The title
I said on another post that I've seen this "spike" wording a few times today and I think it can be a little obfuscating. (From what I can tell, it came from a PrepScholar blog post? Anyway, it's a weird term.) What you really need, and what that "spike" is in practice, is some kind of passion that you pursue and develop throughout high school.
In the simplest possible words, Ivies are looking for students who actually, authentically care about something. Whether that thing is making art, solving mysteries in physics, pursuing social justice initiatives, solving economic problems—they're looking for students who have demonstrated throughout their actions in high school that they care deeply about something, enough to put lots of work into pursuing that thing. Because even if their passion changes, they've shown that they have the potential to invest their time and energy into something they care about. The problem with well-roundedness is that, without that kind of passion, well-roundedness by itself can just come off as careerism, which is a pretty big turn-off for a lot of colleges.
Now, you don't need to publish a book or start a community organization or run for congress or something wild like that to be admitted to an Ivy League school—I did none of those things and got into two of them (this is in 2014, so about 5-6 years ago), and I've worked with plenty of students who've headed off to Ivies over the last couple of years who had well-developed passions, with evidence to back that up, and could express them well in essays. You just need to have something you care about, and you need to have pursued it in a meaningful way.
So, what are you passionate about? What do you care deeply about? Your extracurriculars are pretty heavily varied—which one (or two, or three) among them is (or are) your favorite(s)? How could you develop those interests further? You have plenty of time, and as I'm sure you can imagine, a ~22% chance for Brown is significantly better than their average applicant. That means that, when they look at students with your record, they'll admit about 1 in 5 of them—and they'll choose that one student by virtue of a lot of metrics: "fit" with the school, how well they think they'll be able to take advantage of Brown's resources, and how strongly they communicate and express their passions or, if we must, their "spike."
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