Can computers think?

This was a question we discussed recently in class. Can computers think? Who is smarter, computers or humans?
It was interesting to hear the students response and reasoning. We did not agree if computers could think or not (which is okay given not many people agree…but Michigan's Own Claude Shannon seems to think they do). However most of the students agreed that, even if computers can do math and calculations very fast, people are smarter because they program computers, and essentially telling them what to do.

We talked about Deep Blue, the first computer program that beat the world chess champion in 1997 (playing against Garry Kasparov). However, we agreed that this still does not mean the computer was smarter than Garry, but it could calculate many steps ahead in the game.


We finished our discussion of computer and artificial intelligence by talking about robotic arms and how mathematics is used in designing these things. Especially how something as easy as altering the angle of the robotic arm allows it to hold an object.

The social graph

What do you think of the following two graphs?




They represent how people are related to each other in social networking sites like Facebook. We talked about Facebook in class the other day and this was one of the things we tried to analyze.

Early in the semester, there was a warm up question that asked:
If there were 20 people in a room and everybody shook everybody else's hand, then how many handshakes there will be in total? You might recognize it as a pretty elementary permutation and combination problem from precalculus. We looked at an easier, incremental way of solving the problem in class.
We tried to apply the same analysis to the social graph and trying to gauge how many connection there could possibly be when you look at something as big as Facebook.

In addition, we talked about programming languages and how people instruct computers, leading to binary numbers and how everything that we want to tell a computer has to be converted to a series of 0's and 1's for execution by a computer.

Dan Moses

Dan Moses' visit to our classes was a nice addition. He took a back sit most of the class and observed how things were going. A couple of times he sat along student groups that did not have enough people and participated in the activities. When I got to talk to him over the break, he said he was excited about the addition of Ypsilanti High to the program. When I asked him what he thought about the discipline issues in the class room, he told me it was actually about average for his experience at other schools. The students for the most part seem not to have noticed him, and it seemed like that was what he wanted anyways.

We are still working on the first of the five modules that will be covered this year. This module, called the Trip Line, tries to relate numbers, relationships and equations using place names that are lined along a trip line that students took at the beginning of the class. The content is gradually getting to be mathematical an the students are more or less following.

The discipline issues still need to addressed, nonetheless. There are only a few students who pay attention through the entire class. It is also really interesting to see how the seating arrangements affect student behavior. As the class is structured around groups, the dynamics in each group is pretty essential to how productive that group is. I have seen students who have changed behaviors once they were sitting with a different set of people. Mr. Tuttle does a great job of trying different ways to interest the kids without having to yell at them. The fact that we still have not sent (as far as I know) any student to the principals office is a good example for that.