# Thucydides Paradox

Post Biography

**Thucydides **was a Greek historian and author from Athens, now capital of Greece. His *History of the Peloponnesian War* recounts the 5th century BC war between Sparta and Athens to the year 411 BC. Thucydides has been dubbed the father of “scientific history”, because of his strict standards of evidence-gathering and analysis in terms of cause and effect without reference to intervention by the gods, as outlined in his introduction to his work.

Scholars traditionally view Thucydides as recognizing and teaching the lesson that democracies need leadership, but that leadership can be dangerous to democracy. Thucydides had a deeply ambivalent view: on one hand, Thucydides’ own “wisdom was made possible” by the Periclean democracy, which had the effect of liberating individual daring, enterprise and questioning spirit, but this same liberation, by permitting the growth of limitless political ambition, led to imperialism and, eventually, civic strife.

This common trait on every Thucydides work is also known as Thucydides Paradox. Thucydides Paradox is the common existence of the bad and the good together. However it goes further. As Thucydides was beknown to be the farther of reason and common logic to a mathematical standard, he was always trying to avoid prejudice and to search deeply for the real causes.

In mathematics, we deal with mathematical logic. Theories of logic were developed in many cultures in history, including China, India, Greece, and settled the foundations of mathematics.

Since its inception, mathematical logic has both contributed to, the study of foundations of mathematics. This study began with the development of axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped to prove the consistency of foundational theories. Results provided partial resolution to the program, and clarified the issues involved in proving consistency. The set theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. Contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems, rather than trying to find theories in which all of mathematics can be developed.

This means in simple words that everything cannot be good or bad, every substance consists of two other substances. This is the dual theory.

Thucydides was perceived as simply “the father of realpolitik”. Realpolitk is called the school of political realism, which views the relations between nations as based on might rather than right. His text is still studied at advanced military colleges worldwide, and the Melian dialogue remains a seminal work of international relations theory.

What is Thycudides Paradox?

Thycudides was ambivalent not about its logical and clear thinking, but about the results of it. As he remarked late in his life, the same starting point having all the other circumstances standard, ceteris paribus, doesn’ t produce the same results. This is the base of today science. Science is based on repetitive experiments that produce that same results, this leads to an axiom, and then it becomes a theorem, or a theory. The father of history understood that **same starting point, don’t produce that same results.** Maybe the results seem to be the same but they are not due to the duality of the substance. For instance, consider time 0 to have a set of substance 2. As time progresses we need to have the same set of substance but every one of them as it has its dual sub-substance it has a probality of 4 when time is 1. When time is 2, the probability is 8, when time is 3 is 16, 4 is 32 etc.It is a probability geometrical progress of the same substance. When we reach time 10 we have 2048 probabilities for the same dual set of substances that we begun with.

Thycudides Paradox in every day life

Lets take an example of our every day life. John is a 20 years old student he is dating with mary. Mary is in the same class with him, 20 years old brunette and tall. Suddenly Mary falls in love with another guy and eventually splits up with John. John is frustrated and deeply in depression. Next year, John is 21 and Mary is avaliable, they start dating but John try to protect himself due to his previous experience. And then Mary finds another guy, she falls in love with him but she don’t stop dating John. she has parallel relationships. Next year, Mary and John are not together. They see each other and they start dating again. Mary falls in love with another guy, but she doesn’t start dating with him. She prefers to stay with John and they decided to get married.

Same situation but with several different results. Simple Thycudides Paradox effect.

Thycudides Paradox and the Butterfly Effect.

In chaos theory, the **butterfly effect** is the *sensitive dependence on initial conditions*, where a small change at one place in a nonlinear system can result in large differences to a later state. Recurrence, the approximate return of a system towards its initial conditions, together with sensitive dependence on initial conditions, are the two main ingredients for chaotic motion.Thycudides Paradox says that it doesn’ t have to be a linear system in order to get the same effect, there is not linear system in life. It seems to be but it is not. Even static systems are dynamic in terms of application.

What is my personal view of the above scientifical review?

HISTORY CAN NEVER REPEAT ITSELF. It seems that history repeats itself, but it a decoy. It is not real.You can never have two Alexander the Great, you can never have two Abraham Lincoln. You can never have the same results, even if you had the same initial conditions.

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