Media is the plural of medium, and is a substrate through which information flows. During the AAAS Mass Media Luncheon, speaker Dr. Jeffrey Kirsch , the Executive Director of the Fleet Science Center , asked us for our reactions to the phrase coined by Marshall McLuhan in the 60's: "The medium is the message." Just the day before in the Counter-terrorism Symposium, Keith Devlin spoke about the difficulty of quantifying "information" and its reliability. These discussions led me to think about information like light -- a pure and difficult to measure substance whose appearance is determined by the substance through which it passes. Rather than thinking of information as being stuck in some sort of box to which an elite few hold the key, I recognize that information is difficult to confine. Just as we created the light bulb, neon signage, fiber optics, and lasers to channel light which is typically free to move about, we design means by which we channel information so that it can be viewed, touched, heard, smelled, and sensed as we see fit.

We control some of the media through which information passes: our own mental framework, a blog, a podcast, an imax movie, a newspaper article, our social interactions. But we don't have nearly as much control over the information itself, which is floating everywhere around us in more or less dense and disorganized clouds. So people who choose to be involved in media are attempting to corral information, this unruly light-like substance, so as to harness some of it's power and help others use it as a tool to brighten their lives.

With this metaphor in mind, I see that there is power in heterogeneity. With a variety of media, what remains to be seen is which media will excel at fulfilling which roles. While some media will replace others (like compact fluorescents are increasingly replacing incandescent bulbs), many will coexist or work in concert.

Still there is the concern that people will be blinded by so much information, as if we are in a world covered in a thick blanket of pure white snow. Well, I think that's what sunglasses are for! In other words, people will have to squint for a while before they realize which media they need in order to function, and many members of the public are probably in that squinting phase right now. So when they realize that they need a way to filter out the intensity in order to focus in on some of the details and survive, they will be scrambling to find good journalists.

## Monday, February 22, 2010

## Saturday, February 20, 2010

### Frenemies and Functiononmeters - Countering Terrorism

According to Dr. Gordon Woo, a catastrophe risk consultant who has also studied natural disasters, "It is the social networks between terrorists which ultimately are their undoing." Approximately 1 out of every 20 of a terrorists friends is either someone being watched by a security agency or an informant. He concludes that terrorist cells with six or more members have about an 80% chance of being caught. So one method of decreasing terrorist activities may be to model their extended social networks and the internal mechanisms of their cells. Colonel Steve Horton's research focuses on the question of whether you can use raw data to infer social structure. As a starting point he looks at the records over the last 30 years of bridge game scores to determine relationships between players.

On a different note, Dr. Paul Tannenbaum attempts to link the Research and Development world to the Battle Field by creating "functionometers" for the devices used by soldiers. His hope is that by partially ordering the various functions of a device by their importance to a given mission, he can create a tool which quickly diagnoses the situation for the user. In other words, the tool would be like a gas gauge of functionality ranging from "There's no way you can complete this mission with this device" to "Go for it!".

Considering that several of the speakers for this Symposia were sick, a lot of information was presented. I would loved to have heard more about how mathematics, as one speaker put it, "helps win over the hearts and minds" of insurgents' communities. There are also ways to think of the mental attitude that condones terrorism as an "infection" that can be modeled in the same ways as disease. For information on this and other research done in this area, check out Consortium for Mathematical Methods in Counterterrorism which was founded by Professor Jonathan Farley, the organizer of the symposium.

On a different note, Dr. Paul Tannenbaum attempts to link the Research and Development world to the Battle Field by creating "functionometers" for the devices used by soldiers. His hope is that by partially ordering the various functions of a device by their importance to a given mission, he can create a tool which quickly diagnoses the situation for the user. In other words, the tool would be like a gas gauge of functionality ranging from "There's no way you can complete this mission with this device" to "Go for it!".

Considering that several of the speakers for this Symposia were sick, a lot of information was presented. I would loved to have heard more about how mathematics, as one speaker put it, "helps win over the hearts and minds" of insurgents' communities. There are also ways to think of the mental attitude that condones terrorism as an "infection" that can be modeled in the same ways as disease. For information on this and other research done in this area, check out Consortium for Mathematical Methods in Counterterrorism which was founded by Professor Jonathan Farley, the organizer of the symposium.

### Higher School Mathematics

So, there's the high school mathematics we all know and then there's the mathematics that the students pictured here are doing -- let's call it higher school mathematics! These students were participating in the AAAS high school poster session, and had the opportunity to attend a conference right along side experts in many areas of science.

Justin Lozano focused on solving the rubik's cube and variations using a computer programming approach. Yesterday afternoon, he was among several students whose posters were on display in the exhibit hall. When we talked about how he might use group theory to think about the rubik's cube, he commented "It's interesting that you think of the problem from a different point of view."

Aishwarya Vardhana's poster features her work using linear programming methods to create a program that would show a company how to optimize their use of green energies such as wind and solar energy. And, last but not least...

Justin Lozano focused on solving the rubik's cube and variations using a computer programming approach. Yesterday afternoon, he was among several students whose posters were on display in the exhibit hall. When we talked about how he might use group theory to think about the rubik's cube, he commented "It's interesting that you think of the problem from a different point of view."

Aishwarya Vardhana's poster features her work using linear programming methods to create a program that would show a company how to optimize their use of green energies such as wind and solar energy. And, last but not least...

Varuna Rao worked on facial recognition. She created a database with photographs for reference, and then wrote a computer program that assigns a number to a photo based on certain measurements obtained from the photo and compares different photos by comparing their numbers. She says that now that she's learned about mathlab, she could see redoing her project using that tool, and that in the future, she would like to use more than one number to compare photos to improve her current recognition rate of 45%.

Good luck to all of these students!

### Gangs and Statistical Mechanics?

The Los Angeles Police Department may have a new ally who, while not as all-knowing as Charlie Epps from Numb3rs, will help reduce crime by predicting where and when it might occur. This morning, Professor Andrea Bertozzi spoke about models that she and her team of post-docs at UCLA are developing to model gang violence. Using statistical mechanics, bifurcation theory, and partial differential equations, she aims to predict where and when hot-spots of gang-related activity will emerge. These tools have a long history in the physical and biological sciences, and are similar to those tools used to study the behavior of swarms of insects, which is the subject of some of her past research.

Dr. Bertozzi's newest paper on modeling gang activity will soon be published in the Proceedings of National Academy of Sciences.

In order to model crime occurrence, Dr. Bertozzi consults the LAPD as well as Anthropologist Jeff Brantingham , whose research shows that criminals tend to commit their crimes near their own homes in areas with which they are familiar. The model is designed with this in mind, and consists of a grid with a "house" situated at each vertex, freely moving "burglars", and an "attractiveness" function that depends on both space and time. Different factors determine the attractiveness of a house to a burglar -- these include how close the house is to the burglar's home, whether the house was recently burgled, whether any of its neighbors have been victimized recently, and constants like the presence of graffiti or the type of housing prevalent in the area. Two behaviors emerge from the simulations: one in which a police presence would simply displace the criminal activity and one in which a police presence would actually eliminate the problem. The model compares favorably to data collected over the period of a year in a particular LA neighborhood, and Dr. Bertozzi sees this as a first step in applying mathematical modeling to other social science issues.

Where are the gangs? Gang-related violence modeling is done by post-doc Alethea Barbaro , who studies gang networks, patterns in tagging, and how rivalries arise and dissipate. In response to a question concerning how this work might inform decisions concerning the balance between hiring more policemen and "cleaning up the streets" to reduce the "attractiveness", Dr. Bertozzi responded "Sounds like a good research proposal! These questions are excellent and hopefully will employ people like us for years to come."

## Friday, February 19, 2010

### World of Mathcraft?!

Imagine your avatar immersed in a complex world in which mathematics is the greatest weapon, in which you can "turn the world off", sit down to build a new virtual tool with other players, and pick up again when you are ready to test the workability of your new tool. Mathematician Keith Devlin thinks that such a game is entirely feasible, and could be a new way to attract students to mathematics. Unfortunately, he also thinks that to develop such a game might be an expensive undertaking -- on the order of $100 million. "But if we think of this as a national initiative then compared to Apollo it's not so expensive."

Why should this be a national initiative? The slide above was an illustration that 98% of students' responses to mathematical questions are correct when the questions are posed in a context relevant to the students' everyday lives while the students correctly answered only 37% of the SAME questions in a paper and pencil exam. So one argument for creating math-based games for learning is that they have the potential to replicate the physical experience of using mathematics in everyday life much more effectively than typical textbook problems. Linguist James Paul Gee looks at textbooks as analogous to the dry manuals that accompany games, pointing out that "If you play the game you cannot fail to understand the manual." Furthermore, he distinguishes between quality games and "skill and drill", saying "If we keep doing skill and drill, the only class your kids will care about is Mandarin." However, he acknowledges that many of the people playing technical games are upper class, and that for a game to be successful as an educational tool, there must be an accompanying social network to which players can rely for mentorship and camaraderie. Some of the games mentioned that you can learn about and try on-line were:

Why should this be a national initiative? The slide above was an illustration that 98% of students' responses to mathematical questions are correct when the questions are posed in a context relevant to the students' everyday lives while the students correctly answered only 37% of the SAME questions in a paper and pencil exam. So one argument for creating math-based games for learning is that they have the potential to replicate the physical experience of using mathematics in everyday life much more effectively than typical textbook problems. Linguist James Paul Gee looks at textbooks as analogous to the dry manuals that accompany games, pointing out that "If you play the game you cannot fail to understand the manual." Furthermore, he distinguishes between quality games and "skill and drill", saying "If we keep doing skill and drill, the only class your kids will care about is Mandarin." However, he acknowledges that many of the people playing technical games are upper class, and that for a game to be successful as an educational tool, there must be an accompanying social network to which players can rely for mentorship and camaraderie. Some of the games mentioned that you can learn about and try on-line were:

- Portal -- a game that builds ones physical intuition
- Fold-it (Zoran Popovic )-- a game that helps researchers better understand protein folding
- The products of Dream Box , a company whose CEO, Lou Gray, spoke in the session and whose products have been influenced by the research of math educators like Cathy Fosnot

But how can students really appreciate the mathematics behind the game itself? Professor Frank Wattenberg has his students build simple games or models themselves in which they can see the relevance of exponential decay and differential equations up close and personal. Similarily, Professor Brianno Coller teaches students the basics of control theory by having them learn to "steer" a virtual car -- you can see the simulations he uses on his website.

Commenting on the importance of understanding the nuts and bolts of mathematical models (including their limitations), Dr. Wattenberg commented that to update the old saying "There are three kinds of lies: lies, damn Lies, and statistics", many people would replace the word statistics with "modeling". Perhaps when viewing games as a component of education, it is key to recognize that games themselves are models-- useful models that can enhance our understanding of reality.

### Sea Ice, No See Ice

We're on thin ice around the arctic, and the most well-respected mathematical models have underestimated the loss of sea ice shown by current measurements. In particular, the photo above shows the loss of "multi-year" ice from March 2004 to March 2008. Many people may wonder about whether we have reached a "tipping point" or point at which the loss in sea ice has passed the point of no return. As Donald Perovich, a researcher with a US Army Laboratory, said during his presentation: "It's really a question of whether we will fall off the edge of the stage or fall down the stairs, bumping along the way"

What's the difference between sea ice and the ice from your fridge? The tiny channels of brine which carry algae and make modeling sea ice considerably different from modeling a liquid. In addition to being different on the microscopic scale, sea ice covers vast expanses of water and melts because of effects from underneath (the ocean currents), above (the sun, snow, and atmosphere), and within (topography, permeability). The "albedo" that I talked about in the last post is a ratio of reflected to incident sunlight, and the average albedo of the sea ice changes as the mosaic of ponds and ice evolves through the seasons. First-year ice has a lower albedo and therefore absorbs more heat and melts quite differently from multi-year ice. This creates a feedback loop that causes more ice to melt and lowers the albedo more.... Many of the presentations focused on finding better ways to model the albedo by better understanding pond-formation.

But the view from the picture above is only one slice of the story. I'll say more about ice volume and flesh out more of the picture about Sea Ice later tonight!

What's the difference between sea ice and the ice from your fridge? The tiny channels of brine which carry algae and make modeling sea ice considerably different from modeling a liquid. In addition to being different on the microscopic scale, sea ice covers vast expanses of water and melts because of effects from underneath (the ocean currents), above (the sun, snow, and atmosphere), and within (topography, permeability). The "albedo" that I talked about in the last post is a ratio of reflected to incident sunlight, and the average albedo of the sea ice changes as the mosaic of ponds and ice evolves through the seasons. First-year ice has a lower albedo and therefore absorbs more heat and melts quite differently from multi-year ice. This creates a feedback loop that causes more ice to melt and lowers the albedo more.... Many of the presentations focused on finding better ways to model the albedo by better understanding pond-formation.

But the view from the picture above is only one slice of the story. I'll say more about ice volume and flesh out more of the picture about Sea Ice later tonight!

## Thursday, February 18, 2010

### In Search of Mathematics at the AAAS Annual Meeting: A PREVIEW

Watching the ocean views, graffiti, and tract housing of So Cal pass by my window, I am headed to The American Association for the Advancement of Science Annual Meeting in San Diego. There I will join over 10,000 scientists, journalists, and members of the public as we attend symposia ranging in topic from Astrobiology to Zoology. My mission is to attend as many mathematical Symposia as possible at this years meeting, whose theme is "Bridging Science and Society". Here is a list of the symposia I plan on attending. Each is about three hours long with several speakers from all over the United States and beyond.

- Sea Ice in the Changing Climate: Modeling a Multiscale Nonlinear System

- First-person Solvers? Learning Mathematics in a Video Game
- Traffic, Crowds, and Society

- Real Numbers: Mathematical Technologies for Counterterrorism and Border Security

- TIMSS 2007: Exploring the Dramatic Improvements in Performance in Two States

- Moving Across Scales: Mathematics for Investigating Biological Hierarchies
- Mathematics and the Analysis of Fairness in Political Processes
- Can Singapore Mathematics Enhance Student Learning in the United States?

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