Lec 1
This course is about making mistakes. However, I don’t want you to go home and tell your parents that I am teaching you how to make mistakes.
What is the focus of most of your classes? They focus on teaching content. The content I’d like to cover is relatively straightforward. If you don’t make mistakes then you can probably learn this content without me. However, I’d like to focus on the theme of how to learn from mistakes.
There are lots of ways mistakes are made. When you reach for a coffee cup you need your vision to correct for mistakes you hand makes in finding the cup. Feedback from your eye to the muscles in your hand allows you to survive. When you collect RC data the A/D makes mistakes both in accuracy and precision (sketch the digital signature on the scope as it jumps between bits). There are mistakes between precision and accuracy (the bullseye target is used to show this difference for a voltage measurement: darts together show precision but when not at the target center they are not accurate).
In experimental science a big mistake is not to repeat a measurement. For example, a student measures a voltage with a 6 digit voltmeter and writes the result down without repeating (2.24312 V). Repeating the measurement reveals that only 3 digits are the same (2.24989, 2.24156, 2.24375). Repeating is the simplest way of determining mistakes or error in your measurement. However, this doesn’t address accuracy issues.
Remember when I asked you to draw the circuit diagram for RC decay (sketch what is found in most texts: circuit with battery in it)? Try not to think of this as a test where you will be judged about any mistakes you might make. Rather, try to think of it as a challenge for you to solve.
I’m here to help you learn when you make mistakes and not keep a scorecard of mistakes. You learn by making mistakes. There is a Roman saying (write on the board), “quae (what) nocent (hurts) docent (teaches).” Mistakes hurt. Don’t tell your parents that I’m out to hurt you. What I do want is a demonstration of your effort to address these challenges in the course, such as the lab reports. You are all capable or you wouldn’t be in this class.
Don’t be afraid to sketch these circuit diagrams. I hope you feel comfortable in making mistakes and asking questions.
What did I get in the RC lab reports? Some students effort was to determine RC. Others sketched V vs t and said it looked like exponential decay. Others started trying to use the lab to demonstrate PLC. Some compared RC measured the 1/e time from the data with the product RC
What did I expect in the RC lab? I expected an application of the scientific method. What does that mean? That is, does data support your model RC decay. The model from PH200 is V(t) = V0 Exp[-t/RC]. There are many assumptions that lead to this equation which are not realistic. What might they be? I have seen many student reports which display a graph of the data that the author says looks exponential so the model matches the data. When you finish this class I expect you to be able to write more of a professional looking report. One that quantifies the error to conclude that the data do or do not support a model.
How to quantify errors in modeling (see section 3.7 of Baird’s book “Experimentation”) Use the RC decay as an example. Assuming the decay is exponential then the second prediction of the model is that V(t) = V0 e^[-t/RC]. This is the working equation or one which contains all measurable quantities.
On the other hand, an equation like e/m = V/(B^2 r), where V is the voltage, B is the magnetic field, and r the electron beam radius, is not a working equation if you don’t measure B. In this lab you will measure the current in the wires which generate B.
It is from the working equation that we can determine the effects of all measurable quantities on the model.
How do errors in t, R, C, V lead you to determine if the voltage data support the model? Two ways: Adding errors without calculus. See http://web.uvic.ca/~jalexndr/192UncertRules.pdf Adding errors with calculus -Working eqn using RC decay as an example. Make a table with columns for V from the model, V measured, V0, time, R, and C values.
-Add errors in quadrature. Review calculus: dV = partial V/partial t dt+ partial V/partial R dR + . . . These can add to zero if some are positive and others negative and cancel each other. Use quadrature: Square root of the sum of the squares of these derivative terms.
-Next add to the table a column for this error. Note that each derivative is evaluated at the particular time and R, C values used.
-Do the entries along a row for V model match V measured with the error in that row? Is so then the data support the model. If not then they do not support the model.
Why do people go to college?
What do universities think they provide to students? What is the value of their product (their degree)? http://www.stonybrook.edu/commcms/cas/liberalartseducation.html
Liberal arts schools' value proposition is that students learn critical thinking skills. How do they know this (critical thinking question)? They need to measure that these skills are increased to justify this statement (voltmeter → critical thinking meter). This meter, like a voltmeter, must be reliable (same measurement when repeated) and valid (actually measures what is says it measures). The analog A/D that is used is a Likert scale multiple choice question.
What would someone at a Liberal Arts school say about Mines? “They just train you to use Newton's laws (plug and chug). You don't learn when the formulas are not valid. You don’t look at the assumptions of the model (R and C are constant). You don’t learn critical thinking.”
For example, you have some formula to test if a model fits the data. You plug and chug but don’t really understand what the limits of those formulas are and therefore when they breakdown.
In this class I want you to focus on data and its error (or mistakes) to determine if the data supports a model within error (or mistakes).
It is often more subtle than that. For example, in processing your RC data to eliminate 60 Hz noise you integrate the voltage across the capacitor. What complication does that generate?
Critical thinking is all about understanding mistakes.
I want to focus on the critical thinking aspect since that’s a common theme for value propositions in most universities.
