Proving stuff yourself is hard, and my initial attempts were catastrophic. I wrote one proof that began with a stronger statement than the conclusion I was attempting to draw, rendering the proof useless even in the unlikely case it was otherwise successful. It was not otherwise successful. Jumping through several dodgy implications and logical errors, it eventually arrived at a conclusion that was substantially weaker than what I was attempting to prove. The worst part? I couldn’t even spot my own mistakes, and I thought the proof was probably quite good.
This post is about my approach to real analysis. In many areas of theoretical research, proving things is of paramount importance. Sadly, I didn’t have the foresight to take a heavy math curriculum as an undergrad, and like many, my skills were lackluster at best. My solution? Prove every theorem in an intermediate analysis course.
I was so excited by our event with Peter Singer last year. My small team of core student organizers managed to book a sought-after public figure with almost no money or experience. Hundreds found our Facebook event with no advertising, and about 50 people rocked up to ask the renowned philosopher questions. How did we do it?
I hope people will find this a useful blueprint for how to run cheap, easy events that attract brilliant speakers. And for those with an idea worth sharing, I hope it provides you with a way of getting through to broader audiences from the comfort of your own home (or a tropical island!).
How can governance represent the needs of the people? How can governments disseminate power, and give equal consideration of interests? One proposal is quadratic voting, outlined in the book “Radical Markets”. The authors, Eric Posner and Glen Weyl, propose “Quadratic Voting”. This proposal replaces ‘one person one vote’. It replaces equal influence in choosing governments with equal influence on governance. Equal influence rather than equal say.
Under quadratic voting, everyone receives an equal number of voting credits. These credits can buy influence. Raising an issue for consideration or voting for it once raised. Or voting against an awful proposal, as the case may be. We would all have the same number of voting credits. We could all use them how we like. Perhaps climate change moves you. Or marriage equality. Or mental health policy. Or any number of things. You could your influence on what is most important to you.
Sitting in the botanic gardens, hungover, watching the ducks skim across the water, waiting for the revival we knew only coffee could bring. Attempting a normal conversation. “Have you heard the theory that octopuses are aliens that arrived on a comet?”, my friend asked. I hadn’t.
We examined this strange theory. It apparently relied on the absurdness of octopodes, fantastic creatures with distributed brains, unlikely intelligence, and the ability to squeeze and escape through a hole as small as their eye (see below). The theory was equally absurd, can this creature really be explained by accidental intergalactic space travel?
Recently, I decided to go back to basics, and learn mathematics from the ground up. You will find that post here. Calculus was first on the list. I’m taking the MIT course in single variable calculus, it’s available for free online.
It’s tempting to try and jump a few rungs. We understandably want to learn the fancy applications, the impressive stuff. Instead, I’ve chosen a more mundane route. Getting a strong handle on the basics. Understanding deeply the foundations is underrated. Josh waitzkin, a chess “prodigy” and martial artist, puts it brilliantly in his book:
“[We] began our study with a barren chessboard. We took on positions of reduced complexity and clear principles. Our first focus was king and pawn against king—just three pieces on the table… Layer by layer we built up my knowledge and my understanding of how to transform axioms into fuel for creative insight… This method of study gave me a feeling for the beautiful subtleties of each chess piece, because in relatively clear-cut positions I could focus on what was essential. I was also gradually internalizing a marvellous methodology of learning—the play between knowledge, intuition, and creativity.”
My undergraduate degree was in economics, now I’m studying a master’s in philosophy. I absolutely love philosophy, and I’m excited by the opportunity to dive in deep. Yet there are reasons I’d consider further study in economics, rather than philosophy. Importantly, the job prospects for even the most excellent philosophy students, after a PhD, are frankly dismal. Dismal chances if you’re world class, less for anyone else. In contrast, Economics PhDs seem to have no trouble finding work in the private sector if their academic hopes are dashed. It may not be easier to become a professor, but at least the 3-7 years you’ve invested are useful when applying for other jobs. Second, there are areas of economics which I find deeply interesting. The strategic interactions of game theory are fun, while the combination of mathematical theory and psychology in behavioural economics is also especially interesting. I believe philosophy makes an excellent choice for an undergraduate program, especially when combined with a quantitative discipline. Clear writing and logical reasoning are excellent skills to develop. I am not at all knocking those who pursue a doctorate in philosophy, well aware of the grim career prospects, because they love the pursuit of knowledge and are happy to “waste” those years doing something deeply meaningful to them personally.
“An economics PhD is one of the most attractive graduate programs: if you get through, you have a high chance of landing a good research job in academia or policy – promising areas for social impact – and you have back-up options in the corporate sector since the skills you learn are in-demand (unlike many PhD programs). ” 80,000 Hours