Tuesday, March 30, 2010

Yeah, I got my ass kicked by Topology. Yes I did.

This post at Futility Closet caught my eye:

Here is a book lying on a table. Open it. Look at the first page. Measure its thickness. It is very thick indeed for a single sheet of paper — one half inch thick. Now turn to the second page of the book. How thick is this second sheet of paper? One fourth inch thick. And the third page of the book, how thick is this third sheet of paper? One eighth inch thick, etc. ad infinitum. We are to posit not only that each page of the book is followed by an immediate successor the thickness of which is one half that of the immediately preceding page but also (and this is not unimportant) that each page is separated from page 1 by a finite number of pages. These two conditions are logically compatible: there is no certifiable contradiction in their joint assertion. But they mutually entail that there is no last page in the book. Close the book. Turn it over so that the front cover of the book is now lying face down upon the table. Now, slowly lift the back cover of the book with the aim of exposing to view the stack of pages lying beneath it. There is nothing to see. For there is no last page in the book to meet our gaze.

An interesting (and very cool) twist on the nature of infinity. Or, should I say, infinities, for there is not just one.

There are a lot of curious things about allowing the existence of infinite things, which is one of the primary reasons why I do the kind of work that I do. I was fascinated by the notions that crop up. Like the fact that once you formalize the concept of a "problem" that can be solved and go on to formalize its difficulty, then in very short order you come to realize how tiny our intellect is. (Viz., as I have said too often, there are not only infinitely more problems that we cannot solve, there are infinitely many that we can't even adequately describe. This is very easy to prove, definitively, with easy math.)

But infinities have been bugging people for ages. Aristotle, that most famous of misguided philosophers, once wrote a version of Zeno's Paradox thusly: "In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead."

Obviously untrue, yes? Put in more familiar terms, you can never leave the room that you're in because you must first walk half the distance to the door. And then half again, and so on. But half of a finite quantity is always another finite quantity. Nevertheless, I still somehow manage to walk from my office to the coffee maker every morning, and the Boston Marathon is still run every year despite the algebraic obviousness that it can't actually happen at all.

Things like this have confounded scientists for centuries. There was a time when nobody could comprehend the idea of empty space, since they already knew of radio waves. As a result, they tried to prove (without success) of the existence of a material "ether" that transmitted the wave effects. And when confronted with proof that light is neither wave nor particle, but rather both, their minds rebelled.

And yet today, we're comfortable with the dual nature of matter (both waves as well as particles), and given proof that the ether cannot exist we now simply accept the fact that electromagnetic radiation propogates through empty space without any other medium, and the mathematical notion of limits has long since dispensed with any curiosity about the answer to Zeno.

Dare I say that there is an element of faith involved here?

Monday, March 29, 2010

Snapoutofit



It has been something of a rough weekend and a rough start of a week for me. Some things that are pretty important to me and my own sense of self-worth kind of imploded, and I've been thoughtful ever since.

I'm reminded of a quote by Joseph Campbell:

Where you stumble, there lies your treasure.

That is, where we fail is where we have the chance to learn what our shortcomings are and eventually succeed in overcoming them. Without the knowledge of what we lack, we can't become better. I get that, and I'm trying to put it into action.

It's just that the colossal failure in the first place is a serious bummer.

And now a followup video that never fails to make me smile no matter how bummed out I get:

Monday, March 22, 2010

Fun Facts I & II, and a bit of Political Ranting



The actual full moon is smaller than a dime held at arm's length.  All those photos showing an enormous moon rising over a landscape are.... well, they're fake.

I realize that this fact isn't so fun.  We like to be thrilled and awed, and small pictures of a little moon don't do that.  Awe-inspiring fake pictures do.  But truth matters to me.  More than awe, even.

Along those lines, I once got in major trouble over this:





Why?  Because an acquaintance thought it was real.  Snopes said otherwise, and I just gave her the link.  She actually unfriended me on facebook and stopped talking to me after that.  I mean, woah!

I seem to keep running into this, and it confuses me anew every time.  As a scientist, I'm trained to reassess my world view when empirical facts contradict it.  It's hard to be taken seriously if you insist that the moon is made of cheese when a sample of the moon comes back showing distinctly non-cheese elements.

But in personal lives, people seem to cling to the wildest notions, and with a fury approaching manic obsession.  As if the core of their existence depends upon that thing being true.  This happens in politics all the time, as most of us here in the USA have witnessed (again) in the last few weeks.  And as I well know, it happens very easily in personal lives.

For that former acquaintance of mine, I think that she felt really badly about the general direction that her life was taking, especially in her workplace, which was dominated by a couple of drunken asshole guys.  Misogynists, in fact.  She compensated by clinging to things like that video, which purported to show a girl doing something effortlessly that the Big Strong Baseball Man couldn't.  And me coming along and shooting it down -- well, that just made me part of the problem.  Multiply that by 10 years and I suppose that she had had enough.  Which is okay for me, since we were never close.

But back in my world, I have to wonder if it's really worth celebrating something that is false.  Give me reality, any day.  Give me the first female Speaker of the House and the first black President passing historic legislation that 100 years of white men could not -- THAT is inspiring.   Not that I'm denigrating white men -- I am one, after all.  More that I'm celebrating our collective spirit and abilities.

Say what you will about the recent bill, but seriously, you have to recognize the awesomeness of this historic moment.  It says far more about us as a country and a culture than anything else.  I'm sure that politicians will fuck things up again as usual as quickly as possible, but we have still now seen an aggressive and competent woman out-maneuver a house full of men who swore that they would defeat her, and a black man prove that he can out-politic and play the long game better than anyone else.  If this doesn't prove once and for all that we, as humans, are all generally equal in abilities and natural talent, I don't know what would.

Image from here.

Friday, March 19, 2010

Geek Jokes I



Q: What is a polar bear?
A: A cartesian bear after a change in coordinates.
 

Thursday, March 18, 2010

Screw Computers

So Laura is yacking on the phone with someone about her chemistry class and so I paused our episode of Friday Night Lights and am trying to add a link to Hark, A Vagrant! which is seriously one of the best webcomics ever made (and so clearly I need to marry Kate Beaton toot sweet), but apparently I just keep screwing it up.  I mean, seriously, why can't I just add this website?  It keeps getting translated to the site RSS feed.

Oooooh, I see.  Butsoactually, I'm not screwing up anything, it's just that blogger's bloglist interface sucks worse than Journey, or maybe worse than Poison.  OOH!  I got it: worse than Nickelback!

But no... no, that's just stupid.  Nickelback is really horrible, I grant you that, but they aren't the worst ever, it's got to be someone else.

*OH*.




Yes, yes.  Blogger's link system is worse than CREED.

Tuesday, March 16, 2010

Imagery I


All of these words, they are smoke
They are hanging so thick in the air
Between your face and mine
And they curl and they twist and they change without warning
And I'm never sure if it's what you said
Or what I think you said

Friday, March 12, 2010

Perú

 Tocllaraju, Ishinca Valley, Peru

My friend Danielle is all hot and bothered about doing a climb in Peru.  Specifically, she wants to climb in the Ishinca Valley, where I have done all of one trip.  Danielle is a hot-ass climber: daring, confident, and strong -- but without the standard climbers' baggage of ego.  In fact, she's self-deprecating and fun, someone who laughs at herself as hard or harder than anyone else can, always optimistic in the face of adversity, and her smile is freaky in how it takes over her face with its array of teeth.   In fact, her smile has been known to light small fires from 300 yards away.  In short, a really great person to have around on a high mountain, and honestly a really good person all around.  She doesn't bemoan adversity; she celebrates being alive, all the time, even when that means saying that yeah, We're Wet and Miserable, But Seriously I'm Glad I'm Not In Class.

I taught Danielle to climb.  Or, I should say, I provided the conditions, as a teacher, under which she had the chance to excel, which she did.  Something about her unbounded optimism resounded with me and she always poked me on a regular basis to go on a climb here or there, and so we've always kept in touch.  She came out to visit me a a couple of years ago, and then again last year with our mutual friend Darin, and both times we were blocked from a serious climb of Mt. Baker by conditions but we still had a great time together.

But so she wrote to me this week about climbing in Peru, and I was instantly ready to go.  What could be better than doing something that you love with good people?  Now we're in the planning stages.

I haven't been on a real mountain in three years now.

It's time.

Tuesday, March 2, 2010

This Will Not End Well

 
PC-E NIKKOR 24mm f/3.5D ED lens

So, I bought my birthday present: a Nikon wide angle, tilt/shift lens. Okay, so my birthday is in four months, whatever. I've been lusting after one of these things forever. I mean, FOREVER. What is so great about them, you ask?

Well, for one, there's the tilt: you can tilt the objective lens relative to the sensor plane. Why is that useful? Well, because as you remember from your college physics course, a lens focuses a focal plane to a focal point, so everything within the focal plane appears to be in focus at that point, and tilting the objective tilts the focal plane at an angle to the sensor. By tilting like that, part of the sensor stays in focus, but the rest goes out of focus, resulting in seriously cool shots like this. Stills are cool... but how about time lapses?

And then there's the shift. Ever taken a picture of a tall building? You point up at it, and the finished product looks like the thing is falling away from you. So you back waaaaaaaaay up in order to not point up but rather keep the lens perpendicular to the sides of the building, and then it looks okay.... but at the expense of half the frame filled with hot dog stands, parking lots, and god knows what else. Sure would be nice to be able to shift the building's image into the full frame at that point, eh? Yep, you got it.

Sure, you can fake the tilt effect (partially) in Photoshop. But you can't do it all without the real lens. The artistic possibilities are endless! I want to do a time lapse of my city with Mats Bergström's "Fratres" as the music, so I'm scoping out locales right now.

Sigh.

Gadgets are pretty cool, but I still have an enormous conversation to have soon.

But tilt/shift! TILT/SHIFT!!