Thoughts while watching the waves at Morro Strand S.B.

How did this beach look
        a century or millennium ago?
Did curlews and sandpipers
        chase and flee the ocean waves?
Did hawks soar
        and dip overhead?
How many generations of bipeds
        came and went?
How many empires were built,
        wars fought,
        libraries written
While these same waves washed
        onto this same stretch of sand?

And a century or millennium hence?

“Teach us to number our days,
        that we may gain a heart of wisdom.”        (Psalm 90:12)
“Generations come and generations go
        But the earth remains forever.”        (Ecclesiastes 1:4)

A high school math problem and Euler's formula

I was on my high school's math team in the early '70s, and in one contest there was a problem that stumped us. Basically it was this:

Find two numbers, not 0 or 1, such that each is the square of the other.

If you remember that there is such a thing as a complex number, the problem isn't hard. Trouble was, we had all forgotten about such things in the moment.

But what happened afterward was very interesting to me. I noticed that the solution involved complex numbers, and a particular kind of complex number: the kind with a "length" or "magnitude" of 1. Somehow I noticed what happens when you multiply such complex numbers together.

It was so much fun learning all that, and I was thinking about it again for some reason recently. So I wrote a bunch of stuff down. Not in blogger; this requires LaTeX. Some topics mentioned:

• factoring
• quadratic formula
• addition formulas for sin and cos
• matrix multiplication (2x2)
• Maclaurin series (Taylor series centered at 0) This is the only part needing calculus.
• "isomorphic" which just means that this thing is like that thing and behaves in the same way. Probably I misuse the word somewhere.

It sure was fun to learn that stuff, and fun to think about it again and write some of it down.

I've uploaded my little paper here.

A sermon we'll never hear at MPPC

I picked up the lovely Carol in Los Angeles; she’d attended a conference on the USC campus. We looked at a list of nearby congregations and selected Abundant Life, a mile or two away. Little did we know what awaited us.

I couldn’t see any on-street parking, but the church’s parking lot was nearly empty. An attendant told us to park anywhere. When we walked into the building, we were greeted warmly and asked whom we were visiting.

“We found you on the website,” I said. Our greeter recovered quickly and indicated the sanctuary. We sat near the back, but someone urged us to move a few rows forward, which was fine.

I'll skip over the music (it was great) and the affirmation of faith (I affirmed it with a clear conscience), because I want to tell you about the sermon, which was on the theme of “Staying alive.” It's really important to remember that Jesus died for us to demonstrate his love for us, the preacher said. One consequence is that I don't need to prove my devotion to God by having a death wish. The first Scripture was from Matthew 5:

“Settle matters quickly with your adversary who is taking you to court. Do it while you are still together on the way, or your adversary may hand you over to the judge, and the judge may hand you over to the officer, and you may be thrown into prison…

Matthew 5:25 (NIV)

“Point number one,” the preacher said: “Avoid the system. Avoid the system. Don’t give the system an excuse to pull you in. Fix that taillight. Stop drinking and driving. Stop driving with a suspended license.” Because the system can throw you into prison. The system can literally kill you.

To overcome injustice, the preacher said, we need to pray hard enough, and work hard enough, and vote strong enough to bring about changes. But you can't vote if you're dead!

The sermon was addressed to people of color, which most of the congregation were. There might have been three white people (including the lovely Carol) in the room, and one east Asian (me). All of us were aware that the system isn't as fair or color-blind as we would like it to be. But this was probably the first time that I felt keenly my privileged status among my oppressed brothers and sisters. Rodney King was beaten by L.A. police officers just a few blocks from where we were sitting.

The preacher described having a gun held to his head and being ordered to lie down on his face on the wet floor of a car-wash. He had a suit on, and a clerical collar, and as he lay there, hands zip-tied behind his back, he was yelling at a young hot-head, the son of a parishioner, to “Just chill!” because whatever he wanted wasn't worth dying for; policemen in riot gear were ready to kill that young man.

Thank the Lord, everybody survived that day. But this is a broken world, and not all incidents end peacefully like that.

The preacher went on to talk about how we need to submit to institutions, because God (a God of order, not disorder) ordained these institutions. Which is not to say, he added, that everybody in a position of power actually needs to be there! We need to submit anyway.

He also described what it means to submit: the Greek word being ὑποτάσσω (hoo-poh-tahs-soh) which means to “come up under.” He pointed out a parishioner who was about to join the Marines; he's going to learn about submission big-time. This doesn't mean that his superiors in the Marines are perfect or always right, but he has to be under them.

It's important sometimes, he said, to submit to your boss at work; to keep that job, even though your boss isn't perfect and may not always be right or treat you right. Sometimes, you need to just. Shut. Up.

Red or yellow, black or white (and I might add, young or old), some of us need to hear that, to remember it and take it to heart.

Well, I don't want to recap the entire sermon, but I did want to share the experience with you. I was very glad we went, happy to have fellowship with brothers and sisters whose lives are very different from mine.