Hiding behind chaos and error in the double pendulum

If you want a visual intuition for just how unpredictable chaotic dynamics can be then the go-to toy model is the double pendulum. There are lots of great simulations (and some physical implementations) of the double pendulum online. Recently, /u/abraxasknister posted such a simulation on the /r/physics subreddit and quickly attracted a lot of attention. In their simulation, /u/abraxasknister has a fixed center (block dot) that the first mass (red dot) is attached to (by…

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Notation and Beginners

You’re interested in learning a new mathematical topic. After reading some popular articles that speak in broad terms about the subject, you are energized to go on a deeper dive and learn the details. You open up a textbook, pencil in hand and ready to expand your horizons. You start going through the introductory chapter, motivated with the dream of working through the whole textbook. You make a little progress, but you find yourself pausing…

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Span programs as a linear-algebraic representation of functions

I feel like TheEGG has been a bit monotone in the sort of theoretical computer science that I’ve been writing about recently. In part, this has been due to time constraints and the pressure of the weekly posting schedule (it has now been over a year with a post every calendar week); and in part due to my mind being too fixated on algorithmic biology. So for this week, I want to change things up…

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Discounting

I am very good at finding the bad aspects of any given idea or thing. I wouldn’t call myself cynical. Rather, I have a tendency to find ways to justify not doing something. This has to do with my reluctance to try new things, and I suspect I’m not the only one who does this. Imagine the following scenario. You’re presented with an amazing opportunity, but there is something you have to do. Maybe you…

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On being a gay mathematician redux

Looking back I published the blog post On being a gay mathematician in June 2017. Two years later, I’ve had a generally positive reaction to the post, and I amplified my queer positive message out to the world through my writing and advocacy. I’ve been on a few diversity-type panels and interacted, either in person… Read More On being a gay mathematician redux

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Control of the Future

It’s tempting as a student to think that nothing is in your control. We often feel like our whole lives revolve around the whims of professors and their decisions for assignments and tests. It can be easy to retreat into “reactive” mode, making sure that everything which is thrown at you gets done. When we operate like this, we tend to be exhausted, since we can never look further than a week. The issue with…

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Introduction to Algorithmic Biology: Evolution as Algorithm

As Aaron Roth wrote on Twitter — and as I bet with my career: “Rigorously understanding evolution as a computational process will be one of the most important problems in theoretical biology in the next century. The basics of evolution are many students’ first exposure to “computational thinking” — but we need to finish the thought!” Last week, I tried to continue this thought for Oxford students at a joint meeting of the Computational Society…

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Slick Versus Pedagogical Proofs

In mathematics, there’s almost always an opportunity to make proofs more concise. For example, when you first learn a concept, it might take a while to prove a result using the definitions that were developed. The reason it’s longer to do is because the definitions require you to spell out ideas explicitly. As a result, you might get to the end of the proof, but it takes a bunch of little intermediate steps to do…

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Levelling Up

We enjoy doing comfortable things. We don’t want to stretch ourselves too much, because when you stretch, there’s a possibility of overstretching. We fear this potential negative, so we buck the other way, contenting ourselves with doing activities and pursuing projects that aren’t too risky. It’s not that we don’t want to do better work and overcome new challenges. Ask anybody around you if they want to overcome challenges, and their answer will be “yes”.…

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British agricultural revolution gave us evolution by natural selection

This Wednesday, I gave a talk on algorithmic biology to the Oxford Computing Society. One of my goals was to show how seemingly technology oriented disciplines (such as computer science) can produce foundational theoretical, philosophical and scientific insights. So I started the talk with the relationship between domestication and natural selection. Something that I’ve briefly discussed on TheEGG in the past. Today we might discuss artificial selection or domestication (or even evolutionary oncology) as applying…

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