Knowing oneself is a good starting point. But what does it mean, after all? Is it possible to know yourself at all, particularly with all the tools we are presented with or forced to acquire throughout our lives? Tools, after all, are all limited in nature, presented to you by others, such as language skills, thought processes, and cognitive abilities. Then, do you think you can know yourself, let alone develop your own philosophy of life? With all these difficulties, you set out on one of two differing paths, either one where you become a thinker yourself and be a lighthouse yourself, or another, where you just drift around another lighthouse. Anything beyond could be darkness. The difference between these two seems to lie in asking, seeking, and questioning; that is, in having an inquisitive mind versus embracing, accepting, and believing – in other words, having a submissive mind. It becomes more like choosing a blue pill versus a red one, as is depicted in a recent film, which is a rather successful strategy for guiding the submissive in searching for meaning.

With all these thoughts, let me begin to talk about my journey of seeking the meaning of life – well, in particular my life. With all the boundaries and veils around me set by education and indoctrination, I set sail into different waters, far away. I enjoyed being myself as a subject rather than an object. I freed myself of some knowledge without any facts and was bound by other knowledge. This painstaking unweaving and weaving of myself led me to being who I am now, with numerous toolsets of scientific facts and knowledge, of faith and truths, with numerous veils, some old and some new. And I am somewhat content with what I have now, albeit at times I fear missing the whole point that is the meaning of life. Then, I revert to my comfort zone and feel safer for the moment.

Again, with all the new adventures and relearning of myself, I find myself mostly looking for contentment with life – both my life and others. Contentment, superficially a head-to-toe feeling, gives me a sense of safety and the courage to seek more facts and knowledge in science and faith. Confusion, on the other hand, is my fear. The difference is like having 20/20 vision versus having serious cataracts. In my journey, the beam of a lighthouse illuminated me and made me feel that I have 20/20 vision, by which I can potentially see and get to know everything and be contented with everything, most importantly with myself. But was this just due to this lighthouse or had I developed the tools to be my own lighthouse? With the comfort of not having to probe this question, I preferred to drift near this lighthouse all the time.

Reaching a comfort zone around this luminous lighthouse, and in my contentment, I stalled in searching myself for a while. Each and every time I attempted to sail a little further, I quit, fearful that I could go no further. I then realized that there were many more artifacts around this lighthouse that could help me develop my own tools for my journey. They were quite marvelous and beautiful artifacts. They were also quite handy, as if they were made for my use. I tremendously enjoyed collecting these objects, and sort of built my own little ship under a little projector. And, as if there must always be a catch, some of these artifacts were reflective in nature, and when I looked at them, I saw my own dark side. This soured my enjoyment for seeking and collecting ornaments. As if this was not enough of a sore point in my journey, I got to see others’ dark sides as well, which caused me even further pain. A dualism of saying and doing in many led me to become more cautious, as I tried to shed light into my dark sides. After all, terrible things could happen in the dark. As I enjoyed the moments under the lighthouse, despite the possibility of darkness, I learned that there were also other artifacts that could help me with my dark side and my dealing with others’ darkness. Through formulating and solving these problems, I was delighted to find that these artifacts were even more beautiful than when I thought when I saw them for the first time. Along with these ornaments, I also got to meet some great adventurers just like me, with the same hopes and problems and also with helping hands. I became even more content with what I had at the time.

As time passed, I encountered another obstacle in my journey; I lost my passion for the search. I felt too overwhelmed with the almost constant dualism of saying and doing and tended to lose my patience with the darkness in others and partly in myself. This was too much to take. Was there another artifact around to help me through this obstacle? In search of this “yet to be found” artifact, I again partly got into the process of unweaving and weaving myself. While moving through this stage, I got to see that finding more and more objects could cause someone to become quite pretentious and full of false hope. This newly found “fact” saddened me quite deeply.

Not to be trapped in these obstacles, I needed to put more effort into finding more around me to help me proceed. But it was not easier. On the contrary, it was a lot more difficult. This led me to another “fact”: whatever I was searching for could be only found by someone who persists. I got to see that knowing and doing are quite different, just as saying and doing are different from each other. Nevertheless, I grew more curious about what might come, let it be other precise substances or quasi-unyielding obstacles. Maybe this seek, jump, and find makes the trip joyful and worthwhile.

Where am I right now? With more artifacts and greater contentment with what I have and who I am, I am now more eager to set sail further under the luminous light of this breathtaking lighthouse, full of passion and joy, seeking to see what is to come. Have I developed any sense of knowledge or belief, or a motto for my life? Well, I am at a point right now where I know by heart that there are beautiful objects and ornaments and flowers in the Garden of Eden. They are only visible in the light, and I am much contented that I found a beautiful lighthouse that continuously sheds light on the Garden. I am undecided yet whether I can sail further or stay around in my current contentment.

When I look back, I see that throughout my joyful journey, I tried to keep an inquisitive mind and learn about my dark side while discovering that there are more things waiting to be found and healed. I also learned that being pretentious and contentious is a big obstacle to gaining consciousness in finding the good in life. I also got to see that while seeking, finding, being helped and helping others – sailing, in other words – the whole journey is full of action and reading. Reading myself, others, and all these artifacts, reading the beautiful writing on this beautiful lighthouse was what I was doing all along. This reading and doing made the journey of life actually very rewarding in itself. I now treasure the artifact I get to develop throughout my journey – sometimes alone, but mostly under the light of the lighthouse I came across. I have a strong knowledge of and belief in this artifact. It gives me passion and conscience throughout my journey of life, through which I sometimes walk alone, but mostly with others. It sheds light when I see darkness in myself and in others. It helps me find more precious artifacts and develop even more of them along the way. It helps me find joy even among obstacles. It gives me passion and hope for getting ready to sail away into unseen waters that will take me among the endless artifacts under the light without any darkness. Then, I will say I am more than content and thankful for this great fulfilling journey.

Educators who see the beauty at the center of mathematics and can make their students see it that way, are more likely to be able to get their students’ attention and teach them more effectively. Also, as well as facilitating the study of sophisticated mathematics, this puts mathematics in its proper place so as better to understand the value of what it has to say to human beings. To see the beauty and the pleasure in mathematics can change the negative attitudes of some students and help educators in teaching mathematics.

Often it seems that we pursue mathematics education from either a structural or an applications point of view. From a structural point of view, we insist on building up all of the tools one may need in a sequential, logical order, because an educator will need the students to know all of the smaller pieces before they can build any of the larger ideas. An analogy for this would be if we forced somebody to study all of the nails, screws, bolts, and tools to build a house before we let them even see the plans for the house. This is one of the main reasons that most people who study mathematics in their school years think that it is a pointless exercise in playing with formulas and has no significance in real life. For these people, mathematics might be helpful only in keeping track of their checkbooks after graduation. Some students think that they can calculate whatever they need using computers, but sometimes this is not very effective because students may not understand the logic behind the problems and the results do not mean anything to them or they are unable to detect errors.

The applications point of view leads to making up “word problems” that appear to be about the real world, but everyone knows that they are highly artificial. It also leads to focusing at higher levels on only the applications. Hence, for instance, in calculus we spend a lot of time plodding through various physical applications, without letting students see the bigger picture. Or we spend time in liberal arts mathematics talking about things such as modeling and linear programming, which yield great applications, but are generally tedious and do not give most students much appreciation for mathematics. If we see the beauty at the center of mathematics, as well as introducing ideas that may have application or may build some tools, we can bring students to have a much bigger picture of mathematics at a much earlier stage in their mathematical development.

Educators can include some fun topics in courses that they teach. For instance, they can encourage students to discover the amazing number patterns in nature, such as the Fibonacci sequence in pine cone spirals, pineapples, and cauliflowers, in which the number of pieces increases in the following manner: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 … (add the last two numbers to get the next). Another example is the “golden ratio.” In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is a mathematical constant, approximately equal to 1.6180339887 and recent research shows that people think that the shapes and figures in this ratio are more interesting and aesthetically pleasing to the human eye.

Sometimes, even a small algebra trick can miraculously bring students to love mathematics and be more focused, and then more interested in the deeper aspects later on. Take a look at this symmetry:

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321.

Here are a few more examples showing the beauty of mathematics visually with numbers:

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 +10 = 1111111111

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 = 888888

987654 x 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 x 9 + 0 = 888888888.

Students’ minds can be broadened by seeing the surprising differences that arise when we move to non-Euclidean geometry. Fractal shape examples in nature, such as snow crystals, and things like the Mandelbrot set, which is a set of points in the complex plane the boundary of which forms a fractal, can be introduced with a background and give rise to amazingly beautiful images and ideas. Even such deep and thought-provoking ideas as these can be understood by students when they have curiosity, creativity, and an open mind.

All these examples and others like them can inspire people to see the beauty of mathematics and give them a better understanding and a sense of the expanse of mathematics. With a little more discovery of and exposure to the more beautiful aspects of mathematics, students are much less likely to feel any hatred for mathematics and may develop a much greater appreciation for the creation of the universe.

Ali Kemal Unver is a postdoctoral scholar at the University of California, Los Angeles.

Note

* The golden ratio can be derived by the quadratic formula, by starting with the first number as 1, then solving for the 2nd number x, where the ratio [x+1]/x = x/1 or (multiplying by x) yields: x+1 = x2, or a quadratic equation: x2-x-1=0. Then, by the quadratic formula, for positive x = [-b + sqrt(b2-4ac)]/2a with a=1, b=-1, c=-1, the solution for x is: [-(-1) + sqrt([-1]2 -4*1*-1)]/2*1 or [1 + sqrt(5) ]/2. See the second reference for details.

References

1. http://users.forthnet.gr/ath/kimon/
2. Green, Thomas M. “The Pentagram and the Golden Ratio.” http://www.contracosta.cc.ca.us/math/pentagrm.htm.

I would like to focus briefly on the twentieth century in terms of technological innovations and their impact on the human soul. The Industrial Revolution radically changed our traditional lifestyle. Modern technology engendered many improvements in such areas as production and transportation. These changes were reflected in the literature and art of the period as well.

Views of Technology

In 1909, for instance, the Italian writer Marinetti published The Manifesto of Futurism, a great example of how intellectuals were affected by technology. He states that the world’s magnificence has been enriched by this new beauty, the beauty of speed: We stand on the last promontory of the centuries! Why should we look back? What we want is to break down the mysterious doors of the impossible. Time and space died yesterday. We already live in the absolute, because we have created eternal, omnipresent speed. We will destroy the museums, libraries, academies of every kind, will fight moralism, feminism, every opportunistic or utilitarian cowardice.(1)

This approach is very understandable, because its adherents assumed that modern technology would provide opportunities they had never experienced. The prospects of technology amazed them. But looking back, we see that technology shaped a new type of people who are dependent on machines. Producing tools and making money became cornerstones of modern life. These views threaten cultural values and traditional relationships among people who feel alone in these technologically separated environments. We ask: How much do machines dominate humanity, and why do people feel so deeply abandoned?

We can look at two perspectives from that period. The first is technology as a magical and wonderful creation, promoted by Marinetti and other futurists. The other is characterized by people like Charlie Chaplain who, in one of his movies, shows a worker who screws bolts every day as eventually starting to see everything as a bolt. This is the worst effect of twentieth-century technology: People have begun to feel like machines or parts of machines.

Do people need and deserve more than this? Of course, they do.

The latest version of modern technology is cyberspace, a place where people can find all sorts of information. Locating information and sharing experiences is easier than ever before. The Internet, for example, has become the information superhighway on which people can find almost everything. The Internet and other technological tools have helped create the expression being digital, which refers to people who use a lot of technology. Is this the illusion of technological globalization(2) or electronic democracy will be the end of participatory democracy?(3) Even though this digital medium provides a new source of information, we have not figured out how best to use it or what information to trust on it.

Issues

At this point, we must learn how to use modern technology and regulate information, because we cannot ignore them. These scientific and technological advances will play important roles in future developments. Science and technology in and of themselves are not the problem, nor have they ever been. The real problem is that science and technology are developed, deployed, and controlled by the predatory system of pancapitalism. The mainstream development of knowledge and technology is guided by increased efficiency in militarized production of violence and/or by potential corporate profits in civilian markets.(4)

There is another significant point here: Modern technology has been trying to create a cyberbody. In the future, scientists will be able to produce digital flesh to enhance our abilities. So here is the problem we have to solve: People who have these enhancements installed may begin to wonder if they are humans or robots. We already have seen that people can adjust their bodies in many ways: laser surgery to correct their vision, or synthetic material to replace their teeth.

Cyberfeminism focusing on women’s role in cyberculture is another interesting example of changing the human body. This already has caused some problems. The challenge here is rather how to combine the recognition of postmodern embodiment with resistance to relativism and a free fall into cynicism.(5)

Technology has limited privacy. When we are born, we get a birth certificate that quickly goes online. Educational files, social security files, insurance files, criminal files, consumption files, and so on are all in cyberspace. The Internet has become an on-line marketplace and is continuing to grow.

On the other hand, even though we are so connected, our social relationships with others have fallen apart. Every relationship between teachers and students, buyers and sellers, parents and children, for example, will be changed radically in the next few decades.

The most important question is how can we find a good balance that gives happiness and hope for both our bodies and our souls? We are not just bodies that need to eat, sleep, and rest, among other things; our souls must be nourished. In this technological age, this has led to a conflict”the crisis of modernity”between religious and metaphysical ideas. Nietzsche said that God was dead. Of course he was wrong, because he, like other philosophers, could not have realized that spiritual needs would become so important in modern times.

Today, we still are seeking for something to feed modern society’s spiritual hunger. We will have to find or build a way of thinking that will include metaphysical ideas, scientific innovations, and religious thought. After that, we will be able to put ourselves in a place where people can regulate their spiritual and physical needs. Otherwise, we will never feel that we are free

Footnotes

1. F. T. Marinetti, The Manifesto of Futurism, Le Figaro (February 20, 1909).
2. Steve Gibson, www.kk.kau.se/mct/MCTO199/steve/ right.html.
3. An Interview with Paul Virilio, www.nettime.org/ nettime.w3archive/199904/msgn00456.html.
4. Critical Arts Ensemble Staff, Critical Art Ensemble, The Flesh Machine: Cyborgs, Designer Babies, and New Eugenic Consciousness (Autonomedia: 1998), 7-8.
5. Rosi Braidotti, Cyberfeminism with a Difference, www.let.ruu.nl/womens_studies/library.html.

“Knowing where things are and why is essential to rational decision making.”
Jack Dangermond

Geography matters in almost everything we do, where we live, where we work, and the decisions we make about our environment. By the middle of the twenty-first century, it is estimated that 12 billion people will be living on this planet. This means that our planet will be hard-pressed to meet all our food, water, and fuel needs. Thus, managing each limited natural resource has emerged as perhaps the most crucial problem that we will face in the near future. Fortunately, technologies are becoming available for everybody and may allow us to feed and power the growing population without destroying the environment.

In today’s global community, more information helps you to make an easy and informed decision when it comes to interacting with the high-tech world. Currently, information comes in many different ways from the private and public sectors, such as reports and statistics, digital photos, and multimedia.

In today’s complicated and global world, private and governmental organizations and individuals must daily solve problems in a vast array of areas. Business concerns have to deal with advertising, direct and target marketing, facility management, financial services, manufacturing, insurance, retail siting, and property management. Local governments face issues related to community development, construction, crime analysis, demographics, education, emergency services, environmental management, land management, and tourism. The federal government has to concern itself with all aspects of health care, military and defense, natural resources, oil and gas, pipelines, public health, public information, public safety, tax assessment, and intelligence. And these are only a few of the areas requiring decisions.

All these actions happen in a geographic location and affect each other. How can we solve these complicated problems? How can we collect data and analyze it? More important, how can we devise appropriate solutions? Today, we have the technology to solve these kinds of problems: Geographic Information System (GIS).

The history of GIS is relatively short. The first GIS development and application started in Canada during the 1960s. Due to its dependence on computers and its limited capabilities, GIS technology developed simultaneously with computers. Along with the rapid development of computer capacity after the mid-1970s, GIS technology increased rapidly. Since the 1980s, the number of GIS-related companies has increased rapidly. Some of these companies produce data or specialize in producing GIS software and education, and others concentrate on solving problems. During the late 1970s and early 1980s, the first satellites (LANDSAT [USA], SPOT [France], and IRSS [India]) designed specifically to collect physical data about the Earth and humanity’s impact upon it were launched into orbit. As the vast majority of updateable data was not only for military purposes, but also available for public use, GIS users and developers were able to use it to solve their problems.

GIS has been used to analyze the relationship and patterns of almost all natural phenomena. GIS technology helps its users see patterns that cannot be recognized by just viewing a list or an actual map, for it brings everything together. Working with locational information, GIS has the power to solve problems we encounter every day. Whether GIS users restore habitats, plant vineyards, search for oil, fight wildfires, or measure an endangered species’ population, they also can learn more about the ability of GIS to manage natural resources.

How does GIS work?

GIS is a computer-based tool for mapping and analyzing things that exist and events that happen on this planet. In other words, it is a computer system that assembles, stores, manipulates, and displays geographically referenced data. It integrates such common database operations as statistical analysis and query with maps. This ability sets GIS apart from other information systems, and provides valuable data to a wide range of public and private enterprises engaged in planning strategies and managing various infrastructures.

GIS allows people to create powerful maps, integrate information, visualize scenarios, solve complicated problems, present powerful ideas, and develop effective solutions. It is a tool that can be used by almost everybody: individuals, organizations, schools, governments, and businesses.

In general, GIS has two components: hardware (a desktop computer or workstation) and software. Its software produces the functions and tools needed to store, analyze, and display geographical information. The essential software components are tools to enter input and manipulate geographical information, a database management system (DBMS), tools to support geographic query, analysis and visualization tools, and geographic data that GIS can ingrate spatial data with others.

Essentially, GIS is a type of software application, running on a stand-alone computer or workstation, that analyses and displays multiple layers of geographic information. It can be though a spatial database. First, geographic locations on the Earth’s surface can be stored in computer files as sets of mathematical coordinates. This makes it possible to draw a map on a computer-a map of the world, the Amazon Basin, or your neighborhood. Second, it means that different map files or layers of spatial information with common geography can be displayed simultaneously and analyzed with reference to one another. On an agricultural map, for example, one layer can represent the land’s boundaries, another one can show the local streams, and still another can illustrate any changes in elevation. The analytical power of GIS lets people query the system to extract information from different layers.

GIS also is related to, and shares common features with, several other types of information systems. It can be used by desktop mapping, DBMS, computer-aided design (CAD), and global positioning system (GPS)/remote sensing GIS.

Today, GIS can be used for almost anything. However, its major users are utility companies (gas, electric, and water), cable and television companies, transportation networks (finding the quickest way and service areas on the roads), agriculture (planning crops, analyzing yields, planning the efficient application of fertilizers), federal agencies (USDA, NRCS, NGS), municipalities (urban planning), forestry (timber harvest and growth, roads in the forests, cutting and removing logs, environmental regulations, forest management), delivering products, educating children, and targeting markets. It is useful to botanists and biologists, planners, and petroleum engineers. It also can track customer sales, analyze crime patterns, route delivery truces, display soil types, and find the best location for an expanding business.

Over the past two decades, the development, acquisition, and implementation of GISs has continued to increase. Currently, it is a billion dollar industry in the United States, and is being utilized by both the public and private sector and well as academia. The declining cost of computer software and hardware, the increasingly user-friendly nature of the technology, and its increasing power have caused a rapid increase in the number of GIS uses.

The rapid and continued growth of GIS use in private industry, government, and academia has raised the concern of educational opportunities currently available to GIS practitioners. Since GIS is now a big business that is experiencing rapid growth, many new practitioners seek further education and training. In addition, GIS practitioners have acquired a professional identity that they did not have 20 years ago. GIS analysts, specialists, and project managers have been increasingly demanded both by industry and government.

References

• Dahlberg, R. E. & Jensen, J. R. “Education for Cartography and Remote Sensing in the Service of an Information Society.” The American Cartographers, Vol. 13, (1986): 51-71.
• Huxhold, W. E. et al. Managing Geographic Information System Projects. New York: Oxford University Press, 1995.
• Obermeyer, N. J. and Pinto, J. K. Managing Geographic Information Systems. New York: The Guilford Press, 1994.
• Robinson, J. H. “The Economics of Geographic Information Systems. New Directions for Adult and Continuing Education,” Vol. 52, (1991): 33-42.
• Wikle,T. A. “Continuing Education and Competency Programmes in GIS.” The International Journal of Geographical Information Science. Vol. 12, No. 5, (1998): 491-507.

While almost everybody who has access to a computer is somehow involved with the Internet for a variety of personal reasons, scientists and the academic community also use it for their own purposes. Examples are sharing data and information, browsing technical papers, searching for related documents, and posting their research activities to colleagues and other interested parties. Recent developments have proven to researchers and academia, both of which publish large amounts of technical literature, that the day of electronic publishing is close at hand.

The easiest way to publish electronically is to post documents on the Internet by generating Web pages. In this case, however, the user remains a passive recipient of information, for the Internet’s interactive communication ability is not being used. This particular capability of the Web allows a scientist or researcher to generate Web pages with which the user can interact. One example of such interaction is performing mathematical operations over the Internet. This is very useful and powerful, for it allows the user to become an active receiver by gathering the needed information from that particular home page.

For instance, if you visit Rice University’s home page for its Department of Mathematics, you will find several interactive math tools designed to help students taking the Ordinary Differential Equations course.3 These tools are activated by using Java or MATLAB programming language. For example, Figure 1 shows a tool called PPLANE, which draws the magnitude and direction of a differential vector in an x-y plane. PPLANE also graphs the linearization about equilibrium points, and displays eigenvalues, eigenvectors, nullclines, and stable and unstable orbits. The user can change the differential equation’s variables and then run the associated MATLAB code over the Internet. A licensed MATLAB copy in the user’s personal computer is not required, for the MATLAB routine is run on the server and displays the output on the user’s browser. This makes it easy for the student to understand how the changes made alter the equation’s features.

This technique is very efficient and powerful for a student who is still in the learning process. It also suggests that the Internet’s interactive feature will affect the education system and the way courses are taught in the future.

Another home page that contains a wide variety of interactive math tools is found at the Web site for Dartmouth College’s mathematics department.4 Professor Richard Williamson has written about 30 interactive math programs for common scientific problems. These vary from differential equations to heat equation solvers, from Newton’s method of calculating the root of an equation to simulating a swing’s motion. All of these programs are activated by the user’s input parameters, and display the answer in the same manner.

Another interesting and very useful Web site is http://www.integrals.com (see Figure 2). This interactive site allows the user to take any symbolic integral over the Internet. It is provided by Wolfram Research, which also produces the well-known and widely used Mathematics tool MATHEMATICA. After the user enters an expression, the integrator automatically runs MATHEMATICA on the server, integrates the expression, and sends the result back to the user’s browser.5 This site is already helping many calculus students with their homework, and is quite handy for researchers who deal with complex integrals in their everyday research.

Another useful interactive math Web site can be found at the Geometry Center Web page of the University of Minnesota, Science and Technology Center.6 This site offers such interactive math tools as hyperbolic triangles, Lorenz simulation, and interactive proofs of popular theorems. There is also a tool for taking numeric integrals. If you get tried of doing mathematics, you can take a break and play some Tetris games at the same site. In fact, interactive games on the Internet are also a particular type of interactive math tool. A better graphical version of Tetris can be found at http://www.geocities.com/SiliconValley/Pines/522 7/tetris.htm.

All of the above Web pages show that cybermath has found its way onto the Internet, thanks to the Web’s interactive communication capability. It is not difficult to imagine that students in other majors will apply this useful and efficient tool to their own field, thus making the Web even more interactive

FOOTNOTES

1. http://www.flifo.com/and http://www.reservations.com/, respectively.
2. http://mallblvd.net/and http://www.internet.net/index.html, respectively.
3. http://math.rice.edu/.
4. http://www.dartmouth.edu/~rewn/index.html.
5. http://www.integrals.com.
6. http://www.geom.umn.edu/.

The brain is probably the most complex organized biological structure in existence. We think, learn, compute, memorize, feel, show emotion, and love. The brain is the center of all these activities, and of many other mental and physical functions as well. Each human being has a unique personality, and each individual behaves in a certain way. Our behavior reflects how our brain thinks.

Throughout one’s life, a person’s brain constantly learns. Each input, such as events that affect us, leaves its traces in the brain. We recollect these events later. But how do we learn? How do we remember things? What is the physical dimension of learning, feeling, and remembering? What is the physical significance of brain dynamics? Some of these questions are probably the most difficult questions for neuroscientists and other interdisciplinary brain researchers to answer.

Studies of the brain are as old as the practice of medicine. Although advancements in medicine, with the help of engineering and computer technologies, have been significant in recent years, brain research progresses much slower. Brain research has been a focus of such interdisciplinary sciences as neuroscience, biomedical engineering, electrical engineering, medicine, artificial intelligence, and psychology. However, an exact and detailed understanding of the brain’s dynamics and associating its neuronal activities with certain physical phenomenon remains largely beyond our grasp. The fact that the human brain cannot be used for experimental purposes is another factor in brain research.

THE BRAIN’S STRUCTURE

The brain is considered the human body’s central commanding unit. Along with the spinal cord, it forms the human being’s central nervous system. It poses a modular structure, each module of which is known to be responsible for certain functions, and possesses its own respective complexity. Readers wanting to know more about the brain’s structures should check the literature produced by specialists in the field of neuroanatomy.

Figure 1 illustrates the brain’s structure. The cerebral cortex, essentially a biological sheet of tissue covering the brain, is about 0.08 inches (2 mm) to 0.24 inches (6 mm) thick, and gives a geometrical representation of the brain’s shape. The brain’s stem (not shown) is the area between the thalamus and the spinal cord. It is the center of the most of the brain’s basic functions, such as breathing and the heart rate. The area behind the brain stem is the cerebellum. Located at the brain’s base is the hypothalamus, which, among other things, controls the body’s temperature. It reacts to hot and cold temperatures by sending out signals to adjust the body’s temperature. The thalamus serves as a sink for sensory information, and communicates the received information to the cerebral cortex. Although not proven in human beings, the thalamus serves as the center of sleep spindles, sinusoidal signals emitted by animals while they sleep.

NEURONS

Neurons, the brain’s building blocks, are the only cells that do not renew themselves (all other cells die and are replaced). Each human being is born with approximately 100 billion neurons in his or her brain. Thus, a certain neuron in the brain of a newborn human being is the same neuron when he or she is old. A normal brain loses 3 to 5 neurons each second. Stress, drug and alcohol consumption, and aging may cause more neurons to be lost. For an ordinary human being, however, the total number of neurons lost during an average lifetime is very negligible.

Neurons are probably the most complex and intelligent communication networking ever created. The brain contains billions of cells, each one of which is connected to another. All of them share and transmit and, more importantly, process the information. This feature introduces the intelligence of neurons, the nature of which is not yet completely known to scientists, who remain fascinated by the engineering behind this intelligent networking.

To better understand neurons’ functionality, imagine yourself cruising in your convertible on a two-lane road. As you start to pass the car in front of you, you suddenly notice a car coming toward you. You have no more than 2 or 3 seconds to evaluate the options and respond accordingly: you either accelerate and complete the pass, or slow down and get behind the car you were passing. In either case, you have to consider the speed of the oncoming car, its distance, and some other safety parameters. You eventually evaluate your options and reach the safest decision in less than 2 seconds.

What is the big deal? This is just another ordinary event that we are used to experiencing every day. Behind this seemingly ordinary event, however, a tremendous amount of communication and computation is taking place among the neurons. Stimuli invoked by visual information (the oncoming car) observed by the eyes make their way through the central nervous system to the brain. Neurons receive the stimuli, evaluate them, and pass their response to nearby neurons by electrochemical polarization. Billions of neurons are involved in the process.

This information flow among neurons depends on learning (one’s driving experience). The response, the final decision of neuronal computation combined with learning and consciousness, is delivered to central nervous system so that it can act. The nature of consciousness and how it is linked to neuronal computation remain unknown.

These processes are so automated that we do not consciously realize that each physical, mental, and emotional function is governed by our brain, which, in turn, is governed by its tiny component neurons. These neurons enable us to make such judgments every day, and to communicate with the surrounding environment through sound, sight, touch, smell, taste, emotion, feeling, thinking, and so on.

THE HUMAN BRAIN AND COMPUTERS

The human brain and computers are two different things. One is a living, thinking, learning, feeling, crying, and loving organism. Happiness and sadness, in the form of marginal emotions, are reactions of the brain. Such terminology makes no sense to computers. In that sense, it might be misleading to compare the human brain and computers. However, there are some common functionalities that make such a comparison logical.

Both the human brain and computers have memory. Memory in human brains is defined as “stronger synaptic connections,” whereas computer memories are formed by semiconductor chips. Both can adapt and learn. The human brain can learn easier and faster than a computer, which can only “learn” certain tasks by being programmed with special algorithms. The nature of such “learning” is very limited.

On the other hand, computers can perform many complex tasks much faster than human brains. For example, try multiplying two numbers, dividing the result by 7, and then subtracting 9 from that result. The computational speed of a human brain is much slower than that of a computer.

Due to their high speed, computers perform parallel jobs relatively faster. The human brain also can perform parallel tasks at the same time. For example, it controls the heart rate and blood pressure while performing computational tasks. In addition, the human brain is better at interfacing with the outside world and coming up with new ideas; computers only do what they are instructed to do, regardless of the task’s simplicity or complexity. The human brain distinguishes itself from computers by its extraordinary capability in the areas of imagination and innovation.

Another common functionality is that both transmit information. Computers use semiconductor switches that are either on or off. Everything inside of a computer is represented by either a one (1) or a zero (0). Although neurons in the human brain are either on or off, meaning that they are or are not firing an action potential at a particular point in time, an accumulated charge that activates neurons gives the human brain more flexibility. Neurons are more than just on or off, for their excitability is always changing as they constantly receive information from other cells through synaptic contacts. As stated earlier, this information is carried through electrochemical polarization. Although this electrochemical process does not always result in an action potential, it may alter the chance that an action potential will be produced by raising or lowering the neuron’s threshold.

Another important distinction between computers and the human brain is that the human brain never rests, while computers do after they have been turned off. Even during sleep, the human brain continues to work dynamically. Indeed, it produces distinct signals, called sleep spindles, that may be observed externally while the person is asleep. While an individual’s body rests during sleep, his or her brain recollectively refreshes itself.

UNDERSTANDING THE BRAIN’S DYNAMICS

All activity inside the human brain is conducted through electrochemical polarization, a process that can be observed by placing electrodes on an individual’s scalp. The brain’s dynamics can be observed in the form of an electroencephalograph (EEG) or a magnetoencephalograph (MEG). An EEG, which is relatively less sophisticated than a MEG, maps the brain’s dynamics into electrically recorded brain waves. Multiple electrodes are systematically placed on the scalp, and potential differences are measured with respect to a reference point. In the case of a multichannel EEG, the number of electrodes may be as high as 64 or even 128. Figure 2 shows a single-channel recorded EEG. Potential differences measured through electrodes are sampled and stored in a computer for analysis.

The challenge presented to researchers is how to read multichannel EEGs and extract the information that really reflects neuronal activity. If the patient is epileptic, brain abnormalities may be easily distinguished in a multichannel EEG. From the location of electrodes, it may be possible to identify the general part of the brain giving rise to epileptic EEGs. In clinics, neurosurgeons usually open the patient’s scalp and measure the EEG directly by placing electrode grids over the cortical tissue. Even then, it is a real challenge to identify the defective region and proceed accordingly.

The EEGs of epileptic patients distinguish themselves from other brain activities by their relatively high amplitude. But what about other physical and mental tasks? Can we detect and identify those EEGs that reflect a certain mental task? Scientists from many disciplines are focusing on such questions. Many researchers are combining EEGs, MEGs, magnetic resonance imaging (MRI), and such engineering tools and algorithms as digital signal processing and spectral analysis to identify and understand the brain’s dynamics. The clinical need for such solutions are in high demand.

THE HUMAN BRAIN AND INTERDISCIPLINARY SCIENCE

The human brain has been a research focus of scientists from many disciplines. Scientists in medicine, neuroscience, engineering (electrical engineering and biomedical engineering), mathematics, physics, physiology, and computer science have been conducting either sole or interdisciplinary research for many years. The brain has so many dimensions that no single discipline can cover all of its aspects. Some of these disciplines are described below:

• Artificial intelligence attempts to build knowledge representation on the hypothesis that intelligent systems act intelligently. Hence, if the human brain’s intelligence were represented in a finite domain, this domain could be used by computers to mimic human intelligence. This approach faces a major challenge: human intelligence cannot be represented to the degree that artificial intelligence requires to mimic human intelligence.

• Computational intelligence, on the other hand, approaches the problem from the perspective of such engineering tools and algorithms as neural networks, fuzzy logic, and genetic algorithms. Neural networks and genetic algorithms can learn an underlying task to some degree, whereas fuzzy logic relaxes information representation by providing one more degree of freedom to the binary representation of information: a membership function concept. In this concept, the information has a probability of being a member of a certain class. The human brain’s electrochemical process may not always result in an action potential for a certain neuron(s). The binary concept cannot represent this phenomenon, whereas fuzzy logic may be helpful in modeling the chance of a neuron to produce action potential.

• Engineering provides technical tools and algorithms for conducting research on the human brain. Electrical engineering provides signal processing tools and algorithms for filtering and imaging, and other tools to process EEGs. Many scientists use these tools and algorithms to understand and localize EEGs. It would be very effective to localize human brain abnormalities with the help of engineering tools and algorithms.

Each science and method mentioned above has its own limitations. Combined interdisciplinary research provides more promising results for understanding the brain’s dynamics. Many other methods not mentioned in this article also are being used to study the human brain.

SOME FACTS

An average adult human brain weighs about 3 pounds (1.36 kilograms). A stegosaurus weighed about 3,528 pounds (1,600 kilograms) but had a brain that weighed only about 0.15 pounds (70 grams), or just 0.004 percent of its total body weight. In contrast, an adult human being weighs about 154 pounds (70 kilograms) and has a brain that weighs about 3.1 pounds (1.4 kilograms), or about 2 percent of his or her total body weight. That makes a human being’s brain-to-body ratio 500 times greater than that of the stegosaurus.

DISCUSSION

This is only a very brief description of the human brain and its functionality. As scientists and researchers learn more about the human brain, they realize that what they know is very small when compared with how much they still do not know. All scientific efforts undertaken thus far have opened only a small window on a large universe: our own galaxy, located inside our brain, with the neurons as its stars. Let each neuron be a moon. How much do we know about the moon compared with the universe in which it resides? The answer is the same for the following question: How much we know about the human brain’s neurons and the universe in which they reside?

REFERENCES

• Chudler, E. H., S. Pretel, and D. R. Kenshalo, Jr. “Distribution of GAD-like immunoreactive neurons in the first (SI) and second (SII) somatosensory cortex of the monkey.” Brain Research (1988) 456:57-63.
• Nunez, P. L. “Neurocortical Dynamics and Human EEG Rhythms.” New York: Oxford University Press, 1995.
• Figures 1 and 2 are courtesy of Eric H. Chudler, Research Associate Professor, University of Washington.