How to do Calculus: The Derivative

Not everyone knows calculus and it's too bad because it's good stuff (as far as math goes). This is my attempt to explain one of the main concepts of calculus in one blog post. Watch this video...it's really boring but only takes a few seconds.

The point makes a bunch of random movements. It moves up, slows down, turns around, slows down, turns around, slows down turns around, et cetera and then it stops at its original position. The graph moving to the left describes the point's position as time changes. Here it is sitting still:

The position increases, flattens out, decreases, flattens out, increases, flattens out, decreases, goes negative, comes back positive, et cetera. It changes just like the point in the video. Let's say that the position is in miles and time is in hours. So in the first two hours the point goes one mile.

Hopefully everything above here makes sense. So far we haven't done any calculus.

The first interesting concept you learn in calculus is the derivative. If you take the derivative of a graph like the one I plotted above, you measure the slope of the graph. In the following video, you would be measuring the steepness of the maroon line as time changes. Notice that the maroon line is always tangent to the position graph.

When you measure the slope you measure how much the line rises divided by how much the line moves forward. You would be dividing vertical distance by time, so the units of the derivative would be miles per hour. So taking the derivative of a position vs. time graph gives you the speed (mph) at all times. You could plot the derivative as a function of time and get this:

If you compare the speed graph with the position graph, you can see that when the position graph is steep upwards the speed graph is high. When the position graph is flat, the speed graph is at zero. When the position graph is steeply sloped downward, the speed graph is very negative.

To convince you that the derivative is speed, here's a video of the position graph with a speedometer!

When the point speeds up, the speedometer needle goes up just like you would hope. When the point goes backward, the speedometer needle goes past 0mph.

Hopefully now you understand what a derivative is and that one application of the derivative is to measure the speed of something.

New Favorite Bike Ride

Yesterday I realized how lucky I am to live in Colorado. I had 3 hours to spare between work and music practice at church. Since it would take an hour to get home and an hour to get back to Golden I decided to just go on a bike ride. I commuted to work that morning, so I had my bike and lots of time. So I put together a route that looked interesting.

It went from my office to Bear Creek Lake Park in Morrison and back. Down and back rides are always a bit lame, so I changed the route so I went down to the park on the east side of the hogback and came back to Golden on the west side of the hogback. For the non-Coloradans, a hogback is a long, narrow ridge that is caused by lava coming up a long crack in the rock. That would give me some variation in scenery. It turned out to be a very good thing.

I left Mines with a bit of a headache. As I rode uphill towards the Jefferson County building it got worse and worse. By the time I got to the top of the hill my headache was really bothering me. The blaring sun didn't help. I started going downhill along C-470, but it was the least enjoyable downhill I had had in a long time (second to the time I ate brats for dinner and then had to turn back on Chimney Gulch after a quarter mile). Thank God I was reminded that there's a gas station in Morrison that would likely have Snickers bars (the solve-all candy bar). So after struggling down what would normally be considered and incredibly relaxing long downhill, I stopped by the gas station and bought me a king sized Snickers bar and some Tylenol. I just rode a bit further to Bear Creek Lake Park, O.D.ed on the Tylenol (3 tablets) and ate my giant Snickers bar.

Feeling a bit better, I left the park and headed towards the tiny town of Morrison. For such a tiny town it was amazing how easy it was for me to miss my turn. I had planned on taking the Hogback Road back to Golden, but missed the turn. I rode a few blocks, left the town and took the next right, which lead to Red Rocks Amphitheater. So I rode up some pretty steep hills and got to the park. If you live in the area, you know that this park is, hands down, the most beautiful place in the Denver area. And the road I accidentally took takes you right through the massive sandstone rocks. It was absolutely beautiful and I didn't mind in the least bit that I was going uphill through the park because it just meant I had more time to look around.

I got through the park and back onto the highway, from which the views are only averagely beautiful with hogbacks to the right and mountains to the left. I saw the mountain bikers on the Red Rocks trail and was ridiculously jealous. Now that I've become obsessed with road biking on smooth pavement surfaces I'm just now realizing how amazing mountain biking is. It was really just a matter of getting in shape and forcing myself to ride often enough that I became obsessed with it. Back when I mountain biked, I never became obsessed, but if road biking can be this fun, then mountain biking can be twice as fun! My next big investment would be a mountain bike, but I need a car much more, so my second next big investment will be to buy a mountain bike! I miss mountain biking.

I rode back to Heritage Square and hopped on a nice little bike trail, hidden between a bunch of houses. Zach and I always rode this paved trail after doing the up-Chimney Gulch, down-Apex mountain bike ride. The trail is the perfect way to end a ride. You just cruise down the windy path all the way back to Golden. I learned that cantilever brakes aren't quite as powerful as v-brakes and that road bikes aren't as good as mountain bikes for handling fast sharp turns.

Even with the incredible headache this ride was awesome. It's definitely my favorite road ride in the area. I'm really quite privileged to live in a place so beautiful and so perfect for biking.

The Lean-Over-45-Degrees-in-the-Wind Day

The wind bike guy can be found here.

Wind always makes riding a bike interesting. Today I rode my bike to work for the first time in several weeks because it was cold and then I got sick...and I'm a wimp. Most of the ride was nice. Only a slight head wind for about 9 miles. Then I got to Denver West. It can be the nicest day in Denver and Denver West and South Golden Road can have hurricane force winds at the same time. Today was one of those days.

Wind can be annoying. On the section next to Denver West, the wind was blowing pretty hard in my face. But it wasn't horrible. I just bent over, held on to my drop-downs, and pushed through. It was bothersome, but not horrible.

The way Golden is situated, wind comes rushing down Clear Creek Canyon really fast, so Golden is a quite windy city at times. South Golden Road is a wind tunnel. There are hills on both sides with very few trees, so if you ride your bike on the road, the wind goes either with you or against you. Back in the day when I rode that road every day, it seemed like most days I would get a head wind when I went to school and then another head wind riding home. The wind on South Golden road can be absolutely ridiculous. It was a pain, getting to the top of the hill at King Soopers, but immediately when I started going downhill, the wind went out of control. If I had stopped pedaling, the wind would have brought me to a stop on a moderate downhill. It picked up tiny little rocks and dirt and blew them into my face. The wind was a pain, but I was mostly just in awe of how ridiculous it was.

A lot of people have asked me why I'm going to ride from Canada to Mexico and not from Mexico to Canada. It would make more sense to do it that way in the spring with Southern California being quite hot in the summer and Washington being rainy in the spring. I have three reasons why I'm going towards the south. The first is that I just want some really epic views to start out my ride, to get me excited about the ride and just enjoy myself. The second reason is that going south somehow feels like going downhill. The last reason is that the wind supposedly goes north to south along the Pacific Coast. It will change to blow north when the weather changes, but otherwise I should have a tailwind most of the way to Mexico! When I learned that tidbit of information, I just got even more excited about the ride.

I was doing a great job training until I got sick a week and a half ago. I'm at the point where I'm riding hour long easy rides and, a few times a week, riding more difficult stuff for shorter distances. My list of equipment to buy is shrinking. In the past several months I have acquired a bike, hydration system (aka waterbottle cage and waterbottle), bike shorts, bike pants, slightly broken bike shoes, tent, tarp, sleeping pad, bike computer, Pacific Bike Route maps, and a guide book. I have yet to acquire a riding partner, so if you want to come, let me know. Otherwise, I'll just experience the adventure of the decade by myself.

An Excessively Nerdy Post About Spectra

Recently I've been doing a lot of ellipsometry. Ellipsometry reflects a laser off of a thin film and measures how the phase of the horizontal and vertical polarizations change after reflection. If you do it right, this gives you information about how thick the thin film is and what its index of refraction is. Part of ellipsometry is being able to look at a graph of n and k (the real and imaginary parts of the refractive index) and to identify different processes that are happening in the material. A good ellipsometer scientist can look at an n and k spectrum of Gold and say, "Oh those are free electrons over there and over on this part of the spectrum that's two different electron transitions." They can look at a spectrum and extract lots of information from it.

Here's a great example. For no particular reason, I went to Google and typed the letter a, wrote down how many Google hits it had, then moved on to typing aa, et cetera, all the way to 100 a's.

Lots of information can be extracted from this graph.

The first and most obvious piece of information should be the that Jon Banks has lots of patience and/or is incredibly obsessive over proving a point. This is pretty evident in the amount of time it would take to perform this study.

You can also look at the graph and learn about how people tend not to like to hold down the "a" key for all that long. They get tired of it eventually. This is indicated by the general downward trend, decreasing toward zero. However, there's always some freak that holds the "a" key for 5 days and then posts it somewhere.

If you look at a^72 there's a huge spike. Normally, my first guess would be that it is an outlier. But if you go to Google and type 72 a's, you will find that there are quite a few hits at that particular number of a's. So it is consistent, therefore it is real. This indicates to me that a particular group of people is incredibly obsessed with 72 a's. Or maybe some amazing video on youtube has a comment with 72 a's.

One of my favorite parts of experimental physics is looking at a spectrum and extracting all kinds of information from it.

Con Artist Gets to Celebrate Mardis Gras

As most of you know, I ride the bus from Denver to Golden almost every day. You may also know that weird people live in big cities like Denver. You may also know that one of the best places to find weird people in a city is on the bus. If you are familiar with Denver, you know that the concentration of weird people increases as you approach Colfax. Well, luckily for me, being a weird person enthusiast, I ride the bus that goes all the way down Colfax every day.

I've done my fair share of dropping eaves. I've been informed of more than a couple places to get free weed. I've witnessed drug dealings in the back of the bus. I've seen a crazy woman run like mad at a man in the back of the bus, was topsized by the man, and soon was recognized as one of the man's good friends. I've seen several drunks fall into the arms of an unsuspecting old woman, innocently sitting on the side of the bus. Anyways, I've seen lots of weird people on the bus.

On Sunday morning, I got on the bus to Golden for church. I sat on the left side of the bus, not far from the front. I was just sitting there, listening to my music when a man came up from behind and sat in the seat across the aisle.

Hey man, you know Mardis Gras is coming up and I don't have any beads to wear or anything. Do you have some money you could give me so I can go get some Mardis Gras decorations?

What did you say you needed the money for!?

Mardis Gras decorations.

Sorry man, I'm not going to give you money for Mardis Gras decorations.

---Silence for a few seconds---

I didn't really need the money for decorations. I need it for food.

---The man stuck out his lower lip---

Why didn't you say that in the first place.

I didn't want you to think that I was some drunk.

---Silence...Sad face---

Let me see if I have any money...Here you go.

---No response, no thanks---

---Mexican man walks down the aisle---

Hey man, do you know where the nearest dispensary is?

---Absolutely huge smile on my face. No anger whatsoever. Simply in awe of the man's audacity---

Some lucky con artist is three dollars closer to smoking a bowl for Mardis Gras!

A Quality Book

If I was faster, posting this video would entitle me to a free book. It's a quality book anyway, so here's a promo for the paperback version of A Million Miles in a Thousand Years by Donald Miller.

What story are you telling? from Rhetorik Creative on Vimeo.

Overweight Monday-The Stomach Stretcher For Fat Tuesday

Only the unprepared Lent celebrator limits the pre-Lent celebrations to Fat Tuesday. So today is a holiday, most commonly celebrated in New Orleans, called Lundi Surpoids. It's helpful for stretching out that stomach in time for Fat Tuesday, more commonly referred to as Mardi Gras. Sadly, my cardboard boat trip to New Orleans will not get me there in time for Lundi Surpoids, which is today, but I can celebrate it here in Denver just as well. And that's what I intend to do!

Anyways, the whole idea behind Mardis Gras and Lundi Surpoids is to over-indulge in any pleasure that you plan to give up for Lent. Some people choose to eat lots of junk food on Lundi Surpoids. The professionals drink gallons of water so that their stomach is stretched for Mardis Gras tomorrow. I've chosen to celebrate Lundi Surpoids by slowly moving away from Facebook. I know Mark Zuckerberg's biggest pet peeve is people giving up Facebook for Lent, but he'll just have to get over it.

I am an addict of a few things. The first is coffee. I get headaches if I go a day without coffee. Every day I drink coffee my body gets more and more dependent on caffeine. I even tried a 5 hour energy for the first time yesterday. It had a Nyquil-like effect on me. I honestly don't care about my coffee addiction though because I thoroughly enjoy drinking coffee.

I am also addicted to Facebook. It's horrible. I spend way too much time looking at people's Facebook pages and checking my News Feed for new updates. It's 90% a waste of time and I actually only slightly enjoy Facebooking.

So I'm giving up Facebook for Lent. It's going to be great. According to my calculations, over the entire Lent season, I will gain approximately 23 hours of time to do whatever I want! I could ride 345 extra miles on my bike! I could earn hundreds of dollars! I could sleep for 23 hours! I could read a book! I could do two Lord of The Rings marathons! I could walk to Colorado Springs! I could drive to Las Vegas and back! I could fly around the world! Heck, I could go into orbit!

Boy, I'm gonna miss Facebook when I'm orbiting planet Earth.