You have two separate questions tangled into one. I suggest you need to disentangle them. They are:

1. How should I invest a lump sum for minimum stress?
2. Should I invest my lump sum in my startup?

People seem to be answering number 1, but that rather depends on you having decided that the answer to number 2 is "no". My opinion is that, if you believe your startup has a good chance of success, then yes, swing for the fences. Thirteen thousand is not a huge sum - if you get a reasonably good job, you can easily save up that much in a year. But it will keep you in ramen noodles long enough that you can tell whether your startup will succeed or not. So, your downside is very limited by adult standards, but the upside is presumably quite large.

If I were going to go for the startup, I would split my 13K in two halves. One half goes in a checking account, ready to pay for my ramen noodles for the next six months. The other half goes in a six-month CD, where it will accumulate 32 dollars and fifty cents of interest. Obviously this is not intended to actually make money, it's a precommitment to not touching that half until next year. Then in February, take the money out of the CD and re-evaluate the startup. Does it still seem like a good idea? Great, more ramen noodles. If not, give it up, start looking for a job, and put the remaining 6532.50 in a proper investment account.

For added precommitment, you could try splitting up the first half into a ready sum and a three-month CD, perhaps even some one-month CDs that you roll over until you need them; the interest will be utterly derisory but it's a convenient way of managing your monthly budgets.

Incidentally, if you haven't already done so, for the sake of all the absent gods go and read Paul Graham's essays.

Sane and well-measured advice is therefore wasted on me, and I just wanted to edit in this notice here so that other well-meaning folks don't get tricked into wasting their time trying to talk sense into a total nutcase like me. :)

(I appreciate all y'all, though. ^^ ) ]

Your edit seems to amount to an instruction to downvote and ignore you. I am not sure that it is achieving the purpose you intend (because I am not sure what purpose that could be).

You imply that one should invest where economic growth is expected to be highest.

Note that it does not follow that shares in high growth companies (or countries) will lead to high returns. This is because the expected future growth may well be built into the current price.

That is, if everyone thinks something will be likely worth a lot in the future, the current price will be bid up to reflect this.

It is the uncertainty of the outcome that may arguably cause higher expected returns. If people have a distaste for uncertainty, then the price might be bid down leading to higher expected returns.

This is the idea that one must assume risk (uncertainty) to obtain excess expected returns. It is by no means ubiquitous: assuming risk may reduce expected returns. For example, people assume risk to gain exposure to negative expected returns in a casino (roulette, blackjack, &c). No doubt there are plenty of examples in financial markets where risk does not automatically yield excess expected returns.

I don't have any investment advice, but my general advice is that you should calm down. You seem overly excited.

Let me suggest a way of thinking about investing. Here are a variety of things that an investor might want to do:

1: Minimize Bankruptcy Risk. (Chance of losing all of money)

2: Minimize Downsides. (Chance of losing some moderate chunk of money)

3: Keep Money Liquid. (Have your money be available for other things)

4: Maximize Upsides. (Chance of gaining some moderate chunk of money)

5: Maximize Speculative Upsides. (Chance of becoming rich.)

These are good things, but when investing, you generally don't get to pick all of them. For instance, I think my current strategy for my retirement account does a decent job of getting 1,2 and 4.

Now, you and I don't have to have the same values: As an example: You are throwing all of your money into a startup. That generally goes against 1. If the startup fails, all your money is gone, and so you aren't minimizing bankruptcy risk. And values can change: Your risk tolerance is not a fixed amount.

So a rough way to start is to categorize "In which order of priority are these goals are important to me right now and what will that be like in the future?"

A lot of investment sites also have these kinds of rough tests to get an idea of your risk tolerance so they can suggest advice accordingly, although they aren't necessarily perfect. This link seems to explain some of the issues that come up: http://www.businessweek.com/magazine/content/09_32/b4142059711173.htm

Sane and well-measured advice is therefore wasted on me, and I just wanted to edit in this notice here so that other well-meaning folks don't get tricked into wasting their time trying to talk sense into a total nutcase like me. :)

Sorry, but no can do. Part of the Less Wrong mission is "improving the sanity waterline". We can't sit by and let you be insane. I for one encourage people to spend as much to as necessary to talk sense to you. You signed up for this when you made the post.

3) Me and muflax are actually going to go work full time on developing [this totally amazing educational technology that will completely revolutionize human civilization but you have no reason to care about that until you've seen a demo in action so nevermind].

With muflax, huh. This sounds like it'll be epic to watch, regardless of how it turns out.

but in, like, some African region that has previously been served by, I dunno, jungle-donkeys

I realise you only meant this flippantly, but... it sounds really unpleasantly dismissive to me. Just wanted to flag this.

Good luck with the money, I'm afraid I have no useful knowledge!

Cookbook for standard best practices in the US:

1. Open a Roth IRA account
2. Select a fund for when you retire
3. Contribute $5000 every year to that fund.
4. If you have money left over, or make more than $50,000 per year and so should be saving more than $5,000 per year, set up a general savings account with the same target retirement fund.
5. Keep your other finances in order. Keep enough cash in your bank account to last you at least 2 months, preferably 3 or more, plus $1000. Emergencies will happen. Don't do anything stupid like acquire credit card debt. If you follow only one step, follow this step.

What's your plan B, in case your startup fails (most do)? If your answer is "it won't", I recommend sparing yourself the agony and buying $13k worth of lottery tickets.

Markets are essentially random walks with an upward trend?

Yes, but with a relatively high variance.

“Index funds” are magic boxes that you put money in and your money will grow at the same rate of the market that the fund “indexes”?

This is more or less true (minus some potential entry/manteinance costs)

“Developing world” economies generally grow a lot quicker than those in the “developed world”?

In general this is true, but the variance here is even higher. Lately, though, they are not performing particularly well (see here for example).

And there are enough of these places over the world, and they're independent enough, that natural disasters/political trouble/etc in a few of them still leave a consistent and high rate of average growth? So shouldn't I just put all my money in a fund that “indexes” all these "developing" economies together?

Yes, diversification reduces the risk, but the risk for equities remains in general significantly higher then the one for e.g. government bonds (i.e. losing your money is a real concern).

That said, even with a very good allocation, it should be very hard to make more than 8-10% a year with you investent (not impossible, mind you, chaotic systems are chaotic). This means rouglhy 1-1.3K per year in you condition. Of course, mr. exponential says that the longer the investment, the better (barring future market instabilities). It's up to you to decide if it's worth it. On the other hand, if you don't need the money now, there are other forms of investing that block your capital for a longer period of time, but with much lower risk.

EDIT Maybe it's an obvious advice, but be careful about what you're doing. If there's someone you trust to whom you can ask questions and submit invesment proposals for evaluation, absolutely do it. In any case, try to learn at least the basic features of what you're investing in (e.g. stock markets' returns have fat tails, whch means high probability of heavy losses, various derivatives can have many complicated features). I'll be glad to answer any questions, here or by PM, the best I can, but any specific investment must be evaualted on its own.