On this page, observations of various kinds will appear that are related to big history teaching, as well as to big history
in general.

May 15, 2017 (with later additions)

My in-class experiments with nautical navigation technology around the time of Columbus
have not only yielded the results described in earlier blogs, but they have also led to a reappraisal of the questions of how late-medieval
Europeans succeeded in making the remarkably accurate nautical charts of the Mediterranean Sea known as **portolans** (harbor city maps),
while also acquiring Arabic numerals.

Regarding
the Arabic numerals: although it is well known that Europeans acquired their numerals from the Arabs, there is a problem: in Egypt
and other Islamic countries, numerals are used that are different from those now known as Arabic numerals. Why did Europeans not adopt
those numerals but others, and where did these numerals come from? And might the acquisition of the precise nautical charts and Arabic
numerals by Europeans perhaps be interlinked?

Let us start with the **portolans**. While
studying quadrants and astrolabes used by Europeans for navigation in the fifteenth century, I became interested in their histories,
which stretches all the way back to Greek and Roman antiquity. During that period, Hipparchus, Ptolemy, and other scholars had already
used them for determining celestial altitudes and geographical positions, most notably latitudes.

Those eminent scholars had
already recognized that the world was a globe. They had attempted to measure its circumference, while they had also realized that
geographical positions on the globe could be defined by using a system of latitude and longitude lines, which could be determined
by celestial and geographic measurements.

The Islamic Arabs had further developed this knowledge using quadrants and astrolabes.
A most important determination for Muslims was (and still is) finding the exact direction to Mecca for daily prayers known as the**qibla**. In contrast to Christians, who were –and are– satisfied to orient their churches to the East, assuming that this is the direction
toward Jerusalem, the Islamic peoples were much more precise. They wanted to know their exact orientation toward Mecca.

This
direction could only be established by very precisely measuring both one’s own geographical position as well as that of Mecca, using
the available instruments and mathematics, including the recently introduced compass (originally from China). Today, determination
of the qibla is still done with the aid of qibla compasses, but now also online or using **qibla** apps on cell phones.

All of that
could be done well only if the correct latitudes and longitudes were known for all these places, and also more advanced forms of trigonometry
that were required to perform the calculations. For many centuries Islamic specialists developed and maintained this knowledge, while
ordinary Muslims fostered a daily geographical awareness that helped them to orient themselves to Mecca at the required moments.

This
implies that at the time the **portolans** were made, almost the entire Muslim population must have possessed such a relatively precise
geographical awareness, of which, until that time, no parallels may have existed anywhere else in the world.

Seeking to obtain
the precise geographical data needed for determining the **qibla** must have improved the Islamic geographical knowledge of the southern
and eastern Mediterranean Sea, perhaps to an extent that may not yet be known to most modern scholars.

In addition, Muslims may
not only have charted the territories they lived in, including large portions of the Iberian Peninsula but perhaps also the lands
that they visited all around the Mediterranean. A further exploration of Islamic scholarship may yield traces of such tables and charts,
if they still exist.

Furthermore, most, if not all navigators that plied that large inland sea must have had an interest
in obtaining the best available maps. They may have exchanged such information voluntary or otherwise, even though many of them may
have tried to keep it secret.

Doing all of that would explain how the famous **portolans** emerged, which are far more accurate than
the contemporary late-medieval European knowledge and technology allowed. On such charts, especially the Mediterranean coastlines
are mapped with an accuracy almost equal to modern maps, while the Atlantic coastlines are far less precisely represented.

Most
notably, the northwestern European coastlines are depicted far less accurately. At that time, Muslims were, to our knowledge, not
yet navigating toward the British Isles, even though some of their knowledge and technology had gone there. So, in sum, would these
portolans perhaps have been constructed using the precise Islamic geographical knowledge that had been obtained, perhaps first of
all, for determining the **qibla**?

If this hypothesis is correct, it would suggest rather intensive contacts and exchanges between
Muslims, Christians, and others during that period, by wars and robbery, but quite possibly also by more peaceful encounters and exchanges
such as trade or sheer curiosity.

Many Islamic astronomical and geographical advances are well known to specialists in those
fields. But these scholars rarely seem to have wandered outside of their areas of expertise, and may as a result not have considered
the diffusion of this knowledge and its effects in the Mediterranean area and beyond. It may be about time to reunite all these forms
of scholarship, perhaps much like what happened when **portolans** were drawn and used.

As an aside: because latitude and longitude
lines are lacking on **portolans**, this makes one wonder how these charts were constructed, and what role the very prominent compass
roses and associated rhumb lines may have played in doing so. To my knowledge, this subject may not yet have received the attention
it deserves.

While visiting Egypt in 1979 CE, I did not recognize their numerals easily
and had, as a result, to make a quick and determined attempt to familiarize myself with them, if I wanted to be able to do any successful
shopping.

How could that be, I wondered, while in Europe and elsewhere the current numerals are called Arabic numerals? Why would
those Arabs use different ones? Because I encountered a great many other fascinating questions during that trip to which I did not
have any answers, I left this question, together with many others, on my intellectual back burner for decades.

Clearly, Roman
numerals are not very efficient for determining angles or performing complex trigonometric calculations. Using alphabetical letters
as numerals, such as used in Greek, Hebrew, and Arabic cultures, may have solved that problem to some extent. Yet the introduction
of decimal numerals from India, most notably including the zero, greatly facilitated all of this. This is why in Egypt and elsewhere
in the Eastern Arabic world their numerals are still known as Hindu numerals.

These Hindu numerals were introduced into Italy
around 1200 CE by Leonardo Pisano (Fibonacci) for many uses, including more efficient bookkeeping. This development is usually credited
for the spread of Arabic numerals throughout the European world. However, Fibonacci used Hindu numerals, and not (what are now known
as) Arabic numerals. Where did the Arabic numerals come from, and how did they overtake the Hindu numerals in Europe, while that
apparently did not happen in the Islamic world?

For reasons still unknown to me, in Western North Africa, from Modern Lbyia to Morocco, and in Islamic Spain a notation style of numerals emerged that was different from the Hindu numerals. Those were the numerals that subsequently spread throughout the North Atlantic world as Arabic numerals. How and why did that happen?

For reasons still unknown to me, in Western North Africa, from Modern Lbyia to Morocco, and in Islamic Spain a notation style of numerals emerged that was different from the Hindu numerals. Those were the numerals that subsequently spread throughout the North Atlantic world as Arabic numerals. How and why did that happen?

It would
not surprise me if geographic and celestial measurements as well as calculations performed with quadrants and astrolabes as done in
those parts of the world greatly contributed to this trend. As a result, these numerals may have spread through Islamic Spain, and
later, after the **reconquista** by Catholics, through Northwestern Europe as part of the Islamic knowledge that the Arabs had left in
towns such as Toledo, which as rapidly translated into Latin.

If this hypothesis is correct, then one would expect astrolabes
from the eastern Islamic world to sport Hindu numerals, while their more westerly counterparts would exhibit Arabic numbers. One would
expect the same trend for written documents, most notably books. Such an investigation could be executed by examining at all the books
and astrolabes that have been preserved in libraries and museums, as well as by checking the dates, if available, on which they were
produced.

My preliminary investigation of astrolabes through the Internet has very much confirmed this trend. On the British
Museum Collection website this is exactly what can be found, most notably the Sloane astrolabe, dating from 1290-1300 CE, which is
sporting Arabic numerals, and also this astrolabe, from 1326 CE. Both among the oldest known West European astrolabes.

Also this
Hispano-Moorish astrolabe with unknown date of production, possibly the14th century, shows Arabic numerals, although possibly with
a few remnants of the Hindu numerals.

All of this very much confirms the hypothesis, which was formulated before finding these
examples. But a much more systematic and exhaustive study is required to provide a greater degree of certainty, or a rejection of
it.

Yet I am willing to bet some money on the idea that utilizing astrolabes for celestial and geographic orientation in Europe
while employing the great advances made by the Islamic science has very much contributed to not only introducing Arabic numerals to
Europe but also, in doing so, to the emergence of what US scholar Alfred Crosby has called the unparalleled European ‘quantification
of reality,’ that has provided to so much power over nature as well as over other people.

Over time, this quantification of reality,
including navigation, required not only the addition and subtraction of numbers but also their multiplication and division. While
addition and subtraction can relatively easily be done with great precision using degrees of arc, minutes and seconds, multiplication
and division are very difficult to do while using such units.

This may have stimulated Flemish mathematician and engineer Simon
Stevin (1548-1620) to establish decimal numbers in mathematics, which have proved to be very useful for such calculations.

When
Scottish mathematician John Napier (1550-1617) subsequently invented logarithms as a way to make multiplications and divisions easier,
in an attempt to help mariners simplify their increasingly complex calculations, the foundation was in place for the basic principles
of modern mathematics as we know it today.

One final question remains: what happened to the Hindu numerals introduced into Italy
by Fibonacci? When were they replaced by Arabic numerals, by whom, and why? I have no good answers yet to these questions.

One
final remark: because there can be little or no doubt that Europeans owe a great deal to Arabic Islamic science, we may want to keep
that in mind while dealing with the Arab Islamic world today, with mutual respect for each other, and for what our societies have
contributed to improve life on this planet: our one and (so far) only home in the cosmos.

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