Modernism, Postmodernism, and Digitality

The Map and Math of the Postmodern - the Visionary Becomes the Revolutionary

As we can see there are three eras occurring at once: the era itself, the preceding era, and the era that comes after it. these are jumbled together so that at the beginning of an era there are also the markers of the preceding era and of course, in reverse the era that comes afterward starts occurring with markers of its own. the difference is that the outgoing era is looking for markers as to why it will change and likewise the postcendent will be emerging from the visionary and into the revolutionary period. we have shown before pieces of each of these but we have not put a hole in your together and why it transforms from the preceding era and why it eventually collapses.

The postmodern is not a narrowly defined object, even though its opponents may wish it to be so, and instead, we look for the visionary moments that the era makes itself known by.

While there are a number of things that are occurring, and thus different structures can be assembled from the same raw material with different objectives, when an era is defined pieces of that structure come into focus. one way to do this is to define the overwriting danger that faces society and why it is different from the preceding era and the era that is to come. in this case, the era began on an exact date: July 16, 1945. this was the day of the first atomic blast and set in motion several events that would define the Postmodern.

But even as the era dawns it becomes clear that there must be a preceding time when the movement had already begun to force a new direction. after all, the Trinity test could not have occurred without the work of an atomic bomb. and that would not happen if at least three nations were intent on possessing such a weapon: the United States with its allies the United Kingdom, Germany, and Japan. but also there was the implied threat from the United States of America toward the Union of Soviet Socialist Republics. at the time these five member nations were fighting for control of the world in a modern sense rather than a postmodern sense.

But to begin the math one must realize that there are two almost opposite tremors in mathematics one is the median or center of a Gaussian graph and the kurtosis - the edge of creativity and destruction that emerges from a very small number of people. This tension creates the mathematics that we search for in a cultural system. This means that we look for both statistical tools and giant leaps forward.

If July 16, 1945, was the beginning we first must ask when did these forces first occur? And remember that we must also look to the modern because it was the modern that was directing the forces that were present. At this point, the postmodern was a subsidiary movement and thus we are looking for the visionary parts of the movement. The first step was in physics and mathematics: and we can look and see that von Neumann’s paper which described the movements of a transparent game with no hidden information was the start.

The of a cultural system is that kurtosis occurs randomly but the core of the population Pyramid is clustered together. This means that we need one more mathematical concept to bring the two together, and fortunately, we have exactly the one we need: convolution.

First, what is convolution? It is from the branch of mathematics called functional analysis and it takes two functions, the usual ones are f and g, and takes the integral of the two in combination. It is written as f * g, though it does not mean multiplication as does in most computer languages but the process of integrating the two together to form a third. What is useful is that there are properties that will be described further in this section. In some sense, it is like any other method of combining two functions such as addition, subtraction, modification, or even further afield the cross-relation. In fact the cross-correlation is the adjoint of convolution.

Let us first describe how the convolution is done, it is defined as the integral of the two functions with the input and the length of time. The reason for this odd expression is that we are going to relate convolution to the Laplace transform. And as we know below transformation in history is the many possibilities of a person’s action including those that are hidden.

We will note t as the input and τ as a dummy variable which in the shape of history is a its length of time. This is the common use in mathematics:

This Definition should give us some clues as to what it is doing for the logic of cultural systems: it is a variant of the Laplace in transform and therefore can be useful in driving such transforms. But if this were all it was about it would be of only passing interest.

However, let us take things more slowly. The three things that one should recognize is that convolutions have three algebraic properties:

Commutativity: f∗g = g ∗ f

This is by definition.

Associativity: (f*g)*h = f*(g*h)

This is a little bit harder but a mathematician, Fubini, came up with a theorem back in 1907 and discovered that the integrals, which remember our present, can be ordered in different ways. The gist is that if the integrals are X x Y, in a square and are non-negative then they can be resolved in whatever order makes sense. This means that the two integrals of convolution can be ordered in either direction.

Distributivity: f*(g+h) = f*g + f*h

Further, the confluence has the additional property of being a complex conjugate:

which is useful for Laplace transforms. it also means something particularly in biology in that there is not one but two stochastic individuals to produce a child and either one of them needs to be in the right place which is what the Dirac Delta function implies.

With this information, we can derive an f and a g which represent the median, that is the center of population growth, and the kurtosis. But since the commutative role applies, there will be a peek in one direction which will inevitably be followed by the peak in the opposite direction.

Let me unpack this: f∗g = g ∗ f will form the same shape but in opposite directions, and that shape is the convolution of the two. Thus, f∗g is the upset of g * f but has the same area. What this has to do with cultural systems is that until there is a statistical opening for the large number of people then the kurtosis will only be able to make individual contributions. For example, von Neumann’s proof. Another example is the fission reaction which occurred on 19 December 1938 and was then explained early the next year. This meant that there was a way to release some of the energy which held together the atom. This set off a race to release the energy and produce more neutrons to split other atoms. This means that for the Second World War, there was the vision of a postmodern universe in embryo, but when Dr. Oppenheimer organized a way to build the “gadget” the kurtosis had been gone to moved towards revolutionary. The reason that von Neumann’s discovery was important is because it would eventually lead to international relations which elaborated the mechanism by which two nuclear-armed states could exist in a kind of equilibrium. This means that at the same time that the atomic bomb was being conceived the apparatus to survive the atomic bomb was being pursued as well and during the war, von Neumann teamed up with Morgenstern to write what would become the basis for the construction of a nuclear-armed peace. But there was also the fact of a delivery system that would be far better than a bomber: a ballistic missile. This would make it so that the atomic payload could be delivered within an extremely short period of time and that was the contribution of the Nazi German war machine.

At the same time, there was another piece of the puzzle: that of the statistics. The reason that the pieces were important was that the nations were soon going to war if they had not already, remember Japan had invaded China repeatedly and on 7 July 1937 Japan invaded China and the Nationalist Government slowly tumbled into war. This means that the individual pieces of the atomic bomb were only part of a more general rush toward war. This means that we can describe the kurtosis as f and the statistical as g, and we can construct f * g. This leads to a Laplace transformation but it is statistical rather than continuous.

The pattern must stem ultimately from a direct Delta function which leads to the birth of a new wave of people. But if there is not sufficient income then you were children will be born and not mean that the population pyramid must wait until there is a reason to borrow money to create the mathematically inevitable baby boom. The response does not vary until birth control and is time-invariant.

This means that we can look at the population pyramid from 1930 through 1950. the wartime boom actually starts the process these images are from the U.S. Census & Minnesota Population Center.

We can see that the dropping population by the 1930s was an unusual event and into the 1940s it continued to drop. This is one of the effects of the great depression: many fewer people could have children. But by 1940 income was given to people to build the engines of war and long before the official “Baby-boom.” This means that in the present cultural system, the actual baby boom was started right before World War II by 1940 which we saw in the births graph.

But this means we can stack the postmodern statistical boom with the postmodern kurtosis bone and see how more and more results from the civilization that we are studying become not just a manner of winning the war, which is a modern perspective on what is going on, but going beyond into the post world war environment. This does not mean that the postmodern is inevitable, the discoveries are not meant to be a reflection of a new cultural synthesis but a way of helping the modern win the war and there afterward when the peace. But over time the cultural synthesis began to push back on the modern in ways that eventually became a revolution: in the 1940s von Neumann advanced a mathematical theory with applications to economics, by the 1960s this received the most visceral kind of test.

So we have f*g as a postmodern construction and it grows as with g, since G is the statistical pattern which people can be drawn into activity. But f has a place to because it is what defines the era in an intellectual sense, a cultural sense, and all of the things that command the mind. This means that since much of the human mind is hidden we are talking about a postmodern worldview that subsumes the postmodern.

But as we should suspect the Complex conjugate means that the Dirac Delta functions yield a random set of babies who will pursue whatever livelihood they may. This means that even though the physics of the outside world may be invariant who discovers it and how they use it is completely random: after all two or three years earlier may well have given the Nazi Germans the edge in creating the atomic bomb where the US has not yet committed to the Allied side.

This means that the convolution is random and stochastic and we cannot predict what will happen with the known information because there is unknown information that is not stored in a local variable. So this gives us a first pass at when the postmodern became revolutionary: it begins with the atomic bomb. It also gives us some insight as to when the postmodern was seeded: in the waning years of peace when countries were envisioning a conflict in which no one knew what the outcome would be. But it produced two things: a world engaged in a war footing, which was clearly modern, and as a side product a boom in the number of children, particularly in the US. This was the beginning of the postmodern system even before there was such a conflict.

However, in the 1950s the official version of government was a modern view but with a twist that it had to conform to the postmodern sense. It also made huge strides in creating a postmodern home environment where postmodern children grew up and absorbed the milieu. But this meant that a modern industrial system had to be converted to a postmodern construction: what had been a wartime environment became the norm in the postmodern view. This means that the power structure was modern, because of course it was old, but every year the world became more postmodern.

So when does this moment actually begin? It is at this point that we begin to study what it means to be postmodern and to further elaborate on how convolution is essential for the construction.