What is an algorithm?

0:47 Welcome to Maths Is Not Boring by Kidopoly.com. I'm Mira! And I'm Finn. If you haven't already, tap follow wherever you're listening so you never miss an episode.

0:58 Hey Mira, I was just looking at the map app on this phone. It's crazy how it just knows the exact fastest way to get to the park.

1:06 It is crazy! The phone is following a very specific set of instructions to find that path. But Finn, what if I told you the idea behind those instructions goes back almost 200 years?

1:20 Wait, 200 years? They didn't have phones then. They didn't even have electricity in their houses.

1:27 Exactly! Today we are looking at a set of steps written in the year 1843 for a giant machine made of brass that didn't actually exist.

1:37 Instructions for a machine that wasn't even built. That sounds like a sci-fi story.

1:43 It is a totally true story, and the person who wrote those steps saw something hiding in the math that nobody else on Earth had noticed yet. So Finn. The idea we are looking at today is called an algorithm.

1:56 Algorithm? I've heard people say that word about video games and computers. But what actually is it?

2:03 It is surprisingly simple. An algorithm is just a list of exact steps. If you follow them perfectly, step by step, you complete a task or solve a problem. Oh, like a recipe for baking a cake. Exactly, but for math and logic. And to find the very first time someone wrote an algorithm for a computer, we have to travel back to London in the 1830s.

2:27 Okay, I'm picturing cobblestone streets, horse-drawn carriages, and people in top hats.

2:33 Spot on. In those days, a mathematician named Charles Babbage designed a massive machine called the Analytical Engine. It was going to be a giant mechanical calculator made of thousands of brass cogs and gears.

2:47 Whoa! A calculator made of gears. So you'd have to physically turn cranks to do math.

2:53 He planned to power it with a steam engine, but it was so expensive and complicated that it was never actually built. Most people just thought it was a weird pipe dream.

3:03 Oh, that's a shame. So if it wasn't built, how did anyone write an algorithm for it?

3:08 Because of a brilliant mathematician named Ada Lovelace. She was the daughter of the famous poet Lord Byron, and she loved mathematics. And when she looked at the plans for this giant brass machine, she saw magic in it. So in 1842, an Italian engineer named Luigi Menebrea wrote an article explaining how Babbage's machine would work.

3:30 It was published in French.

3:32 And Ada Lovelace read it.

3:35 She did more than read it. In 1843, she translated it into English. But as she was translating, she started adding her own notes to the end of the article.

3:46 Like when you write in the margins of a textbook.

3:50 Exactly. But her notes ended up being three times longer than the original article. She was adding incredible new ideas. And the most famous part is the very last note, called Note G.

4:04 Note G.

4:05 Sounds mysterious. What was in it? Charles Babbage had given her some mathematical formulas, and Ada turned them into a massive, detailed table. She wrote out the exact, step-by-step instructions for how the machine's gears would need to move to solve those formulas.

4:24 Wait, she wrote the instructions for a machine she couldn't even touch. How did she know it would work? Because the math was true.

4:33 She traced every single operation in her mind. Move this number here, multiply it by this, store it on that gear. She even found a mistake in the formulas Babbage gave her, and she fixed it in her steps. She debugged it before bugs were even a thing in computers. She did! And the formulas she was working on were for calculating a famous, highly complex sequence called the Bernoulli numbers.

5:00 Oh wow! Are we going to calculate those right now? No, we aren't. The wonder isn't the numbers themselves today. The wonder is that Ada saw that you could break a massive, complex problem into a list of tiny, simple steps that a machine could blindly follow.

5:19 Oh, I see. Because the machine doesn't actually understand math. It just knows how to turn a gear when the instructions tell it to.

5:27 Exactly! Because her steps were so detailed and logical, Note G is often called the first computer programme ever written. But here is the part that will really bend your brain.

5:40 Okay, I'm ready.

5:41 Lay it on me. Babbage just thought he was building a calculator to do number crunching, but Ada realised something much deeper. She guessed that if a machine could use numbers to represent things, it could do more than math. Represent things? Like what? She wrote that if the numbers represented pictures and harmonies, the machine might one day compose elaborate and beautiful pieces of music.

6:09 Wait, she predicted computer music? In 1843? Yes, she saw that an algorithm isn't just for doing arithmetic. It's a way of processing any kind of information. Ada had a short life, but that single brilliant insight changed the way we see the world.

6:29 So every time my phone plays a song, or finds a route on the map, or loads a video game, it's doing exactly what Ada Lovelace saw in her head. Just following a list of tiny steps. Exactly.

6:43 The apps on your phone, the weather forecasts, the way spacecraft steer, everything runs on algorithms. Her beautiful idea is literally in our pockets every day. That makes the map app feel a lot more special now. It really is. In fact, every year in October, people celebrate Ada Lovelace Day to honour the incredible things women have discovered in science and mathematics.

7:10 It's a wonderful reminder to look for the magic hiding in plain sight.

7:14 Okay, I have to know. If Babbage had actually built that analytical engine, how big would it have been?

7:21 It would have been about the size of a small shop. Around 15 feet tall, powered by a loud chugging steam engine.

7:29 A steam-powered computer? And how were they supposed to feed Ada's instructions into it?

7:35 Using stiff cardboard cards with holes punched in them, called punch cards. Just like the ones used in weaving looms at the time. The patterns of the holes were the algorithm.

7:45 Alright, Finn, it is time for the quiz. Are you ready? I'm ready. Let's see if my brain's algorithm can find the answers.

7:53 First question. What is the mathematical word for a list of exact steps to complete a task or solve a problem? Next one. In what year did Ada Lovelace publish her famous notes? Question 3. What was the name of the unbuilt brass machine designed by Charles Babbage? Here's number four. What letter of the alphabet was the name of Ada's famous final note?

8:31 Last question. What kind of beautiful art did Ada guess a machine might one day be able to compose? Great job! Let's see how you did. The first answer is an algorithm. For question two, she published her notes in the year 1843. Number three, the answer is the analytical engine. Question four, it was note G.

9:01 And the final answer is music. It still blows my mind that she sat there in 1843 and just imagined how computers could make music without ever seeing one.

9:12 It really is extraordinary. Sometimes the greatest ideas come from just looking at something ordinary and seeing what it could become.

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9:45 See you next time on Maths Is Not Boring. Bye!