We discussed the question "What is science?" One thing we pointed out is that this is a philosophical
question and not a scientific question. Another issue raised is that science was not always seen as distinct
from philosophy, and we gave a few examples of people who were both, like Aristotle, Descartes and
Pascal. Prior to making a distinction between science and philosophy, such people were said to be
studying "natural philosophy."
We considered science as the study of "reactions" in a natural (as opposed to man-made) system. Then we
began to delve into ideas surrounding the "scientific method" -- that to do science we will make observations
of natural systems (scientific knowledge is empirical knowledge), make a hypothesis, and then test that hypothesis
(an experiment).
The notion of falsifiability was raised.
This idea says that a scientific hypothesis should be falsifiable -- an experiment or observation should be able to
establish that the hypothesis is incorrect.
In order to contrast mathematics and science we brought up the distiction between deductive reasoning and
inductive reasoning. Deductive reasoning can lead to absolute validity ("proof") but is limited to formal logic
and mathematics. On the other hand, science uses a type of induction reasoning
(Induction
and Scientific Reasoning Kevin deLaplante on Youtube). Falsifiability tries to bring a level of proof into
scientific reasoning -- in that a scientific hypothesis cannot be proven true but can be proven false (or
contradicted).
(Philosophy of Science I
by Massimo Pigliucci on Youtube)
Wednesday:
We discussed Archimedes (C. 287 BC - c. 212 BC) who lived in Syracuse (Sicily) which was then part of Greece but
taken over by Romans at the end of Archimedes' life (he was killed in the Siege of Syracuse). Archimedes is famous as a
mathematician for calculations of pi, various areas and volumes. He is also famous for his design of various weapons
used to defend Syracuse. But we are focusing on two of his results from physics: levers and water displacement/buoyancy.
We briefly discussed the lever (which we will return to later) as an example of a simple machine. ("Give me a lever
long enough and a fulcrum on which to place it, and I shall move the world.") Other simple machines include
the pulley, screw, and inclined plane. I mistakenly dismissed the suggestion of the wheel, but like the other simple
machines, the wheel and axle can be used to gain a "mechanical advantage". A machine's mechanical advantage reduces
the amount of force required to achieve some task. For example, using a pulley one can lift an object using a force
that is less than the object's weight; however, one pays the price of having to apply the force through a greater
distance. (We will say later that the amount of work required is the same.)
Then we turned to Archimedes and the crown. We talked about density -- that a solid cannon ball and a hollow cannon ball
would have the same volume but different masses -- so that their densities (density = mass/volume) would be different. If the
crown is made pure gold, then it should have the density of pure gold. The density of gold can be establihed by taking
an amount of pure gold and measuring its mass with a scale and calculating its volume -- say if it had a simple box shape
using length times width times height. The crown's volume could not be as easily calculated but Archimedes realized its
volume could be determined by the amount of water it displaces.
We went on to consider than if an object's density was less than water that it floated and similarly that an object seemed to
weigh less when in the water as it experiences a buoyant force. Since the water was previously holding up part of itself,
it will apply that amount of force (equal to the weight of the water displaced) to the object. So an alternative approach to
determining the amount of water displaced is to observe the differnce in weight in air and the "weight" in water.
