Linkage

Recently I've been working as a staff writer at Life's Little Mysteries, a website that explains the science behind the news and life in general. It's kind of a cool site, which has allowed me to research and write about everything from how stealth planes work to how the Egyptian government actually managed to turn off the Internet two weeks ago. After the mob bust that happened recently, I wrote about whether or to what extent the mob still runs New York, and I wrote a piece about men, women, and kissing for Valentine's Day.

Whenever a cool video goes viral on Youtube, like this video of a gorilla in a British zoo walking upright like a human, we find experts to explain the science behind them. Check out the site, and if you have an interesting question for us to answer, please send me an email!

I've also done some freelance writing at Popular Science Magazine and PopSci.com in the past few months. I wrote a long feature on the Pioneer Anomaly (which, as you may recall, I wrote about here first), and another short piece on the evolutionary purpose of tickling. I'm working on a new piece for them on gravity research that should be out soon.

Not much time for Facto Diem these days, but at the very least I will be better about updating the site with links to my articles published elsewhere.

Walking Around

When lost in the desert or a thick forest -- terrains devoid of landmarks -- people tend to walk in circles. Blindfolded people show the same tendency; lacking external reference points, they curve around in loops as tight as 20 meters in diameter, all the while believing themselves to be walking in straight lines.

Why can't we walk straight? A group led by Jan Soulman of the Max Planck Institute for Biological Cybergenetics in Germany recently made gains toward answering this age-old question. By conducting a series of experiments with blindfolded test subjects, the team systematically ruled out body asymmetries as an explanation: Things like uneven legs and right- or left-side dominance did not correlate with walkers' veering directions. They also ruled out random noise in sensory input and/or motor output as the culprit, since this would have caused walkers to meander back and forth in a zig-zag fashion rather than to trace out circles.

Loopy paths, they concluded, are caused by a walker's changing sense of "straight ahead" itself. With every step, a small deviation is added to her cognitive sense of what's straight, and these deviations accumulate to send her veering around in tighter and tighter circles as time goes on. This increasing curvature doesn't happen under normal circumstances, which is to say, when external reference points are visible, because those allow the walker to frequently recalibrate her sense of direction.

Soulman's team is not quite sure where in our inner workings the accumulating deviations arise. Their best bet is placed on the vestibular system -- the system in our inner ears that maintains balance -- which is already well-known to exhibit biases. Some people have vestibular disorders so severe that they find walking in straight lines impossible even under normal circumstances. For most of us, the subtle leftward or rightward bias of our sense of direction would only rear its head if we were trying to find our way through a dense forest, or, perhaps, blindfolded by pirates and made to walk the plank.

The Truth, The Whole Truth

Language is notoriously insufficient when it comes to grasping truth. Words, riddled with connotations and subjectivity and vestiges and misunderstandings, never seem just right. Using them, you can only ever approach the telling of the truth, but can never quite tell it.

Most of us have the impression that the breach lies with all those sources of ambiguity - that if you stripped away confusion and abstraction from language and left behind only perfect precision and clarity, which is to say, the language of logic--math--then you could achieve truth. And in theory (you might think) if you were an omniscient being, you could solve any mystery of the universe with mathematics, whether it be the workings of consciousness, the reason for entropy's rise, or the distribution of the prime numbers. Of course, your equations or proofs would be unimaginably complex. It doesn't matter. Truth seems achievable, in theory, by pure math.

But it isn't. Two of the strangest, most striking, most devastating, and thus most ignored math theorems ever proven, Kurt Godel's First & Second Incompleteness Theorems (1931), imply that math, like all other languages, can only approach truth, but can never grasp it.

Because the second incompleteness theorem follows quite easily from the first without adding much to it, I'll dispense with it and simply try to explain the first theorem. It states that formal systems--read: systems of mathematics generated from first principles (like the concepts of zero, and one, and two, etc.) and the rules that they logically follow (like addition and multiplication)--can never be both consistent and complete.

First, what does it mean for a system to be consistent? It means that no statement and its negation are both provable using the rules of the system. For example, if A is proven true within the system, then for consistency, "not A" must be proven false.

Consistency is the pleasure of mathematics. In the real world--the world of grey areas--A and "not A" usually both have some degree of truth to them, because real-world A's and "not A's" are far more complicated than the A's and "not A's" of math, and thus they are burdened with the ambiguity and confusion I complained of before. Still, in theory, even real world statements could be set up as extremely complex mathematical statements and, in that form, proven either true or false.

What does it mean for the formal system to be complete? It means that everything that is true can be proven true using the principles and rules of the system.

Putting those clarifications together, we can grasp Godel's incompleteness theorem. It says that if a system is consistent (never contradictory), then it lacks the tools to prove all the true statements that exist. Some mathematicians and logicians worry that some of the truths we have already conceived of (for example, the infinite distribution of twin primes) are not provable within math.

On the other hand, if a formal system is complete--if there is nothing true that isn't provable by the rules of the system--then the system is inconsistent. In other words, there must be some statement A in the system for which both A and "not A" are provable.

This is sort of mindboggling and a little hard to swallow, but in fact the theorem is true beyond the shadow of a doubt. Since plenty of links are available, I won't regurgitate the theorem's proof in a non-rigorous form, but the gist of it is this: within any formal system, it is possible to generate a formula that relates to its own provability. In words, the proven formula states: "This formula can't be proven." Contemplating this, you'll realize that since the formula is proven by the system, it must be true. But if it is true, then it can't be proven by the system. This contradiction renders completeness and consistency incompatible. (See for yourself.)

Obviously the heart of the proof relates to famously paradoxical sentences in everyday language, like the liar's paradox: "This sentence is a lie." Apparently the problem with that sentence runs much deeper than the mere ambiguity of words. The problem is fundamental, and Godel made it mathematically rigorous.

And its implications are profound. Because Godel's theorem bars humans from omniscience, many theologians use it to establish a sort of mathematical realm for God. He, not we, can know everything (they say). But in truth (no pun intended), Godel's theorem blocks even God's access to omniscience.

Stephen Hawking and Freeman Dyson interpret the incompleteness theorem to mean that we will never attain a theory of everything - the holy grail of physics. Most mathematicians disagree. They argue that the math used by physics is a proven subset of all math.

The theorem's undeniable implications are enormous enough. In a recent paper, Geoffrey Laforte and his colleagues lament them nicely. They write, "There is no bedrock of mathematical certainty on which the edifice of science must be based, no direct route to mathematical Truth ... We can never be absolutely sure that we have things right, even in mathematics, and still less can we be certain that all truths will eventually be vouchsafed to us."

The incompleteness theorem lurks like an unpatchable hole in the foundation of mathematics, and of human knowledge itself. With no alternative, most mathematicians, logicians, philosophers and scientists choose to step around it, and walk on.

Self-Projection

Video feedback occurs when you point a camera at a display of its own output. Because of built-in processing delays, at every instant, the camera records an image that it projected about 40 milliseconds earlier. Because it records the previously projected image from some distance away, and probably at a slight angle, the recorded image is always a slightly distorted version of the projected one. The distortion gets projected on the display in turn, and then that gets recorded (with further distortions) and projected, and so on: The video output beautifully evolves.

Geometry drives evolution in video feedback. If a camera is zoomed in on its display, it continuously magnifies the projected image by stretching out the tiny details, including noise, in its center. If, on the other hand, the camera is zoomed out, then features get compressed to the center with every iteration of the feedback loop. If the camera is rotated or angled while recording its own output, then the stretching and compressing caused by the zoom happens along spiral paths. (This formula describes image distortion as a function of these various settings.)

Of course, because of the iterative, fractal nature of the video feedback effect, it isn't surprising that it causes familiar and organic patterns to emerge, as seen in the above clip.

Natural Born Killer

It is the pain-causing agent in insect venom and poisonous plant spines, and the diarrhea-inducing ingredient in the cellular juices of pathogenic amoebas: serotonin is an extremely potent chemical. No wonder, then, that just a few molecules more or less of it can send the brain hurtling between happiness and deep emotional unrest.

Serotonin in the brain influences everything from mood to fatigue to hunger to memory, and its levels are so precariously balanced that regulating it requires vast spirals of DNA. While outside factors like diet, sleep, and stress cause serotonin levels to fluctuate, damage at the source has far worse consequences: a single serotonin-related genetic defect can double or triple the likelihood of depression, obesity, or suicide.

Dysfunction in a gene called MAOA, the so-called "warrior gene," even goes so far as to cause psychopathy. The gene inhibits serotonin reception in the impulse-control region of the brain. Combined with exposure to abuse or trauma, studies show that the defect makes people highly susceptible to violent crime. Because the MAOA gene gets passed down only on the X sex chromosome of mothers, more men than women are psychopaths. For a man, only one X chromosome is inherited - the one from his mother, so, lacking an alternative, it gets expressed. A woman on the other hand gets an X from each parent, so that the normal MAOA gene usually inherited from her father can overrule a warrior one from her mother.

A neuroscientist named Jim Fallon of UC Irvine was one of the central figures involved in finding the correlation between the warrior gene and psychopathy. Psychopaths have fascinated Fallon for the past two decades, and perhaps, without knowing it, this was why: Fallon recently learned that no less than seven killers, including the famous Lizzie Borden, decorate his family tree. He subsequently analyzed the DNA and scanned the brains of every living member of his family. All their brain scans were normal (the orbital cortex of psychopaths shows little to no activity), and they all had normal MAOA genes - except one person. Fallon himself has all the trappings of a psychopath. In an interview for npr.org, he said, "I have the pattern, the risky pattern. In a sense, I'm a born killer."

Fallon describes his upbringing as "terrific," and credits it with stopping him from becoming a psychopath. Of course, this frightening insight into his own character, this realization of what he could have turned into if not for the love and kindness of a doting family, has given Fallon a degree of compassion for those genetically like him who didn't have it so easy. Most of us know to be conscious of the abuse and strife that violent criminals may have endured as children. But a setback as concrete as a genetic predisposition - a defect - is somehow even more deserving of compassion. In the words of Barbara Hagerty for NPR, "Enter the new world of 'neurolaw,' in which neuroscience is used as evidence in the courtroom."

The Pioneer Itch

NASA launched sister spacecrafts Pioneer 10 and Pioneer 11 in 1972 and '73, respectively. Their joint mission was to gather information about the asteroid belt, as well as Jupiter, Saturn, and their moons. As the probes hurtled past these objects, they measured many properties of their atmospheres and surfaces; they also took beautiful and now famous photographs of Jupiter's red spot and Saturn's rings.

Then, after the Pioneers completed their "flyby" missions, they kept going. Carrying identical plaques depicting a man and a woman, the atomic transition of hydrogen, and the location of the Sun and Earth within the galaxy--a message to aliens--they are now exiting the solar system in opposite directions: 10 heads toward the constellation Taurus, and 11 aims for Aquila.

In 1995, 11 sent its last blip of data back to Earth. 10 stayed in contact longer, sending sporadic bursts of signal until 2003. After their lines went dead and all was said and done, the Pioneers had indeed lived up to their family name. They provided decades of data for scientists to analyze, and from them we have learned a great deal about distant regions of the solar system.

But as NASA scientists sifted through the last signals sent by the spacecrafts from deep space, a problem emerged. It seemed minor at first - just a small discrepancy between the incoming data and the engineers' predictions, which (I assume) must happen occasionally at NASA. But no amount of rechecking the data or reevaluating predictions could force the two to sync up. The divergence wouldn't go away, because it reflected the divergence of the Pioneer spacecrafts themselves.

On their way out of the solar system, as they struggled through the gravitational field of the Sun and planets, the Pioneers were slowing down. Of course NASA expected this: they had made staggeringly precise calculations of the gravitational pull on the spacecrafts at every point in space, and they knew the exact rate at which the probes ought to decelerate during their uphill climb against gravity. The problem was, 10 and 11 were decelerating too much. Each year, they were 5,000 kilometers farther behind where they should have been on their respective paths. 5,000 kilometers is very little in the context of space travel, to be sure, but it isn't trivial. Some additional, undeniable force is pulling the probes inward toward the Sun, a force about 10 billion times weaker than gravity, and we have no idea what it is.

The scientific community caught wind of the so-called Pioneer anomaly in the late 90s, and in the years since, they have studied, theorized, and passionately argued about it via two international conferences and hundreds, or possibly thousands, of academic papers.

Why do they care so much? Well, the thinking is this: the anomalous effect could stem from errors in the machinery of the Pioneers, such as gas leaks, asymmetrical solar heating, or an unaccounted-for force exerted backwards by the probes' radio transmissions. Theoretically, these types of issues could throw things off course, and if NASA plans to execute deep space missions in future, they need to figure out what's going on.

But as engineers go over every detail of the spacecraft designs, analyze every possible source of error, and find no problem, the erroneous machinery explanation seems less and less likely. Alternatively and much more seriously, physics itself, not the spacecrafts, might be broken. The Pioneer anomaly could be our first clue of a mysterious, extremely weak force that exists in the Universe.

Many scientists who've dedicated their careers to contemplating the Pioneer anomaly think NASA ought to plan a mission specifically aimed to test it. If a spacecraft with an entirely different design and instrumentation shows the same lagging effect in deep space as the Pioneers, then the "new physics" explanation of the anomaly moves forward. If a new spacecraft shows no anomalous motion, then the broken Pioneers idea gets a boost.

Until such a mission, scientific fascination mixed with psychological confusion will continue to surround the Pioneer anomaly. Revolutions in physics often stem from results that subtly deviate from predictions, like when the precession of the perihelion of Mercury led to the overthrow of Newtonian mechanics by Einstein's theory of general relativity. The seed of revolution may be germinating once again. But the maddening thing is, maybe it's not!

Connotations of Color

Check out this infographic displaying the symbolic meanings of colors in various regions of the world. (And see more visualizations made by Dave McCandless at his website, Information is Beautiful.)

The only color connotations consistent across cultures appear to be black for evil, and red for both passion and heat.