Fish Poisons for Anesthesia

I stumbled across a bizzarre video in my recommended videos feed on YouTube yesterday that shows a goldfish getting surgery on his head growth blocking his vision (Note: this video is not for people who are squeamish, although there is no blood):

The video was an interesting find overall, simply because it had no actual correlation with any videos in my watch history. I haven’t watched videos on fish or surgery, so to be recommended with a video featuring both was unusual. To be honest, while I was engrossed by the goldfish surgery, what made me keep watching was the maker, Colum’s Aquaponics’, use of clove oil to sedate the fish.

This brought two thoughts to my mind. The first was that clove oil has been recommended by traditional herbal medicine for toothaches. Typical application may have entailed chewing a clove or putting it between the gums and cheek next to the painful area. According to Colgate, clove oil has also been on the rise as a form of alternative medicine for oral pain in recent times as well [1]. Clove oil contains the chemical eugenol that is responsible for its anesthetic properties and is also used in refined form for modern dental applications [2]. Eugenol is a substituted guaiacol, making it related chemically to other plant compounds like vanillin though with very different effects [3]. Seemingly unrelated, this link between analgesia in humans and anesthesia in fish makes the use of clove oil to numb a surgery appear plausible to me, though a stretch.

Fig. 1: Eugenol, a fish anesthetic found in clove oil (Wikimedia)

The second was that in ancient Hawai’i, there was a method of fishing that involved lacing a stream or tide pool with a plant tincture to sedate the fish and cause them to float to the surface. The plants used included ‘ahuhu (Tephrosia purpurea) containing the fish toxin tephrosin and ‘akia (Wikstroemia oahuensis) [4(published in 1921, source must be treated as a work of its time),5]. Looking at some pictures of ‘akia on the internet, I immediately recognized the plant to have grown all over my elementary school campus back home. That’s pretty weird to think about, but it also makes me feel like I’ve missed out on an opportunity for some fun experiments.  

Fig. 2: 'Akia plant leaves and flowers ('Imiloa)

Hawai’i is not the only place to have practiced poison fishing, though in general the practice is considered destructive and paralleled to other wide-effect fishing methods like blast-fishing. And of course, the limited reach of poison fishing would be no match for the current global demand for fish. Yet while this fishing technique has been passed by in modern times, the plants and chemicals once used for fishing may now find new applications, namely in fish anesthesia for aquatic veterinary care.

I hope you enjoyed this short blurb on the interesting topic of fish anesthesia, and be sure to leave a comment and share your thoughts on the post. These past few weeks have been busy in school, and the first wave of midterms (UPenn doesn’t understand the term “midterm”) has started to hit. I do believe I will be able to post at least every other week, however, as seems to be my current posting schedule, so be sure to look out for future posts. As always, thanks for reading!  

An Analytical Approach to Pamphlet Folding

Most of us can say we’ve endured the frustration of folding letters or pamphlets, trying as much as possible to align the corners for a straight fold only to have them wiggle freely as the crease is made. And in an office like the one I work at, half-folding pamphlets is a fairly procedural task. Whenever this work is entrusted with me, I like to build a rig like the one shown below to minimize the chances of me pulling my hair out.

Fig. 1: Makeshift pamphlet folding rig

It's easy to arrive at a tool like this based on common-sense, but we can also take a more analytical approach as to why a simple 90° corner can make paper folding so much easier. We need to start with a surface-level premise about the universe we live in; as far as we can tell, our universe is comprised of three spatial dimensions, mathematically attributed as x, y and z and experienced as length, width and height, and one temporal dimension. The temporal dimension and the other however many must exist according to string theory or what have you aren’t as important in this task as the three spatial dimensions with which we interact on a daily basis. An unfolded pamphlet can move freely through these three spatial dimensions, as throwing them out the office window will demonstrate when they flutter down to the street below. But while they are sitting on my desk waiting to be folded, they don’t budge. This is because the desk on which they sit is applying an upward force on the pamphlet stack, counteracting gravity and preventing them from moving towards the center of the earth. Balancing forces like this is the foundation of mechanics and is the way that the following discussion manifests in the physical world we live in.

So what else is there to consider? Well, three free dimensions can also be referred to as three “degrees of freedom,” a fancy term that just says a variable can change as necessary. The more degrees of freedom that exist, the harder it is to pinpoint the position of an object that moves freely, like the corner of a pamphlet. What’s also cool about the three spatial dimensions is that even though by default we orient the basis of the defined dimensions to align one direction with gravity because this simplifies calculations, linear algebra tells us that the basis vectors x, y and z are easily translatable to different positions. Now let’s take my desk, oriented by default in the x-y plane, and translate it so that it now exists in the y-z plane. This is kind of similar to if I were floating with my body parallel to the desk, which would make more sense if I were in outer space since there is not as strong a default frame of reference when gravity is not apparent. What we see now is that my desk has somehow become like a wall! Amazing! This tells us that floors, walls and ceilings are not very dissimilar from each other, the common theme being that if I beamed a ball in a closed room, it would bounce off of all surfaces because its free motion in the three spatial directions has been truncated.

Fig. 2: Designation of three spatial dimensions adjusted to rig

Let’s return to the pamphlet folding rig. The rig is comprised simply of three walls: the desk and two others constructed from a box and a paper tray. Additionally, while folding gravity acts on the pamphlets to further constrict movement in the common z dimension, or up, while keeping the dimension still partially accessible so as to get the right side of the pamphlet over the left. My hands as well work to apply force to keep the pamphlet to the left against the box and away from me towards the paper tray while creasing, limiting the x and y dimensions. If we look at the two corners of the pamphlet tucked into the rig while half-folding, all three degrees of freedom have been collapsed, the pamphlets sandwiched between one surface and my hands along all three axes. Not only are these corners restrained, but the geometry of the pamphlet then guarantees that all other corners of the pamphlet should be aligned as well. So while in practice errors on my part and in my shabby rig’s construction limit the effectiveness of this folding method, in theory restricting the three degrees of spatial freedom of the pamphlet should produce a perfect fold every time without the frustration of any dancing corners.

Fig. 3: The final folded pamphlets

While some people may not appreciate such a lengthy analysis of as simple a contraption as a corner for folding pamphlets, I think really delving into why something so common-sense works from a physics standpoint demonstrates how approaching the world from an analytical perspective provides insights that can help everyday people live better lives. I hope you enjoyed this article, and if you have any feedback or questions, leave me a comment below. I love hearing from you guys. Thanks!

Iodine Salt to Treat Radiation?

Fig. 1: Next, movie cover (derricklferguson)

Over winter break I watched the movie Next starring Nicolas Cage with my dad. In the movie, the FBI was able to link a dead woman knifed in her room to a Russian nuclear attack plan because of a few potassium iodide (KI) pills found at the crime scene. The star FBI policewoman (who is also President Coin from the Hunger Games movies!) was quick in realizing that the only reason someone would take potassium iodide pills was to combat radiation poisoning. Before this movie, I had never heard of KI being used for this purpose, and expectedly I was skeptical. Before you judge me, imagine if someone had told you that a sugar pill could prevent you from dying of stomach cancer. That is the same magnitude of ridiculousness that I felt the whole KI pill thing had to be.

But, I was wrong of course. KI supplements are an established treatment for preventing thyroid cancer, one of the biggest health impacts observed after the Chernobyl meltdown [1]. So how is it that something so simple as a salt pill, because that’s what it is, can prevent one of the most odious conditions of modern times caused by a technology that took humans thousands of years to create? Turns out it’s by inhibition [2]. KI pills for thyroid cancer prevention aren’t made up of just any iodine; they are made of the ¹²⁷I isotope, which is iodine’s only stable form [3]. Ingested iodine is taken up by the thyroid gland, and if the iodine is of a radioactive isotope the subsequently produced radiation can cause thyroid cancer. KI pills work by dumping stable ¹²⁷I into the person’s blood stream, flooding the thyroid and reducing uptake of other radioactive iodine isotopes. KI pills only work in preventing thyroid cancer caused by radioactive iodine exposure, however, not other conditions caused by general radiation exposure.

Fig. 2: ²³⁵U fission product properties (Hochel, R. C.)

So, a few other questions obviously arise from this talk of iodide pills, one of which being where do the radioactive iodine isotopes come from in the context of nuclear fission? Fission of heavy atoms results in atoms of lighter weight and free neutrons that propagate the nuclear fission reaction. Some of the fission products of ²³⁵U are various iodine isotopes, including ¹³⁵I (6.33% yield), ¹³¹I (2.83% yield) and ¹²⁹I (0.9% yield) [4]. These are clearly not the main fission products of ²³⁵U, but they can still accumulate in contaminated environments, especially where large-scale nuclear fission reactions were involved such as nuclear meltdowns and atomic bomb testing sites. Another question to answer is how do the radioactive isotopes end up being ingested by people in contaminated regions? Scientists at Dartmouth, New Hampshire were able to measure increases in ¹³⁵I concentration, an indicator also of the presence of undetectable ¹²⁹I, on land but especially in local streams a year after the 2011 Fukushima meltdown in Japan [5]. They cited the increase as due to nuclear fallout from the Fukushima incident that blew across the continent and deposited itself in groundwater sources. This implies that the radioactive iodine isotopes can be both airborne and waterborne. If everything is coated in radioactive iodine, ingestion is believably imminent. To bring us full circle, there was also a run on KI pills in 2011 on the American West Coast due to fears of radioactive iodine finding its way into homes and food supplies there as well [6]. It’s funny how analyzing a simple movie premise can take us all the way to a not-so-late nuclear disaster.

Yesterday was the first day of classes, and soon enough school will be back in full swing. I've based my schedule this semester off of a google calendar with the idea that better organization will make hectic school life just a bit easier, so we'll see how that goes. My course load is two materials science classes, one materials science lab, orgo 2 and an anthropology class on modern culture. I'm hopeful that this semester will go better than last, and I'll keep you guys updated on what goes on. If you like this article or have ideas for another, be sure to leave me a comment below. Thanks for reading!

Can the Earth's Magnetic Field Support a Space Railgun?

Fig. 1: Railgun diagram (HowStuffWorks)

In physics class, you’ve probably learned about railguns and how they use magnetic fields and current to generate a propulsive force. And if you’re anything like me, you’ve probably wondered if we can launch a person or spaceship with one, because why not? What would be even cooler is if we could do it with the earth’s ambient magnetic field. Well, let’s test this idea a little bit.

We know that the force generated by a magnetic field on a charged particle is

1.       F = d/dt(L)q x B = qv x B (L is displacement, q is charge, B is magnetic field, v is velocity)

An equivalent statement more applicable to railguns is 

2.       F = d/dt(q)L x B = IL x B          (I is current)

This change of derivative position is acceptable because it represents a change in reference frame, the displacement derivative in the frame of the charged particle and the charge derivative from a fixed external frame of reference, watching the charges flow by. In the setup of a railgun, B and I are orthogonal and the resultant vector of the cross product is in the direction of propulsion. Solving the cross product yields

3.       F = ILB 

We also know the induced current through the railgun circuit to be related to the generated emf, 

4.       Ɛ = - d/dt(Φ_B) = - d/dt(BA) = - Bd/dt(A)          (Φ_B is magnetic flux, A is area)

By geometric analysis, we know the change in area to be the fixed base length/bar length times the change in height, or

5.       d/dt(A) = L d/dt(h) = Lv          (h is height)

The full expression is

6.       Ɛ = IR = - BLv

7.       I = - BLv/R

Appending our force equation to account for induced current that works against the initial current, we get

8.       F = (I - BLv/R)LB = LBI – (L²B²/R)v

This equation is useful because by setting the magnetic force to zero we can solve for a terminal velocity,

9.       v = IR/LB

This is no good! If we’re to launch someone high into the sky, we need a constant force to produce a constant acceleration to exceed that of gravity. So what if we keep a constant effective current to counteract the current induced by propulsion? Looking at equation 8, we see that this is possible if we establish current as a time-dependent function given by

      10.   I(t) = I₀ + BLv/R                                                 (R is resistance)

      11.   I(t) = I₀ + BL(at)/R = I₀ + BL(Ft/m)/R               (from kinematic equations v=at and F=ma)

The F term here should be substituted with the constant force we predict to be generated by the current adjustment

12.   F = I₀LB

Substitution and regrouping produces

13.   I(t) = I₀(1 + (B²L²/Rm)t)          (m is mass)

This equation can be verified by substitution into equation 8. Now that our force is constant, let’s calculate what current would accelerate the average person [1] on a weightless conductive beam unaffected by air drag 1m in length enough to counteract gravity (a pretty low bar for testing viability of concept). Since the magnetic field generated by the circuit would probably diminish too close to the walls of a 1m launcher, an external field is necessary. Let’s try using the upper end of the earth’s magnetic field strength range [2].

                     14.   F = mg = I₀LB

                     15.   I₀ = mg/LB = (62kg)(9.8m/s²)/((1m)(65x10^-6 N/Am)) = 9.3x10⁶ A

That’s a lot of current, but perhaps possible? Adjusting for a spaceship weighing 1,000 times the average person 10m wide with an acceleration of 1m/s² [3], we get a figure on the scale of 1x10⁷ A. In 2014, the CERN Superconductors team was able to pass 20x10³ A through an MgB₂ superconducting wire, a world record at the time [4]. This record value is clearly magnitudes less than even the current necessary to lift a single person, let alone a spaceship. Looks like the earth's ambient field is a no-go. But! If the person were in a magnetic field of an achievable 1T even, then with currently achievable currents it should be possible to throw them at least into the sky if not into space. Hooray for space railguns!

If you liked this post or have any ideas for another, let me know by leaving a comment. Thanks for reading!

A Prediction of Marine Plastic Debris Growth

Although it is common knowledge that plastic waste finds its way to the ocean en masse as evidenced  regions of high marine debris such as the great Pacific Plastic Gyres, there are few statistics that put exactly how much plastic enters the oceans into frame. A study published in February of this year looked to do exactly that, estimating that in 2010 an approximate 4.8-12.7 million metric tons of plastic entered waterways over 192 coastal countries that year.

This estimate was generated by taking into account local statistics for waste generation per capita and population growth trends to predict the amount of trash that shoreline countries produced within a 50 km region from the coast. An approximation of 11% plastics content for the produced waste was then applied, and transformations were imposed to convert total plastic waste to mismanaged plastic waste and finally to marine plastic debris. The authors of the study state that their estimate is one to three magnitudes higher than estimates made based upon gyre plastic content and justify this by reasoning these other estimates to only account for buoyant plastics. However, this large discrepancy between the predicted value and others brings the accuracy of the estimation into question. In the materials and methods section, the described transformation from mismanaged waste to marine waste was arbitrarily set at a percentage set of 15%, 25% and 40%, values that were deemed conservative based on a described estimation for the San Francisco Bay area.

Fig. 1: Projected plastic marine debris entering the ocean from 2010 on (Article in Discussion)

The study also estimated based on the same model that a cumulative 100-250 million metric tons of plastic waste would enter the ocean by the year 2025. This range was based on an extrapolation of population growth and plastic waste content growth rates in the past, and for this reason may be brought under scrutiny considering emerging efforts to stifle plastic waste pollution. However, the numbers produced in this study still has shock value, which lends them importance. Knowing that these enormous numbers are estimated based on current and past trends should in itself be a wake-up call since the implication is that our current lifestyle is unsustainable and resonates into the foreseeable future. In other words, this study is a call to action for all countries to set measures in place that will curb marine pollution currently and protect our future oceans.

The study goes into further detail about the extent to which efforts to reduce plastic waste in the near future will affect the amount of plastic trash that ends up in the world oceans and also gives a more detailed breakdown of the contributions of each country to marine plastic debris. It is definitely worth checking out and can be found in full text here. Thanks!

Insights into Early Hominin Communication

A recent article published in Science looked to the skull shapes of early hominins, a group comprised of our now-extinct closest ancestors and ourselves, as a prediction of what sort of auditory sensitivity they were capable of, with interesting results. The shape and size of the auditory apparatus in animals affects the intensity with which each frequency register is perceived. In the study, the inner ears of early hominins, chimpanzees and modern humans were scrutinized, and the modeled ear parts of each were used to make predictions regarding the frequencies that were more easily heard, and the results were plotted as shown below. 

Fig. 1: Sensitivity to sound over a range of frequencies (article in discussion)

In the figure, the y-axis corresponds to the log of the ratio of sound power to reach the cochlea, Pcochlea, versus that of the sound source, Po, as a measure of the perceived sound intensity. The researchers conducting the study were able to show that the early hominins had a higher sensitivity to sound at around 3kHz than both chimpanzees and modern humans and generally higher sensitivity to lower frequency sounds as well, showing a decrease in sensitivity at higher frequencies that is more similar in trend to the hearing curve of chimpanzees than it is to humans. Modern humans, in contrast to the others, have a similar sensitivity curve at lower frequencies but extend hearing to higher frequency sound, dropping off near 4kHz frequency. In analyzing this finding, the researchers came to the conclusion that the adaption to a wider frequency range of hearing in modern humans was imperative for the development of consonants in human language. The researchers considered that the phonemes t, k, f and s in particular are associated with higher frequency sound and that the ability to perceive sound over a wide range of frequencies makes these sounds more distinct from each other. Since early hominins were incapable of perceiving the upper frequency range that modern humans can, the researchers postulate that communication between the early hominins would have been vowel-intensive. They make a point, however, of stating that this finding does not confirm any information about the extent to which early hominin language was used or developed; early hominins may have used a “low-fidelity social transmission” form of communication similar to that of modern chimpanzees. Nevertheless, the skulls of these early hominins have given us another insight into what life was like for some of our earliest ancestors.

The complete article on the differences in sound perception described above is available here. While the article is heavy on jargon, the results and discussion sections can be understood without fully understanding the early talk of ear anatomical differences. 

Also, please let me know your thoughts on this trial article in the comments. I am trying something new with the posts here, providing brief summaries of emerging science rather than explanatory articles of everyday phenomena. Feedback helps me decide what content I post. Thanks!

Boiling Water at High Altitudes: A Representation of American Scientific Literacy

A recent survey by the Pew Research Center found that Americans are more likely to answer correctly questions related to basic science concepts than to scientific understanding [1]. Among the bank of questions, ones such as which layer of the earth is hottest and whether uranium is used in nuclear energy were answered correctly more often than ones such as whether the amplitude of sound waves causes its loudness. The question answered incorrectly most often was whether water at higher altitudes boils at lower temperatures with only 34% of respondents knowing that, indeed, it does.

Fig. 1: Results of Pew Research Center survey (Pew Research Center, same as reference 1)

Public scientific literacy is an important goal to work towards for developed countries. As Cary Funk and Sara Kehaulani Goo of the Pew Research Center posit, the ability to understand scientific concepts is crucial to people being well enough informed about current issues such as GMOs and the energy crisis to make educated decisions in the polls. Scientific literacy also makes daily life easier by finding more efficient solutions to everyday problems.

As a small step towards improving scientific understanding, let us discuss why it is easier to boil water at higher altitudes.

Liquid water and water vapor exist in a sort of equilibrium. There are a number of factors that can shift this equilibrium, but one we interact with daily is temperature. Say you spill a glass of water. Of course, a large spill would require immediate attention, but if only a thimbleful of water was spilt, some would be inclined to let it evaporate. Evaporation involves two main processes at play. First, the water is receiving kinetic energy from its surroundings in the form of heat energy. Second, the water is in higher concentration in the spill than in the spill’s surroundings and therefore a concentration gradient is formed at the water’s surface.

So what has this all got to do with boiling water? Well, water boils when transforming into a gas. Therefore, boiling water is a phase transition described by the equilibrium between liquid water and water vapor. Besides temperature, pressure also affect liquid-gas equilibrium as described by the ideal gas equation,

                  1.       PV=nRT (P is pressure, V is volume, n is number of molecules in moles, R is the gas
                   constant, T is temperature)

LeChatelier’s principle states that a system in equilibrium will move away from an induced change. In the case of an increase in pressure, we can see that if n and T remain the same then the ideal gas law describes a shift to decrease V, volume. On the other hand, a decrease in pressure should cause a shift towards a higher V. This means that at lower pressures, water prefers to exist in a gaseous state and the equilibrium shift will cause the water to boil. This is the foundational concept of rotary evaporators, which use the concept of reduced-pressure boiling to remove solvents.

Fig. 2: Deriving atmospheric pressure in atm's (Pearson)

Now all that is left is to link pressure to altitude, which isn’t too hard. By definition, atmospheric pressure is defined as the weight of the atmosphere over an area at sea level [2]. For example, one inch of land at sea level partitions a pillar of atmosphere weighing 14.7 lbs, so atmospheric pressure in PSI is 14.7 lbs/in². A logical extension of this concept would tell us that at any altitude greater than sea level, the pillar of air would be shorter and would consequently weigh less. This is the missing link we were searching for between pressure and altitude. Putting all of the above information together, we see that a decrease in pressure causes liquid water to favor boiling and that an increase in altitude causes atmospheric pressure to decrease. Therefore, water boils easier at higher altitudes.

Scaling the results of the survey to education levels, the Pew Research Center also found a correlation between higher education and scientific knowledge. But this is not a given. Even as college students, we must all work towards insuring that we are among the scientifically literate ready to contribute educated opinions to today's social debates.

Approaching Herbalism from a Scientifically Literate Perspective

Is there really a founding for believing in herbal medicine? This seems to be a question many Americans are asking in a time when the concept of “human is better” is waning in favor of a return to an attitude that acknowledges we have a lot to learn from nature. Much of herbal medicine may seem like hocus-pocus, but scientists are not as against herbalism as some would think.

A first thought when someone mentions herbal medicine might be something along the lines of dried seahorse and mummified gecko. This is especially true for Americans where there is a high Chinese cultural medicine presence and where such practices are often caricaturized by the media. However, not all herbal medicine is so strange. Some common examples of herbal medicine practice could be honey-ginger tea for a sore throat and aloe (Aloe vera) for sunburns, both of which can be commonly bought in major store chains. As it turns out, much of the world uses some form of herbalism [1]. This shouldn’t come as a surprise. It is against human nature to accept illness as it comes, so wherever there are people there is likely to be medicine as well. But living in the time we do, both traditional herbal medicines and contemporary scientifically produced medicines are readily available. So which should we choose?

Fig. 1: Herbal medicine utilization by country (ClubNatu, same as source 1)

Herbal medicine is steeped in traditional medicine practices that developed before the scientific method and its instruments were available. Yet even so, many herbal remedies have come about through a rather logical process. Take even a fictitious, highly religious pre-scientific society where medicines are attributed to gods. If a medicine doesn’t heal its patient, then the instinct is to throw it out primarily because it’s useless and perhaps also because it makes the gods look bad. Our ancestors were smart enough to develop a working knowledge of herbs through thousands of years of trial and error, a highly valued logical test still used today in medicine development.

The argument some give in favor of a return to herbal medicine is that it’s more “natural” than modern synthetic drugs. This is not a well-based argument from a scientific perspective. Instead, we should consider factors such as effectiveness, side-effects, general safety of the herbs and the ecological impacts of its widespread prescription, each of which must be individually assessed per herb. The effectiveness of herbal remedies is a subject of increasing research attention as many have proven to possess clinical efficacy. Aspirin, for example, emerged from a more mild treatment of salicylic acid, a chemical found to exist in the bark of the white willow (Salix alba) tree used in traditional medicine. It has recently become a growing practice to scientifically test a wide number of natural products and traditional remedies as a high-throughput system for scouting out potential new treatments. Some herbal remedies have also been found to offer their effects with less side effects than modern medicine [2]. This could be due to a plethora of possible reasons including active dosage or the presence of other compounds to neutralize negative effects.

Fig. 2: Most popular natural products (including herbs) in the United States (NCCIH)

So where do herbal medicines fall short? All medicines have their associated risks, but a lack of herbal toxicity knowledge and of prescription guideline enforcement brings into question the safety of some herbal medicines [3]. The ecological effects of manufacturing herbal medicines must be considered as well. Paclitaxel, a drug with anti-tumor properties listed on the World Health Organization’s List of Essential Medicines, is a natural product from the bark of the Pacific Yew (Taxus brevifolia) tree [4]. However, wild-crafting this compound would devastate the tree population. Thus there is an inherent economic limitation on herbal paclitaxel, and so the synthetic generation of this natural compound is now the main route of production.

Herbal medicine is a topic that has been making a comeback under the realization that we have much more to discover about our medical pasts through a scientific approach. Personally, I am inclined to believe this is a step in the right direction since it is never bad to know more about plants that could potentially save our health. After all, it takes just one paclitaxel to make the search worth it. Social opinions on herbalism as a form of alternative medicine are shifting towards the positive, and as scientifically educated individuals we should keep ourselves updated on this movement.  

Is That a Point?

If I gave you a sheet of paper and asked you to draw me a nickel, you’d probably draw me a circle roughly an inch in diameter, maybe labeled with a "5₵". If I asked you to draw me a mite, the smart alecks out there would probably dot the piece of paper and give it back. If I asked for a realistic drawing of an atom, the same group would likely hand me back the blank page. This sort of answer is likely meant to be taken as a joke, but it also provides us with an insight into the limitations of human visual resolution.

Human eyes are anything but perfect, and some are less perfect than others. And as the silly drawings of the mite and the atom suggest, the smaller the object the harder it is for the human eye to resolve. By the international standard of measuring human visual resolution, good vision is defined as 20/20 (feet system) or 6/6 (meter system), meaning that someone with 20/20 vision can resolve what a person should be able to see (by designation) 20 ft away at the intended distance [1]. Someone with 20/40 vision sees at 20 ft what someone with 20/20 vision can see at 40 ft away, and someone with 20/10 vision sees at 20 ft what someone with 20/20 vision can see at 10 ft away. As objects get smaller, they seem to us as tending to a point. This occurrence is often referenced in physics where a source with radius r a distance d away from a sensor where d>>r (d is much greater than r) can be approximated as a point source.

But how exactly do we characterize this phenomenon, and at what distance does leaning forward while squinting intently seem… pointless? Let's take a look at the diagram below:

Fig. 1: A Spherical Object Viewed at Different Distances (Orig.)

 On the left side there is a spherical object of radius r₁ being observed by the first eye at a distance d₁ so that the object fills the observer’s field of view (denoted by the first set of dashed lines). The circle surrounding the object with radius r₂ represents the same observer’s field of view at a distance d₂ where d₂>d₁. The corresponding angles are drawn in and labeled as θ₁ and θ₂. From this diagram, we can obtain the equations

                                                                         1.       r₁=d₁tan θ₁

                                                                         2.       r₁=d₂tan θ₂

                                                                         3.       r₂=d₂tan θ₁

Dividing equation 1 by equation 3, we receive the statement

                                                                        4.       r₁/r₂= d₁/d₂

This equation tells us that as d₂ increases, the ratio of the original full-view object radius to the radius of the field of view at d₂ decreases as d₁/d₂=k/d₂ α 1/x (k is used to show that d₁ is a constant). The graph of 1/x is shown below:

Fig. 2: Graph of the Function f(x)=1/x (WyzAnt)

Where the x axis represents an increasing distance d₂ and the y axis represents the ratio r₁/r₂. This finding seems to agree with our experiences, doesn’t it? Namely, as we walk further away from an object it seems to decrease in size relative to our entire field of view, the size difference becoming less noticeable as distance increases further. If we were to walk far enough away, then the object would appear as if it were a point in our vision.

So we now know how to describe the way objects seem to decrease in size at far distances, but at what distance does any sort of difference in the object not matter? That is, when does the object become a point? Based on the human vision resolution assessment described earlier, we know that at 6m, or 20ft, the idealized human should be able to resolve a standardized interval of one arc minute, or 1/60° [2]. From rearranging equation 3, we receive the form

                                                                         5.       d₂=r₁/tan θ₂

Making the substitution of the maximum resolution for a 20/20 person’s vision, 1/60°, for θ₂, we produce the equation

                                                                          6.       d₂=3,438r₁

This equation says that an object with a radius r₁ can be seen from a distance a factor of 3,438 times its radius before a person with good vision can no longer sense its character beyond that of a point. This is like trying to see the face of a nickel from 146 meters away. While seemingly too far a distance to be visible, if we check equation 6 by substituting in the resolution corresponding to an arc minute at 6m, which is 1.75mm [3] (this can be checked with equation 1), then the distance returned is indeed 6m. With this information in mind, the next time you look up into the night sky I challenge you to think about just how big a star is compared to the twinkling dots you see above. Suddenly, it won’t seem so crazy to say we all live on the head of a pin.

Thank you guys for reading this post, and be sure to look out for more to come. If you want to be updated whenever I make a new post, sign up for email notifications on the right side column of the blog so you can have new posts sent directly to your email. Alternatively, if you send me a message on Google+ I'll add you to be notified when I post new content. If you have any suggested topics for future posts or you liked this post, let me know in the comments because I’d love to hear your thoughts. Thanks!

Birthday Borax and An Explanation of Crystal Nucleation

For my birthday a while back, a friend of mine gave me food coloring, a box of borax and spools of thread. I asked what they were for, and she said crystals.

Fig. 1: Borax crystal growing birthday gift (orig.)

Of course! I hadn’t ever seen people grow borax crystals before, only sugar or salt, so I looked up a tutorial on YouTube. The procedure was pretty standard: heat water up to near boiling, dissolve the borax, insert a pipe cleaner or thread and wait overnight for the solution to cool down and precipitate out crystals. But while the procedure is simple, the science behind nucleation is more complicated and pretty interesting.

In order for a crystal to form in solution, molecules of a substance must conglomerate to an adequate size to encourage the spontaneous coordination of more molecules. A cluster of this adequate size is called a "nucleus," and the process of its formation is called "nucleation." Clusters that are not large enough to be nuclei are called "embryos." The nucleation process can be described in terms of Gibbs free energy, which accounts for both enthalpy, related to the nucleus’ internal energy, and entropy. Gibbs free energy is given by the equation

                      1.       ΔG=ΔH-TΔS (H is enthalpy, T is temperature in Kelvins and S is entropy)

For a newborn crystal born homogenously (meaning suspended in a medium without contact with other surfaces), there are two main energy changes that are occurring. The first is a lowering of molecular energy due to the formation of attractions between coordinating substance molecules for reasons described in Why Cold Drinks "Sweat". This change in energy can be describe by the equation

                  2.       ΔG=VΔG_v (V is volume, ΔG_v is the change in internal energy per unit volume)

To find ΔG_v, we will assume that the crystal-solution system is cooled to slightly below the substance's melting point, T_m. At this small undercooling, ΔH and ΔS can be approximated as temperature independent [1]. But first, at T_m the difference in free energy ΔG between a substance’s solid and liquid forms is 0. Therefore,

                                                                      3.       ΔG_m=ΔH-T_mΔS=0

                                                                      4.       ΔS_m= ΔH/T_m

Now, assuming that ΔH and ΔS are temperature independent, we can use the same expression for entropy as used at T_m to find the value of ΔG_v. While we’re at it, let’s assume the crystal nucleus is spherical for simplicity’s sake. The following are therefore true:

          5.       ΔG_v=ΔH_fv-TΔS= ΔH_fv-T(ΔH_fv/T_m)= ΔH_fv(T_m-T)/ T_m= ΔH_fvΔT/T_m (from equations 1 and 4)

          6.       ΔG=VΔG_v=4/3πr³(ΔH_fvΔT/T_m) (from equations 2 and 5, V_sphere=4/3πr³)

The second energy change occurring is an increase in a newborn crystal’s energy because the surface of the crystal is disrupting bonding in the liquid medium around it. This change can be described as

          7.       ΔG=Aγ_s=4πr²γ_s (A is the nucleus’ surface area, γ_s is the surface free energy value
           characteristic of the medium-solid interface)

This expression is just the disruption free energy per unit area multiplied by the surface area of a sphere. Together, these two energy changes dictate nucleation. Putting the two expressions together, we get

          8.       ΔG_hom=VΔG_v+Aγ_s= 4/3πr³ΔH_fvΔT/T_m+4πr²γ_s (ΔG_hom indicates that this equation is for
           homogenous nucleation)

This equation is very useful and can be used to describe nucleation events from borax crystals precipitating to homogenous cloud formation. To tease a little more information out of equation 8, let’s see how ΔG_hom changes in response to a substance clump slowly growing in radius. This rate of change corresponds to the derivative of ΔG_hom with respect to radius r [2];

                                                             9.       d(ΔG_hom)/dr=4πr²ΔG_v+8πrγ_s

The point where ΔG_hom no longer changes with r corresponds to the peak on the following graph of equation 8 and its component parts, equations 2 and 7.

Fig. 2: Free energy of nucleation as radius increases (Materials Science and Engineering, an Introduction)

Equation 2 is shown as a decreasing curve because ΔH_f is negative for crystallization. This makes sense because as a material crystallizes, energy is lost to its surroundings, so ΔH_f must flow out of the system. To find the critical nucleation radius,

                                           10.   d(ΔG_hom)/dr=4πr²ΔG_v+8πrγ_s=0 (from equation 9)

                                           11.   r^*=2γ_s/ΔG_v

Plugging the critical radius into equation 8 and extracting the negative from ΔH_f to avoid confusion, we get

                                  12.   ΔG^*_hom=-4/3π(2γ_s/ΔG_v)³ΔG_v+4π(2γ_s/ΔG_v)²γ_s=16/3πγ_s³/ΔG_v²

This expression describes the magnitude of the energy change needed to get a molecular cluster up to the size of the critical radius r^*, a sort of activation energy [3].

However, homogenous nucleation is relatively difficult compared to heterogenous nucleation, as I’m sure you’ve probably heard. Heterogenous nucleation occurs when a nucleus forms on a surface, such as a dust particle for clouds or thread for nucleating borax crystals. Because of the complexity of finding heterogenous nucleation equations due to complex volume and surface area terms as well as extra surface energy considerations, I will not be posting these calculations. The calculations can be found in reference 3, but the summarized result is that the critical radius in heterogenous nucleation remains the same as with homogenous nucleation while the nucleation free energy lowers and makes the nucleation process more accessible. This is why minimizing dust or rough surfaces is important for growing larger crystals rather than clusters of small ones.

What has been described above is just a small bit of the complexity of crystal growing. Knowledge of nucleation rates and crystal growth is widely used in processes such as tuning metals to have properties fit for specific purposes or growing single-crystal silicon for computer processors, and I’m sure this information will come up again on later posts. But mild difficulty of math aside, it’s cool stuff, huh? As a treat for reading through this post, watch this fun Minute Earth video on the homogenous nucleation of clouds and see if you recognize some of the concepts we discussed.

I’m planning on growing some borax crystals soon, and when I do I’ll likely write an experiment post about it so be sure to come back and check that out. I’ve already had my first few days of classes and so far it seems that I will be able to continue posting once a week, likely on Sunday or Monday. As always, thanks for reading and I’ll be posting new stuff soon!

Primary Colors: Why One Set Wouldn't Suffice

Colors are a ubiquitous fact of human life. Imagine a world without colors; all of the great masterpieces would be painted in gray scale, that potato could be purple or brown and there would be no more blue skies. Experientially, we are highly familiar with the concept of colors, but I would say it isn’t common to understand the more technical side of the world of colors. Let’s explore this more analytical side and it’s applications as we try to answer a question most of us have probably had: why are there multiple sets of primary colors?

At the most basic, colors are categories of light within the visible spectrum that can be described as having either different wavelengths or frequencies since the two variables are directly correlated by the equation

                     1. c=λv (c is the speed of light, λ is wavelength and v is frequency)

The visible spectrum is comprised of the rainbow colors describe by the acronym ROYGBIV (red, orange, yellow, green, blue, indigo and violet). 

Fig. 1: Visible spectrum for humans (Arstechnica)

White is the presence of all wavelengths while black is the absence of light. Technically, there is no physical meaning associated with colors since the color spectrum is defined based on human capacity to perceive and differentiate different colors. That is to say, the visible spectrum and colors would be defined very differently had we been insects able to see UV light [1]. So keep in mind that all of this talk of analyzing colors is human-specific and don’t go off trying to explain it to your dog.

The human eye consists of rods, which perceive low intensity light, and cones, which perceive colors and high intensity light [2]. There are three types of cones, dubbed L, M and S, that respond to different wavelengths of light. The peak sensitivities for these three cone types are 580nm (red), 540nm (green) and 440nm (blue) respectively, adding to a maximum sensitivity at 560nm (in the yellow-green region of the spectrum) [3].

Fig. 1: L, M and S cone response curves and response sum (Cyberphysics)

This should start to sound familiar for those of you who are familiar with the concept of primary light colors or who have ever squinted really hard at a television screen. Aside from these three colors, other colors are perceived by simultaneous stimulation of multiple cone types. The color mixing ratios of red, blue and green light to perceive every color was actually indexed in 1931, creating the RGB CIE 1931 system [4]. The impact of breaking each color into three values of red, blue and green, called the RGB tristimulus values, is that each color can now be defined in three-dimensional space as a combination of three basis vectors representing red, blue and green relative intensity values. The mathematical derivation can be found in reference 4, but the result is the chromaticity diagram familiar to aficionados of tech wanting to know what range of human-perceivable colors their devices are capable of displaying. Look along the edge of the chromaticity diagram and you should find a color wheel for light.

So far we have one set of primary colors consisting of red, blue and green that has widespread applications in electronic devices since many of these generate colors for humans to perceive when watching movies or reading billboards and such. But this set of primaries and its corresponding wheel only apply to the production of light by adding ranges of wavelengths together. This is called additive color. When light is absorbed by colored materials via quantum effects, as has been described in Thoughts in Black Ink, the color perceived is the light range that has not been absorbed. To describe the phenomenon of light absorption to generate a reflected color, the painter’s wheel was invented by Isaac Newton in 1666 [5] with the familiar primaries of red, blue and yellow. What this wheel describes is how subtracting light with certain ranges of wavelengths stacks to reflect light of a certain color when starting with ambient pan-frequency white light. However, this is not strictly subtractive color because the painter’s wheel adds to brown, not black as anyone who has tried to make black paint from the primaries in art class knows. The subtractive color wheel is defined with yellow, magenta and cyan as primaries and should be familiar as the different ink cartridges you probably put in your printer so that your computer can print black in theory (but black ink is cheaper).

Fig. 2: Additive and subtractive color (Mac Developer Library)

Why these three colors? It turns out that if you take the three primary colors of light, red, blue and green, and combine them two at a time, you get cyan, magenta and yellow [6]. And since the color of a surface is what the surface doesn’t absorb, each subtractive primary color cancels out one of the additive primary colors until no light is left. And there you have it, the three most common primary color sets.

This post was made in response to a comment by my friend Lilia back on the article How Soap Helps Us Clean. I haven’t address the comment until now because I knew there would be a biological component to this explanation and cellular biology is not my strong suit, hence the brevity with which I describe the rods and cones of the eye. But if you guys have anything you would like to hear about, feel free to leave suggestions in the comments below and I will do my best to write a post for you. Thanks!

Why Cold Drinks "Sweat"

With a horrible heat wave hitting the Philadelphia area, it’s good to think cool thoughts. Already feeling the heat last night, I left a coconut water in the freezer with the intent to drink it but forgot and so took it to work this morning frozen solid. I figured since it’s so hot outside and the metal can is a good conductor, it’d probably melt pretty quickly. And while the ice in immediate contact did melt, the inside remained frozen and I had to cut the top open with scissors to eat it. Before I figured this out, the can had already shed a puddle at my desk. Have you ever wondered why it is that cold things "sweat."

Fig. 1: My favorite coconut juice brand, Foco (pinstopin.com)

Most of us are familiar with the concept of condensation, having learned about the water cycle in elementary school. We are commonly taught in elementary that water exists as vapor at hot temperatures, condenses to liquid as the temperature drops and eventually expands (not condenses, as ice has a lower density than water due to hydrogen bonding) into ice as the temperature drops further. In high school, we learn about the ideal gas law and how pressure also affects phase transitions, yielding the phase diagram.

Fig. 2: Phase diagram for water (myhomeimprovement.org)

So from this standpoint, we are all familiar with why cold things "sweat." What else is there to it? While the basic principles stand, there are some other viewpoints from which we can view this phenomenon.

Phase transitions can be viewed as being an equilibrium process, as is demonstrated by the fact that an ice and water mix maintains a 0°C temperature. In such a mix, the ice melting and the water freezing are competing processes that are controlled by environmental factors; if you cool the mix the ice expands, but if heated the ice melts. Additionally, the entire mix must either become ice or water only before the temperature can deviate significantly from the equilibrium temperature of 0°C. What’s cool about this process is that if you track the energy entering the ice and water mix, say a glass of iced coconut water (let's treat this as an ideal glass of pure iced water), we can predict the corresponding phase transitions based on molecular kinetics.

When bonds are formed, whether strong or weak, we know that energy is released as heat. The reverse is true as well, breaking bonds requiring energy. The direction of bond energy transfer can be simplistically remembered taking into account the conservation of energy in a two molecule one-dimensional collision. Say two water molecules are moving towards each other and stick together upon impact. Where did the kinetic energy go? Ignoring molecular vibrations, the energy had to have been released as work, or heat. In order to separate the water molecules, we need to get them to move apart, a.k.a. add work, or heat, to yield kinetic energy. In our glass of iced water, this sort of energy transfer is happening extremely fast and on a large scale, one that can be described by Le Chatelier’s principle since the ice and water form an equilibrium.

Fig. 3: Ice-water equilibrium state (JVC's Science Fun)

Now let’s put the iced water outside on a hot summer Philadelphia day. From experience, we know that the ice will melt and the water will become unappealingly warm. If we track the direction of energy transfer, the higher energy hot air must be donating energy to the lower energy iced water simply because this is the default direction of energy transfer in our universe according to the Second Law of Thermodynamics. The added energy must translate into kinetic energy as temperature is positively correlated to molecular kinetic energy. From our two water molecule system we know that a decrease in water molecule association is predicted, favoring water over ice and vapor over water. This manifests as the ice melting and the water warming and eventually evaporating.  

What has been so far described, however, is only focused on the iced water itself. Let’s change our basis to focus on the hot air along the iced water glass instead (assume the water glass does not hamper kinetic energy exchange between air and iced water). Hot air carries a lot of water since at higher temperatures water enters the vapor phase preferentially according to Le Chatelier’s principle. From the viewpoint of the air, the cold iced water is pulling kinetic energy from it, accordingly cooling the air within a certain range of the glass. Plugging this information back into our two molecule system, the energy must be afforded by reducing the molecular kinetic energy of the air, increasing the probability of water existing in associated groups, i.e. water. And this is why a cold drink sweats in the summer.

Since school is starting up again, I will not be able to post as frequently as I have been during the summer. I will try to post at least once a week, and will probably be doing so during the weekend since this is when time is most available. Please have patience with me on this, and as always thanks for reading!

The Fun of Latin and Ballroom Dancing Explained with Mechanics

Last semester, I picked up Latin and ballroom dancing as a hobby. All through high school I didn’t dance, but thanks to the recommendation of a friend I decided to go to free introductory dance lessons. At first it was just fun to socialize, learn some new steps and practice body coordination, but I soon grew to love it. Our Latin dance teacher has a particular habit of describing dance movements in terms of coordinates and physics; rumba walks require your center of mass over your front foot for balance and look best if you extend the axis running from your shoulder to opposite leg as far as possible. This mentality has slowly creeped its way into my brain, and eventually I realized that, hey, dance really is about physics! You don’t know it while dancing, but every movement is purposeful when viewed through a pair physics-colored safety glasses.

When first starting to dance, everything is about mechanical control of your body and constantly asking the question, where is my center of mass (let's abbreviate it as COM) right now? Of course you wouldn’t consciously ask yourself that, but even without asking your body will give the answer. While posing still, if your COM is not somewhere well supported by your limbs, you’ll fall down because relative to the point of floor contact your bodyweight is generating torque on your COM. On a single limb, your COM needs to be over the supporting limb to stay balanced. On more than one limb, your COM should be somewhere between the limbs based on how your bodyweight is distributed towards each (unless the floor is slippery. Then it’s best to choose a limb to center over otherwise your supports will simply fall apart and you’ll hit the floor). When you begin to move horizontally, core muscles contract in order to support your center of mass on its journey from one place to another through fluid motion.

Spinning generates torque along other axes and accordingly makes you conscious of where your body axes are. Since torque acts along levers originating at your COM, all body axes will include your COM. Torque is defined in parallel to Newton’s second law by the equation

                                                              1.       τ=Iα    (torque equation)

Where τ is torque, I is inertia and a is angular acceleration. Inertia is related to the distribution of your body mass in space around a rotational axis. While spinning on an axis perpendicular to the ground like a ballerina or ice skater, contracting your arms from an extended position can reduce your moment of inertia and increase your angular acceleration based on the existing torque. And expanding your body to increase inertia while tilting your axis slightly can slow your spin and generate a simultaneous forward momentum to get you out of the spin and into horizontal motion. Manipulating the position of your center of mass so that it remains relatively stationary while moving around it by torque is what allows break-dancers to do such complicated flips. Dancing is all a game of mechanics.

Fig. 1: Dancing as an act of balancing forces (University of Illinois at Urbana-Champaign)

What makes Latin and ballroom dance special to me is that all of the dances are partner dances. This means double the complication, but also double the fun! Instead of your COM, your tandem COM is what counts. And all movements and spins are done together accordingly. What’s even more exhilarating is that your tandem COM is without your body, so when you go for a partner spin you’ll both be spinning about an axis between the two of you (assuming equal mass). In Latin and ballroom dance, a concept that is stressed is partner connection. This means making sure both of your bodies push against each other at the point of contact in a way that conveys information about how each of you is moving. What this also does is make the tandem COM more stable. When partner connection is weak, your tandem COM can constantly dissolve and reform. This makes both partners unstable and rely on knowing their own COMs to maintain balance. A strong connection means both partners can fully commit to the unwavering tandem COM and structure each motion together. And believe me, you can feel this. It’s really exciting when you and your partner start to move as one, and not having to worry about your own balance allows you to focus on the art of the dance.

This post is a little less reference and math heavy than some of the past ones, which I thought would be a nice break. I just wanted to share what makes Latin and ballroom dance such a special hobby to me. Dancers out there, please let me know if you think my description does dance justice in the comments below. Other Thinkers, I wanna hear your thoughts too. And check out a few minutes of this video of world-class Latin dancers. Thanks guys!