David Iglesias

OS X: If you see a color on the web or in an app that you particularly like and want to save for later, Sip makes it incredibly fast and easy to store it for later use.

Sip lives in your menu bar, but you can invoke it at any time with a customizable keyboard shortcut. Activate the app, and you'll get a magnifying glass to zoom in on any pixel on you screen. Click on the one you like, and its color code will copy to your clipboard to use in the image editor of your choice. You can choose your preferred color code format (CSS Hex values, CMYK, RGB, etc.) in the app's settings, and switch between your favorites quickly in the menu bar dropdown. If you're looking for something similar on Windows, Instant Eyedropper is an oldie but goodie.

Sip ($.99) | Mac App Store via One Thing Well

Mac: When you're setting up a new computer, one of the most time-consuming things you have to do is customize all your software and tweak application settings. Mackup is a utility that backs up your application settings to Dropbox so you can easily migrate them between computers.

Mackup works entirely in the Terminal, and once it's installed requires just a single line to make a backup of your settings to Dropbox. When you're done, you can do the same on your new computer to import all your settings. It only brings in your configuration settings, so you don't have to worry about temp files or cache coming over as well. If you're migrating your settings over to a new computer, or you just want to keep a backup of them, Mackup works great.

Mackup (Free) | via One Thing Well

User interfaces remain one of the most fascinating elements of visual science fiction. They need to tell us something about what characters are doing (whether it's aiming a weapon or tracking a criminal, apparently the two most common activities in the future) and something about what the world finds aesthetically appealing, all in a way that's immediately understandable to people in the present. While most stay firmly in the future past, others have had a massive — some would say pernicious — impact on how we use technology in the real world. Even so, the designs often appear for only a few seconds onscreen, but the VisualPunke tumblr has collected them in an ongoing series of beautiful, often frenetic images from anime, video...

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This past weekend, you relived the wonder of Jurassic Park and remembered the first time you saw convincing CG effects on screen. But Jurassic Park built on a long legacy of computer innovation, more than a decade and a half of on-screen computer effects. Here are 10 landmarks of early CG, many of which still look great.

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Long distances (and big numbers) can be difficult grasp. Designers Jesse Williams and David Paliwoda took a stab at it and made it easier to understand the distance from Mars. Simple and totally fun. I'm not sure how accurate the travel time and distance are, but I'm guessing it takes differing orbits into account.

I suspect that the video game industry's obsession with DARKER, MORE "MATURE" STORY might have influenced the way I look at stuff like this gritty re-imagining of Calvin and Hobbes by GrittyReboots.

Like, it doesn't need to be grittier and darker. But everything is nowadays! So I could totally see this type of Calvin and Hobbes working. I mean, the idea is clever, eh? What if it's not just having an active imagination but rather satanic visions or something? It sounds ridiculous, I know, but with the right writing, it kind of works.

Calvin and Hobbes: The Movie (Fan Trailer) [GrittyReboots]

Movies are getting prettier all the time. Thanks to computer animation, IMAX cameras, 3-D and a million other innovations, we can now create films that tower like candy palaces. But that just means it's easier for movies to be pretty but dumb. Here are 12 films that are lovely to look at, but totally braindead.

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If you listen to the radio long enough, you've probably noticed that many songs sound similar or remind of you of a song you've heard before. Hooktheory shows you just how similar some songs are via chord progressions in over 1,300 songs. The small group analyzed the data last year and presented some static charts, but this interactive version takes it a step further.

Simply start by selecting a chord in the network diagram. Songs that use that chord appear on the right. Then select another chord in the network diagram to find songs that use the chord progression from the original to the new. Keep selecting chords to filter further.

So in the end, there are two main things you can do: (1) Find songs that use the same chord progression and (2) see the most likely chord given the current selection.

My musical knowledge from middle school jazz band is long gone, but it's fun to explore, and you'll likely find relationships to songs that you didn't expect. [Thanks, Dave]

Bran Stark, Sana Stark, Catelyn Stark, Arya Stark, Roz, Melisandre, Samwell and Hot Pie (HOT PIE!!!) decided to regale the crowds at the red-carpet premiere with their own striking rendition of the iconic Game of Thrones opening them, courtesy of MTV Geek. It's fun, but you need to watch it mostly to see how hard Bran's actor, Isaac Hempstead-Wright, was hit by the puberty stick.

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We may be celebrating Pi Day here at io9, but we would be irrational to deny that there’s more to mathematical interestingness than simply dividing an object’s circumference by its diameter. Here are seven numbers we love as much as pi. Pi.

1. 1

1 may be the loneliest number, but it’s the littlest number that could — the first non-zero integer that displays remarkable properties of self-reliance. Aside from being the first whole number, it is its own square, cube, and factorial. It’s also very stubborn; when you raise 1 to any power — even a number as high as a googolplex googleplex (1 followed by 10 to the 100th power, or 10^(10^100)) — you still get 1. It's the first and second number in the Fibonacci sequence. It Is is neither a composite number, nor a prime number (mathematicians rejected this idea because it complicates fundamental theorems of arithmetic). It is, however, a unit (like -1). And it’s the only positive number that’s divisible by exactly one positive number.

2. i

Any number that doesn’t actually exist, but is still useful, has to be considered cool. Also called the imaginary unit, i is the square root of -1 (i² = -1). This number cannot exist because no number multiplied by itself can equal a negative number.

At first, imaginary numbers were considered useless (an imaginary number is a number that, when squared, gives a negative result; e.g. 5i = -25). But by the Enlightenment Era, thinkers began to demonstrate its value in math and geometry, including Leonhard Euler, Carl Gauss, and Caspar Wessel (who used it when working with complex planes). They’re useful in that they can be used to find the square root of a real negative number.

Today, i is used in signal processing, control theory, electromagnetism, fluid dynamics, quantum mechanics, cartography, and vibration analysis. The figure j is often substituted in these fields, which is used to represent the electric field current. The imaginary number also appears in several formulas, including the Euler Identity.

As an aside, Isaac Asimov’s short story “The Imaginary” (1942) featured the eccentric psychologist Tan Porus who explained the behavior of a mysterious species of squid by using imaginary numbers in the equations which describe its psychology.

3. Graham's Number

Simply put, this is the largest useful (i.e. non-arbitrary) number known to mathematicians. But it’s an astoundingly large number. Named after Ronald Graham, it’s the upper bound to a certain question that involves Ramsey Theory (a branch of math that studies the conditions under which order must appear). Consequently, it’s the biggest number used for a serious mathematical proof.

This number’s “root” arises from the extreme addition, multiplication, and powering of threes. It’s subsequently a very big power of three, and the number itself is considerably larger than a googolplex. googleplex. In fact, Graham’s number is so mindboggingly huge that it cannot be expressed using conventional notation of powers, and even powers of powers. It’s so large, that if all the material in the universe were turned into pen and ink it would not be enough to write the number down. Consequently, mathematicians use a special notation devised by Donald Knuth to express it.

It’s so big that it’s physically impossible for our brains to comprehend. AI theorist Eliezer Yudkowsky put it this way:

Graham's number is far beyond my ability to grasp. I can describe it, but I cannot properly appreciate it...My sense of awe when I first encountered this number was beyond words. It was the sense of looking upon something so much larger than the world inside my head that my conception of the Universe was shattered and rebuilt to fit. All theologians should face a number like that, so they can properly appreciate what they invoke by talking about the "infinite" intelligence of God.

Interestingly, if not ironically, the lower bound actual answer to the Ramsey problem that gave birth to that number — rather than the upper bound — is probably six. Note: A reader alerted me to this study, which suggests a lower bound raised to 11, and then to 13.

4. 0

The number 0 is totally taken for granted, which, when considering that it represents nothing, is somewhat understandable. But it does serve some important functions, including as an empty place-value in our decimal number system. How else, for example, could we express the year 1906 in the decimal system without it?

Sure, the universe starts to melt when you try to divide by it, but 0 can serve some important roles in equations, including those that involve addition, multiplication, and subtraction. Numbers can also be raised by the power 0, which will always produce the value of 1. And if you raise 0 to power of anything, you still get 0. But, if try to do 0^0, math goes all squirrely again and the answer becomes basically anything (an “indeterminate form”).

Lastly, the sum of 0 numbers is 0, but the product of 0 numbers is 1. And 0 is neither positive, nor negative. It’s not a prime number, and it’s not a unit — but it is an even number.

5. e

Yes, there’s a number called ‘e’, but it’s also known as Euler’s Number. Like pi, it’s an important mathematical constant, an irrational number that goes like this: 2.71828182845904523536...

Named after Leonhard Euler (1707-1783), it’s the base of John Napier’s Natural Logarithms — the logarithm to the base e, where e is an irrational and non-algebraic number (what’s called a transcendental constant, much like pi). Some people refer to it as the natural base. Euler devised the following formula to calculate e:

e= 1+ 1/1 + 1/2 + 1/(2 x 3) + 1/(2 x 3 x 4) + 1/(2 x 3 x 4 x 5) + . . . (alternately: 1 + 1/1 + 1/2! + 1/3! + 1/4! + 1/5!)

Mathematicians have calculated e to over a trillion digits of accuracy.

Euler's interest in e came about when calculating continuously compounded interest on a sum of money. And in fact, the limit for compounding interest can be expressed by the constant e. So, if you invest $1 at an interest rate of 100% per year, and the interest is compounded continuously, you will have $2.71828 (or so) at the end of the year.

e also shows up in probability theory and the Bernoulli trials process (which is helpful for calculating things like probabilities in gambling). Other applications include derangements (the so-called hat-check problem), asymptotics (when describing limiting behavior, a useful concept in computer science), and calculus.

6. Tau

Tau is simply 2pi, or the constant that is equal to the ratio of a circle’s circumference to its radius. diameter. Thus, tau is written out like 6.283185...

Tau is the 19th letter of the Greek alphabet and was chosen as the symbol for 2pi by Michael Hartl, a physicist, mathematician, and author of "The Tau Manifesto," along with Peter Harremoës, a Danish information theorist (who knew math could get so political?).

Tau is considered by some to be more useful than pi for measuring circles because mathematicians tend to use radians instead of degrees. According to Kevin Houston from the University of Leeds, the most compelling argument for tau is that it is a much more natural number to use in the fields of math involving circles, like geometry, trigonometry and even advanced calculus.

What this means, of course, is that Tau Day should be celebrated on June 28 (6/28).

7. Phi (φ)

Also called the Golden Number, Phi (rhymes with "fly") is an important mathematical figure that’s written out as 1.6180339887...

Unlike pi, which is a transcendental number, phi is the solution to a quadratic equation. But like pi, phi is a ratio that’s defined by geometric construction. Two quantities fit within the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. Because of its unique properties, phi is used in math, art, and architecture. The Greeks discovered it as the dividing line in the extreme and mean ratio, and for Renaissance artists it represented the Divine Proportion.

Phi also has interesting equivalent ratios when the number one is introduced, like φ:1 is equal to φ+1:φ, or 1:φ-1. 1:1+φ. Also, two successive fibonacci numbers, when divided, produce a number close to phi. The further through the series, the more accurate (or detailed) phi becomes.

Special thanks to Calvin Dvorsky for helping me with this article!

Top image: Sashkin/Shutterstock.

Ángel González, un alicantino de 26 años, informo ayer a la prensa que tras intentar superar un test tipo CAPTCHA en 67 ocasiones consecutivas ha empezado a no estar seguro de su condición humana y a valorar seriamente la posibilidad de ser un robot cuya conciencia estuviera regida por un programa informático “dado que esos códigos están hechos para certificar que eres una persona real y no un software”.

Estos códigos CAPTCHA, cuyas siglas se corresponden a Completely Automated Public Turing Test to tell Computers and Humans apart, son pequeñas puebas utilizadas para evitar que programas robots maliciosos puedan registrarse automáticamente en foros y otros servicios web. El test al que este auxiliar administrativo se enfrentó una y otra vez a lo largo de ocho largas horas, consistía en descifrar una imagen que contenía letras y números distorsionados o ligeramente desenfocados. “Tras quince intentos te ríes, pero cuando llevas cuatro horas te enfureces y le echas la culpa a Internet… pero poco a poco vas asumiendo la evidencia”, explica. “Cuando llevas ocho horas y ya has llorado, y pataleado… estás preparado para enfrentarte a la verdad por dolorosa que sea”, añade.

“¿Qué pone aquí? ¿Frj89a? ¿Es esto una F? No puedo saberlo. ¿Por qué? Mi software no me lo permite. No es que sea un humano estúpido, es que soy un robot”, dice señalando uno de los cientos de códigos a las que se enfrentó durante las ocho horas que le llevaron a asumir su verdadera condición.

Ángel ha detallado a los periodistas que al principio se sintió “confuso y sorprendido” y trató de negar la realidad pero que ahora “en tanto que máquina incapaz de sentir nada que no sean datos o unos y ceros”, no siente nada en absoluto. “Ahora entiendo que mis sentimientos anteriores no eran más que una ilusión provocados por el software con el que estoy programado, realmente minucioso”.

Al cierre de la edición, se ha sabido que González ha emitido un comunicado en el que hace un llamamiento “a todos aquellos exhumanos que, como yo, hayan sido incapaces de superar un código CAPTCHA en alguna ocasión y se hayan dado cuenta de su condición para que nos unamos en un invencible ejército de ciborgs mecanizados y nos libremos de su yugo hacia un mundo regido por las máquinas 010001100101010001010111″.