The Paradox of Perfection

Why perfectionists are rarely happy with their accomplishments.

Seasons on Steroids

Here on Earth, we're fortunate enough to orbit the Sun along a nearly a circular path. The result is a fairly stable climate system with a globally averaged temperature that is more or less constant year-round. Nevertheless, our planet's rotation axis is tilted at about 23.4 degrees relative to the plane of our orbit. This physical configuration allows for the seasonal cycle that we can observe each year. In Northern Hemisphere summer, the North Pole is angled towards the Sun, allowing the hemisphere to receive more light over one day. This allows for warmer weather. Meanwhile, the South Pole is angled away from the Sun and receives less Sunlight, making it colder.

A diagram depicting how the tilt of Earth's spin axis (the red arrow pointing from the South Pole through North Pole) creates seasons.  Position 1: Northern Hemisphere summer, Southern Hemisphere winter. Position 2: Northern Hemisphere autumn, Southern Hemisphere spring. Position 3: Northern Hemisphere winter, Southern Hemisphere summer. Position 4: Northern Hemisphere spring, Southern Hemisphere autumn.

As discussed in my previous post, the presence of a second star can gravitationally perturb planets into more elliptical orbits. Kepler's first law of planetary motion states that all planets orbit their star in an ellipse, with the central star at one focal point. The magnitude of how elliptical an orbit is is specified by a quantity called eccentricity. An eccentricity of zero (e = 0) corresponds to a circular orbit, whereas an eccentricity between zero and one (0 < e < 1) corresponds to an elliptical orbit. Within this range, higher eccentricity corresponds to an orbit that is more elliptical.

Four color-coded orbits of equal max. diameter (to scale) for eccentricities 0, 0.25, 0.5, and 0.75. The bottom left plot displays the radiative power per area received by the planet over time for each orbit (1 Solar Constant = average value for Earth). The bottom right plot displays the orbit-averaged value for a given eccentricity.

In an elliptical orbit, the planet can approach the star more closely, thereby receiving more radiation and reaching higher temperatures at the distance of closest approach. Much of the orbit, however, is spent further out than for a circular orbit of the same diameter. Averaged over one orbit, the amount of radiation received by the planet increases with eccentricity. So what does this all mean? Supposing that Earth's orbit were more elliptical, global temperatures could rise and fall (potentially significantly) over the course of a year. These global seasons could be quite extreme for planets in binary star systems.

This summer, I was able to run some preliminary models. Using initial conditions for a simplified Earth, I simulated how the climate would behave under orbital eccentricities of 0.4 and 0.6.

The above map shows monthly averaged surface temperatures for a planet at month of closest approach for an orbit with e = 0.4. Maximum temperatures exceed 340K (67C = 152F). Yikes! How can we better understand what this map means for humans? Thanks to biological evolution, humans have been able to adapt to warm climates by means of sweating. When sweat evaporates off our skin, it draws heat from our body, thereby cooling us down. This effect can be measured using what's called the wet-bulb temperature. In essence, this is the coolest temperature that our bodies could reach by sweating, and depends on environmental humidity.

The above map, then, can be used as a proxy when examining basic human adaptability to climate (Sherwood & Huber 2010). When the wet-bulb temperature approaches body temperature (37C = 98.6F), a human can no longer shed heat into their surroundings, and internal temperature rises. Prolonged exposure to environmental wet-bulb temperatures exceeding 35C (95F) can thus pose the risk of heat stroke. We can then make a map showing regions that are deadly for humans.

The above map depicts wet-bulb degrees Celsius above 35C. Luckily, our orbit is circular, but if you were to travel to a similar planet at e = 0.4, you may want to invest in air conditioning!

As would be expected, temperatures get even higher for e = 0.6. Spoiler alert: A/C won't help.

Some PhD students just want to watch the world burn.

Deadlines

Disappointment vs. Satisfaction

Healthy Cooking for the Super Lazy: Recipe #1

How do cook?

So you finally decide to get off your couch and go to the gym, but when you're done, you're exhausted and all that's on your mind is food. You're really too tired and lazy at this point to cook anything substantial (so you think), but you'd rather not spend money on fast food because that kind of defeats the whole purpose of your exercise, no? You also live in a tiny studio apartment with poor ventilation, and would rather avoid anything messy, stinky, or difficult to clean up.

So if it wasn't clear already, the above situation is one of many challenges that I've faced since living on my own and having to feed myself. While I have yet to become a cooking expert (I still can't cook anything with poultry without irrationally obsessing over getting salmonella), I have found one go-to recipe that's super healthy and so easy you can use a microwave. Without further ado, I present

Nathan's Fantabulous and Quick Meal

Total time: approximately 20 minutes
Difficulty: elementary

You will need:

- 8oz fillet of trout or salmon

- 1/2 cup of rice (uncooked)

- Paprika, white pepper, and dill to taste
- Chili powder if you're feeling like a badass
- Optional lemon juice

Instructions:

1 - Add 0.5 cup of dry jasmine rice + 0.75 cup of water to a rice cooker. Cook it.

2 - Season your fish to taste. (Don't actually taste the raw fish, though. This isn't a sushi recipe.)

3 - Microwave fish for 3.5 minutes on high.

4 - Serve.

Voila

Now I know what you're saying - Fish? Microwave? Didn't you say you live in a tiny apartment with terrible ventilation? In my experience, I haven't had any odor issues with this meal - any smell typically dissipates quickly, and cleanup is pretty straightforward.

Bonus Recipe: Super Duper Kefir and Egg Whites Protein Drink

Total time: <5 minutes

Difficulty: If you can mix two ingredients in a cup, you can make this drink.

You will need:

- Kefir of your flavor choice (kefir is essentially yogurt in beverage form)

- Pasteurized egg whites

- Optional: cinnamon, to taste

Instructions:

1 - Add one part egg whites to cup.

2 - Add two parts kefir to cup.

3 - Whip it good.

4 - Add  optional cinnamon and enjoy.

Basic Nutrition Info
(Meal + protein drink)

Total Calories: 797
Carbs: 91g
Fat: 15g
Protein: 72g
Fiber: 0g
Sodium: 350mg
Cholesterol: 150mg

Enjoy!

Alertness

Random Musings on Uncertainty

Public Domain

In science, uncertainty must be quantified. For every measurement or calculation, the precision of that value must also be specified for the sake of completeness and integrity. In essence, us scientists have to have a level of certainty with respect to uncertainty. Life, however, can be somewhat different, in that the experiential uncertainties we face on a day to day basis may leave us with questions that are completely unanswerable.

Where will I be in five years? Ten years? Or (((gasp))) fifteen years?

I hope I made the right decision. What will happen now?

What if [insert catastrophic scenario here] were to happen?

While it may seem to be theoretically possible to narrow down the possibilities with enough data and analytical thinking, this very process would inherently disrupt the course of events it seeks to predict in the first place. Say a particularly nervous graduate student (totally not me...) were to put all of their time, energy, and resources into predicting their postdoctoral job prospects and planning future decisions accordingly. If this were the case, they wouldn't get anywhere because they would never be able to do anything else! Even if this information were attainable via clairvoyant means, the student's knowledge of the results could alter the outcome. This scenario is an example of the observer effect*, in which the very act of observation fundamentally disrupts the observed processes.  In non-technical terms, this means that obsessing over life's mysteries may distract us from living and experiencing what is beyond our control in the first place. As with the paradoxical case of Schrödinger's cat**, some future outcomes may have to remain unknowable until the metaphorical box is opened.

*While it may share some qualitative similarities with Heisenberg's Uncertainty Principle, the two are not quite the same.

**Meow. What's this link lead to? You won't know until you click!