Medieval Localism, Mathematics and the Printing Press|Chapter 5| Complexity, Information Theory and the Nature of Symbolic systems: The Death of the Gods and the Revolt Against Reason

The Dark Ages

The fall of Rome in Europe, must also be understood with the rise of Islam. Fundamentally, bifurcating what were once well-established Roman trade routes. The dark ages are dark in reference to the complexity of Rome. 

The High Middle Ages-Medieval trade

The advent of medieval trade, fundamentally represents the re-establishment of roman trade routes amongst the fragments of the greater roman empire. The church acted as a substitute superstructure for the Roman state. Allowing for common identification across geography.

Medieval Localism

Despite China having shipping technologies hundreds of years ahead of Europe.  It was not the Chinese who colonized the west indies, let alone the new world. China, being more centralized than Europe, would have one great fleet built by an emperor. Only, for it to be destroyed by the next. While in Europe, an Italian can sail for the king of Spain. This greater decentralization, allowing for more optionality.

Additionally, although there was a king of france. There were also the French nobility. Who, for the most part, had conflicting interests with the crown. As it was the nobility that would be called on to finance wars. Simultaneously, the monarchs needed to take the interests of the church into consideration as well. These competing interests would ensure that the each group could not overstep its boundaries.

The Enlightenment

The printing press-the automated symbol machine

Demand curves being downward sloping means that a decrease in the cost of symbol-creation leads to an increase in symbols. The printing press, allowed for the aautomation of symbol creation. As opposed to having everything handwritten by monks, the printing press, allowed for a decrease in the scale necessary to maintain a consistent information cluster.

The protestant reformation

Martin Luther, and other priests, were able to compete with the larger church apparatus via the distribution of pamphlets. These pamphlets would hold the personal views of the writer. These pamphlets would be read aloud to a crowd of people. As most people, during that time, lacked the ability to interpret alphabetical symbols.

These divergent views would eventually be crystallized by a schism in Christianity, in addition to, the bifurcation into Catholic and Orthodox Christians. This division was a reflection of the two information clusters of the time: the Byzantium and Roman Empire.

Eventually, Europe, previously all catholic, would house multiple forms of christinanity. Leading to an all out religious persecution and war.

Medieval Mathematics (technical)

The Symbolic system of Algebra

Algebra, introduces the notion of abstraction into mathematics. As a symbolic system, algebra allows for the representation of non-numerical symbols in mathematics. Thereby, increasing the set of mathematical objects which can be represented while being subject to the laws of arithmetic. An Algorithm is a precisely stated set of instructions that can be proven to work. The set of algorithms is increasing with an increasing set of symbols. Although not treated as sub fields of algebra, probability theory, calculus amongst other disciplines rely on algebra.

Algebraic Geometry

Algebraic geometry represents an application of a symbolic system to geometry. A codification of the points in space with a number system. In which, a point is defined by its coordinate on the xy-axis. A line, then becomes a pattern of points. Allowing, for the rules of geometry to make calculations.


Calculus represents a study between points in space. Space defined by Algebraic Geometry.

Greek Geometry

A symbolic system applied to geometry would be considered an abomination to the Greeks who specialize in non symbolic geometry. To the Greeks, differences in geometric forms can be quantified. But only in comparison to one another by the scaling of common proportions.

The Greek, aversion to irrational numbers. Stem from the fact that irrational numbers do not scale linearly. That’s what makes them-irrational. It then becomes impossible to compare. As each line differs in their growth pattern. This is because to the Greeks, numbers correspond to geometric patterns. The exactness of a cult of mathematical mumbo jumbo.

The Computer/Indexer Revolution-The Electromechanical symbol machine (technical)

Machine code as a symbolic system

Machine code represents a fundamental evolution in information technology. Where, a recent trend, started by Stepehen Wolfram, to explain the behavior of systems with the use of cellular automata. Whereby, the behavior of these automata are described with computer code not alphanumeric symbols.

Machine code is an algorithm expressed in a symbolic system that machines can understand. A program is an algorithm in a given programming language. Fundamentally, machine code represents the symbolic mapping of work. Specifically, a symbolic system which determines the behavior of an (electronic) circuit. 

Machine code is an electronic mechanical symbolic system. The ability to mechanize algorithms (information transformation). As expressed by the first computer scientist Aida Lovelace. “The Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves.”

The most fundamental rule of computer science is that everything must be named incorrectly. The most fundamental operation that a computer executes is known as an “if statement”. So you told the computer if? If what?

The concept is much better described as an “if then statement”. If some condition is met, then do some operation. The “if then statement” is not merely a better name. It better captures the sequential ordering of protocols. In addition, the temporal nature of computation.

The Indexation revolution

How do computers encode information?

To that, I must make reference to another quantum physicist-(dork Jesus) Richard Feynman. Where, in his computer heuristics lecture, he tries to tell us perhaps the most profound point of the computer revolution-computers do not actually compute.

What do they do? Feynman likens them to an electronic filing system. Which explains what computers are-not what they do. To that, we must turn to the French who have a much better word for it-”Ordinateur”. From the Latin “Ordinat” which means order. Essentially what an “Ordinateur” does is to index. To file in a filing system, is to index something and to retrieve something according to an index. The proper term for a computer should be an indexer. Where the total memory by which you index over can just be thought of as a possibility space of 2n possibilities.

If I wanted to store 8 numbers I would need 23 different possibilities.

Now the quality of the video is unclear. Feynman is using colors instead of 1s and 0s.

This may seem trivial to those with little knowledge of machine learning. But programming can be thought of as, it ultimately is, a mapping onto 1s and 0s. Now machine learning can be thought of as auto-indexation.

The history of man made intelligence has scaled in direct correspondence with that of the computing industry in general. Machine learning algorithms were around before the commercialisation of computing in the mid 60s. But their efficacy, at the time, was limited not by theory but by the nature of computer hardware.

However, if you listen to the supposed ‘experts’ in the field of artificial intelligence, they will tell you that all we need is more “compute” to get better AI. Which is a statement that conveys no information. As what they are essentially saying, the ability for a computer to auto-index is increasing in the number of points to index over. Now the current state of machine learning can be summarized as follows: Machines are better at auto-indexing when they have a human-made index to map onto, supervised learning,  rather than when they are given data over which to auto-index over-unsupervised learning.


Most of what people call a computer comes down to applied combinatorics. What we call increased compute/indexation is just more possible combinations over which to store variables. Whose size is equal to 2^n.Which can also be thought of as the (n) number of 2 digits combinations that an indexer can index over.

Probability theory

Probability theory fundamentally represents a symbolic mapping of a possibility space. Additionally, what is oft understood is the current field of AI has yet to progress past the point that mathematics reached in medieval Europe. With most probability theory being based on mastering the games of chance. Which is exactly my point, these are but mere games. In reinforcement learning, what the computer essentially does is try a series of possible strategies. Based on if these strategies prove successful or not, the computers classify them as either having worked (1), did not work (0) or ended in a draw (1/2). The power of reinforcement learning is dependent on the ability to accurately reward the agent in question. In the case of actual warfare (not chess) one can lose every single battle and still win the war. Therefore when trying to accurately determine weights when it comes to the real world one encounters a dimensionality problem.