I Just Read About That…

SOUNDTRACK: THE TRAGICALLY HIP-Live from the Vault-Volume 4 (2009).

Faithful reader will recall that this disc got trapped in my car’s CD changer.  When I had it the player replaced, they sent the old one back to mysterious Toyota offices far away.  And, about a month or so after sending it out, I received a package from Toyota with my three lost discs (this one, a Black Sabbath disc and, a promo disc I took from the library to try and wedge into the player to get it to eject the other discs (that doesn’t work, by the way) which was, embarrassingly, Ozzy & Kelly Osbourne doing a duet of something or other).

Thank you random Toyota person for keeping this disc, which is not easily replaced, in good condition.

So this concert is from 1994 and was recorded in Brussels on the Day for Night Tour.  I think many fans feel that this is a high point in The Hip’s recording career, and this concert attests to it.  The band sounds fantastic, energetic and really tight.  And the music from this era is just great: dynamic and dramatic.

This disc also adds to speculation that lead singer Gord Downie is a weird guy.  His between song banter is quite peculiar, to say the least (apropos of nothing: “Do you think of your pet as a pet or a member of the family?”).  Which also leads me to wonder if fans in non-English speaking countries (and yes, I know that many people in Brussels do speak English) think or care or even mind when lead singers babble in English to them.  Just curious.

I don’t have any other Vault discs from The Hip, but this one is certainly great.

[READ: During an ∞ of minutes during December 2009 & January 2010] Everything and More

As part of my pledge to read all of DFW’s works, I skipped the fiction and moved straight to this.  I hadn’t heard all that much about this book, except that it was pretty dense.  And, yup it is.

I’m going to give a comparison for any other DFW fans who are thinking about reading this.  If you have read Infinite Jest (and if you’re interested in DFW you should certainly read that before this book), and if you recall Endnote 123: Pemulis’ high tech math formula for calculating Mean Value w/r/t Eschaton, then you will have a fair idea of what you’re in for with Everything and More.  So, if your eyes glazed when you started to read that endnote, you’ll likely want to skip this book altogether.  However, if you plugged through with that endnote and you didn’t care that you didn’t get it, but you kind of enjoyed it because despite the math, it is very funny, well, then you might enjoy this book too.

If you’re a hard core math dude and you understand what things like: ∃ and ∈ and ∉ and ∏ and ℜ and even ∀ then you’ll have no problem with this book.

But math aside, there’s a lot of funny things in this book.  And DFW is in full conversational tone, with several places where he says things like “not sure if this has been mentioned in the book yet” implying that he never proofread the thing, which we know he did.  There’s even a funny observation as to the placement of a picture (“it’s not entirely clear to me why they put [this pencil sketch] here”).  There’s also tons of footnotes.  And most of them are labeled IYI (meaning If You’re Interested), and he totally lets you off the hook if you don’t feel compelled to read these.  Although as with most things DFW does, the footnotes are always tons of fun.

He also shows his great undying affection for his math professor, Dr. Goris (Dr. G).  He quotes liberally from Dr G’s classes, citing examples, funny quotes and the amusing joke that Irrational Numbers are called ‘surds.  There’s also great joke about schnitt (which I’ll explain later).  It even opens with a hilarious (or maybe not) section about the inability to get out of bed in the morning when you think about infinity.

As in for example in the early morning, especially if you wake up slightly before your alarm goes off, when it can suddenly and for no reason occur to you that you’ve been getting out of bed every morning without the slightest doubt that the floor would support you. Lying there now considering the matter, it appears at least theoretically possible that some flaw in the floor’s construction or its molecular integrity could make it buckle, or that even some aberrant bit of quantum flux or something could cause you to melt right through. Meaning it doesn’t seem logically impossible or anything. It’s not like you’re actually scared that the floor might give way in a moment when you really do get out of bed. It’s just that certain moods and lines of thinking are more abstract, not just focused on whatever needs or obligations you’re going to get out of bed to attend to.

And but so, what is this thing about?

Okay, so it’s about ∞ and the history of ∞.  It begins with a great section about the ancient Greeks (Zeno’s Paradox and all that) and slowly moves up through to Aristotle.  I myself have always been a Platonist (yes, in fact, I have made that distinction in my life, which may say more about me than many people know), and have always been kind of anti-Aristotle.  And, for the purposes of this book, that’s a great position to take.  Aristotle turns out to be like the arch-nemesis of ∞.

Aristotle introduced the idea of a Prime Mover.  (And if he didn’t introduce it, he certainly popularized it).  The prime mover basically means that something has to start the ball rolling.  In other words, there is you and then there’s your parents and then their parents and their parents and on and on but somewhere back there something had to start everything, right?  Looked at another way, infinity can’t exist because there has to be a first number.

This attitude was adopted by St Thomas Aquinas and was applied to prove the existence of God.  And, since no one wanted to argue with the existence of God, it basically curtailed anyone in Western civilization from investigating infinity and higher math for several centuries.

And that covers §1 and §2 of 7 total.

§3 covers the bulk of the history to like the mid 1600s. And this is where things start to get heavy and graph intensive. It’s also where you start seeing phrases like, “If you had advanced math you will remember….” It also features an Emergency Glossary!

§4 deals with Newton & Leibniz

§5 gets to the heart of the book, namely Dedekind and Cantor and the period from 1700-1850.  It also features Emergency Glossary II.  We also get to see fun things like The Wave Equation  and The Fourier Series

And just as I’m about to throw the book out the window, we get §5c. which is a biographical sketch of G.F.L.P. Cantor.  And it is fascinating: from the fake story that the Nazi’s made up about him being a foundling (in case he was Jewish) to his crazy relationship with his father Georg W. Cantor [one is tempted to make some kind of George W./ George H.W. joke, but since DFW refrained, I will too].  There’s even quotes from letters “Now I am happy when I see that it will no longer distress you if I follow my own feelings in this decision.  I hope that you will be proud of me one day, dear Father, for my soul, my entire being lives in my calling.” (172).

By the end of §5 we learn about Karl Weierstrass (1815-1897), a large, athletic, gregarious, much-loved fellow (quite the anomaly in higher math study).  He deals with limits and functions (and that’s about all I’m comfortable repeating).

By §6 we get more info about J.W.R. (Richard) Dedekind (1831-1916) who works at defining irrational numbers.  (He’s also affable and well-adjusted).  And he uses the Number Line (hey, something I remember from math!) to prove the existence of irrationals.  He cuts the Number Line in half (which DFW refers to as schnitt (German for “cut,” but by using schnitt, he truncates a lot of verbiage) to show two infinite sets.  And so when he schnitts number line into set A and set B, Dr G made the joke a that a surd is a “schnitt sandwich.”  Awesome.

As the section ends, we learn about Constructivism (a big opponent to Dedekind and Cantor) which more or less leads Cantor to start working on set theory.

And so §7 deals largely with Cantor’s life and work. When describing Cantor’s academic role DFW gives us the glorious footnote: “The German academic system of the 1800s is pretty much unparsable.”

There’s a look at the Uniqueness Theorem, which generates some very important infinity related ideas. And then Cantor’s uses of ℵ. Then we see Cantor’s Diagonal Proof. And let’s not forget Peano’s Postulates! Yeah, I don’t really know what any of these things are, I admit it.

By the time you get to page 297, you get this sentence:

However hard the last P seemed, most everything beyond that in the theory of ordinals is so brutally abtruse and technical that we can only make some general observations.

Yipes.

We’re nearing page 300 (of 305 text pages, not including the 30 + more pages of notes and bibliography).  And now we’re getting mentions of Gödel and his Incompleteness Proof.  And finally in 1963, DFW reveals the oughtta-be-a-blockbuster-movie life story of Paul J. Cohen who “proves that the negation of the general Continuum Hypothesis can also be added to the ZFS without contradiction” (301).

Now, anyone familiar with DFW’s work knows that he tends to end things, if not unfinished, then at least in the middle of things.  So as you get the final paragraph and it starts, “But it is the mathematical Platonists who are most upset by the C.H.’s Undecideablility–which is interesting” (304), you realize this book may just end in mid formula!

However, he tidies things up enough (ie. no such principle has ever been found) and nicely calls back to his opening by ending the book “Mathematics continues to get out of bed.” (305).

So this gloss  is the best I can do with this book.  I didn’t understand probably more than half, heck more like 3/4 of what was going on, and yet I feel like I understand a lot more about the history of math, even if the details are fuzzy.  So, while I’m not sure I enjoyed the book, and I can’t necessarily recommend it to anyone, certainly not without reservations, I won’t say that I disliked it either.

Reviews from math types have been generally positive, although as this book shows, the math world is fraught with dissension and academic backstabbing so it’s possible we’ll never know if this book is good or great.  At least I know I never will!

And in case you’re curious, many of the pictures and formulas in my post come from a cool math site called Mathworld.