Music and the arts, programming, and cooking have a wonderful property in common. They are all extremely compatible with micro-projects. By this, I mean that it's pretty easy for an artist, coder, or cook of any skill level to find a real-world, interesting project that's targeted to any given new skill that they're trying to build. Trying to learn sixth position or expand into the third register on the trombone? Working on callbacks in Javascript? Learning to cook vegan food? The passionate community surrounding these activities will have songs, coding projects, and recipes galore for you to build those micro-skills on micro-projects. Even if you're studying sociology, you can often explore the theories by sitting in a cafe and observing the behavior of people around you.

I think one property people point to when they refer to subjects as "abstract" or "hard" is that they aren't very amenable to such micro-projects. Some examples of subjects like this include math, chemistry, and microbiology. There might be lots of applications you can pursue once you've developed a sophisticated understanding of the subject. If you're able to get an entry-level job in the field, you might be able to get lots of exercise on a small subset of the skills that go into the subject. If you're willing to spend a lot of money, you can sometimes buy the equipment to do at least some practice with these subjects at home, though you might also face regulatory and legal barriers. Perhaps you can find tractable, fun projects that are thematically related to the subject, but they're unlikely to precisely and comprehensively target the material on, say, the level of chapter sub-sub-headings.

Usually, curriculum designers and teachers tackle this challenge with homework problems, exams, labs, debates, and classroom discussion. But there are two problems. First, a self-studier might not have access to all those resources. Second, those tasks often lack the juicy, real-world applied interest that creates a genuine enthusiasm in the student.

If you've had some success with this challenge, or know of useful resources for exploring it further, I'd love to hear about it!

Note: All subjects and experiences are welcome. It's OK if answers stray slightly off-topic or lead off in different directions.

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One source is societies popularizing the subjects. They often have some editions, printed or electronic, covering the more fashionable topics.

As for chemistry, don't go for the interesting stuff at home. It's possible to use household items to demonstrate the general principles at like high school level, but quantitative experiments are much more expensive and often hazardous. Even just storing some things is hazardous, never mind opening the bottles - especially if it's something organic which can have peroxides without you noticing. (And then, explode at some random point in time.) I'd like a chemist to chime in here.

I've heard of people doing glasswork at home, which definitely can help with some experiments in biology, for example. Actually, in case of botany, try the C-fern - it's available commercially, should grow easily (especially if you know how to operate a terrarium), you can even try obtaining mutations in the offspring. (Also, the subject of pheromone communication in ferns is rapidly developing and kind of cutting edge, so who knows what this will grow into :) this is one way to enter science faster :) ) Also in botany, another "easy" (well, easy) model is Capsella bursa-pastoris with her crazy leaves - IIRC, there are four main shapes controlled by two genes, but the plant is a tetraploid. Here, it's actually an open question which leaf shape is more suited to which climatic conditions etc. (so, population genetics). If you can rig a DIC-like lighting on your microscope (you do have a microscope?), it's possible to study the venation of the plant, I remember Fisher sold the medium for the preparations... (if I don't forget to, I'll post a link to the article I have in mind; but even if I do, DIC is a great thing to have, check out the amateur microscopy groups on social media for advice.) Capsella is a (relatively close) relative of Arabidopsis thaliana, the workhorse of plant biotech, so you can have some fun with the ample literature on that one.

There are a few problems with DIY organic chemistry.  The first one is that many of the reagents are toxic.  Some of those are volatile or readily absorbed through the skin.  Others will spontaneously burst into flame when exposed to air.  Sometimes the dangers of working with chemicals is overstated, but sometimes it's very much not.  In academic or industry labs we solve mitigate those problems with fume hoods and personal protective equipment (and no, the exhaust fan above your stove is not an acceptable substitute).  The second problem is that chemical reactions typically generate waste in addition to the products you want.  And it's not the kind of waste that most municipal garbage collectors are willing to accept.  Third, the hard part of organic chemistry isn't running reactions, it's purifying and characterizing your products.  Purifications might be tractable, depending on what you're doing (recrystallization, anyone?) but modern characterization techniques like NMR or mass spectrometry require hardware that's beyond most people's side-project budgets.  A fourth problem, at least in the US, is that buying certain types of chemicals, including some common and useful reagents, will get you on the DEA's radar unless you're buying through an academic or industrial research institution (thanks, wannabe Walter Whites!).  

There are examples of chemistry experiments that are safe and fun to do at home.  As Mary says, you can illustrate many principles with safe DIY experiments but unfortunately I just don't know how to mitigate these very real hurdles to at-home micro-projects in organic chemistry.

I guess one can make soap, as an applied project. Some paper chromatography can be done without a hood, outdoors (but then one still needs to dispose of the materials safely). Gall-based inks are, in a way, on the fence between organic and inorganic (also, playing around with homemade dyes is cool, e.g. from avocado seeds, alder bark or walnut skins - the colours fade, but you can stain paper so it looks old and then draw maps of treasure on it). Cooking is instructive (although people often underestimate the dangers of vinegar "because everybody has it in their kitchen".) Also, blacklight might be fun here.

But my most engaged instructors told us a real chemist develops a "sense of substance", like they often can tell things apart by their physical appearance and not even their chemical properties (given a set of familiar chemicals). There are different shades of colour, different granularities, different translucencies... it's just not something you can show at home. And separately, my botany instructors said they always make a student identify at least three species of a genus, whenever possible. For triangulation. If you give students only one species, that's how they will think of the genus as a whole. Give them two, and they will think about the differences between them, but not about the genus. But give them three, and they see the common features. Again, I don't think it's possible to show sufficient variety of chemical substances at home.

Always enjoying your thoughts. Thanks chemslug. My expectation is that there are more safe and tractable micro-projects out there than the average student takes for granted. But I am also raising these questions to confirm a suspicion I have: that despite our love for the idea of "learning by doing," there are many disciplines where a long slog of paper-based learning, punctuated by a few carefully regulated experiments, has to precede any kind of creative or independent hands-on activity.

LessWrong's steeped in "move fast and break things" Silicon Valley culture, which seems to inform a fair bit of the perspectives on education I see shared here. One reason why I appreciate your comments here is that you bring insight from a less-represented discipline, one with a different set of norms and requirements than we find in Programland.

Do you think that most aspiring chemists would do well to figure out how to set up their own home lab, figuring out how to manage the risks and invest in some equipment? A fume hood costs a few thousand dollars, which is pricey but not completely impossible. Or is there a pretty hard norm that you don't do any serious chemistry outside a professional lab setting? At what point do chemists become qualified to design and execute their own projects?

What an "aspiring chemist" should do depends a lot on age and where they are in the educational process.  For children below high-school age, I think there are lots of great experiments you can do to illustrate principles of chemistry.  Lack of originality isn't a bug there, it's a feature.  In high school, if you think you like science, take chemistry!  There should be a lab component in most schools, so you can at least get a flavor for what working with chemicals is like.  Access to equipment like this is an underrated component of the educational system.  For college students, all the entry-level courses (general, organic, inorganic) are likely to have lab components.  There are a few programs that separate the lab courses from the lectures, but they're the exception.  The experiments won't be cutting-edge, but rather are designed to give students an understanding of chemical principles and what it's like to work with chemicals in a research setting.

Where things get really interesting from a lab perspective is if you can convince a professor to let you into their research lab as an undergraduate assistant.  It's helpful if you're at a research university rather than a small liberal arts college because the lab facilities will be more conducive to cutting-edge research, and there will be grad students and postdocs who relish the opportunity to teach a curious undergrad how to do chemistry.  You likely won't be designing your own project, but will have the opportunity to use modern equipment to do novel research under supervision.  My undergraduate research experience was formative and a huge reason why I do what I do today.  I was also lucky enough to get to pay it forward and mentor undergraduates when I was a grad student and a postdoc.  

Graduate school in chemistry has a (somewhat deserved) reputation as a potentially miserable time.  You get lots of great experience and training, but the hours are brutal and the rewards can be sparse.  Synthesis in particular is a field where no matter how brilliant you are, lots of time in the lab is still essential for success.  At this point you will work with your advisor to design and execute research projects, and success depends on your insight and work ethic.  You can mitigate a lot of the problems with grad school by being careful about which lab you choose and being willing to set boundaries on your work time.  It's also worth noting that I know a lot of really good chemists who started working in industry immediately after their bachelor's, or after a master's degree.

For the adult who has completed their education and wants to start doing chemistry at a level other than "fun home experiments", I don't have great suggestions.  Maybe this is just a lack of imagination on my part as someone inside "the system" but the hurdles I talked about above are pretty daunting.  

Many of the coolest and most useful activities for learning are sealed off from non-professionals, or at least are expensive and time confusing to obtain certification or access. Usually for good reason.

This seems like a fundamental dilemma of the role of school. To make students directly see what’s cool about different subjects, they need lots of hands-on experience. But the vast majority of their time, and most of their evaluation prior to grad school, comes from book work. Access to hands-on projects and a sense of freedom and agency is limited at best.

And ultimately, that’s for reasons of safety and expense, which we can’t just criticize away.

It seems then that a big learning skill is maximizing access to such applied projects.

I wonder, then, if it would be better to orient school around single subjects from an earlier age. It makes more sense to give a student heightened access to mentorship, equipment, and materials if that stuff is their obsession. And for a self-studier, it seems important to figure out first what you want to obsess yourself with, and then focus on getting maximum access to applied learning environments.

From the link.

CH₂N₂ [a gas] may explode in contact with sharp edges, such as ground-glass joints, even scratches in glassware.

Wow.

Too bad it's toxic. Otherwise it could be an interesting anti-ninja weapon.

"This room is filled with CH₂N₂. If any of you draws a sword, you all die."

These are great ideas, thanks! I like both the specific suggestions and the idea of contacting societies popularizing the subjects. I hadn't thought of that idea.

Agreed that there are real issues with doing "interesting" chemistry at home. I do think that this is one area where the idea that students can motivate themselves by finding an "applied" project to work on might not be the best advice.

See here for an example of microscopy, https://journals.biologists.com/dev/article/118/2/575/37992/The-role-of-the-monopteros-gene-in-organising-the

(you might have a problem obtaining chloral hydrate, which is a shame because it's often used for preparations)

although the pictures I remember were probably from this one or thereabouts (but it references the first one anyway); very beautiful, but I've never done it myself https://www.researchgate.net/figure/Vascular-pattern-development-in-wild-type-A-B-and-in-fkd1-C-D-cotyledons-and-mature_fig1_10607469

Practicing the saxophone only has a payoff in saxophone music. Similarly, abstract exercises will often only have a payoff in nice abstractions. For example, solving the wave equation of the hydrogen atom is a classic, but it cannot gain you anything directly because it is merely knowledge, and that same knowledge can be found in a textbook or wiki faster than it can be derived. You're just gonna have to be the sort of person for whom solving the wave equation of the hydrogen atom is a juicy project.

You're just gonna have to be the sort of person for whom solving the wave equation of the hydrogen atom is a juicy project.

That's a nice quote. I'm working on a handbook for how to self-study. Mind if I (tentatively) use it?

Go for it - though it's about selection effects as much as it's advice.

Could you make the question more specific? It's not hard to think of an exercise when studying microbiology (or even a sequence of exercises), it's hard to think of one that has some non-trivial connection to modern science. I'd say, once you find one, it becomes a research question.

Here's another way of stating the exercise:

  1. Take a subject you're familiar with, or ideally are an expert in.
  2. Pick a sub-sub skill out of an introductory textbook on the topic. For example, if your subject is biochemistry, you might pick "RNA aptamers." If the subject is differential equations, you might pick "separable equations."
  3. Propose a micro-project where a student who had an introductory-level grasp of that topic would find it directly relevant. This micro-project should ideally be safe, cheap, legal/ethical, tractable for a self-studying introductory student, challenging/fun enough to be interesting. It should also be at least thematically related to real-world work in that field, in the way that coding a tic-tac-toe game is thematically related to professional programming work.