Solving ‘How to Solve It’

I hit the ground running when I started George Pólya‘s How to Solve It: A New Aspect of Mathematical Method.  Somewhere in the middle, the momentum disappeared, and months later, I feel so relieved to have finished it.  For all that, I give it 5 out of 5 stars…yes, indeed, why??

This is a math/logic/philosophy classic from 1945, dealing with heuristic, “the study of the methods and rules of discovery and invention.”  More particularly, it is a comprehensive guide to problem-solving.   The first 40 pages or so are strictly about “How to Solve It” and classroom strategies, while the rest of the book elaborates on these themes in the “Short Dictionary of Heurstic.”  The back of the book has some sample problems/solutions, which, if I had more time and energy, I wouldn’t mind trying.

Hopefully the word “math” does not turn you away!  That is the one weakness of the book – most of the examples are in algebra and geometry, which, even for me, were often hard to follow.  However, the heart of it is absolutely universal to all types of problem-solving where there are definite choices and paths to follow (e.g. not moral dilemmas, naturally).  A few points I took away from it:

  1. Use descriptive, accurate terminology.  Go back to definitions and terminology. 
  2. Think aloud, ask yourself questions.
  3. Look for, and/or remember, similar problems/solutions.
  4. Vary the problem.
  5. Come up with a helper problem.
  6. Give yourself time and rest when you need it.
  7. Work efficiently.  
    1. That is, when you’re having trouble solving a problem, be clever about how you deal with it.  
    2.  As much as you can, work from question to conclusion, even if it’s only a tiny part of the problem.  Finish each work session with some sense of achievement.
    3. “Set [yourself] a new question about the problem.”  This was the most useful advice to me.
  8. When you start a problem, picture success – the end result!

    Now, as to why this book was such a struggle to read.  As you’ve probably read on my about, I’m working on a computer science degree, a division of applied mathematics.  For that reason, most of the material in How to Solve It is not new to me; I’ve had a lot of classroom experience with these techniques.  The sad thing is, there are many professors who do not apply these methods correctly.  By the middle of the book, I started remembering their approach, and I thought, “Oh, this is that book, the source of my problems…”

    Later, I gave it some objective thought and recalled my worst and best professors.  I came to the realization that nearly all of them follow this pattern of teaching!  What, then, is the defining difference?  The most unhelpful professors are the ones unable to relate to students.  It leads me to think they have forgotten there is a problem to solve.  In contrast, the most illuminating professors come down from their dirigible of knowledge and join their students at square one – with a guidebook in hand, so we don’t get lost. 

    In the end, it’s not this book’s fault.  How to Solve It is a good book with good advice.  If you feel comfortable reading math problems (even if you don’t fully understand them), I recommend reading it before college, or anytime for your own personal benefit.

    "Josef K. was dreaming."

    Last fall, at long last, I got a copy of Kafka’s Complete Short Stories.  (That would be most everything except The Trial, The Castle, and Amerika.)  It’s a book to be savored slowly, piece by piece, while imagining it to be twice its length (~ 450 p.).  I quickly found the best way to read it is jumping back and forth between the longer stories in the front and the micro fiction in the back.

    Franz Kafka – most people love his books or despise them.  That’s pretty understandable.  He’s not the most accessible of authors.  On my part, I fell for his writing after listening to The Metamorphosis; since then, I keep coming back to his books.  Back to their chilling simplicity, back to their gloomy, frequently vulgar depiction of society.  Back to the endless plots that lead nowhere good!

    But of course, there’s more to it than that.  There is a lot of truth in Kafka’s world.  Absurdity, isolation, irony, and confusion.  The real world is not so far off; sometimes it is identical – mazes of bureaucracy and words, the sheer audacity of words.  Kafka’s vocabulary is simple, but his sentences are intricate.  His paragraphs are monstrosities, and he is making a point the whole time.  You feel the claustrophobia in those long, long paragraphs, just as you feel the futility of the protagonists’ repeated attempts at arriving at the solution.  You sink into their struggle to follow protocol and responsibilities, while vague frustrations meet them at every turn.  The reader need not like the protagonists; I rarely do.  It’s the setting that is fascinating, and it’s the conflict that motivates the stories.

    I’ll be very sorry to get to the end of Kafka’s writings – that is why I’m glad to be reading this one slowly.  

    Eugene Onegin Read-Along ~ Chapters 5 & 6

    {Summary of previous part + new questions below the cut.}

    In chapter 4, Tatyana’s impulsive – and, for the era, improper – love letter was rejected by a polite but upfront Onegin.  While Lensky and Olga are living out the fairytale romance leading up to a wedding, Onegin refuses to take part in fulfilling the neighborhood’s gossip about him and Tatyana.  His attitude towards her, in his own words, is that of a friendly acquaintance, scarcely more than brotherly love.  He warns her to be more careful with her feelings, as other people will not treat her with understanding as he has.  Heartbroken, Tatyana must go on as if nothing happened, while still having to face the opinions of her family and inquisitive neighbors.

    Chapters 5 & 6 Questions

    – One of my favorite scenes is Tatyana’s dream.  How do you interpret it?  Any ideas as to why it is usually omitted from major adaptations (including Tchaikovsky’s opera and the 1999 film)?

    – Chapter 6 finds us in the middle of sudden disputes and high drama.  What might be the characters’ motivations for such extreme actions?  Is it substance, or superficiality?  Is anybody right or wrong – and if so, who?

    Ongoing Questions

    – Reactions and/or predictions?

    – Any quotes or passages that stand out?

    Eugene Onegin, first thoughts

    (c) Ken Howard/Metropolitan Opera

    First off – I’m feeling quite sheepish and sorry for my absence during this read-along!  This weekend I am, at last, finally writing my first post and catching up on all of your interesting insights!

    Second apology: for my not-so subtle promotion of the 2013 Met Opera production, now on DVD.  I promise I’m not affiliated with the Met in any way – this is just my favorite adaptation of the story!  If you like opera at all, it’s worth checking out.

    Back to the topic at hand.  This is my fourth year reading Onegin.  How it could possibly be the fourth, I don’t know; it’s just a tradition I started freshman year of college.  Each translation reads like a new book, and this time it’s Charles Johnston.

    So far, I have mixed feelings about Johnston’s.  It might be the easiest to read yet, whether because of accuracies or liberties, I don’t know, though I suspect the latter.  It certainly rhymes better than the Mitchell translation –  there’s something to be said for that.  On the other hand, I feel like the word choices are too – cynical?  Or simply more opinionated, less subtle?  Both a strength and a weakness. I’ll be interested to see how this manifests itself later on.

    Chapters 1 & 2 Questions

    – First impressions of Eugene?

    After I read other participants’ ideas on these early chapters, a thought came to mind that was so obvious but somehow new to me.  Eugene lives on first impressions (no pun intended).  First dances, first loves, new places, new people.  He loves the countryside, at first.  He likes Tatyana, at first.  But he becomes disappointed by everything new he pursues, and I think that is what repels him from Tatyana as well.  He doesn’t want to live old mistakes over again.

    – What do you make of the narrator’s commentary?

    It really used to bug me, but I like it now.  Pushkin is not too lofty or lowly, and he doesn’t try to pull or dare you into the story.  I picture him sitting in a living room or study, talking and telling the story informally to half-critical friends.  No pressure, just an invitation to listen.

    – Thoughts on the characters sketched out in Chapter 2?

    Eugene is delightfully unsociable; I love the bit in stanza 5 where he runs away every time someone comes to visit.  (I’m also guessing he’s kinder to his serfs out of pure laziness, not particular benevolence.)

    Lensky’s character is already firmly established.  He gets quite – unduly? – attached to people, even the late Mr. Larin, whose memorial he visits with genuine sadness.

    Olga is not given much description.  Tatyana’s childhood is actually described, which is significant in such a space-efficient novel.  I like the part “a chilled reaction / to horror stories told at night / in winter was her heart’s delight”.  It sounds ironic that a sensitive girl would like spooky stories, yet I was just the same way.  Also, it’s such a random but telling piece of her personality.

    Chapters 3 & 4 Questions

    – Impressions of Tatyana and Olga?

    Olga is a bit of a mystery – even now we don’t get to really know her.  However, it is implied she is a bit indifferent to Lensky’s romantic verses.  Considering they were childhood friends, maybe she is not actually shallow, but just has different feelings towards him than what he has for her.

    I don’t quite like Tatyana in this translation.  She comes across as particularly emotional and impressionable.  Again, this must be due to the translation, as previously I didn’t have that response.

    – What do you make of Onegin’s reaction to Tatyana?

    Very much in character.  Half of it is arrogance, and the “I’m older and wiser than you!” sort of thing.  The other half is the other half of Onegin, struck by his conscience and genuinely moved to an act of concern, maybe even kindness.

    What I love also about this scene is that Tatyana saw it coming.  The book is full of Romanticism, but it’s these moments of realism that make it so true to life.

    – How does the story, thus far, compare or contrast with another classic romantic novel (of your choice)? 

    I think Eugene Onegin was in many ways ahead of its time.  Invariably, I must compare it to Jane Eyre, since it focuses as much on the heroine’s development as on the romantic plot.  But Eugene Onegin also deals with the effect of society on people’s actions, which makes it a little more universal.  Sort of the best of both Austen and Bronte, I would say.  🙂

    The Brothers Karamazov – 1: A Nice Little Family

    (A number of bloggers I follow write their thoughts on lengthy books as they go along.  In fact, I believe one of them did this for The Brothers Karamazov in the last year or so.  Credit to them for the good idea!)

    Vilhelm Hammershøi - The Collector of Coins - Google Art Project

    For years, I’ve wanted to read this novel.  I enjoyed The Idiot and Notes from Underground, and people only say good things about this one.  Coinciding with o’s Russian Literature 2014 challenge, it seemed high time to put it off no longer!

    The Brothers Karamazov is divided into 4 parts or, if you like, 12 books.  I do like this format.  If I’m to read a long book, short chapters are preferable.  (Moby-Dick is similar, except that there are no parts or subdivisions.)  Anyways – I plan to write a post for each book.  Because “book journalling” inherently requires talking about plot twists, many of these posts will be spoilery. I’ll add page cuts when I get to those parts.

    In book 1 we jump right away to meeting the main characters.  Always a good sign!  The Karamazov patriarch, if he could possibly earn that title, is Fyodor Pavlovich.  He’s a vile wife-abuser who spends most of his time sleeping around.  Moving on to his sons, the brothers of the title.  I was expecting them to be mutual enemies for some reason – so far that is not the case.  The oldest, Dmitri, is described as rather uneducated and quick-tempered.  Ivan and Alyosha are his younger half-brothers.  Ivan is a reclusive, bookish atheist, while Alyosha is a little less withdrawn and also very religious, hoping to become a monk.

    Book 1 simply ends with the family about to come together (for the first time, perhaps?) to discuss Dmitri’s dispute with the father over money and inheritance.  In a quirky turn of events that is very Dostoyevsky, the meeting will take place in the home of Zosima, an elder at the monastery and Alyosha’s mentor.  Alyosha is already embarrassed, afraid his family’s irreverent behavior will offend Zosima, who has become to him, in essence, the father Fyodor should have been.  As in the The Idiot, I predict some very long conversations coming up in book 2.

    In Dostoyevsky’s introduction, Alyosha is said to be the hero of this book.  I can see that – he reminds me a lot of Prince Myshkin.  I guess I’ll inevitably be making this comparison throughout…hopefully not to Alyosha’s discredit. I honestly can’t imagine a more endearing suffering hero than Myshkin (except Gregor Samsa, but that’s from a different author  🙂 ).  Some of you perhaps have read both already – which character did you prefer?