Modern science often seeks most simple reasons for various observations.
Ockham’s Razor = logical principle that encourages
the shaving away
of un-necessary assumptions, or else
cutting apart of two similar theories.
principle: It is futile to do with more things, that which can be done with fewer.
The things
that Ockham was thinking about were
steps (or links) in chains of reasoning.
William Ockham was a 14^{th} century Franciscan monk born in Ockham (Surrey), England.
Despite its inherent complexities/difficulties, mathematics is often simplest and most reproducible way of explaining science.
For physics & statistics, we’ll use our intuition to guide reasoning, allow algebra to do the heavy-lifting involved with testing hypotheses.
Algebra used to describe real-world situations is often called
modeling
or a word problem
.
We will use mathematics (algebra) as an empirical science in which type of algebra is changed to best represent observations.
Mathematics itself is not shifted to represent data; rather equations particular to a situation will be adapted/changed to give best match w/ observations.
We will learn modeling as a new skill
.
Aspects of algebra that you’ve never seen before will
be introduced as their own new science
.
I will present new methods to you;
we’ll analyze the meanings of the new methods;
we’ll also expand the meanings to new situations.
Calculus (Newton’s methods) will not be used (except for a few basic concepts).
Alternative presentations of concepts or methods are encouraged.
Video presentations of physics concepts not always useful
because they’re not an active
experience, and leave
students with nothing to do after video is over.
Course goal: help students prepare for MCAT physics test.
When/if you take that test, you’ll need to spend time on your own preparing for it.
Some commercial test preparation programs (such as Kaplan) help you prepare via test strategies, educated guessing, elimination of unlikely alternatives, etc.
This course will focus upon knowing the material.
I will try to present a well-organized view of what you need to know.
Intrinsic difficulty w/ math.:
Formulas used as assumptions in science mean either:
nothing to the human observer,
far more than human observer intended.
Even if you manipulate formulas using valid methods, meaning of formulas may be broken because of difficulties arising from part a.
Partial cure: whenever we use formulas to represent scientific meaning, we need to have a clear story about both:
assumptions,
methods of algebraic manipulation.
When inferences go wrong, we can trace back through formulas and manipulations to modify either assumptions or methods (or both).
Big message: Do not back down when facing something unfamiliar or difficult.
insist on explanations, & link those in your thinking to arrive at an answer.
Then ask, Does this answer both adequately and
intuitively satisfy the question?
Make physics fun!
roughly equals Make my first
golf outing fun!
; this is not possible.
When you learn to get ball off grass, and start hitting it, the game becomes a challenge. This is an adult person’s version of fun. Achieving difficult goals is fun.
My approach to science: dig deep and see the beauty that exists in a detailed view of the universe.
This damselfly is out there! It’s in the ditches next to your home. It is an organism of stunning beauty. To see it you need to quiet your mind.
Science often requires you to gently look at the universe with the innocence of a three-year-old, and the laser-focus of Isaac Newton.
Attention to detail is a very strong thread in science of the past four hundred years.
To whatever degree you can understand a mathematics-based approach to physics, you should do your best to acquire that vision.
Pay strict attention to detail, identify the parts of an inference, & tell yourself the story of that inferential link, so that it becomes a thing of beauty in your imagination.
Mathematics required is light (not in-depth), but application to physics is very diverse in ideas w/ new snippets of math. used to support physical ideas.
Snippets of mathematics often come out of the sky
, and
jumble of ideas can be challenging if you do not discipline
yourself to reading and study.
You need to pick apart the mathematical links in the scientific story. Note that math. is a foreign language for all humans. We will identify:
mathematical nouns,
mathematical verbs,
mathematical prepositions,
in order to parse mathematical models for physical meaning.
We will also frequently employ a pattern of solving problems where we cycle repeatedly through a series of steps:
INTUITION
VISUALIZATION
EQUATION DEVELOPMENT
EQUATION SOLUTION
SOLUTION INTERPRETATION
Try to avoid crisis mode when dealing with class work (i.e. do not delay preparation until the night before a test).
Develop your own set of classroom notes and examples taken from lectures.
Prepare starting from first day by:
skim through textbook reading,
do a more careful read of text, and create tiny calculations from text examples to train yourself,
re-copy your notes from that day, and begin to attempt exercises from back of each chapter,
purposefully follow the five part sequence of steps to crack apart the more difficult exercises.
Most important: you need to maintain an open mind, and a willingness to learn both the physics and the mathematics needed to succeed.
Be certain to take advantage of opportunities to work w/ other students and benefit from their insights. Do this face-to-face!
Do not be a minimalist in your study and preparation. This interferes with both your ability to transfer knowledge to others, and your capability to innovate and generalize.
Physics classes and laboratories are not an
out-of-body experience. You need to always
participate, be on your toes
, and always think about how
different aspects of laboratory and coursework point toward bigger
generalizations and principles.