Now Playing Tracks



By: Mike Lacker, McSweeney’s

For many years, I have remained a presence in the shadows. You citizens of the Internet have gone about your lives, navigating to this page and that, reading articles, watching videos, exchanging messages with friends, but all the while a single question has clawed at your curiosity each time your focus breaks and you notice the garish blinking ads strewn about your web pages:

Who, who is it that clicks these banner ads?

The time to wonder has ended and the time has come to open your eyes and to see the truth, to discover who has been clicking that which you so often ignore. 

It is I who click the banner ads.

While you check the weather, I find out why California dermatologists hate the one weird skin care secret discovered by a stay-at-home mom. While you read the New York Times, I rollover for more information about how to get my diabetes under control. While you search IMDB, I click for showtimes, tickets, and behind-the-scenes videos for Think Like a Man. Page after page, banner after banner, I click and I click.

It is not for myself that I click these banner ads, not because I yearn for exclusive local deals and belly fat-reducing tips. No, it is for all of you that I click to learn more, rollover to expand, and tap to download. Without me, your banners would go unclicked. And if your banners go unclicked, then who will pay for your web pages? Banners are the steam engine of the Internet, and I must shovel coal into the fiery maw.

It may be a sacrifice, to labor hour after hour, day after day, month after month in my secret lair, one hand on a mouse, the other on an iPad, furiously clicking and tapping every banner ad I can find. My ears have been calloused by movie trailers with autoplaying sound. My eyes have been warped and reddened by live streams of red carpet events presented by auto manufacturers. My hands have turned to gnarled claws from all the cartoon monkeys I have punched. My computer is but a shuddering pile of tracking cookies and spyware following my every move so that the next advertisement I see is slightly better targeted to my gender, age, and browsing history.

Some may see me as a tragic husk, obsessed with duty but without friendship, without warmth, and without love for anything but all of you who I labor so hard to keep safe. I may have hundreds of free ringtones, thousands of exclusive promotional desktop wallpapers, and millions of special offer codes, but what good is a printable coupon for one dollar off a family-sized Stouffer’s chicken lasagna when you have no family?

But a hero is more than himself. I am the thin gossamer line between a free, sprawling internet and an oppressive desert bound in barbed wire and ruled by dollar-hungry warlords. Without me clicking to learn how New York drivers are saving hundreds on car insurance, you would be paying for what you are reading right now, throwing precious coin down an endless digital well.

So if you see a targeted text advertisement for debt reduction next to your email, know that I am there. If you see an animated custom background for the Call of Duty franchise, know that I am there. If you see a three-dimensional computer-animated dog run across the page and cover the video you are watching about dog food, know that I am there. Now get back to your reading, your posting, your downloading. The night will soon be over and there are still hundreds more credit card offers I must post to my wall.


Thomae’s function, named after Carl Johannes Thomae, also known as the popcorn function, the raindrop function, the countable cloud function, the modified Dirichlet function, the ruler function,[1] the Riemann function or the Stars over Babylon (by John Horton Conway) is a modification of the Dirichlet function. This real-valued function f(x) is defined as follows:

  \frac{1}{q}\mbox{ if }x=\frac{p}{q}\mbox{ is a rational number}\\
  0\mbox{ if }x\mbox{ is irrational}. 

If x = 0 we take q = 1. It is assumed here that gcd(pq) = 1 and q > 0 so that the function is well-defined and non-negative.


The popcorn function is perhaps the simplest example of a function with a complicated set of discontinuitiesf is continuous at all irrational numbers and discontinuous at all rational numbers.

Informal Proof

Clearly, f is discontinuous at all rational numbers: since the irrationals are dense in the reals, for any rational x, no matter what ε we select, there is an irrational a even nearer to our x where f(a) = 0 (while f(x) is positive). In other words, f can never get “close” and “stay close” to any positive number because its domain is dense with zeroes.

To show continuity at the irrationals, assume without loss of generality that our ε is rational (for any irrational ε, we can choose a smaller rational ε and the proof is transitive). Since ε is rational, it can be expressed in lowest terms as a/b. We want to show that f(x) is continuous when x is irrational.

Note that f takes a maximum value of 1 at each whole integer, so we may limit our examination to the space between  \lfloor x \rfloor and  \lceil x \rceil. Since ε has a finite denominator of b, the only values for which f may return a value greater than ε are those with a reduced denominator no larger than b. There exist only a finite number of values between two integers with denominator no larger than b, so these can be exhaustively listed. Setting δ to be smaller than the nearest distance from x to one of these values guarantees every value within δ of x has f(x) < ε.


We’re in Chicago next week for the AWP writers conference and will be throwing a happy hour for Tumblr writers of all stripes. We’d love to see you there.

The venue, Uncharted Books, is a new bookstore funded on Kickstarter which had a Tumblr blog before it was born. It’s a dream spot for book-web-community nerds and we absolutely can’t wait to see it (and all of you.)

from the short story “A Clean, well-lighted place” by Hemingway. Well worth a read.

(Source: rachelfershleiser)

We make Tumblr themes