may 2006

Man, I suck at writing papers now. I guess what I really mean is that I suck at writing papers quickly now (this particulary paper I think will turn out pretty well; it's probably my best work in a few semesters for this program), especially science-y papers with lots of research. Those have always taken longer, but still, it used to be if you gave me a topic, a deadline, and a stretch of 6-10 hours, I could crank out anywhere from 3000-6000 words without a problem. I mean, I'd be exhausted at the end of those 6-10 hours, but the paper would be finished, and I'd turn it in feeling pretty good about it.

This paper is due tomorrow, and despite having sworn off World of Warcraft for more than a week and spending most of my free time over the past two weeks thinking about, researching, or writing this paper, it's just been painfully slow grinding out the text. One way or the other, it's all done tomorrow, thank god. But I get the feeling that I'm going to be working on it until the very last minute.

Class canceled again tonight because our professor is still in England. I'm disappointed that we didn't get to meet again—there was a whole book that we were supposed to be discussing over the last three class periods that we didn't get to talk about at all—but honestly, I could use the extra time to finish up my paper. It's in pretty good shape, but there are still a couple of paragraphs needed to firm it up, and I need to sit down and review the document as a whole to make sure the flow is okay.

I don't know if the professor or any of my classmates would be up for it, but I'd like to meet at least once more after the end of the semester is over to give the class some closure, so I'm going to suggest that to the professor upon his return. It won't be the end of the world if we don't do it, because I feel like I have a pretty good handle on the class and I'm pretty pleased with how my paper came out, but it would be nice to have a formal wrap up of the ideas and themes that we've tackled this semester.

Ugh. That was the longest paper I've ever written aside from my honors thesis at Davidson. I am so fucking glad that I'm finally finished with it.

So United 93 came in second place in the box office its opening weekend, making just under $12 million. In this article, the studio behind the movie declared this a big success, making statements like this:

This is a wonderful result. What [the public] said was that it wasn't too soon for a film about September 11.

And this:

We can now kind of put to bed any idea that people are not ready to see this type of movie. The numbers speak for themselves.

Well, I think the numbers speak for themselves, too, and I sure don't interpret them the same way the industry spinmeisters do. Given the large presence the events portrayed in this movie have had in our national consciousness over the past five years, and the across-the-board excellent reviews that this film received, I don't consider coming in second behind a crappy Robin Williams family comedy a success, and I sure don't think these box office numbers indicate that people are ready for a film about 9.11 (and it's sure as hell obvious that most people aren't clamoring for one).

Here's my prediction: most movies, even good movies, drop off 40-60% of their opening weekend box office the second weekend. I'm betting that United 93 will drop off much, much faster than that; I think everyone who had any interest in seeing this movie went to see it opening weekend, and that it's pretty much done now. I wouldn't be surprised if second weekend revenues were 30% or less of opening weekend revenues, and I can almost guarantee that this picture will be out of theaters by the middle of this month.

We'll see, though. I've been wrong about the American masses plenty of times before. But it would restore a little of my faith in them if I were right about this.

The photo for today is called Sunblind, and it's one of my favorite pictures from the last couple of months. And speaking of photography, it's been two years since I bought my current camera, so I think it's about time for an upgrade. I'm seriously interested in an updated version of my current camera—it has most of the same features, but it has a smaller body size, uses two batteries instead of four, has an extra 2 megapixels (6 total), and uses the second-generation of the chip in my current camera. It's also surprisingly inexpensive, I guess because it's target market is semi-serious photographers who want something less than a bulky SLR but something more than a simple pocket-sized point-and-shoot model.

The only thing holding me back: the lack of digital image stabilization, which makes it easier to shoot in low light settings. However, I'm thinking about also purchasing a small mini-tripod that wouldn't be too hard to carry with me if I knew I was going to be shooting in low light but I didn't want to bring along my full size tripod.

We've got some travel coming up in the next month that I'll definitely want to have a new camera for, and since this model is in relatively short supply, I'll need to make up my mind pretty soon to make sure I have it before we go. In some ways, I'd like to give another brand a try, but I absolutely love the image quality on my current camera, and I'm loathe to get one that shoots a little better in low light but doesn't shoot nearly as well in outdoor light—the image chip in my current camera nails outdoor colors in its default shooting mode, and that's honestly how most of my pictures are taken.

I don't know. I'll probably get it. But I'll keep you posted.

Man, the weekends are so much more relaxing without reading/paper writing hanging over my head. We did a lot of stuff, but I more rested and less stressed out than I have in a while.

The box office numbers for the second weekend of United 93 are in, and while they aren't quite as dire as I'd hoped, they're still not good. The percentage dropoff in ticket sales was 55%, which, while not as bad as the 30% I predicted, are still at the very low end of acceptable (for comparison, RV, the top movie for last weekend, only experienced a 32% drop in sales). Moreover, since United 93's initial haul was so low to begin with ($11.6 million), that 55% drop amounts to only $5.2 million in new sales.

Combined with the take during the week, and the film is currently standing at around $20 million in gross ticket sales. Even more telling is the discrepancy between the per-screen average over the two weekends: during it's first weekend, United 93 took in an average of $6,465 per screen. This past weekend: only $2,865 (and only 25 new screens were added, so that's not really a factor). Given these numbers, and given the steady decrease in weekly sales that most movies experience, I doubt that this film will crack the $30 million mark.

The studio is probably reasonably happy with this (although not as happy as they pretended to be in this article), because United 93 only cost $15 million to make, so they're going to make a solid profit off it, especially when you factor in DVD sales, etc. But the next 9.11 film, Oliver Stone's World Trade Center, cost significantly more to make, and is going to take a lot more than just the morbidly curious to turn it into a real moneymaker—the marketing costs alone for Stone's film will likely be more than the entire production costs for United 93. And given the tepid response to United 93 despite uniformly glowing reviews, I think that the morbidly curious are really the only people interested in seeing a film about 9.11 at this point.

Tonight will be our first Orioles game aside from opening day. We've had tickets for a couple of other games, but they coincided with pre-existing plans and we had to exchange them for games later in the season. I think we'll get our fill this month, though—I think before the end of May, we're scheduled to see four games. Let's hope they can build on last nigh's win and start to rebound from their disastrous five game losing streak that concluded over the weekend.

I ended up getting a new camera over the weekend, a Canon PowerShot A700 to replace my PowerShot A80, which I got almost exactly two years ago before our trip to Colorado.

The A700 is a major upgrade in many ways: the image processor is the next generation version of the same chip that was in the A80 (the new DIGIC II chip, the same one that Canon uses in its high-end SLRs), it shoots at 6 megapixels as opposed to the 4 megapixels of the A80, and it has 6x optical zoom as opposed to the A80's 3x optical zoom. The A700 is also much smaller and lighter than the A80 (it only needs two AA batteries; the A80 required 4), which means that it's even more of a pocket-sized camera. And the macro function on the A700 (for taking close-ups of subjects) is much, much better than than the A80; not only can I get much closer to an object and still stay in focus, but the camera also focuses much faster than the A80 (startup and reset times are also a lot faster on the A700).

The only thing that made me hesitate before buying the A700 was the lack of a flip-out LCD screen, which the A80 has and which makes shooting at unusual angles a lot easier, because you don't have to contort yourself to frame the shot. But the likelihood of Canon producing a camera that includes this feature and includes all of the other stuff that I like about the A700 in the near future is pretty small, and I really wanted to get a new camera before we start our summer travels. And besides, I've taken plenty of good pictures without needing the flip-out screen—even with the A80, I didn't need to use it that often. It would have been a nice bonus feature to have, but the overwhelming number of positives for the A700 easily outweight this one negative.

So far I've only taken a few photos with it (none of them have been the daily photo yet; those will probably start showing up next week), but the color handling and clarity seems to meet the high expectations that I have for Canon's cameras, and I can't get enough of the macro function—I've always wanted to take closer close-ups, but I was severely limited by the A80's macro range.

Creed is rapidly becoming my favorite secondary character on the Office. His best lines from last night's season finale, spoken to the camera after swiping his neighbor's chips during a casino night charity fundraiser:

Oh, I steal things all the time. It's just something I do. I stopped caring a long time ago. You should see how many supplies I've taken from this place. Honestly, I love stealing things.

Absolutely brilliant.

I can already tell that this is going be one of those Fridays when everyone shows up for work, but no one's going to do a damn thing all day except wait for 5:00 to come. I bet a lot of folks won't even wait that long—once the senior staff starts to bail, it will set off a domino effect.

Starting with today's pictures, all my daily photos from now on will be from the new A700. I doubt you'll notice a difference, especially because I reduce them so much for the web, but I just wanted to note this for the record.

Does anyone else think it's a coincidence that the two people who got killed off a couple of weeks ago on Lost are the same two who just finished up court cases for DUIs they got while filming the show in Hawaii? Yeah, me neither.

I still like Survivor, and still watch it regularly, but here's why Survivor finales will always suck: first, because there is very rarely anyone worth rooting for in the entire cast and second, on the rare occasions when there is someone worth rooting for (like Rupert or this season's Terri), they never make it to the finals because all the other players realize that they stand no chance against the deserving player in a vote and so they get rid of them at the first opportunity.

The producers can usually pick enough weirdos to keep the interpersonal stuff interesting up until the final three or four players, and the process of winowing down the contestants is interesting to watch, but I honestly just don't care who wins—take me up until the moment the final two contestants are solidified and I'm good.

In my office, the last two weeks of May are like the last two weeks of December: we've admitted our class, we've got commencement and Memorial Day coming up (which most people turn into a five-day weekend, since commencement is typically the Thursday before Memorial Day and the university gives us all a holiday because they need our parking spaces for the visitors), and then our summer schedule of vacations and flex time starts. So all we're really doing right now is sitting around waiting for the summer to start, and the few people that show up every day don't really have all that much to do.

It's nice to have a break, but it's so hard to sit inside all day and either pretend to do work or do non-work work like developing summer project plans and doing performance reviews. It's only Wednesday, and we had a half day yesterday for our annual office luncheon, but the days drag by so slowly that it feels like it should be Friday already.

I had a dream last night where I was in the house where I did most of my growing up. It was completely empty, but I was there with some other people (no one from my family) and I found a secret room off of what was likely intended to be a dining room or formal sitting room but which was mostly unused when we lived there (although it did hold a pool table for a brief period).

But when I went into this room, I found that it was more than just a secret room, it was a whole other house inserted in the center of the house that I knew. It even had it's own entrance that you could only use if you were coming from the inside to go outside; you couldn't see it from the outside of the real house unless you already knew it was there.

This other house was cluttered with objects that would normally have been tossed into the attic, and it had terrible brownish-orange shag carpet, but other than that it was a pretty nice space, with lots of big windows (only a small portion of this secret area existing on the same level as the real house; the rest of it seemed to exist on an externally invisible level above the house that I knew).

I don't remember who was with me or why I was there, and I have no interpretation for this dream, other than that it might have something to do with the stressful situation I'm going through with my sister Carrie right now. I'm still very upset about this whole thing, but after my last breakdown about it, I put it away and haven't consciously thought about it until yesterday, when it came up obliquely during a conversation with Julie and I started to get stressed out over it again.

I really don't know how to resolve this situation, but I don't anticipate it ending well. I just hope that, if I can't work things out with her, that it doesn't cost me anyone else in my family, either.

I got my grade for last semester's class, and it's my lowest in the program so far: a B+. This doesn't really come as a surprise to me (although I thought my paper was pretty good), because my professor not only has a Ph.D. in theoretical physics from Oxford, he's also the editor-in-chief of the Hopkins Press, meaning that he has very high standards for both the scientific content of our papers and the way that content is organized and written about. He also didn't seem like the type to have the typical laxity of grad school grading, and he probably only gave out one or two A's out of our class of twenty or so people.

I haven't gotten my comments back from him yet, but I'm guessing that I either got some of the science wrong or didn't cover some aspect of my topic as thoroughly as he would have liked. But like I said, I think it's actually a pretty decent research paper, my best since the modern art class I took a couple of years ago, and it's also about a topic that I think is pretty interesting, so I'm sharing it with you below.


"So Dim a Light":
A Brief History of Olbers' Paradox
and the Dark Night Sky

Why is the sky dark at night? This question seems deceptively easy to answer, especially if you have a solar system-centric view of the universe, which is why no one really asked the question, even informally, until the 1500s, and why it took another couple of hundred years before Wilhelm Olbers formalized the question into the paradox that bears his name in 1823.

The most obvious answer as to why the sky is dark at night is simple: because the sun and its light are no longer in view. And this is a critical piece of the puzzle; without the rotation of the Earth, which causes most points on the face of the planet to be turned away from the sun for approximately half of each 24 hour diurnal cycle, early astronomers would have never had the chance to see the planets, stars, and galaxies that make up the rest of our solar system, galaxy, and universe, much less to formulate the composition and structure of those elements that leads inevitably to the question of why the night sky is dark.

Here is a basic delineation of the paradox: if the universe is filled with an infinite number of stars (or at least a large enough number to cover every point in the night sky), and these stars are uniformly distributed throughout the universe, why then is the night sky not as bright as the daytime sky? In such a universe, every sightline in the night sky would eventually terminate in the surface of a distant star, meaning that your eye would receive photons from every direction, and that therefore the night sky lit by stars would appear to be as bright as the daytime sky which is dominated by the light of our local star, the sun.

But this is obviously not the case; not only is the night sky significantly darker than the daytime sky, there are also vast areas of darkness between the visible stars that call out for some sort of explanation, and as you might have been able to guess from my paraphrasing of the paradox, the explanation for these lightless gaps between the stars has entirely to do with the ideas that the astronomers, physicists, mathematicians, and even poets who have attempted to answer this question have about the characteristics of our universe (size, structure, amount of matter/energy, and age, among other factors). In other words, the riddle of the night sky becomes a cosmological question, and it cannot be satisfactorily resolved until the paradox's resolution is intertwined with a cosmological model that includes in its basic assumptions an explanation of the dark night sky.

By the middle of the 20th century, most physicists believed that Olbers' paradox had been resolved, or at least resolved enough so that further study was mostly unnecessary. But the answer to the paradox had changed by the late 20th century, and even today there is still significant confusion among both the scientific and lay communities as to which factor is the dominant one in explaining darkness at night (although there really is no question; it is a matter of education more than lacking a solid quantitative answer). Additionally, there are still several elements that form part of the complete answer to the question of the darkness of the night sky that remain unresolved today, and the history of how and why this question was asked, what solutions were proposed as answers, and what elements of the full answer have yet to be answered definitively make up a fascinating subhistory of physics since the time of Johannes Kepler.

For many centuries, the absence of the sun was all that was needed to explain darkness at night. In Aristotle's fixed, static universe, the stars were all fixed on a large sphere that encircled the spheres that corresponded to the sun and planets of our solar system. The simple explanation for the gaps between the stars was that there were a limited number of stars on the fixed stellar sphere, and the light from this fixed number of stars was not enough to equal the amount of light put forth by our own sun; hence, the sky was darker at night.

In 1576, Thomas Digges offered a slight change to the Aristotelian model. Digges' father Leonard was the author of a popular astronomical guide called Prognostication Everlastinge, and when this book was republished in 1576, son Thomas added his own essay to his father's work, entitled "A Perfit Description of the Caelestiall Orbes." The main thrust of this essay was to communicate the heliocentric ideas recently introduced by Copernicus to an English-reading audience, but Digges also added his own original thoughts about the fixed sphere of stars that also first raised the question that would eventually come to be known as Olbers' paradox. Digges suggested that this fixed celestial sphere was not a thin layer encircling the other planetary and solar spheres, beyond which was nothing, but rather that the sphere of the fixed stars extended out infinitely, and was filled with an infinite number of stars:

[I]n respect of the immesity of that immoueable heauen, we may easily consider what litle portion of gods frame, our Elementare corruptible worlde is, but neuer sufficiently be able to admire the immensity of the Rest. Especially of that fixed Orbe garnished with lightes innumberable and reachinge vp in Sphaericall altitude without ende. (Digges, "A Perfit Description," reprinted as Appendix 1 in Harrison 1987, 212-213)

But if the model proposed by Digges is accurate, then wouldn't this lead to a bright night sky, the very contradiction described by Olbers' paradox? Remarkably, Digges answers this question in his next sentence with additional information about the stellar sphere:

Of whiche lightes Celestiall it is to bee thoughte that we onely behoulde such as are in the inefioure partes of the same Orbe, and as they are hygher, so seeme they of lesse and lesser quantity, euen tyll our sighte beinge not able farder to reache or conceyue, the greatest part rest by reason of their wonderfull distance inuisible vnto vs. (Digges, "A Perfit Description," reprinted as Appendix 1 in Harrison 1987, 213)

In other words, although the celestial sphere extends infinitely and contains an infinite number of stars, we only see a small fraction of those stars because the rest are too far away for us to see. We now know that Digges' answer in regards to optics is incorrect (although the basic concept bears a striking similarity to one of the modern resolutions to Olbers' paradox), but at the time it seemed perfectly reasonable. As Edward Harrison, a modern Olbers' paradox scholar and physicist puts it in his 1987 work on the history of Olbers' paradox, Darkness at Night: A Riddle of the Universe (which includes Digges' original text as one of its appendices):

What could be more natural, given the state of optical science in the sixteenth century, than the simple idea that the most distant stars, despite their great number, were too faint to be seen? At its birth, the riddle of darkness at night received what seemed a perfectly sensible answer, one which was accepted by many astronomers who followed. (Harrison 1987, 37)

Johannes Kepler, best known for his laws of planetary motion, also believed in Copernicus' heliocentric universe, but he did not accept Digges' ideas on an infinite stellar sphere with an infinite number of stars. Rather, Kepler still adhered to the basic Aristotelian concept of a fixed celestial sphere with a finite number of stars which bounded our solar system and beyond which was nothing. Kepler argued that the varying brightness of the visible stars was not due to the varying distances at which they lay (because Kepler believed that they were all approximately the same distance from Earth), but due to differences in the intensity of their brightness.

As it turns out, a more advanced understanding of optics shows the flaws in both Digges' and Kepler's hypotheses:

Rays of light are slightly scattered, or diffracted, when entering the pupil of the eye or the aperture of a telescope.... Diffraction of light entering the pupil prevents the eye from resolving angles much less than about one arc minute.... A golf ball 150 meters away subtends an angle of one arc minute.... A golf ball at a much greater distance appears to have the same size as at 150 meters.

As a rough guide, we can say that the limit of resolution on a photographic plate in a good telescope is in the vicinity of one arc second. A golf ball at nine kilometers (5 1/2 miles) subtends an angle of one arc second.... The nearest stars subtend angles a thousand times smaller than one second of arc, and all stars, however distant, appear the same size when seen by the unaided eye and with the telescope. (Harrison 1987, 49)

According to this understanding of light and optics, Digges' reason for the patches of dark sky in between the visible stars cannot be right because in an infinite, static universe with an infinite number of stars, even the feeblest light from the most distant stars would reach us and be visible, especially when combined with the light from other light sources that would appear in the same area of the sky (with an infinite number of sources, the meager light from many sources too weak to be seen by the human eye individually would work in concert to create a combined light source that could be detected). And Kepler's conviction that all the stars in the celestial sphere are roughly equidistant from our solar system is wrong because, beyond a certain point, all the light sources will appear to be the same size, even if there are significant differences between their distances from the observer.

Of course, this particular point of Kepler's would not be proven wrong until two centuries later. However, his convictions about the stellar sphere were put to the test again when, in 1609, Galileo created his own telescope and reported many new findings about the heavens, including moons around the planet Jupiter and a multitude of heretofore unseen stars that were not visible with the naked eye. Galileo described these and other discoveries in a work entitled The Starry Messenger, which was published in 1610. Kepler realized that the discovery of this vast number of new stars was a potential threat to the Aristotelian model of a fixed stellar sphere, especially to the idea that the number of stars in the universe was finite (because if there were tens of thousands of new stars visible with the aid of the earliest telescopes, then there could be many, many more—perhaps an infinite number—that could be awaiting discover with more sensitive instruments).

Kepler immediately fashioned a response to Galileo's writings, which was also published in 1610 as a pamphlet entitled Conversation with the Starry Messenger. In this essay, Kepler uses the dark sky to disprove Galileo's conclusions that the stars were bodies similar to our own sun, and that there were vast numbers of them located great distances from our solar system:

Suppose that we took only 1,000 fixed stars, none of them larger than 1 minute of arc (yet the majority in the catalogues are larger). If these were all merged in a single round surface, they would equal (and even surpass) the diameter of the sun. If the little discs of 10,000 stars are fused into one, how much more will their visible size exceed the apparent disk of the sun? If this is true, and if they are suns having the same nature as our sun, why do not these suns collectively outdistance our sun in brilliance? Why do they all together transmit so dim a light to the most accessible places? (Kepler, Conversation with the Starry Messenger, as quoted in Harrison 1987, 50)

If the stars in the celestial sphere were similar in nature to our sun, Kepler argues, then why is the sky not ablaze with their light? Even if you just take the 1,000 or so stars visible with the naked eye, much less the additional thousands reported by Galileo with his telescope, their combined surface area is much greater than that of our sun, which means that they should provide more light during the night than our own sun does during the day. The fact that the night sky was dark was proof to Kepler that the stars in the stellar sphere were smaller and less bright than the sun, which meant that our solar system would get to keep its place of prominence in Kepler's heliocentric conception of the universe.

Kepler's desperate clinging to Aristotle's fixed celestial sphere convinced few, however, and by the latter half of the 17th century, most astronomers believed that the universe was a static body composed of a finite number of stars similar to our sun set varying distances from our solar system, surrounded by a void of nothingness. The dark sky at night was because there were simply not enough stars to cover the sky given the universe's vast size, and that the lightless gaps between the stars were glimpses of the emptiness that lay beyond the universe. There was no need to specifically address the question of darkness at night according to this model of the universe: the answer was simply that there were not enough light sources to light the sky, given the size of the universe.

This explanation isn't entirely correct because that particular model of the universe is not entirely correct, although the size of the universe and the number of stars in the universe are important elements in our modern resolutions of Olbers' paradox. Nonetheless, with the prevalence of this model and its seemingly obvious answer to the question of the night sky's darkness, it was not until a slightly different model of the universe suggested by Isaac Newton became dominant that the question of the dark sky at night was taken up by Edmund Halley.

In his younger years, Newton believed in a universe consistent with the one we just described: a static, finite number of stars surrounded by an empty void. However, after he developed his theory of gravity, it became necessary to believe in a universe of infinite size; otherwise, he believed, the gravity of the bodies in the universe would have long since become attracted to one another and collapsed into a single mass (remember, he still conceives of the universe as static; in our expanding Big Band universe, the initial force from the creation of the universe keeps galaxies moving away from one another rather than collapsing into a single body). In order to reconcile the equilibrium believed to be present in a universe of static, fixed stars, Newton had to adjust his model of the cosmos. Instead of a universe of limited size with a finite amount of stars, he needed an infinite universe with an infinite amount of matter (and therefore stars):

[I]f the matter of our Sun & Planets & ye matter of the Universe was eavenly scattered throughout all the heavens, & every particle had an innate gravity towards all the rest & the whole space through wch this matter was scattered was but finite: the matter on ye outside of this space would by its gravity tend toward all ye matter on the inside & by consequence fall down into ye middle of the whole space & there compose one great spherical mass. But if the matter was eavenly diffused through an infinite space, it would never convene into one mass but some of it convene into one mass & some into another so as to make an infinite number of great masses scattered at great distances from one another throughout all ye infinite space. And thus might ye Sun and Fixt stars be formed. (Newton, "Letter to Richard Bentley," as quoted in Harrison 1987, 72-73).

So in order to reconcile the great masses of planets, solar systems, and galaxies that existed in the universe with Newton's own formulations of gravity (which stated that these clumps of matter should be attracted to one another), Newton needed an infinite number of great masses scattered evenly over an infinite amount of space, so that the attraction that two great masses would naturally have for one another would be offset by equivalent attractions from great masses in other directions. If the universe were made up of an infinite number of matter clusters spread uniformly throughout the infinite universe, the structures like the Milky Way and our solar system would be free to develop within that state of larger equilibrium. Without an infinite amount of mass, the universe would collapse in on itself, because all the matter in the universe would eventually be attracted to and join with other bits of matter, until all the matter in the universe had come together in a single body.

With Newton's reformulation of the universe, the question of the darkness of the night sky once again became relevant, because now there should be an infinite number of luminous bodies. Edmund Halley (of Halley's Comet fame), a contemporary and colleague of Newton's, was the first to reexamine the seeming disparity between a dark night sky and a universe filled with an infinite number of stars. Halley actually offered surprisingly little insight into either the nature of the universe or to the question of the dark sky riddle, but his work on the subject is an important bridge to the work of Jean-Phillipe Loys de Chéseaux. Although Halley's solution was essentially the same one that Digges had proposed more than a century earlier, Halley applied newly discovered mathematical formulas relating to the properties of light and optics that paved the way for Chéseaux's far more rigorous mathematical treatment of the subject, which in turned paved the way for the astronomer for whom the paradox is named, Wilhelm Olbers.

Two short papers that Halley presented to the Royal Society in 1721 (and reproduced as appendices in Harrison's book) directly address the dark sky question. In the first part of each paper, he restates Newton's later conception of the universe: a static, infinite field with an infinite number of uniformly distributed stars, all keeping each other in a state of equilibrium. Given this model, which would mean that any line of sight should eventually terminate at the surface of a star, Halley needs to address the apparent contradiction of the dark night sky:

Another argument I have heard urged, that if the number of Fixt Stars were more than finite, the whole superficies of their apparent Sphere would be luminous, for that those shining Bodies would be more in number than there are Seconds of a Degree in the area of the whole Spherical Surface, which I think cannot be denied. But if we suppose all the Fixt Stars to be as far from one another, as the nearest of them is from the Sun; that is, if we may suppose the Sun to be one of them, at a greater distance their Disks and Light will be diminish'd in the proportion of Squares, and the Space to contain them will be increased in the same proportion. (Halley, "Of the Infinity of the Sphere of Fix'd Stars," reprinted as Appendix 2 in Harrison 1987, 218-219)

In this last sentence, Halley refers to the formula that says that the apparent luminosity of a star, or the area of its disk, is proportional to the reciprocal of its distance squared; this means that if you double your distance from a star, its brightness appears to decrease by a factor of four. In the end, he reverts to essentially the same argument put forth by Digges when he proposed a universe in which our solar system was surrounded by an infinite field of stars:

[T]he more remote Stars, and those far short of the remotest, vanish even in the nicest Telescopes, by reason of their extreme minuteness; so that, tho' it were true, that some Stars are in such a place, yet their Beams, aided by any help yet known, are not sufficient to move our Sense; after the same manner as a small Telescopical fixt Star is by no means perceivable to the naked Eye. (Halley, "Of the Infinity of the Sphere of Fix'd Stars," reprinted as Appendix 2 in Harrison 1987, 219)

This explanation is virtually identical to Digges: the light from the most distant stars is too feeble to reach us, which is why the night sky is not awash in light despite an infinite field of stars sending their light to us from every point in the sky.

In 1743, Swiss astronomer Jean-Phillipe Loys de Chéseaux picked up where Halley left off, although he used much more precise estimates of the distances of the fixed stars and their luminosity, and he used these estimates and the luminosity formula previously discussed to calculate how bright the night sky should be given an infinite universe populated by an infinite number of uniformly distributed stars:

[I]t follows that if starry space is infinite, or only larger than the volume occupied by the Solar System and the first-magnitude stars by the ratio of the cube of 760,000,000,000,000 to 1, each bit of the sky would appear as bright to us as any bit of the Sun, and therefore the amount of light received from each celestial hemisphere—one above and the other below the horizon—would be 91,850 times greater than what we receive from the Sun. (Chéseaux, "On the force of light and its propagation in the ether, and the distances to the fixed stars," reprinted as Appendix 3 in Harrison 1987, 221)

So how does Chéseaux explain this apparent contradiction between the math and the observed reality? In a completely new way, one that would eventually lead to the solution proposed by Wilhelm Olbers:

The enormous difference between this conclusion and experience demonstrates either that the sphere of fixed stars is not infinite but actually incomparably smaller than the finite extension I have supposed, or that the force of light decreases faster than the inverse square of distance. This latter supposition is quite plausible; it requires only that starry space is filled with a fluid capable of intercepting light very slightly. (Chéseaux, "On the force of light and its propagation in the ether, and the distances to the fixed stars," reprinted as Appendix 3 in Harrison 1987, 221-222)

Rather than simply assuming that rays of light from the most distant stars are too weak to reach us, even when combined with the light from an infinite number of other distant sources of light, Chéseaux offers up the possibility that there is some sort of intervening matter that causes the luminosity of the stars to decrease at a rate much greater than the inverse square of distance.

This was an important step forward in resolving the dark sky riddle given Newton's model of the cosmos, and led to Olbers very similar construction of the problem and very similar solution. His one important contribution was his belief that a perfectly equal distribution of an infinite number of stars was not necessary to maintain Newton's equilibrium; rather, the same equilibrium could be achieved with clusters of matter containing the stars, such as our solar system or our galaxy; as long as these larger clumps of matter were arranged correctly, you could achieve the same equilibrium, and you would still have the riddle of the darkness of the night sky to contend with. Here is Olbers' solution to the paradox that bears his name, from a paper published in 1823:

In our inferences drawn from the hypothesis that an infinite number of fixed stars exists, we have assumed that space throughout the whole universe is absolutely transparent, and that light, consisting of parallel rays, remains unimpaired as it propagates great distances from luminous bodies. This absolute transparency of space, however, is not only undemonstrated but highly improbable. (Olbers, "On the transparency of space," reprinted as Appendix 4 in Harrison 1987, 225)

Olbers, too, suggests that it is the lack of absolute transparency of space that causes the sky at night to be dark; without specifying the nature of the intervening matter that absorbs the distant starlight or offering any proof as to its existence other than the night sky itself, Olbers seems to consider the matter to be settled.

Chéseaux's and Olbers' comparable ideas about some type of matter that intercepts and absorbs light, preventing it from reaching earth, falls apart in the face of conservation of energy; over time, the matter absorbing the light would theoretically be heated and start to give off luminous radiation of its own. Even if the starlight was transformed from visible light into some other form of radiation by this pervasive, unknown matter, it would still emit some sort of radiation, and all that extra radiation in the sky would have significant effects for observers on Earth, even if that radiation was not detectable as light in the visible spectrum. The absorption claims put forth by Chéseaux and Olbers were refuted regularly over the years by scientists such as John Herschel, Edward Fournier d'Albe, and Hermann Bondi (who all had their own ideas about the resolution to the paradox, and who therefore needed to eliminate Olbers' absorption hypothesis before laying out their solutions), as the law of conservation of energy was formulated and came into sharper focus.

Chronologically, Lord Kelvin offers the next significant quantitative insight into the resolution of Olbers' paradox, but his ideas as it related to this problem were not widely known or widely accepted in his own time, even though they were to eventually form the basis for one of the two prevailing modern solutions to the riddle. (I am choosing to skip past the discussions of a hierarchical solution to the paradox, since these solutions seem absurd even given our more limited knowledge of the structure of the universe in the 19th century; these solutions feel like relics from Newton's infinite, perfectly distributed universe, which required equal spacing between stars or clusters of matter of roughly equal density, and we have yet to see any proof that a rigid hierarchical structure required by these models exists in our universe.) Instead, we jump ahead to the mid-20th century, after Einstein's equations on general relativity and the curved nature of space had become dominant in our conception of the universe. These equations required a non-static universe—either expanding or contracting—as opposed to the static, unchanging universe of earlier models, and observation soon proved that the universe was in fact expanding. It is the writings of Hermann Bondi, whose popular Cosmology explored the nature of the expanding universe, that give us our next solution to the riddle of the dark night sky in terms of popular acceptance by the scientific community, and it is to his work that we will turn our attention before returning to Kelvin by way of Edward Harrison.

It is appropriate that we are looking at Bondi after Olbers, since it is Bondi who is thought to have popularized Olbers' paradox as the name of the dark sky riddle. Bondi was one of the primary supporters of the steady state model of the universe, which was a rival of the big bang theory for a time, and which states that the universe is infinitely old, has existed in the same conditions that we can observe today (meaning that all the stars we can see shining have been burning at that same intensity for the whole of creation), and that new matter is being created as the universe ages in order to keep the average density of the universe the same as it continues to expand.

The main argument offered by the expanding steady state universe as to why the sky is dark at night is that, because the universe is expanding and most celestial bodies appear to be moving away from us, the light from those bodies gets redshifted to the point where it is too faint to be detected. Even when the steady state model was disavowed by most cosmologists by the discovery of uniform background radiation in 1965, many still considered the redshift argument sufficient to explain the darkness of the sky at night. Harrison explains how strongly this argument took hold:

Go out at night, astronomers urged members of their audience, and look up at the dark starlit sky. Although countless stars cover the sky, you will see relatively few because most are reddened into invisibility by the expansion of the universe. The darkness of the night sky proves that the universe is expanding. Here was a theme, prefaced with a few words about the Doppler effect, that captured the imagination of a wide audience. Some astronomers went so far as to claim that the expansion of the universe was the necessary as well as the sufficient condition for a state of darkness at night. (Harrison 1987, 192)

Even though Harrison acknowledges that this argument might be valid in an expanding steady state universe, he realized that it just wouldn't work for a big bang universe with a finite beginning, a finite amount of mass, and in which stars emitted visible radiation for only a limited amount of time. Harrison approached the problem from a different angle to find his solution for the dark night sky: instead of looking for reasons why the energy from distant stars was not reaching us on earth, he turned the problem on its head and instead calculated the amount of energy that would be required to create a bright sky at night and comparing that to the energy available in the entire universe based on our best estimates:

[When we] annihilate all matter in its various forms everywhere in the universe and convert it to thermal radiation..., we find that the radiation has a temperature of about only 20 degrees Kelvin.... This temperature is very much less than the 6,000 degrees Kelvin at the surface of the Sun. Thus, all the energy in the universe in the form of matter, when transformed into thermal radiation, still falls a long way short of creating the intensely bright starlit sky feared by Halley, Chéseaux, Olbers, and many other astronomers. Independently of whether the universe is expanding, contracting, or remaining static, a bright starlit sky requires 10 billion times more energy than can be obtained by the drastic measure of converting all matter into radiation. (Harrison 1987, 196-197)

As far as Harrison is concerned, this is the only solution that is needed, and this is essentially the same solution that he published in his 1965 paper, "Olbers' Paradox and the Background Radiation Density in an Isotropic Homogeneous Universe." His 1987 book, Darkness at Night: A Riddle of the Universe, from which the above quote is taken does a masterful job of reviewing the history of the paradox, and includes several appendices of primary sources that are difficult to locate elsewhere. Even though he acknowledges that there are other factors that may contribute to the darkness of the night sky, the energy solution (as he refers to this argument) is all you really need to resolve the paradox: "The energy solution shows that there is not enough energy in the universe to create a bright starlit sky. This solution overrides all other proposed solutions." (Harrison 1987, 197).

However, there is another important modern resolution to Olbers' paradox that is usually considered hand in hand with the energy solution, because this solution is applicable in a universe with a finite age, or at least in a universe in which the stars have been shining for a finite amount of time and with sufficient distances between the stars such as the one suggested by the current prevailing big bang model. This resolution needs only three basic ingredients: a limit on the speed of light, which has been known since the 17th century, a certain amount of distance between our planet and the vast majority of stars in the universe, and the knowledge that the universe has existed for less than a certain finite amount of time. Given these elements, you need not focus on the light from stars scattered throughout the universe, but rather only those that exist within the visible universe, because any star that is farther from us in light years than the age of the universe would be impossible to detect; its light would not have had time to reach us yet. This explanation is generally known as the finite age resolution.

Curiously, although this solution has been accepted as one of the correct solutions by modern cosmologists, it was actually presented by three figures from the 19th century whose comments on the subject don't seem to have been widely accepted during their own time, but whose writings were dug up by modern cosmologists, who realized that their solutions were essentially correct. In the game of assigning credit for the first correct solution, each has their champions, and so I will present them chronologically.

The first, fascinatingly enough, comes from Edgar Allan Poe's "Eureka: A Prose Poem," which details Poe's scientific and metaphysical views. "Eureka" was based on a lecture entitled "On the Cosmogony of the Universe" given in New York in 1848, and the poem itself was published later that same year. The portion most relevant to Olbers' paradox follows:

Were the succession of stars endless, then the background of the sky would present us an uniform luminosity, like that displayed by the Galaxy—since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under a such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all. (Poe, "Eureka," as quoted in Cappi 187)

And there you have it: the earliest known statement of the finite age solution. Although many modern cosmologists writing on Olbers' paradox acknowledge Poe's contribution, they seem unwilling to give him full credit for coming up with the first correct resolution of the paradox because his solution does not offer any quantitative data that can be reviewed and analyzed. Nonetheless, Poe solution is essentially correct, and Alberto Cappi goes to great lengths to give Poe credit for this and other scientific ideas from "Eureka" in his 1993 essay "Edgar Allan Poe's Physical Cosmology."

Another individual whose contributions to solving the riddle of the dark sky are even more overlooked than Poe's is German astronomer Johann Heinrich Mädler, whose discussion of the paradox in the 5th edition of his popular book Der Wunderbau des Weltalls, oder Populäre Astronomie also seems to yield the finite age solution:

The velocity of light is finite; a finite amount of time has passed from the beginning of Creation until our day, and we, therefore, can only perceive the heavenly bodies out to the distance that light has traveled during that finite amount of time. (Mädler, Der Wunderbau des Weltalls, oder Populäre Astronomie, as quoted in Tipler 316)

This revision was added in 1861, a scant 13 years after Poe's "Eureka", and Mädler's champion F.J. Tipler goes to great lengths to take credit away from Poe by highlighting incorrect elements elsewhere in "Eureka" and trying to convince the reader that Poe's general cosmology is so flawed that he ought not be given credit for correctly explaining the dark night sky. Nevertheless, Poe's statements about the night sky do not depend on his cosmology being absolutely accurate, and taken on their own, it is clear that these statements are in fact what has come to be known as the finite age resolution of Olbers' paradox. One can't help but feel there is a little interdisciplinary rivalry at work behind Tipler's need to discredit Poe; Tipler seems intent on giving credit for the first correct solution to the paradox to a fellow scientist rather than a scholar better known for his fiction, poems, and essays than his scientific musings.

The final 19th century figure who proposed the finite age solution is also the most well-known: Lord Kelvin. Despite Harrison's acknowledgement of Poe's solution, he, too, seems to want to give credit to a fellow scientist who provides quantitative data and scientific analysis rather than to a humanities-centered theorist, and it is Kelvin who gets credit in Harrison's 1987 book on Olbers' paradox, Darkness at Night, for being the first to provide a rigorous finite age solution. Kelvin's ideas were originally presented in a series of lectures at Johns Hopkins University in 1884, and were later published in 1904 as Baltimore Lectures, a volume that revised and expanded upon the lectures given in 1884. His additions to the discussion include empirically derived estimates as to the size of the visible universe, the distances between the stars, the number of stars (both luminous and non-luminous), and the visible lifetime of stars, as well as equations which took these factors and showed that there were simply not enough stars shining in the visible universe to produce a bright sky at night. One of Kelvin's solutions is the finite age solution, and Harrison seems inclined to give Kelvin credit for the first quantitative proof of Poe's qualitative musings.

Given that the same solution to Olbers' paradox was put forth by three widely read cultural figures long before the discovery of the expanding universe and the redshift explanation trumpeted by Bondi, it is surprising that the finite age resolution was not more widely accepted (or at least considered seriously) at an earlier date. The acceptance of the finite age solution coincides with the energy solution proposed by Harrison in 1965, the same year that the detection of uniform cosmic background radiation confirmed the big bang theorists' assertions that the universe has a finite age. It seems that the idea of a universe that was infinitely old, an idea that had existed from the time of Aristotle, was simply too entrenched for most astronomers to let go of it until confronted with unassailable proof that the universe has existed for a finite amount of time (indeed, the main rival to the big bang model before 1965 was the steady state model, which required a universe of infinite age in which all the stars in the universe have been burning with their current brightness, a model that has more in common with Aristotle's model than its advocates might care to admit).

When Harrison published his book Darkness at Night in 1987, it was pretty clear that he considered the riddle of Olbers' paradox solved, and that his book, with its inclusion of religious and philosophical history alongside the scientific history (although in previous eras there was not nearly as much distinction between these disciplines as we seem to have now) was meant to provide a start-to-finish review of the subject. It is something of an irony, then, that this is the same year that Paul S. Wesson published his article on Olbers' paradox, "The Extragalactic Background Light and a Definitive Resolution of Olbers's Paradox." The purpose of this article is not to introduce an alternative theory, but rather to confirm Harrison's findings that the energy and finite age solutions are the correct ones, and that although redshift contribution from the expansion of the universe contributes to the dark night sky, its significance pales in comparison to Harrison's solution. Or as Wesson put it: "The intensity of intergalactic light is determined to order of magnitude by the lifetime of the galaxies and is only reduced by a factor of about 2 by the expansion of the universe." (Wesson 1987, 606)

The coincidence of Harrison's book and Wesson's article being published in the same year represents a passing of the torch, for Wesson continues to write regularly about Olbers' paradox, its correct resolutions given our current understanding of the universe, and the misperceptions about the paradox (particularly the relative unimportance of the redshift as a resolution to the paradox) among both science professionals and laypersons.

Given how many times our understanding of the universe has changed in such a significant way that we were forced to return to the riddle of the dark night sky and offer a new resolution based on our most recent model of the universe, declaring the paradox resolved should not be done lightly. However, I stand with Harrison and Wesson in saying that the paradox has now been resolved, due primarily to the energy and finite age solutions (although absorption, hierarchy, and redshift, all of which were proposed as solutions at one point, could be/are contributing factors, either of the energy or finite age solutions is sufficient to resolve the paradox in the universe as we now understand it). What makes me more confident in these solutions is that they are based on much more accurate and a much higher volume of data than any of the solutions that came before them; it would take a significant increase in the estimated amount of matter in the visible universe to override the energy solution, and likewise, a significant increase in the age of the universe and the number of luminescent stars in the visible universe to overturn the finite age theory. Although anything is possible in the world of science (even considering only the last 50 years, we have seen major changes to our model of the universe on both a macro and a micro level, and there are still many significant discoveries awaiting the invention of new detection devices and/or the insight of our legions of scientists), and one of the themes of this course was the irony in the title of our primary text, "The Tests of Time," it seems unlikely that new data would change our model of the visible universe to the degree needed to invalidate the energy or finite age resolutions to the dark night sky riddle posed by Olbers' paradox.

And as for who I think deserves credit for coming up with the first correct modern resolution to Olbers paradox? As an English major with a particular interest in 19th century American literature, and because his solution is chronologically the earliest, I have to go with Poe. But because I believe that convincing one's peers that you have the correct answer is just as important (if not moreso) than simply arriving at the correct answer, significant credit needs to be given to Edward Harrison and Paul Wesson; Harrison for being the first to popularize the energy solution and to recognize the validity of the finite age solution; and Wesson for quantitatively demonstrating the significance of these solutions in relation to other possible contributing factors, and continuing to work to correct misconceptions about the paradox and its resolutions among both his peers and the lay scientific community.


Arpino, Maurice, and Fabio Scardigli. "Inferences from the dark sky: Olbers' paradox revisited." European Journal of Physics 24 (2003): 39-45.

Cappi, Alberto. "Edgar Allan Poe's Physical Cosmology." Quarterly Journal of the Royal Astronomical Society 35 (1994): 177-192.

Chéseaux, Jean-Phillipe Loys de. Traité de la Comète. Lausanne: Bousquet et Compagnie, 1744, appendix 2, 223-229. Reprinted in Edward Harrison, Darkness at Night: A Riddle of the Universe, 221-222. Cambridge, Massachusetts: Harvard University Press, 1987.

Digges, Thomas. "A Perfit Description of the Caelestiall Orbes." In Prognostication Everlastinge. London, 1576. Reprinted in Edward Harrison, Darkness at Night: A Riddle of the Universe, 211-217. Cambridge, Massachusetts: Harvard University Press, 1987.

Halley, Edmund. "Of the infinity of the sphere of fix'd stars." Philosophical Transactions 31 (1720-1721): 22. Reprinted in Edward Harrison, Darkness at Night: A Riddle of the Universe, 218-219. Cambridge, Massachusetts: Harvard University Press, 1987.

Halley, Edmund. "Of the number, order, and light of the fix'd stars." Philosophical Transactions 31 (1720-1721): 24. Reprinted in Edward Harrison, Darkness at Night: A Riddle of the Universe, 219-220. Cambridge, Massachusetts: Harvard University Press, 1987.

Harrison, Edward R. "Olbers' Paradox and the Background Radiation Density in an Isotropic Homogeneous Universe." Monthly Notices of the Royal Astronomical Society 131 (1965): 1-12.

Harrison, Edward R. Darkness at Night: A Riddle of the Universe. Cambridge, Massachusetts: Harvard University Press, 1987.

Harrison, Edward R. "The Dark Night-Sky Riddle, 'Olbers' Paradox.'" In The Galactic and Extragalactic Background Radiation, 3-17. Dodrecht, Holland: Kluwer Academic Publishers, 1990.

Moore, G.S.M. "Resolution of Olbers' Paradox for Fractal Cosmological Models." Progress of Theoretical Physics 87, No. 2 (1992): 525-528.

Olbers, Wilhelm. "Ueber die Durchsichtigkeit des Weltraumes." In Astronomisches Jahrbuch für da Jahr 1823, ed. J.E. Bode. Berlin: Spächen, 1823. Trans. "On the transparency of space." Edinburgh New Philosophical Journal 1 (1826): 141. Reprinted in Edward Harrison, Darkness at Night: A Riddle of the Universe, 223-226. Cambridge, Massachusetts: Harvard University Press, 1987.

Overduin, J.M., and Paul S. Wesson. Dark Sky, Dark Matter. Bristol and Philadelphia: Institute of Physics Publishing, 2003.

Pegg, David T. "Night Sky Darkness in the Eddington-Lemaître Universe." Monthly Notices of the Royal Astronomical Society 154 (1971): 321-327.

Tiper, F.J. "Johann Mädler's Resolution of Olbers' Paradox." Quarterly Journal of the Royal Astronomical Society 29 (1988): 313-325.

Wesson, Paul S., and K. Valle and R. Stabell. "The Extragalactic Background Light and a Definitive Resolution of Olbers's Paradox." The Astrophysical Journal 317 (1987): 601-606.

Wesson, Paul S. "The real reason the night sky is dark: Correcting a myth in astronomy teaching." Journal of the British Astronomical Association 99, No. 1 (1989): 10-13.

Wesson, Paul S. "Olbers's Paradox and the Spectral Intensity of the Extragalactic Background Light." The Astrophysical Journal 367 (1991): 399-406.

Not that too many of you will care, but my raiding group downed Nefarion, the final boss in a very tough 40-man raiding instance, for the first time last night, which is a major accomplishment—there are only four other groups on our server on our faction that have acheived this, and all the others are hardcore raiding groups that raid 4-6 times a week (as opposed to our two scheduled nights).

I can't back it up with absolute data, but I'm pretty sure we were the fastest group to do this as well—the group that finished right before us was in the instance 6-8 weeks ahead of us, and they only dropped Nef two weeks before we did (and it would have only been one week if we had been a little better prepared on our last shot at him—there was one weak spot in our strategy that we have since corrected).

Like I said, I doubt too many people who read this will care, but this is the culmination of months of teamwork for our raid group, and it's a major accomplishment for us.

Mom was in town on business again this past weekend, so Dodd, Julie, and I met her on Saturday to see some museums and hang out. I mainly wanted to see the japanese prints at the Freer, but we were also thinking about visiting the American history museum, since it's scheduled to close in September for two years of renovations. We did take some time to look around the Freer but it was such a nice day that we mostly ended up just walking around the mall and sitting outside of museums rather than going inside them. (I'm always amazed at how much time Dodd spends examining things in museums, especially since he doesn't seem all that interested in art, etc. Me, I've got attention deficit in museums—I see something I like and I spend time with that and skip everything else, but Dodd really takes his time to give each object/painting a chance, which is impressive.)

During lunch Dodd gave us his big news: he was accepted into law school at the University of Baltimore, and he'll be starting their part-time program in the fall, attending evening classes while continuing to hold his full-time job. It's very cool that he's finally going to take a shot at this—being a DA has been his dream job since he interned at the DA's office in our hometown during his college years—and this situation is just about perfect for him, since the school is already on his commuting route and the fact that he'll be working full-time hopefully means that he won't have to go into too much debt. Congratulations, little brother—you've got some hard work ahead of you, but if this is truly what you want, then that's all that's standing between you and your goal.

For some crazy reason, Hopkins always holds its commencement ceremonies on a Thursday, usually the Thursday before Memorial Day weekend. And since they don't need all the pesky staff hanging around taking up valuable parking spaces, they make us use one of our two floating holidays on that day.

Usually that's a very good thing—you throw in another vacation day on Friday, and you've got yourself a nice five day weekend for the cost of a single vacation day. Occasionally, Julie has taken these days off, too (she doesn't work on the main campus, so she's not subject to the same holiday schedule we are), and we've taken a trip somewhere. This year, however, we're not planning to go anywhere because we've got our tenth anniversary trip coming up in a couple of weeks, and since Julie's not taking any days off, I've got a choice to make: either take that extra day and have a nice long weekend with two days to myself (during the day, anyway), or go in on Friday and save that vacation day for another time.

Given the fact that there's not a whole lot to do at work these days—still waiting for our summer projects schedule to get firmed up—I'm tempted to take the day off, but the fact that I'd just go in and bascially do whatever I wanted for 8 hours makes the decision that much harder, because it seems silly to take a vacation day when I'm not going to be working that hard in the first place.

Anyway. Depending on what I decide, I may or not be posting here for a few days, because as is my custom, if I'm on holiday/vacation, then I don't typically post here. So you'll be able to discern my decision by whether or not there are any new posts here for the next five days.

A nice five-day holiday weekend, followed by a short week of only four days at work, followed by another week off for vacation. This is what summer's all about...

Another gem of a line from a spam email, this one from the subject line:

If it weren't for physics and law enforcement, I'd be unstoppable.

You and me both, brother.

Finally, a great night at Camden Yards watching the O's. Although the weather was unseasonably warm, and we were watching Rodrigo Lopez start for the fourth time this season (want to guess how many games we've been to this year? I'll give you a hint: it's more than three but less than five), the Orioles went up two runs in the first inning and never lost the lead again, although the win was never certain. Each time the Orioles would score, the Devil Rays would answer with runs of their own in the next inning.

When the game finally reached the ninth inning, the O's were up by two runs, and the closer, Chris Ray, sent the first two Devil Rays back to the dugout in short order. But then he walked the next batter, putting the tying run at the plate, and the Devil Rays brought up a lefty pinch hitter, Greg Norton, to face right-handed Ray. Ray got him to at least one strike, and then the impossible happened: the ball soared to deep left center, looking for all the world like a game-tying homerun. But then the impossible happened again: Orioles center fielder Corey Patterson leaped and grabbed the ball from over the wall, saving a homerun and his team's win. The icing on the cake: it was Patterson's two solo homeruns in the sixth and eighth innings that were the difference in the 7-5 final score.

It was just a perfect baseball night. Those are rare enough no matter which team you're watching, but they've been especially hard to come by for the O's as of late. I'm happy we got to have at least one this season.
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