Archives For Philosophy

Here’s a conundrum for you: Using only technology available hundreds of years ago, how could you determine the speed at which light travels? We know now that light travels at 299,792,458 m/s, or, to put it simply, “very, very fast.” In fact, we are so sure of this value that we use it to define the meter, where one meter is equal to the distance that light travels in 1/299,792,458 of a second. Today, we have access to technology which allows us to calculate this value. Time-of-flight devices pulse bright flashes of light which are reflected off a mirror, and the difference in time (down to nanoseconds) combined with the distance from the source/detector and the mirror provides an accurate measurement of the speed of light. Additionally, one can take advantage of cavity resonators or interferometers to obtain the same value. However, these devices did not always exist, yet estimates for the speed of light predate their existence. How was this accomplished?

In a first account of the discussion on light propagation, Aristotle incorrectly disagreed with Empedocles, who claimed that light took a finite amount of time to reach Earth. Descartes, too, claimed that light traveled instantaneously. Galileo, in Two New Sciences, made the observation that light appears to travel instantaneously, but that the only observation is that light must travel much faster than sound:

Everyday experience shows that the propagation of light is instantaneous; for when we see a piece of artillery fired, at great distance, the flash reaches our eyes without lapse of time; but the sound reaches the ear only after a noticeable interval.

To determine the speed of light, Galileo devised a time-of-flight experiment similar to the one described above, where two individuals with lanterns would stand at a distance, uncover and recover them upon seeing a flash from the opposing partner, and calculate times between flashes. By starting very close to account for reaction times and eventually moving very far away, one could see if there is a noticeable change in latency. However, this experiment is challenging, to say the least. Is there a simpler method?

Enter Danish astronomer Ole Roemer. Known in his time for accuracy in measurement, arguments over the Gregorian calendar, and firing all the police in Copenhagen, he is best known for his measurement of the speed of light in the 17th century.

While at the Paris Observatory, Roemer carefully studied the orbit of Io, one of Jupiter’s moons. Io orbits Jupiter every 42 and a half hours, a steady rate. This discovery was made by Galileo in 1610 and well-characterized over the following years. During this time, Io is eclipsed by Jupiter, where it disappears for a time and then reemerges sometime later. However, Roemer noticed that, unlike the steady state of Io’s orbit, the times of disappearance and reemergence did change. In fact, Roemer predicted that an eclipse in November 1679 would be 10 minutes behind schedule. When he was proved right, the Royal Observatory remained flabbergasted. Why was this the case?

The figure above, from Roemer’s notes, highlights Earth’s orbit (HGFEKL) around the sun (A). Io’s orbit eclipses (DC) are shown, defined by Jupiter’s (B) shadow. For a period of time, at point H, one cannot observe all eclipses of Io, since Jupiter blocks the path of light. However, when Earth is at positions L or K, one can observe the disappearances of Io, while at positions G and F, one can observe the reemergences of Io. Even if you didn’t follow any of that, note simply that while Io’s orbit does not change, the Earth’s position relative to Jupiter/Io does change as it orbits the Sun. One observing Io’s eclipse at point L or G is closer to Jupiter than one observing an eclipse when the Earth is at point K or F. If light does not travel instantaneously, observations at points K and F will lag, because light takes a bit longer to reach Earth from Io.

In order to calculate the speed of light from this observation, Roemer needed information from his colleagues on the distances from the Earth to the Sun. Additionally, there are other complications. Nonetheless, using the measured distance from the Earth to the Sun at the time (taking advantage of parallax), Roemer announced that the speed of light was approximately 220,000 km/s. While more than 25% lower than the actual speed of light, it remains astounding that one could estimate this speed using nothing but a telescope, a moon, and a notebook.

Giovanni Cassini, a contemporary of Roemer, was not convinced at first. However, Isaac Newton noted the following in his Principia, from Roemer’s observations:

“For it is now certain from the phenomena of Jupiter’s satellites, confirmed by the observations of different astronomers, that light is propagated in succession and requires about seven or eight minutes to travel from the sun to the earth.” 

In other words, philosophers now began to accept that light travels in a finite amount of time.

Over the course of many years, others continued to estimate the speed of light using creative methods. James Bradley, in 1728, noticed that the positions of stars changed during rainfall, using these observations to estimate the speed of light with great accuracy (Bradley: 185,000 miles/second; Speed of Light: 186,282 miles/second). In 1850 in France, Fizeau and Foccault designed a time-of-flight apparatus like the one described in the opening paragraph. As opposed to using modern technology, the apparatus uses a rotating wheel to simulate blips of light. With a wheel of one hundred teeth moving at one hundred rotations per second, the speed of light could be calculated to within the accuracy of Bradley’s observations. Albert Michelson, in the 1870s, repeated the measurements on a larger scale, again with a series of mirrors.

What can be gleaned from this story is a powerful lesson. At times, the simplest observations can result in the most compelling findings. What it required in this case was careful note-taking and a bit of intellect. Even without those, simple observation cannot be understated.

Diving Through Dimensions

February 10, 2013 — 1 Comment

I recently made a purchase of a hand-blown Klein bottle. For those not familiar with the concept, a Klein bottle is an unorientable surface that was constructed by sewing two Möbius strips together. These surfaces are interesting in that we have a three-dimensional structure that appears to have two surfaces. However, closer inspection reveals that these two “sides” are both the same surface. This is thus a projection of a lower number of dimensions onto a higher order. If you are interested in these, I recommend a beautiful little short story by A.J. Deutsch, “A Subway Named Mobius.”  

Another projection that may interest you is known as a hypercube, or tesseract. This is not the same tesseract from Madeleine L’Engel’s A Wrinkle in Time, but parallels could be drawn. A hypercube is a four-dimensional object projected onto three dimensions. Within the hypercube, one should see eight cubical cells. Look closely at the projection on the link above. There is a large cube, a small cube, and six distorted “cubes” connecting them. This distortion is a byproduct of the projection onto a lower number of dimensions. To better illustrate this distortion, consider a three-dimensional cube projected as a wireframe onto two dimensions. As opposed to searching for eight cubical cells, we can see six “square” cells. There are two squares, one in the front, and one in the back. These are then connected by four additional “squares.” This projection of a three-dimensional cube onto a two-dimensional surface follows the same concepts of the four-dimensional hypercube projected into three-dimensional space.

However, we cannot visualize four spatial dimensions. This makes the concepts of additional dimensions quite confusing. Should we believe that such dimensions exist? Another interesting story on this topic is that of a world known as Flatland. The story, written in the 19th century, describes a world where only two dimensions exist. Males are placed into social classes by the number of sides in their structure, where circles are the highest order of priests. Females are line segments and, as you can imagine, are quite dangerous if approached from the “front.” The novella delves into the natural laws of this world, the communities, the buildings, and the social norms of this world. The story then focused on a Square, who is visited by a Sphere in his dreams. The Sphere describes the third dimension to the Square (Spaceland), but he cannot understand it. Only by introducing the Square to Lineland and Pointland can he begin to believe in a place called Spaceland. It is a wonderfully-entertaining pamphlet, and I highly recommend reading it.

Let us assume, however, that in another iteration of Flatland, one that follows all the same natural laws of our three-dimensional Spaceland, the Square is not visited by the Sphere. For some reason, the Square is deluded into the heresy that another dimension exists. Without knowledge from some higher-order Sphere, how can he, the Square, demonstrate the existence of a third dimension? Is it even possible?

We need to make two assumptions. First, this version of Flatland follows all the rules of our world. Second, Flatland is a sheet within our world, meaning that there is space above and below Flatland, but the inhabitants of Flatland are unaware of “up” and “down.” Taking these into account, we can then answer this question quite simply. The Square can perform a fairly simple experiment. I must state, however, that this experiment will only provide evidence of a third dimension, and other models of the Flatland Universe could reach the same conclusion. That being said, bear with me.

In our world, at certain spatial dimensions (not very small, and not very large), forces exerted by two objects from the forces of gravity or electromagnetism propagate in three-dimensional space. This results in a reduction of the forces exerted by the objects upon one another as the radius between them increases.  The law they follow is an inverse-square law, where the force exerted is proportional to 1/R^2. However, when we are in a universe limited to only two dimensions, assuming isotropy, there would be no additional spreading in a third dimension, leading the force to follow a simple inverse law, where force is proportional to 1/R. If the Square took two magnets at a reasonable size and distance and measured the forces acting upon them as the radius was changed, he could make a plot of force versus radius. The relationship would presumably follow an inverse-square law, and the Square would have evidence that a third dimension exists! Again, this would be met with scrutiny from the Circles.

Though we cannot always visualize additional dimensions or scales, we can perform experiments to not only demonstrate their existence, but to observe phenomena at an otherwise unobservable scale. This is an aspect of experimentation that I find fascinating. I hope my introduction to dimensional projections, if nothing else, will bring a new perspective on observations around you.


This time of year is a busy one, made busier with my additional work on a science outreach project. I will post details on this project once our Kickstarter page goes live. It will be an exciting one, and I promise to provide details on the techniques I employed for my portion of the promo video. This busy time of year led me to write less posts, but do not fret. Today I discuss a topic slightly removed from science and medicine, and that topic is science fiction. This should provide a nice reprieve for a holiday season.

A friend recently asked, “What genre do you read the most? And what is your opinion of science fiction?” Both of those questions require complex answers, and I am not an authority on the latter topic. However, I’ll tell you what draws me to science fiction, even though most of my reading is on Pubmed or arXiv and novels I read are rooted more in ethics and philosophy than in science fiction or fantasy (see: “Zen and the Art of Motorcycle Maintenance”, “Ishmael”). Science fiction is more than phasers, hyperdrive, ansibles, and soylent green.

The genre begins at our present reality and extends it. Concepts from science,medicine, and even politics are nudged to new heights, and a story is birthed. Suspension of disbelief is often required. Unlike fantasy or even magical realism, the story is deemed plausible, as explanations are required from the author. For example, faster than light communication, a technology that breaks our current understanding of the universe, requires some mechanism. This extension of reality allows writers to do something wonderful. They explore social structures, morality, religion, and more. It is this that makes the genre wonderful. While I may not agree with the science in science fiction, that word, “science,” implies a level of critical thinking. The memorable stories from the genre apply such critical thinking to contemporary issues, and they delve into fundamental questions in philosophy. This is not a requirement for the genre, but it is what draws me to its best works.

Every genre has traits like this. Biographies, for example, relay information about a person’s life experiences. However, these books may also impart wisdom through lessons gleaned by the protagonist. In Team of Rivals, we learn that a former President was inspired by a cabinet with whom he disagreed. In one of Richard Feynman’s memoirs, we learn lessons of love and humility. For example, he tells the story of a pen commissioned by NASA that could write in microgravity. After months of work and significant money spent, the team revealed their “space pen” to the Soviets. Moscow responded, stating that they solved the problem by using pencils! This lesson, gleaned from a memoir, taught me a valuable lesson. This function of biographies is what raises their quality and timelessness. Fantasy provides similar critiques of society, yet it functions as an escape mechanism from the challenges of a difficult life.

Nonfiction educates, yet it is limited by the constraints of reality. Science fiction takes realty and extends it. Star Trek asked, “What makes us human?” Ender’s Game delved into questions of militarism and genocide. Many writers, such as Orwell, Huxley, and Bradbury, created dystopias where a flicker in decision making led to a scary world. These were rooted in the contexts of the time, and we still reference such works when critiquing current societal measures.

So, what is my take on science fiction? While myriad laws are broken in the writing of these novels, I am drawn to them. These novels apply the scientific method in a work of fiction. They ask a question about an alternate reality, create and experiment with this reality with an artistic license, and draw a set of conclusions from the simulations they employ. We can debate the lessons learned from such novels. That debate alone is further evidence that the works initiated a conversation.

However, remember this: Orson Scott Card really has no idea how time dilation works.

Every year, I read an article written in 1972 by P.W. Anderson, More is Different. This exercise provides two functions. On one hand, it is a kind of ritualistic experience through which I can reflect on the past year. On the other, it allows me to revisit the paper with an expanded knowledge base. The paper revisits an age-old discussion in science: Are less fundamental fields of research simply applied versions of their counterparts?

In 1965, V.F. Weisskopf, in an essay entitled In Defence of High Energy Physics, delineated two types of fields. One, which he called intensive, sought after fundamental laws. The other, extensive, used these fundamental laws to explain various phenomena. In other words, extensive research is simply applied intensive research. In many ways, various fields are closer in proximity to fundamental laws than others. Most of neuroscience is more fundamental than psychology, in that it is reduced to smaller scales and focuses on simpler parts of a more complex system. This psychology, however, is closer to its fundamental laws than the social sciences. Again, where psychology focuses on the workings of individual and small-group dynamics, social sciences use many of these laws to explain their work. Molecular biology is seen as more fundamental than cell biology. Chemistry is less fundamental than many-body physics, which is less fundamental than particle physics. The argument by Weisskopf seems to be in favor when discussing fields in terms of their size scale.

Changes between size scale, however, leads us to a discussion of symmetry. Anderson begins his discussion with the example of ammonia. This molecule forms a pyramid, with one nitrogen at its ‘peak’ and three hydrogrens forming the base. A problem arises, however. When discussing a nucleus, we see that there is no dipole moment, or no net direction of charge. However, the negative nitrogen and positive hydrogens form a structure that disobeys this law, or so one might think. It actually turns out that symmetry is preserved through tunneling of the nitrogen, flipping the structure and creating a net dipole moment of zero. Simply put, symmetry is preserved. Weisskopf’s argument continues to hold, even with the scale change.

However, when the molecule becomes very large, such as sugars made by living systems, this inversion no longer occurs, and the symmetry is broken. The fundamental laws applied at the level of the nucleus now no longer hold. Additionally, one can ask: Knowing only what we learned about the symmetry of a nucleus, could we then infer the behavior of ammonia, glucose, crystal lattices, or other complex structures? The fundamental laws, while still applied to the system, do not capture the behavior at this new scale. On top of that, very large systems break the symmetry entirely.

Andersen goes on to discuss a number of other possibilities. In addition to structure, he analyses time dependence, conductivity, and the transfer of information. In particular, consider the crystal that carries information in living systems: DNA. Here, we have a structure that need not be symmetric, and new laws of information transfer arise from this structure and its counterparts that would not be predicted from particle physics or many-body physics alone.  Considering the DNA example, we must then ask ourselves: Can questions in social sciences, psychology, and biology be explained by DNA alone? We are often tempted, and rightfully so, to reduce these complex systems to changes in our DNA structure. This much is true. However, can we predictably rebuild the same social psychology from such a simple code? With the addition of epigenetics, we are trying to do so, but I argue that we are not yet there. In fact, I argue that we never will be there.

The message here is that larger, more complex systems, while built upon the fundamental laws of their reduced counterparts, display unique phenomena of their own. We can continue to reduce complex systems to smaller scales. In doing so, complexities and phenomena of the larger systems are lost. Starting only with knowledge from the fundamental laws, can we predict all of the phenomena of the larger scales, without prior knowledge of those phenomena? Probably not. This is another kind of broken symmetry, where traverse fields in an intensive direction will lead one in the formulation of a fundamental laws, but traversing in the extensive direction from those fundamental laws will lead to more and more possibilities that need not be the one from where we started. As scales grow, so too does the probability of broken symmetry.

Thus, when stating that “X is just applied Y,” remember ammonia.


Another kind of flood

November 2, 2012 — Leave a comment

Earlier this week, a large storm, whose pressure was at the level we would expect from a category four hurricane, threatened the east coast of the United States. This storm turned inland toward the coast of New Jersey, and its northern winds flooded the city of New York. The Jersey coast is still in disrepair, homes are flooded, power is down, many have been injured or killed, and thousands have been displaced.

Disasters occur every day. However, this particular one was enough to shut down the largest public transportation system in the United States, and an entire state has been pummeled. During a time when we see a country divided, I worried about the consequences of this storm. Would politicians use it for political gain? Would those in unaffected regions ignore the calamity and complain that their local grocery was out of poppyseed bagels? Would the cities be unable to handle such a situation? While some may fall into this category, the majority have not.

Hurricane Sandy brought with it torrential downpours and surges that flooded an entire region. However, the aftermath brought a flood of a different nature. Residents from around the region, country, and world helped in whatever way they could. I spoke with a few people who were in the British and Australian Red Cross divisions, who were visiting for vacation. They stopped the trip short and used their past experience to help us. Friends and classmates dedicated countless hours to volunteer at shelters, hospitals, and various cleanup efforts. Those with more than their share gave their excess clothing and money to those displaced by the storm. Politicians crossed the isle and worked together. Medical students sacrificed a few hours of study time to triage patients. Graduate students did what they could to comfort patients at our local hospitals. People from all walks of life came together and found their way to do what they were able to do best. I was amazed at the self segregation of volunteers based upon expertise or past disaster relief experiences. This demonstrated, in a surge of realization, the flood of humanity that outpoured when neighbors were in need.

For those who are currently affected, please know that you are not alone. For those that are not, call your friends and family. I need not say this, but it couldn’t hurt to remind everyone.

I will not write about my experiences in this storm other than to say that I am safe and that I am humbled by those who have been with me the past few days. I am proud of my neighbors, my city, and my country in times like this.

I will also not add any information on the science or educational aspects of the storm. I hope this will give readers a chance to reflect in the same way this post was a reflection.

The blog will return to its regular programming shortly.

Orwellian Semantics

September 30, 2012 — Leave a comment

I have numerous issues with the bad habits of modern writing, including an overuse of the passive voice, laziness through use of metaphor, and an abundance of technical jargon or pretentious vocabulary. My writing often falls victim to this, especially with my personal poor habit of the use of the passive voice. It becomes problematic in medical or technical communication when jargon and abbreviations render listeners incapable of understanding. In political speech, we hear perversions of metaphorical language, with a bit of Latin thrown in where a Saxon word would suffice. This lack of precision becomes problematic, and such issues were discussed by George Orwell in his fierce essay, ‘Politics and the English Language.’

I’ve often heard, in casual conversation or, worse, in public arenas, the phrase ‘it’s only semantics’ or a phrase of that nature. This implies that the person is either lazy in speech or uninformed. I like to think that our downfall is sloth rather than lack of knowledge, so I will assume that these people know the premises behind semantics, what they imply, and why they are so very important. If that is true, then the speaker is simply tired of the disconnect in language that is being proposed.

Let’s assume one hasn’t read the precision of Ernest Hemingway, the frugality of EB White, or the aforementioned essay by Orwell. I’ll relate semantics to the study of information, information theory. Let’s trace a message from you to me,if we were speaking or writing to one another. A message begins at its source, such as a thought or argument in your brain. You must codify this message into language, either written, spoken, signed by hand, or some variation. That message is transmitted, by air, telecommunications, visually, or the like, to me. I must then, as the receiver, decode the message. Thus, information passes from you to me. A problem at any level leads to a breakdown in our conversation and, according to the optimist Orwell, decline of civilization.

Semantics is the study or philosophy of how we communicate with and understand one another. In terms of the information theory example above, this refers to the coding and decoding of speech. The words we use attempt to convey information. If the words are not precise, the information will be lost or misunderstood. If you heard me state that ‘John is a wild card, but Jane is solid,’ would you say this is precise? Sure, in context, you might understand the message, but that is no excuse and is thus laziness of speech. If you heard ‘John’s exam performance varies based upon his mood, but Jane always performs well,’ you can already see an improvement in the message’s precision. Again, we should remain as precise as possible, no matter the context.

In communicating between those in medicine, those in science, those in economics, and those in countless other fields, I can see this lack of focus on semantics. We become lazy and begin to use metaphors, jargon, or lack of descriptive terms. We then become annoyed when a person begins to focus on the meaning behind individual words or phrases, stating that it is only semantics. Thus, I believe this phrase stems from a laziness founded in sloth.

I am a horrid writer. Specifically, I mean that I tend to use the passive voice too often, use unnecessary words to balance the flow of a sentence, and often lack precision. However, I believe very strongly in proper communication. Many say this has to do with listening, but the act of listening is limited by the quality of the message transmitted.

This post stems both from issues in my research proposal revisions and with my status lying at the meeting point between medical and graduate students. They don’t understand each other quite often, and my split personality feels a sense of cognitive dissonance. I urge those in any field to practice in precision and recoding of speech for those outside your field. I’m working on it, too, and it is difficult to break bad habits.

A Eureka in Base 10

September 24, 2012 — Leave a comment

Recently, I was preparing a short manuscript on some of my recent data. While performing a few simple calculations and keeping track of various tasks with my hands (i.e. counting with my fingers), a realization struck me. Our ten fingers are the foundation for base 10! This is such an obvious concept to most readers, but it is one that took me by surprise. The ten fingers and ten toes then provide a foundation for base 20. This realization is just one of many in my life. They are low-tier eureka moments, one where the concept is not all that difficult to understand, but a flash of insight nonetheless occurs. These are the events in life that lead not to a great discovery, but instead open our minds to another level of understanding.

However, I’d like to talk a little bit about the eureka effect. It has been rumored that Archimedes coined the term when developing the principle that buoyant force of a mass in liquid is equal to the weight of the liquid it displaces, but that probably isn’t true. He probably never uttered the phrase, “eureka.” The basic formula is as follows. First, one reaches a mental block of sorts. We have all been there. After studying for hours or looking at a particular problem for quite awhile, we feel that there is a limit to our knowledge. There is of course some limit in capacity, but we may not have reached a limit in our insight and rarely reach limits of capacity. Then, a sudden moment occurs where one appears on the opposite side of this barrier. This leads to a new level of understanding and answers to problems previously deemed inaccessible. My example of the “base 10” problem wasn’t a classic eureka moment, in that I was not preoccupied with the concept. However, the sudden stroke of insight definitely felt like one.

This moment is not purely metaphysical. Groups studying brain activity with fMRI found sudden bursts of high-frequency activity in the right anterior temporal area of the brain. Furthermore, it was uncovered the sleep enhances these moments by reconstructing memory in a facilitative manner. Not only do numerous people find themselves beneficiaries of such exciting bursts of insight, but groups have themselves been preoccupied with the mechanism behind overcoming preoccupation.