Thorns

“The bird with the thorn in its breast, it follows an immutable law; it is driven by it knows not what to impale itself, and die singing. At the very instant the thorn enters there is no awareness in it of the dying to come; it simply sings and sings until there is not the life left to utter another note. But we, when we put the thorns in our breasts, we know. We understand. And still we do it. Still we do it.”

Colleen McCullough, The Thorn Birds.

 

Dance of Galaxies

Whenever I watch a science documentary, I think of Carl Sagan and the book version of Cosmos and the seemingly limitless ocean of inspiration that was presented to me in those pages, to draw from in times both good and bad. Cosmos has such a ridiculously sacred place in my heart that I’ve been very guarded and skeptical about the follow-up series that is currently being shown on many channels. However,  watching episode 3 tonight, an irrepressible jolt of happiness returned once more to poke through my melancholy fog, when Neil deGrasse Tyson described the collision of galaxies. I sense in the concluding quote, the lyrical hand of Ann Druyan:

[…] one last prophecy: Using nothing more than Newton’s Laws of Gravitation, we astronomers can confidently predict that 7 billion years from now, our home galaxy, the Milky Way, will merge with our neighboring galaxy, Andromeda. Because the distances between the stars are so great compared to their sizes, few, if any, stars in either galaxy will actually collide. Any life on the worlds of that far-off future should be safe, but they will be treated to an amazing billion-year-long light show, a dance of a half-trillion stars, to music first heard on one little world by a man who had but one true friend.”

[When Knowledge Conquered Fear (Episode 3)]

Footnote humor

I found today an enjoyable little footnote in Elliptic Tales, a recent book on elliptic curves and number theory written by Boston College professors Avner Ash and Robert Gross. The book is a tough and ambitious undertaking with the goal of explaining one of the most difficult areas of mathematics to a general readership. Even though I have a little more mathematical training than a lay reader, the book has been slow going, partly because of the difficult subject and partly because real life events have been too important to spare any reading time at all.

In the middle of the book, the authors define abelian groups. Briefly, an abelian group is a set of elements G endowed with a mathematical operation R that satisfies five properties:

  1. Closure: If a, b lie in G, then a R b is also in G.
  2. Associativity: (a R b) R c = a R (b R c).
  3. Symmetry: a R b = b R a.
  4. Existence of a neutral element z such that a R z = a.
  5. Existence of an “inverse” element, such that for every a, there exists -a, such that a R (-a) = z.

From there, the authors go on to describe a generator subgroup. This is a subset of G and consists of a few elements from G that can be combined using the operation R to generate the all elements of G. For example, if R is taken to be the addition operation, then the elements of the set {2,5} can be combined according to 2m + 5n to generate the entire set of integers using appropriate values for m and n. Here, m and n are not really multipliers (since the operation of multiplication hasn’t been explicitly defined) but just a shorthand way of writing 2 + 2 + … m times + 5 + 5 + … n times. Thus {2, 5} is a generator because 2 and 5 are relatively prime. With this explanation on generators came a sly footnote that made me smile:

We make the convention that the one-element group is generated by nothing at all. Since 0 has to be there, it doesn’t need to be generated. Theological analogies will be left to the reader.

A Rough History of Disbelief

I’ve wanted to write this post for several years, ever since I watched a BBC documentary titled Atheism: A Rough History of Disbelief. It was presented as a quiet, sometimes autobiographical, and decidedly old-fashioned video essay narrated by the disarming and wonderful Jonathan Miller.

The 3-hour series steers clear of the sensationalism that spoils many modern programs and debates on atheism. Instead, it charts the history of atheism over the past two thousand years, touching upon its primary proponents and highlighting some of their prominent scholarly works. The slow and calm nature of the film – and indeed the fact that many portions of it are put forth unadorned with rationalizations and inviting considerate, non-inflammatory debate – is quite an achievement given the sensitive nature of its subject.

My track record at convincing people to watch 3 hours of anything, let alone a documentary on atheism, would be classified (rather too charitably) as “not good”. Still, for those with the time and the interest, I’m linking to its three parts below:

  1. Shadows of Doubt
  2. Noughts and Crosses
  3. The Final Hour

A Catbird in a Snowstorm

Home is eight miles away, it is snowing,
I tell myself to be careful.
Both lights are still working: that’s a relief,
I zip up the jacket, buckle the helmet,
And sense the endorphins coming on.
There is ice on the frame, snow on the seat;
the catbird has been outside for long.
But now, bike and rider are cautiously ready
For the slow, steady ride home.

We test for slippage and seek grippy patches of road
Our senses are on red alert;
Is that salt below, or mud, or is it black ice?
We brake with care, and a hint of prayer
But the bike stays true; like it always has.
It’s not fast, it’s not light, it isn’t pretty,
But it knows me, and I know it.
Briskly we try out speeds, test cadences,
And settle on a comfortable clip for a snowstorm,
Pedalling faster, going slower than normal.

We can’t relax, even on the home stretch;
White sidewalks converge ahead,
Though snow obscures their virtual meeting point.
Below, the frame glistens red catching the taillight;
The catbird’s steady blinking heartbeat.
Snowflakes sparkle, always 3 feet ahead of us
Issuing outward like fireflies from a fantastic tube
We feel quiet, hearing no wind, no horns, no people
Only the sound of labored breath
And pin-pricks of snowflakes on a cold leathery face.

The catbird and I have gone many hundreds of miles
We are both silent and we are both lonely.
But we are not tired. Life burns madly in us;
Sad but fierce.

[Written almost a year ago, soon after biking from Boston Common to my apartment in Cambridge, past midnight in the middle of a snowstorm. “Gray Catbird” is my doughty commuter bike, and we have many stories to tell.]