Modernism, Postmodernism, and Digitality
Mathematical Basis
Mathematical Basis
Basis in Observation and Theory
As the Cultural System needs to be based on all observation and theory, we need to establish both the observation and how to utilize mathematics to create a theory. The most important point is to be able to show how a logical theory works. This means that we need to have a set of vectors and make them orthonormalized to be able to see the Cultural System that is operating through historical events and by population.
A Cultural System means that there are several logics that will flow from it but can be transformed from one to the other. This also means that there are logics that cannot be moved from one to the other, meaning that the Cultural System for both is incompatible. This means that a Cultural System is a framework for building individual logic and interrelating the various logics so constructed to each other. This means reducing instructions from one logic to another to finite expressions even if those expressions are not in the manner of language either written or spoken. That is to say that the expression may have text and subtext transmitted at the same time.
In 1866 a cable was laid down under the sea. the Atlantic by telegraph and reducing the time it took for news, quotations in markets, and messages from one person to another. But this was not an easy task because the first attempt on 16 August 1858 was very slow, and the cable broke in September. As Thomas A. Dames dryly notes “There was general failure to anticipate engineering difficulties throughout the project…”[i] this meant that attempts were made in 1856, 1858, and 1862, Before finally achieving success in 1866.[ii] It was called a “bold, Beautiful Failure” in IEEE Spectrum on 31 October 2019, and such was the power it had to members of the field. This was because not only was there an earlier on the financial side but there was new physics involved as well – both theoretical and experimental.
Since this is a popular presentation the mathematics can be looked up and a YouTube video that makes key points.[iii]
The physics at the time showed itself as the problem of “retardation” of the signal. This was immediately apparent when the first sentence from Queen Victoria to then Pres. Buchanan took hours to reach the other side. While the elaborate details can be looked up in the original paper which was published in December 1855 and explained in a rigorous analytical way by a book on Fourier analysis, what is interesting from this book’s perspective is it was not just one paper but a series of six papers which created a mathematical theory of magnetism, the Thermo electrical effects, and showing how this theory explains why the slowness of the effect is created. In other words, there is an underlying theory as to why the slowness occurred. What Thompson deduced: “We may infer that the time required to reach a stated fraction of the maximum strength of the current at the remote will be proportional to kcl2.” Where l is the length squared instead of merely the length which is why there is a “retardation” in the signal. This observation harkens back to Newton and the square of the masses for gravitation and is the key concept for all of what would now be called classical physics, which was disrupted by Dirac and Einstein.
Thompson then goes on to state what is obvious once one has thought of it: because the cable disperses the transmission by the square of the length, there is no regular speed of transmission only the transmission based on the length of the cable. This is why short distances work out quite nicely because the cable being short disperses the voltage and it is why long cables need to have a longer time to disperse the voltage because the length squared is longer.
What this means is that it is not merely an error but a fundamental observation and this meant that it had to be fixed from the beginning.[iv]
What this means is that the transatlantic cable was more than merely a scaling up of shorter distances, which was already being done, but a new idea that needed mathematical rigor, technological precision, and financial acumen. What this means is that the transatlantic cable was the point where a new form of logic burst onto the scene, and I call this Neoclassical, in the sense that it was the Enlightenment powered by calculus. But as we see this infected more than just electrical wiring but a new sense of how the world should be looked at whether in comedic or tragic novels, and as we will show in other ways as well.
This was proof that a new Cultural System was able to do what the old Cultural System could not do: it could lay down a cable and transmit through dots and dashes a message from one side of the Atlantic to the other. That it was capable of doing this is because slightly over a decade earlier in 1855, the old Cultural System could not do this. There was a mathematical and physical basis that needed engineering to perform the operation. This does not mean that laying down a transatlantic cable is the start only that it confirms that a new Cultural System is no longer merely a visionary idea but has become revolutionary in its manner.
This is a new approach because as it currently stands history is one of the least mathematically oriented fields, with economics being the most common math available. Instead, this is based on linear algebra and therefore on biology, because it is biology that introduces key concepts to history. With these key concepts comes a welter of new ideas for history and to examine and work through whether or not they have a reason in his history.
[i] Dames, Thomas A. 1965. “The Transatlantic Cable.” The Military Engineer 57, no. 380: 401–3. http://www.jstor.org/stable/44574898. 401.
[ii] Science Museum Group. Chart of the Atlantic showing the proposed course of the Atlantic Cable, 1856-1857. 1862-176. https://collection.sciencemuseumgroup.org.uk/objects/co32895/chart-of-the-atlantic-showing-proposed-course-of-the-atlantic-cable-1856-1857-chart-graphic-document.
[iii] The original paper is: Thomson, William. “III. On the Theory of the Electric Telegraph.” Proceedings of the Royal Society of London 7 (January 1856): 382–99. doi:10.1098/rspl.1854.0093. Smithies, F. “Fourier Analysis, by T. W. Körner. £60. 1988. ISBN 0-521-25120-6 (Cambridge University Press).” The Mathematical Gazette 73, no. 463 (1989): 63–64. https://doi.org/10.2307/3618232 gives a mathematical look at the subject, including the key one needs to figure out the resistance by Ohm’s Law. The YouTube video is here:
[iv] The addendum is the “William Thompson” goes on to be “Lord Kelvin” and he is remembered by the Kelvin scale which has degrees as centigrade but it’s zero point is the absolute zero where the entropy of a cooled gas as reached its minimum point. This means of course that the Enthalpy is also zero, that is the internal energy has reached zero.