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!

Why are People so Afraid of Science and Math?

Math source: freeimages.com/valium88

"LOL, I'm terrible at math. I could never understand what you do."

"That stuff is way beyond me. I'm no rocket scientist!"

"Calculus? I barely got through algebra!"

When I talk to people about my research, I'm used to getting these types of responses, typically accompanied by wide-eyed looks of astonishment, confusion, fascination, and/or fear. Oftentimes it feels like I'm some kind of crazy person trying desperately to communicate my enthusiasm to an audience that speaks a completely different language than I do. Most of the time, I try to take these situations in stride and hope that people walk away knowing just a little bit more about what I do. Nevertheless, I still finish these conversations feeling somewhat disappointed that scientific illiteracy and innumeracy are so prevalent, and at the same time, so accepted. You would never hear someone be proud to say "LOL, I suck at reading!"

I'm not here to shame people for lacking a full understanding of quantum mechanics or general relativity. What I am questioning, though, is why the general public seems to be so intimidated by anything related to science and math. On a personal level, it's frustrating to feel like I can't easily communicate what I do to non-scientists without leaving them scratching their heads in confusion. At a societal level, it's even more frustrating to see a substantial fraction of high-profile politicians debating the existence of anthropogenic climate change and a large movement of misguided parents refusing to vaccinate their children against preventable diseases.

I'm under the impression that people are scared away from these fields at an early age. Given how cumulative mathematical topics tend to be, it is easy for grade school students to fall behind at some point and to struggle to catch up during the remainder of their education.  Such circumstances would lead these students to assume that they lack the natural aptitude for anything quantitative.

"I'm just not a math person..."

While it may be hard for many who know me to believe, I've been a victim of this mentality on occasion, myself. Due to some learning differences related to processing speed (i.e. how quickly the brain processes information that it takes in), there were times when I struggled with my more mathematical coursework. During my undergraduate experience at Caltech, these difficulties were especially apparent considering that everything was taught at a highly accelerated pace. The curriculum often felt like a speeding school bus that would never stop - if you fell off, you were left behind on your own with no one to help.  With the right academic accommodations, however, I was able to graduate comfortably and to reach where I am today.

Given my own success in spite of learning difficulties, I believe that anyone is capable of understanding even the most advanced scientific and mathematical topics with the right education and support. With America's haphazard, cookie-cutter approach to teaching this material, it's no wonder that many of us fall off the school bus too early and develop the self-fulfilling prophecy that is "math anxiety" (which shouldn't even be a thing).

Even assuming that a large fraction of the general population were numerically challenged by nature, people tend to forget that scientific inquiry relies just as much on imaginative and creative thinking as it does on numeracy.  After all, computers are meant to assist scientists, not to replace them.  In the end, the same basic principles behind the scientific method (asking questions, making testable predictions and observations, etc.) can be applied to research in just about any field, from sociology and psychology to marketing and economics. Strip away all the fancy-talk, and science can be accessible to anyone.

"Sometimes it sounds like you're speaking a different language!"

To be fair, jargon can be difficult to understand, even among accomplished scientists in separate fields.  When a community of researchers starts relying too heavily on specialized terms that have different meanings or no meaning at all to others, a communication barrier can develop. It is for this reason why it is critical that scientists are able to discuss what they do with the general public in understandable language.  For some fields, this may be more difficult than others, but with a solid knowledge of the material and proper communication skills, any researcher should be able to make their work comprehensible to a broader audience.

Summary Points:

• When you tell a scientist "You're so smart, I could never understand what you do," that's almost more of an insult to their communication skills than a compliment to their intelligence. Instead of immediately tuning out, try to listen and ask questions. Maybe you'll find our work just as interesting as we do!

• No one is a "math person" by nature. Just about anyone can do algebra, or even calculus, with the right educational support.

• Math anxiety often develops because we ignore differences in learning styles. If my childhood education had measured quantitative intelligence using tests of speed and fluency alone, I would have probably fallen behind quite early. Additionally, little support is offered for students who fall off the proverbial school bus.

• A lot of research areas are jargon-heavy. It is essential that scientists (and mathematicians) are able to communicate what they do without the use of specialized terms specific to their field. Anyone's work should be accessible to the public.

For the sake of ending this blog post with humor, I thought I'd select a few random research papers from various fields and translate their titles into normal-people speak.

Astronomy

Actual title: Two New Candidate Planets in Eccentric Orbits

What it sounds like: Two Republican Planets in Peculiar Orbits Announce Candidacy for President

What it actually means: Two Potential Planets Discovered in Elliptical Orbits

Physics

Actual title: Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC

What it sounds like: Some Moron Seen Attending Christmas Mass of 125 AbC with the DEF Experiment at the GHI

What it actually means: New Particle with a Mass of 125 Giga-electronvolts Observed with the Fancy-Schmancy Equipment at the Large Hadron Collider

Atmospheric Science

Actual title: Development and Application of a Cubic Eddy-Viscosity Model of Turbulence

What it sounds like: Some Dude Named Eddy Made a Model Describing Crazy Viscous Cubes

What it actually means: How We Make and Use this Fancy-Schmancy Model to Describe Atmospheric Turbulence

Chemistry

Actual title: Electronic Properties of Disordered Two-Dimensional Carbon

What it sounds like: Electronic Estates of Schizophrenic Carbon Squares

What it actually means: How Impure Sheets of Carbon Interact with Electricity

Biology

Actual title: Phosphorylation of 3'-azido-3'deoxythymidine and Selective Interaction of the 5'-triphosphate with Human Immunodeficiency Virus Reverse Transcriptase

What it sounds like: ;aljwieht;oi:OAIH:lken;oiah;dP:AIOYHIOUC:H39989;:J":IOBNHK:XHPkkdh

What it actually means: *Shrugs* Any biologist willing to help me out here?

Honorable Mention Quotes of Scientific Ignorance:

"The idea that carbon dioxide is a carcinogen that's harmful to our environment is almost comical."

"Astronomy? What can you tell me about my sign?"

"How do we know dinosaurs really existed?"

"What journal are you planning on publishing your thesis in?"

"The Huffington Post."

"If humans came from monkeys, why are there still monkeys?"

Forgive (Yourself) and Forget (Everyone Else)

Sometimes I feel like one of those wind-up toys. On particularly bad days, stress and tension build up until I'm at my limit and I just have to go bonkers for a bit before I can continue on with my life. Being naturally curious, I try to identify when and how these nuggets of negative energy accumulate and at what point the critical threshold is reached before I can't handle any more.

In this sense, a better analogy would be that of a balloon. In this example, all of those negative thoughts and feelings that we tend to hold on to would be the air inside the balloon, and the emotional limit would be the point at which it pops. The size of an individual's balloon can vary, along with the rate at which air enters and exits.

For those of us who happen to be very self critical, we tend to internalize this negative air quite frequently and let it create tension within our mental and emotional balloon. In addition, such an attitude often makes it difficult to let go of perceived troubles and release pressure. The result is the presence of a lot of unnecessary stress and anxiety that can only hinder our ability to live a more fulfilling life. After all, it's quite difficult to stay grounded when you're filled with so much hot air (I'm having too much fun with this).  Eventually, the balloon has to pop, and all of the pent up energy is released in the form of outbursts, breakdowns, etc.

As someone with a busy mind, I occasionally make the mistake of interrupting people in an effort to remain engaged in conversations. Sometimes it feels like I have an unfortunate sixth sense for when someone's about to start speaking, because on many occasions, I can enter a conversation at the exact same time as someone else. Whereas a healthy response in this situation would be to apologize, let go, and move on (I'm getting better at that), I instead fixate on the awkward and grow very self conscious of when I choose to speak up. Rather than actually focusing on what others around me are saying, I retreat into my own head in order to manage the building stress from all the negative thoughts I'm holding on to.  As expected, this tends to exacerbate the situation.

If there's one thing I learned from the internet, it's that you shouldn't read the comments section on most websites.  Similarly, it's probably best not to read the comments section of your mind.  So what's the moral of the story? We're all human and we all slip up sometimes, so let yourself feel embarrassed, forgive yourself, forget about what others are thinking, and continue being awesome.

Planets in Binary Systems

Lucasfilm

In the previous post, I discussed how the oscillating orbits of planets within binary star systems could create extreme climate cycles as a result of the fluctuating energy input.  What exactly is going on in these systems, though? In this post I seek to describe more technically what is referred to as the Kozai-Lidov mechanism by which a second star can alter the shape of an inner planet's orbit.

In binary systems, planets can orbit in two configurations. The first, like that on Tatooine in Star Wars, has the two stars at the center with the planet orbiting around both. For these circumbinary systems, dynamical stability requires that the planet orbit at a distance significantly greater than the separation between the two stars.

The second configuration, which my research focuses on, has the planet orbiting one of the two stars, with the second circling the system further out. Under these circumstances, the gravitational influence of this stellar companion can augment the eccentricity of the planet's orbit  (science speak for making the orbit more elliptical) via the Kozai-Lidov mechanism.  For this to occur, the orbits of the secondary star and the planet must be inclined relative to each other by a sufficiently large angle (approximately 40 degrees or greater).

In the setup above, the planet (p) orbits the primary star (1). The secondary star (2) orbits with a large inclination angle i relative to the orbit of the planet.  The angular momentum of the planet in the direction parallel to that of Star 2 is conserved.

Under this configuration, the angular momentum of the planet's motion in the direction parallel to that of the secondary star is conserved. This quantity, denoted as Lz, depends on the eccentricity of the planet's orbit e along with the inclination i.  As Star 2 tugs on the planet, the decreasing inclination between the two orbits is traded for eccentricity, and the planet's orbit becomes more elliptical.  This dynamical exchange between eccentricity and inclination occurs in cycles with a frequency that depends on the masses of the stars and the radii of the two orbits.  The oscillation occurs more rapidly for a system with a more massive secondary star, a less massive primary star, and a planet which orbits further out.  This means that the effect is most prominent when the secondary star has a substantial gravitational influence relative to the primary.  The maximum eccentricity that the planet can reach depends only on the initial inclination angle.  If the orbit of the secondary star is eccentric, however, Lz is not strictly conserved and arbitrarily high eccentricities can be attained.  The phenomenon was originally studied with reference to asteroids in highly elliptical orbits that were influenced by Jupiter's gravity, but in recent years has been applied to the dynamics of extrasolar planets.  

These cycles can be visualized in the plot below.  An eccentricity of zero corresponds to a circular orbit, while an eccentricity of 1 is the maximum limit.  Higher eccentricity corresponds to a more elliptical orbit. The setup involves a planet orbiting a star 1.4 times as massive as our Sun at a distance twice that of Earth. The secondary star is 0.4 times as massive as the Sun and orbits at a distance 20 times greater than that of Earth's orbital radius.  Under this configuration, the planet's eccentricity cycles from nearly zero to approximately 0.4 over a timescale on the order of 10,000 years. At this eccentricity, the average stellar flux received by the planet would be about 1.1 times greater than if the orbit were circular. If Earth's orbit were this elliptical, its annually averaged temperature would be warmer by about 5 degrees Celsius, although seasonal temperature variation would be substantially greater.  Within one orbit, the planet's energy input would vary by a factor of over five between the nearest and farthest points from the primary star.

So what are the implications for planetary habitability?  One potential research question would be whether or not these cycles could thaw a planet like Earth out of a state of global glaciation. On the other end, these spikes in eccentricity may render an otherwise habitable planet too warm to sustain liquid water.  Under these circumstances, would the planet retain its total water supply in the atmosphere, or would it lose vapor to space and dry out over the course of its lifetime? Such questions pertaining to the habitability of these planets have yet to be investigated.

Planetary Habitability

Within the past decade, we've discovered a lot of new planets around stars other than our Sun (for an up-to-date catalogue, visit www.exoplanets.org)  These extrasolar planets, or exoplanets for short, can exist under conditions very different than for planets in our own Solar system. From Jupiter-sized giants orbiting their host star more tightly than Mercury to tidally locked rocky planets with permanent day and night hemispheres, the diversity of observed worlds is impressive and suggests that habitable worlds may differ substantially from Earth.

The most broadly accepted definition for a 'habitable' planet is one which can sustain liquid water at its surface. While it is theoretically possible that life could arise by other means, life as we know it depends on the presence of liquid water. In our search for exoplanets that could sustain life, we are mainly interested in identifying planets within a range of orbital distances referred to as the 'habitable zone.'  

While the stellar flux (ie the radiative energy received by a given surface area over a certain amount of time, a quantity related to temperature) depends only on the orbit's radius, surface temperatures (and by extension the habitability of the planet) may be governed by the climate system.  Venus, despite being at the inner edge of our habitable zone, has a thick carbon dioxide atmosphere which leaves the surface too warm for life to develop. At the other extreme, planets with no atmosphere cannot be habitable, as liquid water cannot exist at zero pressure.  

Over a planet's lifetime, the stellar flux may vary due to several processes: [1] Stars getting brighter with age [2] Planets migrating inward or outward due to dynamical interactions [3] Orbits may not always be circular. With a changing energy input, the habitability of a planet over time depends on the stability of the climate system and its feedback processes. Positive feedback processes amplify temperature change.  One example is related to the reflectivity of ice vs oceans. Increasing global temperatures would melt ice, thereby reducing the planet's overall reflectivity and allowing for more absorption of light.  This would increase temperatures even further.  One primary negative feedback which maintains equilibrium here on Earth is related to weathering processes between the atmosphere's carbon dioxide and minerals at the surface. A positive perturbation to global temperatures would melt ice, thereby exposing more land and increasing average precipitation rates. As a result, weathering rates would increase, thereby pulling more carbon dioxide out of the atmosphere, weakening our greenhouse effect, and reducing temperatures back to equilibrium.  The strength of these feedback mechanisms can influence a planet's resilience to changes in thermal forcing.

On Earth, our orbit is nearly circular, allowing for a more stable climate system over time. This may not be the case, however, for many planets within binary star systems. With the presence of a second star beyond the orbital radius of the planet, gravitational dynamics may warp the shape of the orbit to be more elliptical, thereby varying energy input over the course of the orbit.

At sufficiently high angles between the orbit of the planet and the secondary star, the shape of the planet's orbit would oscillate. Over short enough timescales, these oscillations may create potentially extreme  climate cycles. Depending on the strength of the climate's feedbacks and how elliptical the orbit becomes, a planet like Earth could periodically freeze or boil over if it were to temporarily exit the habitable zone. Whether or not such events would render the planet permanently uninhabitable would have to be determined via climate modeling.

With the gravitational influence of a second star (upper right), the shape of a planet's orbit can oscillate between circular and elliptical, causing potentially extreme climate cycles. Note: The timescale over which the orbit changes shape is much longer than that over which the planet orbits the primary star.

Given the growing number of planets detected within binary systems, it is important to understand the limits of habitability under the physical conditions that would be expected with the presence of a second star.  If such worlds could indeed maintain stable climates with liquid water, the extreme climate cycles would present developing life with many challenges that were never present on Earth. I'll leave those topics to the biologists.

I'll end this post with some imaginative thinking about what a double sunset would look like on such a planet. Perhaps two stars may be better than one.

Public Domain Image Modified by Nathan Baskin

Random Musing of the Day

"Frantically seeking closure is a futile endeavor when life throws you open-ended questions."