First post of 2018! Exactly two months after my last one. I have been short on topics to write about these past months, but finally here we are!

The inspiration for this post is simply giving a recommendation: 3Blue1Brown, a YouTube channel dedicated to explaning math concepts, has recently published two videos on the Fourier transform: video 1 and video 2.

I’ve long admired 3Blue1Brown as perhaps the best scientific channel on YouTube (among those I know, clearly): it has intriguing ideas for topics, clear explanations with intuitive concepts and good animations. You watch raptly for 20-30 minutes and when it’s over, you learned some cool stuff and you didn’t even need to take notes or follow complex proofs.

These last two videos have reinforced this opinion: despite having studied the Fourier transform in university, not surprising given that I studied computer engineering, the video taught me quite a bit about what the transform itself represents. And the big surprise came in the second video, where instead of continuing on the path set in the first one, the author explained the surprisingly intuitive relationship between the Fourier transform of a wave, and what it can be used for, and Heisenberg’s uncertainty principle for quantum particles. Having studied a bit of quantum mechanics as a pastime, I found this both super enticing and mindblowing. Thanks, 3Blue1Brown, for making my weekend.

Since I started down that path, let me mention one of the first videos I watched, which is still one my favourites: this video on the Moebius strip. Like many others, I knew of the Moebius strip as a nice theoretical concept, an example of why math is weird and is able to describe complex or impossible structures. But what does the Moebius strip come from? It must have arisen from somewhere: a tool to describe a phenomenon or to solve a specific problem. And indeed the video will tell you the full story, and damn now I want more hours in my day to study topology…

Studying some topic I am interested in as a hobby is one of my favourite things to do. Studying for me might mean read one book; watch a series of videos; or follow a full online course from beginning to end (in-person course counts too, although that’s generally harder to organize and fit in our busy lives). Or even just find a problem that makes me curious and try and solve it. This depends on the topic, my level of interest, my current amount of free time…

This started with computer science, at the time where I was a high school student with tons of free time to spare, and a desire to really know how computers worked and program them to do what I wanted. At the time I felt like an alien: nobody around me saw “study” as nothing more than a boring necessity. Sure, there were plenty of subjects I didn’t care for, and teachers with whom I didn’t click. Liking everything is impossible. But there was always at least one topic that made my eyes sparkle so much I would read the textbook way beyond what was covered in the lessons to know more. That lesson where they would explain some new concept and it just left me standing there in awe. I remember the first time they told me what an integral is and how they work…

Nowadays I can easily meet people with similar attitudes all over Internet, so my hobby studying is not that weird or isolated. But if you have never done it, I recommend it. The feeling of spending time over a hard topic and finally having that moment of clarity is always worth it.

So what’s next on my list? Not topology for now. I recently read a couple of cool books about the science behind cooking, and wrote down a bunch of notes. With some time and processing, I plan for them to become a blog post.