As someone who teaches basic mechanics to hundreds of college students each year, I see again and again the frustration many students have in understanding and manipulating the symbolic constructions we use to describe motion, forces, particles, etc. Beside standard mathematical notation (which is already challenging for many), the symbolic representation of physical quantities includes letters from both Latin and Greek alphabets, some of which are obvious to an English speaker (e.g., *m* for mass, *F* for force) and some of which are not (e.g., *p* for momentum, *µ* for the coefficient of friction), and none of which may be clear to someone accustomed to an Arabic or Chinese alphabet or spells mass as *khối lượng* (as the Vietnamese do). There is also a fair deal of redundancy (e.g., *g* is used for both the surface gravity on Earth and for the mass unit of grams) that can lead to confusion. Most importantly, decoding this symbology draws mental energy away from understanding the underlying concepts, leading to the strange situation in which we end up teaching “concepts” and “problem solving” as distinct activities. It is no wonder that most students decide Physics is just too hard.

I recently attended an inspiring talk by UCSD Cognitive Science professor David Kirsch, as part of a workshop series on creativity hosted by the Center for Human Imagination. David’s primary thesis was his investigation into how the choreographer Sir Wayne McGregor and his Random Dance company is able to consistently produce award-winning performances. A side discussion emerged on how information can be conveyed in different formats (e.g., reading or speaking) or basis sets (e.g., through tables or diagrams), and how some format convey certain information more efficiently or accurately than others. As this was a talk on creativity and dance, this immediately got me thinking that a *physical* representation for *physical* phenomena may be more conceptually clear than a written representation. Furthermore, if such a representation could be made *functional,* it might bridge the gap between the conceptual and problem-solving aspects of physics and resolve some of the issues faced by novice students.

### Equations vs. Descriptions

To illustrate the challenge of our current symbolism for physics, let’s take Newton’s Universal Law of Gravity:

To the untrained eye, this looks not unlike gibberish. But it is only because the equation contains a great deal of information packed into a very compact form. I read this equation as stating (with parenthetical clarifications):

The gravitational force of object 1 acting on object 2 [F_{12}, the arrow indicates this quantity has both magnitude and direction] is equal in magnitude to the Universal Gravitational Constant [G] times the product of the two masses [M_{1}and M_{2}] and divided by the square of their separation [r_{12}^{2}], and which acts in the opposite direction of the line connecting object 1 to object 2 as an attractive force [-^r_{12}, the carat symbol indicates this quantity has direction and unit magnitude].

Got it? Clearly the equation is a lot quicker to write, and it is also easier to manipulate using mathematical operations. However, the subsequent long sentence conveys more the meaning behind gravitational force and how it works (i.e., an attractive force that depends on mass and separation).

With much practice, one can readily translate between these representations. As another example, consider Isaac Newton’s [translated] definition of mass as put forth in his 1687 treatise *Philosophiae Naturalis Principia Mathematica* (the text that laid out modern mechanics):

“The quantity of matter is that which arises conjointly from its density and magnitude. A body twice as dense in double the space is quadruple in quantity. This quantity I designate by the name of body or of mass.”

He is careful here to lay out not just how mass is defined, but how it changes if you change the size of an object. In language of equations, this is simply:

MASS = DENSITY × VOLUME

or

using standard notation. More compact, easier to remember, and easier to manipulate, but less meaning. How do we make an equation that simultaneously conveys meaning and retains mathematical functionality?

### Gestural Language for Physics

Physical gestures for physical concepts are not new of course, being necessary for the 0.5% of the US population that is deaf. There are several sites established for defining and distributing signs for Physics terms, including the British Science Language (BSL) Glossary, the American Sign Language ASL-STEM Forum and the NEEDS Outreach Project glossary, and interest in this issue has broadened since a recent New York Times article highlighted the development of sign language for science terms. One particular segment in this article hints at the potential power of physical gesture in more clearly conveying physical concepts:

“If I wanted to indicate mass, I would probably hold up a balled fist,” said Kate Lacey, an interpreter at George Washington University who often works with science students. “Then, to indicate weight, I’d drop that fist toward the floor.” The implication is that weight represents gravity’s effect on mass, which is about as clear a definition as one is likely to find.

Such elegant personifications of tricky scientific concepts leave some deaf students feeling sorry for those who rely on their ears.

While I greatly respect the work that is being undertaken, and as I freely admit my ignorance of sign language and deaf culture (although I do have a sign name), my impression is that many of these signs are falling into the same traps as traditional symbolic representations; that is, they do not fully merge conceptual understanding with a functional physics language. First, there is the ongoing issue that the various sign languages are not in mutual agreement, and issue that is not resolved in the development of new signs for physics. Second, many of the gestures are still based on letters within the language, which results in a similar disconnect between concept and notation; the signs are no different from writing an equation down. Third, many of the signs are current or near-future anachronisms. Consider the ASL sign for time, in which a signer points toward a watch on her arm; how long will this representation be culturally meaningful?.

These problems are illustrated by the following three signs from the websites listed above, all meant to describe the term “acceleration” (click on the images to watch the signs in action):

Which one is most conceptually accurate? The first sign waves the symbol for “a”, which simply reproduces current notation; the second appears to be referring to a car’s speedometer, a potential pitfall should our culture lose the car (I finally figured this our after seeing the man’s mouth pucker as if he was making an engine sound); the third I have to admit not quite understanding at all. None (in my opinion) represent a natural, conceptually accurate representation of the change of one’s velocity with time, which is acceleration.

I believe it is possible to go further with this, not just in terms of accurately representing the concepts behind these terms, but to make this language symbolically functional – to be able to reproduce and manipulate equations, analyze physical situations and express measurement, and just maybe conduct formal calculations through physical movement – *a dance of physics*.

### The Goals of this Project

Based on the ideas, issues and examples detailed above, I propose an endeavor to create a physical language for physics that encompasses the following guidelines:

- The language can use movement, gesture, voice and/or percussion, but no other elements beyond the human body;
- The language must be able to accurately represent physical quantities, relations and phenomena, including directionality and magnitude;
- Language elements must be derived from and/or accurately reflect the underlying concepts as faithfully as possible;
- Language elements must not be based in one particular language or culture, since physics is a universal science;
- Language elements must not be anachronistic, either currently, in the past, or within the next century;
- Language elements must be interoperative and combinable to form more complex quantities and concepts;
- The language must include basic mathematical functions to manipulate physical quantities;
- Numerical quantities (numbers, constants, variables) must be representable, and if possible in a form conducive to calculation; and
- Rules governing “grammatical structure” must reflect mathematical logic and operation.

In forthcoming posts, I’ll detail some of my work toward this endeavor, including physical and historical reasoning on how to represent certain quantities; crowd sourcing methods to solicit, select and test various gestures and movements; examples of equation making and manipulation, and of analyzing physical phenomena; and how this work could be developed for aesthetic practice. Stay tuned!

how this project going on ?