Modernism, Postmodernism, and Digitality
The Marker
One of the new words explained here is called the “Marker.” Initially, it seems as if it is merely a label that signals that there is a change but that is realized at a deeper level. The marker is merely a signpost. However, this is not the case because history is slightly different from other linear algebra forms.
This is true of the marker, even though the marker is only represented in retrospect, there is a sense that something is happening and the individuals at the time will be able to say in vague terms what it is. The marker is then known about, and people are drawn into it as well as people who are opposed to it for the same reason: the marker is a sign that the Cultural System it is part of is changing.
In a leader portion of the book, the sigmoidal curve will be shown, as well there is the Lyapunov point, which is also applied. Because the nature of history is that it is recursive, we will often see that this recursion applies to the mathematization of certain terms. An example is the coming to market of a new technology: it looks like a sigmoidal curve but has a dip at the beginning because there is a detail that has to be explored. In this book, several markers are used, and each one has a dip: the electrical field for the transatlantic telegraph cable, the quantization of particles, the nuclear weapon, the color television set, and the search engine are all examples of this curve which has a down dip at the beginning.
To take an example, which will be explained mathematically later, the color television set has been known about for some time. There were several ways of doing it, but the way that was finally settled upon had the advantage that its scale was not limited to a certain amount and the television screen could occupy nearly the scale. This required that there be a way to create color television with dots, and the easiest way was to settle on three dots for color and one dot to synchronize. After this had been selected as the appropriate mechanism, there was a dip because of the complexities of manufacture, and then the sigmoidal curve took over in a manner of recursion.[i]
This means that a marker is actually a phenomenon that has connections with time. Individuals move through time at the same rate biologically but not intellectually or hormonally. However, time predominates when a marker is in place. That means that instead of having, for example, multiple genes determining the physiology of an organism, the Primary Component Analysis will be in terms of time with the covariant analysis being found in the other variables. The other variables may be combined as per usual.
This means that a marker exists in two forms: one is as a sigmoidal curve the other one is as a marker on a larger sigmoidal curve which says that there is a change in the sigmoidal curve. For example, the change from the logarithmic curve, that is ex, to a resistance curve which has some resistance where the limits of the environment begin to take place as bacteria run into the sides of a petri dish.
For example, in 1854 the Atlantic Telegraph Company began to lay what was thought of as the first cable from Ireland to Labrador. By 1858 they tried to begin telecommunications between London and Washington DC. There was transition but it was so slow that something needed to be fixed. Thus, there was a bump in bytes per second in 1858 but it was so slow that the cable was not profitable. It was only when a technical discovery by the leader named Lord Kelvin made it possible to transmit information at a reasonable pace that more cables could be laid. This is not uncommon, there is a technical difficulty as part of the marker which slows down the progress until the Cultural System leads individuals to solve the problem, and then the marker rockets upwards.
This brings us to the second use of the word marker, when a dividing line is drawn between before and after, this is the point where individuals understand that the marker has reached what is called a “tipping point” which generally means that the introduction of the marker is assumed by individuals who then make use of the marker’s existence. These two uses are inverses of each other, the sigmoidal curve reaches an inflection point which is often related to the reach of the marker. This then leads us to the Dirac Delta function as a breakpoint.
Dirac Delta Functions as Breakpoints
When looking at history one must realize that every person mentioned has at least one thing in common with all of the others: they were conceived and given birth and the moment of conception can be thought of as a break modeled on the Dirac delta function: with no Dirac Delta Function, there is no conception. That means we can model at least one population by a Dirac delta function which then sets off a potential person.
This can be modeled by taking a delta function, which is the start, and using a statistical function afterward to start the solutions. That is:
This the delta function, Which then integrates as:
In this case, we use the letter “c” to represent conception and we will ignore, for the moment, unsuccessful conceptions and only worry about successful conceptions. In this case, we will use this to represent the beginning one function. Since we are describing individuals, one aspect is conception.
We need to add some statistical function at x > t or:
A new individual works in exactly the same way and therefore another function would then be multiplied by a statistical function which shows at the given moment the development of a new individual. Since this needs time to occur we can then state, using the term “i” as the statistical lifecycle function of the individual
:
Because there was a definite start, and afterwards there was a function that represents the bandwidth of the cable, we can say not only is the bandwidth greater than zero but any mechanism that takes input from the bandwidth will also be nonzero after t.
This means that there is a mathematics to Cultural Systems and to individuals in the whole population that can be modeled by this delta function and some statistical functions. But we then need to weigh the basis vector, so that we can compare Cultural Systems in a framework. There are reasons for this for the same reason that logarithmic plotting is used for economic behavior: suddenly a mass of information can be seen.
The next step is to realize that on top of the Delta, the function will be a statistical function that fits with the data. The simplest kind is the statistical function which matches the curve of an individual, and the curve goes from zero to zero. This curve represents the lifespan of an individual from conception to birth, to growth, and then decay with the possibility of producing more life at the appropriate moment. Thus, the Delta function combines with the statistical function.
But this can be the basis for other objects. Because before there is a paper that introduces a concept, there must be a beginning within the mind of a person which then is written down and communicated by letter, paper, book, or other means. For example, when William Thomson wrote a paper entitled “A Mathematical Theory of Magnetism” in January 1851 for the British Royal Society he set in motion a debate that ended up changing the transatlantic telegraph cable. This too is a Dirac Delta function but instead of a child, it was a paper that communicated information to others. The similarity is that both a person and a paper are statistical functions, the difference is that only humans can communicate beyond the moment whereas other animals can make sounds, smells, and objects which degrade over time.
This leads us to the second major point: these are not merely functions but functions that can lead to Dirac Delta functions in turn, thus making them recursive. From here on all functions can be assumed to make other functions in the same way that a computer function can do so, that is all functions are recursive unless otherwise mentioned. This is different from many other mathematical bases but is relatively common in biology and meteorological disciplines.
Key points of Dirac Delta Functions:
1. In History a Cultural System is that which all members of a population are exposed to.
2. Many of the functions in vector space lead to a mathematical representation of a logical system.
3. Many of those functions are triggered by Dirac delta functions, and are thus random in their results. This includes population.
4. The Dirac delta functions in history are recursive.
Population Pyramids
One result of the Dirac Delta function is the Population Pyramid. Because the result is conception followed by the statistical function representing birth. The Population Pyramid is represented by a stack of people in five-year increments from zero years of age through to the end of life. Though it does not explicitly tell when an individual can breed, it is implicit in the construction. Human beings are animals and must pass on their genetics either by coupling or by making contributions to the raising of young. For some people this is all that they contribute, and in some cases rather marginally. We can’t ask more of a person in some cases.
This means that other people can look at the state of the population pyramid and deduce what sort of behavior is likely. Generally, the population pyramid is represented by stacked histogram bars running upwards from birth through death. The types of population pyramid are labeled stationary, expensive, and constrictive with attention paid to a “youth bulge” that can make a specific segment of the population a concern for all in the country, as the “Baby Boom” during and after the Second World War. Because many people look solely at the length of histograms there are several niceties that are often overlooked. Again, taking the “Baby Boom” as an example, because groups of people were set into an industrial capacity for the war, especially in the United States which was active but not yet in a declared state of war, some members of the “Baby Boom” started during the war for example in the shipbuilding centers and in Detroit for production of tanks and planes. The children had many of the aspects of the Baby Boom rather than of the Silent Generation which preceded the Baby Boom.
A classic example is President Joe Biden who was born during the war on 20 November 1942 near Scranton, which was part of the industrialization of war material. That is, he is really the first wave of the Baby Boom rather than the end wave of the Silent Generation.
This means that we can deduce the population pressure on a government or corporation. The classic example is how in the 1930s the population of Germany is going to peak within the next 10 years and therefore the notion of a war is on the mind of any particular government. When the Nazi party comes into power, they want a war and they know that increasing the population is essential to their end, even if the increase is not through marriage. When we look at various periods, we can see how the population pressure as represented by the population pyramid guides the actors in that epoch.
This is known even before the definition of a population pyramid formally exists because the actors will know of the pressures even before they have an exact numerical value. For example, Malthus wrote, in his An Essay on the Principle of Population in 1798:
I see no way by which man can escape from the weight of this law which pervades all animated nature. No fancied equality, no agrarian regulations in their utmost extent, could remove the pressure of it even for a single century. And it appears, therefore, to be decisive against the possible existence of a society, all the members of which should live in ease, happiness, and comparative leisure; and feel no anxiety about providing the means of subsistence for themselves and families.[ii]
So long before the population pyramid was expressed the idea was well known to experts on demographics and political economy, which was the forerunner of economics.
The amount of information available in the Population Pyramid is more than merely the replacement of people, but instead the window of the entire population which is looking at the world in a particular stance. Children look at the world differently than others, adolescents look at the world differently than others, and so on. Once one has to work a job to gain those things that one desires, it becomes less easy to look at each individual detail than when one is a child, and everything seems to be new. There is often a bloom of interest when a civilization goes into a trade-oriented society: the people who are young see things differently.
But still in all the most important change is when a segment of the population is fertile. this is most practically true for the female half of the species since they go through eggs, which are limited in number until they go through menopause. As we will show this is not the only interaction in which members of the population contribute to the future, but it is the first example of how mathematically it can be shown. Now it is like most ideas presented in this book statistical in nature in that there are outliers in either direction: people who cannot reproduce and those who can reproduce beyond the norm. And because a single person can set off a Dirac Delta function of other kinds such as a book in the form of History a single birth can be significant.
The depth of information from a population pyramid is, as President Dwight D. Eisenhower once said about the bikini “What it reveals is interesting, what it conceals is vital” because there is a difference between the statistical use of humans which is different from the sampling difference. This is because one human birth has only the significance of any other human birth, but in the area of history one book can influence a much larger segment of the population: the Qur’an, The Holy Bible, and the Vedic Samhitas are examples, to the point where individual contributors are forgotten.
The statistical pressure of the Population Pyramid can therefore be described in a Fourier transform sense in this way, where existing members reproduce downwards
:
Now to reproduce there has to be an exchange of messages generally between one male and one female, in the present day there may not even be direct exchange or the exchange may be for payment rather than reproduction. This then leads to a Dirac Delta Reproduction message which then creates a potential child. This then as a downward pressure from potential parents to the next batch of children:
Later they will explore how this downward pressure creates an upward pressure which runs into the problem that the statistical upward pressure is not aligned to the sampling downward pressure. This is almost a basic mantra of this book: the most obvious way to gain advantage is often the worst way on a general statistical basis.
But going back to the diagram, the Dirac Delta Reproduction yields the statistical function that leads to a birth. We shall use “*” to denote that I will denote as a recursive function and will eventually lead to potentially more as i*
This is what the population pyramid ultimately depends on with each birth, there is the potential of the DDP in the future. However, while it replicates the statistical value of a single birth, with its demands for food, lodging, shelter, and other necessities, it does not capture all of the other more specific features of a birth. In short, it gives us the people without the politics.
The next step is to look at the Fourier and Laplace transformations and see if the downward pressure can be replicated by the upward pressure that birth entails. If so, it means that there will be a constant downward pressure arrayed against an upward pressure.
Key Points of Population Pyramids
1. One useful Fourier transformation in history is the population pyramid.
2. The population pyramid self-replicates but is also formed by other pressures, such as war.
3. There is a bottom upwards in Fourier transformations and a top downwards in Laplace transformations.
[i] This is why John Fitzgerald Kennedy was both the last Modern President in this Cultural System and the first Postmodern President: he made promises that were the last gasp of Modernity, such as the flight to the moon which stood at the pinnacle of the second world war promise of going ever farther and he did so in a black and white television set piece. But he also made film, which was color and was broadcast later on in color. And he made Postmodern promises of a new era “born in this century.” Whereas LBJ was always too late, being filmed in color making black and white promises, both good and bad. The good was the freedom of all Americans and the bad cordoning off communism in South East Asia. The color exposed the flaws in LBJ’s Cultural System while B/W hid those of JFK. For example:
the moon promise is in B/W.
[ii] Malthus, Thomas Robert, 1798. "An Essay on the Principle of Population," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, 5.