Things SPARC

I often get asked about what I learned from the SPARC summer camp. This is hard to describe and I never manage to give as a good of an answer as I want, so I want to take the time to write down something concrete now. For context: I attended SPARC in 2013 and 2014 and again as a counselor in 2015, so this post is long overdue (but better late than never).

(For those of you still in high school: applications for 2016 are now open, due March 1, 2016. The program is completely free including room/board and you don’t need rec letters, so there is no reason to not apply.)

The short version is that about 1/3 to 1/2 of the life skills I use on a regular basis are things I picked up from SPARC. (The rest came from some combination of math contests and living in college dorms.) On paper SPARC seems like a math or CS camp, but there is a strong emphasis on practicality in the sense that the instructors specifically want to teach you things that you can apply in life. So in addition to technical classes on Bayes’ theorem and the like, you’ll have classes on much “softer” topics like

  • Posture (literally about having good body posture)
  • Aversion factoring (e.g. understanding why I’m not exercising and fixing it)
  • Expanding comfort zones (with hands-on practice; my year I learned to climb trees)

and so on. This makes it hard to compare to other math camps like MOP (though if you insist on drawing a comparison, I think most MOP+SPARC students agree they learned more from SPARC).

Some more testimonials:

Now, here is my own list of concrete things which SPARC has taught me, in no particular order:

  • Being significantly more introspective / reflective about life. Example: realizing that some class/activity/etc. are not adding much value to life and dropping them.
  • Being interested in optimizing life in general; I now find it fun to think about how to be more productive and live life well the same way I like to think about hard math problems.
  • Thinking about thinking: things like mental models, cognitive biases, emotions, aversions, System 1 vs System 2,
  • Becoming very aggressive at conserving time. I’m much more willing to trade money for time, and actively asking whether I really need to do something, or if I can just axe it.
  • Using game theory concepts to think about the world. College tuition is expensive because this is the Nash equilibrium. Recognizing real-life situations which are well understood as games, like prisoner’s dilemma, chicken, etc.
  • Applying Bayes’ theorem and expected value to real life. Trying out X activity has constant cost but potentially large payoffs, hence large positive EV.
  • Being able to use probabilities in a meaningful way. Being able to tell the difference between being 90% confident and 70% confident in an event happening.
  • Actively buying O(n) returns for O(1) cost.
  • Being more willing to take less conventional paths, like essentially dropping out of high school to train for the IMO (I describe this in the first FAQ here). Another good example I haven’t done myself (yet) is taking a gap year.
  • Using Workflowy. It’s a big part of why I can think as clearly as I do. In context of SPARC, this is a special case of understanding the idea of working memory, which is also an idea I picked up from camp.
  • Writing a lot more. This is probably actually a consequence of the things above rather than something that I directly learned from SPARC; some combination of understanding working memory well, and being much more reflective.
  • Peer group and culture. This is a bigger one than people realize. In the same way that math contests establish a group of people where it’s cool to think about hard math problems, the SPARC network establishes a group of people with a culture of encouraging people to think about rationality. It’s very hard to be good at reflection in an isolated environment! SPARC lets you see how other people go about thinking about how to live life well and gives you other people to bounce ideas off of.

I’m sure there’s other things, but it’s hard for me to notice since it’s been so long since I had to live life pre-SPARC. And there’s some things that other people learned from SPARC that never stuck with me (lots of the social skills, for example). Much like your first time attending MOP, there will be more things to learn than you’ll actually be able to absorb. So the list above is only the things that I myself learned, and in fact I think the set of things you acquire from SPARC more or less molds to whichever particular things matter to you most.

Conversations

I’ve recently come to believe that “deep conversations” are overrated. Here is why.

Memory

Human short term memory is pretty crummy. Here is an illustration from linguistics:

A man that a woman that a child that a bird that I heard saw knows loves

This is a well-formed English phrase. And yet parsing it is difficult, because you need a stack of size four. Four is a pretty big number.

And that’s after I’ve written the sentence down for you, so your eyes could scan it two or three times to try and parse it. Imagine if I instead said this sentence aloud.

Other examples include any object with some moderately complex structure:

Let ABC be a triangle and let AD, BE, CF be altitudes concurrent at the orthocenter H.

This is not a very complicated diagram, but it’s also very difficult to capture in your head unless you’ve seen it before — and again, that’s after I’ve written it down for your viewing pleasure.

Now imagine what you’re talking about isn’t just six lines and seven points, but “what do you think the point of college is?”, or “should a high school diploma be required to obtain a driver’s license?”, or “what is algebraic geometry about?” (all examples from my life, mind you). The answer to these questions is far more complex than the trivial examples I’ve given above. To try and talk about these things merely by voice seems fruitless.

It’s worth pointing out that you can get away with things that have a lot of breadth as long they do not have depth — loosely, as long as there are not too many dependencies. To give an example, the linguistics example is tricky because all the subjects and verbs depend on each other. The geometry diagram is tricky because the points are all tied together in a certain way. But I could read the first chapter of And Then I Thought I Was A Fish out loud, or tell you the story of the cute girl I met three summers ago, because the parts don’t depend (as much) on one another: at any point in a story you can remember the last couple sentences and still enjoy the story. But if I try to read you the first chapter of The Rising Sea: Foundations of Algebraic Geometry, it would make a good bedtime story only because you’d probably fall asleep.

It just strikes me as bizarre that people talk about “deep” issues without writing a single thing down. I think if you’re having lunch with a friend and discussing something like this, you ought to at least have a piece of paper out on the table where you can both jot down the main ideas of what’s been said. It doesn’t need to have every word because then you just get bloat, but still, at least get the key insights somewhere visible. (That’s what presentation slides and blackboards are for, right?)

Computation

The other strange thing is that in conversations, you have to process and respond in real-time. You can only spend as long thinking about a sentence as it takes for the next one to be said.

This is fine if I ask you a question such as “what is your birthday?”, because lookup queries are fast. It’s fine if I ask you “what did you think of X book you read?”, again because it is just a lookup query. Note that this is true even if you spent a long time reading and thinking about the book, because the computation was already done. It’s even fine if I ask “what is two plus five?” because it takes not very long to add.

But if I ask “what do you think about the war on drugs?” and you haven’t been thinking much about it, then the best answer you can give is “I don’t know”; because you can’t do a lookup query for an answer you haven’t computed yet.

Put another way, suppose someone asks me some complex question like “how do I get better at math contests?”, and I respond “do a lot of problems that are right above your ability”. One of two possible things just happened:

  1. I had already thought about this question, and this is a pre-computed answer, or
  2. I came up with this in the half second between the end of your question and the start of my response. (Though you can increase this time by pre-pending “uh”, “like”, “I think”.)

In other words, the fast nature of conversations prevents anything other than cache lookups and first impressions (or I suppose possibly a combination of both). And if the issue you’re talking about is sufficiently complex, first impressions are likely not so insightful. So if I sound really smart in a conversation, the only reason is that you’re asking questions I already pre-computed good answers for.

In other words, the best you can do from a typical conversation is learn what people’s existing ideas are. There isn’t a tractable way to generate new ideas from feedback, just because the time-scale involved is too small. Eliezer Yudkowsky makes a similar point in a Less Wrong Post:

If you want to sound deep, you can never say anything that is more than a single step of inferential distance away from your listener’s current mental state. That’s just the way it is.

Hypothesis

I will now point out that both issues I mentioned have easy partial fixes. If I’m correct, then deep conversations can be substantially enhanced if we use paper or blackboard or anything else, and agree it is socially acceptable to take a minute to respond. Neither of these actions will completely alleviate their respective problems, but trust me when I say having 60 seconds to think is a world of difference compared to 2.

Both of these initially struck me as weird conclusions, but they do seem to make sense on closer inspection. In fact, I have actually seen both done in practice (albeit not simultaneously). So this means I have a way to test what I’ve written in this post now…