Assignment #1 – Finding evidence to support the argument that math IS a practical art

Due: Friday, April 5th

Objectives:

  • To connect a topic of interest to you with mathematical concepts and techniques.
  • To refine your ability to search for specific information, even if it is unfamiliar.
  • To practice the thinking skills of analysis and synthesis by describing connections between seemingly unrelated topics.

Tasks:

  1. Choose a topic area of interest to you. You should try to be very specific at first, because that will permit the most rewarding connections if successful. You can always become more general later. After completing the full assignment, write your final (non-math) topic here:

Final Topic / Kung Fu
  1. Find an article, web page, or section of a book/research journal that includes a superficial connection between your topic and mathematics. Photocopy or print the paragraph or page that makes the connection, and attach it to the back of this form. Examples of this type of connection might be a joke, game, or problem that could be assigned in school. I'm guessing this will be the first link you can find between your topic and some type of math. The explanation will probably not be technical, or there may be no explanation at all. Write the source of your information (author and title, magazine and issue, or website URL) below.

Source /
  1. Find a second article, web page, or section of a book/research journal that has a reasonably detailed discussion of mathematical ideas that relate to your topic. You may not be able to find a single source of this information – you will probably need to expand, then refine your search to find the relevant mathematical information. (Think of this like “Six Degrees of Kevin Bacon,” except that you should be able to go from your topic to a math discussion with at most two intermediate steps.) If you find a discussion of statistics related to your topic, you must go a step further and find some mathematical explanation related to specific terminology or ideas in statistics. Photocopy or print the paragraph or page that discusses the mathematical idea, and attach it to the back of this form. Include the source of the information you find when you do the write-up described in part 4.
  1. Finally, write a paragraph or two that explains how the mathematics you found is related to your topic. (This is especially important if you had to go through several steps to find the math topic.) To the best of your ability, explain what type of math is being used, and what questions about your topic it can help answer. Your writing should be neat, readable, and fairly understandable by a knowledgeable classmate. You will be sharing these in class.

<From

WingChunKuen.Com »Archives»Readings»

Yuen Kei-San Wing Chun Kuen

by Lo Sum with Lee Chi Yiu

(Real Kung-Fu)

Throughout the history of China, time has given rise to diversified Sects of Kung Fu, among them, Tai Chai (Great Ultimate),Baro Kwar (Eight Trigram), Yin Yee Kuen (Form of Intention) Choi Lee Fat (Choi, Lee, & Buddha), Hung Kuen (Hung family), Yuk Mun Pal (Jade Gate Style), Mo Don (Wudang), Lung Ying (Dragon Shape), Wing Chun Pal (Wing-Chun's style), etc. To be truthful of the readers, it is necessary to say that among these, some are very ancient. They were invented by the country folks of the primitive age. These people had no knowledge of the basic principles of mathematics, dynamics, biophysics and anatomy. So naturally the Kung Fu Systems they derived have irrational move ments and are contrary to logic. Very few Kung Fu Schools have integrated the laws of nature into their Systems of Kung Fu.

One which has is the Wing Chun School of Kung Fu, a system whose principles are all in compliance with the laws of nature and whose movements are unique. This system was disclosed to a country girl named Yim Wing Chun by a Shaolin nun called Ng Mui.

For over two centuries, her tactics were kepts to only a couple until 1952, when Yip Man diaulged the system to the public in Hong Kong. In the last few years, a second form of Wing Chun appeared in Hong Kong and is called Yuen Kei San Wing Chun. These are the two sources of Wing Chun, the most scientific system of Kung Fu. It is known to the Kung Fu world as the speediest, most lethal and practical form of combat. But because of these factors, the movements do not look spectacular nor do they possess the gracefulness that other systems have, and few people really master this system to a high degree.

There are two famous fighters from Yip Man Wing Chun: William Cheung Chuk Hing, now in Melbourne, Australia, and Wong Sheung Leung, now in Hong Kong. The late movie star Bruce Lee first learned from his friend Bill Cheung who, on leaving Hong Kong fo further study in Australia, took Bruce Lee to his instructor Yip Man. Yip Man pretended to teach Bruce but was actually reluctant to do so. The reason was that Yip Man was a conservative Chinese. He kept to the rule that he not teach non-Chinese, and Bruce Lee was not a pure blooded Chinese, but a Eurasian. So Bill Cheung then took Bruce Lee to his fellow student Wong Sheung Leung and Bruce continued learning from Wong. The principles with which Bruce so fascinated many Kung Fu prectitioners are but only elementary principles of the Wing Chung School.

<From

UWA 2nd YEAR BIOPHYSICS COURSES

Vision Science Program Biophysics 243
Modules (4 pts each)
BIOSPHERE 563.201
BODY PHYSICS 563.204 / BIOSENSING 563.202
BIODATA 563.203
Semester 1 timetable

On-line reference text mirrored here by courtesy of Kenneth R. Koehler

MODULE A: BIOSPHERE 563.201 (4 pts)

Topic A1: BIOMOLECULAR ENSEMBLES (13 lectures)

Basic Fluid Dynamics

Viscosity, continuity, Poiseuilles equation, (Newtonian fluids: parabolic velocity profile) Bernouilli's equation, Navier-Stokes equations, Reynold's number (laminar & turbulent flow)

Examples of turbulence

Application of Poiseuilles equation to the study of bifurcation in an artery

Hemodynamics

Pressure wave transmission through an elastic vessel, models of blood flow: non-viscous (Moens-Korteweg model) & viscous (hydrodynamic model), calculation of impedance

Cardiovascular system

Homeostasis (principle of negative feedback control), measurement techniques, pressure, flow (doppler ultrasound, doppler laser)

Classical equilibrium thermodynamics

Statistical basis, entropy, disorder & information, enthalpy, Gibbs free energy, Hess's law, fluctuations

Linear nonequilibrium thermodynamics

Linear irreversible theory for systems close to equilibrium, Onsager's principle, Prigogine's principle, connection between fluctuations & dissipation

Diffusion

Diffusion potential, Fick's laws, active and passive transport

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Navier-Stokes Equations

The motion of a non-turbulent, Newtonian fluid is governed by the Navier-Stokes equation:


The above equation can also be used to model turbulent flow, where the fluid parameters are interpreted as time-averaged values. The time-derivative of the fluid velocity in the Navier-Stokes equation is the material derivative, defined as:


The material derivative is distinct from a normal derivative because it includes a convection term, a very important term in fluid mechanics. This unique derivative will be denoted by a "dot" placed above the variable it operates on.

Navier-Stokes Background

On the most basic level, laminar (or time-averaged turbulent) fluid behavior is described by a set of fundamental equations. These equations are:


I have been interested in the art of Kung Fu for a very long time, and finally began training in the art about six months ago. In fact, I had a belt test last night, and it occurred to me that I could try to connect Kung Fu to mathematics. This seemed like a good example to offer my students since I had no idea what connection(s) I might find.

I began my search on Yahoo! with the obvious search terms: “Kung Fu” and “mathematics.” This led me to the WingChunKuen.Com website whose page is attached. It mentions that this particular style of Kung Fu tries to integrate the laws of nature into their style. The site mentions mathematics, dynamics, biophysics, and anatomy as sources of ideas that could influence a Kung Fu system because each provides insight into the ways of nature. Picking up on these keywords, I then did a search using the words “dynamics,” “biophysics,” and “mathematics.” That search did not lead to something of clear interest, so I experimented and had success when I replaced “mathematics” with “body.” That led me to the description of a second-year biophysics course sequence offered by the University of Western Australia's Physics department. This is included as my second page.

Since I had not quite reached an actual discussion of a mathematical idea, I borrowed keywords from the biophysics page. One last search using the phrase “Navier-Stokes equation” provided the type of page I hope my students will find. This is attached as my third page. Though it is a bit more complicated than I understand, the web site states that the equation describes the motion of a non-turbulent fluid.

Despite the many intermediate steps, there seems to be a reasonably direct connection between the Navier-Stokes equations and Kung Fu. The Navier-Stokes equations deal with the motion of a non-turbulent fluid. In Kung Fu, there is a considerable focus on keeping blood and ch'i (the life force) flowing through the body. Blood is obviously a fluid, and I think it flows without much turbulence through the arteries and veins. Ch'i seems to me to be more of an idea than a physical thing, but my Kung Fu school includes training in “circulating your Ch'i,” which makes it sound like a fluid as well.