Because I am giving an exam tomorrow (Thursday, February 25) 7-9+ pm, I will not be holding office hours.  I will, however, be email accessible and will answer any questions you may have that way.  

I want to take this opportunity to thank you for this class.  It has lived up to my hopes and expectations so far, and I hope it has for you too.  I sometimes regret that we don't have more personal interaction, but I am grateful to get personal insights from each of you via reading reactions.  I would also be pleased to talk with any of you about more history topics out of class - but I expect that will happen more as we work more on your final papers.  

§-5.2.2 Quick Answers

Many people are noticing that the mathematics has become less substantial.  This is giving you a view of what was happening in Europe.  Substance will pick up again in Chapter 6.  Europe is going through a rough time.  Consider this - Suzuki could've just said "nothing much happened until the Renaissance", but isn't it more compelling to see what is actually happening and to connect the story together?  At least this way you can judge for yourself.  

The Julian calendar uses 365.25  years, but *that* number is wrong, and it was starting to have effects already.  Leap years are part of the Julian calendar, introduced by Julius Caesar.  I do not know when people knew the *cause* of the seasons.  The cycles have been known for millennia, but I don't know when we understood the cause.  

Problems of buying items at different costs (animals &c) were widely common then, like they remain to be now.  In fact, it's pretty easy to see many of our standard problem times showing up throughout history.  

It's a good question if Alcuin generalised his sum for pigeons.  Seems perhaps not explicitly, but probably could've if someone asked him "what about 102 steps?"

It's a very good question how Bede's finger numeration compares to Abu'l Wafa's.  The image that I shared and that the book shares is Pacioli, much later than both.  (I think the difference between 1 and 7 is in the thumb).  These systems were actually used for commerce.  

The Royal Charter for the University of Paris allowed the students and faculty more protection under the law (the same as the church), but held them to the same (unmarriable) standards as the church.  The king can give such accommodations, simply, because he is king.  

Both lunar and solar information seem to figure into the eastre computation.  However, they don't quite, since it's uses an ecclesiastical sun and moon, made by the church to make computations easier [perhaps].  Ultimately eastre computation is more about a choice than about computing something accurately.  It gets to be whenever people say it is.  This is still done this way.  

It sounds reasonable to me that Abelard is one of the first professors.  

An opinion shared:  "And to my knowledge the Children's Crusades were actual events.  Most of the children who followed their leader, a boy named Stephen in France, across Europe to Marseilles.  Where they were taken to Alexandria by merchant ships and were sold into slavery."

More information from classmates:  "I noticed from the figure given here on page 127 and the one showed in-class that a lot of the finger symbols are the same that are used in Indian Classical Dancing that is done today. I thought it was interesting that some of the same finger symbols were used in both mathematical computation and dancing, and that they are still used today."

Did Gerbert know about zero?  It's not clear.  Others in the world did.  I expect he did, but perhaps just didn't understand it.  I'm not sure.  I don't think there's any notation that Gerbert is responsible for developing.  Ultimately, he didn't do much, but it is curious that there was a mathematician pope.  

Dots in capital roman letters far preceded this discussion and have nothing to do with decimal points.  

The pope isn't giving lands back for possession, but for control.  So Gerald is giving away ownership so that he can preserve control and to not lose ownership to his neighbours.  

I don't know what to make of the fact that Charlemagne couldn't write.  

Nadir is low point.  The nadir of papal prestige is the low point.  

Michael "the drunkard" wasn't so fond of Bardas being responsible.  

There is, indeed, lots of USian and Western mythology (Columbus was the first to the Americas, the world was thought flat) that is merely there to tell a pretty story.  Much to learn.  

Yes, the Franks become France.  No, the French aren't the only kings to be given nickname titles.