As I blogged at the end of February, the regular teacher wanted me to show this class McFarland USA, my favorite Cross Country movie. Well, she and I planned for a special treat today -- this time I bring in my own DVD, and she has an external DVD drive connected to the computer. During the earliest class we can't get the DVD to work. Instead I help some students with their trig homework, but I choose not to describe the problems on the blog today.
Fortunately I figure out how to work the DVD during tutorial, and so I play the movie for the third and fourth period classes. I leave the DVD behind so that she can finish the movie next week, after the AP Spanish exam.
The sixth and seventh period classes are Spanish III, not AP. These classes are watching the second part of a different movie. Its title in Spanish is Los Ninos del Cielo, and the original language of the movie is Farsi. (But Persian New Year was a month and a half ago, so it doesn't fit our Cinco de Mayo celebration.) With the movie in two non-English languages plus the fact that I start halfway during the movie, I'm slightly confused with the plot when I first start watching. I soon realize that the main character, the young Ali, is about to run in a race! Unlike McFarland USA, this movie actually mentions the distance of the race he's training for -- 4K. (The Cross Country race in McFarland is around three miles or 5K.) In all classes, I talk about my own days as a runner, ask the students in the class whether any run Cross Country, and compare the races in the movies to our own.
In both McFarland USA and Los Ninos del Cielo, shoes are important -- the runners are so poor that they can't afford new shoes. Coach White notes that the McFarland guys are fast despite not owning any good running shoes. He buys them cheap pairs of racers before the first meet and more expensive shoes in time for the State Meet. Meanwhile, Ali must share his old shoes with his little sister. He participates in the race because one prize is a new pair of tennis shoes. Ali hopes to give the shoes to his little sister.
I figure enough Spanish words to understand the main plot:
zapatos -- shoes
el par de tenis -- pair of tennis shoes
tercero -- third (The shoes are actually the third place prize.)
Today we cover Lesson 15-9, the last lesson of the U of Chicago text. We're following the digit pattern strictly this year, and so the Chapter 15 Test must be on Monday. It's our second Monday test of the year, since the Chapter 8 Test was also on Monday. On the other hand, we had only one Friday test (Chapter 6) and a Thursday test before the Good Friday holiday (Chapter 14).
I've decided that I want to finish Godel, Escher, Bach on Monday as well. It's a nice day to end our side-along reading, and I already know that I won't have much time for posting on Tuesday.
But there are still three Chapters left in the book. Despite barely writing about Chapter 17 yesterday, I want to describe both 18 and 19 today (just as I combined Chapters 8-9 on April 18th) and save Chapter 20 for Monday. Both Chapters are long, and so I'm leaving a lot out yet again.
Dialogue 18 of Douglas Hofstadter's Godel, Escher, Bach is "SHRDLU, Toy of Man's Designing." It begins as follows:
"One day, Eta Oin wanders into the MIT Artificial Intelligence Laboratory, where she runs into the brilliant young computer program, SHRDLU. It happens that SHRDLU is just dying for someone to try out the newly developed human being 'Dr. Tony Earrwig.' SHRDLU explains that this Earrwig is fairly intelligent in the limit domain of analyzing a conversation about a 'toy world' containing blocks of various shapes, sizes, and colors -- blocks which sit on a table, and which can be picked up and moved around. Eta Oin, fascinated, begins enthusiastically typing to SHRDLU. Earrwig dangles over her shoulder and provides a sort of running commentary, as promised."
Obviously, this Dialogue has nothing to do with Achilles or the Tortoise. Let me include the first few interactions with the computer:
1. Eta Oin: pick up a big red block.
SHRDLU: OK.
Dr. Tony Earrwig: SHRDLU answers "OK" when it carries out a command. In order to pick up the red block, it had to clear it off by finding a space for the green one and moving the green one away.
2. Eta Oin: grasp the pyramid.
SHRDLU: I DON'T UNDERSTAND WHICH PYRAMID YOU MEAN.
Dr. Tony Earrwih: There are three pyramids in the scene, and SHRDLU knows that phrases beginning with 'the' are intended to refer to a specific object the speaker has in mind.
Let's skip to the end of the interaction:
43. Eta Oin: is there anything to the right of the red pyramid?
SHRDLU: YES. FOUR THINGS: THE BOX, THE RED CUBE, THE BLUE PYRAMID AND THE BLOCK NAMED SUPERBLOCK.
Dr. Tony Earrwig: Once an object has a name, the name is used to help identify it in responses.
44. Eta Oin: thank you.
SHRDLU: YOU'RE WELCOME!
Dr. Tony Earrwig: SHRDLU's grammar is written as a procedure, which gives SHRDLU the capability to carry out special sorts of parsing for idioms.
Chapter 18 of Douglas Hofstadter's Godel, Escher, Bach is "Artificial Intelligence: Retrospects." It begins as follows:
"In 1950, Alan Turing wrote a most prophetic and provocative article on Artificial Intelligence. It was entitled 'Computing Machinery and Intelligence' and appeared in the journal Mind."
I've written about many of the ideas from this chapter in previous posts, starting with Turing himself, who consider the question "Can Machines Think?":
"This, he suggests, is contained in what he calls the 'imitation game': it is nowadays known as the Turing test."
Indeed, Imitation Game was the name of the movie about Alan Turing. I blogged about that movie when it first came out, during the first year of this blog.
Turing's answer to his own question is, essentially, someday they will. But he anticipates objections:
"Aware of the storm of opposition that would undoubtedly greet this opinion, he then proceeds to pick apart, concisely and with humor, a series of objections he counters, using his own descriptions of them."
Unfortunately there is not enough time for me to reproduce the humorous and ingenious responses that he formulated. Instead, Hofstadter returns to the Dialogue:
"In the Dialogue preceding this Chapter, you have seen an authentic exchange between a computer program and a human."
One of the most famous exchanges is called "Doctor." I'll link to the Berkeley Logo page, where Brian Harvey writes more about both ELIZA and "Doctor":
http://people.eecs.berkeley.edu/~bh/v2ch9/doctor.html
Some more examples of applications of AI include language translation, checkers, and chess. Here Hofstadter mentions a Geometry proof rediscovered by AI -- the "quick-and-dirty" Pappus proof of the Isosceles Triangle Theorem where a triangle is congruent to itself via SSS. He also mentions computer music -- this is something that I'm trying to accomplish using Mocha.
Dialogue 19 of Douglas Hofstadter's Godel, Escher, Bach is called "Contrafactus." Here's how this Dialogue begins:
"The Crab has invited a small group of friends over to watch the Saturday afternoon football game on television. Achilles has already arrived, but the Tortoise and his friend the Sloth are still awaited."
Achilles: Could that be our friends, a-riding up on that unusual one-wheeled vehicle?
Let's meet our new character, the Sloth:
Sloth: This is the first time I can recall making the acquaintance of a Bicyclops. Pleased to meet you, Achilles. I've heard many fine things said about the bicyclopean species.
Once again, let me skip to various lines from this Dialogue:
Crab: One and the same. And there was one work that made me think of you, Mr. Sloth -- a marvelous piano concerto for two left hands. The next-to-last (and only) movement was a one-voice fugue. You can't imagine its intricacies. For our finales, we played Beethoven's Nine Zenfunny. At the end, everyone in the audience rose and clapped with one hand. It was overwhelming.
...
Achilles: Such a graceful maneuver! What would we do without instant replays?
Announcer: It's first down and 10 for Out-of-Town. Noddle takes the ball, hands off to Orwix -- it's a reverse -- Orwix runs around to the right, handing off to Flampson -- a double reverse folks! - and now Flampson hands it to Treefig, who's downed twelve yards behind scrimmage. A twelve-yard loss on a triple reverse!
...
Achilles: Why does it have so many knobs and fancy dials?
Crab: So that you can tune it to the proper channel. There are many channels broadcasting in the subjunctive mode, and you want to be able to select from them easily.
...
Announcer: It's fourth down for Out-of-Town, with Home Team receiving. Out-of-Town is in punt formation, with Tedzilliger playing deep. Orwix is back to kick -- and he gets a long high one away. It's coming down near Tedzilliger --
... (the channel is changed) ...
Achilles: Smash it, Tedzilliger! Give those Out-of-Towners a home run for the money!
Announcer: -- but it seems to be a spitball, as it takes a strange curve. Now Sprunk is madly scrambling for the ball! It looks like it just barely grazed Tedzilliger's bat, then bounced off it -- it's ruled a fly ball. The umpire is signaling that the formidable Sprunk has caught it for Out-of-Town, to end the seventh inning. It's a bad break for Home Team. That's how the last play would have looked, football fans, if this had been a game of baseball.
... (Oh, so that's what broadcasting in the subjunctive mode means!) ...
Announcer: And now let's watch the subjunctive instant replay.
Tedzilliger's fading back to pass. He spots Palindromi ten years outfield, and passes it to the right and outwards -- it looks good! Palindromi's at the 35-yard plane, the 40, and he's tackled on his own 43-yard plane. And there you have it, 3-D fans, as it would've looked if football were played in four spatial dimensions.
...
Crab: Believe it or not, Mr. Sloth and I went to a country fair the other evening, and the TV was offered as the first prize in a lottery. Normally I don't indulge in such frivolity, but some crazy impulse grabbed me, and I bought one ticket.
Achilles: What about you, Mr. Sloth?
Sloth: I admit, I bought one, just to humor old Crab.
... (Actually, the Crab didn't win the lottery!) ...
Announcer: And that, folks, was how the afternoon at Mr. Crab's would have been spent, had he won the Subjunc-TV. But since he didn't, the four friends simply spent a pleasant afternoon watching Home Team get creamed, 128-0. Or was it 256-0? Oh well, it hardly matters, in five-dimensional Plutonian steam hockey.
Chapter 19 of Douglas Hofstadter's Godel, Escher, Bach is "Artificial Intelligence: Prospects." It begins as follows:
"After reading 'Contrafactus,' a friend said to me, 'My uncle was almost President of the U.S.!' 'Really?' I asked. 'Sure,' he replied, 'he was skipper of the PT 108.' (John F. Kennedy was skipper of the PT 109.)"
And this whole Contrafactus reminds me of Futurama and the "What If? Machine." Anyway, Hofstadter mentions a counterfactual that he found printed in a magazine:
If Leonardo da Vinci had been born a female the ceiling of the Sistine Chapel might never have been painted.
And if Michelangelo had been Siamese twins, the work would have been completed in half the time.
Much of this chapter is devoted to Bongard problems. These are so visual that I might as well just provide a link to them:
https://www.foundalis.com/res/diss_research.html
Hofstadter also draws a concept network relating many concepts in Geometry, such as "square," "triangle," and "polygon." The hierarchies in the U of Chicago text are sort of like concept maps, except that all the concepts are related using "is-a." (A square is a polygon.) But Hofstadter's concepts may be joined by other relations such as "composed of" and "has feature."
Afterward, the author returns to his analogy from molecular biology. Comparable to AI in a cell are enzymes whose purpose is to act as a filter to recognize only certain types of "messages." He proceeds to discuss fission and fusion of symbols or DNA. Then he compares his Crab Canon (the Dialogue that could be read forwards and backwards) to the process of meiosis (cell reproduction along with genetic recombination).
Hofstadter concludes this present ten "Questions and Speculations" about AI. But those questions, dear readers, is what I would have blogged about, if I'd had unlimited time to type this post.
This is what I wrote last year about today's lesson:
Lesson 15-9 of the U of Chicago text is on "The Isoperimetric Theorems in Space." These are the 3D analogs of the theorems we discussed on Friday.
Isoperimetric Theorem (space version):
Of all solids with the same surface area, the sphere has the most volume.
Of all solids with the same volume, the sphere has the least surface area.
We don't even bother trying to prove these theorems. As we've seen, the 2D proofs are very difficult, so imagine how much more so the 3D proofs would be.
This is the final lesson in the U of Chicago text. Here is how the U of Chicago closes the text:
"The Isoperimetric Theorems involve square and cube roots, pi, polygons, circles, polyhedra, and spheres. They explain properties of fences, soap bubbles, and sponges. They demonstrate the broad applicability of geometry and the unity of mathematics. Many people enjoy mathematics due to the way it connects diverse topics. Others like mathematics for its uses. Still others like the logical way mathematics fits together and grows. We have tried to provide all these kinds of experiences in this book and hope that you have enjoyed it."
Well I for one have certainly enjoyed this text, and I hope you, the readers of this blog, have as well.
This lesson mentions the ancient Carthaginian queen Dido. I wrote about her last year as well:
"According to one of the legends of history, Dido, of the Phoenician city of Tyre, ran away from her family to settle on the Mediterranean coast of North Africa. There she bargained for some land and agreed to pay a fixed sum for as much land as could be encompassed by a bull's hide."
"Her second bright idea was to use this length to bound an area along the sea. Because no hide would be needed along the seashore she could thereby enclose more area."
We know that the solution to the Isometric Problem is the circle -- the curve that encloses the most area for its length. We've also seen questions in which we are to maximize area by building a fence along a river to enclose a rectangular area -- the answer is a rectangle whose width is exactly half of its length. Combining these two ideas, we can solve the Dido problem:
"According to the legend, Dido thought about the problem and discovered that the length of hide should form a semicircle."
So we see that without water, the largest area is a circle -- with water, it's a semicircle. If we restrict to rectangles, without water the largest area is a square -- with water, it's a semi-square (that is, half of a square, or a rectangle whose width is half of its length).
"[Dido's new lover] Aeneas was a man on a mission, and he soon departed to found a new civilization in Rome. Dejected and distraught, Dido could do no more for Aeneas than to throw herself on a blazing pyre so as to help light his way to Italy...Rome made no contributions to mathematics whereas Dido might have."
By the way, let's tie this back to Pappas and ask, what numerals would Dido have used? Carthage is actually derived from the Phoenician culture. Notice that the Square One TV video "The Mathematics of Love" seems to imply that the Phoenicians used our (current) numerals (in contrast with the Roman), even though Phoenician has nothing to do with Hindu-Arabic. So in the end, I don't know what numerals Carthaginians might have used.
Since the test is on Monday, let me post the Chapter 15 review questions as well. My new first page includes two questions each from Lessons 15-3 and 15-4 and one each from 15-1, 15-5, 15-6, and 15-7.
Last year's Page 2 contains some questions from Lessons 15-3 and 15-8. But there are also some questions from different sections.
Questions 9 through 11 are on the equation of a circle, Questions 14 and 16 are on the volume/surface area of a sphere, Question 15 is on the Pythagorean Theorem, and Question 17 is on the relationship between radius and tangent.
The new version of the test still contains these questions from four other chapters, but now most of the questions are from Chapter 15.
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