Saturday, September 13, 2014

drink some water and go home

My high school calculus teacher was fabulous. Fabulous because of her cute outfits and fun sense of humor, but mostly because of her incredible gift for teaching math. Mrs. Weiss made custom notes, homework, quizzes, and tests that set us up for success. She taught us the ideas behind calculus, not just how to solve calculus problems. She taught us the why. By the end of the year, I could see functions and graphs forming in my head after just glancing at numbers or problems. Don’t tell my mom, but my trick in college was to do integration problems in my head at the bar. When I couldn’t integrate anymore, it was time to drink some water and go home.

On the very first day of class, Mrs. Weiss told us “calculus is the study of how things change.” That didn’t sink in immediately, but I understood it over time. And last night, as I struggled to find my keys in the dark, it popped into my head again.

Here in Alaska, summer is sadly at an end. Fall is in full swing, and the day lengths are changing. I got home last night a few minutes after 9:00, as I usually do, and for the first time since summer had to use a flashlight to find my key. It’s that dark now. How does something so gradual and metered sneak up on you all at once? It seems like such a noticeable change all of the sudden. (In my earlier blog post shut up you stupid little birds, I touched on how the whole season changy, day length changy thing works and how it’s exaggerated at extreme latitudes.)

As I turned the key to my dark apartment, a graph popped into my head. An infinite sine curve. The graph of how the day length changes must be a beautiful, perfect sine curve.

In calculus, the derivative of a function is the rate at which something changes at any given point along that graph. If we want to know at which time during the year the changes in day length are greatest from one day to the next, we look at the derivative.

On our graph to the right, the path of the graph levels out to almost not changing at all around the solstices (June 21 and Dec 21). This means the derivative is 0 or very close to it right around the solstices, and that the sun may only set or rise a matter of seconds later or earlier than it did the previous day.

The derivative is greatest on September 23 and March 20 (the equinoxes). You can visually see here that the graph is taking a steep nose dive/climb.  Here in Haines, there may be more than five minute or so difference in how much daylight we get from day to day around the equinoxes.

So maybe I’m not crazy for thinking the days seem to be getting really short all the sudden. The autumnal equinox is in a matter of days, and the change is especially noticeable because we’re losing daylight at a faster rate than we have been all year. The graph is plunging.

It’s worth noting that yet another function can be tied into this little story. Depending on what latitude you live in, you see this day length change at varying magnitudes. At the poles, 24 hour light/night is experienced, which would mean the peaks of the graph are higher and the valleys are lower. It also means the derivatives are greater. Conversely, at the equator, they experience 12 hour days and 12 hour nights year round, so there are no peaks and no valleys. Their graph is completely flat.

So what is the derivative of the graph for the folks that live on the equator where there is no change in day length?

If you can’t tell me, you need to drink some water and go home.

Friday, September 5, 2014

an elegant tango

Throwback in high school.
Tiny little arms.
My whole life I’ve been skinny. Like, get called into the counselor’s office because they think you have an eating disorder skinny. Like, strangers think it’s acceptable to say “eat a sandwich!” instead of “nice to meet you” skinny. Like, eat two Big Macs and large fries and still lose 5 pounds skinny.

I’ve been steadily putting on weight since high school, about 3 pounds per year. I rarely weigh myself and instead focused on taking in as many calories as I could to climb my way out of the “underweight” section on that chart at the doctor’s office. “One day I’ll fill out and be able to sit on hardwood floors,” I told myself.

So you can imagine my surprise when I stepped on the scale a few weeks ago and saw that I’ve gained 15 pounds in about 6 months. I mean, I’ve kind of been noticing some more padding in my belly area as the rest of me has stayed thin. I’ve been kind of proud of my hard-earned fat. But when my sister saw a photo of me and asked if I was “prego,” it dawned on me that I need to regulate how and where I continue to gain my weight.

Men and women are shaped differently, in large part due to fat distribution. Classically, in art and otherwise, women considered to be most beautiful are those with little waists and bigger hips. Science set out to quantify this, and found there is in fact a golden ratio to tell you how hot you are (as if the rest of the world and media didn’t already assume that role).

The results are in and turns out that men find women with waists that are 70% the circumference of their hips to be most attractive. It is thought that this ratio signifies the most fertile women that are best built for carrying and delivering a baby. Makes plenty of sense, right?

Consider evolutionary signals, as discussed in my earlier post stop it, your bib is turning me on. An itty bitty waist and a round thing in your face may often actually signal a fertile woman, but not always. Think of how many women today struggle with infertility, many of them proportioned according to the 70% rule. So is the 70% rule an honest signal of fitness? Has modern medicine and birthing protocols tampered with the honesty of this signal?

You like this, don't you?
There’s a whole field called evolutionary aesthetics, which basically looks into inherited traits that have an effect on the psychological perception other members of a species have of an individual. Why are our lips red? Why do we hate the sight of poop? Why do babies show preference to circles over squares? Why do our brains tend towards things colored with vivid blues and greens?

Since evolutionary aesthetics deals with psychological perceptions throughout the development of a species, over hundreds of thousands of years, it must take into account the changing social environments that affect those psychological perceptions. You see, the perceptions of these traits are not static. For instance, it has been found that men show more preference for larger women when they are hungry. Come back after lunch break, and those same men show subtle preference for smaller women. Should the world fall apart and sink into famine, Vogue will be out of business. Larger women with more resource acquisition abilities will be the hot new things.

I love the elegant tango that happens between natural selection and psychological perception. It’s created the human shape we have now. And the human body may be one of the most inspiring forms, with all of its of curves and colors and lines and fluidity, that our species has recognized yet.

Even if there’s a little bit of it hanging over my jeans right now. The gentle sag of fat over one’s Abercrombie skinny jeans can be inspiring, right?

Oh my god I’m going running right now.