Mechanical clocks and lenses were among the ideas that I referred to as
advances in engineering and materials knowledge. (02)
Sundials may have been popular in the village squares, but Islam and Byzantium
had been using horologes (water clocks, fancy hour glasses) for accurate
timekeeping since the 7th century, and I think they actually go back to the 1st
century. And of course, European naval vessels "struck the bells and turned
the glass" into the 18th century, but they rather postdate the 13th century.
Mechanical clocks were definitely a European advance in the 13th century. (03)
One can argue about polyphonic music. Experts have pulled out 8th century
monks who had two-part chants. It is true, however, that it became an accepted
form of ecclesiatical and, for the first time, popular music (rounds) in 13th
century Europe. (I believe polyphonic music arose independently in India about
the same time.) Polyphonic instrumental music came a bit later, and first
bloomed in the 16th century. (04)
We should not, I think, be surprised to see that the rising mercantile economy
begot bookkeeping practices and a corresponding growth in basic mathematics.
The first banking practices, including letters of credit, also began in Europe
in this timeframe, although they were constrained by usury laws. Banking was
already long established (perhaps 400 years) in the Arab world. It had a
mercantile economy in 900, and it involved moving goods over great distances.
Notably, banking was also practiced in the kingdoms of the upper Niger in the
14th century, largely because the region produced gold in significant
quantities and imported everything else. They probably adopted practices from
the Arab world they traded with. (05)
These are fascinating subjects, but it is not clear that they have anything
much to do with knowledge engineering. (I suppose we are touching on the work
of the FIBO folk, but they probably don't care much about 13th century
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
> Sent: Thursday, April 03, 2014 4:19 PM
> To: ontolog-forum@xxxxxxxxxxxxxxxx
> Subject: Re: [ontolog-forum] Hermeneutics and semiotics
> On 4/2/2014 4:14 PM, Barkmeyer, Edward J wrote:
> > The mercantile economy began to make inroads in the feudal economies
> > in the 11th century, but it did not come to dominate until the end of
> > the 13th century.
> The 13th c is the critical turning point. Merchants always drive the economy,
> but mathematics can make a big difference. I recommend
> Crosby, Alfred W. (1997) The Measure of Reality: Quantification
> and Western Society, 1250-1600, Cambridge: University Press.
> Crosby notes the rapid growth in measuring and calculating:
> * Modern mechanical clocks (tower sized) were invented around 1270.
> The hours, as measured by sun dials, didn't differ much between
> summer and winter in Africa, but variations were huge in northern
> Europe. In 1270, there were no clocks. By 1300, nearly every
> European town had a clock in the church tower or was building one.
> * In the middle of the 13th c, painters began to introduce three-
> dimensional effects. By the end of the 13th and early 14th c,
> Giotto developed perspective.
> * In music (another of the four mathematical arts), polyphonic music
> developed in the 13th century. To coordinate the voices, the new
> music (ars nova) divided music in *measures*.
> * Also in the 13th c, Fibonacci was the first European mathematician
> to adopt Arabic numerals. The bookkeepers and bankers adopted them
> in the 14th c.
> Quotation from Crosby, p. 206
> > About 1300, in that wondrous era of eyeglasses, clocks, ars nova, and
> > Giotto, some Italian accountants began using what we call double-entry
> > bookkeeping. Possibly, in its origins, it had some relationship with
> > algebra (from the Arabic al-jabr, and not by accident), which also
> > divides the grist that comes to its mill into two categories,
> > insisting that what is plus in one column can only be minus in the
> > other, and vice versa.
> > What we do know is that at the beginning of the fourteenth century
> > Rinieri Fini, agent of a Florentine banking house at the fairs in
> > Champagne, and Tuscan merchants working out of Nimes in the south of
> > France were keeping their books with assets and liabilities posted
> > separately. This was just a beginning. Yet to come were a number of
> > features of technical language, abbreviation, and form that we
> > consider characteristic of and even essential to bookkeeping.
> Crosby also notes that the success in measuring and counting inspired
> theologians to quantify "indulgences" by the days deducted from a soul's
> suffering in purgatory. This might sound silly. But modern parole boards and
> employee appraisals aren't much better.
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