390 Quick Answers 25 March

PSAs:  Math and Science Fiction colloquium on Wednesday at 3:30p in N. 204.  (hence no office hours on Wednesday). 

If you're a math major and you started at Geneseo in Fall 2022 or Spring 2023 (including transfers), you are required to complete second year advising this year (if you did last semester, that suffices).  The two sessions are Thursday 28 March 4p and Wednesday 3 April 4p both in Fraser 104.
 
Refocus on your paper draft.  5 April is 1 week from Friday.    Please please please be diligent and dedicated in working on your drafts now.  I am always happy to talk with anyone about it.  I will read paper drafts in the order I receive them.  I will talk about them in person, but I will not be reading drafts online and giving feedback before they are due.  I strongly recommend visiting either the writing learning centre or the history writing learning centre.  If you turn your paper draft in on 5 April, I may return it to you as late as early May.  Please submit them early.

It’s a fine time to say - your final will be like the midterm, only twice as much.  2-3 questions on 1600+ and 2-3 questions on the entire course.  You might take a chance at this point to look over the midterm questions to give some inspiration for final topics.  Your "actual current average" is now updated and it is what it says it is.  Trust _that_ not another column.   Is there anything I need to know about how it went technically?  Can you see my feedback?  Next Time - your exam will be automatically submitted after 2.5 hours.  Do not let that happen to you. 

It’s also a fine time to be grateful that 1. you can type your essay exams [and to lament for your predecessors for whom this was not the case], 2. I’m only asking you to keep the tiniest bit of all that we do.  Learn what you like.  Please see that engagement is what’s most valued here.

Those presenting at GREAT Day need to schedule two rehearsals with me before your talk.  They may not be in the same week.  They may not be the same week as GREAT Day.  Be careful.

Be very careful in putting the timing together in Chapter 7.  Let’s look at the dates for the three sections.  We’re jumping back and forth.  England isn’t behind … yet, but they are about to be. 

You had a week to do these reactions.  I'm surprised these are the ones that are late instead of early.  I am glad that we'll be settling back into our regular pattern (with the exception of eclipse day). 

Lecture Reactions

I don't think Stevin was encouraging to always use the notations on the decimal places.  They're like training wheels. 

This is how Descartes is spelled.  He's kinda (or "kind of") a big deal. 

I said little about it in class, but someone gave me an opportunity to say more, aside from the machine pictured, Leibniz had a fascinating device that you could trace a curve and it would draw the derivative, or you could use it backwards and it would draw the integral. 

When you learned Calculus I you were told, repeatedly, emphatically, there is no such things as dx and dy as separate measureable entities and dy/dx is not a fraction, but one quantity.  You might of have ignored it, but I promise you were told this.  For Leibniz, originally, they _were_ measurable quantities, but what you care about now is the ratio of what Leibniz would call dx/dy (because he exchanged the role of x and y, following Descartes [ok, he didn't exchange them, we did later, but they were not in the association we use]).  I don't know when they switch to current usage.  I guess you can watch for it. 


For those who could notice a difference, I believe the well-tempered (modern) tuning sounds better largely because it is so much more familiar.  I am on your side on this, but it makes sense.  I think music adopted the idea from mathematicians.  It wasn’t forced upon them.  Yes this is the well-tempered of Bach’s titles which were new at the time.  Why were octaves and fifths thought to match up eventually?  Probably because the system was defined “locally” first, not stretching up the necessary 7 octaves to match up.  The way the system is defined has this logical consequence that just happens to not quite work arithmetically using small whole number ratios.  Playing notes on a piano is merely pressing a key.  Playing notes on a string instrument is about choosing the correct string length.  Choosing the correct string length is easier with small number ratios.  This is the end of our musical topic.  Probably don’t write about this.  

Oh, I remember this shows up now: ± ∓ are used only in pair to mean use either the top of both or the bottom of both.  I also remember that most of you don’t know this, so it’s good to talk about. 




Reading Reactions

Ok, the equals is a cute story.  I’m glad you all liked it so.  That’s why I was holding it back.  We’ll see a little more. 

Prosthaphaeresis is using trigonometry (tables) to multiply.  It is _not_ used to compute trigonometry.  It converts multiplication of two numbers into addition of two numbers, like logarithms do.  Remember accurate astronomy requires manipulating large numbers with high accuracy.  Would you rather add or multiply ten digit numbers? 

Harriot is a nice place to point to someone who was ok with negative roots.  We’ve been wondering where this would come.  Harriot was ok with complex roots.  The symbol i is due to Euler - yet to come.  Never too early to start pronouncing Euler.  

Trigonometry functions (and next logarithm functions) were looked up in books.  Mathematicians compute them once and others (including other mathematicians) look them up.  There has never been a time in history when either are computed by hand widely even by mathematicians.  Someone does it once, and everyone looks it up, until we have calculators, which are like a table in a machine.  

Ok, I feel bad about not talking about Wallis more, and a couple people independently found that he created the infinity symbol, and I know you like notation, so … there.  ∞.  Enjoy.  

Yes, there is some feeling that infinitesimals are not rigourous.  They can be made so.  There’s definitely a recurring question in calculus about how to be careful.  Leibniz’s infinitesimals were dx and dy.  He could find the ratio precisely dy/dx without knowing the values.  You didn’t do calculus this way, instead you used limits.  We’ll see where they come from later.  

This is the very beginning of the topic of journals.  This will be another theme going forward.