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A Closer Look: Scientific Models
What is a scientific model?
As stated in the video, a scientific model
is a “testable idea… created
by the human mind that tells a story about what happens in nature.” Another
definition is “a description of nature that can predict things
about many similar situations.” Models are developed when a scientist’s
creativity and insight are combined with data and observations about
many similar scenarios. Scientists try to identify and generalize patterns
in
these observations, and use mathematical language to predict the outcome
of related situations. The value of a model is that we can trust its
predictions about similar situations even if we don’t encounter
each situation.
Let’s look at a simple example. Although most people
in 1492 thought that the Earth was flat (because that is what they observed),
nearly all
educated people knew that the Earth was a sphere. The difference in the
spherical model of the Earth and the prevailing model of the time led
to differences in predictions: Columbus, for example, knew you could
not “fall
off” the edge of a spherical Earth. By knowing the radius of that
sphere, one could calculate its circumference (C = 2 * Pi * r) and thus
plan an expedition to have enough supplies to reach a far-off destination.
 
In
the same way, basic evidence was used to determine that the Earth is
round, some of the most powerful insights into nature can be obtained
from
a model based on a few simple ideas. It is this kind of model that
we will be developing in this series for the structure of matter.
What makes a model “good”?
Any model is based
on a certain set of observations. A good model must be able to explain
as many characteristics of these observations
as
possible, but also be as simple as possible. This second point
is a restatement
of the “Occam’s razor” principle alluded
to in the video. To extend our spherical-Earth example, sailors
in the fifteenth century
also noticed that a ship appears to “sink” as it
goes over the horizon — the last part of a departing
ship you can see is the top of the mast. The “spherical
Earth” model
explains this well: the curvature of the Earth becomes visible
as you deal with greater
distances. This model also explains why the “sinking” illusion
happens regardless of what direction the ship moves away from
you: a “spherical
Earth” curves “downward” in all directions
from someone standing anywhere on its surface. Both aspects
of this
observation are
explained well by our model.
In addition, a good model must
be able to explain phenomena that are seemingly different
from the ones we used to develop
the
model in the
first place.
For instance, even though the “spherical Earth” model
was used to explain sailing phenomena, educated people were
able to link this idea
to lunar eclipses. A lunar eclipse happens when the Earth
passes between the Sun and the Moon. If we subscribe to the “spherical
Earth” model,
we would expect the shadow of Earth to be round as it passes
across the Moon — and indeed, it is. This new, seemingly
different situation is explained with the same model.
An example of a model
that doesn't
stand up
as well to Occam's razor is the "continuous," "continuum," or "plenum" model
of matter presented in the video. In an extended interview,
science historian Al Martinez described how a proponent of
the continuum
model might use
it to explain how a container of air (like a syringe) weighs
the same whether the air in it is compressed or not.
Dr. Martinez
pointed out that a particle theorist can easily explain that
there are the same number of particles of air
in both the
open and closed
syringe, but that they occupy less space. A continuum theorist,
however, would have to cite Aristotle’s theory of four “elements,” which
states that everything in the world is made of some combination
of Earth and water, the “heavy” elements, and
air and fire, the light elements. According to the continuum
theory, the air
that is contained
in the syringe would actually be composed of a combination
of air, fire, earth, and water. Hence, when you push in the
plunger of
the syringe, you
would lose some of the light matter and some of the heavy
matter through the walls of the syringe, allowing for a net
difference
of zero in the
weights.
Likewise, the continuum theorist would say that
when you pull the plunger out, air flows back in through
the walls
of the
syringe. The question
then becomes, If there's now more matter in the syringe,
why doesn’t it
weigh more than it did when there was less? According to
another feature of Aristotle’s theory, some of the
air that comes into the syringe actually has negative weight,
or levity, because it contains
air and fire.
Because it has levity, it tends to go upwards, which counteracts
the heavy matter that flooded in, this accounting for the
fact that, again, the difference
in weight is zero.
In this example, it is clear that the continuum
explanation is less elegant and economical than the particle
one. It's
interesting
to
note, however,
that it took from Aristotle's time until the eighteenth century,
when more was learned about gases, for the continuous model
of matter to
finally get "cut" by Occam's razor.
When do scientists
change a model?
No scientific model has ever been totally
complete. When credible observations of a new situation come into conflict
with the
predictions of a model,
something must be changed because either the data or the
model is incorrect. Although Columbus used the “spherical
Earth” model to predict
the length of his voyage to the Indian subcontinent, his
estimate of the Earth’s radius was much smaller than
what we now know it to be. Thus, Columbus underestimated
the circumference of the Earth
and the length of
his voyage to India. (Fortunately for Columbus, there were
two other rather large continents for him to reach before
he ran out
of supplies.) Later,
the model of Earth as a sphere was refined to include a better
estimate of its radius, and thus make better predictions
about distances to locations
on its surface. The model was correct, but its parameters
had to be refined.
We will see in the rest of the series that our particle
model will not have to be thrown out when it doesn’t
sufficiently explain new data, but adding some detail or
refining some parameter of
the model will explain
these new observations.
Limitations of models
All models have limitations — no
model can possibly explain every detail of a scientific phenomena. For
instance, if we wanted to predict
the distance we would need to travel from one side
of the country of Nepal to the other, we could predict it using our “spherical
Earth” model,
but we’ll find our estimate is far from accurate.
Why? Although the Earth is a sphere, there are many
topographical features on its surface,
including the Himalayan Mountains, which span Nepal.
Although we could add all the mountain ranges in the
world to our “spherical-Earth” model,
this would make the model quite complex and defeat
the utility of having a simple model to make useful
predictions.
Similarly, we will find that, while our
particle model
explains many things about matter, it is not comprehensive — for
example, it cannot predict why certain materials have
different electrical
properties. We could add
further refinements that are outside the scope of this
course to enable it to do so, but it would make our
model so complicated
that it would no
longer be useful to us.
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