Challenges

This has been a hard week for me.

On Tuesday I got back my midterm for intro to AI. The material for the course is mostly stuff I'd already done before, so Ive never been too worried about my grade. And, seeing that I got 85% on the midterm, I was correct. What had an undercurrent of an effect on me, which I didn't feel until that evening, was that my score was below both the mean and the average.

And all of a sudden, I started questioning myself. Am I really cut out to be in grad school? Can I make the original contributions that are required of me?

Then there's the anxiety of not knowing how I did in my machine learning midterm last week. Although I have taken a machine learning course before, this course is much more statistically oriented. While I am not completely clueless about statistics, the only course I took on it was in my junior year. I was definitely not up to scratch with my probabilities and density/mass functions, and it was a struggle to understand what the class was about.

It's strange, because I imagine that's how some people must feel even in high school. For people who are not particularly gifted at math, or science, or whatever subject, being required to take those courses must have been difficult for them. I have never had that problem - most of the courses I took even in college came easily to me, and very rarely did I really have to push myself to even get by in a class. With the combination of machine learning, and being below average in AI, I got a glimpse of what school must have felt like for some people.

Last summer when I first worked at CTY, one of the things which struck me the most during orientation was something not about me or the staff, but about the kids. Someone who has worked at CTY for many years commented that while the kids can do a lot of things by themselves, at some point when they get older they /have/ to work with each other, because what they're doing is simply beyond the capability of any single person. I remembered that comment, and even put it in my journal, because I wondered if that was the case for me too. Just as before CTY the students might not have needed to work together, and therefore have poor teamwork skills, I could phrase my own life in those terms. Everything up to and including college had a fixed upper boundary on what you could do. In elementary school you had to master multiplication, in high school it was calculus, and in college some selected topics within a certain field. I was smart, so I did all this without problems, but I wasn't smart enough to skip all the way to college or grad school before my age.

But once college ends, the world is wide open. In grad school and in research, the things you are learning may not have an agreed upon answer. The question might not even have been asked. Each professor that you deal with personally have expertise, and what they studied might not even have occurred to you. It is exciting for the same reason, but it also meant that things will not come easily anymore. The material is more recent - no longer are we studying the creation of some guy in the renaissance (calculus), but concepts and algorithms developed in the last 50 years, maybe even the last 10 years.

I was just suddenly overwhelmed by all of this, and wondered if I really would make my mark among all these giants.

The feeling passed by Wednesday afternoon, but the advice remains: pull yourself together, Justin.

A Little Mathematical Proof

Did you know that if you take any non-negative integer, then subtract the sum of its digits, the answer will always be divisible by 9?

For example, today's date is 11/06. 1106-(1+1+6) = 1098, and 1098/9 = 122.

Curious why? Here's a more general proof [pdf], that the difference between a number and the sum of its digits (if written in base b) will always be divisible by (b-1).