Let me add to your description of the "Loci method" (also the basis of ancient Ars Memoria). You are using spatial memory (which is probably the evolutionarily oldest/most optimized) to piggyback the data you want to memorize.

There is an easier way for people who don't do that well in visualization. Divide a sheet of paper into areas, then write down notes on what you are trying to remember. Make areas somewhat irregular, and connect them with lines, squiggles, or other unique markers. When you write them, and when you look them over, make note of their relative position - formula A is in the left top corner, while formula Z is down and to the right of it, just beyond the spiral squiggle.

For a lot of people, this works just as well as Ars Memoria, and is a lot easier to learn and execute on the fly.

As someone who just finished my sophomore year as a math major, I think I can give some useful advice in the vale of tears that is a mathematics degree.

All in all, it comes down to how much your GPA matters to you versus how much math matters to you when choosing courses. Even if you are ridiculously smart, most of the stuff you see after calculus and linear algebra is going to be pretty damn hard, and in order to get something substantial out of those courses you'll have to spend a large amount of time staring at symbols.

So if you want to maintain a good GPA, limit your desire to speed ahead and focus on the recommended courses. You'll then have the time to be able to really understand the material and have good grades. Even if you were at the top of your class in high school, your GPA will benefit from understanding this. I would even recommend going slower than the pace set by the administrators. No matter how ready you think you are for a certain course, there will be a point where you have absolutely no clue what the fuck is going on. Trust me.

In my opinion, you will get as much out of doing this as you would if you sped ahead but kept the same work ethic. I use this heuristic: If I want to take another math course and have the same GPA and an increased net mathematical knowledge gain, I need to increase my work ethic by ten. If I'm missing a pre-requisite, I need to increase it by twenty. Grad courses are a hit or miss; sometimes they can be an easy, relaxed way to get into higher math, and sometimes they can be insanely hard.

Now, if you don't care about your GPA, then take as many math courses as you can. That's what I did. Worked my ass off for B's and C's. The only reason why it works for me (in terms of my level of satisfaction with my choices) is that I don't (and didn't) do much of anything other than math. So I was able to really delve into all of these topics and come out with internalized knowledge - but I had to sacrifice my ability to complete assignments on time and prepare adequately for exams. Had I focused on getting A's... I might've been able to do it, but it would be at the expense of optimal learning (not that I didn't try to get A's with my "internalized knowledge", I'm just really driving home the point that this shit is hard, especially in timed situations).

I guess what I'm getting at here is: don't overestimate yourself if you want to keep doing and loving math. Know your breaking point, or at least remember that you have one - you will hit it, and it will hurt. Even if you are not super into math and just want to use it another things, the core courses are still very hard and this advice is still valid. And if you do want to skip ahead and do as much as possible, think about how much harder you think you will have to work, and multiply that by ten. This is if you actually want to get anything out of these courses - I'm sure you can skip ahead and get A's, but you won't have gained much. Unless you're Gauss. (On that note, you will encounter a lot of this, even as an undergrad).

Memory skills and the ability to do quick arithmetic in your head (the two go hand in hand). I would suggest reading some of Dominic O'Brian's books, and then visit the various mnemotechnic forums. Most of the techniques you will find are geared towards memorizing for competitions, but with slight adjustments they can be used anywhere.

It seems a little silly at first, but it has probably been the biggest return on investment I have ever made. I started practicing these techniques last summer, and when school started I used them (Method of Loci especially - basically you just imagine a spatial location you know well and place images representing the things you want to memorize at unique points in your spatial journey) to memorize as much as I could, using spaced repetition software (mentioned somewhere else on this thread) to lock the most important things in.

Now, instead of writing down copious amounts of notes in class and not understanding a single thing, I just sit, listen, and memorize. I'll also write down broad labels for things I need to make sure I remember (i.e if we are talking about "normal subgroups", I will write down "normal subgroups", but memorize the rest. This is just to have a hook to the topic so I can look it up later if I don't remember something). By focusing on the images I am creating in my head, I've noticed that it even helps me focus more intensely on the topic that the images are referencing. By the time class is over, I can run through the entire lecture as if I was reading a book. This is the best part, really; it's completely flipped my idea of studying on its head. Now I can just sit in the park and think, and it will qualify as studying because I have an entire book in my head with images to play around with.

I've also used it to memorize entire textbooks (not word for word, more like "page for page"). Again, it seems silly and pointless at first, but it really works wonders when you get the hang of it. Instead of belaboring over a topic that you don't understand and then an hour later looking back 10 pages to see the illuminating point, all you have to do is rewind a "walk through your friend's house" or "a drive to the beach". At first it will take 10 times longer to do this than it would to just read the book. Currently, it only takes me about twice as long. I just have to make sure I go back through it in my head later on so I can plant it in my long term memory (spaced repetition is amazing for this).

It takes a hell of a lot of work though, if you want it to be more than a gimmick. And there doesn't seem to be much information for people who want to use it for scholarship rather than for their shopping lists. Even posts I've seen here about the method of loci seem pretty dismissive of its utility, that it doesn't help you understand. I think these claims are somewhat valid, but it's like using Mathematica to solve integrals and then claiming that it doesn't help you understand them. Well, yeah. But you could construct a 3d plot of an integral, and even make it interactive to see how it changes when you change some of the variables. Surely that will help you understand more. It's the same thing for mnemonics. I could memorize a book word for word using these techniques and not understand a single thing; or I could take concepts and ideas from a page, mold a visual representation of them in my head, and make sure that my notion of how the representation acts and looks is congruent with these concepts and ideas. Then as I learn more, I go back and adjust this image for any discrepancies, and also use the image in later scenes when the concept/idea comes up again. Kind of like OOP in your imagination. They don't have to be valid physical models for your concept, only approximations of the idea as you understand it in visual form. It surprised me how illuminating these approximations can be - more than once I have attempted to create a visual image only to get stuck and realize "Ah, that's what I don't understand!".

Even if creating images doesn't help you understand, using this method is still an amazing way to create hooks for stumbling points in your reasoning. It's like having a jumper cable for your mind at all times. For any topic or concept you know you understand but have trouble at certain points, just make an image reminding you of the key elements and place it in your chosen spatial journey. When you need your reasoning, moving through your spatial journey and seeing these images will trigger a domino effect and you'll slide right through with no trouble.

Anyway, sorry for the jumbled wall of text. I'm trying to communicate how fucking useful this has been for me, but it's a little difficult with this kind of personal topic. So even if you find my reasons too subjective, I implore you to really try it. Not with the mindset that it's a stupid little parlor trick, but that it has the possibility to be a huge improvement in how you assimilate knowledge.

First, thank you for publishing this illuminating exchange.

I must say that Pei Wang sounds way more convincing to an uninitiated, but curious and mildly intelligent lay person (that would be me). Does not mean he is right, but he sure does make sense.

When Luke goes on to make a point, I often get lost in a jargon ("manifest convergent instrumental goals") or have to look up a paper that Pei (or other AGI researchers) does not hold in high regard. When Pei Wang makes an argument, it is intuitively clear and does not require going through a complex chain of reasoning outlined in the works of one Eliezer Yudkowsky and not vetted by the AI community at large. This is, of course, not a guarantee of its validity, but it sure is easier to follow.

Some of the statements are quite damning, actually: "The “friendly AI” approach advocated by Eliezer Yudkowsky has several serious conceptual and theoretical problems, and is not accepted by most AGI researchers. The AGI community has ignored it, not because it is indisputable, but because people have not bothered to criticize it." If one were to replace AI with physics, I would tend to dismiss EY as a crank just based on this statement, assuming it is accurate.

What makes me trust Pei Wang more than Luke is the common-sense statements like "to make AGI safe, to control their experience will probably be the main approach (which is what “education” is all about), but even that cannot guarantee safety." and "unless you get a right idea about what AGI is and how it can be built, it is very unlikely for you to know how to make it safe". Similarly, the SIAI position of “accelerate AI safety research and decelerate AI capabilities research so that we develop safe superhuman AGI first, rather than arbitrary superhuman AGI” rubs me the wrong way. While it does not necessarily mean it is wrong, the inability to convince outside experts that it is right is not a good sign.

This might be my confirmation bias, but I would be hard pressed to disagree with "To develop a non-trivial education theory of AGI requires a good understanding about how the system works, so if we don’t know how to build an AGI, there is no chance for us to know how to make it safe. I don’t think a good education theory can be “proved” in advance, pure theoretically. Rather, we’ll learn most of it by interacting with baby AGIs, just like how many of us learn how to educate children."

As a side point, I cannot help but wonder if the outcome of this discussion would have been different were it EY and not LM involved in it.

This seems to state that Rand was incapable of accepting that someone could be better than her, which I think was an exaggeration of her bloated ego.

Sure. But is the interpretation of EY significantly different if instead of AR the woman that's AR the myth? I know a number of Objectivists who really do believe that AR was the most important person in history. It's very different from reading the Analects, in which Confucius, mourning a gifted pupil, tells another pupil that the dead pupil was five times as clever as Confucius was. Regardless of whether or not Rand had the properly calibrated humility of science, she definitely failed to inculcate it in her friends and students.

I think I showed why this statement was untrue, and I don't think anyone can argue how arrogant it sounds (though that is a personal gripe I have with it).

Sure. "Particularly good at math" may mean very different things to you and EY. Math was Rand's favorite subject, but if EY means "Math Olympiad winner" by "particularly good" then those are different standards. Compare to Asimov, who was a professor of biochemistry.

I don't think her portrayal was very fair, is all. Yes, compared with other criticisms out there, this looks like praise.

Compare these statements. Are there criticisms out there that you think are fair?

I think Rand is an important person, and I suspect I've read more Rand and know more Objectivists than EY. But I don't think EY is obligated to invest very much before criticizing Rand, especially because his primary criticisms are of the Objectivist movement, and only indirectly criticisms of Rand. We know that Objectivism is not the rationalist movement it could be. (Many of the Objectivists I've introduced to LW have taken an instant liking to it, seeing all the places where LW-style rationality connects to or supersedes Objectivist thought.) Because the Objectivist movement revolves around Ayn Rand, it's probable that she had a big part to play in the creation of their culture. Maybe Branden was the main pusher of hero-worship- but Rand had an affair with him, rather than warning against hero-worship and cultivating dissent.

But taking a step back, it's hard to see why Rand's treatment in EY's post is significant. Is it because you think people on LW ought to have a higher opinion of Rand than they currently do? Because you think the story would be more effective at showing how to not become a cult if it included more nuance or references to Rand's life? Some other reason?

I don't think it's necessary to attack a person's character for the sake of rhetoric, especially when the highlighted aspects of that person's character are exaggerated.

What attacks on Rand's character did EY make?

I went back and reread Shermer's article, that EY links, and EY's post, and when comparing the two of them EY's post is a defense of Rand. "This could have happened to anybody; it might even happen to us! Let's try to learn from their example so that it doesn't." Shermer goes into the details of the nasty breakup between Rand and Branden- EY takes at face value that the spouses were okay with it, and labels it a private matter.

What am I missing, here? Quotes from EY's post will help.

This is a defense of Ayn Rand the woman and a response to her portrayal in the essay The Guardians of Ayn Rand.

I think you have misread the essay if you think a defense of Rand is a response to the essay.

Rand deserves a place in the history of philosophers for being willing to argue for individualism, capitalism, and science, but not for the creation of Objectivism. Openness and advancement are the hallmarks of important philosophical traditions.

She thought the creation of Objectivism was a big deal, and, well, she can be forgiven for not understanding how history would see her. Isaac Newton, for example, thought his theological work was far more significant than his physics hobby, and even wrote more about alchemy than about physics.

One of the points EY was making is that, when you talk to a scientist about Newton's rabid hatred of Catholics, they shrug and say that's not related to the physics- and being a genius is no guarantee your opinions are right. If you talk to an Objectivist about Rand's flaws- well, suddenly those are relevant to the philosophy.

Let's take an example where Peikoff tinkered with Rand: homosexuality. Rand thought it was disgusting, and involved "psychological flaws" or "unfortunate premises." After her death, both Peikoff and Branden disagreed with Rand about homosexuality- Branden going so far as to call her "absolutely and totally ignorant" about it. And, today, something like a fifth of Objectivists are gay. (The materialism and family resentment that comes so clearly in her novels resonate with a lot of gays, and I suspect the strong male heroes also play a role.)

And sexuality seems much more like philosophy than it is like chemistry. You can find the SDN that differentiates straight men from gay men but that doesn't tell you how you should treat them- that's something you should be able to figure out by observing humanity.

How are you using "justify" here? Do you mean "show to be morally permissible?" In that case sure, free country, etc.

Do you mean "show to be good role model behavior?" Not so much.

Do you mean "show to be in strict accordance with objectivism, which is a source of justification?" This is quite possibly Rand's own intent with the whole "what I say is objectivism" route, but if objectivism is to have any hope of meeting mild standards for good philosophy, said route cannot work.

From this side of the author/audience divide, what I feel like you are doing when justifying is repeating things that others said that made you feel okay about the thing being justified. But we, your audience, are not you, and so repeating things that worked for you probably won't work for us. You have to break things down and then build them up again to try and find the truth about a specific question.

But she rationally ostracized people who disagreed with her because she herself has said that she completely and fully embodies her philosophy

Well there's your problem.. If one wants to actually do anything with philosophy, one does not want to lug around the complete specs of Ayn Rand's brain, even if one has them. And, applying the copernican principle, there's no particular reason why the right way to think about the world (to the extent that that means something) should be expressed as the complete specs of Ayn Rand's brain. Instead, good philosophy should be fairly concise (compared to the information contained in a single human brain, at least), and shouldn't be specific to a certain race or culture, or even to humans, necessarily.

The only factual inaccuracy (and you've spent more time looking at this post than I care to, evidently, so maybe I've missed something) I see is the math bit. And that's even a stretch. I'd say it's a reasonable interpretation that Rand didn't meet the "particularly good" standard. I've certainly never seen any of evidence that it is beside the third hand account (Professor > Rand > Barbra) presented in the post. And even if she was unusually talented, she didn't really use any significant math in her philosophy or writing, which probably lead to the decay of the talent.

But basically, anything that divides humans into tribes is "mind killing". It doesn't have to be politics - any polarizing issue will do. Religion is the other prototypical example. But even inane things like Mac vs. PC can be mindkilling to an extent - anything that's polarizing. And Rand was one of the most polarizing figures of the 20th century.