Monday, February 28, 2005

Math Problem IV

There are approximately 6.3 billion (6,300,000,000) human beings on the Earth at the present moment.

Imagine that each person on the planet is given a coin which is scrupulously calibrated to be absolutely fair, equally likely to come up heads or tails. (Persons who are neurologically undeveloped, damaged, or ill will have a coin flipped on their behalf by a family member or neighbor.) At exactly midnight, GMT, everyone flips his or her coin and records the outcome (heads or tails). Then the process is repeated again at 12:02 AM, and 12:04 AM, and so forth, every two minutes, until every coin has come up heads at least once and tails at least once, at which point the coin-flipping stops.

What time is it (GMT) when the coin-flipping stops?

Answer in comments.

Activity: How many times will the last coin-flipper have seen his/r coin come up either all heads or all tails? Is s/he likely to believe that the coin is fair and unweighted? Divide into small groups and discuss the emotional impact of this exercise on the coin-flipper if A) s/he is inclined to be skeptical of the claims of others or B) s/he is inclined to assign religious meaning to the exercise.

How would you defend the fairness of the coin to the skeptic in A)?

How would you explain to the believer in B) that s/he had not been singled out for special treatment by a deity, that inevitably a long string of H or T outcomes was going to happen to somebody?

Monday, February 21, 2005

Political Science Worksheet I

Greetings to those who followed the link from King of Zembla.

In each of the following exchanges, assume that you are Scott McClellan, G. W. Bush's White House Press Secretary. Compose a response to any one of the following (hypothetical) reporters' questions.

1. Q: The President has recently renewed his proposal to open the Arctic National Wildlife Refuge to oil drilling, despite public skepticism on the part of some Administration advisors and oil company executives that ANWR has sufficient oil reserves to make its production worth the cost of drilling. Does the President still support ANWR oil exploration, and why or why not?

2. Q: Can you comment on reports that the Pentagon has discontinued prescribing the anti-malarial drug Lariam following assertions that it leads to mental instability in some soldiers? Are there plans to investigate the role of the medication in the effects reported by soldiers, and if it turns out that there is a link, is the White House prepared to go on-record as promising compensation to soldiers and their families?

3. Q: Does the President have a sexual fetish for bald men? And was this a factor in Jim-Jeff Gannon-Guckert getting access to the briefing room despite lack of proper press credentials?


Answers will be graded based on the number of points they earn according to the following criteria:

(30 points) response does not incriminate anyone at White House
(25 points) response does not incriminate friends or associates of White House
(20 points) blames Bill Clinton
(15 points/each) blames any group composed entirely of American citizens
(15 points/each) blames European allies / other allies
(15 points) answers a question other than the one which was asked
(15 points) amounts to a claim that the question does not need to be answered
(15 points) amounts to a claim that the question cannot be answered
(15 points) is completely unparsable
(12 points) is more than 7 or fewer than 3 sentences in length
(10 points) discourages other reporters from asking similar questions
(7 points) any appeal to a political principle not actually supported by the Republican Party (church/state separation, reproductive rights, business regulation, bipartisanship, global cooperation, right to privacy, gun control, etc.)
(5 points) sincere-sounding platitude about bipartisanship
(5 points) references an Administration official other than the President or Vice-President without identifying him or her
(3 points/each) platitude about Iraqi people
(3 points/each) platitude about American businessmen or business practices (in general)
(3 points/each) platitude about Republican party, its leaders, or its supposed ideals
(3 points) condescending tone
(3 points) optimistic spin
(1 point/each) uses the words "freedom," "family," "responsibility," "accountability / accountable," "friendship," "full disclosure" "legitimate" (either pronunciation), "clarify," "exchange," "communication," "integrity," "strategy," "co-operation," "credibility," "security"

55 points or less – F
56-75 points – D
76-95 points – C
96-115 points – B
above 116 points – A


Special note from Ms. Guilford: Lurkers are encouraged to try their hand at this one. Send an e-mail containing your answer to me here. Identify which question you are attempting to answer, and the name to which you would like your response attributed, if posted publicly. The highest-scoring response will be posted on this blog, as well as, potentially, any other responses which amuse me. I reserve the right to edit for length and clarity.

-J.G.

Wednesday, February 16, 2005

Music Project II

You will need:

large uncarpeted room (a school gymnasium is ideal)
48 identical freestanding shelving units (preferably open on both front and back, and with adjustable-height shelves)
1500 mousetraps
1503 hi-bounce "superballs" (27-33 mm in diameter)
125 12-egg egg cartons
glue
45 identical electronic synthesizers, with amplification equipment
recording equipment for the synthesizers (either MIDI cable – preferred – or microphones)
plywood sheets (optional)
cardboard or card stock (optional)
rubber bands (optional)
1-6 stepladders (optional)
pennies (number variable, optional)
camcorder
VHS videotape (if camcorder is non-digital)
safety goggles for all students and instructor

The class will divide into three groups for the execution of this project, as it is very complex. These groups will be designated by number. Students may select their own groups, provided that 1) the groups wind up approximately equal in size and 2) no groups cause disruption to the project or to other students. If these conditions are not met, the instructor may reassign groups at his or her discretion.

Group 1 (Physical)
1.1) Assemble the shelving units. You may find it convenient to utilize an assembly-line sort of process. If the units are constructed in such a way that the shelves need not all be at the same height, make sure to include some variation in the heights. Allow a minimum of eighteen inches between shelves.

Group 2 (Detail)
2.1) Cut the egg cartons into individual cups. You should be able to get 12 cups from each carton.
2.2) Trim down the edges of the cups until they are about 20-25 mm deep.
2.3) Either set the mousetraps or use rubber bands to hold them in an open position. Apply a dab of glue near the center of the extended arm (Carefully!) and place one of the egg cups on the dab of glue.
2.4) Allow the glue to dry.

Group 3 (Technical)
3.1) If you wish to prevent certain note ranges from being played, as for example very low or very high notes, cut the cardboard or card stock into strips as wide as the keyboard's keys are long. For most keyboards this will be about four or five inches.
3.2) Insert the strips you just cut into the spaces between the keys, for the ranges of keys you want to block from play. You may need to use multiple strips adjacent to one another, if you desire to block long ranges of notes.
3.3) Set the default voice on the synthesizers to the same option for each. For best results, you should use a voice with a sharp attack and long decay, for example a piano voice with sustain, or bells, or chimes.

Group 1 (Physical)
1.2) Identify the most convenient entrance/exit to the room, and at the opposite end, begin setting up the shelving units. The gym teacher may insist that you apply the rubber "feet" to the bottoms of the units. Avoid dropping or dragging the units, to protect the floor surface. Place the units far enough apart to enable a person to walk between them (roughly 3 or 4 feet), but no more distant than that.

Group 2 (Detail)
Now we will begin to load the mousetraps onto the shelving units. Start with the top shelf (use stepladders if necessary). You should be able to fit about three mousetraps along the width of the units, and seven or eight along the length.
2.5) Set the mousetrap, and place a superball into the cup. Slide the mousetrap gently along the surface of the shelf until it reaches the desired location, then begin on the next trap.
2.6) When one shelf is full, proceed to the next-lower shelf.
2.7) When all shelves on a unit are filled, call members of Group 1 to place another unit and continue from step 2.5 until a row of 16 shelving units has been filled with mousetraps.

Group 1 (Physical)
1.3) When one full row (16 shelving units) has been placed and loaded with mousetraps, tell Group 2 to pause loading, and inform Group 3 that they need to place the synthesizers in the spaces between units.

Group 3 (Technical)
3.4) Disable the automatic shutoff feature of the synthesizers (if possible).
3.5) When notified that a full row of shelving units has been placed, connect a set of fifteen synthesizers to sources of electricity, and amplification and/or recording devices. (Wireless devices are preferable but may not be available.) Place the fifteen synthesizers in the spaces between shelving units.

Group 1 (Physical)
1.4) The class may decide to cover the wires with sections of plywood in order to cover the wires leading from the synthesizers to amplification and recording equipment. If this is desired, cut the plywood to fit over the wires and place stacks of pennies underneath the plywood, at the corners, to keep the surface more or less level. There should be adequate clearance for the wires underneath the plywood; do not just set plywood directly on top of the wires.
1.5) When the wires have been covered, begin the next row of shelving units as in step 1.2. Maintain a separation between rows of at least two inches, to guard against inadvertent bumping of the shelving units.

Group 2 (Detail)
2.8) When synthesizers have been placed between the shelving units in the first row, proceed to the second row, repeating the process in steps 2.5 to 2.7.

Group 3 (Technical)
3.6) When the second row of shelving units has been set up and loaded with mousetraps, place synthesizers in the spaces between units as in steps 3.4 and 3.5.

Group 1 (Physical)
1.6) When synthesizers are placed in the second row, cover exposed wires with plywood again as in steps 1.4 and 1.5, and begin placing the final row of shelving units. Be sure to leave at least five feet of space open at the side of the gym by the third row of units, as people will need to be able to walk around to load shelves and install synthesizers.

Group 2 (Detail)
2.9) When synthesizers have been placed between the shelving units in the second row, proceed to the third row, repeating the process in steps 2.5 to 2.7.

Group 3 (Technical)
3.7) When the third row of shelving units has been set up and loaded with mousetraps, place synthesizers in the spaces between units as in steps 3.4 and 3.5.

All Groups
1.7; 2.10; 3.8) When all shelving units have been set up, loaded with mousetraps, and synthesizers placed between them, use the remaining mousetraps and superballs to fill in additional gym floor space, if any. You may have mousetraps and superballs left over. (Be sure to leave at least 3 superballs out for the instructor, in any event.)

Instructor
I.1) If the gymnasium has a balcony, take the class (and any other students or instructors who wish to view the performance) to the balcony; otherwise, you may seat the class high up in the bleachers. If no seating is available, you may proceed from the floor of the gymnasium.

Group 3 (Technical)
3.9) Begin recording with the camcorder (as well as any computerized links from the synthesizer to recording equipment).

All Groups / Instructor
1.8; 2.11; 3.10; I.2) Put on safety goggles.

Instructor
I.3) Throw one of the superballs toward the center of the shelving units and synthesizers, or invite a favored student to throw one. If it fails to set off any mousetraps, or the mousetrap is set off but fails to initiate the desired chain reaction, try again with one or both of the remaining two superballs. If these still fail, superballs may be retrieved or unloaded from accessible mousetraps until a chain reaction is successfully initiated.
I.4) When performance has ended, students may proceed to the floor to set off any mousetraps which failed to go off, and collect the superballs, mousetraps, synthesizers, and other equipment for the next class. A few students should be designated to count the returned items and ensure that no items (for example, stray superballs) remain in the gym.

Philosophy Project I

We have just concluded our viewing of the movie The Matrix. In the movie, a group of extraterrestrials have hooked all human beings into the eponymous "Matrix," a mechanism by which humans in a vegetative or comatose state can be used to generate power or nutrients or something for the extraterrestrials. In the movie, the overwhelming majority of human beings are not aware that they are being used in this fashion, and the extraterrestrials are using advanced virtual-reality technology to provide the brains of the humans with impressions and experiences resembling late-twentieth-century everyday life.

I will divide the class into groups of three or four. Groups are to brainstorm for methods by which a person could determine whether he or she was in the world posited by The Matrix. Ideas will be presented to the class next week.

Grades will be based on 1) likelihood that the method you propose will be successful (as determined by your classmates), 2) originality of the idea you present, 3) presentation skills, 4) class participation, and 5) handling of cross-examination about your method from other members of the class.

The second part of the project will be a short (5 pp. or less) essay in which you should address the following questions:

A) Was it more or less difficult to come up with testing ideas than you expected it to be?
B) What did you learn from the class attempts to test the theory?
C) Is it necessarily even a bad thing to be living in the Matrix? Why or why not?
D) Was it uncomfortable to contemplate the idea that you might be a subject in the Matrix? Why or why not?

Math Problem III

An indoor swimming pool is 12 feet in width by 30 feet in length. The shallow end is 3.5 feet deep and the deep end is 8 feet deep, and the depth of the pool changes linearly from the deep end to the shallow end.

One standard box of Jell-O brand gelatin (6 ounces) makes four cups of Jell-O when set up.

Calculate the number of boxes of Jell-O which would be required to completely fill the swimming pool. Assume that the volume of the filtration equipment is negligible and that the pool is to be filled with Jell-O completely.

Conversion factors you may need:

1 cubic foot = 7.481 gal
1 gal = 16.0 cups

Advanced students:
A) One package of Jell-O, prepared according to the directions, makes 8 servings of Jell-O which each have 80 calories. What would be the total caloric content of the swimming pool so filled?
B) If a standard caloric intake for an adult is 2000 calories per day, for how many days could a single adult live off of the swimming pool filled with Jell-O? Assume that there is no spoilage and that the Jell-O in the swimming pool is nutritionally adequate to support life.

Answers are located in the comments.