we are going to see an increasing number of academics thinking not so much about their paper CV, but rather about their [videos].

I’ve realized that a big part of the problem with mathematics education around the world might be that: the second piece of the picture—algorithmic computation—is a lot easier to teach than either the first—conceptual understanding—or the third—problem solving.

I am in Austria right now; having spent a week in Innsbruck visiting Hans-Peter Schroeker and Manfred Husty, I am now in Graz at the Technical University, and I am talking with Anton Gfrerrer, Sybi…

Programming languages lie at the intersection between the binary, deterministic, silicon world of computers and the inexact, chaotic, organic world of human consciousness and communication. To me, functional programming is the practice of applying mathematical formalisms to real-world programming problems.

And yeah, I think that sense of future shock is what has disappeared, which was in retrospect a very rapid turnover of styles one was accustomed to. ​ Music is the site where the major symptoms of cultural malaise can be detected I think. ​ what’s missing is a popular experience of newness.

This article was discussed on Hacker News, and was cited in The Mathematical Gazette. Introduction This is a follow-up to a post from earlier this year discussing the likelihood of encountering two…

I have suspected for years that the classic buffet line system is a deeply flawed method, so I decide to simulate different methods to find out better ways

it suggests that present funding mechanisms are likely to be far from optimal, in part because they do not focus enough on research autonomy and risk taking. ​ But when viewed through the lens of Progress Studies, the implicit question is how scientists (or funders or evaluators of scientists) should be acting. The success of Progress Studies will come from its ability to identify effective progress-increasing interventions and the extent to which they are adopted by universities, funding agencies, philanthropists, entrepreneurs, policy makers, and other institutions. In that sense, Progress Studies is closer to medicine than biology: The goal is to treat, not merely to understand.

If the ‘90s internet was a weird, largely unproductive place where you escaped from reality, today’s internet is where much of reality happens, and meatspace is where you escape from it. It barely even makes sense anymore to refer to “the internet” as an alternate domain. We’re all basically online all the time, passively if not actively.

Is there an argument to be made that they choked off real innovation over the past decade. ​ We’re still using the same exact apps and they kind of look and feel the same.

So please: imagine your closest relationships, and imagine losing them in an instant. Figure out what would be left unsaid and say it. ​ I’m grateful for my friends/family who didn’t ask — they showed up. ​ On our year traveling the world, Alex and I would often look at gravestones near old decrepit churches. At some point in history, these gravestones were new and people would perhaps lay flowers on them. Years later, maybe a relative or two would come by on an anniversary or birthday. Decades later, maybe some stranger from the same village would recognize the name and smile slightly. But soon, the marker is anonymous. When we saw many of them, the march of nature had worn them into illegibility. Tombstones are a shout in the dark, but eventually the echoes subside. So this post is my digital tombstone for Alex. I like to think it’s better because it’ll help me remember her. And maybe help you know her a little better so you can remember her as well.

Every now and then, at brunches with other couples, baby showers, weddings, endless cocktail parties for your company, I would have looked at you, myself, and the other wives, each woman coiffed and preening, and wondered about the women we could have been had we chosen ourselves over you and your brethren. The women we could have been had we decided to pursue our untapped talents instead of helping you pursue your greatness. The women we could have been had we been raised to believe we were more than negative space, waiting to fill into and be filled by men. The women we could have been had we chosen the path of our creation versus the path designated. I would have mulled these thoughts, and you would have caught me, alerted by the pensive, frozen smile on my face. You would have placed your hand on the small of my back, reminding me that I am yours, and asked, “You okay, baby?” I would have replied, “Of course, my love.”

When is the last time you had a great conversation? A conversation that wasn’t just two intersecting monologues, which is what passes for conversation a lot in this culture? ​ Although I couldn’t articulate why exactly, intuitively I agreed: I didn’t want to talk about myself either. That was boring. ​ When you think about it, this makes total sense. Whenever you’re “catching up” with someone, you’re often just dumping the details of your life onto another person. It’s as though the notebook of your life fell out of sync with the notebooks of others, and to compensate you hurriedly transcribe the notes from one notebook to the other. Then, the other person reciprocates. As John O’Donohue said, it really feels like two intersecting monologues. ​ Instead, it’s about intentionally searching for launch points – conversational ramps we can use to reach a shared reality far more powerful and enduring than the one we physically occupy. It’s those shared experiences that make great conversation.

You need a design eye to design, and a non-designer eye to feel what you designed. ​ the more I learn about the many ways of human expression—music, architecture, even sports, the more I enjoy observing the masters at work. How could one not enjoy observing functional beauty and the care for detail? ​ —the more advanced you are, the less you need to consciously think about it. The less you think about what you do, the more virtuosity you will be able to achieve. ​ Again, this is a rule of thumb. That not everybody can sit down at a piano and play away like Glenn Gould is not the piano’s fault. Your skills need to match the tool you are using to assess its quality—you can’t test-drive a car if you haven’t learned to drive. But everyday objects should only require everyday skills. This is what makes web design so hard.

In my previous blog post, Programming with Universal Constructions, I mentioned in passing that one-to-one mappings between sets of morphisms are often a manifestation of adjunctions between functo…

Subscribing a subject to a cold observable broadcasts its notifications to multiple observers, thus making it hot. Woah, so this is what multi casting is about! So it’s clear there are only two scenarios where it’s correct to use subjects: - The source is external and cold, and I want a hot observable. - The source is local and I want a hot observable. use either `Defer` or `Publish` to change the temperature accordingly That’s where `Publish` is useful, as described earlier in this post. `Publish` converts a cold observable into a hot observable; however, it returns `IConnectableObservable`, which requires a call to `Connect`.

This has been the longest year of my life, and at 34, that feels like a gift.

When you feel like you’ve learned whatever there is to learn from what you’re doing, it’s time to change course and find something new to learn so that you can move forward. You can’t be content with mastery; you have to push yourself to become a student again. So, perhaps, instead of asking that dreaded question, “What next?” turn it into this question: “What do you want to learn?”

When we’re not so different from people around us, it’s irresistible to become obsessed about beating others. ​ Still here’s my answer: If one must go to college, I advise cultivating smaller social circles. Instead of going to class and preparing for exams, to go to the library and just read. Finally, not to join a fraternity or finance club, but to be part of a knitting circle or hiking group instead. ​ In Canada, people apply to major in certain subjects; if they earn admission, it’s not so easy to switch, so there’s less of this intellectual loitering that one finds on American campuses. And when I attended a German university, students told me that German 18-year-olds don’t usually go directly to university after high school. Instead, they take a year off to travel, work, or volunteer. These experiences create difference and maturity, thus better inoculating people against mimetic contagion. ​ Girard presents a model of human conflict that is Shakespearean, not Marxist. That is, he thinks that people are not engaged in class struggle, in which proletarians unite against the bourgeoisie; instead, people reserve horror and resentment for people most like themselves. ​ If one is a Girardian, then there is perhaps no greater catastrophe than the growing tendency of the American meritocracy to be incubated in elite colleges. Is it not worth fretting that the people running the country are coming in higher numbers from these hothouse environments at a young age, where one is inflamed to compete over everything and where tiny symbolic disputes seem like life and death struggles? How much of the governing class has fully adopted this attitude, and to what extent can we see our recent political problems to be manifestations of this tendency?

Find something that’s important to you in 2019 – social, political, economic, whatever – and with a little effort you can trace the roots of its importance back to World War II. There are so few exceptions to this rule it’s astounding. To me, the war is fascinating to study not because of what happened, but what it went on to influence. What are the other Big Things – the great-grandparents – of important topics today that we need to study if we want to understand what’s happening in the world? The three big ones that stick out are demographics, inequality, and access to information. As America’s offices diversify faster than its retirement communities, the minority-white labor force will be supporting the majority-white retirees. The point is that we can’t just look at how rich the top has become, or at how stagnant the bottom is. It’s the gap between the two that causes one group to push back against the other. It’s almost certain that the educational system will be upended. The current arrangement of needing a college degree in order to have a good chance at becoming and staying middle class, but taking on life-changing amounts of debt to do so if you don’t have family assistance, can’t last. I have no idea how it ends. But there’s practically no chance that in 30 years the story is, “Everyone just kept taking on education mortgages at age 18, tuition kept rising at double the rate of inflation, and it was all OK.” It’s going to break somehow. The range of political opinions has always been extreme, but what we’ve seen over the last decade is what happens when the warm blanket of ideological ignorance is removed. The world is driven by tail events. A minority of things drive the majority of outcomes. It’s one of the most important concepts in investing, where a few positions may account for most of your lifetime returns.

This situation crops up so often in mathematics that the acronym “TFAE” (for “The Following Are Equivalent”) has become a standard part of a mathematician’s education.

Designing media to reflect how people think and learn

In math, we might show a student a peer’s strategy, then ask them to solve a new variant of the problem. In the humanities, we might show a student a peer’s essay beside their own, then ask them to draw lines between all the places they and their peer were making the same argument.