I will now explain some practical techniques that I would give someone in your position. It looks like you have already implemented some of them. FYI I haven’t provided much background on any of the techniques, so if you want any more information on any of the mentioned techniques check out my post on the CFAR material as well.

Value Awareness

• Reframe the situation to find hidden values. You can do this, for example, by asking: “If I was already at the public school would the choice to switch to the private school be just as hard”. If there is a difference, then analysing why can often reveal hidden values.
• Use goal factoring to find hidden values. This entails finding some alternate set of actions through which you could get what you want cheaper and then analysing why you don’t choose to go with the cheaper option. For example, boarding at the school would resolve move of the problems you have, e.g. travelling and not having enough social time with the other students. I don’t know if this is an option, but if it is and you don’t want to do it then the reason for this should be in your considered valuations.
• Find out which aspects of the choice are cruxes. You can do this by creating a list of the valuable or aversive things related to the two choices and then eliminating one of them at a time to see if the choice you would make is significantly altered. If it is, then you have found a crux.
• Reference class hopping. Try and think about if your choice ever wavers. That is, if there are moments when you really want to change schools. If this happens, then it indicates that there may be some large underlying issue that is prompting the desired change. An example might be that your desire to change schools spikes when you are feeling excluded, like you are not part of the clique or like you can’t connect deeply with anyone at the school. A large underlying issue, in my opinion, indicates a problem that you should at least try to resolve before making any drastic decisions.

Prediction Accuracy

• Take an outside view. Can you find anyone who has made the same choice already?
• Trial the change to see what it will actually be like. This is probably not applicable for your situation, but it is normally one of the first things to look into.

Agency

It can often be good to spend most of your effort on thinking about how to fix existing problems rather than moving to a whole new situation. It is common for people to not think about or to underestimate the costs involved with change. In your case, example costs would be having to get to know the new teachers and students in the public school. An example of fixing a problem could be seeing if it is possible to set up a math club at your private school.

• Think through all the cruxes that you figured out earlier and try to come up with as many solutions as you can that would deal with those cruxes. For example, instead of taking the trip to the private school each day you can look into boarding at the school. Once you have come up with these strategies you can take a much more intricate approach to the choice, perhaps, employing multiple strategies to deal with different aspects relating to the choice.
• Get the advice of others especially those who can relate and are close to the problem, e.g. teachers, parents, friends etc. Be sure not to present the solution as a false dilemma, i.e. to change schools or not. Instead try to explain the situation as fully as possible. This could involve going through all the cruxes and the strategies you have come up with the resolve them. There are two extra benefits to this as well:
  1. It can often help you come up with a solution that should have been obvious. This is because there is difference between thinking you have fully understood a problem and being able to fully explain it to another person.
  2. It allows you to see the problem from a different perspective. It can, at times, be easy to miss the ramifications for other people of the choices that we make.

First, I would say look for the possibilities to make the boarding school work as best as possible.

What can you do directly? Have you considered actually boarding at your current school? Is that financially doable? If it's really an issue of coming home late every day, are there any activities that go late on some days, so that you have some long days, and then some short days? How can you adjust your schedule to make things work? You're going on 16, aren't you? Are you going to get a car for that commute? That might make life easier. On activities, have you looked at them all? You're young. Try things. Art. Music. Dance.

( I really can't recommend Dance strongly enough as something to get into young. It's fitness that can last and be used a lifetime. And it's a gold mine for young men, as there are a dozen girls trained in dance for every guy. I took up social dance after grad school. I'm 50 now, and dancing with girls half my age because I can. Me and my friends were just young morons for turning up our noses at dance. This falls under "try things" too. I had no idea I'd enjoy dance so much, or of all the benefits it would bring.)

After you look at your options for what you can do, I'd go talk to administrators at your school to see if they can help. Tell them you love the place - you LOVE the place - but you have issues because of being off campus and the on campus requirements keeping you from home. Could they reduce the participation requirements? Could they help further financially to get you boarding on campus? Maybe part time? What kind of high school doesn't have a math team?

Private boarding schools should have a good deal of flexibility in what they can do financially. Particularly with room and board, I expect that's just adding you to fix costs that the school already incurs.

I got a similar scholarship to a private (but not boarding) school. Though smart, I was not always so good a student. They counseled me and worked with me.

They want you to stay. They want you to succeed. They don't want you to bail.

Work for the best deal you can manage, and then decide.

The private school sounds like it would leave you better prepared, and certainly better credentialed to get into the best school you can.

The college you go to, and the friends you make there, have a huge effect on the rest of your life. I would expect the same principle applies to snooty boarding schools. You make connections that can last you decades. The college you go to matters if you want to go to grad school (because your grad school matters, particularly if you want to stay in academe).

The trade off you make now will be paying off in compounded interest for the rest of your life. It's a good time to suck it up a little for a long term gain.

I've noticed that when people tell me I have to do things, I enjoy them much, much less.

Everybody is like that. Particularly at work. Everything is a battle of status and control. It's not helpful. Try to let it go.

What non-trivial falsifiable assertions (or, better yet, predictions) does this theory make?

The application seems great, but the list of permissions it needs is scary ("perform operations like adding, and removing accounts and deleting their password", "use the authentication credentials of an account").

Thanks! I think I will go with "Fernus imaginatus", because I wanted just something fern-like but without allusions to real plants - a name for a spherical fern in vacuum, if you wish.

How do you say in Latin 'Fern imagined' (like a real species name)?

Found this website selling very cool mattresses. Anyone tried them?

"very cool" = connected to a smartphone, collecting data about your sleep, adjustable by clicking a button

What do you guys think of the theories of Ernest Becker, and of the more modern terror management theory?

The basic argument as that many, if not all, human behaviors are the result of our knowledge of our own mortality and our instinct to deny and forget about it in order to seek some kind of literal or symbolic immortality (by living forever, or writing a famous book, etc.) Religion exists to tell us that it's okay to die, culture to make us forget about religion, so we don't examine it too closely or think about death in general (it can still be scary because the evolutionary instinct to survive is still there). This definition of "culture" applies to nearly every domain of human achievement, including this very website. Less wrong exists to raise users' self esteem or self-concept so that the feel some security in a symbolic kind of immortality (I'm rational, I'm a transhuminist--of course I'll survive!)

I suggest you read the links I gave above for further explanation. There have also been scientific studies on mortality salience (here's a review) which seem to support the theory.