Category Archives: dynamics

Personalized Model Learning

Property release:3 Model release:Q,E,J

 

Much of what we do in the Creative Automata (CA) Lab is oriented around multiple representations of a single abstract mathematical concept--such as integration in calculus or sorting in computer science. How can we personalize approaches for learning something like integration? Is it possible to leverage our multiple cultures to engage and motivate the learner? The lab just submitted our video entry to the National Academy of Engineering (NAE) Grand Challenges for Engineering Video Contest called E4U2. Sharon Hewitt from the CA Lab designed and produced this video. The video segments include representations of a virtual analog computer based on the sand-like flow in PowderToy, as well as several personalized models of the Lotka Volterra model. Instead of  making models for other people, consider that you can learn about modeling by making these wonders for yourself. In this arts-based approach, you will also interest other people in modeling.

 

Personalized Simulation Modeling

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Artists created the first virtual realities -- sometimes in the forms of cave drawings, paintings, and friezes.  The above photograph is a woman who is experiencing the virtual experience of stereo viewing of a remote object or scene with a stereoscope. As modeling and simulation researchers, we should think of new ways to represent models of observed phenomena. Do you use equations, statistical plots, or diagrams with pointy arrows and boxes? With the rapid expansion of the web, we are reaching a state where multiple representations for any abstract concept are at our fingertips. Seeing one abstract concept 300 different ways. This is especially important for those outside of engineering. Modeling and simulation, as a discipline, is becoming so widespread that we need to bring the academic knowledge of our area into the hands of everyone. We are not going to reach the masses with limited human experiences for modeling. That means diversity in model representation. Want to model something but not in Simul8 or Arena, but instead in Minecraft? Go for it. For the professional engineer, Minecraft is the wrong choice. But for teaching the student who grows up in these new powerful multi-player virtual worlds, why not use environments that attract them rather than conforming to a perceived set of standards employed mainly by a limited set of professionals. Strap on your Victorian-era stereoscope and come with me on a different sort of simulation modeling adventure.

 

It's About Time

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A long time ago, I told a friend that I was starting to move more deeply into the field of modeling and simulation. The friend said to me "It's about time." How true. For no particular reason other than it being January 1st, I thought it appropriate to celebrate the 555 timer integrated circuit (IC), which was designed in 1971 by Hans Camenzind. This is one heavily-used IC, and it can be purchased well under one US dollar depending on the source. The above picture is called a block diagram -- which is a high level design description of how the IC functions. If you looked inside, you'd find mostly transistors with resistors and a couple of diodes. Think of the 555 as something that can create a well-timed oscillating square wave, or just a "one shot" pulse of a given width. An egg timer, but more precise. Having just sung the praises of this IC, we also need to put this technology into context with regard to time management. The most accurate time is kept by atomic clocks, such as those employing cesium. In the semiconductor world, there is also a tug of war, sort of, between MEMS-based oscillators (oscillators built into the silicon) and quartz (which you may have seen on an Arduino or other similar micro controller). All of these technologies are "about time." With the Internet of Things (IoT), computers built around micro controller chips are getting much smaller, more powerful, and are cheaper (although not yet at the < $1 level). For example, you can make your own bare bones Arduino for about $4. You can program a 555's behavior in software rather than through voltage dividers and a capacitor. What will 2015 bring us? There is no time like the present.

Big Process

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Big Data: it is (still) all the rage. And rightfully so because we have access to more data than ever before. The "bigness" of data refers mainly to the sheer magnitude or volume of data available for our consumption. This volume has increased exponentially and shows no sign of abatement. But data indicates one side of the coin. Process is the flip side. Without process, the data repository is a large pile of undifferentiated pieces. Even a "data structure" is a process in disguise since the structure reflects a procedure that must read and write to this structure--thus creating it. This idea of process, in a miniature scale, can be seen in programming. Once upon a time, the program and the data occupied the same memory space, and to the unaided eye, the computation looked like a collection of hexadecimal bytes -- which ones were the data and which were the operations? Who knew? A careful deciphering and knowledge of the opcodes showed us the way. Today, the idea of "process" is essential if one has lots of data. How are the data sensed, processed, merged, diverted, massaged, and transformed? Like a petrochemical plant, the raw materials (e.g., data) are useless without a clearly engineered, and formally represented, process flow. Big data needs big process and big model.

Preserve the Model

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Van Gogh produced compelling artwork ahead of his time. This one is called "Wheat field with cypresses" from 1889. The original is in the National Gallery in London. How do we archive this kind of work? Clearly, digital scans of all varieties and wavelengths can be employed to record the static painting. But that is the final product. No art is static. It is all dynamic, time-based media, to use a phrase coined within media studies. The only reason why we think of Van Gogh's artistry as static is that there is no recorded process of how it was created over time. Contrast this situation against the products of modern cinema and video games.  These products are the result of complex models of geometry and dynamics. So, if you want to archive a video game, best to archive the process, the shape, and the behaviors. Preserve the simulation models rather than an end-product.  How something changes over time is precious and ultimately more valuable than what emerges from the end of a creative pipeline. Even with packages such as Photoshop or Gimp, there is a process that is stored as a dynamic stack of human interaction events. That is what we ought to be saving wherever possible. The focus on process, and on model, can also have an effect on how we think of art-not only from the perspective of archiving. Musicians and performers are used to modeling. Maybe, the rest of us should jump on board.

Design for a Model

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The above design is from William Lawson's "A New Orchard and Garden" which was published in 1618, and available from Project Gutenberg. Note the hexagonal tree configuration labeled B. Design is with us everywhere from Lawson's garden to the physical feel and visual layout of your phone. Design is also central to the task of modeling. I was recently reading Chris Conley's Leveraging Design's Core Competencies, and was struck by the importance of three concepts: #2: the ability to work at a level of abstraction appropriate to the situation at hand, #3: the ability to model and visualize solutions even with imperfect information, and #7: the ability to use form to embody ideas and to communicate their value. These concepts are central to modeling as employed within STEM (Science, Technology, Engineering, and Mathematics).  In Computer Science, we employ models for many tasks. These models are designs for artificial languages. Send this information through node X, and split the result across nodes Y and Z. Plant the apple tree at node A, which is fed from stream B.

Abstraction and Sushi

Abstraction is part of what makes us human. We are able to reason about things by forming abstractions. I enjoy eating sushi, but what is sushi except as a conceptual category of raw fish with rice?  I feel a need to understand sushi, the concept, by eating different kinds of sushi or by reading about sushi in an article, or by looking at many pictures. By doing so, my understanding of the sushi abstraction is made clearer. So, abstraction is not all in the mind; I need to physically experience many examples of sushi to strengthen the mental concept....the abstraction. We can approach abstraction in mathematics and computing in the same way. By seeing many examples of "plus", I come to understand what "plus" means. The above video was a short lecture I gave on the topic of abstraction to students and parents visiting the University of Texas at Dallas (UTD) during Engineering Week. If abstraction is made strong through experience, new possibilities emerge. A "plus" is made real around us, while also giving us increased understanding of this concept.

Engineering Week

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Our Creative Automata Lab had its open house during the Engineering Week celebrations on Saturday, February 22nd (yesterday between 10am and 2pm CST in Dallas). The turnout was phenomenal. I have to thank the organizers of the week-long event and to all of my students who created amazing demonstrations for everyone. What are the summary points? People like to touch things, play with them, and understand fairly complex mathematical and computing phenomena by experiencing them firsthand; hearing, seeing, and interacting. Writing on the whiteboard doesn't cut it any more. The two 3D printers (Maker Bots) in the lab were exciting for visitors not so much because 3d printing is a new phenomenon, but because these printers have visible moving parts. You can see what is happening because the printers  are designed to show their internal components, a bit like the Centre Georges Pompidou in Paris. We'll be sorting out lessons-learned from the event for some time to come. Next up will be blog posts on our exhibits and the video that was compiled based on student thoughts and the lab mission.

 

Steampunk Automata

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There is something interesting about the Steampunk movement. Steampunk takes inspiration from the past to reinvent the future. I am reminded of the fictional worlds created by H. G. Wells and Jules Verne. The above image is from Indulgy and is an example of Steampunk and fashion. There are subtle connections to 19th century engineering where scientists such as Maxwell and Kelvin did modeling of mathematics that was touchable, where cause and effect were clear and visible. We see the raw elements of computing (e.g., information flows) everywhere we look and yet it is with classic machines from the past that we find information-rich experiences as indicated in Organum Hydraulicum. Steampunk, and its inroads into theatre, fiction, and fashion may be partially a result of our deep human need to touch, see, and hear information. To model, Steampunk style.

 

The Sands of Calculus

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Physics sandbox programs such as PowderToy create an entertaining environment for playing with mechanics. Sometimes, the physics is a bit surreal, as with MineCraft, but that is fine as long as the rules are uniform, repeatable, and easy to understand. I worked on a design with Scott Easum here in our lab, and he produced a nice sand integrator inside of Powdertoy using a digital counter thats someone else had developed within the Powdertoy community. The learning theory is simple: if a student likes PowderToy, then deliver content such as calculus to that student through PowderToy. The goal of this machine is to measure the area of the circle. Note the digital counter with some very small multi-colored pixels beneath it. These pixels form a structure that represents a digital circuit required to make the counter work. The count begins once the sand starts pouring into the circle. The circle's area can then be measured mechanically using a feedback mechanism so that when the container is full, the overflow sand triggers the digital display to stop counting. The final count is read off to yield the area (an adjustment coefficient is required to obtain the area in common metric units). The operating principle is similar to the hourglass. Unlike the hourglass, though, we can quickly create any geometry we like in PowderToy and use our sand calculus machine to determine the area of an arbitrary shape.

Inter-Species Dynamics

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The Lotka-Volterra model representation challenge was discussed earlier as a goal for our lab in preparation for Engineering Week, culminating in a set of demonstrations to be given on February 22, 2014. The image shown is a partial screen shot of a simulation created by Karen Doore, a PhD student in Computer Science, also working in the Creative Automata Lab. The time-based dynamics of predator-prey are seen on the right hand side and may look familiar to most modelers of ecological systems where predators and prey interact, causing the population levels to oscillate. The diagram on the left differs from the representational norm--it is an interactive Javascript sketch of an analog water computer. The water computer stems from an underlying modeling language formalism called System Dynamics. Water levels depict the predator and prey populations rising and falling. Input and output valve settings are a function of population levels sensed with water floats. The equations are also represented in a way that the coefficients change inside the equation text, but not shown in this figure due to lack of space. Here are the implemented equations:

\frac{dP}{dt} = -Pm + bHP ; \frac{dH}{dt} = Hr - aHP

Castle Clock Teaching

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For my Fall 2013 simulation class, I decided to try something a bit different than the usual verbal onslaught of modeling methodology with mathematics and scattered applications. We used a type of learning that is most commonly known as object-based learning, and frequently practiced in museums such as the one in University College London (UCL). An object is chosen as the focal point of collaborative discovery. So, we chose al Jazari's 13th century water clock which goes by "Castle Clock" because of its original physical location. Al Jazari was one of history's great masters of mechanical invention. The clock is an astronomical computer, like all time pieces. This turned out to be a fun and useful learning experiment but it had its challenges as well. The issue is that the academy (which is to say most places of formal learning) is splintered into multiple disciplines. So, while the students in the class had a roller coaster ride through history, culture, systems dynamics, computer science, physics, language, and mathematics, this approach runs counter to how we normally teach students, and how students and faculty get credit for their work. My gut feeling is that as the academy evolves, this mode of learning will become more common and the credit and disciplinary issues will evolve with it. At UTD, we are making inroads here and things look quite positive.