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What Was The Most Significant Error Of Ptolemy’s Geography

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Famous Quotes Containing The Word Geography:

Ptolemy’s Map and Geographia

    The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience.

The Configuration Of The Pontus Euxinus In Ptolemy’s Geography

GeographyGeographyGeographyDmitry A. Shcheglov

  • S.I. Vavilov Institute for the History of Science and Technology,St. Petersburg, Russia
  • S.I. Vavilov Institute for the History of Science and Technology,St. Petersburg, Russia

Correspondence: Dmitry A. Shcheglov

Correspondence: Dmitry A. Shcheglov

Received: 05 Jul 2019Published: 01 Apr 2020Geography

Despite its universal recognition and extraordinary role in history,Ptolemy’s Geography remains one of the least understood geographical works of thepast. This is largely due to the fact that until recently there was neithera reliable edition of the Geography nor a recognized methodology for analysing thiskind of source. Everything began to change with the new edition fromStückelberger and Graßhoff , which not only provided a complete and verified text of the Geography forthe first time but also included anelectronic database of all localities mentioned in it and their Ptolemaiccoordinates. With this edition, Ptolemy’s Geography has become a veritable bonanza of knowledge for researchers from different fields and a testing ground forcompeting approaches and hypotheses .

Understanding Ptolemy’s Geography means reconstructing his working method andsources. Therefore, the question arises regarding what we know about them fromPtolemy’s own words and our general understanding of ancient geography.


Two Recensions Of Ptolemy’s Geography

The original of the Geography was lost and its text is reconstructed from themedieval manuscripts, the earliest of these date back to the end of the13th century. The manuscripts are divided into two recensions, commonlydenoted as and , both dating back to antiquity. The recension is recognized as the earlier and more authentic, but it isrepresented by the sole manuscript Vaticanus graecus 191 , whichcontains many errors, especially in numerals, and omits all of the coordinatesfor the eastern half of the map from Geogr. 5.13.16 onwards . The recensionincludes many manuscripts, but, judging by many signs, it is secondary to . Thus, both recensions should be considered, but in the caseof significant discrepancies that cannot be explained by copying errors, the version should be preferred.

Both recensions contain scribal errors, which are not always easy to detect.The recension causes more difficulties: while , which is areconstruction based on the collation of many manuscripts, has been alreadycleaned of errors as much as possible, retains its original manuscript textwithout corrections. As is represented by only one manuscript, itis often difficult to determine whether there is an error or whether simply offersan alternative variant to .Nevertheless, several glaring inconsistencies in the version can becorrected in accordance with .

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The Accuracy Of Ancient Cartography Reassessed: The Longitude Error In Ptolemys Map

2016, Isis


This essay seeks to explain the most glaring error in Ptolemys geography: the greatly exaggerated longitudinal extent of the known world as shown on his map. The main focus is on a recent hypothesis that attributes all responsibility for this error to Ptolemys adoption of the wrong value for the circumference of the Earth. This explanation has challenging implications for our understanding of ancient geography: it presupposes that before Ptolemy there had been a tradition of high-accuracy geodesy and cartography based on Eratosthenes measurement of the Earth. The essay argues that this hypothesis does not stand up to scrutiny. The story proves to be much more complex than can be accounted for by a single-factor explanation. A more careful analysis of the evidence allows us to assess the individual contribution to Ptolemys error made by each character in this story: Eratosthenes, Ptolemy, ancient surveyors, and others. As a result, a more balanced and well-founded assessment is offered: Ptolemys reputation is rehabilitated in part, and the delusion of high-accuracy ancient cartography is dispelled.

Journal of Ancient History

. 2015. . 36. 2. . 209239.

The Error In Longitude In Ptolemys Geography



Abstract It is well known that all longitudes in Ptolemys Geography are cumulatively overestimated, so that his map is excessively stretched from west to east as compared with the modern map. In recent years, a number of scholars have suggested that this stretching can be explained as a result of the change in the value of the Earths circumference from a larger one proposed by Eratosthenes to a lesser one by Posidonius. As a result, all distances converted from linear units to angular became overestimated. This explanation has a necessary presupposition that the error in longitude on Ptolemys map grows linearly. This article argues that the error in longitude on Ptolemys map varies considerably depending on longitude, latitude and region. In particular, it grows most slowly in the Eastern Mediterranean, which is probably due to the fact that this region was the center of the ancient world. Therefore, the error in longitude on Ptolemys map cannot be explained by one universal reason, but only by a combination of different factors.

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Longitudes Error And Earth Size

There are two related errors:

  • Considering a sample of 80 cities amongst the 6345 listed by Ptolemy, those that are both identifiable and for which we can expect a better distance measurement since they were well known, there is a systematic overestimation of the longitude by a factor 1.428 with a high confidence . This error produces evident deformations in Ptolemy’s world map most apparent for example in the profile of Italy, which is markedly stretched horizontally.
  • Ptolemy accepted that the known Ecumene spanned 180° of longitude, but instead of accepting Eratosthenes‘s estimate for the circumference of the Earth of 252,000 stadia, he shrinks it to 180,000 stadia, with a factor of 1.4 between the two figures.

This suggests Ptolemy rescaled his longitude data to fit with a figure of 180,000 stadia for the circumference of the earth, which he described as a “general consensus”. Ptolemy rescaled experimentally obtained data in many of his works on geography, astrology, music, and optics.

Ptolemys World Map The Pinnacle Of Map Making In Antiquity

The world at the beginning of the 2nd century CE was one of great empires. In the east, the Han Empire had consolidated its control at home and was expanding into central Asia. In part seeking the famous horses of the Bactrian Kingdom resulting in the first and only direct clash between the Chinese and Hellenic worlds.

In India, the Kushan Empire was spreading further into the subcontinent, taking its unique blend of Greek, Bactrian, Persian, and Indian culture with it.

Meanwhile, in the west, the Roman Empire stood strong. With the appointment of the Emperor Nerva to the Principate after the assassination of Domitian, the period of Roman rulers known as the five good Emperors began. A period in which Rome would attain the absolute zenith of its power and territory, the height of the Pax Romana, the longest period of peace the Mediterranean world has ever experienced.

The west would never see such a period of unity and peace again. The optimism and purpose created by the Empire, provided the perfect conditions for an era of unprecedented inquiry and growth. A new spirit of examining and documenting the world led to some significant advancements. Among these were the continued development of the discipline of geography.

Looking at Ptolemys map, what can it tell us about the world of the 2nd Century CE?

West to east, the map stretches from the Canary Islands to Korea, showing that the Romans had at least some knowledge of what lay far beyond the limits of their Empire.

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The Lack Of Improvement

So the errors of Ptolemy’s theory were visible with a simple instrument already available during his lifetime. The error was over 100 times beyond the observation limit. It is not possible that no classical scientist after him noted that. The classical world had a lot of interest in astronomy. Astrology was a popular application and people wanted personal calculations with the most accurate theory.

Ptolemy could not predict the most impressive celestial event – the position of the shadow of a solar eclipse. Not even whether the eclipse would be total or partial. He could only predict the time for lunar and solar eclipses much like the Babylonians long before him.

But by careful observation and some calculation the position of the solar eclipse shadow was predictable in advance. So even without a mathematical genius observations would get appreciable results. Another benefit of an observatory would be the longitude measurement for long range voyages.

Theon of Alexandria, the last known member of the famous library there, became known for his prediction and observation of a solar eclipse in 360. Strangely this very same Theon wrote about Ptolemy’s work without any improving remarks.

Special Case: Ptolemys Geography

Schemes of Annotation in Ptolemy’s Geography

For a representative statistical analysis, we need significantly more data than have been preserved and attributed to Eratosthenes and Strabo. It is therefore very tempting to use our major geographical sourcePtolemys catalogue of toponyms given in his Geography with its more than 6300 pairs of coordinates expressed in degrees of latitude and longitude . Why not calculate all the possible mutual distances between the identified localitiesFootnote 85 in this catalogue and apply statistical methods to this really big data set? Another advantage of using Ptolemys catalogue would be that to establish the set of geographical coordinates, Ptolemy should have had to reduce the known distances to the arcs of the great circlesand those are exactly what we need to estimate the length of a stadion.Footnote 86 Nevertheless, we cannot directly use the Ptolemaic data and we will now explain the background to the problem.

Table 2 shows the circumference of the Earth for Eratosthenes and Ptolemy for two values of the stadion discussed in this text. Obviously, Eratosthenes Earth is too big when the length of the stadion is equal to 185 m, but for a stadion equal to 157.5 m Eratosthenes result matches the actual circumference very well. By Ptolemys reckoning, in both cases, the size of the Earth is too small. This crucial error significantly distorts Ptolemys cartographyFootnote 88 and inevitably compromises the results of any statistical analysis.

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Discovery Of The World I

In the Middle Ages, few people ventured far from home. Most, in fact, spent their entire lives within the confines of small villages. To stray far, one might never find his way back.

Except for Marco Polos trip to China, little in the way of discovery took place for 1,000 years. Three things turned the world around.

The need for spices was one. When the trade routes to the Eastern spice markets were cut off, the quest for a sea route to the Orient began. The crusaders also spurred the Age of Discovery. They returned from Constantinople with long-forgotten maps dating back to the Roman era.

Many of these maps and atlases were copied and consulted. But it was only with the invention of printing that the maps and charts became widely used and disseminated. Columbus himself consulted the ancient Ptolemaic maps and because the ancients had miscalculated the circumference of the earth, thought he could follow a new trade route to China by sailing in the opposite direction. He was right, at least, in that respect and bumped into America, making the most significant discovery in the history of the world.

This section begins with the resurgence of the ancient maps and follows the great explorers and discoverers into the Space Age. It is difficult to gauge the pace at which the secrets of the worlds geography would have unfolded had it not been for printed books, maps, and atlases. Printing not only sparked interest in new lands, but aided in their discoveries.

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Uncertainties In Identifying The End Points And Configuration Of The Coastlines

There are several difficulties regarding the starting and ending points ofthe coastlines. For instance, Pliny only vaguely describes both the European and theAsian coasts as stretching from the mouth of the Pontus to the mouth of the Maeotis or from the Bosporus to theMaeotis Lake without indicating specific points. We can only assumethat the geographers whose reports he transmits defined the end points of thecoasts in nearly the same way as other sources that were fortunate enough to havesurvived. The limits of the Asian coastline are defined with nouncertainties: both Strabo andPseudo-Arrian measure it from thesanctuary of Zeus Ourios on the Bosporus, which corresponds to Ptolemy’ssanctuary of Artemis , to Achilleion at the narrowest point ofthe Kerch Strait. The start and end points of the European coastlines varyin different sources. As its start point, Pseudo-Arrian also takes thesanctuary of Zeus Ourios, which seems inconsistent as it is situated inAsia. Its end point is defined differently in different sources:Panticapaeum in Varro , who possibly followed Eratosthenes Myrmekion or Parthenion in Strabo and Porthmion inPseudo-Arrian. Meanwhile, Ptolemy locates Parthenion on the coast of theMaeotis, which is too far from its mouth , and does not mention Porthmion atall21.


These two major contradictions between Ptolemy’s and Pseudo-Arrian’s datarequire additional explanation .

The author declares that there is no conflict of interest.

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Determining The Length Of Coastlines In Ptolemy’s Geography

How can we compare Ptolemy’s coastline length data, presented in the form ofcoordinates, with the information from other sources, expressed in terms ofcustomary distance units? The correct solution would be to reconstruct howPtolemy converted distances reported by his sources to the coordinates ofhis gazetteer and to reverse his method in order to extract the originaldistance data. Unfortunately, Ptolemy left us almost no clues as to hismethod. My contention is that it the most reasonable solution in thissituation is follow the simplest and most natural approach, namely to takePtolemy’s Geography as what it essentially is, i.e. as a catalogue of sphericalcoordinates. A distance between two points on a sphere which are specifiedby the coordinates of latitude and longitude is an arc of the great circlethat can be calculated using the rules of spherical trigonometry.Accordingly, I propose to calculate the length of Ptolemy’s coastlines asthe sum of individual arcs joining coastal points multiplied by the lengthof a degree of the great circle which he defines as 500 stades . The distance between points A and B located on a sphere can becalculated using the formula cos × sin ×sin+cos×cos,where SAB is the distance between points A and B, AB is the longitudinal interval between them, A andB are their latitudes, and all these values are expressed indegrees of the great circle19.

The Crucial 4th Century

Claudius Ptolemy by Mindy Kuertz

The main time of book burning was probably the second part of 4th century. According to historical records, people burned their own whole libraries in fear of witchcraft accusations. The accusation to be in possession of magical books could cause a terrible death by slow torture over a fire. Books of the classical liberal arts were considered magical books and burned that way.

Unlike the prevailing historical record written by Christians, the archaeological record shows evidence of a very violent and brutal destruction of classical monuments and peoples.

Exactly during this most dangerous time lived Theon of Alexandria, main representative of the classical sciences. He was not killed but wrote commentaries about the books of Ptolemy. It seems possible that he was Ptolemy.

That would explain the fraud Newton found well. It may be a deliberate break point set by Theon only another astronomer could find. Someone without experience in practical measurements would not note it. That nobody would note the fake of observation data of older astronomers is granted by this timeline, too. Older books were no longer available to check it.

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Early Modern Ottoman Empire

Prior to the 16th century, knowledge of geography in the Ottoman Empire was limited in scope, with almost no access to the works of earlier Islamic scholars that superseded Ptolemy. His Geography would again be translated and updated with commentary into Arabic under Mehmed II, who commissioned works from Byzantine scholar George Amiroutzes in 1465 and the Florentine humanist Francesco Berlinghieri in 1481.

Reply To Shcheglov On Ptolemys Map

The Greeks were outstanding mathematical geographers. Eratosthenes measured the circumference of the Earth with outstanding accuracy. Unfortunately the sources from this era are largely lost. Our main source is the much later work of Ptolemy, from a time when intellectual quality had deteriorated. Ptolemys geography is not great, but its errors are due to corruption of an earlier, excellent theory.

That is what I and others suspect. An article in the latest issue of Isis claims to disprove us:

As an aside, heres a pro tip for academic novices: If you have little of substance to offer, make sure to lay it on thick with self-congratulatory posturing about how your work is supposedly based on more careful analysis and more balanced and well-founded assessment, showing everything to be much more complex than others think. After all, who would dare disagree with someone who is so careful and balanced and ever so sensitive to complexities?

Contrary to his smug proclamations, the authors case is flimsy. For one thing he immediately admits that, indeed, Ptolemys error can be solved in a single stroke by recalculating his map with Eratostheness excellent value for the circumference of the earth, yielding an uncannily accurate map . But he alleges that this is a mere coincidence . What is his evidence for this?

The author also maintains that the hypothesis contains numerous logical fallacies , namely:

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