FYI August 04, 2017

1854 – The Hinomaru is established as the official flag to be flown from Japanese ships.
The national flag of Japan is a white rectangular flag with a red disc in the center. This flag is officially called Nisshōki (日章旗, “sun-mark flag”) in the Japanese language, but is more commonly known as Hinomaru (日の丸, “circle of the sun”). The flag embodies Japan’s nickname as the Land of the Rising Sun.

The Nisshōki flag is designated as the national flag in the Law Regarding the National Flag and National Anthem, which was promulgated and became effective on August 13, 1999. Although no earlier legislation had specified a national flag, the sun-disc flag had already become the de facto national flag of Japan. Two proclamations issued in 1870 by the Daijō-kan, the governmental body of the early Meiji period, each had a provision for a design of the national flag. A sun-disc flag was adopted as the national flag for merchant ships under Proclamation No. 57 of Meiji 3 (issued on February 27, 1870), and as the national flag used by the Navy under Proclamation No. 651 of Meiji 3 (issued on October 27, 1870). Use of the Hinomaru was severely restricted during the early years of the Allied occupation of Japan after World War II; these restrictions were later relaxed.

The sun plays an important role in Japanese mythology and religion as the Emperor is said to be the direct descendant of the sun goddess Amaterasu and the legitimacy of the ruling house rested on this divine appointment and descent from the chief deity of the predominant Shinto religion. The name of the country as well as the design of the flag reflect this central importance of the sun. The ancient history Shoku Nihongi says that Emperor Monmu used a flag representing the sun in his court in 701, and this is the first recorded use of a sun-motif flag in Japan. The oldest existing flag is preserved in Unpō-ji temple, Kōshū, Yamanashi, which is older than the 16th century, and an ancient legend says that the flag was given to the temple by Emperor Go-Reizei in the 11th century.[3][4][5] During the Meiji Restoration, both the sun disc and the Rising Sun Ensign of the Imperial Japanese Navy became major symbols in the emerging Japanese Empire. Propaganda posters, textbooks, and films depicted the flag as a source of pride and patriotism. In Japanese homes, citizens were required to display the flag during national holidays, celebrations and other occasions as decreed by the government. Different tokens of devotion to Japan and its Emperor featuring the Hinomaru motif became popular during the Second Sino-Japanese War and other conflicts. These tokens ranged from slogans written on the flag to clothing items and dishes that resembled the flag.

Public perception of the national flag varies. Historically, both Western and Japanese sources claimed the flag was a powerful and enduring symbol to the Japanese. Since the end of World War II (the Pacific War), the use of the flag and the national anthem Kimigayo has been a contentious issue for Japan’s public schools. Disputes about their use have led to protests and lawsuits. The flag is not frequently displayed in Japan due to its association with ultranationalism. To Okinawans, the flag represents the events of World War II and the subsequent U.S. military presence there. For some nations that have been occupied by Japan, the flag is a symbol of aggression and imperialism. The Hinomaru was used as a tool against occupied nations for purposes of intimidation, asserting Japan’s dominance, or subjugation. Several military banners of Japan are based on the Hinomaru, including the sunrayed Naval Ensign. The Hinomaru also serves as a template for other Japanese flags in public and private use.

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1805 – William Rowan Hamilton, Irish physicist, astronomer, and mathematician (d. 1865)
Sir William Rowan Hamilton PRIA FRSE (4 August 1805 – 2 September 1865) was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques. His best known contribution to mathematical physics is the reformulation of Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the modern study of classical field theories such as electromagnetism, and to the development of quantum mechanics. In pure mathematics, he is best known as the inventor of quaternions.

Hamilton is said to have shown immense talent at a very early age. Astronomer Bishop Dr. John Brinkley remarked of the 18-year-old Hamilton, ‘This young man, I do not say will be, but is, the first mathematician of his age.’

William Rowan Hamilton’s scientific career included the study of geometrical optics, classical mechanics, adaptation of dynamic methods in optical systems, applying quaternion and vector methods to problems in mechanics and in geometry, development of theories of conjugate algebraic couple functions (in which complex numbers are constructed as ordered pairs of real numbers), solvability of polynomial equations and general quintic polynomial solvable by radicals, the analysis on Fluctuating Functions (and the ideas from Fourier analysis), linear operators on quaternions and proving a result for linear operators on the space of quaternions (which is a special case of the general theorem which today is known as the Cayley–Hamilton theorem). Hamilton also invented “icosian calculus”, which he used to investigate closed edge paths on a dodecahedron that visit each vertex exactly once.

Early life
Hamilton was the fourth of nine children born to Sarah Hutton (1780–1817) and Archibald Hamilton (1778–1819), who lived in Dublin at 38 Dominick Street. Hamilton’s father, who was from Dunboyne, worked as a solicitor. By the age of three, Hamilton had been sent to live with his uncle James Hamilton, a graduate of Trinity College who ran a school in Talbots Castle in Trim, Co. Meath.[2]

His uncle soon discovered that Hamilton had a remarkable ability to learn languages, and from a young age, had displayed an uncanny ability to acquire them (although this is disputed by some historians, who claim he had only a very basic understanding of them). At the age of seven he had already made very considerable progress in Hebrew, and before he was thirteen he had acquired, under the care of his uncle (a linguist), almost as many languages as he had years of age. These included the classical and modern European languages, and Persian, Arabic, Hindustani, Sanskrit, and even Marathi and Malay. He retained much of his knowledge of languages to the end of his life, often reading Persian and Arabic in his spare time, although he had long since stopped studying languages, and used them just for relaxation.

In September 1813 the American calculating prodigy Zerah Colburn was being exhibited in Dublin. Colburn was 9, a year older than Hamilton. The two were pitted against each other in a mental arithmetic contest with Colburn emerging the clear victor. In reaction to his defeat, Hamilton dedicated less time to studying languages and more time to studying mathematics.[3][4][5]

Hamilton was part of a small but well-regarded school of mathematicians associated with Trinity College Dublin, which he entered at age 18. He studied both classics and mathematics, and was appointed Professor of Astronomy just prior to his graduation (BA, 1827, he was awarded MA in 1837). He then took up residence at Dunsink Observatory where he spent the rest of his life.[4]

Optics and Mechanics
Hamilton made important contributions to optics and to classical mechanics. His first discovery was in an early paper that he communicated in 1823 to Dr. Brinkley, who presented it under the title of “Caustics” in 1824 to the Royal Irish Academy. It was referred as usual to a committee. While their report acknowledged its novelty and value, they recommended further development and simplification before publication. Between 1825 and 1828 the paper grew to an immense size, mostly by the additional details that the committee had suggested. But it also became more intelligible, and the features of the new method were now easily seen. Until this period Hamilton himself seems not to have fully understood either the nature or importance of optics, as later he intended to apply his method to dynamics.

In 1827, Hamilton presented a theory of a single function, now known as Hamilton’s principal function, that brings together mechanics, optics, and mathematics, and which helped to establish the wave theory of light. He proposed it when he first predicted its existence in the third supplement to his “Systems of Rays,” read in 1832. The Royal Irish Academy paper was finally entitled “Theory of Systems of Rays,” (23 April 1827) and the first part was printed in 1828 in the Transactions of the Royal Irish Academy. The more important contents of the second and third parts appeared in the three voluminous supplements (to the first part) which were published in the same Transactions, and in the two papers “On a General Method in Dynamics,” which appeared in the Philosophical Transactions in 1834 and 1835. In these papers, Hamilton developed his great principle of “Varying Action”. The most remarkable result of this work is the prediction that a single ray of light entering a biaxial crystal at a certain angle would emerge as a hollow cone of rays. This discovery is still known by its original name, “conical refraction”.

The step from optics to dynamics in the application of the method of “Varying Action” was made in 1827, and communicated to the Royal Society, in whose Philosophical Transactions for 1834 and 1835 there are two papers on the subject, which, like the “Systems of Rays,” display a mastery over symbols and a flow of mathematical language almost unequaled. The common thread running through all this work is Hamilton’s principle of “Varying Action”. Although it is based on the calculus of variations and may be said to belong to the general class of problems included under the principle of least action which had been studied earlier by Pierre Louis Maupertuis, Euler, Joseph Louis Lagrange, and others, Hamilton’s analysis revealed much deeper mathematical structure than had been previously understood, in particular the symmetry between momentum and position. Paradoxically, the credit for discovering the quantity now called the Lagrangian and Lagrange’s equations belongs to Hamilton. Hamilton’s advances enlarged greatly the class of mechanical problems that could be solved, and they represent perhaps the greatest addition which dynamics had received since the work of Isaac Newton and Lagrange. Many scientists, including Liouville, Jacobi, Darboux, Poincaré, Kolmogorov, and Arnold, have extended Hamilton’s work, thereby expanding our knowledge of mechanics and differential equations.

While Hamilton’s reformulation of classical mechanics is based on the same physical principles as the mechanics of Newton and Lagrange, it provides a powerful new technique for working with the equations of motion. More importantly, both the Lagrangian and Hamiltonian approaches which were initially developed to describe the motion of discrete systems, have proven critical to the study of continuous classical systems in physics, and even quantum mechanical systems. In this way, the techniques find use in electromagnetism, quantum mechanics, quantum relativity theory, and quantum field theory.

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