A Riddle part two

I've had some time to formalise the notes a little more nicely - I think they look a lot better and are easier to understand if they're latexed.

A Riddle

So for my slog problem, what I really want to do is talk about the relationship between context-free grammars, context-sensitive grammars, and regular expressions, but I have a lot of notes for those and I don't know if I'll have time to type up those notes.

In the absence of that, here's something a friend and I were discussing...

Consider a plane consisting of 100 seats. Unfortunately, the airline company which is probably American Airlines has managed to botch up all the boarding passes, so nobody who boards the plane has anything printed under the 'seat' field on their boarding pass. If they don't know their seat number, they have been instructed to select at random. Luckily, most people recall their original seat number, and everybody on the plane is extremely non-confrontational (maybe they're Canadian): if they approach their seat and find someone already sitting in it, they won't make a fuss, they merely select another seat at random.

If the first person who boards the plane is the only one who forgets where he's sitting, and therefore picks a seat at random, what is the probability that the last passenger to board will be sitting in his originally-assigned seat?

So I haven't updated this in a while...

...or have I???

What actually happened is my computer died so I've been hiding out in the CDF labs more and more often until Boxing Day rolls around and I can maybe buy a new computer a little more cheaply. (Ah, the joys of being flat broke.) In other news, I really really love the CDF labs.

So I've backdated the posts that I had written up and saved in blogger until such time that I got a moment to properly format and publish them.

I love Latex

No, really. I really, really love Latex. As in it's a little bit pathetic how sad I got when I found out I couldn't use it for one of my essays in another class because they are jerks insisted on Times New Roman.

(In retrospect I think you can actually finagle Latex into showing a Times New Roman like font face but at that point, what's the use, it already looks like something from Word. Luckily Cog Sci doesn't seem to mind if I don't use Times as long as my citations are still okay. Come to think of it I really should be working on Cog Sci at the moment...)

But that's not why I love Latex. No, I love Latex because of how amazingly easy it can be to create mathematical formulae and things, and it even has IPA symbols for geeky wannabe linguists like me, which is just so awesome, and and and and then, when we started automata, I found a site that helped me make this for assignment 3:

which just looks so pretty.

Here's some code!

First you have to add the tikz package and tell Latex what you want from it:

And then, you can just go to town:

You can also make the arrows dashed and dotted and such (although I didn't). All you need to do is change the [->] bit to [->, dashed] or dotted, as you like. Double-headed arrows with [->>].

(In all fairness, Latex has its shortcomings - in that it compiles really strangely and hitting make sometimes requires you to make several times over because Bibtex isn't complying or things like that. But I can't even imagine how painstaking it would be to overthrow all of Tex live to make the underlying code neater, so I'll happily forgive others for not doing it either. Also unlike Microsoft Word it's free. Freeeeeeee.)

A complete digression from CSC236 things

So we saw in Cog Sci today the difference between propositional and procedural statements. I got a friend to help me out with this one. For example, let's consider the following problem: 

How can you connect these nine dots with four straight connected lines (aka, you can't lift your pen from the paper)?


(the answer and more under the cut)

Midterm 2 studying

So I might have lied to work and told them I was sick when I wasn't. I'm not proud. I admit I should have had the time management skills to have accomplished both a good job studying and the ability to handle a shift before a test. But I'm fairly certain they got by fine without me and people have called in 'sick' when they were hungover probably not sick and I'm also extremely certain nobody in CSC236 also works with me and I was kind of sick a little bit in that I coughed earlier (does that count?) and ... I just really really wanted a good mark on my test.

That said I do think I did pretty well. It was mostly on the recursive correctness part of what we've learned, though it required using the Master Theorem. I think I like proofs of recursive correctness a lot, mostly because they involve a lot of talking. Most of my proofs ever proofed have been half math half talking about why the math works, so having it be more English is a format that is really reassuring.

Though I very nearly submitted something that would have shown the TAs that I don't understand exponent rules. I'm really glad I caught that one.

Arrgh

So this just in, I can't read a calendar or a table. I thought the assignment was due on the 4th for some reason? It was not due on the 4th. It was most definitely due yesterday. I most definitely did not submit anything.

...At least it'll be easy for the TA to mark?

The 4th is the last day to drop courses and switch to pass/fails for Fall semesters. That might've been why the 4th was in my mind.

Still. How not to read a calendar: this right here.

Test discussion, and propositional variables

I think the test went well? It's difficult to say. It was one of those tests where at no point was answering anything problematic in some way, and at no point did I run into something that looked like it could have been an error ... but at the same time I'd feel genuinely queasy claiming I aced it. Maybe I'm just being superstitious. At any rate I think I'll have to see what happens when it gets returned.

Not finding structural induction on the test made me a bit sad, which might be because I'd focussed much of my studying on structural induction because a part of it still kind of eludes me. I'd done a bit of studying on this because I feel like it's one of those things I "understand" but don't fully understand. Superficially, it's pretty simple to just say that structural induction is just a little more abstract a version of the other induction flavours we've seen. But I think that explanation is - in addition to being a little too vague - eliminating the question of what is a propositional variable anyway.

So there's this test tomorrow...

I don't feel like I've studied enough but at the same time I'm unsure how much more I can prepare. I understood the lectures, I've read the notes a few times now, and I've been doing practice problems and still I feel like I'm really not that well prepared for it. Maybe looking at some past exams will help me convince myself I'm prepared?

It might be because this past weekend got eaten up by another class's assignment, and today got eaten up by work and studying for another class's quiz. (Taking this many courses is difficult without also working, but combine working and it's a bit much.) I don't know, I guess I'm just used to studying for midterms by devoting time directly before the midterm, and because the time has been stretched over different days in different weeks, it feels like it's not enough, even if it's the same amount of hours.

It might also be because I found the assignment easy (long, but easy). As in, I was expecting it to be super gruelling and challenging and impossibly difficult, and was surprised when it actually wasn't all that bad, really, and I was able to do it on my own. Well, I say this now, but the marks haven't come back yet.

I guess we'll find out tomorrow.

It's Bad Joke Sunday!

P: All numbers are (somehow) interesting.

Proof (by well-ordering): Suppose there are a set of numbers that are uninteresting. By the well-ordering theorem there is one number among them that is the least such number.

But then that makes it interesting! Contradiction. Therefore, P holds for all numbers (which are all interesting).

(I should be reeeally working on assignments.)

Continuous but not differentiable

Today I learned about functions that are continuous but not differentiable. I'm mostly sharing this because it came up in the context of a hilarious why, math, why would you do this to us kind of conversation and I figured many people in CSC236 could relate to that feel. I don't think it has anything to do with anything in CSC236 other than that, to be honest, but it's kind of neat!

Lessons learned for Assignment 2 + Midterm

I should really start texing solutions much, much earlier. It might be because I don't use an IDE for something like LaTeX (just a notepad file and the command line) but it takes me a looong time to debug anything.

Also the midterm is in a week. The midterm is in a week. I could swear it was September tenth yesterday.

Studying for Tutorial 1

This came up on the Wednesday night before our first tutorial quiz (I’m in the Thursday night section). I was mildly worried about it although (for me anyway) it wound up being much easier than I anticipated. I usually find that if I overworry, I overprepare, and that makes me do better, though, so I’m not so unhappy about overworrying because everything goes better than expected. This is the one benefit to being a giant ball of nerves.

Anyway, because I was such a ball of nerves I got a friend to quiz me with induction proofs that he’d yoinked off the internet so that I hadn’t seen them before. The proofs were of varying difficulty. One of them was the standard sum-type sort: 

which is easy enough once you get the trick of splitting the summation into terms that can be induction-hypothesised (from base case to n) and extra terms (the n+1th term). Then it’s straightforward algebra to combine the two into something that looks like the induction hypothesis but with a quick change of variable n -> n+1.

The other was one that looked like:

which we saw later in I think the third week or so, and here you’re supposed to use the fact that the relation LessThan is transitive (so for A < B, and B < C, you know certainly that A < C) and a term-by-term comparison to show the B < C part. Then you’re essentially done. 

Anyway, the rest is less a discussion about the proofs themselves and more about my ridiculous anxiety issues, which I really wish would just go away!

That is not an inventive title!

About me: I'm a 2nd year Cognitive Sciences and Linguistics student. I'm interested in AI and computational linguistics, and admit to mostly taking this course because it's a milestone on the prerequisite path to CSCs 384 and 485, but that doesn't mean I don't find it interesting in and of itself!

I like art and museums. When I'm not in class, I work at a Starbucks as a coffee-serving robot.