The Nature and Growth (and Shrinkage) of Modern Mathematics

The Nature and Growth (and Shrinkage) of Modern Mathematics

I've struggled with math since elementary school.  In the 1990's, in my 20's, a late mentor of mine, Dave Mitchell, suggested the book The Nature and Growth of Modern Mathematics by Edna E. Kramer might help me overcome some of that.

It was slow reading for me, and over the course of a few years I made my way through a few chapters.  Until early 2001, when I moved to Pune, India for a year.  Since I was only going for a year, it wasn't among the few books that I packed up to take there with me.

Then I ended up spending a decade in India before I moved back to the United States.  When I did move back to the U.S. I moved to New York City, and didn't have easy access to my large library in storage out in Waldport, Oregon.

With the coronavirus pandemic this year, I figured I'd buy another copy and pick up reading it again.  I found a used one easily enough but there's a problem with it.  In the 20 years since I last read it, the print has shrunk to minuscule, Holy Cow! unreadable size.   (yeah, yeah, I know, it's my aging eyes...)

As for math, I actually did excel at math twice as a boy, in elementary school.  But each time the teachers punished me for it and I learned my lesson, never again excel at math.

The first time was in 2nd grade at the Fellowship Farm School in Piscataway, NJ.  My best friend, Brian, and I worked ahead in our math workbook, enjoying, having fun.  But when our teacher. Mrs. Cooper, found out she punished us.  Back then standard punishment was having to stand against the wall in the hallway during class, and then stand against the wall of the lunchroom during lunch, only eating quickly after everyone not being punished had finished.  We faced this for a week.

I never again worked ahead of the class in math again.

Then the second time was in 4th grade, in a new school, Waldport Grade School, where I was a new student, having moved there in October 1978. Mrs. Elsie Apt gave us the assignment to write all the numbers from 1 to 10,000.  Not all at once, over a few weeks, with some days a set of 100, or 500, or at most 1,000.

Quite an onerous assignment.  However, at some point in it I noticed a weird repetition in the digits of sequences of numbers.  It didn't take me long to figure out how to exploit that to make the writing of all the numbers go quicker.  Especially where the digit 1 (one) repeats in the same position of 10 or more numbers (bearing in mind the maximum repeats is 1,000 but the lined pages only had so many rows...)

Even with other numbers, I could just go down the lines, write 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 over and over till the page was full, then move to the next digit of all the numbers and repeatedly write something like 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, then got to the 3's and so forth and so on...  

Of course, my skill at handwriting and related isn't so great that this wasn't obvious from the way I turned in the page. 

Sample of 210 - 219

Mrs. Apt considered this to be cheating.  And I had to rewrite a number of pages.  

So, despite learning something more valuable about numbers than the teacher probably intended, I got punished for it.  Lesson learned, don't excel in math!

On the plus side, that school year my mother was a volunteer whale counter for the Oregon State University Marine Science Center, so I wrote a lot of those number pages, plus other homework, from the top of the Yaquina Head Lighthouse.  So that's a hell of a good memory.

My Photo of the Yaquina Head Lighthouse from 2016.

Close-Up U.S.A.

Close-Up U.S.A.

When I was a kid in the 1970s and my parents were preparing to drive across the country and find a new place to live, they bought a boxed set of maps from National Geographic named Close-Up U.S.A.  Now, as a kid, I misread the title, thinking it meant the heteronym, like a business at the end of the day would "close up the shop," I thought the USA, my home country, was closing!

It was a relief some time later to realize that the title meant something more like "I'm ready for my close-up now," and the U.S.A. wan't actually closing.  And it was kind of funny for years to think of my childhood misunderstanding.

However, now in March 2020, the U.S.A. is sort of closing up, like "close up shop" kind of closing.  With the novel coronavirus pandemic spreading and people getting sick with the COVID-19 from it.  The president is belated closing our borders, starting first with travelers from China, but now from Europe (minus the one European country where this president owns commercial properties).

States are closing schools all over.  New York State just shot down all Broadway plays in order to reduce the number of people in close proximity.  Several states have put a limit on the number of people gathered together.

It'll probably get more restricted before it gets back to normal, whenever it does...

The U.S.A., bit by bit, is closing!

Here are some photos of Close-Up U.S.A. thought I found on the internet.  None of these photos are mine.

Review - "The Time Traveler's Wife" by Audrey Niffeneggar

The Time Traveler’s Wife — by Audrey Niffenegger

I knew this was a movie quite a long time ago, but assumed it was a chick flick and I wouldn’t be interested.  Then recently I read it in a list of science fiction books that mentioned that the story really did involve time travel, which got me interested in it.

I’m glad I saw that list as I really enjoyed this book.

The woman in the title is Clare, and the story revolves around her future husband, Henry.  Henry has a genetic disorder that causes him to occasionally, and without any control over it, travel through time and space to somewhere else, with only his body, no clothes or shoes, or even fillings in his teeth.  Wherever he was, his clothes just fall empty to the ground.  How long he stays is unpredictable.  He’s frequently beaten up, but has learned to fight, to steal, to pick locks, etc. in order to get clothes, food and water on his travels.  Most of his travels, at least the ones detailed in the book, are too familiar places, including hanging out with himself at other ages.

He repeatedly goes to a meadow near Clare’s house, beginning when Clare is six years old and Henry is 28.  They become friends quickly, but by then Henry knows they’ve already met and married in “real time”.   One one of his trips, when he’s older, he recites for Clare to write down a list of dates that he memorized for when he travels to her, so she can always have a set of clothes prepared for him.

Time moves on, Clare gets older…. She hasn’t told many people about Henry because as the few she has don’t believe her, other than her having a childhood “imaginary friends.”  Henry’s already told her they get married in her future, and as she becomes a teenager she keeps trying to seduce him, but he remains a gentleman.  Clare’s friends, who don’t know about Henry puzzle over why she won’t date boys through high school.

Once they meet in “real time” Clare recognizes Henry, who is younger than he was the first time he traveled to Clare’s meadow, so he has no idea who she is.  But they hit it off, and he quickly dumps his current girlfriend so they can date and marry, etc.

It takes a little effort to keep track of the dates and Clare and Henry’s ages.  But it’s worth it.

As the book moves on previous chapters’ foreshadowing starts to clarify, for the characters and for the readers.  It gets a bit sad once it’s clear that according to Ms. Niffenegger’s time travel rules once he’s experienced something, there’s nothing anyone can do to change it, it’s happened, or it will happen exactly as he saw it.  What’s going to happen becomes utterly inevitable, even if we don’t want it too.

Ms. Niffenegger doesn’t go into the mechanics of Henry’s travel, and that’s just as well.  It’s just something that happens and the story goes with it.

Overall I very much enjoyed this book, and I’m looking forward to the eventual sequel the author is working on (following one of Henry’s relatives with a similar genetic condition).

Book Review: A Dance with Dragons by George R. R. Martin

tl;dr
Good, but overly long, with parts sort of dragging and the plots not moving forward in proportion to the length of the book.

A Dance with Dragons Review

(spoilers if you haven't read the first four)

I finally caught up with A Dance with Dragons the fifth book in the George R. R. Martin’s A Song of Ice and Fire series while I was out sick for this past long weekend, spending most of the time reading and drinking cup after cup of hot herbal tea.  I was entranced by the book, and yet, by the end a little disappointed.

It had been six or seven years since I read the first four books of A Song of Ice and Fire and I debated for almost three years rereading them before starting this one or not, but ended up not spending the time on it.  With too many spoilers on social media from people watching HBO’s Game of Thrones I figured I’d better read it now before the TV series gets up to this part of the story. Fortunately there’s a good wiki online that I could reference for where the characters were and what they’d done in the first four books.

For the most part he goes between points of views of a small number of characters a lot, so once into this book’s stories for them, there isn’t too much going back to remember from years ago.  That mostly comes when switching to a new point of view, or for references to other characters.

Daenerys, Tyrion and Jon Snow make up most of the book, with a few chapters here and there from others, led by Theon Greyjoy and Bran Stark.

Daenerys’s chapters are kind of dull and repetitive till near the end.  Maybe Martin planned that, as it showed her dilemma, she loves her “children” the freed slaves, so much she’s stuck in complete inaction for most of the book.  She can’t leave them, and she can’t lead them, either, out of fear of hurting them.  One major downside of scenes in Meereen is that Martin built up an incredibly richly detailed world in Westeros, but much of the Slaver’s Bay part of Essos feels too cartoonish, not clear, with people having unfamiliar names that hold no meaning to most of us readers.

Jon Snow’s chapters also have a lot of nothing much happening up north at the Wall, and as a reader, I spent a lot of time waiting for some action.  They mostly laid the groundwork for upcoming conflicts, without doing much or going anywhere.

Tyrion’s chapters started slow, with him mostly struggling with father issues he just escaped in Westeros, but then moved things ahead, and had lots of unpredictability from one to the next.  He’s one of the most amusing characters in the series, and by far one of the brightest, so things from his point of view can be fun.  Even when he’s having a bad time he’s busy thinking of how to manipulate everyone around me.

With Theon Greyjoy, who we learned to hate for his earlier betrayal of the Starks, Martin sticks him in situations where we actually begin to feel sympathy for him.  In this book he’s actually not the worst guy in the group he’s with, as hard as it can be to believe…

With a few chapters of Bran Stark we explore magic farther.  He learns more about being a warg and dreaming.

In this book Martin seems to have copy pasted a little bit.  Not the single characters repeating phrases, “words are wind” or “wherever whores go” things, but actual narration and action, a few times.  Two of the young women characters make love to their men the exact same way, with the exact same thoughts while it’s happening, yet there’s no chance they’re friends who’ve exchanged talked or exchanged letters to think alike, and I don’t see that we, as readers, are supposed to see them as parallels for each other.  I think Martin got lazy and copied it.

Similarly, several times that high born characters have to pass for smallfolk, they make the same mistake saying “my lord” and are corrected by another high born character who tells them to slur the words into “m’lord” and “say it like your mouth is full of mud”.  The same wording in unrelated characters and incidents.

And how many times did he write that “they ate bread fried in bacon grease, while the lords and knights above the salt at the bacon”?

The end of the book had a few surprises and cliffhangers, for sure.  Now I’m eagerly awaiting the next one, “The Winds of Winter,” whenever that comes out.

Overall, it was hard to put down, individual chapters felt fast paced and fun.  But honestly, it could’ve been better.  At the end, “word are wind,” and it was a very long book, but the overall stories didn’t feel like they progressed in proportion to the length of the book.

Not Reading

For the last couple of decades I've read and read and read, with most of my free time being spent with books.  Typically I read 50-100 books a year.  I get up in the morning and read while I eat breakfast, read while I use the bathroom, read while I brush my teeth...  In the evenings I read while I eat dinner, read on the couch for a bit, read while I brush my teeth, and so on...

But since coming to New York City in September last year, I've hardly read any books at all.  It's very strange to me, but I've thought about it and I guess it's a couple of things.

I haven't bought any comfortable furniture to read in.  There's the less than comfortable, cheap Ikea dining chairs, or the floor.  From the floor, though, there's no good lighting that'll come from behind to read, only overhead.  The lighting can be solved by using the iPad for reading, instead of a dead tree book...

When I have free time on the weekends, I just want to get out of the apartment, walk around and explore the city.  After ten years in India where I found getting out and walking to be uncomfortable (traffic, lack of sidewalks, noise, pollution, heat, feral dogs, etc.) now that I'm in a city where I'm comfortable walking, I don't want to spend as much time inside.

In the evenings, I don't feel like I have much time, and what I do I spend writing to Leena and reading friends' things on Facebook, and maybe a bit of light stuff on the web, like Slashdot.  But it's very quickly bedtime.

About the only time I'm really reading any books is when I'm in the bathroom...  And that's the most comfortable furniture, too...

When will I read again?  Maybe when it gets too hot to be outside in the summer.  Or when the newness of New York City wears off a bit.  And when I get a nice comfy chair or couch...

What makes a book?

Nearly every day on the subway I see ads for audible.com, selling audiobooks, of mostly pretty popular titles.  Some trains have ads all the way across, from one end to the other, like this:

But one thing it got me wondering is...  

What is a "book"?

I've always thought of books as paper with printed words or pictures or combinations, and more recently with ebooks, electronic versions of printed words and pictures and combinations.  But the key thing to me is that a book is words.

But these audio books, are they still books?  Where's the dividing line between a book and a performance?  How often would we go to a play and after it's finished say "wow, that was an amazing book!"?  We might say it's based on an amazing book, but we don't refer to the play as the book.

I've only ever listened one audiobook, a performance, definitely a performance, of The Hobbit, performed by one of my favorite actors, Nicol Williamson (more famous for playing Merlin in Excalibur). This is something done long before audiobooks were commonplace, so I don't know if modern ones are similar.  In it, he did all the narration and all the voices, giving each character a distinctly different voice.  I've listened to it a hundred times or more since my mother got the tapes in the late 70's.  Williamson has probably become my favorite actor simply because of how many times I listened to that through my child hood...

And I sometimes wonder what a modern audiobook might sound like.  But I expect to be disappointed if I ever listen to one, because I can't imagine many actors doing as good a job as Williamson did for my favorite story.

But back to the original question in my mind, I have no doubt that the one I have heard was a performance, not a book.  I never thought of it as a book, but only as a dramatic performance of a story.  And maybe that's part of why I don't want to listen to an audiobook, by calling it a book instead of a story or a performance, my expectations are set for disappointment.

How I Lost My Faith in God

At one time I know I believed in God, but I don't any more. Sometimes I wonder what happened.

I guess the first part of it is when I was 9 and we moved away from New Jersey. In New Jersey we used to go to Etz Ahaim synagogue on a regular basis. I went to Hebrew school there every week and we attended all the high holy day services there.

But then when we moved to Waldport, with the nearest synagogue being well over 100 miles away, in Portland, we no longer went to services at all. My parents got me several tutors over time to help prepare me for my bar mitzvah, which we also had at Etz Ahaim in the summer when I turned 13, for which we flew across the country and stayed with my grandparents.

Looking back on the tutoring, though, it was focused solely on my being able to read my Torah portion. During that time I didn't learn any more about Judaism, being a Jew or even Hebrew vocabulary, only what I need to read my part, without understanding it. And to keep from taking it appropriately seriously, my father used to time me with a stopwatch when I was reading it, always pushing for faster and faster times as the goal, rather than the usual, normal sing-song rhythm.

Sometime around then, too, my parents started making me earn my TV time by reading "approved" books. For that I had to read 45 minutes for every half hour of TV I wanted to watch, in advance. Most of the books my mother picked were about the Holocaust.

And there, I think was another major reason I lost my faith. How can a youth read all those books about death and murder, with little or no guidance, and still think there really is a God?

As I became a teenager, while not consciously thinking about not believing, I was also reading a lot of swords & sorcery literature and some horror. For quite some time I felt H.P. Lovecraft had the perfect description of what I thought in the story Herbert West -- Reanimator, in which he states 'that all life is a chemical and physical process, and that the so-called "soul" is a myth.'

There's times when I think about what I believe and I really hope I'm wrong, that there is a God, heaven and all that stuff, as the idea of absolutely nothing after death is kind of full. But there's quite a difference between hope and actually believing, and I simply don't believe.

And seemingly at odds with that, I do enjoy some of the rituals of Judaism, and symbolism. That's in some ways part of my identity, as I grew up with my family celebrating the Jewish holidays and going to services, at least before we moved to Oregon. In that regard, one of my favorite stories is about Hillel the Elder, who was challenged to teach the Torah while standing on one foot, and he did, saying "The whole of the Torah is to treat others as you would be treated, the rest is just commentary" (there are quite a few variations on the story, whether it was him or his student who stood on one foot, and slight changes to his actual quote, although they all have the basic idea.)

With further thought I've come to decide that I believe in God as a symbol, but not as an entity.

Useless Dwarves in The Hobbit

Rereading The Hobbit by J.R.R. Tolkien earlier last year, for the umpteenth time (and having listened to the audio tapes of it hundreds of times) it occurred to me for the first time that most of the dwarves are useless and are only there to fill out the numbers, without actually doing much of anything else. Maybe it's been discussed in other criticism, but I've never really read any.

By the end of the story I noticed that there are only four distinct, dwarven roles in the story.

• Balin and Dwalin are interchangeable in the role of the oldest dwarf, and the ones who take the best care of Bilbo.
• Fili and Kili are interchangeable in the role of the youngest dwarf, and the most active and quickest moving.
• Thorin is obviously the leader, the King Under the Mountain.
• Old fat Bombur is the bungler, the one who's appetite and clumsiness get them into situations that only Bilbo can get them out of.

The rest are just filler to get the number thirteen.

Sure, they're used in places, like to make the unexpected party amusing and fun and show us more about Bilbo as a host, or later to get Beorn to accept them. And of course, how would the goblins' song sound "six birds in five fir-trees..." it definitely wouldn't ring as well as fifteen.

Nor would Smaug's observation "why not say 'us five' and be done with it" be nearly as impressive as his distinguishing the smell of fourteen distinct entities. And that would eliminate the title "Mr. Lucky Number" which I suppose is what makes Bilbo, Bilbo.

Still, it's one of my favorite stories anyway...

Shakespeare, kick-in-the-rear...

My first exposure to Shakespeare was as a little kid in Piscataway, when we used to chant "Shake spear, kick in the rear!". Not that any of us had a clue what that meant.

Then there were the two plays I had to read in different English classes in high school. Those were awful experiences. My freshman year we had to read Romeo & Juliet, which maybe it's a great play, but let's face it, even though 13 year old boys like I was were all lusting after the girls, but we had zero interest in romance...

My sophomore year we had to read Julius Caesar, which with violence and bloodshed had an appealing sound to it. But reading it in class was just a terrible. We sat in rows and each person read a line then it moved on to the next. We had students from the drama club who read their parts with great skill and emotion and we had kids who struggled to sound out big, complex words, like "there" and "Cay, Cay, Cay-E, Cay-E-Sar". And me, I'm a lousy performer so I'd spend the whole time nervously counting students and counting lines to try and figure out which was going to be mine so I could memorize it quickly and get through it as absolutely fast as possible, then panic whenever someone shortly before me would end up reading two lines instead of one, throwing off the count.

By the end of those I never wanted to read or see Shakespeare again in my life, and associated Shakespeare with fear, panic, embarrassment and boredom.

After I started my career in Portland, in the early 90's though, my mother bought season tickets to the Oregon Shakespeare Festival in Portland, which every year included five or six plays from various authors and one Shakespeare comedy. Those comedies ended up being hilarious and were the ones I looked forward to every year.

Since then I've planned to read a comedy, but never got around to it till a few months ago when I picked up The Comedy of Errors.

I've seen the play performed and thought it was a whole lot of fun, as well as a few movies with similar plots. Unfortunately, once I got into reading it, it was awfully boring. And I realized that by itself there's not much, it really needs performers to bring it to life. I was left quite disappointed.

For quite some time I've read lots of books or seen movies that refer to other Shakespeare plays, mainly dramas, Hamlet, Macbeth (like Scotland, PA that is a modern retelling of it) and others and they've become more interesting. But I think the one that affected me the most was Blue Mars by Kim Stanley Robinson in which one of the characters narrates, to us readers, about how he studied one play in which you can see the fortunes of two characters one going up and one going down, crossing like a big X right in the middle.

So not knowing them very well, I picked up Hamlet, which is one of the names I'm most familiar with. I was disappointed that it was Macbeth that had the witches I wanted to read about, but I can read that later. Unlike A Comedy of Errors, it turns out Hamlet has a good plot, good story and good characters.

Hamlet was a good story to read, and stood on its own without performers.

Now I'm looking forward to reading some more. Definitely I see Macbeth when I next get to a bookstore that has it, and I should dig out Blue Mars and try to find which one Robinson refers to (Richard something or other?).

Book Shopping on Sunday

I went book shopping on Sunday to Landmark in SGS Mall for my couple-of-times-a-year shopping and picked up a load of books. Mostly fiction with a few software development books tossed in for fun.

• "Song of Kali" by Dan Simmons - I've actually read this before and some of it is incredibly chilling. The best was when one character was describing his initiation into a secret Kali-worshipping cult and says that unlike most idols of Kali, the one in the temple had no severed head dangling from her fingers, and the new novices all knew there would be one by the end of the night.
• "Queen of the Damned" by Anne Rice - One of my two favorite vampire tales.
• "Diary" by Chuck Palahniuk
• "Absurdistan" by Gary Shteyngart
• "2 States" by Chetan Bhagat - Bhagat is incredibly popular in India and it looked like half the people at the checkout were buying this, his brand new one. All of his books, so far, have a number in the title.
• "Conan Chronicles I" by Robert Jordan - I've read these all before, and Jordan is amongst the best of the pastiche writers. His Conan stories are certainly not Howard's, but hey, they're not bad.
• "Conan Chronicles 2" by Robert Jordan - I've read these all before, and Jordan is amongst the best of the pastiche writers. His Conan stories are certainly not Howard's, but hey, they're not bad.
• "King Rat" by China Mieville
• "Priestess of the White" by Trudi Canavan
• "Last of the Wilds" by Trudi Canavan
• "Voice of the Gods" by Trudi Canvan
• "Bone in the Throat" by Anthony Bourdain
• "Gone Bamboo" by Anthony Bourdain
• "Bangkok Tattoo" by John Burdett
• "Divine Justice" by David Baldacci
• "Tall, Dark & Handsome" by Nisha Minhas
• "The Marriage Market" by Nisha Minhas
• "Witches' Brew" by Terry Brooks
• "The Tangle Box" by Terry Brooks
• "Up In Honey's Room" by Elmore Leonard
• "A Winter Haunting" by Dan Simmons
• "Hamlet" by Shakespeare - I used to hate Shakespeare dramas after a few bad experienced in high school, but I've read enough other stories since then that reference Hamlet in one way or another that I figure it's time to read it.
• "Real World Haskell" by O'Sullivan, Goerzen & Stewart - I don't know what Functional Programming actually is, but with a name like Haskell, I want to learn the language. That way if anyone ever asks me "do you know Haskell?" I can laugh and say "are you kidding? it's my middle name!"
• "Learning Rails" by St. Laurent & Dumbill
• "Head First Rails" by Griffiths - The Head First series is fantastic, lots of humor and good tutorials, and I want to learn more about Rails...

The worst problem there, besides the incredible crowds, was that I wore a pair of Birkenstock sandals that I haven't work outside much, so the soles aren't scuffed up rough, making it hard to walk on the smooth polished stone floor of the store. It was a bit like walking on ice and I had to take small, careful steps to avoid slipping and sliding.