I think Discord servers based around specific books are an underappreciated form of academic support/community. I have been part of such a Discord server (for Terence Tao’s Analysis) for a few years now and have really enjoyed being a part of it.
Each chapter of the book gets two channels: one to discuss the reading material in that chapter, and one to discuss the exercises in that chapter. There are also channels for general discussion, introductions, and a few other things.
Such a Discord server has elements of university courses, Math Stack Exchange, Reddit, independent study groups, and random blog posts, but is different from all of them:
Unlike courses (but like Math SE, Reddit, and independent study groups), all participation is voluntary so the people in the community are selected for actually being interested in the material.
Unlike Math SE and Reddit (but like courses and independent study groups), one does not need to laboriously set the context each time one wants to ask a question or talk about something. It’s possible to just say “the second paragraph on page 76” or “Proposition 6.4.12(c)” and expect to be understood, because there is common knowledge of what the material is and the fact that everyone there has access to that material. In a subject like real analysis where there are many ways to develop the material, this is a big plus.
Unlike independent study groups and courses (but like Math SE and Reddit), there is no set pace or requirement to join the study group at a specific point in time. This means people can just show up whenever they start working on the book without worrying that they are behind and need to catch up to the discussion, because there is no single place in the book everyone is at. This also makes this kind of Discord server easier to set up because it does not require finding someone else who is studying the material at the same time, so there is less cost to coordination.
Unlike random forum/blog posts about the book, a dedicated Discord server can comprehensively cover the entire book and has the potential to be “alive/motivating” (it’s pretty demotivating to have a question about a blog post which was written years ago and where the author probably won’t respond; I think reliability is important for making it seem safe/motivating to ask questions).
I also like that Discord has an informal feel to it (less friction to just ask a question) and can be both synchronous and asynchronous.
I think these Discord servers aren’t that hard to set up and maintain. As long as there is one person there who has worked through the entire book, the server won’t seem “dead” and it should accumulate more users. (What’s the motivation for staying in the server if you’ve worked through the whole book? I think it provides a nice review/repetition of the material.) I’ve also noticed that earlier on I had to answer more questions in early chapters of the book, but now there are more people who’ve worked through the early chapters who can answer those questions, so I tend to focus on the later chapters now. So my concrete proposal is that more people, when they finish working through a book, should try to “adopt” the book by creating a Discord server and fielding questions from people who are still working through the book (and then advertising in some standard channels like a relevant subreddit). This requires little coordination ability (everyone from the second person onward selfishly benefits by joining the server and does not need to pay any costs).
I am uncertain how well this format would work for less technical books where there might not be a single answer to a question/a “ground truth” (which leaves room for people to give their opinions more).
(Thanks to people on the Tao Analysis Discord, especially pecfex for starting a discussion on the server about whether there are any similar servers, which gave me the idea to write this post, and Segun for creating the Tao Analysis Discord.)
This is a pretty cool concept.
Does life extension (without other technological progress to make the world in general safer) lead to more cautious life styles? The longer the expected years left, the more value there is in just staying alive compared to taking risks. Since death would mean missing out on all the positive experiences for the rest of one’s life, I think an expected value calculation would show that even a small risk is not worth taking. Does this mean all risks that don’t get magically fixed due to life extension (for example, activities like riding a motorcycle or driving on the highway seem risky even if we have life extension technology) are not worth taking? (There is the obvious exception where if one knows when one is going to die, then one can take more risks just like in a pre-life extension world as one reaches the end of one’s life.)
I haven’t thought about this much, and wouldn’t be surprised if I am making a silly error (in which case, I would appreciate having it pointed out to me!).
There’s 2 factors here.
Suppose there’s a life extension treatment that resets someone to age 20. It’s readily available to most first world residents, with the usual methods of rationing. (wait lists for years in European countries, the usual insurance scam in the USA)
A rational human would yes, buy space in a bunker and do all of their work remotely. There would be many variations of commercially available bunkers and security products, and the recent pandemic has showed that many high value jobs can be worked remotely.
However, the life extension treatment doesn’t change the ‘human firmware’. Novel experiences and mates will still remain highly pleasurable. Staying in the bunker and experiencing life via screens will likely cause various problems, ameliorated to some degree with artificial means. (vr headsets, etc)
So there will be flocks of humans who keep taking risks, and they will do the majority of the dying. I think I read the average lifespan would still be about 3000 years, which seems like a large improvement over the present situation.
In addition, this would probably be just a temporary state of affairs. (‘a dreary few centuries’) Neural backups, remote bodies, deep dive VR—there are many technologies that would make it practical to go out in the world safely. And a survival advantage for those humans who have the neurological traits to be able to survive the bunker years.
But, yes, I also think that society would slowly push for cleaning up many of the risks we consider ‘acceptable’ now. Cars, guns that are not smart and can be fired accidentally, air pollution, electrical wiring and gas plumbing—we have a ton of infrastructure and devices where the risk is small...over short present human lifespans. Everything would need to be a lot safer if we had expectations of thousands of years otherwise.
Lately I have been daydreaming about a mathematical monastery. I don’t know how coherent the idea is, and would be curious to hear feedback.
A mathematical monastery is a physical space where people gather to do a particular kind of math. The two main activities taking place in a mathematical monastery are meditative math and meditation about one’s relationship to math.
Meditative math: I think a lot of math that people do happens in a fast-paced and unreflective way. What I mean by this is that people solve a bunch of exercises, and then move on quickly to the next thing. There is a rush to finish the problem set or textbook or course and to progress to the main theorems or a more advanced course or the frontier of knowledge so that one might add to it. I think all of this can be good. But sometimes it’s nice to slow way down, to focus on the basics, or pay attention to how one’s mind is representing the mathematical object, or pay attention to how one just solved a problem. What associations did my mind make? Can I write down a stream-of-consciousness log of how I solved a problem? Did I get a gut sense of how long a problem would take me, and how reliable was that gut sense? Are the pictures I see in my head the same as the ones you see in yours? How did the first person who figured this out do so, and what was going on in their mind? Or how might someone have discovered this, even if it is not historically accurate? If I make an error while working on a problem, can I do a stack trace on that? How does this problem make me feel? What are the different kinds of boredom one can feel while doing math? All of these questions would get explored in meditative math.
Mediation about one’s relationship to math: Here the idea is to think about questions like: Why am I interested in math? What do I want to get out of it? What meaning does it give to my life? Why do I want to spend marginal time on math (rather than on other things)? If I had a lot more money, or a more satisfying social life, would I still be interested in doing math? How can I get better at math? What even does it mean to get better at math? Like, what are the different senses in which one can be “better at math”, and which ones do I care about and why? Why do I like certain pieces of math better than others, and why does someone else like some other piece of math better?
As the links above show, some of this already happens in bits and pieces, in a pretty solitary manner. I think it would be nice if there was a place where it could happen in a more concentrated way and where people could get together and talk about it as they are doing it.
Above I focused on how being at a mathematical monastery differs from regular mathematical practice. But it also differs from being at a monastery. For example, I don’t think a strict daily schedule will be an emphasis. I also imagine people would be talking to each other all the time, rather than silently meditating on their own.
Besides monasteries and cults, I think Recurse Center is the closest thing I know about. But my understanding is that Recurse Center has a more self-study/unschooling feel to it, rather than a “let’s focus on what our minds and emotions are doing with regard to programming” feel to it.
I don’t think there is anything too special about math here. There could probably be a “musical monastery” or “drawing monastery” or “video game design monastery” or whatever. Math just happens to be what I am interested in, and that’s the context in which these thoughts came to me.
Who will be funding this?
Many people want smaller, more focussed communities over big ones. One issue with that is funding, and large funders (govts, corporates) often cant carefully curate the values and metrics needed to build such comunities.
(I have only given this a little thought, so wouldn’t be surprised if it is totally wrong. I’m curious to hear what people think.)
I’ve known about deductive vs inductive reasoning for a long time, but only recently heard about abductive reasoning. It now occurs to me that what we call “Solomonoff induction” might better be called “Solomonoff abduction”. From SEP:
It suggests that the best way to distinguish between induction and abduction is this: both are ampliative, meaning that the conclusion goes beyond what is (logically) contained in the premises (which is why they are non-necessary inferences), but in abduction there is an implicit or explicit appeal to explanatory considerations, whereas in induction there is not; in induction, there is only an appeal to observed frequencies or statistics.
In Solomonoff induction, we explicitly refer to the “world programs” that provide explanations for the sequence of bits that we observe, so according to the above criterion it fits under abduction rather than induction.