Cycles in American History - 4
The double headed snake of republican and democratic movement.
Of Ideas and Bodies
In the last section, we show that Fourier Transforms could be used to generate Population Pyramids since Fourier Transforms generate frequency domain functions which is what population pyramids are generated formed, but Laplace Transforms generate s-domain complex functions. This paper then argued that the s-domain incorporated a large set that the Fourier Transforms in the social science sphere and that one particular transaction that could be modeled in the Laplace transform which could not be modeled correctly in the Fourier transform was the notion of an idea.
In this section of the paper, it was already hinted at that the Fourier transforms are impinged by the Laplace transforms, and therefore a proof to this effect should be made. First, the paper shall show what exactly we mean and then the paper shall prove it. This means joining the bottom-up to top-down to the Fourier Transform and Laplace Transform. There Is no simple description of what a Fourier transform versus a Laplace transform is in terms of top-down and bottom-up. The Fourier transform can model certain kinds of top-down systems but is more appropriate for bottom-up modeling. The top-down solutions that the Fourier transform models are those which derive from direct contact.
A simple example comes from Halberstam’s The 1950s book and the series of documentaries that are available on YouTube. The book is about how the exclusion of the 1960s was set up in the 1950s. a great deal of the book and of the miniseries that was made from it was exploring how the source of an idea was planted by a Fourier transformation and excluded to a toss transformation when it became large. The chain of McDonald’s, the rock ‘n roll of Elvis Presley, the “Beat” generation of Kerouac, the burning desire for sex in novels such as Grace Metalious’ Peyton Place, and anger, particularly of African-Americans, towards how they were treated by the society at large as shown by the killing of Emmet Till at the bottom and Louis Armstrong and Bill Russell at the top.
This collision of the Fourier transform and Laplace transform is not about bottom-up versus top-down and their expression through the bottom-up is generally amenable to the Fourier transform but when a signature event goes to a top-down idea then the Laplace transform gives it the traction that would be missed on the Fourier transform with its focus on the bottom up.
This is because the demand is already there and can be seen in the Fourier transforms conversion of a time domain function to a frequency domain function. Whereas the Laplace transform shows how an idea from below can become dominant once it gains sufficient traction either by money or by other means.
At this point shall show some examples of a Laplace transform impinging on a Fourier transform. One example is the state of being Russian Federation on a population pyramid. Compared to the European population pyramid one can see two very large dips in the Russian Federation pyramid and the balance of males to females. Some of this was because of the difference between males and females in society, but the generalized dips are from other sources, and not all of the male depletion is from ground-up forces which would be the case if all of the depletion is from ground-up sources. As reported by the Davis Center at Harvard:
In Russia, the age-sex pyramid looks like an unstable Christmas tree. The indentations every 20-25 years represent the long-term cyclical impact of the country having lost so many people in World War II. Each subsequent recovery is narrower, suggesting that the number of fertile women in each generation is getting smaller and smaller. That doesn’t bode well for the birth rate.
The lopsided “Christmas tree” of male-to-female cohorts has a Fourier base on the fact that there is not where children can be born with the males to populate them. But the original cause was “having lost so many people in World War II.” Which was not an allocation problem but a top-down decision by Nazi Germany to invade Soviet Russia. That is a Laplacean top-down decision rather than a Fourier bottom-up.
Now let us take a look at China, which was committed to one child per family and dominated the scarcity of children. While it was officially started in 1980 it was not up to or sometime in the 1970s. As Visual Capitalist comments: “The one-child policy defined China’s demographic transition for over three decades.” It lasted until 2015, though there were many exceptions some being official and others being unofficial. The most obvious one is that each couple could request a second child if the first one was female. One can see the gap during the time of the one-child policy, and again this is not an allocation of people bought a top-down decision which does not accord well with the Fourier transform but a Laplace transform with a Fourier transform preference for males thrown in.
The final example is the United States. Have, most of us, heard of the Crash of 1929. However, the crash of the stock market does not explain the depression and recession that followed in the 1930s extending not only to the United States but over the entire capitalist world. This is because the idea of constructing credit was the dominant mode of monetary policy at the time rather than loosening credit to cushion the inevitable shocks of a crash in some areas of the investment side of the economy. Again, one can see the large effects through the 1930s. The birthrate drags along the bottom through the 1930s and picks up in 1939. This argues that the baby started before the Second World War in a few places, but the major area started in 1947.
These examples show that a proof that there are two modes needed to model the nature of a sociological, economic, and political science point of view. Halberstam’s book endlessly points out the pattern of an outlier be the means to set a counterexample which then becomes a trend. That is to say, a Fourier transform produces an idea at the bottom, the Laplace transform covers the spread of the idea from the top down, and then the Fourier transform models the idea from the bottom up.
An example is the chain McDonald’s. The founders of the chain were hoping to reduce enough revenue to support themselves, but Kroc became convinced that this new chain represented not only a new way to eat for the person who needs food but also had only a small card to get but a concept. We now call this concept “fast food” and it dominates a segment of society where he did not before. people needed to be trained in the concept of how fast food operated. The idea of replacing the diner, which was the dominant mode of consuming food for this segment, with an entirely different mode shows how the Laplace transform becomes invaluable in terms of the complex plane that it works on. It is not just an idea for a sandwich but an entire concept of how the restaurant should be positioned for the buyer. Then it became a Fourier transform in that business people could franchise the idea and spread it throughout the country.
This pattern repeats itself over and over again, from the area of “The Beats” which were an elite consumption of novels and poetry, to the mass consumption of popular as is shown by Elvis Presley, to the editor, Kitty Messner, who decided that Peyton Place had a niche in the publication landscape and was unconventional in that world of publishing. The generational model needs to be reformed because the Fourier Transform does not carry through the unusual and particular. This mode is better represented by the Laplace transform over the Fourier transform. The idea that the Fourier transform reduces a long tail which then is better able to be described by the Laplace transform and then taken up as an idea by the Fourier transform is the heart of the discussion.
As originally presented the idea of a “long tail” or kurtosis is the core part of the argument: while the Fourier transforms adequately captures the center of demand it does not capture the idea generation which is often the result of unusual people making unusual decisions for unusual ends. The problem with the Fourier transform is that its frequency domain often misses the importance of an original idea or a pattern that explodes.
The proof:
1. Every Fourier Transform has a Laplace Transform. (Definition)
2. Not every Laplace Transform has a Fourier Transform. (Definition)
3. All Fourier Transforms are only on real numbers. (Definition)
4. All Fourier Transforms produce Range Domain data. (Definition)
5. Thus, in a Fourier Transform Model reproduction occurs when there is contact in a real mode. (Biological Definition)
6. A model of individuals can be constructed in Fourier Terms as long as the result is truncated. Since reproduction is necessary for Population Pyramid to work such truncation is necessary in at least 1 part. Thus, for the population pyramid, the Fourier Transform has a convergence factor. (Truncation as part of reproduction)
7. The other parts of the population pyramid have similar stopping point restrictions. (Truncation as part of interaction)
8. Thus, no matter how complicated the Fourier Transformation is it must be stable because someone has to observe the transaction. (Stability Definition)
9. But the same cannot be said of a Laplace Transformation because a “new idea” still has Laplacian weight but may not have a Fourier Transform Weight. (Definition of the word “new”)
10. This means a Laplace Transform may not have been communicated, may be unstable because “new ideas” may not have been tested, and may not work out. Even so, the Laplace Transforms will plot at the s-plane. Ideas are essential to human consciousness and yet violate the stability of Fourier Transform but not Laplace Transforms. (Definition of the word “new” and definition of Fourier Transforms and Laplace Transform.)
11. A Laplace Transform can interact with the Fourier Transform by interacting with reproduction behavior and thus become stable. (For example, e.g. World War II was the limiting factor in child reproduction in the USSR, the “One-child Policy” in China, and the Depression in the United States.) (Note that a “new” idea is not the same concept as a good idea or the same concept as a spreadable idea.)
12. Just as we can compare the biological Fourier Transform with the Sociological Population Pyramid to compare what the difference is between biological reproduction and the population pyramid; we can compare the population pyramid with the Laplace Transformed s-plane to discover the unexplained differences in the Fourier Transform)
We must note the note only reproduction of those with the country are counted but they still are counted as reproductive events someplace and if they are not counted by a Fourier Transform, they will be spotted by the Laplace Transform method of 12. This will not capture all of the Laplace Transformation examples because some will not transform into stable and real.
This means that the paper has proved that unlike biological development the population pyramid requires a Laplace Transform.
The next section of this paper is to look more closely at the Laplace Transforms that take place in the social sphere. The paper has outlined that they very often are from unusual sources, but a more exact definition must be had to reach for the bivalent mode rather than the generational approach. This definition will have to be inexact because the is not enough research on this topic.
It also needs to state what is implied, that the twin modes of top-down and bottom-up need to have a third mode: middle-out. This middle-out comes into being by trying to make stable and real the Laplace Transforms to effectively use them in the Fourier Transform mode.