Well, if real interest rates are negative, everything reverses, and you should start favoring more expensive things now.
Also, it’s possible to be realistic and say things like “if 2 + 2 = 5, then 5 = 2(1+1) and therefore isn’t prime”.
richard_reitz
Karma: 327
Definitely. I wanted to make that point because, until I read Varian, I accepted the naive argument and not everyone here has studied economics, and the less they know, the more this entire “financial effectiveness” post is aimed at them, and this is something I found completely nonintuitive before reading about it and transparently obvious afterwards.
The best textbook on memory I’m aware of is Baddeley Eysenck Anderson. It is quite good, but some of the definitions are vague, so you’ll need to reference Wikipedia,.
Memory palaces, more formally known as Method of Loci, are well-supported by the academic literature. Brienne’s presentation is a fantastic introduction, in line with all the academic literature I’ve read.
I use Anki. It gets the job done quite well, and although other software may be just as good or better, I’m left with no desire to try anything else. See janki method for implementation suggestions.
I’m in the middle of a course on memory; according to my notes, making outlines is a good way of studying for a test and thinking about things in terms of future plans is “perhaps the best way of remembering stuff” (so, if I wanted to remember regular expressions, I might imagine doing this with them).
According to Scott, bacopa is “a memory-enhancing drug that performs very well in studies”—assuming you take it consistently for 3 months. According to my soylent spreadsheet, this is the most cost-effective source. According to Reddit, this is source with the lowest amounts of heavy metals (which are well within limits set by FDA). Reddit also has dosing recommendations. Apparently is also an axiolytic, so yay. Note that bacopa tastes nasty, so many people pay a bit extra for pills, although I find the taste trivial to deal with if I have a glass of water to wash the powder down with.
Memory researchers do, in fact, make a distinction between accessibility (can I retrieve a memory?) and availibility (does the memory trace exist?).
Yes. Lots of them. Right now, my memory deck has about 200 cards, and I’m only about 2⁄3 done with the course. I’ll point again to Baddeley Eysenck Anderson. You seem primarily interested in long-term memory (although that may be an artifact of not knowing a lot about memory; a large benefit of having a textbook on memory is to point out “unknown unkowns”), so here are some big ones off the top of my head.
Implicit and explicit memory (also known as declarative and nondeclarative, respectively).
Episodic and semantic memory (are subsets of explicit/declarative memory)
Also procedural memory (a subset of implicit/nondeclarative memory).
You should also be aware of the testing effect and distributed practice, which, along with forgetting curves, form the basis of Spaced Repetition Software. Since many things don’t lend themselve to Anki, like riding a bike, it’s enormously beneficial to know about these independently.
Also Source monitoring, which leads to my favorite term, cryptomnesia.
There is an easy way of watching the lectures. It involves paying Harvard University $1,250 whenever the class is next offered. Their video streaming is on par with Youtube circa 2007, but at least it works.
There is also a free way of watching the lectures, but it involves me breaking a contract I made with Harvard University, which I’m all manner of unwilling to do. However, they’ve made the video to the first lecture publicly available in the course description, so there’s that.
Yes (4 credits).
Nootropics Depot. If you dig around the comments of the Reddit link, you’ll find that it’s the same one as the first one in the OP there.
I’ll give you that nutrition/exercise is very high on the list of things to do to optimize memory, but I’m skeptical that it’s more important than mnemonics.
Personally, movement from fairly wretched nutrition/exercise to Lifestyle Interventions to Improve Longevity/Optimal Exercise-compliant nutrition/exercise has helped lots and lots, but (for the limited cases it applies), Method of Loci helped more.
There’s two problems here. First, we have duplication of labor in that we have something like 1% of the population doing essentially the same task, even though it’s fairly straightforward to reproduce and distribute en masse after it’s been done once. This encompasses things like lesson plans, lectures, and producing supplementary materials (e.g. a sheet of practice problems).
This leads into the second problem, which is a resulting quality issue: if you have a large population of diverse talent doing the same task, you expect it to form some sort of a bell curve. As noted above, we can take any lecture, tape it, and broadcast in en masse fairly easily. When we choose a system where each student is subjected to their instructor’s particular lecture, a relatively small portion of them get an excellent lecture, a very large portion get an average lecture (rather than an excellent lecture), and a relatively small portion get an execrable lecture (rather than an excellent lecture). If you’re really ambitious, you could even get the top, say, ten lecturers together and have them collaborate to make a super-lecture, and then get feedback on that particular unit, so they can improve the superlecture into a super-duperlecture.
(IMO, this is still a suboptimal way to do things. Try that process on textbooks (which are much easier to write collaboratively), and instead of getting feedback on hour-long chunks, get feedback on section-sized chunks (which, depending on the subject, can something like one-tenth the size). A good textbook is also cheaper to write, cheaper to distribute, more updateable, and better didactic material to begin with.)
It’s worth noting that there’s still a few wrinkles. Most importantly, there’s really no such thing as a “best” lecture, lesson plan, problem set, or textbook; the “goodness” quality depends, not just on the lecture’s content, but the intended audience. Think of this as a callibration issue. For instance:
Last I checked, MIT uses Sadava as their introductory biology textbook. If you dig around the reviews, you will find endorsements of another introductory biology book by Campbell that claim it’s “SO much easier to understand. It’s better organized, more clearly written”. When I found myself needing to relearn introductory biology (this time with Anki so I actually retain the knowledge), I tried Campbell, since that’s what my high school used, but gave up not halfway through the first chapter, frustrated by the difficulty I had understanding, the poor organization, and unclear writing; I find Sadava, however, to be much easier to understand, better organized, and more clearly written. Is the quoted reviewer lying, perhaps paid off by Big Textbooks? Perhaps, but a much better explanation is that Sadava is more technical; it’s much closer to the “definition-theorem-proof” feel of a math text. This makes it a fantastic text if you’re most students at MIT (or a typical LWer), but much less so if you’re in the other 99% of the population. This also solves the callibration problem: write two (or more) supertextbooks.
(This also neatly explains why MIT sometimse seems like the only school that uses good textbooks and why SICP only has 3.5 stars on Amazon.)
A second wrinkle is individual attention, which I tend to be dismissive of (if the textbook is good enough, you shouldn’t need any individual attention! And it’s not like the current education system, with its one-way lectures, is very good at giving very much individual attention), but if we’re optimizing education, there probably is more individual attention given to every student. However, because of reasons, I suspect that most of it should come from students in the same class, not staff. Also, it belongs after the reading.
A third wrinkle is a narrowing of perspectives. In any particular domain, there’s usually several approaches to solving problems, often coming from different ways of looking at it. In the current system, if you wind up on a team and come across a seemingly intractable problem, there’s a good chance that someone else has happened across a nonstandard approach that makes the problem very easy. If we standardize everything, we lose this. This is somewhat mitigated by the solution to the callibration problem, wherein people are going to be reading different texts with the different approaches because they’re different people, but we still kind of expect most mathematicians to learn their analysis from super!Rudin, meaning that they all lack some trick that Pugh mentions. The best solution I have is to have students learn in the highly standardized manner first, and once they have a firm grasp on that, expose them to nonstandard methods (according to my Memory text, this is an effective manner for increasing tranfer-of-learning).
The argument goes “paying 20k camera-people for one year can replace 2M full-time equivalent jobs next year, which can either go into something more useful without changing anything else (1). Of course, once you’re going to do that, you’d do well to look into seeing what elements of anything else could be changed to make it even more awesome.”
If we optimize properly, I believe we wind up open-sourcing textbooks, somewhat like Linux. We have a core textbook, which has recieved enough feedback to make sure that everything is explained well enough that students generally don’t come away with misconceptions, but because they’re open source, every time you need to write for a particular audience, you have something to work from. LaTeX also supports comments, which makes it easy to include nonconventional perspectives for interested students (i.e. the ones who really need them).
But, yeah, pooling resources. Definitely something we should do more of and WHY HASN’T THE FREE MARKET SOLVED THIS 10 YEARS AGO?
(1) Fermi estimate is as follows: Cursory search indicates Harvard offers a bit over 3k undergraduate classes. Round it up to 5k to include secondary school and the few undergraduate courses not offered at Harvard (for instance, I can’t find an equivalent to 8.012.) Multiply by 4 for different levels, and we arrive at 20k camera-people needed to tape all these courses. (It’s actually less than that, since most courses are one semester.)
Cursory Googling indicates there are 3700k teachers in America; add in other English-speaking countries and eliminate primary- and graduate-level teachers should bring you to 4M teachers (I’m guessing that we add more teachers from English-speaking countries than we lose from not considering primary- and graduate-level teachers, since most classes are at these levels.) Assume that half their teaching job is replaceable by the videos we’ve created, and we’ve freed up the equivalent of 2M full-time jobs.
This is very much a Fermi estimate, but I feel I was liberal enough with the camera-people portion (we’re only hiring them a few hours a week!) to say that the cost of getting high-quality video of all secondary and undergraduate courses is 1% of the savings it should theoretically yield every year in the future. This upper limit goes down once we start writing textbooks instead of taping lectures, especially since most secondary and undergraduate courses already have very good textbooks to work from.
Yeah. I’ve taught myself several courses just from textbooks, with much more success than in traditional setups that come with individual attention. I am probably unusual in this regard and should probably typical-mind-fallacy less.
However, I will nitpick a bit. While most textbooks won’t quite have every answer to every question a student could formulate whilst reading it (although the good ones come very close), answers to these questions are typically 30 seconds away, either on Wikipedia or Google. Point about the importance of having people to talk to still stands.
Also, some textbooks (e.g. the AoPS books) have hints for when a student gets stuck on a problem. Point about the importance of having people to help students when they get stuck still stands, although I believe the people best-suited to do this are their classmates; by happy coincidence, these people don’t cost educational organizations anything.
I’m tinkering with a system in which a professor, instead of lecturing, has it as their job to give each of 20 graduate students an hour a week of one-on-one attention (you know, the useful type of individual attention), which the graduate student is expected to prepare for extensively. Similarly, each graduate student is tasked with giving undergraduates 1 hour/week of individual attention. This maintains a professor:student ratio of 200:1 (so MIT needs a grand total of… 57 professors), doesn’t overly burden the mentors, and gives the students much more quality individual attention than I sense they’re currently getting. (Also, I believe that 1 hour of a grad student’s time is going to be more helpful to a student than 1 hour of a professor’s time. Graduate students haven’t become so well-trained in their field they’re no longer able to simulate a non-understanding undergrad in their head (an inability Dr. Mazur claims is shared among lecturers) and I expect there’s benefit from shrinking the age/culture gap. Also, no need to worry about appearing to be the class idiot in front of the person assigning your grade and potentially not giving you the benefit of the doubt on account of being the class idiot.) (Also, it has not escaped my attention that this falls apart at schools that are small or don’t have graduate students. And there’s other problems. Just an idea I’ve had floating around that may be enough in the right direction to effect a positive change.)
Turns out you’re not the only one who wants to know this. Seems your best bet is to use C-S-v to paste raw text and then format it in the article editor.
Since this review, Axler has released a third edition. The new edition contains substantial changes (i.e. it’s not the same book being released under “n+1 edition”): though there’s little new material, exercises appear at the end of every section, instead at the end of every chapter, and there’s many more examples given in the body of the text (a longer list of changes can be found on Dr. Axler’s website). I feel these revisions are significant improvements from a pedagogical perspective, as it gives the reader more opportunity to practice prerequisite skills before learning the next thing. The changes also lower the requisite mathematical maturity, which is a good thing (insofar as it makes the book more accessible), although it won’t push the reader to develop mathematical maturity as much. Overall: the third edition came out when I was halfway through the second edition and I felt that the improments merited switching books.
“Baby Rudin” refers to “Principles of Mathematical Analysis”, not “Real and Complex Analysis” (as was currently listed up top.) (Source)
It has been requested that I post my own take on efficient learning. As I spend half a page describing, this is not yet ready for publishing, but I’m putting out there because there may be (great) benefit to be had. After all, there is low-hanging fruit if you’re willing to abandon traditional methods: simply doing practice problems in a different order may improve your test score by 40 points.
White noise is fine; irrelevant sound effect operates on anything that sounds like it may be human speech, which turns out to be any sort of fluctuating tone.
As another person who’s used Anki for quite some time (~ 2 years), my experience agrees with eeuuah. I would also add exceptions to “just Google it.”
It’s easier to maintain knowledge than to reacquire it. The prototypical example here is tying a tie. Having a card that says “tie a four-in-hand knot”, and having to do that occasionally, turns out to be a lot easier than Googling how to tie a tie, especially if you do it infrequently enough that you need to re-learn it every time.
You need to maintain working memory. The prototypical example here is math. Sure, I can look up the definition of an affine subset, but if I’m in the middle of a proof and I need to prove X is an affine subset of V and then need to look up the definition of affine subset, then I suffer a break in my working memory, which sets me back quite a bit.
You need to remember that the fact exists. The prototypical example here is theorems. Being able to Google the Law of Total Probability doesn’t help if I don’t remember that it exists, and it doesn’t tell me when I can apply it. Having an Anki card for Law of Total Probability does both these things.
You need knowledge in a context where you can’t use Google. The prototypical example here is school. Even outside of school, though, there’s situations where it just won’t do to pull out your phone to Google something.
It should be noted that there’s a nonobvious opportunity cost here; specifically, money spent on the more expensive product can’t be invested.
For example, mechanical keyboards seem like something that costs more up front that’s cheaper in the long run. They cost about an order of magnitude more than membrane keyboards, but last about ten times longer, so you only need one mechanical keyboard to ten membrane keyboards, so the cost equals out in the end. Since the typing experience is much better on mechanical keyboards, by paying more up front, you essentially get a much-improved typing experience for free.
But, the extra money you spent on the nice keyboard could’ve been invested (or used to pay down debt) instead. If there’s a an annual real interest rate of 10%, then buying 10 membrane keyboards at $10 over 10 years and investing the money you didn’t spend nets $45, not counting re-investing (1). Note that these numbers are made up to make the math simple; in particular, the real real interest rate isn’t that high.
Also, the membrane keyboard you buy in year 10 isn’t going to be the membrane keyboard you buy in year 1.
(1) Using present value, in year 1, instead of paying $100 (cost of the mechanical keyboard, ten times the cost of the membrane keyboard), I pay $10 and invest $90 which, at 10%, yields $9. In year 2, you pull $10 out of the investment to buy the second membrane keyboard, so now you have $80 invested, yielding $8 returns. 9+8+...+1 = (9^2 + 9)/2 = 45.