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<h1 class="Title"><a href="index.htm"><img src="Lambda.jpg" align="bottom" border="0" height="202" width="223"></a></h1>
<h1 class="Title">ANCIENT NUMBER SYMBOLISM: GLOSSARY</h1>
<h2 class="Subtitle"></h2>
<h2 class="Subtitle">Joel Kalvesmaki</h2>
<p class="Caption">Updated 4 October 2004</p>
<p class="Caption">Part of the <a href="index.htm">Theology of Arithmetic</a> website.</p>
<p class="Normal"><b>arithmetic</b>
</p>
<blockquote>
<p class="Normal">The mathematical science of absolute quantity (see <b>quadrivium</b>). The term is based on the
Greek word <i>arithmos</i>, translated "number," but with plurality implied: <i>one </i>was for the ancient
Greeks, not a number, but the source or principle of number. Arithmetic, then, treats the progression of numbers,
their basic division into odd and even (the two fundamental classes of numbers in antiquity), and basic operations
such as addition, subtraction, multiplication, and division.</p>
</blockquote>
<p class="Normal"><b>arithmology</b></p>
<blockquote>
<p class="Normal">This term was reintroduced by A. Delatte, who observed it in the title of an
anonymous treatise preserved in an eighteenth century manuscript. The word appears to be a <i>hapax legomenon</i>,
and late in Greek literature, but it is useful nonetheless. Scholars apply it generally to any kind of number symbolism
or numerology in the ancient world.</p>
</blockquote>
<p class="Normal"><b>astronomy</b></p>
<blockquote>
<p class="Normal">The mathematical science of relative magnitude (see <b>quadrivium</b>), more conventionally,
the mathematical science of the motions and relations of the heavenly bodies. Some ancient authors combine, others
separate, stereometry<b><i> </i></b>from astronomy. Ancient astronomers did not distinguish <i>astrology</i> from
<i>astronomy</i>, although they seem to have used the same science to different ends, thereby forming the basis
for the distinction, which first appears around the sixth century A.D. As the fourth mathematical discipline, it
is also the most complex.</p>
</blockquote>
<p class="Normal"><b>gematria</b>
</p>
<blockquote>
<p class="Normal">See <b>isopsephy</b>.</p>
</blockquote>
<p class="Normal"><b>geometry</b>
</p>
<blockquote>
<p class="Normal">The mathematical science of absolute magnitude (see <b>quadrivium</b>). The term is based on
a combination of Greek words meaning "land" and "measure," probably indicating its roots in
land surveying. Ancient geometry usually dealt with objects in one or two dimensions. Some authors subsume three-dimensional
objects under geometry, but others create a separate category, stereometry. Geometry also included trigonometry
and the science of proportions between line segments, as seen in Euclid.</p>
</blockquote>
<p class="Normal"><b>isopsephy</b>
</p>
<blockquote>
<p class="Normal">Better known today as <i>gematria</i>, this literary device is built upon the ancient convention
of assigning the letters of the alphabet numerical values. Letters, words, or entire sentences could then be composed
or interpreted based upon the sum of their numerical values. Isopsephy first emerged as a literary phenomenon in
Greek during the Hellenistic period, not much before earlier than the first century A.D. It was adopted from the
Greeks in the first or second century A.D., and later used in Arabic. There is no clear evidence that the practice
caught on in Latin. The term <i>isopsephy</i> derives from Greek terms that mean literally "equal count,"
and refers to the specific practice of taking a verse or phrase and finding another one equal in count to it. It
is also correct to refer to the practice as <i>psephy</i> and the numerical value of a word or phrase as its <i>psephic</i>
value. The term <i>gematria</i> is a Hebrew calque on the Greek <i>grammateia</i>, and was initially applied to
different kinds of techniques for literary interpretation, but in the sixth century A.D., the term began to apply
specifically to isopsephy. <i>N.B., many scholars would like to assign the linguistic origins of isopsephy to Hebrew,
and its origin in Biblical times. I argue in my dissertation, and will argue in future studies, that there is no
basis for this claim.</i></p>
</blockquote>
<p class="Normal"><b>mathematics</b>
</p>
<blockquote>
<p class="Normal">The modern definition of the term encompasses a great variety of pure sciences, ranging from
simple arithmetic to string theory. The Greek word upon which ours is based, <i>mathema</i>, refers generally to
something learned, but more specifically to sciences concerned with quantity and magnitude. Under the scheme of
mathematics that would become the basis of the medieval <b>quadrivium</b>, these four <i>mathemata</i> were <b>arithmetic</b>,
<b>geometry</b>, <b>music</b>, and <b>astronomy</b> (sometimes called stereometry). Throughout this website, I
use <i>mathematics</i> in the classical sense (and in the sense used in English until the eighteenth century),
to refer to all four sciences, and not just arithmetic, geometry, and other disciplines thought of today as constituting
mathematics.</p>
</blockquote>
<p class="Normal"><b>music</b></p>
<blockquote>
<p class="Normal">The mathematical science of relative quantity (see <b>quadrivium</b>; but note that music failed
to make it into many ancient lists of what constituted <b>mathematics</b>), but more conventionally, the mathematical
science of tonality. Musical tones were thought of in terms of relations between two numbers, e.g., the octave,
which exhibits the ratio two to one. Of the four branches of ancient mathematics, music is the least well preserved.</p>
</blockquote>
<p class="Normal"><b>number symbolism</b>
</p>
<blockquote>
<p class="Normal">The use of numbers to represent other realities, or to bring together them into relation with
each other. This is often achieved through epithets given numbers. For instance, seven is called <i>Athena </i>or
<i>ever-virgin</i> because it is neither the product nor the factor of any number ten or less. In a case like this,
the arithmetical properties of seven illustrate the properties of virginity, and vice versa. To take another example,
Platonic texts often use the numerical connection between the seven planets and the seven notes in the scale to
discuss the music of the spheres. In this case, the number seven serves a connective tie between otherwise disconnected
realities. Compare <b>numerology</b>.</p>
</blockquote>
<p class="Normal"><b>numerology</b>
</p>
<blockquote>
<p class="Normal">Loosely, any non-mathematical use or interpretation of numbers. Most English dictionaries specify
that numerology treats the occult significance of numbers. This qualification is important. Like <i>astrology</i>,
in its modern usage <i>numerology</i> should refer to acts of prognostication and magic that use numbers to uncover
or to manipulate the hidden realities of the world. There are about a half dozen major types of Greek numerical
prognostication, and an unknown number of variants. Magic regularly uses numbers, albeit not as intently or creatively
as prognostic texts. Compare <b>number symbolism</b>. <i>N.B.: I catalogue in my dissertation the major forms of
Greek numerical prognostication, as well as the manuscript evidence for each type. I also argue</i> <i>that it
is improper to apply to the exegesis of writers such as Philo or Clement of Alexandria the term </i>numerology<i>
since they are not interested in the occult significance of numbers, but in the hidden realities of the world and
Scripture, which are accessed through a literary, symbolic use of numbers.</i></p>
</blockquote>
<p class="Normal"><b>quadrivium</b>
</p>
<blockquote>
<p class="Normal">This is the Latin term, first coined by Boethius (under the slight change of spelling, <i>quadruium</i>),
to describe the four mathematical disciplines (see <b>mathematics</b>). Although the term was developed late, the
quadrivium as a cornerstone of ancient pedagogy goes back at least to late antiquity, if not before. Evidence from
the era of Plato, Aristotle, and their predecessors suggest that the number and order of the mathematical disciplines
was not standardized. It first took on the traditional fourfold order—<b>arithmetic</b>, <b>geometry</b>, <b>music</b>,
and <b>astronomy</b>—under
the popular influence of pseudo-Pythagorean writings circulated and
epitomized in textbooks composed in the second century A.D. and later.
In this scheme, especially popularized by Nicomachus of Gerasa, there
is the science of quantity, and that of magnitude. Each of these
subdivide further into the study of quantities/magnitudes as either
absolutes, or in relation to each other (numbers as <i>properties</i> or as <i>relations</i>). Arithmetic
is the science of absolute quantity; music, of relative quantity; geometry, of absolute magnitude; astronomy, of
relative magnitude. <i>NB: most scholars date the origin of the quadrivium to Archytas and other pre-Platonic thinkers.
The position I outline here I argue for in my dissertation.</i></p>
</blockquote>
<p class="Normal"><b>stereometry</b></p>
<blockquote>
<p class="Normal">See <b>geometry</b>.<b></b></p>
</blockquote>
<p class="Normal"><b>tetraktys</b>
</p>
<blockquote>
<p class="Normal">This is a Doric Greek term for the first four numbers (one, two, three, and four), the sum of
which is ten. It was often thought of in the form of ten pebbles arranged in the shape of an isosceles triangle.
The ancient Pythagoreans regarded the term as sacred, and used it for oath taking.</p>
</blockquote>
<p class="Normal">
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