Abraham Ortelius Theatrum Orbis Terrarum Please explain Theatrum Orbis Terrarum? Ortelius' Theatrum Orbis Terrarum, the "first modern atlas" (of 53 maps). Did Abraham contribute to this? In 1573 Ortelius published seventeen supplementary maps under the title Additamentum Theatri Orbis Terrarum.
What else is important to know about this ?
What else is important to know about Theatrum Orbis Terrarum besides publishing maps ?
On 20 May 1570, Gilles Coppens de Diest at Antwerp issued Ortelius' Theatrum Orbis Terrarum, the "first modern atlas" (of 53 maps). Three Latin editions of this (besides a Dutch, a French and a German edition) appeared before the end of 1572; twenty-five editions came out before Ortelius' death in 1598; and several others were published subsequently, for the atlas continued to be in demand until about 1612. Most of the maps were admittedly reproductions (a list of 87 authors is given in the first Theatrum by Ortelius himself, growing to 183 names in the 1601 Latin edition), and many discrepancies of delineation or nomenclature occur. Errors, of course, abound, both in general conceptions and in detail; thus South America is initially very faulty in outline, but corrected in the 1587 French edition, and in Scotland the Grampians lie between the Forth and the Clyde; but, taken as a whole, this atlas with its accompanying text was a monument of rare erudition and industry. Its immediate precursor and prototype was a collection of thirty-eight maps of European lands, and of Asia, Africa, Tartary and Egypt, gathered together by the wealth and enterprise, and through the agents, of Ortelius' friend and patron, Gillis Hooftman (1521-1581), lord of Cleydael and Aertselaer: most of these were printed in Rome, eight or nine only in the Southern Netherlands.  In 1573 Ortelius published seventeen supplementary maps under the title Additamentum Theatri Orbis Terrarum. Four more Additamenta were to follow, the last one appearing in 1597. He also had a keen interest and formed a fine collection of coins, medals and antiques, and this resulted in the book (also in 1573, published by Philippe Galle of Antwerp) Deorum dearumque capita ... ex Museo Ortelii (reprinted in 1582, 1602, 1612, 1680, 1683 and finally in 1699 by Gronovius, Thesaurus Graecarum Antiquitatum. vol. vii).  The Theatrum Orbis Terrarum inspired a six volume work entitled Civitates orbis terrarum edited by Georg Braun and illustrated by Frans Hogenberg with the assistance of Ortelius himself, who visited England to see his friend John Dee in Mortlake in 1577 and Braun tells of Ortelius putting pebbles in cracks in Temple Church, Bristol, being crushed by the vibration of the bells in the description on the back of 'Brightovve' Map 2, Third Edition 1581 CANNOTANSWER
The Theatrum Orbis Terrarum inspired a six volume work entitled
Abraham Ortelius (; also Ortels, Orthellius, Wortels; 4 or 14 April 152728 June 1598) was a Brabantian cartographer, geographer, and cosmographer, conventionally recognized as the creator of the first modern atlas, the Theatrum Orbis Terrarum (Theatre of the World). Along with Gemma Frisius and Gerardus Mercator, Ortelius is generally considered one of the founders of the Netherlandish school of cartography and geography. He was a notable figure of this school in its golden age (approximately 1570s–1670s) and an important geographer of Spain during the age of discovery. The publication of his atlas in 1570 is often considered as the official beginning of the Golden Age of Netherlandish cartography. He was the first person proposing that the continents were joined before drifting to their present positions.

Life
Ortelius was born on either 4 April or 14 April 1527 in the city of Antwerp, which was then in the Habsburg Netherlands (modern-day Belgium). The Orthellius family were originally from Augsburg, a Free imperial city of the Holy Roman Empire. In 1535, the family had fallen under suspicion of Protestantism. Following the death of Ortelius's father, his uncle Jacobus van Meteren returned from religious exile in England to take care of Ortelius. Abraham remained close to his cousin Emanuel van Meteren, who would later move to London. In 1575 he was appointed geographer to the king of Spain, Philip II, on the recommendation of Arias Montanus, who vouched for his orthodoxy.

He travelled extensively in Europe and is specifically known to have traveled throughout the Seventeen Provinces; in southern, western, northern, and eastern Germany (e.g., 1560, 1575–1576); France (1559–1560); England and Ireland (1576); and Italy (1578, and perhaps two or three times between 1550 and 1558).

Beginning as a map-engraver, in 1547 he entered the Antwerp Guild of Saint Luke as an illuminator of maps. He supplemented his income trading in books, prints, and maps, and his journeys included yearly visits to the Frankfurt book and print fair, where he met Gerardus Mercator in 1554. In 1560, however, when travelling with Mercator to Trier, Lorraine, and Poitiers, he seems to have been attracted, largely by Mercator's influence, towards the career of a scientific geographer.

He died in Antwerp.

Map publisher
 
In 1564 he published his first map, Typus Orbis Terrarum, an eight-leaved wall map of the world, on which he identified the Regio Patalis with Locach as a northward extension of the Terra Australis, reaching as far as New Guinea. This map subsequently appeared in reduced form in the Terrarum (the only extant copy is in now at Basel University Library). He also published a two-sheet map of Egypt in 1565, a plan of the Brittenburg castle on the coast of the Netherlands in 1568, an eight-sheet map of Asia in 1567, and a six-sheet map of Spain before the appearance of his atlas.

In England Ortelius's contacts included William Camden, Richard Hakluyt, Thomas Penny, Puritan controversialist William Charke, and Humphrey Llwyd, who would contribute the map of England and Wales to Ortelius's 1573 edition of the Theatrum.

In 1578 he laid the basis of a critical treatment of ancient geography by his Synonymia geographica (issued by the Plantin press at Antwerp and republished in expanded form as Thesaurus geographicus in 1587 and again expanded in 1596. In this last edition, Ortelius considers the possibility of continental drift, a hypothesis proved correct only centuries later).

In 1596 he received a presentation from Antwerp city, similar to that afterwards bestowed on Rubens. His death on 28 June 1598 and his burial in the church of St. Michael's Abbey, Antwerp, were marked by public mourning. The inscription on his tombstone reads: Quietis cultor sine lite, uxore, prole ("served quietly, without accusation, wife, and offspring").

Theatrum Orbis Terrarum

On 20 May 1570, Gilles Coppens de Diest at Antwerp issued Ortelius's Theatrum Orbis Terrarum, the "first modern atlas" (of 53 maps). Three Latin editions of this (besides a Dutch, a French, and a German edition) appeared before the end of 1572; twenty-five editions came out before Ortelius's death in 1598; and several others were published subsequently, for the atlas continued to be in demand until about 1612. Most of the maps were admittedly reproductions (a list of 87 authors is given in the first Theatrum by Ortelius himself, growing to 183 names in the 1601 Latin edition), and many discrepancies of delineation or nomenclature occur. Errors, of course, abound, both in general conceptions and in detail; thus South America is initially very faulty in outline, but corrected in the 1587 French edition, and in Scotland, the Grampians lie between the Forth and the Clyde; but, taken as a whole, this atlas with its accompanying text was a monument of rare erudition and industry. Its immediate precursor and prototype was a collection of thirty-eight maps of European lands, and of Asia, Africa, Tartary, and Egypt, gathered together by the wealth and enterprise, and through the agents, of Ortelius's friend and patron, Gillis Hooftman (1521–1581), lord of Cleydael and Aertselaar: most of these were printed in Rome, eight or nine only in the Southern Netherlands.

In 1573, Ortelius published seventeen supplementary maps under the title Additamentum Theatri Orbis Terrarum. Four more Additamenta were to follow, the last one appearing in 1597. He also had a keen interest and formed a fine collection of coins, medals and antiques, and this resulted in the book (also in 1573, published by Philippe Galle of Antwerp) Deorum dearumque capita ... ex Museo Ortelii ("Heads of the gods and goddesses... from the Ortelius Museum"); reprinted in 1582, 1602, 1612, 1680, 1683 and finally in 1699 by Gronovius, Thesaurus Graecarum Antiquitatum ("Treasury of Greek Antiquities", vol. vii).

The Theatrum Orbis Terrarum inspired a six-volume work titled Civitates orbis terrarum, edited by Georg Braun and illustrated by Frans Hogenberg with the assistance of Ortelius himself, who visited England to see his friend John Dee in Mortlake in 1577, and Braun tells of Ortelius putting pebbles in cracks in Temple Church, Bristol, being crushed by the vibration of the bells.

Later maps

In 1579 Ortelius brought out his Nomenclator Ptolemaicus and started his Parergon (a series of maps illustrating ancient history, sacred and secular). He also published Itinerarium per nonnullas Galliae Belgicae partes (at the Plantin press in 1584, and reprinted in 1630, 1661 in Hegenitius, Itin. Frisio-Hoil., in 1667 by Verbiest, and finally in 1757 in Leuven), a record of a journey in Belgium and the Rhineland made in 1575. In 1589 he published Maris Pacifici, the first dedicated map of the Pacific to be printed. Among his last works were an edition of Caesar (C. I. Caesaris omnia quae extant, Leiden, Raphelingen, 1593), and the Aurei saeculi imago, sive Germanorum veterum vita, mores, ritus et religio. (Philippe Galle, Antwerp, 1596). He also aided Welser in his edition of the Peutinger Table in 1598.

Contrary to popular belief, Abraham Ortelius, who had no children, never lived at the Mercator-Orteliushuis (Kloosterstraat 11–17, Antwerpen), but lived at his sister's house (Kloosterstraat 33–35, Antwerpen).

Modern use of maps
Originals of Ortelius's maps are popular collectors' items and often sell for tens of thousands of dollars. Facsimiles of his maps are also available from many retailers. A map he made of North and South America is also included in the world's largest commercially available jigsaw puzzle, which is of four world maps. This puzzle is made by Ravensburger, measures  × , and has over 18,000 pieces.

Imagining continental drift
Ortelius was the first to underline the geometrical similarity between the coasts of America and Europe-Africa and to propose continental drift as an explanation. Kious described Ortelius's thoughts in this way:

Ortelius's observations of continental juxtaposition and his proposal of rupture and separation went unnoticed until the late 20th century. However, they were repeated in 18th and 19th century and later by Alfred Wegener, who published his hypothesis of continental drift in 1912 and in following years. Because his publications were widely available in German and English and because he adduced geological support for the idea, Wegener is credited by most geologists as the first to recognize the possibility of continental drift. Frank Bursley Taylor (in 1908) was also an early advocate of continental drift.  During the 1960s geophysical and geological evidence for seafloor spreading at mid-oceanic ridges became increasingly compelling to geologists (e.g. Hess, 1960) and finally established continental drift as an ongoing global mechanism. After more than three centuries, Ortelius's supposition of continental drift was proven correct.

Bibliography

 
 
 Abraham Ortelius, Theatrum Orbis Terrarum. Gedruckt zu Nuermberg durch Johann Koler Anno MDLXXII. Mit einer Einführung und Erläuterungen von Ute Schneider. Second unchanged edition (2. unveränd. Aufl). Darmstadt, Wissenschaftliche Buchgesellschaft, 2007.

Notes

References

Sources
 
 
 
 
  (an edition of Ortelius's letters)
  
 
 
 
 
 
 
 
 
  (Translated from the fourth revised German edition.)

Further reading

See also
 Theatrum Orbis Terrarum (Theatre of the World)
 History of cartography
 Early modern Netherlandish cartography
 Golden Age of Netherlandish cartography

External links 

 

16th-century Flemish cartographers
1527 births
1598 deaths
Early modern Netherlandish cartography
Belgian cartographers
Belgian geographers
Scientists from Antwerp
People from the Duchy of Brabant
Flemish geographers
In statistics, a truncated distribution is a conditional distribution that results from restricting the domain of some other probability distribution. Truncated distributions arise in practical statistics in cases where the ability to record, or even to know about, occurrences is limited to values which lie above or below a given threshold or within a specified range. For example, if the dates of birth of children in a school are examined, these would typically be subject to truncation relative to those of all children in the area given that the school accepts only children in a given age range on a specific date. There would be no information about how many children in the locality had dates of birth before or after the school's cutoff dates if only a direct approach to the school were used to obtain information.

Where sampling is such as to retain knowledge of items that fall outside the required range, without recording the actual values, this is known as censoring, as opposed to the truncation here.

Definition
The following discussion is in terms of a random variable having a continuous distribution although the same ideas apply to discrete distributions. Similarly, the discussion assumes that truncation is to a semi-open interval y ∈ (a,b] but other possibilities can be handled straightforwardly.

Suppose we have a random variable,  that is distributed according to some probability density function, , with cumulative distribution function  both of which have infinite support.  Suppose we wish to know the probability density of the random variable after restricting the support to be between two constants so that the support,  .  That is to say, suppose we wish to know how  is distributed given .

where  for all  and  everywhere else. That is,  where  is the indicator function. Note that the denominator in the truncated distribution is constant with respect to the . 

Notice that in fact  is a density:
.

Truncated distributions need not have parts removed from the top and bottom. A truncated distribution where just the bottom of the distribution has been removed is as follows:

where  for all  and  everywhere else, and  is the cumulative distribution function.

A truncated distribution where the top of the distribution has been removed is as follows:

where  for all  and  everywhere else, and  is the cumulative distribution function.

Expectation of truncated random variable 
Suppose we wish to find the expected value of a random variable distributed according to the density  and a cumulative distribution of  given that the random variable, , is greater than some known value . The expectation of a truncated random variable is thus:

where again  is  for all  and  everywhere else.

Letting  and  be the lower and upper limits respectively of support for the original density function  (which we assume is continuous), properties of , where  is some continuous function with a continuous derivative, include:
 
 
 
 and 
 
 

Provided that the limits exist, that is: ,  and  where  represents either  or .

Examples

The truncated normal distribution is an important example.

The Tobit model employs truncated distributions.
Other examples include truncated binomial at x=0 and truncated poisson at x=0.

Random truncation 
Suppose we have the following set up: a truncation value, , is selected at random from a density, , but this value is not observed.  Then a value, , is selected at random from the truncated distribution, .  Suppose we observe  and wish to update our belief about the density of  given the observation.

First, by definition:

, and

Notice that  must be greater than , hence when we integrate over , we set a lower bound of . The functions  and  are the unconditional density and unconditional cumulative distribution function, respectively.

By Bayes' rule,

which expands to

Two uniform distributions (example) 
Suppose we know that t is uniformly distributed from [0,T] and x|t is distributed uniformly on [0,t].  Let g(t) and f(x|t) be the densities that describe t and x respectively.  Suppose we observe a value of x and wish to know the distribution of t given that value of x.

See also

Truncated mean

References

Theory of probability distributions
Types of probability distributions An Englishman in Auschwitz is a 2001 book written by Leon Greenman, a Holocaust survivor. The book details his experiences in the Auschwitz concentration camp.

The book is a result of the commitment of English-born Greenman to God "that if he lived, he would let the world know what happened during the war". In short, the book describes the  reminiscences of his days of imprisonment in six concentration camps of the Nazis. Greenman describes the arrival of his family (consisting of himself, his wife, Esther, a Dutchwoman, and their three-year-old son, Barney) at the Auschwitz-Birkenau concentration camp in these words: The women were separated from the men: Else and Barny were marched about 20 yards away to a queue of women...I tried to watch Else. I could see her clearly against the blue lights. She could see me too for she threw me a kiss and held up our child for me to see. What was going through her mind I will never know. Perhaps she was pleased that the journey had come to an end.

References

2001 non-fiction books
Personal accounts of the Holocaust