Cycles in American History - 3

The double headed snake of republican and democratic movement.

The Exception to the Rule

The generation provides the rule, but the exception is often both very early and very late. One of the periods of example is the figure of Ludwig van Beethoven. While the rest of the composing world in the center had moved on from classicism, as it is now known, Beethoven, for reasons of his deafness and a drive to explore ranges of harmonization and contrapuntal extension of the line, fixed his gaze on classicism which resulted in his “late” works which combined classicization with the Baroque form of line which he found in Bach, and even more so in Handel. The most extreme is in the ninth Symphony and in the late string quartets and piano sonatas which combined the harmonic plan of the classical sonata form, again another term which has been used in a more generic sense than it was used at the time. See Rosen in Sonata Forms, The Classical Style, and The Romantic Generation, but be aware of his propensity for 12-tone elaboration on the subject.

 Now we must prove what has been speculated here: that there are two separate patterns, one is generational and can be said to be democratic and the other is institutional and can be said to be republican. There are two caveats: one is that the lowercase letter still applies, and the other one is that there is a third form which will be called the middle out. But the second half will be delved into later in this study.

 In many books and essays finding a problem with the conventional form is often used to promote the idea of the heterodox form of the ideal. But this problem is that simply because one theory is wrong does not mean that an alternate theory is correct. Both the orthodox and heterodox may be wrong but in different ways. The first step after having shown that the statistical form is wrong is to elaborate on why the alternative is correct. This might seem obvious to some, but this paper must go through the elaborations of the example even though most of these arguments have been proven in the general case, but this particular example, must show that the specific case is a specified case of the general.

In other words, we must show that the statistical analysis has a “long tail” that interacts with the general trend to produce wide irregularities in the general case. Or to speak the Greek: kurtosis, which is the measure of how wide the Gaussian or logarithmic curve can vary. These are often divided into platykurtic, mesokurtic, and leptokurtic: for thin, medium, and longer tails, which says essentially that the kurtosis centers on a medium distribution of three as mesokurtic. Then this paper must show in the particular form that the kurtosis affects the distribution. That is the must prove that the “butterfly effect” is in force in the generational pattern. We must show that in the same way that Beethoven is Beethoven, even though the rest of the world had moved on from the classic to being romantic without seeing that the classic could be updated all from before and from afterwards. That is the Romantic needed the Baroque and Classical forms to advance in the Romantic style. Which is why Mendelson, Schumann. Schubert, Liszt, and Chopin were in, their ways, interested in the Baroque forms as interpreted by classical idioms to produce romantic work.

 To express this in the statistical form: we must show that the kurtosis of statistical analysis of population has an effect all in the frequency distribution by the kurtosis having a recursive effect both in the Gaussian distribution and the logarithmic frequency. Or more colloquially: the exception produces an effect on the general in a statistical way both in the subject of daily living and of the top end in a logarithmic sense. This means that the outliers have meaning and that these outliers in one direction have more skewness than the other.

The reason for this is that the winners have an outside weight over the normal and the losers. This involves the “imaginary” numbers, though the term imaginary is misleading at best and simply raw at worst because one does not know at the time that the kurtosis has yet formed. After all, the time variable is the definer of “winner.” This is to say one cannot know that there is a winner because time has not occurred. And in many cases, there is no substitute for time because the evolution of time is the shortest form. There is no shortcut to finding out who won. Evolution does not care that the trilobites are the most common form of living thing because eventually, all will be extinct in a time-dependent print. Ditto for dinosaurs. Time is another dimension, and one cannot shorten it to the other three. The s-plane has its own rules and Laplace is a god.

What I mean by this is shown by an example: Lincoln’s Gettysburg Address.

First, it was not the main event at the reburying ceremony. Before the days of cinema live performance was the rule. As has been said many times, the chief orator was Edward Everett, a member of the House of Representatives, Senator, Governor of Massachusetts, president of Harvard, and the Vice Presidential candidate of the Constitutional Union Party, which was the “moderate party” between the extremes of the Republican and Southern Democratic parties and along with the “Northern” Democratic Party wished to delay the conflict over slavery. It gained the electoral votes of Kentucky, Tennessee, and Virginia. But by the time 1863 had come, Everett was on Lincoln’s side and supported him only a year later for his renomination.

 Second, we do not know the exact words of the address because there are two drafts and several different versions published in newspapers. Again, the exactness of spelling, writing, and exact wording was only just beginning with the date addition of a dictionary to the Bible as one of the core holdings of humans the most basic form of literacy. The best guess is obtained from the government itself. But you are not quite sure to this day. Again, exactness is only measured by how the words are copied down.

 This being the case the Gettysburg Address was not instantly famous or uploaded as the greatest form of rhetoric that the American political mind could muster. It was very much like Franklin Douglass’ speech on “What to the Slave is the Fourth of July?” in that it grew in retrospect. And this is the point: evolving is the key aspect of the specific rather than the generation standpoint. James Joyce was another example in the field of literature. Sylvia Plath was dead before her work was truly known. That does not the that the specific is against the generation because what is the generation but a collection of words, music, dancing, and other forms of daily life. For example, going by train in the United States was popular until it wasn’t when the airplane replaced the train as the primary way of going from place to place. However, very often it is the striking exception that creates a movement that defines what generation believes. And this was certainly true of the Gettysburg Address. From turbulent words on a stage that had multiple meanings to many different people to a second preamble to the Civil War Amendments.

So, what we have is more than anecdotes but less than a theory. But a theory needs mathematics and particularly two steps: that the kurtosis of the extremes causes the mode to respond and that it is recursive to the degree this generation’s exception is the next generation’s statistical mode. This is where this paper will talk about the nature of time. Specifically, the Laplace Transform in relationship to cultural evolution.

A Fourier Transform can be thought of as the generations model if it is thought of as the time domain function is to a frequency domain function. This is well known in genetics where evolution is a time-frequency function over a range. This, not uncoincidentally, is the exact presentation of the Population Pyramid because they are the same in that they measure a set of animals who reproduce over time. There are differences: biology measures alleles while a population pyramid measures all of the effects of human biology and society. But this means that a Population Pyramid is only a specialized form of evolutionary pyramid. The Fourier Transform is only defined for all real numbers which is a way of saying that only real individuals can breed.

A Laplace Transform is also a way of taking a mathematical complicated object and transforming it into a more amenable form. Whereas the Fourier Transform is a set of real numbers, the Laplace Transform does not. This means that a Laplace Transform can be complex numbers not just real ones. These sociological, economic, and psychological terms mean that a Fourier Transform engages those individuals who meet each other while the Laplace Transform is not limited to actually meeting each other. A real line in the social sciences is an absolute contact between two people and thus can be modeled as a Fourier Transform. So, the Generations model can be thought of as a Fourier transform whose deformations must result in the physical movement of individuals.

 To take one example, the original 13 colonies were kept out of the inner part of the continent by the Appalachian Mountains. The idea was to bridge this barrier and there were only two easily accessible land routes: in New York through the Hudson River and in Georgia where the Appalachians ceased. There were sea routes through Québec and New Orleans, which were held by the French. However, once the states became independent there became a need to travel westward for space and agricultural land. The Appalachians needed to be preached, either by one of the four quick ways, that is the two land bridges and the two sea bridges, or by slowly settling through the Appalachian Mountains by the hard movement over the mountains, as in Virginia to the Western part of the state and then beyond to Tennessee and Kentucky.

 This happened and produced the Jacksonian evolution which had governmental consequences because the stakes on the western side of the Appalachians needed to attract settlers and one of the allures was the right to vote. On the eastern side, there were often many restrictions on the right to vote including being a tax-paying citizen whereas the Western side gave out the right to vote to any free, white, male citizen. In other words, there were restrictions on the Western states as well but there was an allowance in that they did not need to have money. And money was in short supply in the Western states anyway. This meant that settlers would go to the Western side, that is the western part of New York, the Western part of Pennsylvania, the western part of Virginia, Kentucky, Tennessee, Ohio, and beyond these two the Mississippi Valley for not only the chances that they had of owning land but the enticement of being a voting citizen.

The difference between the Laplace Transform and the Fourier Transform is that the Fourier Transform requires a real movement while the plus transform requires only the idea of that movement. This still entangles the two transforms in many ways, The movement of the Mormons to Utah was full of a physical movement and an idea, and therefore a Fourier Transform and a Laplace Transform but this is entirely possible because some movements can be done either with a Fourier Transform or Laplace Transform. But some can only be done with a Laplace transform. This means that individuals who no longer are in the reproductive part of the cycle have a great deal more influence in the Laplace transform than in the Fourier Transform because that is what real movement in this context means. That idea can be thought of as a potentiality. This means that the mind is more prominent in the Laplace transform.

 This then means that the generational model which implies the Fourier transform giving a frequency distribution as with the population pyramid is inferior to a dual transform with Fourier and Laplace transforms both because the difference between an evolution framework and civilization is that the mind has as much influence as the body.