LOOK AT THIS SCHEDULE
LOOK AT IT
- ENGL 291: Beginning Poetry Writing
- ENGL 492: Advanced Nonfiction Writing
- MATH 395: Analysis of Algorithms
- MATH 420: Complex Variables
- MUSA 321: Concert Band (of course)
- STAT 452: Mathematical Statistics
Plus two sections of STAT 251, which are represented by the little red boxes.
PARTY TIME! I’m super excited.
I’ve walked 1,000 in my Sauconys since March!
Okay, well, technically, I hit the 1,000-mile mark on Tuesday, but I wanted to reach 1,200 total miles for the year before I posted anything. ‘Cause I’m like that.
4 miles’ worth of wear:
1,000 miles’ worth of wear:
Pardon how messy my desk is in the “after” shot. I’d just drawn a bunch of crap so there were pencils/shavings everywhere.
Anyway. If anyone’s in the market for some durable running/walking shoes, I highly recommend Saucony Kinvaras. They’ve only just started to become unwearable after 1,000 miles—mainly because there’s a huge hole in the heel of one of them—but they’re still ridiculously comfortable. Also, did you see how brightly colored they are?? Awesome. Always a plus.
NEW SHOES TOMORROW! Stay tuned.
Well this was cool to do.
What the colors represent:
- Red: states/provinces where I’ve not spent much time or seen very much.
- Amber: states/provinces where I’ve at least slept and seen some sights.
- Blue: states/provinces I’ve spent a lot of time in or seen a fair amount of.
- Green: states/provinces I’ve spent a great deal of time in on multiple visits.
I like how I’ve been all over the West Coast and the Great Lakes area, but very few other places (I went to Boston for that APS conference in May 2010; my grandparents used to live in St. Louis).
I also realized after making this that I’ve also been to Washington, D.C., but since that’s its own thing and not technically in a state, I decided to leave it as it is.
If you click here, you can make one of your own!
Today I’m going to talk about probability!
Suppose you just went grocery shopping and are waiting at the bus stop to catch the bus back home. It’s Moscow and it’s November, so you’re probably cold, and you’re wondering to yourself what the probability is that you’ll have to wait more than, say, two more minutes for the bus to arrive.
How do we figure this out? Well, the first thing we need to know is that things like wait time are usually modeled as exponential random variables. Exponential random variables have the following pdf:
where lambda is what’s usually called the “rate parameter” (which gives us info on how “spread out” the corresponding exponential distribution is, but that’s not too important here). So let’s say that for our bus example, lambda is, hmm…1/2.
Now we can figure out the probability that you’ll be waiting more than two minutes for the bus. Let’s integrate that pdf!
So you have a probability of .368 of waiting more than two minutes for the bus.
Cool, huh? BUT WAIT, THERE’S MORE!
Now let’s say you’ve waited at the bus stop for eight whole minutes. You’re bored and you like probability, so you think, “what’s the probability, given that I’ve been standing here for eight minutes now, that I’ll have to wait at least 10 minutes total?”
In other words, given that the wait time thus far has been eight minutes, what is the probability that the total wait time will be at least 10 minutes?
We can represent that conditional probability like this:
And this can be found as follows:
Which can be rewritten as:
Which is, using the same equation and integration as above:
Which is the exact same probability as the probability of having to wait more than two minutes (as calculated above)!
WOAH, MIND BLOWN, RIGHT?!
This is a demonstration of a particular property of the exponential distribution: that of memorylessness. That is, if we select an arbitrary point s along an exponential distribution, the probability of observing any value greater than that s value is exactly the same as it would be if we didn’t even bother selecting the s. In other words, the distribution of the remaining function does not depend on s.
Another way to think about it: suppose I have an alarm clock that will go off after a time X (with some rate parameter lambda). If we consider X as the “lifetime” of the alarm, it doesn’t matter if I remember when I started the clock or not. If I go away and come back to observe the alarm hasn’t gone off, I can “forget” about the time I was away and still know that the distribution of the lifetime X is still the same as it was when I actually did set the clock, and will be the same distribution at any time I return to the clock (assuming it hasn’t gone off yet).
Isn’t that just the coolest freaking thing?! This totally made my week.
Have you ever had a dream set in a really specific place—and not a familiar one, like your house/school/work/whatever—and then, like three years after you have that dream—return to that location in another dream?
That happened to me last night. I was in this huge field in Oklahoma. I knew I had been there before in a dream I’d had a long time ago, and I was so happy to be there again. I knew where everything was and I knew one reason that I liked the field was because there was this giant kite-shaped cloud that was always hanging above it (which, of course, I saw as I looked up in the dream). It was just this incredible feeling of familiarity. I don’t remember a place ever feeling so familiar in a dream before.
Does that ever happen to you?
Here are some pendulums:
I didn’t want the video to end!
According to the site, one complete cycle lasts 60 seconds. In that period, the longest pendulum oscillates 51 times and each successively shorter pendulum makes one additional oscillation more than the last—thus, the shortest oscillates 65 times.
I really like how when they’re all out of sync it looks like they’re slowing down and coming to a stop, but then they sync up a little again and it’s like, “BOOSH we’re still going!”
Somewhat unrelated, but here’s another mathy vid that I didn’t want to see the end of. Which of the three panels captured your attention the most? On the first watch it was the middle panel, on the second watch it was the far left panel for me.
…it’d have to be this.
I don’t even know why. But it speaks to me on a genetic level.