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Friday, March 28, 2008

Epicycles & Electrons, Part III



Truth and utility are different. Consider a tool I learned to use while in the Navy, the maneuvering board, or moboard, pictured here. The way it works is this: you note the distance to another ship and the bearing and mark it with an X. Then, after a set number of minutes, you do it again. With this information, you can determine how close the other ship will come to you. A skilled user can determine maneuvers to increase that distance or to position your ship in some position relative to it. It is also a good way to recognize vessels on a collision course with you, Constant Bearing Decreasing Range, CBDR in Navy parlance, or stationary objects, which will present as having a reciprocal course and equal speed as own ship.

The first assumption of the moboard is that your ship is stationary. Everything moves around your ship. It is a very useful tool, and I bet many captains still require their officers to be competent with it.

Now consider Ptolemy again. Why can’t the Earth be the center of the solar system? We know that the idea of stationary (and simultaneous, btw) is arbitrary. There really is no such thing as stationary. Let’s make our convention that the Earth is the center, the Sun and the Moon revolve around the Earth, as do the planets, although obviously their orbits are distorted by the gravitational pull of the Sun. [FN1] The only reason not to do this is the math would be more complicated. There is no so-called truth about what is stationary and what is moving.

But that’s wrong, isn’t it? Although stationary is a convention, it is more true to describe the Earth as orbiting the Sun and the boat as approaching the buoy. There is a truth, perhaps a relative truth, outside of utility.

[FN1] You cannot make the Earth non-rotating. If the Sun was to be modeled as moving completely around the Earth every 24 hours, there would be forces involved that would have to go unexplained. Also, it’s speed in relation to the Earth would be a problem.

6 comments:

Christian said...

The Earth can be the center of the universe. The only problem is that is model is of very limited usefulness.

I agree with Josh's earlier post that a model is judged on the basis of its usefulness and predictive power. As my control systems professor once said, "all models are false", it's just that some models are less false than others.

I'm wrestling with the ideas of "truth" and "model". Is a "true" (or complete) picture of something knowable, or can we only hope to create ever more refined models of what we think "truth" is?

I'm inclined toward the later, in which case models are again judged by their predictive power and usefulness. By extension, we infer that "useful" models represent some objective reality.

JimII said...

Chris,

In the month board example don't we use a model that is false but useful, while the Bohr model involves a model that is trying to be "true"? Isn't there something fundamentally different between the two models' goals?

Matt Dick said...

The key here is "prediction". As Chris points out, models should predict something. Your moboard predicts relative position and motion of ships, and as such a model it arrives at a useful truth.

Bohr's model predicts the behavior of electrons.

Both are false but useful, yes? I agree that the Navy doesn't use the moboard because it reveals any kind of truth, and the Navy would let sailors knit sweaters if it produced correct firing solutions, but at its core, any model is employed if it produces results -- either useful to the Navy as it strives to predict relative locations, or to the physicist as he strives to understand the basic nature of the world.

Christian said...

Within the context in which it is used (avoiding collisions), can one say the moboard model of the universe is false? Likewise, within the context of simple chemistry (e.g. valance electrons and filling shells) can one say the Bohr model of the atom is false? For what they try to do, and what they can do, I don't see much in the way of qualitative difference between these models.

What's different perhaps is the historical context under which each was derived, and the intended use for each model. I agree with you there. Bohr was struggling to come up with a new and more complete atomic picture, so he incorporated all available knowledge. The US navy (or whatever navy it was) wanted a tool to make sure their ships didn't run into each other, so they ignore any non-essential information for this requirement.

This seems analogous to the bind superstring theory is in right now. On the one hand, it is a useful model for understanding why particle masses and forces are what they are. On the other hand, it is difficult to test. So, how do we know if superstrings are the "truth" or a convenient "moboard" for thinking about the universe?

james said...

I think Jim is trying to make a distinction between models which strive to predict a result/measurement/event, and models which try to "describe the world as it truly is." In the example of the moboard, its creators knew from the outset that the given conditions that model would use were not "real" (i.e. in no way sensible to our ability to perceive the world is the ship sitting still while the ocean, land, and other ships stream around it). The moboard is an accurate predictive tool, but at the same time a knowingly "false" model of the universe.

On the other hand, weren't Ptolemy and Bohr and others like them engaged in "model making" that strived to not only match mathematical prediction to events, but to do so within the bounds of a "more accurate" physical representation of the perceptible universe? Didn't Bohr hope that "discrete electrons spinning in discrete orbits about a nucleus" was, at least to a greater degree than previous models, what an atom was "really like?"

Perhaps the distinction between the two categories can be eliminated if we consider how "realistically" the moboard inventors represent the aspects of the perceptible universe that their model directly addresses - newtonian relative motion and time - and ignore what it only tangentially imitates - cartesian position.

Or perhaps you can chalk it up to the difference between "science" and "engineering."

Somewhat tangentially, can scientific progress, physics at least, be defined by how much it has given up trying to match its models of how the universe "really is" to any kind of direct human perceptibility (in favor of mathematical rigor)? (Parhaps only to the layman, as the more removed the theories get, the more sophisticated the tools become to allow us to sensibly [i.e. with our natural senses] perceive predicted events and effects that in description would strike us as nonsensical, even though that perception is sometimes indirect.)

Finally, Jim, were you wondering if this discussion of models could be applied to perceptions of God or the divine? Are there, or can there be, "models" of God which are useful, even "predictive" (of human realtionships, emotions, love, redemption, inspiration, etc.), while not being representative of "how God really is"?

JimII said...

James,

Jim, were you wondering if this discussion of models could be applied to perceptions of God or the divine?

I sure was. I wanted to let you know I did read your comment before finishing up, but yes the whole EE thread was intended to be an extended metaphor for modern understandings of God and the pursuit of understanding God.