Monthly Archives: February 2014

Breaking Bad: Making Meth… I Mean Aspirin!

Breaking Bad

Image: Ursula Coyote/AMC

Today I made aspirin. Next up… meth! I kid. At chemistry lab tonight, we synthesized aspirin–it was pretty cool.

I find it amazing how creative and yet utterly logical that chemists have to be to come up with a procedure for synthesizing a specific chemical. In order to arrive at a destination (aspirin in this case), the chemist has to follow a very specific procedure. Well, not necessarily. There are multiple procedures and multiple ways in which each step can be accomplished, and that’s where the creativity comes in.

Let’s say you want to make C9H8O4 (i.e. aspirin). From the formula, we know that each unit of aspirin contains 9 carbon atoms, 8 hydrogen atoms, and 4 oxygen atoms. The problem is, we can’t just take 9 moles of carbon, 8 moles of hydrogen, and 4 moles of oxygen, put it all in a bag, shake it for a few minutes and open the bag to find aspirin. Oh, no! We’d probably be left with a pile of carbon at the bottom, oxygen gas in the middle, and a bunch of highly flammable hydrogen awaiting us at the top of the bag.

The puzzle is, how to we utilize the different properties of different chemicals to create a specific chemical that we don’t yet have? Well, in our case, we mixed salicylic acid (the stuff you put on warts) and acetic anhydride (it’s basically dried vinegar) together and added a few drops of phosphoric acid to speed things up. Then we applied heat, which caused the stuff to magically react to form something that was not in the test tube to begin with. Who would’ve thought? But now our aspirin is contaminated by an excess of acetic anhydride. How can we get rid of it? I know, let’s add water! (I’m trying to think like the chemist who invented the procedure.) That will turn the acetic anhydride into vinegar which can be filtered out of the aspirin crystals. That’s basically the process we used to synthesize crude aspirin. If you’re interested, you can find the full procedure here.

Our class’ synthesis of aspirin was simple by chemistry standards, but it gave me a peek into the mind of a chemist. A chemist is much like a chef. A chef has an extensive knowledge of the properties of different foods and spices. He or she thinks logically–following multi-step procedures in a specific order to create a product worthy of awe. The chef is precise–too much or too little of any spice will ruin the product. The true chef is also creative–the true chef experiments and designs new procedures that yield amazing new products. The chemist, I’ve come to see, is much like the chef. There is careful precision, there is a lot of logical planning and procedure-building, but there’s also creativity and experimentation. If I wasn’t so set on making Star Trek a reality, I would be quite happy being a chemist.

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Categories: College, College Life, Science | Tags: , , , , | Leave a comment

How to use your Video Camera as an Infrared Detector

Many modern video cameras have a “night” mode, which allows grayish video of close subjects to be taken, even in utter darkness. This feature means that such video cameras can be used as infrared (IR) detectors–they can pick up infrared light that is invisible to the human eye.

The video camera I’m using today is a Sony DCR-SR45. It’s not a high end camera, and I purchased it used, but it has “Nightshot Plus,” which I’m interested in today.

Here’s how the night mode works on these cameras:

1) An infrared light on the front of the camera illuminates the subject with infrared light. You might see the near-infrared output of this light as a faint red glow if you look directly at the video camera when it’s in night mode.

Infrared light source on video camera

2) The infrared sensor in the camera picks up on the reflected IR light to render the picture. If you’ve ever used such a camera, then you know the video it produces when you’re using night mode is grayed out and looks something like the following:

Nightshot Mode

So what can we do with this IR detector? Well, one of the easiest things we can do is check if our TV remotes are working. Most TV remotes work by broadcasting an IR signal to the TV. To the naked eye, this IR light is completely invisible, but not to our IR detector. Check out the side-by-side video captures of a TV remote without and with night mode:

IR remote through video camera with nightshot

If you want to try it for yourself, just point the TV remote at your video camera (which should be in night mode) and press a button on the remote. If you’re watching the screen on the video camera, you should see the little bulb on the tip of the remote turn into a rapidly flashing light.

To the naked eye, the infrared light from the TV remote should be completely invisible, but even video cameras without night mode may detect some infrared light (see the left picture above). Turn it into night mode, however, and the IR emission from the remote becomes practically blinding.

Another interesting use for your IR detector is to tell from a distance whether a heat source is radiating thermal energy in the form of IR radiation. Recall from physics class that heat is transferred three ways: conduction, convection, and radiation. If you run really hot water through a faucet and take a look at it through a video camera on night mode, you won’t notice anything unusual. This is because the hot water isn’t transferring much heat through IR radiation. If you hold your hand close to the stream of hot water you won’t feel much. Touch it, however, and the heat from the water is conducted into your hand. Now take a look at a radiative heater through your IR detector, and you’ll see something interesting. In regular video, the heat source in the heater appears orange but it’s well-defined. Turn on night mode, and the heat source turns into a bright diffuse glow. It’s particularly interesting, to watch such a heater warm up through a video in night mode. When the heating tubes (or coils) are cold they look well defined (but monochrome) in the video. As they heat up, they become enveloped in a diffuse, white glow.

Visible-IR Comparison of Radiative Heater

If you’re the nefarious type, you may find our IR detector very useful. Security cameras with nightvision capabilities usually illuminate their field of view with infrared LEDs. To the naked eye, this illumination is invisible, but point a video camera with night mode toward a house with nightvision security cameras, and those security cameras stand out like spotlights.

One thing I haven’t tried yet is to point the video camera in night mode toward a circling police helicopter to see if they’re using an infrared spotlight to illuminate the ground. Some day I’ll check it out. I’ve always been curious whether or not our local police chopper uses IR technology to track suspects.

Categories: Poor Mad Science, Science, Technology | Tags: , , , , , | Leave a comment

CourseNotes: MAC 1105 College Algebra

I am your friend! - Calculator

I am your friend!

When I enrolled in college, my placement scores allowed me to skip college algebra. I decided to take it anyway because it had been several years, and I was sure I was rusty. I’m so glad that I took it. I’m currently studying calculus and analytical geometry, and I gotta tell you. If you’re taking algebra, don’t slack. If you do you will seriously regret it when you get to calculus. You can breeze through pre-calculus and trigonometry without being an algebra ninja, but not with calculus. It’s just like my calculus professor said–the hardest part about calculus is algebra. You’ll repeatedly use algebraic techniques that you thought you would never see again. The slope formula? That thing will beat you silly the first week in calculus if you don’t learn it now. In calculus, you will literally use everything you even just glanced at in algebra. Furthermore, your calculus professor will be disappointed that you didn’t see more things in algebra.

I don’t have a lot of advice for students taking algebra, but following are some of my thoughts. I’m sure your professor will drill it into you, but I should probably say it too… good note taking and practice are the key.

Modelling

Modelling problems, otherwise called “application problems” or “word problems” are often the most difficult part of mathematics for most students. It takes me more time to solve a modelling problem than it takes to solve other problems, in fact, I would even say that modelling problems are more difficult than other problems. However, where I differ from a lot of math students is the attitude I have toward them. I like them. I find them challenging. To me, they’re puzzles, and I love solving puzzles. There is a very real benefit to doing modelling problems and that is that it takes all that abstract mathematics and turns it into real, useful, tools.

Most of the modelling problems encountered in college algebra involve geometry, interest calculation, mixtures, uniform motion, rate of work done, or proportions. My suggestion is that you try to figure out a general procedure for each different type of problem. Some of these procedures involve the applications of formulas. For example, for simple interest calculations we use the formula I = prt (interest = principal * rate * time) and for uniform motion we use d = rt (distance = rate * time). For other types of modelling problems, you can learn specific tactics that make it easier to solve any problem of that type. For example, draw the problem if it involves geometry, and for mixtures; make a table. The takeaway here, is that general solutions/equations/procedures are extremely helpful when you’re ready to solve specific instances.

Absolute Value Equations and Inequalities

I’ve always had trouble with absolute value equations and inequalities, and so I think do a lot of other people. I try to remember the specific procedures, for example; |x| = a means x = a or x = -a, but come test time, I end up confused and unable to remember the procedures. The only thing that saves me is to think logically about a given case. It often helps me to draw a number line and then mark it up with interval notation and arrows to show the values that x can take.

When working with absolute value, it helps me to think of it as distance. For example |x – 3| is just the distance between x and 3. Distance is always positive–just like absolute value. If given the problem |x – 3| < 9, I would start by drawing a line with an arrow at each end (my number line). I know that the distance between x and 3 is less than 9, so I mark a spot for 3, a spot 9 units to the left of 3, and 9 units to the right of 3. I know that x must be between those outer two points in order for it to be within 9 units of 3. Then my answer is simply 3 – 9 < x < 3 + 9 or -6 < x < 12. What is |x|, you may ask? Well, it’s just the distance between x and zero.

Your Calculator

Your calculator is your best friend. Learn it well. Your calculator will save your life repeatedly when you’re in the midst of battling an exam… assuming you’ve learned how to use it. You must learn how to graph functions and use the trace and intersection features. This will allow you to double check your algebraic work as you go along. You also need to know how to enter an equation and then use the table and VAR features to try different values for x. These skills are guaranteed to save your ass and to save you time in the long run.

Also, be sure to read my post on avoiding mistakes in algebra.

Categories: College, Course Notes, Math | Tags: , , , | Leave a comment

Phi Theta Kappa Membership

Phi Theta Kappa Certificate

Phi Theta Kappa Certificate

The other week I received an email from my calculus professor (she’s the advisor for my college’s chapter of the society) notifying me that I qualify for membership in Phi Theta Kappa–the honor society for 2-year college students. Among other eligibility requirements, one must have completed at least 12 credit hours and have a current GPA of at least 3.5.

The eligibility requirements are pretty low, I think, but I still feel a sense of pride for the invitation. Besides, gaining membership had been one of my goals. It’ll look good on my diploma and my resume, and it may get me some fat scholarships depending on the university I apply to in a year.

I went ahead and paid the $75 fee to join–hopefully, it’s worth it. What do you think? Is membership in Phi Theta Kappa particularly beneficial in any way?

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On Being Debt Free

No credit card debt

This is a good feeling!

Having debt sucks! Last year at this time, I had $2600 in credit card debt, $1300 that I still owed on my ridiculously amazing laptop, and several thousand on an auto loan.

In the last year, with a part-time job and being full-time in school, I paid off all of my credit card debt, my laptop, and about $3000 on my auto loan. I accomplished it by changing my priorities, getting a part-time job, cutting down my expenses, selling most of my belongings, and living frugally. It’s a good feeling to be pretty much debt free.

I know that $2600 isn’t a lot of credit card debt, but it hangs over you like a crowd of menacing clouds, and even a small amount like that sucks up interest, and it takes a long time to pay off when your income is limited. At the time, I was spending a lot of time on an entrepreneurial endeavor. A colleague from a former job and I were trying to make a go of it selling Amish furniture online. Like all startups, it took a lot of time. Unfortunately, the sales were not yet at the point where it could support our lifestyles, and so I supplemented mine with credit cards. It’s an investment, I thought. Once the sales really start rolling in, I’ll be able to easily pay of the credit card debt that I used to buy food and pay bills.

Then last march I made the life-changing decision to pursue a college degree. After several years of babying our company, always believing that huge sales were just around the corner, I decided, essentially, to cut my losses. I’m still a partner in the business, and it’s actually doing pretty well at this time, but the commission checks we pay ourselves are nowhere close to covering life expenses. Besides, I’ve always known that I don’t want to do online marketing for the rest of my life–it just doesn’t exhilarate me like studying math and science does. Although I’m still considered a partner, I don’t put much time into the business, and it’s not on my list of priorities for the future. Making the decision to pursue a degree forced me to face reality, and find an alternate source of income.

Now I mow lawns. Seriously. I maintain forty or so lawns, I trim trees, bushes, and hedges on the side, and sometimes I fill in for another lawn care company. I work about 2-3 days a week, and last year I made between 15k and 20k doing this. It’s  not much, but by cutting my expenses, and living frugally, I was able not only to survive, but actually to pay down existing debt. It helps that for much of the year I can live rent free by “house sitting” a relative’s winter home. I don’t like mowing lawns. After years as a white collar worker, it hurts my pride. Sometimes, pride just has to be swallowed for the greater good.

My ridiculously amazing laptop was also one of those “investments”. I thought I needed it for the business, and the manufacturer allowed me to purchase it for monthly payments of $30 or so. The interest was high–like 30%–but I figured I would have it paid off within a month. It took most of a year. Now I know that I don’t actually need an i7 processor, a backlit keyboard, and an extra-large battery. Live and learn.

As for my auto loan, I’ll have that completely paid off in a few more months. I purchased a nice, used SUV about a month before I got laid off from my well-paying job (three years ago). I had money, but my girlfriend (fiancee now) and I were heading to Switzerland for a vacation, so I decided to take out a loan on the vehicle and wait to pay the rest until we were back from Switzerland. Life had other plans. We cancelled the Switzerland trip and swallowed the $1500 or so in tickets we had purchased. I just didn’t feel comfortable going without a stable income. Two years later, all of the money I had planned on using to pay off the car had been spent on food and other bills, and I was falling back on credit cards while we were trying to get rich selling Amish furniture.

Now, two and a half years later, my SUV is almost paid off. I haven’t taken out any student loans–those will probably come when I transfer to a university. As of right now, I am essentially debt free, and it feels great.

Categories: Affording College, College | Tags: , , , , | Leave a comment

Analyzing and Improving your Math Test Scores

My Calculus Test Grade

My Calculus Test Grade

Yesterday I finally got my calculus test results for the test I took last week. My grade was 90% (plus 3 percentage points for extra credit work I did). That the class average was under 64% is irrelevant. As a perfectionist with a 4.0 GPA, my grade is unacceptable. The question is, how am I going to make sure it doesn’t happen again?

The first step is a critical analysis of where I went wrong. The second step is to figure out what was wrong with my learning and test preparation strategies, and the last step is to adjust my learning and test preparation strategies so it doesn’t happen again.

It has been my experience that errors I make on a math test fall into three different categories:

  1. Format errors
  2. Calculation errors
  3. Conceptual errors

The first, format errors, occur when you don’t obey the formatting rules outlined or assumed by the professor. For example, if you’re asked to show work and you don’t or if you’re supposed to call a nonexistent limit “DNE” instead of “it no work”, I would call those formatting errors. The second is calculation errors, and those are caused when you don’t pay attention to detail, or you fail to check your work. The third is the worst kind of error because it signals a conceptual misunderstanding of the material the test is testing you on.

  1. Format errors: Sloppiness, failure to follow guidelines
  2. Calculation errors: Failure to check work or pay attention to detail
  3. Conceptual errors: Failing to understand the material at the conceptual level

Before the test, our professor repeatedly told us that we have to show work in order to receive credit. Well, silly me, on a two-part problem which required the same kind of thinking on both parts, I decided it would be sufficient to show work on one part and just do the next part in my head. Ouch, -1 point. On another problem, I got a -2 for not being explicit enough with my answer. I answered “discontinuous at x = 3 because undefined”. The correct answer was “f(3) is not defined”. I think my professor was getting tired or something when she graded that one. On another one I used absolute value bars when I should have used brackets and a negative sign. I still got the right final answer–my method was just not the traditional one. All in all, 4 out of 10 of the negative points I got was due to avoidable sloppiness–format errors.

On two of the problems, I demonstrated a failure of understanding at the conceptual level. I lost 5 points for mistaking a tangent line to a curve at a specific point for the derivative function of the curve. It took me an hour to figure out where I went wrong–a definite failure at the conceptual level. The one other point loss came from an inability to remember (or to figure out) whether or not a function is differentiable at a removable discontinuity.

To fix errors of the first kind (i.e. format errors) I need to pay more attention to my professor’s guidelines, and I need to follow them to the letter. It wouldn’t hurt to show way more work than I think is necessary. It probably would be a good idea to give my answer in multiple ways just to make it obvious that I know what I’m doing. I didn’t make any calculation errors, but these are fairly easily fixed by checking work religiously and by at least two different methods. Errors of the third kind (i.e. conceptual errors) can only be fixed by analyzing my learning strategy and adjusting it to reinforce and check whether I’m actually understanding the material at the conceptual level. A good review done prior to the test should also help keep the conceptual stuff fresh come test time. So here’s how to fix each of these math test errors:

  1. Format errors: Pay attention to and follow your professor’s guidelines and generally accepted math syntax. Don’t forget your units.
  2. Calculation errors: Check your work as you’re going along then later come back and double-check it with a completely different method.
  3. Conceptual errors: Study, study, study. Constantly review to keep the conceptual stuff fresh in your mind. You need to know the “definitions” so you have a conceptual foundation to fall back on.

That’s it. We’ll see what my grade is on the next calculus test…

Categories: Math | Tags: , , , , | Leave a comment

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