Teaching Physics: Knowing vs. Understanding

Paul G. Hewitt makes a noteworthy point in emphasizing the meaning behind symbols in a physics equation, but there is even more to his story. While he focuses on classical physics, the climax of revelation through equations is rooted in modern quantum theory. Newtonian physics “taught” many to lean on the idea of a purely deterministic world whereas the quantum implications touch free will and the basis of human consciousness. These ideas are all touched on by simply considering the implications of an equation. It is one thing to know how to utilize an equation, but mastery can only come through also fully understanding the origins and conceptual roots of a mathematical framework.

While an incredible amount of information can be taught and learned through analyzing the message in any equation, simply understanding the underpinnings of the formulas still leaves individuals mentally separated from the origins of the equations, as if the creation of them is some esoteric work. It almost feels as if, when we work with equations, we are borrowing someone else’s tools. Even students with much experience in physics or mathematics are often left guessing as to how an equation was born.

The key to full understanding lies in derivation — derivation in the sense of determining the inertia of some shape when rotated about an axis as compared to “deriving” Newton’s second law. The derivation process begins with a question. “We have some system here, and we need to describe it using the tools [equations] we have. How do we describe [x aspect] about the system?” Keep in mind that this is derivation as a form of teaching and not experimentation or theory development. Following the question comes the adaptation of one’s current knowledge to the problem at hand. Known foundational equations are rearranged and substituted into each other, the method of the calculus is probably employed, and the end result is tested against the aspect of a system to be described in order to confirm its validity.

Many students today cannot visualize or describe relationships between equations dealing with similar aspects of systems (for example, F=ma and K=(1/2)mv^2). Some do not even know that relationships exist! Mentally, this creates a disconnectedness between mathematical descriptions and deceptively leads students to believe that physics is ultimately a system of memorization. Students do not see the harmony and rationale behind many equations, how from several foundational concepts, today’s physical framework can largely be purely derived. This limits students’ ability to adapt a formula to fit a problem (see Hewitt’s mention of part (a) of the tennis problem in the aforementioned article). Equations become associated with a particular problem type and then are neglected at first sight of a (seemingly) unfamiliar problem.

Notice how the process of derivation mirrors that of experimentation (here I am focusing on experimentation for purpose of teaching and not the modern trend of theory giving rise to experimentation). First, a question is posed or an interest is piqued. Then, by using and modifying foundational information, one can come up with some sort of mathematical description of the experimental subject. Finally, the mathematical model is tested against experiment and observation.

The derivation process reveals to students the purpose and origins of an equation. The need for such an equation is presented and students are then exposed to the actual use of mathematics in producing the equation. This naturally demonstrates the deep harmony behind many equations in physics and reinforces the meaning behind each concept in the equations. Thus it is not enough to understand even the meaning of the symbols in each equation but it is necessary that students understand the connectedness of the physical mathematical framework.


Photo shoot: Kadra

Samples from a shoot midday in May, only a few clouds in the sky. No post-processing.

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Car-to-car communication

I recently read an article on car-to-car communications detailing a possible implementation of this concept. I’m not a pessimist, but following is my initial reaction and thoughts.

The idea of car-to-car communication to provide detailed traffic reports, to alert drivers of possible dangers, and to network people on the road is a good idea. However, how will this simplify driving? I don’t think it will — it will only complicate things. I have witnessed plenty of people who have a hard time holding a steering wheel and concentrating on the road. If they use a GPS, operate the stereo, or use a cellphone while driving, they suddenly appear as if they were DUI. Before a method of integration is determined to seamlessly incorporate car-to-car data into the drivers’ experiences, these “safety features” will only be a distraction. Sure, most people could handle it just fine, but for those who already feel stressed simply being behind the wheel?

Crazy drivers are crazy drivers. No software will change that. Until seamless methods of integration are developed to add all of this extra information into the driving experience, the “safety benefits” (for individual drivers) of car-to-car communication are merely over-hyped security blankets used to gain support for a developing industry. Whatever sells.

Regarding wireless security, I am not too concerned. What concerns me more is the possibility that this useful-by-name technology will someday become so admired that it will become standard (that is, if you don’t want it, you’ll need to pay a price for nixing it). This is just another layer for taxation and insurance companies to farm for money. What if I don’t want my car to be a wireless beacon, hotspot, etc? Yea, I’ll probably end up having to pay to not have this “safer” feature.

I am all for car-to-car communication, but until useful data can be delivered to the driver in such a way that it is a natural part of the driving experience (non-intrusive, that is, not distracting), the reputation for this technology is all wishful thinking.

Peak Detector

First off, please note that the following schematic is only one way of accomplishing the construction of a peak detector. There are several modifications to my design that would greatly increase the practicality of the design (and from a business standpoint, would decrease costs and reduce manufacturing complexity). I’ll make note of these after I demonstrate the schematic and run through a brief explanation.

Below is one branch of my peak detector featuring a lowpass filter.
Lowpass Filter Branch

Working from left to right, we first come across a voltage source (PSpice was used to design and simulate this schematic). The voltage source represents signal coming from the positive wire from a headphone “splitter”. Typical input voltages from an iPod (volume slider at 50%) is in the range of 50mV.

The 180Ω resistor and 10μF capacitor comprise the passive lowpass filter.

Next in line is the pair of cascaded op amps. Both are acting as inverting amplifiers. Note that the first one has a gain of (-1)(160kΩ / 2kΩ =) -80. The negative simply indicates that the AC signal is inverted. The next op amp acts as a unity gain inverter (-1)(10kΩ / 10kΩ =) -1. This simply re-inverts the AC signal.
For this project I used 741’s biased with ±12V.

Finally, we have our LEDs (modeled as a stand-in 100Ω resistor since PSpice does not have a readily-available element for an LED).

Why is the gain so large?
The operational amplifiers need to be able to produce an output that can overcome the LEDs breakdown voltage. Typically, LEDs have a breakdown voltage between 2 and 3 Volts. So we’ll need to amplify the input signal significantly to produce noticeable flashes in the LEDs.

Why two op amps?
Two operational amplifiers were used because at the time of this project’s conception, I was just experimenting with operational amplifiers (and cascading these elements). The use of two op amps is actually very inefficient in this case. Another op amp is just another element to bias and another piece that could fail (unlikely, but saturation — much more likely — will also botch the peak detector’s performance). Also, since audio signals are AC, generally the positive half of the waveform is accompanied by a near-equal negative half. Thus, there is no need to re-invert the inverted signal. The LEDs will still flash, but their flashes will be a half wavelength out of phase. (This phase difference is undetectable by human perception.)
Assuming only one operational amplifier is used, the inverting op amp can be replaced with a non-inverting op amp.

To what frequencies do each channel respond to?
The lowpass responds to frequencies between 0Hz and 600Hz.
The bandpass responds to frequencies primarily between 600Hz and 1,800Hz.
The highpass responds to frequencies above 1,900Hz.

I have not provided the math for this, but if you’re dying to know, I can provide this.

How can I adjust the frequency sensitivities of each branch?
To do this, you’ll need to adjust the respective inductance, capacitance, and resistance values of the filters. Again, I’ll provide or point to the math if desired.

Here are the branch schematics for the lowpass, bandpass, and highpass configurations. These schematics show my first design (with the unnecessary op amps).
Lowpass Schematic
Bandpass Schematic
Highpass Schematic

Fedora: Logging into a GUI as root

Recently I have been experimenting on a Fedora development server. I had a need to login to the GUI as root and found that my credentials always produced “Authentication Failure”. After reading around for some time, as far as I understand, after Fedora 10 the development team has, by default, disallowed logging into the GUI as root. While I won’t go into the annoyance that such a strange limitation has caused, here’s how to reclaim GUI root login abilities.

If you already have a non-root user account with which you can use a GUI, follow Cyberciti’s instructions.

If you were like me and did not create a user profile when installing Fedora (I’m toying around on my dev server and have no need for protection from root or a need of another user account), you won’t be able to login to open a terminal. Fortunately, you can open a terminal at the login screen.

Press Ctrl+Alt+F2 to switch to a terminal. Here you can login (the only choice, if you find yourself needing to use this method, is to login as root — root is dangerous; you can break everything and not be warned about any of it, so use at your own risk). Now from here, you have two options.

Method 1:
Create a new user. I consider this the safer option since you can then login to the new user’s account and work with the necessary configuration files in a GUI. To create a new user, use this template (while logged in as root):

useradd [-p password] name

Replace “name” with the username of the new user, and the -p parameter specifies that the following string is the user’s password.From here, exit the terminal by pressing “Alt+F1”, login to the new user’s account, and proceed with Cyberciti’s instructions above.

Method 2:
This method is for the command-line savvy. Enter the terminal from the GUI login screen and login as root. Use the vi editor to edit the necessary files mentioned in Cyberciti’s instructions. Here are great usage instructions for the vi editor. Of course, first backup each file that will be tampered with in the event that something goes wrong.Opening the first configuration file in the vi editor can be accomplished with:

vi /etc/pam.d/gdm

After either method, it may be necessary to restart your computer before the changes appear to take effect.

Idea: Universal Coupon Bank

I was talking to someone today about customer loyalty programs and coupons. In this case, corporate was planning on pushing out 24,000 coupons to registered customers. The plan is to have an online coupon activation where each customer is given a unique customer ID. To protect against customers generating coupons, each coupon will be validated for a particular customer ID and paired email address. Immediately I thought, “hey, they’re giving out coupons without actually giving them out.” Save paper, save time. It seemed like a great idea to me.

Then as the conversation continued, I realized that this wasn’t their intention (they weren’t too concerned with digital coupons for the sake of not using paper — they just wanted a cheap way to distribute coupons to registered customers without worrying too much about coupon generation or actually physically mailing coupons). This is a small fast-food company we’re talking about, by the way. I saw great potential but also a huge issue. Today, the last thing most people want is to memorize another username and password, another customer ID. The idea is great, but having customers remember their customer ID seems quite unfriendly.

What if there existed a web-based service where users could create an account. Businesses could then offer a digital version of their coupons that could be credited to a user account. Like checking in with “Places” when you leave your home, you could “check in” at the in-store register with your coupon profile. If you have a coupon credited to you by the store you’re shopping in, this coupon can be “used”. You get the discount or promotion and the web service destroys the coupon. Just like using a coupon from the mail, minus the physical coupon. The upside to this service is that businesses would hopefully adopt and support the use of this service, so one account will hold a shopper’s coupons for many stores.

No need to memorize customer IDs, no need to tote many coupons around and clean up after expiration dates, no need for membership cards. Just remember one username and password, or even link the service to your Facebook, Twitter, etc (obviously more privacy issues will ensue, then).

Is this already being done? Am I out of the loop?

Tech Tools to Boost College Graduation

Computer Lab

Computer Lab (FreeImageWorks.com)

Recently Read Write Web featured an article discussing the Gates Foundation aim to increase college graduation rates by funding the use and development of “tech tools” to aid students in college education. Tech tools for the sake of education are absolutely necessary and are very much a good investment, but there is a bigger problem at hand (independent of the amount of technology employed) in regards to relatively low graduation rates.

Many colleges these days are so non-collegiate, if that makes any sense. A large part of the purpose of “going to college” is to prove to professors and future employers that

  1. I (the student) am responsible for my own education. I can diagnose my academic issues and seek the necessary help.
  2. I am able to manage my time well and motivate myself for my education and academic challenges.
  3. I work to master (or excel in) my field’s theory and practice, and I will eventually obtain a degree to prove this.

ReadWriteWeb (RWW) outlined the challenges that grant winners were to focus on. The second mentioned is quite curious. If one needs to spend more money on and develop technology for “encourag[ing] deeper learning and more engagement”, I’m convinced that the issue does not arise from the academic environment nor available technology. It’s true that not everyone will enjoy what they study in college or what they do at work (unfortunately this describes many people), but if one needs to be motivated towards deeper learning in college, it is perhaps best that the individual reevaluates the purpose of college in his/her life.

Learning Analytics are also great, but again as RWW outlined, the purpose of these analytics are to monitor students’ progress and offer better support. Again, this is wonderful in theory, but the act of actually doing this could be detrimental. I can see a classroom attempting to cater to each student’s needs actually handicapping students that take this for granted. Of course I’m being extreme here, but I don’t think it’s too hard to see that when a course caters to individuals’ academic needs, it removes the necessity of self evaluation. That is, students will be even less driven to identify their academic struggles and to seek the help that they need. This process is part of the maturity that should be fostered at a college (because, unfortunately, it seems this is becoming “too complicated” for students even in high school).

Regarding my third point about the purpose of college:
It seems that many today see college more as an opportunity to obtain a degree with an education on the side rather than a place to master theory and practicality in a particular field or focus and then receive a degree to prove this. Of course, another problem in this observation is the nature of degrees themselves (an average student can very well obtain the same degree that an “excellent” student can), but I will not focus on that.

It is necessary that colleges have the proper technology available to compliment a student’s education, but it is missing the point of higher education when technology is used to encourage understanding. If a system holds students’ hands too often, it is more likely that the student will not be challenged to mature academically nor as a responsible human being in general (to the extent that a challenging school would encourage this). Of course, I am being extreme again, and this idea certainly does not cover every student, but the possibility still exits.

I’m happier to see the Gates Foundation targeting middle schools with these hopes (implementing “tech tools”), as RWW outlined, as I think that employing technology at this level in education is much more stimulating and will motivate students to motivate themselves.

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