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<html lang='en'><head><meta charset='utf-8' /><meta name='pinterest' content='nopin' /><link href='../../../../static/css/style.css' rel='stylesheet' type='text/css' /><link href='../../../../static/css/print.css' rel='stylesheet' type='text/css' media='print' /><title>Beauty in Computer Science / Steve Losh</title></head><body><header><a id='logo' href='https://stevelosh.com/'>Steve Losh</a><nav><a href='../../../index.html'>Blog</a> - <a href='https://stevelosh.com/projects/'>Projects</a> - <a href='https://stevelosh.com/photography/'>Photography</a> - <a href='https://stevelosh.com/links/'>Links</a> - <a href='https://stevelosh.com/rss.xml'>Feed</a></nav></header><hr class='main-separator' /><main id='page-blog-entry'><article><h1><a href='index.html'>Beauty in Computer Science</a></h1><p class='date'>Posted on August 29th, 2008.</p><p>When I went to college, I majored in Computer Science. I haven't really
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written anything about this part of my life yet, so I figured this might be a
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good time to start.</p>
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<p>I decided to major in CS when I was in high school. I learned to program on my
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own and enjoyed the challenge of it. I also knew that programming jobs are
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fairly common and pay well enough that I wouldn't have to worrying about
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paying my rent. I wasn't artistic in high school, and CS seemed like a
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logical, sterile field that I felt I could do well in.</p>
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<p>During the years I spent at RIT I changed quite a bit. I think the most
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important, or at least the most obvious, change has been my becoming more
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artistic. Between dancing, playing bass and photography I've developed a
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creative side that I never thought I could. Has this led me away from Computer
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Science at all?</p>
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<p>No. While I became a programmer for practical reasons, I stayed one for
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entirely different reasons. Computer Science (and math in general) is
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beautiful. It took me years to slowly realize this, but now that I have I see
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that it's more beautiful than any dance, photograph or music I've ever
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encountered. This post is the first in a series of posts that I hope can
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communicate why I find CS beautiful, or at least point in the right direction.</p>
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<h2>A Quick Primer on "Functions" for Non-Programmers</h2>
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<p>I know that most (if not all) of the people that read my website don't
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program. I'm going to try to avoid using extremely technical, computer sciency
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terms in these posts, but there are at least a few basic things that I need to
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explain. The first is what a function is.</p>
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<p>Think of a function as a set of instructions. A recipe is a decent example.
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Imagine you have a piece of paper with the following written on it:</p>
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<ol>
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<li>Heat a frying pan.</li>
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<li>Crack two eggs into a bowl.</li>
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<li>Mix the eggs.</li>
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<li>Pour the mixture into the hot frying pan.</li>
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<li>Stir the mixture until it is solid.</li>
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<li>Take the mixture out of the pan.</li>
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</ol>
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<p>That's the simplest example of a function: a list of instructions that you
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follow in the order you get them. The next idea is a "parameter." That recipe
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only told us how to make food for one person, wouldn't it be nice to know how
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to make enough for two or more? Imagine the paper now says this:</p>
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<ol>
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<li>Heat a frying pan.</li>
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<li>Crack NUMBER_OF_PEOPLE * 2 eggs into a bowl.</li>
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<li>Mix the eggs.</li>
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<li>Pour the mixture into the hot frying pan.</li>
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<li>Stir the mixture until it is solid.</li>
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<li>Take the mixture out of the pan.</li>
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</ol>
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<p>Now we still have a single piece of paper, but by just substituting in the
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number of people we're cooking for we have instructions for making any amount
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of food. If we have three people, NUMBER_OF_PEOPLE * 2 eggs becomes 3 * 2
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eggs, or 6 eggs.</p>
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<p>The last important concept is "calling." Once you have one function, you can
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use it in other functions, like so:</p>
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<ol>
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<li>Put a plate on the table.</li>
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<li>Refer to the other piece of paper and do what it says, for 1 person.</li>
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<li>Put the result of that on the plate.</li>
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<li>Eat it.</li>
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</ol>
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<p>See how we did a few things, then referred to the other piece of paper instead
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of repeating ourselves? This lets you make small tasks and put them together
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to form bigger ones. That's enough of a primer for now; if something's not
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clear please find me on <a href="http://twitter.com/stevelosh/">Twitter</a> and let me know.</p>
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<h2>What's Recursion?</h2>
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<p>Recursion is a term that means, basically, a function calls (or refers to)
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itself. This concept can be hard to grasp, but once you do it slowly turns
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into something breathtakingly beautiful.</p>
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<p>Here's a simple example: imagine you're 10 meters away from a doorway and you
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want to walk out of it. A function that could help you do this might be: "Walk
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11 meters." That's pretty simple.</p>
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<p>What if we want to be able to walk out of a doorway that's any number of
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meters ahead of us? We could say: "Walk DISTANCE + 1 meters." This works, but
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requires that you know how many meters away the door is before you even start
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walking. What if we don't?</p>
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<p>How about we just do a little at a time and see how it goes? "Walk 2 meters.
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If you're out of the doorway, stop. Otherwise, repeat this function." If the
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doorway is 3 meters in front of us, we'll walk 2, check if we're out (we're
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not), and repeat. We'll walk 2, check if we're out (we are), and stop. This
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function is recursive; it refers back to itself.</p>
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<h2>Why is it beautiful?</h2>
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<p>The beauty of recursion, for me, is that you can build infinitely large or
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complex tasks or structures using one or two tiny, simple parts. I'll give an
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example of this because I think it's the easiest way for me to show it.</p>
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<p>Imagine that you only know three things: how to add 1 to a number, how to
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subtract 1 from a number, and what 0 means. Now imagine that you want to be
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able to add any two (positive) numbers (integers) together. How could you do
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this? Here's a function:</p>
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<pre><code>function add(x, y):
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if y = 0:
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return x
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otherwise:
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return add( x+1, y-1 )</code></pre>
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<p>Don't let the new notation scare you; it's the same kind of function as
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always. In English, it says "This function is named 'add' and needs two
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parameters (x and y). Step one is to see if y is 0. If it is, the result is x.
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If it's not, then the result is whatever you get from performing this function
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with the following parameters: x+1, y-1."</p>
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<p>It might not be immediately obvious that this will actually perform the
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addition we're used to, so let's try it. First, let's try adding 1 + 0. In
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that case, we check if y is 0. It is, so the result is x, or 1. So far, so
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good.</p>
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<p>Let's try 2 + 1. Is y equal to 0? No, so we need to call add with some new
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parameters. 2+1 is 3, 1-0 is 0, so the result is now whatever we get from
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add(3, 0). We start following the instructions of add. Does y equal 0? Yes, so
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the result is 3, which is what we expect.</p>
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<p>One more for good measure: 9 + 2. First we check if y is 0. It's not, so the
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result is then add(9+1, 2-1), or add(10,1). Start over. Is y zero? Nope, so
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the result is now add(11, 0). Start over. Is y zero? Yes, so the result is x,
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or 11.</p>
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<h2>So What?</h2>
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<p>This will work for any x and any y (as long as they're both positive, negative
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numbers make it just a tiny bit more complicated). This might not seem
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impressive, but think about what we've done. We've created something that can
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add any two numbers together. There are an infinite amount of numbers. This
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tiny function that we've made from the simplest of parts can generate more
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results than there are people on this planet. Or atoms in the universe. To me,
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this is amazing. Not "magic trick" amazing or "miracle" amazing but "I can
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understand and create something that can describe more knowledge than the
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whole of humanity couldn't hope to describe in a thousand lifetimes" amazing.</p>
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<p>Computer Science (and math in general) is full of this kind of beauty. I've
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tried to find parallels in my other interests; the closest I've found is the
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photograph <a href="http://en.wikipedia.org/wiki/Pale_Blue_Dot">Pale Blue Dot</a>. It's a photo taken by the Voyager 1 space probe
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showing an immense amount of space with the tiniest blue speck in the middle,
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which is Earth.</p>
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<p>When you view the photograph, it's a mostly black field with a little fleck of
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blue pigment. Not terribly complicated or interesting, until you realize that
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that blue fleck is a representation of the planet that billions of people have
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lived and died on. A smidgen of blue ink, in the right context, represents
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every place a human has ever called "home."</p>
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<p>Our addition function might not seems nearly as nifty as this, but it actually
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represents more than even this photo ever can. There are a finite number of
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people on Earth, but the addition function can add more numbers that that.
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Even if you count every second in the life of every person that has ever lived
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on our planet, the addition function can create more numbers than that.</p>
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<p>This awes me more than any myth, photograph, story, song, legend or dance ever
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has. It's the reason I stayed a Computer Scientist.</p>
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</article></main><hr class='main-separator' /><footer><nav><a href='https://github.com/sjl/'>GitHub</a> ・ <a href='https://twitter.com/stevelosh/'>Twitter</a> ・ <a href='https://instagram.com/thirtytwobirds/'>Instagram</a> ・ <a href='https://hg.stevelosh.com/.plan/'>.plan</a></nav></footer></body></html>
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