SUMMARY / RELATED TOPICS

Father of the Nation

The Father of the Nation is an honorific title given to a person considered the driving force behind the establishment of his/her country, state, or nation. Pater Patriae seen as Parens Patriae, was a Roman honorific meaning the "Father of the Fatherland", bestowed by the Senate on heroes, on emperors. In monarchies, the monarch was considered the "father/mother of the nation" or as a patriarch to guide his family; this concept is expressed in the Divine Right espoused in some monarchies, while in others it is codified into constitutional law as in Spain, where the monarch is considered the personification and embodiment, the symbol of the unity and permanence of the nation. In Thailand, the monarch is given the same recognition, demonstrated loyalty is enforced with severe criminal statutes. Many dictators bestow titles upon themselves, which survive the end of their regime. Gnassingbé Eyadéma of Togo's titles included "father of the nation", "older brother", "Guide of the People". Mobutu Sese Seko of Zaire's included "Father of the nation", "the Guide", "the Messiah", "dajsh, "the Leopard", "the Sun-President".

In postcolonial Africa, "father of the nation" was a title used by many leaders both to refer to their role in the independence movement as a source of legitimacy, to use paternalist symbolism as a source of continued popularity. On Joseph Stalin's seventieth birthday in 1949, he was bestowed with the title "Father of Nations" for his establishment of "people's democracies" in countries occupied by the USSR after World War II; the title "Father of the Nation" is sometimes politically contested. The 1972 Constitution of Bangladesh declared Sheikh Mujibur Rahman to be "father of the nation"; the BNP government removed this in 2004, to the protests of the opposition Awami League, led by Rahman's daughter Sheikh Hasina. A motion in the Parliament of Slovakia to proclaim controversial pre-war leader Andrej Hlinka "father of the nation" failed in September 2007; the following people are still called the "Father" of their respective nations. Highlighted names indicate people. List of national founders Victory title Pater Patriae Founding Fathers of the United States Founding fathers of the European Union Fathers of Confederation Family as a model for the state

Eliphaz (Job)

Eliphaz is called a Temanite. He appears in the Book of Job in the Hebrew Bible. Eliphaz appears mild and modest. In his first reply to Job's complaints, he argues that those who are good are never forsaken by Providence, but that punishment may justly be inflicted for secret sins, he denies that any man is innocent and censures Job for asserting his freedom from guilt. Eliphaz exhorts Job to confess any concealed iniquities to alleviate his punishment, his arguments are well supported but God declares at the end of the book that Eliphaz has made a serious error in his speaking. Job offers a sacrifice to God for Eliphaz's error. Eliphaz, the first of the three visitors of Job, was supposed to have come from Teman, an important city of Edom, thus Eliphaz appears as the representative of the wisdom of the Edomites, according to Obadiah 8, Jeremiah 49:7, Baruch 3:22, was famous in antiquity. The name "Eliphaz" for the spokesman of Edomite wisdom may have been suggested to the author of Job by the tradition which gave this name to Esau's son, the father of Theman.

In the arguments that pass between Job and his friends, it is Eliphaz who opens each of the three series of discussions. His primary belief was that the righteous do not perish; this argument is, in part, rooted in what he believes to have been a personal revelation he received through a dream: "Can mankind be just before God? Can a man be pure before his Maker? He puts no trust in His servants. How much more those who dwell in houses of clay". After mulling it over, Job responds to this "revelation" of Eliphaz, "In truth I know that this is so. If one wished to dispute with Him, he could not answer Him once in a thousand times." Eliphaz refers to his revelation again for emphasis in Job 15:14-16. Bildad refers to Eliphaz's revelation in chapter 25, although he presents the concept as his own. Job rebukes him for it: "What a help you are to the weak! How you have saved the arm without strength! What counsel you have given to one without wisdom! What helpful insight you have abundantly provided! To whom have you uttered words?

And whose spirit was expressed through you?" Job pokes fun at Bildad asking him what spirit revealed it to him because he recognizes the argument as Eliphaz's spiritual revelation. Although quick-witted, quick to respond, Eliphaz loses his composure in chapter 22, accusing Job of oppressing widows and orphans, a far cry from how he had described Job: "Behold you have admonished many, you have strengthened weak hands. Your words have helped the tottering to stand, you have strengthened feeble knees, but now it has come to you, you are impatient. Is not your fear of God your confidence, the integrity of your ways your hope?"Eliphaz misconstrues Job's message as he scrambles to summarize Job's thoughts from chapter 21. "You say, ‘What does God know? Can He judge through the thick darkness? Clouds are a hiding place for Him, so that He cannot see. Job was observing that in this life God chooses not to prevent evil. Conventional wisdom told Eliphaz that God should punish the wicked as that would be the just thing to do.

Job, saw it differently, in 24:1, Job laments. "Why does the Almighty not set times for judgment? Why must those who know him look in vain for such days?" Job yearns for the justice Eliphaz claims exists – an immediate punishment of the wicked. However, that didn't hold true according to Job's observations. Job doesn't question God's ultimate justice, he knows justice will be served. Job asks, "For what hope have the godless when they are cut off, when God takes away their life? Does God listen to their cry when distress comes upon them?"

Computable topology

Computable topology is a discipline in mathematics that studies the topological and algebraic structure of computation. Computable topology is not to be confused with algorithmic or computational topology, which studies the application of computation to topology; as shown by Alan Turing and Alonzo Church, the λ-calculus is strong enough to describe all mechanically computable functions. Lambda-calculus is thus a programming language, from which other languages can be built. For this reason when considering the topology of computation it is common to focus on the topology of λ-calculus. Note that this is not a complete description of the topology of computation, since functions which are equivalent in the Church-Turing sense may still have different topologies; the topology of λ-calculus is the Scott topology, when restricted to continuous functions the type free λ-calculus amounts to a topological space reliant on the tree topology. Both the Scott and Tree topologies exhibit continuity with respect to the binary operators of application and abstraction with a modular equivalence relation based on a congruency.

The λ-algebra describing the algebraic structure of the lambda-calculus is found to be an extension of the combinatory algebra, with an element introduced to accommodate abstraction. Type free λ-calculus treats functions as rules and does not differentiate functions and the objects which they are applied to, meaning λ-calculus is type free. A by-product of type free λ-calculus is an effective computability equivalent to general recursion and Turing machines; the set of λ-terms can be considered a functional topology in which a function space can be embedded, meaning λ mappings within the space X are such that λ:X → X. Introduced November 1969, Dana Scott's untyped set theoretic model constructed a proper topology for any λ-calculus model whose function space is limited to continuous functions; the result of a Scott continuous λ-calculus topology is a function space built upon a programming semantic allowing fixed point combinatorics, such as the Y combinator, data types. By 1971, λ-calculus was equipped to define any sequential computation and could be adapted to parallel computations.

The reducibility of all computations to λ-calculus allows these λ-topological properties to become adopted by all programming languages. Based on the operators within lambda calculus and abstraction, it is possible to develop an algebra whose group structure uses application and abstraction as binary operators. Application is defined as an operation between lambda terms producing a λ-term, e.g. the application of λ onto the lambda term a produces the lambda term λa. Abstraction incorporates undefined variables by denoting λx.t as the function assigning the variable a to the lambda term with value t via the operation. Lastly, an equivalence relation emerges which identifies λ-terms modulo convertible terms, an example being beta normal form; the Scott topology is essential in understanding the topological structure of computation as expressed through the λ-calculus. Scott found that after constructing a function space using λ-calculus one obtains a Kolmogorov space, a T o topological space which exhibits pointwise convergence, in short the product topology.

It is the ability of self homeomorphism as well as the ability to embed every space into such a space, denoted Scott continuous, as described which allows Scott's topology to be applicable to logic and recursive function theory. Scott approaches his derivation using a complete lattice, resulting in a topology dependent on the lattice structure, it is possible to generalise Scott's theory with the use of complete partial orders. For this reason a more general understanding of the computational topology is provided through complete partial orders. We will re-iterate to familiarize ourselves with the notation to be used during the discussion of Scott topology. Complete partial orders are defined as follows: First, given the ordered set D=, a nonempty subset X ⊆ D is directed if ∀ x,y ∈ X ∃ z ∈ X where x≤ z & y ≤ z. D is a complete partial order if: · Every directed X ⊆D has a supremum, and:∃ bottom element ⊥ ∈ D such that ∀ x ∈ D ⊥ ≤ x. We are now able to define the Scott topology over a cpo. O ⊆ D is open if: for x ∈ O, x ≤ y y ∈ O, i.e. O is an upper set.

For a directed set X ⊆ D, supremum ∈ O X ∩ O ≠ ∅. Using the Scott topological definition of open it is apparent that all topological properties are met. ·∅ and D, i.e. the empty set and whole space, are open.·Arbitrary unions of open sets are open: Proof: Assume U i is open where i ∈ I, I being the index set. We define U = ∪. Take b as an element of the upper set of U, therefore a ≤ b for some a ∈ U It must be that a ∈ U i for some i b ∈ upset. U must therefore be upper as well since U i ∈ U. If D is a directed set with a supremum in U by assumption sup ∈ U i where U i is open, thus there is a b ∈ D where b ∈ U i ∩ D ⊆ U ∩ D. The union of open sets U i is therefore open.·Open sets under intersection are open: Proof: Given two open sets, U and V, we define W = U∩V