(Sorry about the title, but a good pun is its own reword)
Radix is a Latin word, meaning “root”. It is, perhaps, apropos that it functions as the etymological root for many words we use today! Most immediately floral is “radish”, which is a root crop, but also political radicalism, meaning to change a structureÂ from theÂ root up, as well as words such as radius and radial, whichÂ stem out from a center point. The mathematicalÂ branch ofÂ radix words is of courseÂ radix itself, as well as aÂ radical. Mathematically,Â radix itself can have two meanings. One is the base of a numerical system. The one we are most common with is likely the base-10 decimal system, as we use it for counting, but others are also used. However, there is another form ofÂ radix, which is the date orÂ root from which the user of an instrument such as an Equatorie uses to calculate the planets in their travels. Unfortunately for me, it was the first sense, the base for a numerical system, which I spent the majority of my time researching. However, much like a root system, the concepts flow back and forth between each other, intermingling. I will start by briefly explaining what a Radix is in the astronomical sense, and then providing a bit of relevant reading information before finishing with some more open endedÂ seeds of thought.
A useful metaphor is to think of a the radix as the setting for a decoder ring; a set of tables or formula won’t produce the right results unless you’ve calibrated your instrument to the right radix. In theÂ Equatorie of the Planets which we read, there were instructions for a calibration to 1392, which was labelled with “Chaucer”, causing much excitement and agitation. It is from that date as aÂ root from which many of the calculations are made. For an example of this in use, the Franklin’s tale is of value. The passage starting around line 1273 focuses on what their clerk friend is bringing to work his ‘magic’, and it mentions his tables (from Toledo), his tables and computations of planets movements, hisÂ rootes, his geares, and his centris, which are the calculations and proofs to more accurately determine a planet’s precise location. Radixes would have been updated in order to be more useful, and so having older and future radixes on hand already computed would act as a sort of astral almanac (Schmidt 14). The Man of Law’s tale also includes the wordÂ roote as a person’s birth. Calculating the exact positions of the zodiac on your time of birth was either incredibly complicated if you were doing it yourself or quite expensive if you were paying someone else to do it, and so would be a luxury few could afford.
Of particular note here is not just thatÂ roote is used, but that it is specifically the plural; multiple roots or radixes would be at hand for an astronomer to use for various situations to make their computations easier. Considering their attempts to predict the movements of the planets based on incorrect geocentric theories, the computational gymnastics necessary to do predictions with any sort of accuracy were understandably expansive. Tables were formed based on what radix was used as a base, with the Incarnation being a popular choice, as well as various beginnings of standard calendars (Julian at this time) or the Arabic calendar. Speaking of Arabic, theÂ wordÂ radix was translated intoÂ the Arabic wordÂ jidhr,Â which Gerard of Cremona traced back to the LatinÂ radix as a primary meaning (Mantello 349).Â To use the Islamic tables, Christian astronomers had to translate the calendar over to a Christian one in order to make use of the tables to make their own tables from their own radices.
The radix as a counting base has fewer direct references or discussions in our readings, but because of how fundamental a number base is, it winds its way throughout literature, usually under theÂ radar. The major numeral base is base 10, which makes up our standard numbering system, fundamentally because of the average human having exactly ten handy counting markers in fingers. Other popular bases are 2, 5, 10, 12, and 60. The Sumerian sexagesimal base is the rootÂ of seconds and minutes, as well as navigational numbers. The expression of a sexagesimal system in a decimal system seems so ingrained in the scientific culture that it passes without mention. The history and scholarship into number systems isÂ fascinating, but unfortunately out of the purview of this short research assignment.
Generally speaking, a radix in either mathematical connotation is an attempt to demarcate and divide the natural into the discrete. An astronomical radix measures the beginning of an epoch such as the Incarnation, the Flood, or the Hijra. There is a trend towards humans wanting to find beginnings or origins that persists throughout history, an attempt to find a point in time that is as concrete and immutable as a physical object. As a pertinent example for the obsession with originality and authenticity, the Equatorie we read in class gained its current level of scholarly focus due to the association with Chaucer and the chance that it could be demonstrably in his own hand.
For reading of the history of astronomical radixes,Â History of Astronomy by John Lankford, our previous reading ofÂ The Authorship of the Equatorie of the Planetis by Kari Anne Rand Schmidt,Â A Survey of European Astronomical Tables in the Late Middle Ages by Jose Chabas, andÂ Medieval Latin: An Introduction and Bibliographical Guide by Frank Anthony Carl Mantello are all good sources to start. If for some reason you want to research numerical systems,Â Numbers: Their History and Meaning by Graham Flegg andÂ The Universal History of Numbers by Georges Ifrah (Translated by David Bellos et al) would be excellent jumping-off points.