Lazy

I started writing a different blog post but it just wasn't coming together the way I'd hoped. I might salvage it someday, but for now I'll just recycle content from Facebook last month.

Some background: At the beginning of the month, one of my aunts updated her status to something about finding something different to be grateful for every day during December. I did that and by the end had decided it was an interesting enough challenge that I'd continue to find something to be grateful for every day until I forgot. Here's my list:

December

1. I'm grateful for my sisters.
2. I'm grateful that Qiushi hid his textbooks in the barbecue.
3. I'm grateful that Smith's puts cat food and scented candles in the same aisle
4. I'm grateful to be essentially done with grad school applications. I'm grateful to have attended my siblings' piano recital. I'm grateful for my friends; to name only the ones I encountered today, this includes Hailee, Jamie, Tiffany, Drew, Laurel, Sabah, Lisa, Lindsay, Rhiannon, and Steven.
5. I'm grateful for my college ward. Today was the one of a very small number of testimony meetings I actually enjoyed.
6. I'm grateful for a healthy body. I'm also grateful for mountains.
7. I'm grateful for Linkin Park. Today it's the song 'Iridescent,' and no, I don't care how un-Linkin Park-y it sounds.
8. I'm grateful for John Peterson.
9. I'm grateful for bananas and the internet.
10. I'm grateful I have the weekend to study, because I'm not going to feel like doing much next week.
11. Spending the day with modern algebra has reminded me how funny it is to impose the group axioms onto groups of people . . . I'm grateful for algebra.
12. I'm grateful for downtown Ogden.
13. I'm grateful for the opportunity to do research as an undergrad, and interesting research at that. That said, I'm also grateful to be done putting together today's presentation.
14. We caught a few cheaters during a final I proctored today. I'm grateful for a mind which does not require that I cheat to succeed.
15. I'm grateful for things that make me laugh. This includes: RedLetterMedia's Star Wars reviews; the weekly 'Parents Just Don't Understand' column at CollegeHumor; and Britney, who this morning said "I hope my soul-mate isn't at the HC, because this is what 'I don't feel like getting ready but I still want breakfast'-Britney looks like."
16. I'm grateful for my dad, Eric. I'm also grateful for bicycles. I'd feel even more grateful for bicycles if it wasn't stupid finals week. Then my dad and I could go for a bike ride and he could remind me how his now-52-year-old body used to be fast like my 21-year-old body. Happy Birthday, Dad.
17. I'm grateful for all of my cousins. If you are one of my cousins, pat yourself on the back for being awesome.
18. I got home today and found cheese-flavored popcorn on the table. I needed to get the orange powder off my fingers but didn't want to wipe my hands on my black shirt or my white shorts. I'm grateful for the orange tablecloth.
19. I don't want to think of something to be grateful for today. Right now I'm just grateful that things are the way they are.
20. I'm grateful for public transportation.
21. Yesterday my parents noticed some of the outside Christmas lights glowing even though they weren't turned on, so today my dad and I wandered around the front yard with a metal pipe and a digitial multimeter trying to figure out why. We think radio waves are inducing a current in the rain gutter spouts, which in turn is inducing a current in the light strings . . . I'm grateful for physics.
22. I'm grateful for physical therapy, for making my sister less broken. And I'm grateful for this Christmas tree ornament The Bald One made a year or two ago.
23. Dec 23 - I'm grateful for the folks in the ward I grew up in. Special shout-out to Kylee, Mandy, and Scott.
24. I'm grateful for all the wonderful teachers I've had (and not just the ones at school). I thought about listing them all by name but that would take too long. I guess I'll mention Mrs. Taylor because she'll get a kick out of it.
25. I'm grateful for Simon and his 3 keys to happiness: good food; good friends; good family.
26. I'm grateful for the people who have seen me at (or near) my worst and don't completely hate me for it. Obviously this includes my parents, along with Kjersti, Bonnie, and Laurel.
27. I'm grateful for my family's safe passage to Arizona today, as well as yesterday's opportunity to indulge in unbridled hedonism in Las Vegas.
28. Oops, looks like I missed yesterday. If I had posted, I would've been grateful for good books.
29. I'm grateful for pillows.
30. I'm grateful for the conversations which take place at the times they are needed most. I'm also grateful for my Grandpa Mac for showing how true love endures all.
31. I'm grateful that even though I'm spending New Year's in a hotel in Page, Arizona, at least it follows a safe day of travel and we brought "Ferris Bueller's Day Off" along.

January

1. I'm grateful for family traditions.
2. I'm grateful for Nerf guns.
3. I'm grateful for the days where it feels like you got something done, even if it's just a couple gallons of citrus juice and a 1.5-hour Nerf gun fight.
4. I'm grateful for old friends who you can talk to without remembering how long it's been. Today that applies to Kylan and especially Bonnie.
5. I'm grateful for Star Trek. I'm grateful for Sarah and her amazing blog.

Help me get a date with Taylor Swift!

For Christmas this year, I want you all to write a letter to Taylor Swift suggesting that she and I go on a date next time she's in Salt Lake (Sept. 28, 2011, I think). It doesn't have to be anything extravagant. When you're done with that, have all your friends and neighbors write, too. Invite them to the Facebook event or send them the link to my blog.

Thanks in advance! Y'all are the best!

Facebook event: http://www.facebook.com/event.php?eid=110043245733150&num_event_invites=0

Blog: http://musingsofamathman.blogspot.com/2010/11/help-me-get-date-with-taylor-swift.html

Taylor Swift

Taylor Swift Entertainment

242 West Main Street

PMB 412

Hendersonville, TN 37075

USA

F.A.Q.

The questions I am most frequently asked since starting this blog are:

• I want to have your child. Can I can I can I?
• I want to name my firstborn son after you. Do I have to pay a licensing fee?
• What's with the waveform on top of your page?

Actually, nobody has asked that third one yet, but that's the question I'm going to answer.

When I started this blog, I put a nontrivial amount of thought into how things should look and 'feel.' The mood I was trying to convey is that which comes to my mind whenever I hear Elliot Goldenthal's Batman fanfare.

"But Zachary, Blogger allows you to embed audio on your blog. You could've had that music play whenever someone visited your blog."

No. I could not bring myself to do that, for two reasons:

1. This isn't Myspace.
2. This isn't the 1990s.

So since I couldn't play the music audibly, the next best thing was to display the music visually. Now you know.

To listen to the music I'm describing, go here.

To see a low-resolution video of the music in its original context (the opening titles and scene in Batman Forever), go here.

To see the first thing I thought of when I italicized the words 'play' and 'display,' go here.

Nuggets

As I was going through some old papers today I came across several scraps of paper on which I'd written little notes to myself. Some of these were simple To-Do list reminders, but a lot of these were reminders of periodic flashes of clarity. Some of them are quite specific to things happening in my mind and therefore uninteresting to anyone but myself, but some of them are quite general and, I think, insightful. With that, read on, blog world:


If we discarded every idea which fails to appear in nature, we'd have no imaginary number system, and by implication, the most precisely-tested theory in history, Quantum Mechanics, would not exist.

Without reason, faith becomes dogma. Push yourself; challenge your faith to solidify it. You won't get better if you don't push yourself; try it and see what happens. Keep in mind whether there are/should be boundaries on where to look.

Be happy but not complacent. Appreciate the constants, especially in college when everything is changing. Appreciate the changes, too, though.

Pop-Ups

There are things I think about, and there are things that I think of only briefly. This list consists of items in the latter category. Most of these (especially near the beginning of the list) occur with some frequecy.

Sometimes it's scary how well my iPod knows what I want to listen to.

I've been alphabetizing things for most of my life, and weekly for my job over the past couple years, but it still feels like 'V' should come after 'W'.

If you have turn signals, use them. Heck, I don't have blinkers and I still signal. And if I see your signal and I'm in your way, I'll almost always move for you.

I have yet to grow tired of Linkin Park, and Hybrid Theory never gets old.

Analytic functions are awesome.

You owe Lindsay two bucks.

I prefer hiking uphill; I prefer running uphill; but I HATE biking uphill. And downhill isn't always better. The best is level or very slightly downhill.

It's easier to rebuild an economy than an ecosystem.

"Un bel di vedremo" would sound so much better without the singing.

Taylor Series are also awesome (though of course they are pretty much the same thing as analytic functions).

Usually when we say "So-and-so is a good person," we tend to mean "So-and-so is a not a bad person." Someone once said "I've never met a bad person." But there are a few good people I know. They are (in no particular order): Drew Thompson, Karianne Rencher, Sean Davenport, Lindsay James, Tiffany Law, Katie Hobbs, and Amie and David Carman. I'm sure I've met a few more, but my mind is blanking.

That Was Fast . . .

I noticed a couple of weeks ago that both my watch and the clock on my bike computer were running a couple minutes slow. I knew I'd set them both according to my cell phone clock back a few months before. Realizing it would have been too great a coincidence for both timepieces to have dying batteries (dying at the same rate, I should add), I concluded that relativistic time dilation was to blame.* Naturally I wondered how fast I must have been going to have observed this effect.

First, a few words on special relativity. In classical physics, if you and I are driving towards each other at 55 mph and 60 mph, we are approaching each other at 115 mph. It turns out that this breaks down at speeds approaching the speed of light, so one of those speeds is multiplied by a number which depends on the speeds involved. It's a rather remarkable fact that such a major problem in physics can be solved by doing exactly what you did already, but with an extra multiplier. For a more thorough explanation, read Wikipedia.

First, some knowns:

• The clocks were 2:20 slow as of 9:21 am on August 9, 2010
• There were 1341 miles on the odometer at the same time (presumably this should also suffer from relativistic effects).

Next we need to estimate the total time spent travelling on my bike. Most of my riding was commuting, broken down as follows:

• ~8.2 miles from home to train station; typical times were ~25 minutes
• ~3.5 miles from train station to campus; typical times were ~22 minutes
• ~3.5 miles from campus to train station; typical times were ~13 minutes
• ~7.7 miles from train station to home; typical times were ~30 minutes

In a typical day, then, I traveled 22.9 miles in 90 minutes. These times include time stuck at traffic lights. The effect will be counteracted by not adding in the time spent on additional rides, which deserves some mention.

In addition to my daily commute, I probably rode another 85 miles over the summer on other rides. If we subtract the 85 from 1341, we are left with 1256 miles. This divided by 22.9 miles per day yields 54.847 days of riding. Multiplied by 90 minutes per day, we get a total travel time of 4936.245 minutes for the summer as measured by the cycle computer (this is the proper time interval in special relativity).

We now know the proper time interval and the time interval for the reference frame described by Earth's surface (4963.245 minutes plus the 2.333 minutes difference between my clocks and Earth clocks). Using the Lorentz transform (where v is my speed, c=671 million mph is the speed of light, and g takes the place of the traditional gamma),

4965.578 minutes = g * (4963.245 minutes)

=> g = 1/sqrt(1 - v^2/c^2) = (4965.578 / 4963.245) = 1.000470055

=> v = c * sqrt(1 - 1/1.000470055^2) = 0.0307 c,

that is, 3.07 % the speed of light. Putting this into more familiar units and rounding down out of modesty, this is roughly 20 million miles per hour. On average, of course.

My bike computer also has a built-in speedometer. It frequently hovers at or above 20 mph. I guess the manufacturer was off by a few orders of magnitude.

*Even though my phone travels on my bike just as much as my watch and bike computer, it should be immune to relativistic effects since it syncs with a clock somewhere else.

Happiness

Good food,

Good friends,

Good family;

Namaste.

-- Simon McFall