Category Archives: mathematics

Computer Science & History


Artificial Intelligence (AI) isn't a new phenomenon. For that matter much of what we value in the way of formalism in Computer Science, isn't new either since computers were analog (and human) before they were digital. Abstract concepts such as memory, state, event, iteration, and branching are ubiquitous in the real world. One exploring these concepts should not have to stare at a computer screen to learn them.  The concepts are larger in scope than found in digital technologies. Jessica Riskin wrote a nice historical piece entitled Frolicsome Engines on the history of AI through mechanical automata, . In Computer Science (CS) we tend to be historically, if not culturally, illiterate. There are many issues at play here, with the main issue being that within Engineering, there are few electives since the goal is to educate students for specific skill sets. Maybe topics such as philosophy and history are tangential to CS? The core skill sets, theoretical or practical, stem from early mathematical research in the 1930s. Before the 1930s, I suppose we tend to think of the history of computing as non-existent. Do other areas in science or the liberal arts such as mathematics, physics, and chemistry suffer the same fate of removing history from their curricula? Do math teachers not talk of history when covering geometry, algebra, and calculus? I don't have a good answer to that, but I do need to start digging for answers.

You Don't Know Jack

Love Jack? Turns out to be an icon at the university where I work: University of Texas at Dallas. To be perfectly honest, none of us really knew Jack before the start of the Spring 2016 Creative Automata class, however, because of my students' admirable diversity, we can really know more about Jack. This is the biggest project to date, and the Jack adventure began with a challenge to the students to explore the sculpture (which is located in the courtyard of the ATEC building) from different perspectives. What perspectives could be better than those that are natural to the students' interests and backgrounds?  The class contains computer scientists, artists, and designers--often with students crossing over among areas and interests. A smartphone app accompanies the main Jack web page, so that when one is near the Jack, the perspectives can be browsed. Interested in the artist's history, how Jack relates to computer science and mathematics, modeling & simulation,  graphic design, digital fabrication, the connection of art to science? It's all there. A beacon is next to the sculpture to facilitate object-based learning discovery across STEAM (Science, Technology, Engineering, Art, and Mathematics). You can also start with STEAM and browse based on interest.

Why the STEAM Argument is One-Sided


Full steam ahead. Or should I say STEAM ahead? STEM stands for Science, Technology, Engineering, and Mathematics and has been a driving force initiated by the National Science Foundation to focus education policy within technical areas and their associated disciplines. More recently, the letter "A" has been added to create a new movement called STEAM. The "A" stands for the arts, and according to a leading site devoted to STEAM, STEM + Art = STEAM. Since I spend much of my time thinking about the interconnections between STEM and the Arts, I welcome the STEAM movement. And yet, I have deep concerns about the movement's three published policy goals stated on the STEAM site:  (1) transform research policy to place Art + Design at the center of STEM; (2)  encourage integration of Art + Design in K–20 education; and (3) influence employers to hire artists and designers to drive innovation.  These are worthwhile goals, but notice how all three goals seem to be about getting STEM-oriented folks to hire artists and designers, and placing art & design at the middle of STEM? Let's flip this. What about having STEM at the center of Art and Design? I am not suggesting doing away with the three STEAM goals, but I am recommending some sort of balance by extending or broadening these goals; the current ones are lopsided. I strongly advocate new ways of starting with design and the arts, and then surfacing STEM concepts from within art and design. For the STEM subset of computing, this advocacy resulted in the aesthetic computing movement. Recently, this approach has taken root in learning systems thinking in the art museum.  I am not the first to suggest this if we consider the larger literature base of  blending STEM with the Arts. Take Martin Kemp's book The Science of Art where he explores mathematics and optics via art. Also, the MIT Press Leonardo journals edited by Roger Malina has extensive historical coverage of intersections of STEM and the arts.  Leonardo was founded in 1968, and so its publications contain a treasure trove of knowledge, suggesting new ways to get to the heart of STEAM.  To advocates of STEAM, my suggestion is to rethink of STEAM as two-way traffic: two steam locomotives, two tracks, perhaps with some switches here and there.

Computing in the Wild


What is computing? What is computer science? These questions would seem to have easy answers, but the field of computer science is still in its infancy compared with fields such as physics, and the mothership--mathematics. The term "computer science," somewhat unfortunately, seems inextricably linked to a family of artificial devices we call computers. But can you think of any other major discipline with this characteristic? We do not refer to astronomy as telescope science, chemistry as mass-spectrometry science, or mathematics as compass-and-rule science. In mathematics, for instance, educators will observe mathematics at play in nature. In the above image, the mathematical symmetry of the pagoda and the geometric branching structure of trees and bushes are all too evident. And yet, in computer science, we seem fixated on the box. However, computing, with its focus on information, has potentially a much larger role to play in our world. Recently, we created another video that dives into computing to illustrate three major paradigms, ways of seeing information management and flow outside of the box. None of this is to downplay the relevance of post 1940s growth in what we know as computer science today. Computers assist us with our daily chores, our workplace tasks, and our entertainment options. But if computer science is to approach the ubiquity of mathematics in our world, we must venture beyond "code" and back to the idea that computing can be just as much about describing what we see, and how we see it--in the wild through an information lens.

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.


Naked Rabbits


This is a circuit created by a Creative Automata Lab research assistant David Vega. The circuit is a physical incarnation of the Fibonacci difference equation f(m) = f(m-1) + f(m-2), where "m" equals the current month in decimal. We begin the Fibonacci sequence by iteratively solving, beginning with f(0)=f(1)=1. These values jump start the difference equation: f(2) = f(1) + f(0), f(3) = f(2) + f(1), and so forth. The sequence ends up as 1,1,2,3,5,8,13,21,34 until we decide to stop. These numbers are termed Fibonacci numbers. There are all kinds of interesting real-world patterns related to these numbers, including the spiral pattern found within a nautilus shell. This equation represents an idealized model of rabbit population growth. The equation was re-represented as a visual Max/MSP patch, and then translated into an equivalent electronic circuit using Teensy 3.1 microcontroller boards. The boards, populating the breadboard above, are connected using serial communications, and there is "software clock" that regulates the data flow. In Max/MSP this clock is programmed as a [metro] (short for metronome) object. This circuit will be transformed yet again into a tangible artwork where the Teensy boards are housed in 3d printed rabbit objects. I'll post another entry when we get to that stage. You've probably heard of "embedded systems," so this is a case where the embedding is meant to draw in the participant in a way not really possible with the textual difference equation.

Sensing Simulation Models


When I teach modeling and simulation, I tend to focus mostly on the structure of models. I start with a thorough discussion of time and systems concepts, and then move on to cover different sorts of dynamic models in both discrete and continuous space. In the past, I had relied on using examples purely from the real world in emphasizing the importance of modeling. For example, all fast food restaurants, manufacturing lines, and theme parks have one thing in common: queuing networks. A queuing network is a dynamic model abstraction of what happens in these things: objects (often people) wait in line, get served, and move on.  In teaching queuing, and other, models, I am trying something new this Fall. I am starting with human-interaction and media being the means by which to get students interested in modeling. For example, the single server queue (SSQ) shown above has an operation that can be both seen and heard. This one is programmed in Max/Msp (which is a visual language with strong roots in music, imagery, and video). The SSQ is experienced, by tying events to an audio synthesizer. Everything is in software. An SSQ becomes an audiovisual instrument.


Bipolar Thinking


Bipolar thinking could mean many things, but I refer to it as thinking with two poles, connecting art and science. let's call the poles the north and south poles since the earth can be used as a metaphor. At the north pole, we put down a flag labeled "mental concept." The art of abstraction, as with mathematical thinking, is to dwell near the north pole. At the north pole, representations involving the senses do not exist. One must walk in the direction of the south pole, which means in any direction, for more sensory experience. The term "abstract" is used in art as well, however, art relates to the senses and for pure abstraction found in mathematics, there is only thought. At the south pole, we have pure experience. Let me give an example from mathematics: the circle. We learn in mathematics that the circle is a concept, an idea and that anything you hear, touch, or see is not a circle-- it is a representation of the circle concept. This means that things drawn on paper, spoken, or writing the word "circle" are not circles. Where do you position yourself on the earth: do you inhabit the poles, or are you somewhere near the equator? Maybe you live in Iceland or Borneo? My suggestion is that we should be constantly walking between two poles without being overly attracted to either one. Every time I see an object that reminds me of a circle, I celebrate the uniqueness of that object, taking time to experience it. But then, I am drawn to the wonderful reduction, abstraction, and concept of circle--all of the experienced objects are identical near the north pole. This bipolar thinking is common at the lab because we are creating representations of math and computing concepts. Thankfully, we do not actually have to pack our snowshoes.

Maker Day


It all began on a day when I was visiting a friend of my fathers. I was fairly young and found a book on his shelf when I noticed the above diagram embedded somewhere in the book: a lituus. A what? It was something wonderful looking, and I had to know how it was made. You can make them by hand using plotting, but when I was first introduced to computing (the old card punch days), my first programs were graphical. I wrote something that read an equation (any equation), and plotted it out in ASCII characters. OK, so it wasn't very elegant looking but I had no direct access to a line plotter. The thing that fascinated me was the making. I could make a machine that did something. There was something intensely liberating about that realization. Today, the President announced Maker Day which will be tomorrow, June 18th. The first Maker Faire will be held then to coincide. It is becoming easier to make anything you want from cardboard or wood to 3D printed plastic. And, yes, you can make a lituus. Out of chocolate? Why not.