mind/memory with irrelevancies. We have enough of these already.

Physiological effects. What makes for good memory, what enhances it, what improves it, and what does not? We make a very short list of pro's and con's.

Pro - Memory	Con - Memory
Diet - using flavenoids of many types	Fats - saturated and hydrogenated
Cognitive training, both strategy and core types	Stress, acute and chronic
Oxygen	Sleep depravation
Proper sleep	Alcohol
Odor	Lack of mental functioning - use it or lose it
Music
Other trigger actions - to be discussed in Part II

Let's mention only briefly at this point the seminal work of Frances Yates, who unraveled ancient techniques of memory in world without paper or any of the aids we use now.  This involves making memories more than the recall of memories.
 
References: Many basic references are on Wikipedia. At the cited links, there are numerous specific references, many of which are technical.

• Aristotle, On Memory and Recollection. See http://ebooks.adelaide.edu.au/ to read or download.
• Martha C. Nussbaum and Amélie Oksenberg Rorty,  Essays on Aristotle's De Anima
• Yates, Frances, The Art of Memory (1966) ISBN 9780226950013
• http://en.wikipedia.org/wiki/Flashbulb_memory
• http://en.wikipedia.org/wiki/Retrospective_memory
• http://en.wikipedia.org/wiki/Memory_improvement

American Presidents and their Mathematics

Many of our presidents were trained in or used math at some point in their careers. An interesting note is that when someone has a productive disposition toward math, i.e. sees the value of and confidence in using mathematics to resolve problems they will use it to resolve many problems, not apparently related to math. It becomes a way of thinking. In this short note we look at some of the US presidents so disposed. Mathematical training was of course an important part of the curriculum as taught to many of our earlier presidents. They were schooled in algebra and geometry. Calculus is another matter. Let's look at some of them.

George Washington

• George Washington (1732-1799) was early in his career a surveyor. The mathematics of surveying includes foremost the techniques of planar measurement. These include the right triangle, oblique angles and triangles, azimuth, angles, bearing, bearing intersections, distance intersections, coordinate geometry, law of sines and cosines, interpolation, compass rules, horizontal and vertical curves, grades, and slopes. This sounds much like what is now the standard curriculum in four years of high school math.  Naturally, much of this involves algebra, the concept of a unknown, and the solving of algebraic equations.
  
  
  
  Thomas Jefferson
  
  
• Thomas Jefferson (1743-1826) invented a crypto system in 1795, just a few years before becoming president. It was so effective and secure (for the time) that it was used by the US Army from 1923-1942. The idea is remarkably simple. Take any number of disks with the letters of the alphabet on the outer rim, all mounted on an axle to make them rotatable. The disks were numbered, say from 1 to 10. The disks could be arranged in any order by restacking them. If the sender and receiver both know the correct stacking order a message could be transmitted. Here's how. Using a particular stacking order, the message is encrypted by rotating the disks to create a message. Now copy any row from the disks, looking like complete gibberish. Send this message. The receiver, stacks the disks properly and then rotates them to form the "gibberish" message, and then looks for the row that makes sense. The odds of there being two intelligible messages is remote. This can be checked first by the sender - just to be sure. The Jefferson disk had 36 discs. With just ten discs, this cypher is child's play to decrypt with modern computers, being there are only 10!= 3,628,800 possible rearragements of the disks. However, Jefferson method employed 36 disks. This implies there are 36!= 371993 326789901 217467999 448150835 200000000 ≐3. 7199×10⁴¹  possible rearrangements, making cracking it more difficult - impossibly difficult by hand. However, there are many decrypting tricks that could be employed to render this type of cypher not as difficult as it may appear. This cypher was re-invented by Etienne Bazeries a century later. Etienne Bazeries considered it uncrackable. One vulnerability of the encryption is that both parties need to know the key (i.e. the correct ordering of the disks). This is an example of a rotor encryption system, not unlike but far simpler than the World War II German encryption system, Enigma.   For a picture, please see http://en.wikipedia.org/wiki/Jefferson_disk.  To confirm Jefferson's interest in mathematics we add the following.
  
  
  
  
  
  
  From the writings of Thomas Jefferson, the letter to Thomas Lomax Monticello on Mar. 12, 1799 contains the following passage:
  DEAR SIR, -- I have to acknolege the receipt of your favor of May 14 in which you mention that you have finished the 6. first books of Euclid, plane trigonometry, surveying & algebra and ask whether I think a further pursuit of that branch of science would be useful to you. There are some propositions in the latter books of Euclid, & some of Archimedes, which are useful, & I have no doubt you have been made acquainted with them. Trigonometry, so far as this, is most valuable ...
  
  As is apparent, Jefferson is writing to Mr. Monticello about what materials he should read and understand in his personal advancement in scholarship. Jefferson also advises Mr. Monticello about other scientific subjects worthy of study. In another letter*, dated July 5, 1814, Jefferson talked about the value of formal education in the classics.
  
  But why am I dosing you with these Ante-diluvian topics? Because I am glad to have some one to whom they are familiar, and who will not receive them as if dropped from the moon. Our post-revolutionary youth are born under happier stars than you and I were. They acquire all learning in their mothers' womb, and bring it into the world ready-made. The information of books is no longer necessary; and all knolege which is not innate, is in contempt, or neglect at least. Every folly must run it's round; and so, I suppose, must that of self-learning, and self sufficiency; of rejecting the knolege acquired in past ages, and starting on the new ground of intuition. When sobered by experience I hope our successors will turn their attention to the advantages of education. I mean of education on the broad scale, and not that of the petty academies, as they call themselves, which are starting up in every neighborhood, and where one or two men, possessing Latin, and sometimes Greek, a knolege of the globes, and the first six books of Euclid, imagine and communicate this as the sum of science. They commit their pupils to the theatre of the world with just taste enough of learning to be alienated from industrious pursuits, and not enough to do service in the ranks of science. *The unusual spellings above are from the period.
• Abraham Lincoln (1809- 1865) was also a surveyor in his youth. Remarkably, having little formal schooling, Lincoln learned the required mathematics required independently. Lincoln, who had little formal schooling, was blessed with a prodigious memory, and a life-long passion for literature including Shakespeare, Burns, and Byron.  He also studied the law independently, though he never really immersed himself its subtleties.
  
  
  Abraham Lincoln
  
  
• James A. Garfield (1831-1881) produced in 1876 an independent trapezoidal proof of the Pythagorean theorem: For any right triangle with legs a and  b, the hypotenuse is given by the formula c²=a²+b².  BTW, there are about 300 proofs if this, arguably the most famous theorem in mathematics. It was published in the New England Journal of Education. In his early years, he was a school teacher. He apparently enjoyed any tasks of a mathematical nature, such as when he was appointed chairman of a Subcommittee on the Census.  As a note, one does not just simply set at the desk one day and develop an original anything.  Rest assured, Garfield had thought long on the matter and was well versed in the many proofs known at this time.
  
  
  James A. Garfield.
  Other presidents that surely were well schooled in mathematics include courses in calculus.
• Herbert Hoover (1874-1964) was a Mining Engineer. 
• Jimmy Carter (1924-) was a Nuclear Engineer. 

P.S.  If you want to get to really serious math, geometry in particular, consider Napoleon Bonaparte (1769-1821).  He invented original theorems in geometry quite far beyond the Pythagorean theorem to the extent that two of the absolute best French mathematicians (Laplace, Lagrange) and others of his day were duly impressed. They involved the so-called Mascheroni constructions. Laplace and Lagrange are even today revered as outstanding mathematicians in mathematics history.   It is difficult to imagine any contemporary politician either interested or capable in mathematical argument - regardless of the country. 

Petraeus, Allen and their emails

The Two Generals

What is so utterly unbelievable about the Generals Petraeus and Allen is their apparent naivety. 
Here they are experts at secure communications.  Here they are intelligent and capable officers.  What could ever overcome them to believe that any communications on the open net is secure and undiscoverable?  These firms, such as gmail, yahoo, hotmail and more, actually do a lot of data mining.  Anything appearing interesting is flagged. Even I know this.  This is why it is good advise never post anything of any sensitive or derogatory nature through these messengers. 

At this point, I feel certain that what ever company was the email provider has the complete transcript of the communications.  So much for security.

It is simply inconceivable these guys have been doing this.  While Petraeus and Allen are great patriots, warriors, and consummate generals, actually how dumb can they get?

I do feel bad for them and the country (mine) that may lose their services - they are phenomenal public servants.  However, we the people are the bigger losers in this game of mayhem and indiscretion. 

The Republicans are Dead – Long live the Republicans

What is to become of the two party system?

The Republican Party, as now constituted, will never win a national election again.  Four years of difficult ground work lies ahead.   The fundamental message of the Republicans is one of individual initiative as the only path to prosperity. Let’s focus on jobs and demographics.

Jobs.

• The continuing Republican mantra for no tax increases does not resonate with anyone except those making big money.  In fact, no one believes that corporate executives, big bankers, and Wall Street brokers that make high six and seven figure salaries with access to lavish bonuses deserve any break.  They create no jobs; they create no new businesses; they merely manipulate financial structure.  Indeed, they profit only from the work of others.  They can truly pay more.  Their bonus structure will compensate them for higher taxes.  Nothing much can done about that.
• Small businesses do create jobs.  Small businesses create wealth.   All seem to agree on this - on both sides of the aisle.  This is the sustaining message of the last presidential cycle.  Most agree small business should not be pummeled by increased taxes.  Therefore, there should be a differentiated tax structure that exempts small business owners from tax hikes.  They will be encouraged to build their businesses and to create needed jobs.
• Small businesses should be granted some type of automatic waivers from the expected exponentiating insurance costs in the coming Affordable Care Act.  Substantial regulatory restrictions on creating new business and extant small business should be lifted.
• Corporate America should be given incentives to keep their funds at home.  It seems that only a calculated minority respond to an appeal for “love of country.” This appeal, possibly a Gov. Romney misjudgment, would have been effective in the country in which he grew up.  Me too. That country is no more.

Demographics

•         Actually the Republicans did win the election.  A simple calculation shows that at least 20%, maybe higher, block voted for the Democrats.  No thinking, no consideration, just vote the ticket.  This leaves only 80% of the voters in play.  For Romney to have nearly split the total vote means he captured about 62% of the true voting population.  It was not enough.

•         The true vote consists of considered voters, on both sides, that actually believe in the foundations of what the candidate proposed.  This is the American way. 

•          However, if anyone has 20% of the vote locked up, all that is required is a strategy of appealing to a limited number of constituencies, their base and a few more.  This is profound fact and affects strategic campaign calculations. And it works.

Finally, the Republicans must get on message and keep the wild-eyed candidates out of the action.  For example, in the presidential primaries, anyone on the far right can easily gain 20-40% or even more of the Republican electorate.  Divisive this is.  It makes them look good, but they are DOA in the general.  Republicans must appeal to all, and more importantly be perceived as interested in all.  To nearly 50% of the electorate, taxes are simply not a considered factor.  Any pledge, or stress, to not raise taxes on all matters nothing to most – not even one scintilla.   Only with a viable Republican Party can this country achieve balanced governance – with active compromise - as in years past.

If Republicans wish to lower tax rates, they may first need to raise them.