Friday, July 29, 2016

Multiplication on your fingers

There were no calculators in the Middle Ages.  So if one needed to make a calculation, one might do it either in one's head or on one's fingers.  For adding or subtracting, an abacus came in very useful, as I discussed in an earlier post, but it's hard to do multiplication on an abacus.

Medieval people did however work out a way to do multiplication on their fingers.  Here's how it worked.

First, they memorized the "times table" (as school children often call it) up through 5 X 10.

Then they pondered the nature of the "ten's place" and "one's place."  In the number 46, for example, the 4 is in the "ten's place" (four tens), and the 6 is in the "one's place" (six ones).  This is extremely easy to visualize on an abacus.  On an abacus one adds, for example, 27 and 25.  Add the numbers (beads) in the ten's place (on the second wire) and get 4.  Add the numbers in the one's place (first or bottom wire) and get 12.  The 2 goes in the one's place in the answer, and the 1, which is in the ten's place, is added to the 4 already there, by flicking a bead over.  The answer is 52.

Okay, all those following along at home, remember how they explained numbers back in middle school, get out your abacus if necessary, and let's keep going.

For multiplication, they had a finger-calculating method to be used when both numbers were between 5 and 10 (if one number was smaller, you had to just have memorized the answer).  One hand represents each number.  On each hand, put up the number of fingers by which the number is greater than 5.

Example, suppose you are multiplying 7 X 7.  On each hand, you put up two fingers, because 7 is two greater than 5.  Now add the upright fingers together.  This is the ten's place.  So the ten's place in your answer will be 4.  Now look at your hands again, at the tucked-down fingers.  There are 3 of them on each hand.  Multiply them together, 3 X 3.  The answer is 9.  This goes in the one's place.  So the answer is 49.

Or multiply 6 X 8.  One hand has one finger sticking up, the other three.  Add them together.  You get 4 for the ten's place.  And how many fingers are tucked down?  Four on one hand, two on the other.  Multiply them to get 8 for the one's place.  Answer, 48.

Or multiply 6 X 10.  One finger sticks up on one hand, five on the other (because 10 is 5 more than 5).  Add them.  The ten's place is 6.  The tucked down fingers are four and none.  None times four is none.  So just a 6 for the ten's place and nothing for the one's place, giving 60.

Or multiply 6 X 7.  One finger from one hand plus two fingers from the other hand, added together, gives 3.  But multiplying four tucked-down fingers from one hand times three tucked-down fingers from the other hand gives 12.  So the 2 (of 12) goes in the one's place, the 1 gets added to the ten's place.  Answer, 42.  The meaning of life.

Practice.  Fool your friends.

UPDATE
My brother the engineer worked out the mathematical formula that explains this:

GIVENS
a = First number (left hand)
b = Second number (right hand)
5 ≤ a ≤ 10
5 ≤ b ≤ 10

THEN
(a - 5) = Number of fingers UP on left hand
(b - 5) = Number of fingers UP on right hand
(5 - (a - 5)) = Number of fingers DOWN on left hand
(5 - (b - 5)) = Number of fingers DOWN on right hand

THE CALCULATION
((Number of fingers UP on left hand) + (Number of fingers UP on right hand) x 10) + ((Number of fingers DOWN on left hand) x (Number of fingers DOWN on right hand)) =
(((a - 5) + (b - 5)) x 10) + ((5 - (a - 5) x (5 - (b - 5)) =
((a + b - 10) x 10) + ((10 - a) x (10 - b)) =
(10a + 10b - 100) + (100 - 10b - 10a + (a x b)) =
a x b

QED

Sunday, July 24, 2016

Eyeglasses in the Middle Ages

The Middle Ages was a very inventive period, and one of the things they invented was eyeglasses.

Many people have always been nearsighted or farsighted, but until glasses were invented there was nothing to do be done about it.  A lot of medieval manuscripts look as if written by a nearsighted person writing with his nose very close to the parchment--the letters are tiny, sometimes hard to decipher without a magnifying glass (or a modern nearsighted person taking off her glasses).  Alternately, a lot of medieval people must have been farsighted, to make out details in high stained glass windows that require most of us to use binoculars.

Medieval people worked with glass especially for church windows, but also for decorative purposes and as a stand-in for jewels.  It doesn't take much to discover that glass can bend light, to focus it at different spots if it's convex or concave.  The Arabs had written on optics, giving ideas to thirteenth-century scholars.  The first known depiction of a person wearing glasses dates from the end of the thirteenth century.  During the fourteenth century, eyeglasses became relatively common among the well-to-do.


The above image dates to around 1400.

(Bifocals, by the way, were invented by Benjamin Franklin in the eighteenth century.  Until then, someone might need two different pairs of glasses.)

We now take glasses so much for granted--not to mention contacts and laser surgery to correct sight--that we may not appreciate what a useful invention they were.  Without them, a lot of people would have wandered half-blind through their lives.

Including me.  I would have been hopeless in the twelfth century.

Here's a safety tip.  If you ever see what appears to be a sort of green curtain across part of  your vision, it means your retina is coming detached from the back of your eye.  Do not hesitate.  Do not let that ooky feeling of thinking about eyeballs and sharp instruments in the same sentence deter you.  It won't go away by itself.  Diet, exercise, and herbal supplements will have no effect.  In a few days the green curtain will be replaced by the black curtain, and then you're blind in that eye.  Don't let that happen to you.  For one thing, you'll be asleep during the operation and will miss the sharp instrument-meets-eyeball moment.

(If you're concerned, and I appreciate your concern, mine was successfully caught at the green-curtain stage.)

Sunday, July 17, 2016

The Sign of the Rose

As I've noted before, we indie fantasy authors have to work to promote our ebooks.  And I tried something new with my latest, "The Sign of the Rose."  Here's the link on Amazon.


I enrolled it for a campaign in "Kindle Scout."  They eventually did not select my book, but it was an interesting experience.  For a successful "KS" book, Amazon themselves publish and promote and advertise it, which would be great.  There are so many good books on Amazon (and bad ones), that it's easy to get lost.

Amazon is essentially crowd-sourcing the decision of which indie books to publish.  Authors (like me) are invited to put their books up on the Kindle Scout site, where the first two chapters are available to give readers a preview.  Amazon restricts entries to full-length books and to certain fictional genres only (mystery, romance, science fiction/fantasy, and general literature).  Readers can preview the books for free and vote for their favorites by "nominating" them.  They can nominate up to 3 (and can change their minds if they find a better one).

At the end of 30 days, Amazon looks at the ones that have been the most popular and chooses from those which ones it will publish.  To reward nominators, those who have a "winning" book among their nominations at the end of the 30 day period will get the entire book, free, a full month before anyone else.

Kindle Scout is, as the name suggests, designed for ebooks to be read on a Kindle.  But since my novel was not picked up by KS, I've also made it available as a print book, for those (like me) who prefer a physical book to reading on a screen.

Hope you enjoy the book!  It's as close as I've ever come to writing real historical fiction set in the Middle Ages.  There's no magic in it, and it's definitely inspired by medieval history.  In fact, the inspiration for the book is a story written in Old French around the year 1200, "Guillaume de Dole."  I loved the strong heroine and the plot twists and thought modern readers would enjoy the story too.  (I did recast it.  Medieval authors routinely did things like have the hero and heroine fall passionately in love just by hearing about each other, without ever meeting.  Or authors would forget to include an important plot point and just mention much later that it had happened.)

What we call "romance" was invented in the twelfth century, as was so much else.  This book is a romance in the medieval sense--adventure, glory, and love all mixed together.  But I think it also passes muster for the modern definition of romance, although no bodices are ripped.

For those of my fans who want Yurt-or-nothing (and I know you're out there), never fear, more Yurt is coming.  But that pesky day job slows my writing way down (so inconsiderate), and this story just showed up in my brain late in the winter and demanded to be told.

Friday, July 15, 2016

Origins of Parliament

As I discussed in an earlier post on Magna Carta (promulgated in 1215), English Parliament had nothing to do with the "great charter" during the Middle Ages.  Parliament came along three generations later.

But today Britain's Parliament and Magna Carta are both considered to have something to do with "English liberties," so one can see why they are often run together in people's minds.

So where did Parliament come from?  The word is from the Old French, indicating a place or gathering where people talk (parler) and discuss.  It had long been established in all of medieval Europe, going back to the beginning of the Middle Ages, that kings were not supposed to make unilateral decisions.  If they did, they were tyrants.  Rather, they were supposed to work through councils made up of the powerful men (and very occasionally women) of the realm.

In England, kings who knew what was good for them called councils of the powerful whenever they had something important to decide.  At different times different collections of people might be asked to come.  These powerful people were considered to represent the populace and nation as a whole.  Such councils were called parliaments during the thirteenth century.

In 1295 a parliament was called which was later described as the "model parliament."  The people who were summoned then to advise the king became the model of who was supposed to be called.  No one at the time thought they were "founding Parliament," but the next few parliaments summoned the same people, and it became a tradition.

The "model parliament" had two wealthy burgers from each town and two knights from each shire, as well as all the powerful dukes and counts and the bishops and abbots of the realm.  The towns represented in 1295 continued to be the towns represented in Parliament until the nineteenth century, when changes had to be made—some major cities had grown up which had not existed in 1295, and other medieval cities had shrunk so much that they scarcely had more than the two people needed as representatives.

During the thirteenth century the Parliament settled down to have two "houses," the House of Lords, made up both of the great aristocrats and of the church leaders, and the House of Commons, made up of the burgers and knights of the shire.  The modern British Parliament still has these two houses, although the Commons has had almost all the power for the last couple centuries, the reverse of the medieval situation.  Parliament long had judicial as well as legislative functions; Britain got a separate Supreme Court only in 2009.

Early in the fourteenth century, a generation or two after the model parliament, both France and Spain developed similarly institutionalized forms of councils to advise the king.  In France the Estates General persisted (although frequently ignored by the kings) until the French Revolution.  Interestingly, the French had three "estates" rather than England's two "houses."

In France, the three estates were the church (separated out from powerful lay lords), the nobility (which included knights who would have been in the Commons in England), and wealthy townspeople.  France's regions also continued to have "parlements" in the medieval and early modern periods, regional assemblies which were primarily judicial.




The above image is of the Houses of Parliament in Westminster (what Americans would think of as part of London).  It is not medieval.