Saturday, September 19, 2009

Girls Do Math!

The Schrodinger Equation

I wasn't a fan of math through most of elementary and high school.  I had mediocre math teachers during my early years.  I'm sure it was a product of my female generation.  More attention was given to the boys rather than the girls by female math teachers.  What's up with that?  It's sounds counterintuitive.  I would have thought that a female teacher would spend more time helping girls do better in math.  However, teachers in the past reinforced gender stereotypes by expecting boys to excel.

I remember in seventh grade having the worst time with fractions and percentages.  My teacher, Miss S. (I'm protecting the guilty person) was not very helpful to me.  I kept praying our class would move on to an easier subject.  In hindsight, why didn't Ms. S. spend more time with me after school?  I think she expected me not to succeed.  Today I wouldn't think of using that approach with my daughter.

In high school, I enjoyed algebra but disliked geometry.  I think my geometry teacher was more worried about retirement than educating us.  Mr. G. would mumble a lot and keep his back to us while teaching.  Thankfully, Mr. P made trigonometry and analytical geometry more fun.   Mr. P. had a sense of humor and tried to keep us engaged during his instruction.

After spending nine years in parochial schools, I missed out on the advanced math track.  Catholic schools didn't start algebra until ninth grade.  That meant I missed taking calculus my senior year.   I tried to take it over the summer at the local community college before my senior year.  Unfortunately, I didn't score high enough in the college's math assessment test.

It was frustrating not being able to take calculus like my other senior classmates.  This was a portent to  my experience with math during college.  I believe, if I had taken calculus in high school, I would have had more confidence in learning it in college.

Well, the math department at my college was interesting!  Most professors were foreign and they had very thick accents.  I tested below algebra so I was required to take Math Concepts for two quarters.  Then I had to enroll in a trigonometry course before I could register for calculus.  I'll be honest, I felt like I was on another planet with these math instructors.  My grades were mostly Bs and Cs.

Why was it such a struggle for me?  I believe I lacked confidence in my mathematical abilities.  I also think most of my math professors were poor instructors.  I didn't feel self-assured in math until my last calculus class.  Do you want to know why?  I had an excellent math instructor and he was a  high school math teacher.  Talk about being paradoxical.  Why couldn't my math professors be as good as this man was?  He was passionate about his subject matter and treated his students as individuals.  I got an "A" in that course.  I knew I wasn't a failure anymore in math.

Do I have confidence today in my mathematical abilities?  Yes.  I know now that I can solve any equation with the right tools and patience.  I've come a long way with my abilities.

Currently, after a seventeen year hiatus, I am using calculus and linear algebra to solve quantum physics equations.  It took me a little while to regain my footing in mathematical language but I am doing it.  I am not a numerical ne-er-do-well.  Ha, ha.  Take that all you unhelpful math lecturers!

Fortunately, my situation is not the norm for present day female math students.  There no longer exists a gender gap in math thanks to the encouragement teachers give young women.  I am hopeful for my daughter.  I believe she won't have deal with the gender stereotypes in math.

The Myth of the Math Gender Gap

Friday, September 11, 2009

My Servitude With Food

I just finished David Kessler's book, "The End of Overeating."  His name might sound familiar since he was the FDA Commissioner during the Bush and Clinton administrations.  He also is a pediatrician and lawyer who has tried to regulate cigarettes, another American vice.

Kessler's book is thought provoking except for the first half of the book.  I already know how the food industry manipulates consumers to buy over processed, high calorie food.  I wanted to learn something new and he delivered towards the end of the book.  Kessler writes about the psychological and physiological effects with eating.  He talks about how we are cued with a food memory just by going to the location where we ate a certain food.  The anticipation of eating a ice cream cone or hamburger happens just by driving that restaurant.  We are constantly bombarded with cravings because of our food memories.

Kessler seems to think we are doomed for a lifetime of obesity.  In a way he's right.  American culture is heavily weighted towards food.  We don't have to go far to find a fast food restaurant or convenience store full of high calorie, salty and sweet sustenance.  Kessler contrasts this with eating in Europe.  The French and the Spanish don't think to eat between meals because snacking is not an European habit.  It's very American and we don't like going hungry for very long.

The types of food we eat have changed with industrialization.  White rice, potatoes and white bread are easy to digest and offer little nourishment to our bodies.  We should instead be eating vegetables that don't occupy a major portion of our dinner plate.  Why don't we eat what's good for us?

"Overeating" describes the problem.  Our brains are wired for high calorie, easily processed edibles.  Likewise, we use food as a reward rather than support for our body.  It also takes about twenty minutes to feel full so quick consumption can make us miss that message.   This explains why American's have such a difficult time staying thin.  We look for convenience foods because we are always in a rush to go somewhere.  We especially don't take the time to enjoy our dinner hour.

I tried using this knowledge for eating this week.  I decided to consciously pay attention to my responses while consuming sweet, salty or fatty foods.  I tried to stop zoning out while eating this type of food.  It's hard to do when you are ravenous.  I also leave food on my plate now.  I try to eat the minimum portion to feel slightly full.

I try not to snack anymore.  I am starving for lunch and dinner.  It was challenging at first because I sometimes get a headache if I don't eat dinner right away.  However, I now like being hungry for my main meals.  I also like feeling not stuffed after eating.

I put a picture on my refrigerator of the new jeans I want to purchase after I lose ten pounds.  I want to give myself non-food rewards when I reach my goals.  Its unfamiliar territory but I want to prevent food from having power over me.

After a week of these new habits, I have lost four pounds.  That's a good thing since I am still recovering from minor surgery and can't exercise.  Do I think this habit will stay?  I hope so.  Kessler seems to indicate that our drive for rich foods doesn't stop.  At least I understand why it's so difficult to interrupt the cravings.

David Kessler's  The End of Overeating

The Cleveland Clinic: Psychology of Eating

Controlling Food Urges by Dr. David Kessler

Saturday, September 5, 2009

Quantum Mechanical Way of Thinking

Atanasoff-Berry Computer
(Wikipedia, 2009)

I’m asking you to read this whole blog without skipping any details. I know that is a lot to ask of my readers but this is a topic that few people understand. I will try to make it clear as possible.
Why should you read it? Do you own a cellphone? Do you have a computer at home? Do you use a DVD player? All these devices need quantum mechanics in order to operate. We are indebted to the brilliant people that discovered quantum mechanics.
What is quantum mechanics? It is the study of matter at the molecular, atomic, or microscopic level which doesn’t follow Classical or Newtonian Physics. Scientists found during the early 20th century that they couldn’t use Newton’s laws to describe electromagnetic radiation or light emitted from a black body. A blackbody is a perfect vessel that absorbs but doesn’t reflect light. It will emit radiation like infrared, visible or ultraviolet light according to its increasing temperature.

Scientists had to come up with a different way of thinking to solve the problem with electromagnetic radiation. They realized that light didn’t contain an infinite amount of energy. Max Planck was the first person to suggest that photons (or particles of light) were quantized. This means that each photon of ultraviolet or infrared light contains a specific amount of energy.
Planck suggested using a constant, h (which is a specific number) to figure out how much energy was contained in that photon of light. Albert Einstein came up with an explanation for the photoelectric effect. If ultraviolet light is absorbed by a metal plate, electrons are ejected from the plate. He used Planck’s idea the blackbody behavior to describe the photoelectric phenomenon. Einstein suggested that each photon or particle of light contained a specific energy which was proportional to the light’s wavelength multiplied by Planck’s constant (E = h x v). Einstein later won the Nobel Prize for this in 1921.
This opened the door to quantum mechanics. Scientists began asking themselves if electrons could be particles or waves. Niels Bohr postulated that electrons were quantized into different energy levels. He tried to explain the wavelengths of light that were emitted from excited hydrogen gas (see picture below). Bohr incorrectly described the electrons as orbiting particles around a nucleus.
Louis de Broglie suggested that electrons and other matter under certain conditions would behave as a particle or wave. When light is passed through two narrow slits, an interference pattern. This is evidence of wave properties. Clinton Davisson and Lester Germer demonstrated an interference pattern with an electron beam and a crystal of nickel. The wave properties of electrons were then described mathematically by Erwin Schrodinger. His wave equation helped predict the probability of locating an electron in a certain position. Schrodinger later won the Nobel Prize for his work with electron wave equations in 1933.
With Schrodinger’s equation (which is considered quantum mechanics) the electron configurations were described for hydrogen. Heisenberg, Dirac, and Pauli added more mathematical descriptors that helped identify the shape of atoms larger than hydrogen. Scientists learned how to predict the behavior of atoms once they understood their structure.
With the advent of atomic structure, the information age had begun. The first computer was made in 1939 by Dr. John Atanasoff and graduate student Clifford Berry. The Atansoff-Berry Computer (ABC) was a simple machine that used the binary system and electricity. It used Boolean algebra which is the basis for “on” or “off” (also known as 0 or 1). The second and more well known computer was Electronic Numerical Integrator and Computer ENIAC in 1945. It was the size of a suburban house and was originally designed to calculate artillery firing tables for the Army. Since it was completed after the war, the military used ENIAC for its nascent nuclear weapons program.
In 1947 at Bell laboratories, the first transistor was made of gold contacts and germanium. This early semiconductor couldn’t have been created without quantum mechanics and the understanding of how atoms behave. Present day microprocessors are multicore silicon chips with halfnium-infused circuitry. These microprocessors run at 3.2 GHz (gigaHertz) speed.

Lasers wouldn't have been created without Einstein's theory about photons. Electrons can absorb and emit photons so a laser is a light emitter at a specific frequency like infrared. Lasers are used for CD-ROMs and DVD players. We wouldn't be in this information age without quantum mechanics.

I hope this essay has helped you understand quantum mechanics a little better. It's a fascinating topic that has many applications. Who knew that Planck, Einstein and Schrodinger (to name a few would) leave behind a useful legacy. Here's to quantum mechanics and the information age.

Astronomy Podcast (Quantum Mechanics)