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Journal Entries

Definition

In my first journal entry I wrote that I believed that calculus is a way of finding solutions to problems that can't be solved with conventional math, by using abstractions.  I was partially correct in that many parts of calculus do require abstract thinking.  But that's not really what calculus is.  Calculus is a way of dealing with motion.  It's a way of finding out exactly how something is moving.    Without calculus it was impossible for us to know what the instantaneous velocity of something was.  We could only know the actual rate of change if it was changing at a constant rate; then its derivative or the slope of its tangent line is equal to the slope of the original line.  When we had something that had a variable rate of exchange, we tried to find the average velocity, but this was inaccurate.

(Source: William Zinsser's Writing to Learn, NY: Harper & Row, 1988, 156 )

Dialogue

T.S. Eliot:  I only suggest that the world becomes a vicious cyle--it is for you to decide whether this is positive or not.  Judging from past history, I would say that man can't get out of his rut--his nature is basically evil.    Especially since the industrial revolution, we have seen how quickly technology and success bring out the greedy selfishness in man.  It's almost laughable.

Me:  Why do yo choose to laugh at these problems rather than doing something about them?  Isn't laughing an acknowledgment that you can't deal with the problems?

T.S. Eliot:  Laughing is also a way of preserving one's sanity.    I wrote the poems to express my own ideas; perhaps they have opened some eyes and minds, but I doubt it.  You can't fight society and human nature.

Me:  I disagree.  I think we can do something about our problems or at least help others find satisfaction with their own lives.  I prefer to "cling to your notions of an infinitely gentle, suffering thing."

T.S. Eliot:  Perhaps you will be "moved by fancies," but you will soon look back on these immature idealistic ideas with scorn.  The more things change, the more they remain the same.  History will repeat itself for eternity--if we make it that long (which I doubt).

(Source:  Jessie Yoshida's "Writing to Learn Philosophy" in Roots in the Sawdust, ed. Ann Ruggles Gere, Urbana, IL: NCTE, 1985, 121-122)

Role-Play

I am lava all around,
    Gases emerging and burning into steam,
        Taking everything that stands before me
            I move sluggishly across the land.
Slowly,
    My outer layer cools,
        But my inside still turns
            Forming a tunnel.
I feel movement beneath,
    Rushing air,
        The still liquid part
            Tries to fill the tunnel
                cooling as it descends.
Forming
     A column of basalt
        dangling from the roof of the cavern.
I am
    A pillar formed from fire,
        Now frozen as ice.
I am
    A stalactite.
I am.

Source:

Guided Imagery

A Hike Through the Rain Forest

We're starting on the bark-covered trail into the wild wonder of the Rain Forest. There's moss growing over the trail so you can barely tell there's bark underneath it. I can tell they haven't covered it with bark in a long while. The river is moving rather rapidly, dodging the rocks and fallen trees and branches. The sun is coming out and shining rather brightly. The forest is still cold though. It's like there's a giant reflector over the forest reflecting the heat so it will stay cold. We're taking a break to rest up a bit. There's an old nursing log with some trees and rocks by and on it. We like this place because there's a good place to sit and rest. There's a lot of action going on here. Some birds are in the trees above us. We're back on the trail now.   Some moss hanging from a tree brushed my face. It's fascinating how it just hangs from this tree...

adapted from

Application

Today I noticed something interesting on the golf course. I was standing on the ninth tee watching the people on the first tee. The first guy hit the ball, and I was watching it travel through the air, and then I heard the club hit the ball. This was the first time I had ever seen and heard the difference between the speed of sound and the speed of light. The next guy got up to hit the ball, and as he swung I looked at my watch.   About a second later I heard the familiar WHACK!!! I realized that if I had had a more accurate watch I could have figured out the distance from me to the other golfer.

adapted from

Question

I spilled some of the liquid collected in fraction #7...I wonder if only solvent spilled? I can't imagine how only solvent would have leaked out, though, since the product is dissolved in the solvent...I know how I could find this out, by looking up the melting point of the product.

Source:

Double-Entry

50 = lw

50 = (2w)(w)

50 = 2w²

25 = w²

25 - w² = 0

(5 - w)(5 + w) = 0

w = -5 or 5

Its length is 10 and its width is 5.

The difficulty I had with this particular
problem was that I could not figure out a way to express the unknowns in such a way that I was solving for one variable. Another problem was that I was misled by the phrase "50 square meters." I interpreted it literally to mean 50m². That brought a new dimension into the problem. How was I going to solve for m²? After some discussion, I found that I could express the length two ways. One was to simply express it as (l), the other was that since it was twice as long as (w), whatever (w) was could be taken twice to determine (l). Therefore, (2w)(w) is equal to the length times the width which is in turn equal to 50 square meters, or the area. I also learned that a square meter simply means that in a given area a certain number of squares can be found. For example, in 50 square meters there are 50 squares that measure 1 meter on each side.



 

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