PrepTest 129

Topic: Science

Paragraph 1

• Paragraph note
  • Fractals explained (self-similar — each part looks like the whole) and Koch curve example ( _^_, each segment also looks like _^_ )
• Views, minor Meta-Structures, and the author's attitude
  • Definition of "self-similarity": A shape where each little part looks like the whole shape (second sentence)
  • Example of an important fractal that exhibits self-similarity, according to the author:
    • The Koch curve, which is a straight line with a bump in the middle, but each smaller line has bump, repeated ad infinitum (third through last sentence)
  • Author's attitude: "significant" (third sentence); "provides some insight" (third sentence)

Paragraph 2

• Paragraph note
  • Use of computers in fractal geometry (not limited by what can be drawn/displayed, so can create more complex fractals)
• Views, minor Meta-Structures, and the author's attitude
  • Author's view:
    • Computers illustrate why many people are interested in fractals, given that programming simple steps can create very complex patterns (last sentence)
  • Comparison, according to the author:
    • Creating an image of the Koch curve without a computer will be limited by how small we can draw or display each line segment; however, using computers to make Koch curves doesn't have such a limit (third and fourth sentences)
  • Author's attitude: "dramatically illustrates a major attraction" (last sentence); "simple processes" (last sentence); "incredibly complex patterns" (last sentence)

Paragraph 3

• Paragraph note
  • Debate over usefulness between enthusiasts (a new form of math that can describe complex natural forms) and skeptics (hasn't yet created theorems/proofs)
• Views, minor Meta-Structures, and the author's attitude
  • Public's view:
    • Captivated by complex images (first sentence)
  • Fractal enthusiasts' view:
    • Fraticals represent a new mathematical system that can describe natural/mathematical forms (first and second sentences)
  • Comparisons, according to the fractal enthusiasts:
    • Fractal geometry will become as important as calculus (second sentence)
    • Fractal will allow mathematicians to describe the shape of a cloud as easily as architects can describe a house with traditional geometry (second sentence)
  • Fractal skeptics' view:
    • Fractal enthusiasts are too focused on images and need to show that fractal geometry can prove theorems (third through last sentences)
  • Comparison, according to the fractal skeptics:
    • Pre-fractal math has proven many theorems about fractals, but fractal geometry has only proven a few theorems that couldn't have been proven without fractals (fourth sentence) and only a few have been demonstrated
  • Author's attitude: "captivated" (first sentence); "astonishing" (first sentence)

Main Point: The ability of fractal geometry to generate complex patterns from simple processes has captivated the public and some practitioners, but others are skeptical that it can be used to prove theorems and thus have a lasting role in math.

Describing a Debate: Even though the author doesn't bring up the debate until the last paragraph, this passage best fits the Describing a Debate Meta-Structure.* In such a passage, the author describes two sides of a debate without taking a side or attempting to reconcile the two sides. (If the author takes a side or attempts to resolve the debate, the passage is better understood as a "Resolving a Debate" passage.) In this passage, the author uses the first two paragraphs to explain the passage's subject matter (fractal geometry) before finally presenting the debate over that subject matter's usefulness. The author doesn't take sides in the debate beyond saying that the subject matter can produce some wild images.

In passages that utilize a Describing a Debate Meta-Structure, the main point generally describes both sides of the debate (or the assertion that there is a debate). We constructed our anticipated main point around both sides of the debate, while also including the public's fractal fascination for good measure.

*That said, we could call this an Old Approach/New Approach passage, with pre-fractal geometry as the old approach and fractal geometry as the new approach. That said, pre-fractal geometry doesn't play a huge factor in this passage, so we think this passage is better understood as a Describing a Debate passage.

Example: The passage dedicates a fair amount of real estate to the Koch curve example, making this example the most prominent minor Meta-Structure in the passage. This part of the passage describes the process by which that curve is generated and illustrates certain features of fractals (namely, self-similarity). The Koch curve is also discussed in the context of computer generation. This example is meant to explain to the reader what fractals are, and it's ancillary to the debate raised in the third paragraph, so it's more likely to show up as the topic for a few Minor Point, Application, or Argument Structure questions.

One more note about this example: the description of the Koch curve process is really hard to follow if you're not drawing it out. That doesn't mean you need to draw it out, as it's unlikely that there will be a lot of questions on it. But if you have the time, running through the relevant steps one or two times can be helpful for the questions that do involve the specifics!

This passage's main point can trip up some test-takers. How come our anticipated main point only summarizes the third paragraph? Aren't main points supposed to be comprehensive and summarize the entire passage?

These are good questions and valid concerns! But it's important to remember that in Reading Comp, arguments are far more important to the passage than details. The first two paragraphs only include details. They describe what fractals are and how people generate them using computers. These details essentially provide background information on the passage's subject matter.

We don't get arguments until the third paragraph. Each side presents their argument on the utility of fractals. "Fractals are useful because they'll help mathematicians describe natural shapes easily." "Fractals are not yet useful because they don't support a system of theorems and proofs." These arguments feature details (the evidence both sides use), but they also feature conclusions — evidence-backed opinions that each side has about fractals. Much as we understand arguments through the conclusion in LR, we’ll understand passages through their conclusions in RC. These conclusions help identify what's really important in the passage. We'll use those conclusions to define the passage's Meta-Structure and main point.