When math just doesn't make sense

I was browsing through my system logs when suddenly, boredom washed over me like a waxer on the McKenzie building's marble floors. Naturally, I fired up fortune and played with it for half an hour. After finding a funny WC Fields quote or two to add to my signature file, this popped up:

(1) X=Y                         ; Given
(2) X^2=XY                      ; Multiply both sides by X
(3) X^2-Y^2=XY-Y^2              ; Subtract Y^2 from both sides
(4) (X+Y)(X-Y)=Y(X-Y)           ; Factor
(5) X+Y=Y                       ; Cancel out (X-Y) term
(6) 2Y=Y                        ; Substitute X for Y, by equation 1
(7) 2=1                         ; Divide both sides by Y
                -- "Omni", proof that 2 equals 1

What a wonderful puzzle! I have seen a couple proofs like this before, but had never been able to sort it out to my satisfaction. Work on it for a while yourself, then read the last paragraph of my blog for today for the solution.

This week is devoted to packing everything into tiny boxes in preparation for our drive down to college on Monday the 5th. Charlotte's done fairly well in sorting and cleaning her belongings. I, on the other hand, still have piles of books, polo shirts, and unidentifiable Korean candies scattered around my room in a roughly horseshoe-shaped gauntlet. I've talked myself out of bringing any novels to read. This pains me greatly, since I just received many new ones for my birthday three weeks ago and haven't yet had the opportunity to pore over them. The necessity of having enough room in the van and the realization that I won't have any time to read them at school anyway have sadly impressed themselves into my mental packing list even as a parent might unknowingly impress his shoe into your stealthy playdoh earthworms while taking a basket of laundry upstairs to sort. *sigh*

Whether we'll actually be able to fit into the van is becoming more and more of a concern. I'm trying to cut back the things I'm bringing. Now that I have my slim LCD monitor, I won't be needing my computer desk -- I'll just set up shop on the desk in the room. If my roommates also have desktops, I'll move it onto my bed somehow. Charlotte's friend Sarah Grace is coming with us, though I don't anticipate her bringing as much as Charlotte is. Charlotte has a HUUUUUUGE pile of ... stuff in HALF of the foyer. She says that's not everything either. We're also bringing something down for a friend who stayed at PCC for the summer.

Speaking of PCC, they made the following announcement today about hurricane Katrina. I'd link to it, but our school's website is an amorphous blob of jelly that for some reason has unpredictably non-persistent content.

Monday, August 29, 8:30 a.m.
Hurricane Katrina is currently making landfall in the southeast Louisiana/Mississippi area. Pensacola is far out on the edge of the storm and is experiencing only tropical storm winds. At the present time, local channel 3 television is reporting winds in our area of 20-30 miles per hour, which is not unusual in stormy weather. Channel 3 also reports that the weather we are presently experiencing is the worst that we will have, though they anticipate it will continue for several hours. At the college campus, we have had one-half inch of rain since midnight. We are expecting gusty winds until later in the day, and students will remain in their shelter areas until the winds calm significantly.

Hopefully, I'll get to talk to some of my friends who are still down there tomorrow sometime. Another friend is supposed to fly to Pensacola on Friday via New Orleans, so I suppose he'll have to have a flight or two rerouted.

In a little over three hours, Dad and I will go to the Sunrise Grill for our Tuesday morning Bible Study with some of the other men from Bethany Chapel. We've been reading through C. H. Mackintosh's Short Papers, and today's article is The Law and the Gospel. The passage under study is the familiar story of the Good Samaritan, found in Luke 10:25-35. Mackintosh applies the story in a rather novel way. He points out that Jesus tells the lawyer who approached him that the end of the law is to love the Lord your God with all your heart, and your neighbor also. Mackintosh reiterates the point found in scripture that the law was given to condemn man in his own righteous, and that it is the grace and love of Christ alone that can save us from sin and death. Here are a few choice quotations:

The law makes no provision for imperfect obedience, however sincere. It makes no allowance for infirmity. Its one brief, pointed inquiry is, “Have you continued in all things?” If you say No (and who can say otherwise?) it can only curse you. Why? Because it is perfect. Were it to pass over a single transgression, it would not be a perfect law. Its very perfection insures the condemnation of the transgressor. “As many as are of works of law (that is, as many as work on the principle, stand on the ground, occupy the platform of works of law) are under the curse,” and cannot possibly be anything else. This establishes the point unanswerably. The law can only prove to be a ministration of death and condemnation to the sinner, simply because he is a sinner and “the law is holy, and just, and good.” It is no use for a man to say, “I am not looking to the law for life or justification, but merely as a rule and for sanctification.” As a rule for what? For the sanctification of what? If you say, “for my old nature,” the answer is, so far from being “a rule of life,” it is “a ministration of death;” and so far from sanctifying the flesh, it condemns it, root and branch. If, on the other hand, you say it is for the new nature, then is your mistake equally obvious, since the apostle expressly declares that “the law is not made for a righteous man” (1 Tim. 1: 9).

...

The law and the sinner are complete opposites — wholly irreconcilable. I must get a new nature, stand upon new ground, be in the new creation, before I can delight in the law of God. “I delight in the law of God after the inward man” (Rom. 7: 22). But how do I get this “inward man,” this new nature? How do I get into the new creation? Not by works of law of any shape or description, but by faith of Jesus Christ. I become united to Christ in the power of a new and endless life, upon which the law has no claim. I died in Christ. Hence the law has no further demand on me. If a man is in prison for murder and dies there, the law is done with him, inasmuch as the life in which the crime was committed is gone. Thus it is with the sinner who believes in Jesus. God sees him to be dead. His old man is crucified. The sentence of the law has been put into execution upon him in the Person of Christ. Had it been executed upon himself, it would have been death eternal, but having been executed upon Christ, His death is of infinite, divine and eternal effectiveness. Moreover, having the power of eternal life in Himself, He rose, as a Conqueror from the tomb after having met every claim. And wonderful to declare, the believer, having died in Him, now lives in Him forever. Christ is his life; Christ is his righteousness; Christ is his rule of life; Christ is his model; Christ is his hope; Christ is his all and in all (Rom. 6, 7; Gal. 2: 20-21; Gal. 3, Gal. 4; Eph. 2: 4-6; Col. 2: 10-15).

You can see the full article and all of Mackintosh's writings on this page. Just search for the title of the article.

Wow! You made it to the end of the post! The Math Forum @ Drexel has a page here on precisely this problematic proof. I admit that I didn't come up with anything better than the error occurred between the 4th and 5th steps. The problem -- and this is the problem with all such apparently impossible proofs -- is that we unwittingly divide by zero. I didn't accept the answer until I worked out the problem several more times myself. Now, I wonder how often I have made this mistake in my math courses. There were so many times when I'd work a problem through and get gibberish, that I wonder if some of that could have been prevented by simple preventative error checking. Perhaps this problem and its solution should be presented to all algebra students as soon as possible in order to avoid simple errors later in their mathematical studies!

Gone but not forgotten

It's that time of year again! My prolonged absence from my blog has been filled with much hurrying and scurrying across Georgia. These last few weeks have been filled with PCC students scrambling to enjoy such carnal pleasures as wearing jeans to Walmart and brushing with orange toothpaste. ;) Seriously, I am very eagerly anticipating returning. There's so much exciting stuff I get to learn and who knows what the Lord will do in my life this semester!

Yes, I have already begun thinking about packing. I haven't exactly formulated my list yet, but I have a rough idea that I'll be needing socks and underwear this semester. Thanfully, I already have a plethora of socks -- mostly white.

Charlotte has 19 skirts! My little sister is coming this year to begin studying Commercial art, and I can't believe the sheer ... volume of stuff she wants to bring! I don't think there's gonna be room for all of us in the vehicle. One of her friends is coming down to PCC too and supposedly is riding with us.

I'm going to have to cut back to two carry-on bags or something, and ONE of them is GOING to be my computer!!! The other might have some khakis in it. Hmm.... of course, I suppose I could always pack my computer WITH khakis.

In "When Worlds Collide," they pack their spaceship that will take them to the new planet with books as insulation, providing both plentiful shock-absorbing material and plenty of reading material for a long life without such conveniences as, say, oh, Earth.

The hunter safety course that I picked up in Thompson is now finished! Yesterday, I took the test and printed out my score sheet, only to discover that our county was having the rest of the examination last night at 6:00. Sadly, it was too late to preregister, and we had plans to go to visit with some missionaries from Albania anyway.

They were really nice! The point was emphasized that a missionary should seek his support solely from the Lord and not go around to all the churches in the area to raise a large amount of money before going to the field. It's along the same lines as George Muller's trusting in the Lord alone for his needs, and doing quite well. God says that he will provide all our needs, and as I've been seeing more and more in my studies of C. H. Makintosh's Short Papers, the point that the center of God's will is where you're safest and freest has really been driven home.

A group of men from our assembly, including my Dad and myself, meet every Tuesday morning at the Sunrise Grill for a Bible study and have been discussing Makintosh's papers. It's been a great experience!

Charlotte and I are busily ripping our CD collections of music that passes at school so we won't have to cart along hundreds of CDs. There are still a few I need to bring in bodily form to share with other people though. Time to get back to packing and folding towels!

Crista is gone

Today, Crista and I drove to Atlanta and visited China Town. Crista was flying out of Atlanta to go and visit Stormie for a week or so-long vaction. Watching movies with on-the-seen shoots at the China Town in LA, I naturally assumed it would be a mysterious place fraught with crime bosses, shipping docks, and creepy old guys with long wispy beards trying to sell you weird pets. Sadly, Atlanta's China Town is only a little shopping center with several (very tasty) restaurants, a courtyard garden with a koi pond, and a few shops.

This did not take up the three or so hours we had planned to squander investigating the shady corners of the Chinese underworld in downtown Atlanta before Crista needed to be at the airport, so we decided to just drive around and go wherever looked like fun. We found the Atlanta Farmers Market. It wasn't huge, and it really looked like a grocery store inside rather than having the expected inordinate truckloads of bok choy, but it was great fun nevertheless. We vowed before entering not to get a cart lest we buy something, but my resolve was broken in less than a minute after seeing a big bag of lychees for $1.99 a pound! Yay! We can't get these at home!

Lychees are a very sweet and fragrant subtropical fruit native to China. They were introduced to the United States sometime in the 1800s; my Dad remembers eating fresh lychees growing up in Florida. They're really cool fruits: they have reddish leathery skins on the outside, but the fruit inside is a pale translucent blah with the consistency of something like a muscadine. They have hard and shiny seeds inside them, being of the same sort of fruit as a peach.

I'm going to try planting a few of the seeds and see whether they will sprout (and then survive) for me. I'd like to bring them with me to college, but they require full sunlight. :(

Crista and I finally broke away from the market with only a few additional purchases and I dropped her off at the airport. I got home around 5:30, so I think I spent about 5 hours on the road today... maybe a little more. Next week on Tuesday, I have been assigned the solemn honor of retrieving her from Atlanta. Perhaps next time we'll infiltrate Atlanta's Thai (food) underworld!

Weddings, Piano, and Paint

It's been a while since I last checked in! I arrived home safe and sound and have been working hard to relax. Yesterday, I drove to Newnan, GA for a friend's wedding. It was held at Dunaway Gardens in an outside, natural ampitheater. I drove home last night and got in about 1:00 this morning. Today, we finished priming all the bedrooms, the foyer, and the trim, so painting the rest of the house should be fairly straightforward once we get around to it. Mom said she didn't think we'd get around to it tomorrow, though. :(

Another friend, Daniel, supposedly got married in Texas today. His brother called my phone while we were painting, but nobody heard it ring, and by the time we noticed it was really late. (And then I forgot my phone at Crista's house when we left for home.) ^^;; Congratulations, Daniel and Amy!

Practicing the piano has been a nice break now. I'm working on the concertos for this coming semester, and really need to pick out some other pieces to get started working on. I've been working on a couple sacred pieces to play as preludes, because folks keep asking me to play for church. *guilt* Hopefully, I'll get to watch Mrs. Joyner play hymns to gain some more insight into hymnplaying. :)

Time to go again! My friend Joy has noticed that I only post on my blog from 12:00 - 1:00 am. It's the only time that's free! Really! ;)