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The Roman Virtues
These are the qualities of life to which every citizen should aspire. They are the heart of the Via Romana--the Roman Way--and are thought to be those qualities which gave the Roman Republic the moral strength to conquer and civilize the world:
Auctoritas--"Spiritual Authority": The sense of one's social standing, built up through experience, Pietas, and Industria.
Comitas--"Humor": Ease of manner, courtesy, openness, and friendliness.
Clementia--"Mercy": Mildness and gentleness.
Dignitas--"Dignity": A sense of self-worth, personal pride.
Firmitas--"Tenacity": Strength of mind, the ability to stick to one's purpose.
Frugalitas--"Frugalness": Economy and simplicity of style, without being miserly.
Gravitas--"Gravity": A sense of the importance of the matter at hand, responsibility and earnestness.
Honestas--"Respectibility": The image that one presents as a respectable member of society.
Humanitas--"Humanity": Refinement, civilization, learning, and being cultured.
Industria--"Industriousness": Hard work.
Pietas--"Dutifulness": More than religious piety; a respect for the natural order socially, politically, and religiously. Includes the ideas of patriotism and devotion to others.
Prudentia--"Prudence": Foresight, wisdom, and personal discretion.
Salubritas--"Wholesomeness": Health and cleanliness.
Severitas--"Sternness": Gravity, self-control.
Veritas--"Truthfulness": Honesty in dealing with others.

"FIDES" is often (and wrongly) translated 'faith', but it has nothing to do with the word as used by Christians writing in Latin about the Christian virute (St. Paul Letter to the Corinthians, chapter 13). For the Romans, FIDES was an essential element in the character of a man of public affairs, and a necessary constituent element of all social and political transactions (perhaps = 'good faith'). FIDES meant 'reliablilty', a sense of trust between two parties if a relationship between them was to exist. FIDES was always reciprocal and mutual, and implied both privileges and responsibilities on both sides. In both public and private life the violation of FIDES was considered a serious matter, with both legal and religious consequences. FIDES, in fact, was one of the first of the 'virtues' to be considered an actual divinity at Rome. The Romans had a saying, "Punica fides" (the reliability of a Carthaginian) which for them represented the highest degree of treachery: the word of a Carthaginian (like Hannibal) was not to be trusted, nor could a Carthaginian be relied on to maintain his political elationships.

Some relationships governed by fides:

VIRTUS, for the Roman, does not carry the same overtones as the Christian 'virtue'. But like the Greek andreia, VIRTUS has a primary meaning of 'acting like a man' (vir) [cf. the Renaissance virtù ), and for the Romans this meant first and foremost 'acting like a brave man in military matters'. virtus was to be found in the context of 'outstanding deeds' (egregia facinora), and brave deeds were the accomplishments which brought GLORIA ('a reputation'). This GLORIA was attached to two ideas: FAMA ('what people think of you') and dignitas ('one's standing in the community'). The struggle for VIRTUS at Rome was above all a struggle for public office (honos), since it was through high office, to which one was elected by the People, that a man could best show hi smanliness which led to military achievement--which would lead in turn to a reputation and votes. It was the duty of every aristocrat (and would-be aristocrat) to maintain the dignitas which his family had already achieved and to extend it to the greatest possible degree (through higher political office and military victories). This system resulted in a strong built-in impetus in Roman society to engage in military expansion and conquest at all times.
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january 2018 by nhaliday
How do you measure the mass of a star? (Beginner) - Curious About Astronomy? Ask an Astronomer
Measuring the mass of stars in binary systems is easy. Binary systems are sets of two or more stars in orbit about each other. By measuring the size of the orbit, the stars' orbital speeds, and their orbital periods, we can determine exactly what the masses of the stars are. We can take that knowledge and then apply it to similar stars not in multiple systems.

We also can easily measure the luminosity and temperature of any star. A plot of luminocity versus temperature for a set of stars is called a Hertsprung-Russel (H-R) diagram, and it turns out that most stars lie along a thin band in this diagram known as the main Sequence. Stars arrange themselves by mass on the Main Sequence, with massive stars being hotter and brighter than their small-mass bretheren. If a star falls on the Main Sequence, we therefore immediately know its mass.

In addition to these methods, we also have an excellent understanding of how stars work. Our models of stellar structure are excellent predictors of the properties and evolution of stars. As it turns out, the mass of a star determines its life history from day 1, for all times thereafter, not only when the star is on the Main Sequence. So actually, the position of a star on the H-R diagram is a good indicator of its mass, regardless of whether it's on the Main Sequence or not.
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december 2017 by nhaliday
[1509.02504] Electric charge in hyperbolic motion: The early history and other geometrical aspects
We revisit the early work of Minkowski and Sommerfeld concerning hyperbolic motion, and we describe some geometrical aspects of the electrodynamic interaction. We discuss the advantages of a time symmetric formulation in which the material points are replaced by infinitesimal length elements.

SPACE AND TIME: An annotated, illustrated edition of Hermann Minkowski's revolutionary essay:
nibble  preprint  papers  org:mat  physics  electromag  relativity  exposition  history  mostly-modern  pre-ww2  science  the-trenches  discovery  intricacy  classic  explanation  einstein  giants  plots  manifolds  article  multi  liner-notes  org:junk  org:edu  absolute-relative 
november 2017 by nhaliday
GPS and Relativity
The nominal GPS configuration consists of a network of 24 satellites in high orbits around the Earth, but up to 30 or so satellites may be on station at any given time. Each satellite in the GPS constellation orbits at an altitude of about 20,000 km from the ground, and has an orbital speed of about 14,000 km/hour (the orbital period is roughly 12 hours - contrary to popular belief, GPS satellites are not in geosynchronous or geostationary orbits). The satellite orbits are distributed so that at least 4 satellites are always visible from any point on the Earth at any given instant (with up to 12 visible at one time). Each satellite carries with it an atomic clock that "ticks" with a nominal accuracy of 1 nanosecond (1 billionth of a second). A GPS receiver in an airplane determines its current position and course by comparing the time signals it receives from the currently visible GPS satellites (usually 6 to 12) and trilaterating on the known positions of each satellite[1]. The precision achieved is remarkable: even a simple hand-held GPS receiver can determine your absolute position on the surface of the Earth to within 5 to 10 meters in only a few seconds. A GPS receiver in a car can give accurate readings of position, speed, and course in real-time!

More sophisticated techniques, like Differential GPS (DGPS) and Real-Time Kinematic (RTK) methods, deliver centimeter-level positions with a few minutes of measurement. Such methods allow use of GPS and related satellite navigation system data to be used for high-precision surveying, autonomous driving, and other applications requiring greater real-time position accuracy than can be achieved with standard GPS receivers.

To achieve this level of precision, the clock ticks from the GPS satellites must be known to an accuracy of 20-30 nanoseconds. However, because the satellites are constantly moving relative to observers on the Earth, effects predicted by the Special and General theories of Relativity must be taken into account to achieve the desired 20-30 nanosecond accuracy.

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion [2].

Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)! This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time.
nibble  org:junk  org:edu  explanation  trivia  cocktail  physics  gravity  relativity  applications  time  synchrony  speed  space  navigation  technology 
november 2017 by nhaliday

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