 Dear Fellow Scholars, this is Two Minute Papers with Károly Zsolnai-Fehér, and today we are here to answer one question. What is a convolution? I have heard many university students crying in despair over their perilous journeys of understanding what convolutions are and why they are useful. Let me give a helping hand there. A convolution is a mathematical technique to mix together two signals. A lot of really useful tasks can be accomplished through this operation. For instance, convolutions can be used to add reverberation to a recorded instrument. So I play my guitar here in my room and it can sound like as if it were recorded in a large concert hall. Now, dear Fellow Scholars, put on a pair of headphones and let me rock out on my guitar to show it to you. First, you'll hear the dry guitar signal. And this is the same signal with the added reverberation. It sounds much more convincing, right? In simple words, a convolution is a bit like saying guitar plus concert hall equals a guitar sound that was played in a concert hall. The only difference is that we don't say guitar plus concert hall. We say guitar convolved with the concert hall. If we want to be a bit more accurate, we could say that the impulse response of the hall, which records how this place reacts to a person who starts to play the guitar in there. People use the living hell out of convolution reverberation plugins in the music industry. Convolutions can also be used to blur or sharpen an image. We also had many examples of convolution on your own networks that provide efficient means to, for instance, get machines to recognize traffic signs. We can also use them to add sophisticated light transport effects, such as subsurface scattering to images. This way we can conjure up digital characters with stunningly high quality skin and other translucent materials in our animations and computer games. We have had a previous episode on this, and it is available in the video description box, make sure to have a look. As we said before, computing a convolution is not at all like addition. Not even close. For instance, the convolution of two boxes is a triangle. Wow. What? What kind of witchcraft is this? It doesn't sound intuitive at all. The computation of the convolution means that we start to push this box over the other one, and at every point in time we take a look at the intersection between the two signals. As you can see, at first they don't touch at all. Then, as they start to overlap, we have highlighted the intersected area with green, and as they get closer to each other, this area increases. And they are completely overlapped, we get the maximum intersection area, which then starts to dwindle as they separate. It is a miracle of mathematics that by computing things like this, we can rock out in a virtual church or a stadium, which sounds very close to the real deal. And before we go, a quick shout out to immersive math, a really intuitive resource for learning linear algebra. If you're into math, you simply have to check this one out. It's really cool. Thanks for watching and for your generous support, and I'll see you next time.