Speed and speed-squared.

I've been playing around with being quantitative about energy in my Advanced Inquiry class.  We're finding this pattern in our data:

• for every SECOND an object falls, its speed gains 10 m/s.
• for every METER an object falls, its "speedsquared" gains 20 m2/s2.

But it's not coming from a place of modeling - just fumbling around for some kind of pattern.  Speed-squared is totally meaningless to us.  And heaven help me I can't figure out a reasonable way to reason about "speed-squared." It just seems like a consequence of F = ma, and nothing meaningful in its own right.

Surely someone in PEG or somewhere has come up with some kind of way of thinking about why we square the speed to determine the energy?  -- Something that says "this, conceptually, is what a speed-squared means"?

Help?

Or, if you can't help, at least bask in the cool realization that "g" tells us change in velocity over time, while "2g" tells us change in velocity-squared over distance.  I hadn't put that together before!

On defining zero speed.

Taking a break from my thoughts on work and energy to share a snippet of a paper I want to write- maybe for the Physics Teacher- based on a little episode from my inquiry class.  It parallels some of my claims about terminology and definitions that I make in the work-and-energy paper.


In a recent class discussion, students discussed in small groups their ideas about the shape of a speed/time graph for a falling ball released from rest.  The class shared their ideas and was divided on whether the line should be straight (an argument from a group that called upon someone’s knowledge of g = -9.8 m/s/s to account for this slope) — or if it should be a “J” shape.  While the rationale provided for the straight line was correct, the explanation for the “J” curve was compelling and hard to discredit:

1. Definition of “at rest”: imagine you set up a camera to take a picture of the ball being released from rest.  If you can take two pictures that show the ball to be in the same place, then the ball is at rest.  Otherwise, it is in motion.
2. If the ball starts from rest, there must - by definition of ‘rest’ - be a “flat” region on the speed/time graph - however short that period is - before the graph starts to rise.  This is a “J” ( or at least: _/ ) shaped graph.

I had never realized this before - but (hearkening back to my dissertation yet again!) there are all sorts of patterns-of-activity in the world where we care about whether or not something is at rest: I want to take a non-blurry picture of my dog; I want to swat and kill that fly; I need to make sure that egg isn't going to roll off my countertop; I need the cop with his radar gun to actually measure zero speed while I'm at a stop sign.  In all of these, the zero-speed is important only to the degree that there's a region of time when we are at zero speed. And in these activities, "being still" is qualitatively different from all other forms of motion.  And it certainly isn't dx/dt = 0.  It is dx/dt = 0 AND d2x/dt2 = 0.  That's what the two-picture definition of at rest means.

Until the students had articulated point 1 - a definition of “rest” - I had never clearly articulated the difficultly of understanding that zero speed can last for an infinitesimally brief period of time. There's no trouble in thinking that, as you accelerate to 60 mph, you're at 30 for an infinitesimally brief time - but zero is different.

“Rest” is a “duration” statement — zero speed is not.

I have some ideas about where to go from there- how to tease apart "at rest" from "zero speed." But I'll save that for later.

Small Paper Chunk: Two perspectives

Modeling and inferential reasoning
The distinction between inferential reasoning and reasoning through modeling speaks to a question regarding the nature of physics and our goals for an introductory physics student.  For if the goal of introductory mechanics is for students to construct or learn a suite of mathematical statements that they can employ to determine trajectories of objects and transfers and transformations of energy, then learning and applying the mathematical formalism is sufficient. From this perspective, we can interpret attention to epistemology, identity, and modeling within introductory physics as supporting activities that facilitate inductive and deductive formal reasoning with physical laws. Indeed, much of energy is treated this way, as a set of equations that are shown to be true, but are not themselves causal statements.

If, however, the goal of introductory mechanics is to develop or learn coherent, mechanistic models for events in the world (hammer and van zee, nersessian, Lehrer & schauble 2006), then mathematical formalism and inferential reasoning can be seen not as the hallmark of scientific reasoning, but support for the activity of modeling.  The mathematical formalism may be necessary - even an emphasis of instruction - but it cannot be sufficient, as it provides us with correlations between, say, force and acceleration, or work and changes in energy, but the mathematical statements do not communicate causal relationships - that forces cause acceleration, or that changes in energy are due to forces applied over a distance.
...

if we take the position that introductory physics should engage students in modeling as a way of reasoning about events, it is necessary to know what kind of ‘events’ we’re modeling and what kinds of entities are causal.  But this poses a problem for instruction, because we could come up with any number of  “events” for which we seek causes: for example, in addition to the change in speed over time (acceleration), we could define an acceleration-like entity “the change in speed over distance.”  In addition to transfers of energy due to differences in temperature (heat), or transfers of energy due to forces (work), we could construct a category “all energy transfers mediated by a rope.”  The reason physics has not constructed such categories is because there is no theory in which such categories are relevant; the theory defines the relevant categories. 

Therein lies the instructional dilemma: without defining a category of energy transfers and transformations called “work” (which presumes regularities in the transfers and transformations of energy), how can we construct a model that explains those regularities? And without the model, why should we have cause to construct the category ‘all transfers and transformations of energy caused by forces’?

Standard instruction resigns itself to defining terms and showing them to be useful.  An alternative approach, Atkins & Salter (2010) note, is to allow theory and conceptual objects to bootstrap each other along through iterative modeling, representations, and theory development.  In exploring students’ construction of a definition for blurriness, they have argued that “Rather than the starting point for inquiry, [a] definition [of blurriness] is a conclusion of the inquiry—an idea that was negotiated, challenged, tested, refined and ultimately adopted. In doing so, students moved from vague descriptions to precise, mechanistic accounts, developing the theory necessary to make this definition possible.”

Below we describe how Energy Theater together with freebody diagrams allows the teachers to observe patterns and regularities and use those to construct the idea of work.

More on work...

Work as a transformation or transfer of energy
Before proceeding, we discuss what we mean by “work” and how this is different from many standard introductions to the topic.  The easiest way to describe what is “work” is via an analogy to force:

Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.

In this first law, Newton defines a particular kind of “event” for which there is a cause: an object moving at a constant speed, or an object at rest, is not an “event” - there is no happening to explain.  (In this way, he departs from the idea that all objects tend to a state of rest.)  A change in motion is an event, and force is the entity responsible for that event.  Force, that is, is not the change in velocity — it is the entity responsible for that change.  Force is a causal entity; a change in motion is the result.  Calling a force a “push or a pull” is empirically true given the definition of force (and is even implied by calling force a thing that can be “impressed” on an object), but it is not itself the definition. And calling a force “an acceleration” mixes up the cause (F) with the effect (ma).

Similarly, work is a change in energy (a transfer or transformation of energy) caused by a force.  (By way of comparison, heat is a change in energy caused by a temperature difference.)  Work is the “event” and the cause for the event is a force applied over a distance.  Like the student who mistakes ma for the force, rather than the effect of the force (and mathematically equivalent to the force), many texts mistakefor the work, rather than the cause of the work.

Why does this matter?
If we the goal of physics to provide us with coherent, mechanistic explanations for events in the world (hammer and van zee), it is best that we know what kind of ‘events’ merit explanation and what kinds of entities are causal. Work is an event - not a cause. And in seeking the cause, we are—as with Newton’s First Law—led to forces as a causal entity.

... Herein lies the total genius of Energy Theater — while it took Newton some serious thinking to decide that an object in motion will stay in motion (and so was not “an event” worth explaining), Energy Theater makes the important 'events' visible - every transfer or transformation event is either an instance of work or heat.  What the teachers have done is begin to parse work from heat, and relate work to F.d.

Are you troubled?
What might give you pause is to say: wait! - I thought work was a change in KE, not all transfers and transformations in energy. It just so happens that every energy transfer or transformation is “laundered” through the kinetic energy bank - so it just so happens that to keep track of enery transfers and transformations, you need only account for changes in KE.  So a transfer or transformation of energy (caused by a force) is equivalent to accounting for changes in kinetic energy KE.  This is the genius of the teachers’ 1st and 2nd laws (1. When forces transfer energy, they transfer kinetic energy. 2. Kinetic energy is present in all transfers and transformations (potential energy always transforms into or from kinetic energy). ) 

What puzzles me
I didn't know this prior to teaching it.  Maybe this is the beauty of responsive teaching - you do more than you knew you could-- it is generative teaching.

♥ Nersessian ♥

I like the parallels I draw here between Neressian and the Energy Project.  And Nersessian's emphasis on modeling as a form reasoning that is not just plain old inference is really nice.

Question: am I using "deductive-nomological" correctly? If not, what's the term I'm looking for?


Modeling as a form of reasoning
A typical (textbook) approach to introducing the work-energy theorem begins with a definition of work, a definition of kinetic energy, and presents a proof of the relationship between work and changes in kinetic energy (e.g., Serway, PSSC? Project Physics,   ).  This deductive-nomological approach stands in stark contrast to the approach taken in the Energy Project, where teachers, through creating and refining models of energy transfers and transformations, determine relationships between forces and these changes in energy.

This difference in approach resonates with a distinction identified in the philosophy of science literature. As Nersessian writes, describing differences between her account of the evolution of Maxwell’s Laws and others’ accounts, 

“Most philosophical and historical accounts accorded the models Maxwell created in deriving the field equations only ancillary status. On my reading of the historical records, this looked implausible. The models seemed to be central in his reasoning process. I believed the difference in interpretation to lie in my willingness to view modeling as a form of reasoning, while the other accounts derive largely from a position in which reasoning is taken to comprise applying formal rules of inference (deductive or inductive) to systems of propositions. ... Analogical models employed in empirical studies of problem solving are generative (see, e.g., Gentner & Gentner 1983). That is, reasoning with them provides information about the target problem they represent that goes beyond what is available directly from the problem.” (Nersessian, 1995, 208; emphasis added)

Similar to the philosophers Nersessian critiques, traditional physics instruction emphasizes the formal rules of inference when asking students to reason with and reason towards physical laws.  Traditionally, instructors reward students for such inferential reasoning in their homework and exams; deductive reasoning is the standard style of reasoning required in solving problem sets.  While instructors may ask students to explain their reasoning on such assignments, these explanations still offer scant opportunities for students to do the more creative, idiosyncratic and generative work of modeling. (Notable exceptions to this approach include Brewe, Hestenes, Salter & Atkins, Hammer.)  And yet modeling is not only a generative form of reasoning, but it is fully consistent with rigorous scientific practices (e.g., Nersessian, Giere, Hestenes).

Work:F.d::Force:ma

I'm feeling more confident about the claim from my last post.

Work is not F.d any more than Force is ma.  Work is a transfer or a transformation of energy (due to a force being applied), just like force is an entity that changes an object’s velocity.

So while I initially rewrote the 5 Laws to switch the language of “forces” to “work”….

1. When forces transfer energy, they transfer Work transfers kinetic energy.
2. Kinetic energy is present in all transfers and transformations (potential energy always transforms into or from kinetic energy). 
3. A force on an object in the direction of motion Positive work increases kinetic energy. A force on an object opposite the direction of motion Negative work decreases kinetic energy.
4. Transfers of energy are due to work done by a contact force. Transformations of energy are due to work done by non-contact forces.  
5. Forces transfer or transform energy proportional to their magnitude. Work is proportional to force.

 I don’t think that’s right!  It’s the language of transferring/transforming energy that should be changed to “work”…

1. When forces transfer energy, they transfer kinetic energy.
2. Kinetic energy is present in all transfers and transformations whenever work is done (potential energy always transforms into or from kinetic energy).
3. A force on an object in the direction of motion increases kinetic energy does positive work. A force on an object opposite the direction of motion decreases kinetic energy does negative work.
4. Transfers of energy are due Work by a contact force transfers energy. Transformations of energy are due to Work by a non-contact force transforms energy.
5. Forces transfer or transform energy do an amount of work proportional to their magnitude.

Energy theater has “work” as a concept built right in because you - the little chunk of energy - already recognize the every important action of transferring or transforming as a distinct action.  Work isn’t F.d! Work is any time that little energy person/block moves or changes form because of a force!

What is work?

I want to claim that:

Work is a transfer or transformation of energy that is mediated by a force.

(And it just so happens that work equals F.d.)

It's analogous to saying force is a push or pull, and it just so happens that the strength of that push or pull = ma.  No. It's analogous to saying that forces are influences that change an object's velocity, and it just so happens that F=GMm/r^2.

My sheepish physics question: is that right?

I think it's right. It puts "work" squarely in the ontology of light and heat, explains why work and heat aren't the same thing, gives it units of energy, relates it to force.  But I've never heard it described it that way.  (Our typical answer about why our muscles aren't doing work when we hold up a book is a formulaic answer ("well, f.d is zero") instead of "your hand isn't transferring energy to the book.")

My research question: Does anyone know of any research/work (haha) on this topic about what work is?

Small Paper Chunk: Law 3 & Law 5

The analysis of the laws/corollaries/conditions starts with what could be considered the teachers' zeroth law.  I then continue with Laws 3 & 5.  Still the focus is on the physics content of the laws they developed, and building towards a relationship between those laws and the w-e theorem...

As you read, some questions:

(1) Where the genesis of the law is critical for understanding (and agreeing with) the law, I include some information on the scenarios teachers considered and how it led to the law - but in general, I'm really not interested in using this paper to spell out carefully how each of these laws was developed. The paper would be unwieldy and I'm not prepared to do that analysis.  Is this okay?

(2) Anywhere you think I'm reading MORE into the teachers' laws than is there, and don't qualify that, please let me know. 


Law 3: A rationale for the dot product
A force on an object in the direction of motion increases kinetic energy. A force on an object opposite the direction of motion decreases kinetic energy.

The goal of Law 3 is to relate the forces applied to the sign of changes in kinetic energy. If we limit our consideration to forces that are parallel to an object’s motion and applied over the same distance (as was the case for scenarios in our class discussion), then Law 3 can be mathematically written as:

(Footnote: This is, of course, generally true and not limited to parallel forces, but such a generalization was not present in the teachers’ 5 laws.)

That is, if the force and the displacement vectors are parallel (yielding a positive dot product), then the change in kinetic energy is positive (a gain in kinetic energy); if they are anti-parallel, then the change is negative (a loss of kinetic energy). 

Law 5: A direct, linear relationship between forces and changes in kinetic energy

One of the most challenging scenarios for the teachers to describe was that of a basketball being pushed underwater at constant speed.  We first analyzed the energy transfers and transformations using energy blocks, and later a description of forces was added.  (We do not here provide a description of the conversations and ideas that led to this final description— but will note that this was a multi-day effort, with extensive conversations regarding why the energy was not stored in the ball itself, and ultimately relating the density of water and the ball to the forces and energy story.) 

A summary of the motion of the energy blocks is provided in Table 1 (the teachers did not construct such a table - this simply characterizes one of the steps they enacted with the blocks); the force diagram, with hash-marks indicating relative magnitude, is shown in Figure 1.  (We imagined the hand to be without significant volume, like a thin string pulling the ball underwater.)

When these two representations were constructed synchronously- that is, when the force diagram  (Fig. 1) was visible on the white-board diagram where we moved energy blocks about - we noticed that that the number of cubes we moved was proportional to the size of the force vector. This is illustrated in Table 2, which relates forces on the ball to energy transfers and transformations in the ball.  (Again, the chart is a summary of the teachers’ ideas, but they did not construct this representation.)

This pattern brought us to conjecture, test, and reach consensus on Law 5:
                  Forces transfer or transform energy proportional to their magnitude.

Law 5 is similar to Law 3, but instead of focusing on the sign of the changes in kinetic energy, it provides information on the magnitude of those changes, and could be written:

Combining equation (5) with equation (4) yields the expression:

(footnote: Implicit in the teachers’ representations of energy transfers and transformations was the idea that displacement was also proportional to the magnitude of ΔKE; that is, with each successive movement of the basketball, they repeated the energy transfers and transformations shown above.  However, this was never explicitly incorporated into their laws.)

An aside: Why the 5 Laws are Not Too Different from the W-E Theorem

Here I take the 5 laws and replace "force that transfers energy" with "work" and "force in the direction of motion" as "positive work"... Suddenly (I think) the laws feel awfully familiar!

After I realized this, I feel like I learned what "work" is! - Force:momentum :: Work:kinetic energy. I think I've had the ontology of work wrong (or really poorly understood) all these years.  (Over and over again, I find that intro physics is a playground where I can spend the rest of my intellectual life.)

In structuring the paper, I wondered if I should put this right after the teachers' laws - but opted not to. 

I wish those teachers would be coming back this summer to pick up where we left off! - At any rate, I can't wait to share this paper with them :)

Small Paper Chunk: Corollary A

Corollary A: Newton’s Zeroth Law and establishing conventions

Corollary A: When there are energy transfers/transformations in/from/to object “A” these are due to forces on object “A.”

Corollary A is one that—while never explicitly addressed in Newton’s laws or the work-energy theorem—is similar to Scherr and Redish’s (2005) description of what they term “Newton’s zeroth law.”  This law states: “At any instant of time, an object responds only to the forces it feels at that instant.” Scherr & Redish explain that the crucial piece of information here is that “objects respond...to forces that they feel rather than to those they exert.” Similarly, in CorollaryA, the teachers link energy changes in an object to forces that the object feels rather than the forces it exerts.

While Newton’s Zeroth Law for forces may sound intuitive to many (I speed up because I am pushed, not because I push back), applying this rule to energy transfers is less intuitive: objects lose energy not because of forces they exert, but because of forces they feel. This corollary claims that a weightlifter loses energy not because he pushes the weight up, but because the weight pushes back down on him. Stranger still, the force we identify as being responsible for decreasing energy in the weightlifter (the force on the weightlifter by the weights) is not the force that is responsible for increasing the energy in the weight (the force on the weights by the weightlifter).

This question of which-force-goes-with-which-energy-transfer arose in several contexts, but most notably as we enacted energy theater. As teachers, representing energy units, moved from one object to another, they attempted to declare which force was responsible for their transfer from one object to another. Through coordinating the energy theater with a free-body diagram (on whiteboards laid on the floor), we came to decide that energy leaving the hand was due to the force of the box on the hand and energy entering the box was due to the force of the hand on the box. The choice of representation - energy theater - and the desire to attribute a force to each change in energy forced this question and, consequently, the construction of Corollary A in way that other representations do not.

It is tempting to say that in this corollary the teachers are (implicitly) reading too much into the following two possible formulations of the work-energy theorem

... insert equations: f(ba).d = delta ke or -f(ab).d=delta ke

Equations 2 & 3 are, by Newton’s 3rd Law, precisely identical; there is no empirical way to answer the question “Which of these two forces is responsible for the weightlifter’s energy loss?” Choosing which force in a 3rd-Law Pair is related to an object’s change in kinetic energy is simply a matter of convention: once the arbitrary choice is made, it should be applied consistently, but one cannot determine that a change in energy is due to one particular member of the force pair. 

Later we will argue that attributing causality—imagining that one particular force in the pair is responsible for one “step” in energy’s transfers and transformation—while empirically indefensible, is cognitively useful and fully consistent with scientific practices.  That is, a more scientifically precise statement for Corollary A would be: When there are energy transfers/transformations in/from/to object “A” we say that these are due to forces on object “A.” — but in terms of how scientists speak (Ochs) and reason (Darden? Nersessian?), the idea of causality is both common and productive.

With this initial relationship between forces and energy changes in place, we can now explore more precisely how those forces on an object change an object’s energy.

Small paper chunks: The Five Laws of Energy

Rachel mentioned using her blog to try out small chunks of a paper. So, dear readers (Hi Amy! Hi Rachel!), I'll try that here.

To begin, the paper I'm working on discusses the 5 Laws of Energy that teachers in the Energy Project generated.  My goal initially was to make this a "content" paper - that is, let's stop talking about the epistemic affordances of responsive teaching and the representational affordances of energy theater, and look at what kinds of conceptual ideas get developed in such a setting.  I'm now looking at a broader message (see below), but the completed part of the paper is all about the content expressed through the 5 Laws, and that's what I'll start by sharing.  These laws are:

1. When forces transfer energy, they transfer kinetic energy.
2. Kinetic energy is present in all transfers and transformations (potential energy always transforms into or from kinetic energy).
3. A force on an object in the direction of motion increases kinetic energy. A force on an object opposite the direction of motion decreases kinetic energy.
4. Transfers of energy are due to contact forces. Transformations of energy are due to non-contact forces. 
5. Forces transfer or transform energy proportional to their magnitude.

(I then include the corollaries and conditions that are also addressed by the teachers.)

The paragraph that sets up the paper's aims is...

These laws may seem—at best—weakly related to the work-energy theorem. In the following section, we discuss these laws, corollaries and conditions and their relationship to the work-energy theorem. We begin with the claim that the content of these laws recapitulates significant ideas in the work-energy theorem.  Furthermore, rather than merely correlating forces and energy, these laws represent a framework in which the teachers model energy and forces in powerful ways, and it is through developing and refining those models that the work-energy theorem begins to emerge.  We discuss in what way the teachers’ laws are consistent with a modeling framework and the advantages of such an approach.  Finally, we suggest that the model the teachers developed was afforded by the representations they used, particularly Energy Theater and free-body diagrams. 

My questions:

(1) Am I right that, to most, the laws seem only weakly connected to the work-energy theorem? (In the paper I detail the theorem before making that statement.) - I remember Rachel saying something like "I have no idea what those mean, so it must be something cool!" Having looked at how those laws relate to the work-energy theorem, it now seems so obvious to me as to not be as "weakly connected" as I originally thought.

(2) This will probably be answered by the unwieldyness of the paper itself, but does that set of goals for the paper (what the laws mean, why they represent a development of a mechanistic model for energy, and how the particular representational format brought them about) seem like a reasonable scope of a paper? 

(3) What journal? PRST-PER is what I was thinking... seem reasonable?

(4) Finally, I feel a bit like ET is Hunter's baby; Energy Project is Rachel, Sam, and many other colleagues' creation. Am I stepping on toes by putting together a paper on this? Who should/would like to be in on my project?

... in the next posts, you'll see me go one-by-one through the teachers' ideas and relate them to normative physics. 

Hestenes modeling

I have some gaps in my knowledge of the PER literature.  But I also read some weird things others don't, and I assume this variation is healthy for a field of researchers.  Nonetheless, I'm embarrassed to say that I only yesterday read Hestenes' 1992 AJP paper.  What a blast! - It's like a physicist starts to discover the same things that Lakoff talks about in my favorite Women, Fire and Dangerous Things.  It's all about how theories create theoretical objects; a paper I have 10% written is all about this interaction between theory development and constructing objects/terminology/categories.  Giddyup.

“Point particles do not exist in the Physical World; they are conceptual objects created by Newtonian theory.  They are defined by Newton’s Laws, which specify their properties.”

So then WORK does not exist in the Physical World (of course). It is a conceptual object created by ___ (? the work-energy theorem ?).  And further, I think we can claim that the teachers in the Energy Project constructed a theory that - almost! - creates the entity WORK.

Some early sketches of this idea...

From Hestenes, 1992 paper re: the Newtonian Modeling Game:

Board:     The three-dimensional Euclidean space of some physical reference system
Pieces:     Point particles or model objects composed of particles.
Objective: To produce validated models of material objects and processes in the Physical World.

Legal moves:
(1) Particles can be assigned any initial positions or velocities in the reference system consistent with specified interactions.
(2) Particles can be assigned any interactions consistent with the general interaction laws.
(3) Particle trajectories must be calculated from the general dynamical laws or derived from them.
(4) A model is validated by matching it to physical phenomena in accordance with the defining laws.

For The Energy Project, I think the big change is that we're saying: HEY! mass isn't the only thing worth tracking! - ENERGY is also worth tracking.  We can have a modeling game for energy, too.  Many discussions of energy in physics track the object, and assign it an energy value - they don't track the energy itself.  But following the energy is really important - especially in things like biological systems (b/c I just taught photosynthesis...).

So we can say the following for Modeling Games in the Energy World:

Board:     A collection of objects that can possess energy in some physical reference system.
Pieces:     Point-like “units” of energy
Objective: To produce validated models of material objects and processes in the Physical World. (? same goal, different pieces at play ?)

Legal moves:
(1) Energy units must be assigned a form and an object (that’s it. not a velocity, position, trajectory, etc.)
(2) (Energy does not interact with energy)
(3) Energy can undergo any transfers or transformations consistent with the... laws?
(4) An accounting of energy transfers and transformations is validated by matching it to physical phenomena in accordance with the defining laws.

THEN... what are the laws?

1. I think the definitions of forms:
          KE = 1/2 mv^2, GPE = mgh, TE = ... etc.
2. I think the other laws would be the ones that the teachers generated...?

So, brand new readers out there, particularly if you're familiar with the Newtonian Game paper, some questions:

 (A) Do you think: "ooooh, she's on to something!" or "yes, Leslie. Welcome to our energy party. You're only 2 years late."
 (B) Can you see parallels between the "forms" of energy teachers create and how this is consistent with Hestenes' modeling paper? I can, and I think it's cool, but maybe not?
 (C) Thoughts about the parallels I'm making between the Newtonian Game and the Energy Game?
 (D) I have to admit. The first time I saw Energy Theater I thought "what in the world are they so excited about?" - I am a total convert now. I think Hunter is some kind of genius.
 (E) I want to also say that there's some bootstrapping going on - theories create objects, but objects help with creating the theory, too... maybe the 'forms' of energy does this.

_____ makes energy flow

I'm working on a paper now about some laws that teachers in a professional development program created regarding forces and energy.  In their work, they discuss forces as being the entity that cause a transfer of energy.  I wondered what kinds of causal language physics uses about energy flow -- do we say work causes energy to flow?

So I googled "_____ causes energy to flow."

1. intention.
2. cooling to a lower temperature than the pure solvent's freezing point
3. constantly chanting
4. qigong
5. order energy (site is about atheism)
6. coriolis coupling
7. light energy
8. the vacuum
9. an intention
10. a question
11. energywork
12. pressure in the lower abdomen
13. exerting dynamic pressure on teh astral body
14. clarity
15. 3 or more windows or doors in a row (feng shui)

If instead you google "____ causes energy to transfer."

1. temperature
2. water (convection)
3. power switch
4. electron-lattice interactions
5. Coriolis force (! again !)
6. The current of an electron flow
7. flow of charges
8. core collapse (in a star)
9. our unique design (of a bowhunting bow)
10. indexing systems
11. a force or disturbance
12. the resonant interaction between the central wave and its sidebands (on a ship)
13. contact between the fluorophore
14. excitation of the donor
15. When an air molecule hits the little bulb at the end of a thermometer it