Thursday, December 22, 2011

Golden Ratio


The Golden Ratio is one of the amazing mathematical concepts commonly thrown around in psychology and math classrooms. Its essence is associated with the perfect aesthetic form. Golden ratio enthusiasts say that the proportion is present in classic paintings from Leonardo da Vinci and Giotto di Bondone, old world architecture, music and even poetry. The larger and more important question is whether the ratio is present because of a deliberate inclusion of it or if it has appeared because of an underlying force. Are all of the great painters, musicians, poets and architects great because of a talent or are they great because they have tapped into the human psyche and somehow knew what people liked? What is it about φ (phi), the name of the number associated with the phenomenon in question (other names include golden ratio, golden number, golden cut, to name a few), that causes it to show up in both the realm of the man-made and non-man-made? Furthermore, why is φ a basis for beauty?
Whole paper:
http://www.mediafire.com/?t494e6yykml1om2

Monday, December 5, 2011

Training the Kit generation

My lab has a huge listserv(?) to send out to all of our orthopaedic surgery labs, and one of the emails last week was not the usual meeting, or broken machine. In short, it was an article explaining that kids need to be able to understand what the science they're doing is, not just to read the instructions and try super hard to make the experiment work. I think that's incredibly relevant, and the person sending it was spot on in saying it's important in today's society.
Little aside, one of the witty people send back something that I chuckled at.
"What? You expect men to actually read the instructions AND understand them? "

I hope this link goes to the right source. But if not, you can look it up for yourselves. The paper is Nature America, and the article is "Training the Kit generation" ENJOY!

Newton > Goethe, pt. 1


Newton introduced a method for producing the beautiful Julia fractal.


Georg-Johann Lay. Julia N z3 -2z 2.jpg. 2008. Graphic. n.p. Web. 5 Dec 2011.


-Niko

Monday, November 21, 2011

Urpflanze

http://commons.wikimedia.org/wiki/File:Urpflanze.png

Turpin, Pierre. Die Kunst der Künste, "Urpflanze.png." Last modified 6/03/2010. Accessed November 21, 2011. http://commons.wikimedia.org/wiki/File:Urpflanze.png.

Jackie Brand

Bat Skeleton

unknown, . Popular Science Monthly Volume 9, "File:PSM V09 D563 Skeleton of flying fox.jpg." Accessed November 21, 2011. http://commons.wikimedia.org/wiki/File:PSM_V09_D563_Skeleton_of_flying_fox.jpg.


This is by Bri Ward
For my final project I will be comparing several different skeletons to compare the functionality of the forelimb in the different animals.

NBA Lockout Continues, Stars starve

Stevenson, Paul. Body Worlds Anatomy Exhibit, "Ausstellung Körperwelten." Accessed November 21, 2011. http://www.flickr.com/photos/pss/2252443224/.

History of Science. Yea, it's with the German department.

Modified Mink Skeleton Picture

Mariomassone, . "File:Minkskeleton.jpg." Last modified March 17, 2010. Accessed November 21, 2011. http://commons.wikimedia.org/wiki/File:Minkskeleton.jpg.

SQUIRREL


Kyle is my name. Flying squirrels skulls cost $45 and this whole set is $195. I was able to prepare the same skeleton by skinning the squirrel and feeding his body to the bugs in the Natural Science Museum. Very cooooool.


http://www.skullsunlimited.com/userfiles/image/variants_large_5121.jpg



GERMAN HISTORY OF SCIENCE IS COOL

The Winter Least Weasel (aka Ermine)

For my skeleton preparation I was told I was doing a Winter Least Weasel, and since mine had a black tipped tail, Prof Hinshaw told me it was specifically then an Ermine, which is adorable. Here I included a picture of a least weasel, so you can see what I was dealing with, and how cool and cute they are. My specific specimen was winter, so the coat is a gorgeous white. I will upload a picture once I find a suitable picture.



Law, Kevin. British Wildlife Centre, "File:Stoat at British Wildlife Centre.jpg." Last modified Aug 17, 2008. Accessed November 21, 2011.

ERMINE!!!!
Galvani, Luigi. "Wikimedia Commons." Last modified 08/16/2007. Accessed November 21, 2011. http://commons.wikimedia.org/wiki/File:Luigi_Galvani_Experiment.jpeg

Galvani, in an experiment designed to explore the response of animal tissue to electric charges, produces unexpected results
:


Winterhalder, Louis. "Wikimedia Commons." Last modified 1902. Accessed November 21, 2011. http://commons.wikimedia.org/wiki/File:Picayune_Frog_Waiter_1902.jpg.
-Niko

Goethe's Color Wheel.


Goethe, Johann W. Goethe's Color Wheel. 1810. Goethe's Theory of Colors. Wikimedia Commons.

This is Goethe's color wheel, published in "Theory of Colors." Goethe believed that colors arose only at the edges between light and dark due to his observation of light through a prism, wherein colors are only visible when there is contrast between light and dark. What Goethe didn't realize is that the separation of light into colors from the prism is only visible at the edges of light and dark, and is not visible in a purely white area
even though it is occurring. The image above is Goethe's version of the color wheel. It is interesting to note that Goethe related different colors to different moods (such as "gut"--good--and "gemein"--mean) written on the inner half of the wheel.

Frog Anatomy




The anatomy of the frog can be seen here. For my final project, different parts of the frog will be electrically stimulated.
-Callie
McIntosh, Jonathan. NMH, "File:Frog anatomy.JPG." Last modified 2004. Accessed November 21, 2011. http://commons.wikimedia.org/wiki/File:Frog_anatomy.JPG.

Wednesday, May 4, 2011

Bryan Mazor - History of Science Final Paper Project

What Can Be Learned From The Relationship Between Einstein’s Science and His Religion

Bryan Mazor - History of Science Final Paper Project


There can be seen in history many instances in which religion and science have been at opposite sides of human methodologies. Common subjects that pertain to this relationship have been Copernicus and Galileo’s heliocentrism and Darwin’s theory of Evolution. These theories were both held to be in contempt with religious thought, so organized religion has done their best to combat these theories. Extremists on both sides of the arguments have given people a bitter taste regarding the relationship between religion and science. As both scientific theories began to gain ground and acceptance against the traditional religious thoughts the strife only became more and more pronounced. From Pope Urban VIII placing Galileo under house arrest (Hoffman 21) to arguments about whether to teach Evolution or Intelligent Design in schools, this argument about either religion or science has endured with vigor. But is this the way it will always be? Is it possible for a coexistence of these subjects within the common man? A powerful symbol of hope regarding a possible coexistence can be seen in the thoughts of the German scientist Albert Einstein. Einstein is regarded as one of the greatest minds this world has ever known, and will be forever remembered for his multiple and groundbreaking contributions to science. As his theories regarding relativity and the structure of the universe redefined how we must look at the world, he held within a strong sense of religion. For Einstein, there is a distinct relationship between religion and science, a relationship that is not one of opposites. Coexistence within the mind of one of the greatest scientists of all time certainly offers hope of a coexistence that can exist with us all. Religion and science had a distinct give and take for Einstein, a relationship that can be summarized with the quote: "Science without religion is lame, religion without science is blind."

Einstein was a religious man, but in an uncommon regard. Raised by a Jewish family and customs and received catholic instruction from schools in compliance with Bavarian law. Although he went through a stage at a young age of being quite religious, at the age of twelve, apparently upon the discovery of science, his religious vigor came to a sudden stop and “He did not become bar mitzvah” (Pais 38). From there he began to stray from organized religion and only weakly associated himself with Judaism. He did, however, remain religious, an idea shown in Count Kessler’s diary regarding a dinner party conversation between Alfred Kerr and Einstein:

Professor! I hear that you are supposed to be deeply religious?” Calmly and with great dignity, Einstein replied, “Yes, you can call it that. Try and penetrate with our limited means the secrets of nature and you will find that, behind all the discernible concatenations, there remains something subtle, intangible and inexplicable. Veneration for this force beyond anything that we can comprehend is my religion. To that extent I am, in point of fact, religious (Kessler 322).

Einstein’s religion is not a mystery. Einstein published many essays on his thoughts on religion and its relationship with science. Einstein referred to his theological beliefs as the “cosmic religion,” describing multiple reasons for religion such as fear and moral ideals, but the cosmic religious feeling as the most noble:

Only exceptionally gifted individuals or especially noble communities rise essentially above this level (moral religion); in these there is found a third level of religious experience, even if it is seldom found in pure form. I will call it the cosmic religious sense. This is hard to make clear to those who do not experience it, since it does not involve an anthropomorphic idea of God; the individual feels the vanity of human desires and aims, and the nobility and marvelous order which are revealed in nature and in the world of thoughts. He feels the individual destiny as an imprisonment and seeks to experience the totality of existence as a unity of full significance (Einstein 48).

This is the theology that Einstein followed, one not of organized religion or one in which one believes in God out of fear of misfortune or because it provides comfort about death. Einstein’s religious feelings came from the sense of wonder he felt when looking at the world. From these religious sentiments it is not hard to draw the connection from this theology and to Einstein’s science. In fact, Einstein regarded this cosmic feeling as the most powerful scientific motivator: “I assert that the cosmic religious experience is the strongest and noblest driving force behind scientific research” (Einstein 52). It is no wonder Einstein pursued his magnificent theories with such vigor; he truly was searching to understand the universe at even its deepest levels. This method or research and the cosmic mentality can be seen in every step of his theories on relativity; from the motivating force behind his inquiry to the beautiful conclusions. With every interaction that Einstein studied he tried to not only derive mathematical equations to describe the interaction, but also to capture the inner meaning and deeper motivation behind it all: “When I am judging a theory I ask myself whether, if I were God, if I would have arranged the world in such a way” (Isaacson 335). Einstein’s theories were not a front against religion, but a study to understand the deeper meaning behind the way God operates.

At the advent of Einstein’s research in the very early 1900’s there was not unquestionably consistent theory on relativity. Galilean or Newtonian relativity was widely accepted for many years, and is so intuitive that it is hard to refute. Essentially Galilean relativity states that in inertial states of motion (motion that is not accelerated), it is impossible to discern the difference between absolute stillness. This can be seen any time one flies in an airplane and observes people walking around, as you and the airplane are all moving with no acceleration the system as a whole acts as if it is not moving. This theory was a necessity for Galileo to assert that the Earth was orbiting around the sun. However Maxwell’s equations asserting light as an alternating wave between electric and magnetic fields caused problems to Galileo’s relativity. Under Galileo’s relativity there were no special reference frames, no reference frames had preference; velocity can only be measured relative to other objects. Waves in order to propagate, however, require a medium. Maxwell proposed an all-pervading aether as the medium in which light can propagate, an aether that existed within state and matter. This aether was also without motion, like a liquid filling space yet did not hinder the motion of anything like planets. This directly conflicted with Galilean relativity, for an unmoving aether would provide for an absolute reference frame in which the velocity of everything can be measured. These theories were in direct conflict, and motivated Albert Michelson and Edward Morley to devise an experiment to measure the absolute motion of the earth relative to the aether. This famous Michelson-Morley experiment led to a null result, that the earth is not moving relative to the aether: “Thus according to the theory of aberration there should be an aether wind, but according to the Michelson-Morley experiment there was none” (Hoffman 80). And here enters Einstein. For Einstein witnessing modern thoughts about the universe must have been disgusting; there was not way his God would have created the universe in such an inconsistent way. The aether was very ugly with its unmoving velocity and properties that allow matter to just flow right through it. The Michelson-Morley result seemed to indicate that there was no absolute reference frame. And so Einstein’s intuition, motivated by his thoughts of a beautiful universe, led for him to denote two principles. One is that if we are in an unaccelerated body, the motion has not affect on the properties inside it. This is similar to Newtonian and Galileo’s ideas, except Einstein extended this idea to all physical phenomena, not just mechanics but also electromagnetic interactions. The second principle was that light propagated at the same speed, c, no matter the speed of the source of the light (Hoffman 91). These principles would have been obviously appealing to Einstein for their simplicity and beauty. These were principles that God would not dare to break, for they would lead to chaos; the laws of physics cannot change. Maintaining the integrity of these two principles, however, would have adverse affects on the some of the most established perceptions like time and length. In order to maintain that the speed of light is always constant, a body moving at a high velocity will feel time slowing down and size’s contract. This is because if this body were emitting light, the speed of light cannot be c plus the speed of the body, as the speed of light is always constant. Instead, because velocity is simply the distance traveled divided by the time it takes the travel this velocity, if the length is contracted and time is slowed, the light emitted by the body will still propagate at c. If time can be changed according to the relative velocity between two objects, however, it becomes difficult to ascertain which event necessarily came before the other. Events that could be perceived as occurring at the same time could be viewed as occurring at different times if observed from a different reference frame with a different velocity. Although the relativity of time and length must have been difficult for Einstein to swallow as a consequence of this theories, they would prove to be correct and would prove to unite all existing theories of relativity under one roof. The un-intuitive nature must have just added to the appeal for Einstein. Always the rebel, being able to challenge all of our perceptions while maintaining its logical and mathematically integrity would have been of great appeal: “Banesh Hoffmann, who in the thirties had worked on his theory with Einstein for some time and who called Einstein a ‘creator and rebel’” (Jammer 29). There is something intrinsically beautiful that can be taken from special relativities odd time and space interactions; that space and time are unified in one related “fabric” of the universe. One doesn’t just move from place to place in three-dimensions, but also move from event to event in the fourth-dimension, time. The rate in which a person moves through time can change according to velocity, but events don’t happen, they are. The majesty of this view would have appealed to Einstein, there is an intrinsic set order to the universe, past present and future are just human concepts. Also upon taking derivations about relativistic (the term to describe bodies experiencing interactions predicted at high velocities according to special relativity) force being applied to a body and approximating the expression for a body with zero velocity will yield Einstein’s most famous equation, E=mc2. This equation epitomizes Einstein’s science; simply, beautiful, and profound. In one relationship Einstein related mass and energy, things that to all human perceptions are very unrelated. But God would make the universe this way, completely out of energy. Einstein’s theory of relativity would prove to be true and has been tested many times and held up, but his greatest work was yet to come, what is now known as general relativity.

General relativity came to being in Einstein’s mind in a similar way as special relativity, he could not consider this view of the universe beautiful enough for God to have created it this way: “Einstein’s general theory of relativity had its origin in an aesthetic dissatisfaction” (Hoffman 129). For Einstein, the preference to inertial unaccelerated reference frames in special relativity bothered him. In his mind, all reference frames, including ones being accelerated, should be considered inertial:

Then there occurred to me the happiest thought of my life, in the following form. The gravitational field has only a relative existence in a way similar to the electric field generated by magneto electric induction. Because for an observer falling freely from the roof of a house there exists-at least in his immediate surroundings-no gravitational field. Indeed, if the observer drops some bodies then these remain relative to him in a state of rest or of uniform motion… The observer therefore has the right to interpret his state as ‘at rest’ (Einstein).

No doubt this happiness came from the cosmic religious feeling, to be able to unite all states of motion under a united theory of relativity. This led Einstein to begin to relate the properties between two states of uniform acceleration, under the principle that the laws of physics would be the same in both. One state was that of a laboratory in a gravitational field, the other was one in which an angel accelerated a laboratory at a rate of acceleration equal to that of the gravitational field. It can be seen that any sort of experiment held in one laboratory will yield the same results as the other laboratory, dropping a ball on earth will cause the ball to fall and letting go of a ball in the angel laboratory will also give the perception of the ball falling to the floor. Einstein did not stop at simple interactions like this, however, and he worked to extend this to all physics: “It would have been most inartistic to have so fundamental an equivalence to apply only to mechanics and not to all of physics. God would not have made the universe this way” (Hoffman 132). So Einstein began to explore the equivalence between all interactions in the earth laboratory and the angel laboratory. From this he began to see that light can bend in gravitational fields, and that time is also dilated in gravitational fields. Gradually he began to relate the force of gravity to something more geometric; a force associated with curves in space-time. The curvature in space-time can simply explain how light can be bent, because space it self is being bent. Also this bend in space-time accounts for gravitational acceleration as being an inertial state, space is bent as so that objects will just be naturally accelerating. Although Einstein used complicated mathematical concepts, the end result of his general theory of relativity is undeniably magnificent. It can be envisioned as balls resting on a trampoline, the trampoline representing space-time and the balls planets. Just as the balls depress the trampoline, very massive objects depress space-time and attract other objects towards it. Einstein was able to describe the universe as a fabric of space and time in which nothing can travel above the speed of light, time is relative, and bends in this fabric are known as gravitational fields. The theories predict extraordinary behavior, but in a way unparalleled in majesty as Einstein once declared: “Hardly anyone who has truly understood this theory will be able to resist being captivated by its magic” (Hoffman 158). The complicated interactions that occur added to the magic for Einstein. A theory that contains both wonderful interactions that only a God could take intuitively yet was captured in comprehensible theories, equations, and images. Einstein had not veered from his view of physics and God in the creation of these theories, but worked with both ideas in harmony to revolutionize physics:

I’m not an atheist, and I don’t think I can call myself a pantheist. We are in the position of a little child entering a huge library filled with books in many languages. The child knows someone must have written those books. It does not know how. It does not understand the languages in which they are written. The child dimly suspects a mysterious order in the arrangement of the books but doesn’t know what it is. That, it seems to me, is the attitude of even the most intelligent human being toward God. We see the universe marvelously arranged and obeying certain laws but only dimly understand these laws. (Viereck 186).

Einstein had accomplished the difficult task of being the child that could look at the stacks of books in the library and discerned alphabetical organization without knowing its true deeper purpose but by suspecting the existence of a deeper meaning. Einstein’s cosmic religious feelings provided not only his motivation to understand the universe but also the beauty behind all of his theories, a true symbiotic relationship between religion and science.

Einstein’s theories of relativity have profound implications in describing our universe, especially regarding time. Although modern religions have been hesitant to either accept or contest these implications, for Einstein this had profound implications regarding his theology: “The fundamental tenet of Einstein’s cosmic religion is that science furthers religion” (Jammer 155). Einstein scientifically proved that the universe should be looked at like an infinite series of “snap shots” of three-dimensional events, and one simply moves from “snap shot” to “snap shot,” as phrased by Hermann Weyl: “the objective world simply is, it does not happen. Only to the case of my consciousness, crawling upward along the lifeline of my body, does a section of this world come to life as a fleeing image in space which continuously changes in time” (Weyl 116). Einstein believed this consequence of hit theories of relativity whole-heartedly. For after his lifelong friend Michele Besso passed away, Einstein wrote to Besso’s family: “Now he had departed a little ahead of me from this quaint world. This means nothing. For us faithful physicists, the separation between past, present, and future has only the meaning of an illusion, though a persistent one” (Jammer 161). Einstein clearly received comfort from this fact, comfort from his theories regarding life and death, a comfort that usually comes from faith. For Einstein, the ancient religious view of time being unmoving and unrelenting was not more. The thought that time and the relativity of events is just a human affair has clear theological consequence, consequence’s Einstein fully accepted. Most notably is the concept of determinism. If the universe is to be viewed as all events in space and time in one image, and human existence is imply moving along the line of time to the next existing “image,” then our fate seems to be already determined. Under this worldview, the events in which we will encounter in the future have already been determined; we have just yet to consciously experience the events: “James Hopwood Jeans, expressed the idea that the theory of relativity implies strict determinism, the concept of the world as a ‘block universe,’ and the denial of free will, because clearly the Parmenidean doctrine that there is no ‘becoming’ but only ‘being’ requires that free will is at best an illusion” (Jammer 181). Einstein was not opposed to these ideas, he believed that a true god would not concern itself with the wants and needs of humans: “A God who rewards and punishes is for him unthinkable, because man acts in accordance with an inner and outer necessity, and would, in the eyes of God, be as little responsible as an inanimate objects is for the movements which it makes” (Einstein 51). Likening the actions of a human to that of the moments of a planet rotating about the sun is a bold assertion, but one that is based in the reality presented by relativity. Just as the measured observation of when a sun-flare breaks the surface of the sun can be changed by moving at speeds close to the speed of light, the time of your birth can be observed to occur at different times if one is moving at a velocity close to that of the speed of light. For Einstein these became accepted truths. Just as most modern religions no longer strongly assert that the earth is the center of the universe, or that Adam and Eve came to being mere thousands of years ago, for Einstein the thought that events in the future have not already happened is plain fallacy. Einstein’s theories regarding the universe cam to be quickly accepted into Einstein’s theology as truths that must be accommodated for in his religious views, his science had relinquished the “blindness” about what his religion should be.

Not all believe that science and religion hold a symbiotic give and take relationship as Einstein did. Some proponents believe that science can be used as evidence that there is no creator and no divine power, and that religion only hinders scientific progress. One view that is held is that scientific discoveries provide proof and solace for atheism, and helps provide proof of atheism being the correct theology:

An atheist before Darwin could have said, following Hume: 'I have no explanation for complex biological design. All I know is that Cod isn't a good explanation, so we must wait and hope that somebody comes up with a better one.' I can't help feeling that such a position, though logically sound, would have left one feeling pretty unsatisfied, and that although atheism might have been logically tenable before Darwin, Darwin made it possible to be an intellectually fulfilled atheist (Dawkins 6).

Dawkins asserts that scientific discoveries, in particular Darwin’s theory on evolution, provide evidence that there is no God. This is contrasting with Einstein’s view that with every scientific discovery we are simply discovering the way in which God operates. There is no way to possible interpret which idea’s are correct; the reason this argument even exists in the first place is the wholly lack of evidence that can point to either God’s existence or non-existence. Dawkin’s prefers to use science to prove the point that there is no God; Einstein prefers to use science to show the actions of God. How this science is used spiritually is completely subjective. The motivations are similar, the results are similar, and spirituality is a private matter. Dawkins is just the opposite end of the battle between religion and science. Religious institutions battle science to try to maintain religious beliefs, Dawkins is battling religion to maintain scientific beliefs. Within Einstein, however, there exists the middle ground. Just as the world is a Gaussian distribution, with extremists on both sides, the majority of the world is moderate. Einstein’s beliefs can appeal to the moderate side within people. Einstein shows that even within one of the most impressive scientists the world has ever known, there can also exist spirituality. There is no reason to feel the need to choose between either being religious or scientific. God has a tendency to exist where science cannot yet explain, and as science is trying to explain these parts of our knowledge, friction will start to accumulate when science begins to prove where religion once answered. Where Dawkin’s is trying to shed light on all of the interactions in this world to try to disprove God, Einstein in the first place does not believe God should be used to describe the present unknown: “For a doctrine which is able to maintain itself not in clear light but only in the dark, will of necessity lose its effect on mankind, with incalculable harm to human progress” (Einstein). For Einstein religion is not about explaining what cannot yet be explained, that is for future science. Religion that tries to explain what can be logical is irrelevant. Religion is something deeper, yet more human. It can provide the “meaning” behind the universe. Where science can provide the “how” in which the universe acts, religion provides the “why.” For atheists they answer the “why” with randomness, with Einstein he did not try to answer the “why,” but merely accepted that it was impossible to discern this “why” and that left room for something supernatural. There are no absolutes in this world; there is uncertainty in everything, especially regarding what has no evidence. Where there is no evidence, this becomes the epitome of uncertainty, thus there is no correct, logical way to answer the question of which spirituality is correct. Einstein offers proof of accepting this fact. "Science without religion is lame, religion without science is blind." Religion can offer the “meaning” behind scientific discoveries, but absolutely no particular meaning. Trying to explain this meaning will be a fruitless waste of time, time that can be better spent in scientific discoveries. Science can offer more and more ways in which we can see the world, and can offer more ways in which religion can provide meaning to the spiritually inclined. Religion should not try to answer physical phenomena, and Science should not try to provide deeper moral meaning. Science answer different questions, and can co-exist within all of us.

Wednesday, April 27, 2011

The Tapetum Lucidum


William Bradley

The History of Science

April 2011

The Tapetum Lucidum

The variation among different creatures in the animal kingdom is astounding. There are so many different methods and mechanisms used in evolution, and we can see that in many of the creatures alive today. The tapetum lucidum (commonly shortened to “tapetum”) is no exception. It is a thin reflective layer in the eyes of many animals that reflect a specific color when light is shone upon it. This information is learned only by observing, just as Goethe did during the formulation of his theory of colors. His entire theory was based solely on his observations through experimentation and, possibly, dissection. This is similar to what we wish to achieve in this study. Through dissection, observation, and an assimilation of research articles, we can come closer to fully understanding the purpose and functions of the tapetum. We can then use this information to formulate hypotheses on related questions. For example, why is the tapetum not a part of every animal’s eyes, specifically humans? This question among others may easily be answered after we have collected and analyzed the results of this research and dissection.


Purpose:

To analyze and experience, through dissection, the tapetum lucidum in a sheep’s eye and pig’s eye.


Experiment and Observations:

Sheep eye: I started the procedure by trimming the excess fat off of the eye. I decided to use my camera and the flash on it to take a picture of the front of the eye to see if the tapetum was visible through the translucent cornea. Surprisingly, it is possible to see a blue tint through the cornea. Next, I cut the eye in two halves, front and back. Once the eye was separated and the fluid removed, I was able to see the cornea immediately in the back of the eye. This may be the result of a damaged specimen, since the layer of photoreceptors should be in front of the tapetum. I then was able to peel the tapetum out of the eye, and view it up close. There is a tiny dark spot in the middle of the tapetum. This spot is where the optic nerve met on the outside of the eye, and where the visual sensory information would be sent to the brain for processing. I initially observed that near this point on the tapetum, the tapetum was much brighter, reflective, and white. But, once you look at the tapetum at a different angle, the blue areas move around as they reflect the specific wavelength (bright blue ~ 475 nm) directly at your line of sight.

Pig eye: I basically began dissecting the pig’s eye in the same way that I dissected the cow’s eye. I trimmed off the excess fat, and cut it open into the same halves. I attempted to take a picture of the front, but I didn’t get any results of color, which I was initially looking for. It didn’t take long for me to realize that pigs actually do not have a tapetum. At first I was disappointed, but I realized I could use the pig’s eye as a comparison for the cow’s eye and the tapetum in general. The inside of the eye looked almost exactly identical, but where the tapetum would have been in the cow’s eye, the pig’s eye only had the blood vessels and grey matter, which would have been red had there been blood flowing through the organ.


Conclusions:

Viewing the tapetum in the cow’s eye allows us to get a better idea of the structure itself, and how it functions. The color reflection changes if you view it at a different angle, and it is interesting to see the focal point of the eye where the information is sent through to get to the optic nerve. In humans, this is the “blind spot” or the range in our line of sight that cannot be seen. In the pig’s eye, we can still find this spot, but it is much harder since a reflective coating doesn’t surround it. We can also use the pig’s eye as a comparison between animals that do have the tapetum and animals that do not. The pig’s eye had some grey matter where the tapetum would have been, but we can speculate that it would have been visible or red, had there been blood flowing through it.


Unfortunately, there exists a limit on what we can observe with the naked eye even in a dissection. The importance of dissection is underlined in many different sources. In Goethe’s Color Theory, it is almost impossible not to assume that he has performed a dissection on an eye, whether the eye was from a human or not. He knows much about the retina and the cornea, both of which are structures that no one at the time could have really discussed as he did unless they were well educated and had seen the structures fully. Barbara Stafford, in an article written on dissection, discusses the importance of it when she quotes P. N. Gerdy’s Anatomie des formes extérieures, “ . . . anatomy functioned like an enlarging glass. It magnified the smallest detail, rendering distinct hidden morphologies” (1). The dissection proves to us that the tapetum exists, and gives us a historical perspective into the research that has been done on the tapetum over time. But by using existing research, we can get an idea of the actual function of the tapetum, as well as how it has changed over time.

Through our observations, we find that the tapetum reflects one wavelength of light (which changes depending on the species). Basically, as laid out in a comparative study by F. J. Ollivier, D. A. Samuelson, D. E. Brooks, P. A. Lewis, M. E. Kallberg, and A. M. Komáromy, the tapetum, “normally functions at low light levels to provide the light-sensitive retinal cells with a second opportunity for photon-photoreceptor stimulation, thereby enhancing visual sensitivity” (2). The tapetum reflects a specific wavelength of light back into the photoreceptors of the eye after the light has already passed through one time. This allows for greater sensitivity to light in low light conditions. We saw this in effect in our dissection when the light from the camera reflected off of the tapetum.

Now that we have an idea of what the tapetum does, we need to know the reasoning behind the specific color of different animals. A different study by Ivan R Schwab, Carlton K Yuen, Nedim C Buyukmihci, Thomas N Blankenship, and Paul G Fitzgerald shows that, “tapeta have a tendency to reflect wavelengths most relevant to the animal” (3). This study showed that the tapetum reflects the wavelength of light important to the animal. For example, the study discusses the fact that the tapetum in deep-sea fish almost all reflect the light wavelength of 475 nm (cyan-green) because this is the only wavelength that can ever reach those depths. We can, perhaps, speculate that a cat or dog may reflect a more greenish color to reflect light off of plants or grass.

The next question that is important to us is the reason why there exists no tapetum in many animals. The study by Ollivier, Samuelson, Brooks, Lewis, Kallberg, and Komáromy states that the animals that do not have the tapetum are primates, squirrels, birds, red kangaroo and pig. These animals have very few things in common, so this helps us in identifying how the tapetum has evolved over time, which we will discuss later. These animals are all, however, diurnal creatures. This makes intuitive sense, since a creature that is active during the daytime will have less of a need for an increase in light reception. As we saw in our dissection of the pig’s eye, these creatures have a “red or orange to pale gray fundus reflection” (4). In our pig eye, the area where the tapetum would be was a pale grey. This could, however, be solely from an absence of blood in the separated and treated organ. In a live pig, the eye could be red as well. By observing human eyes, we see the red blood vessels in the back of the eye when a light is shone upon it. This causes the undesirable “red-eye” feature of many pictures taken of humans. Primates, along with the other creatures listed above, are diurnal creatures, and thus did not have an evolutionary need for a tapetum.

Given the “random assortment” of the animals with the tapetum, it is safe to assume that the tapetum developed independently among specific species. The “parent creature” could not have been very early in the mammalian evolutionary chain, thus, the evolution happened on multiple occasions. In the study by Schwab, Yuen, Buyukmihci, Blankenship, and Fitzgerald, they conclude that, “the tapetum may have arisen independently in both invertebrates and vertebrates as early as the Devonian period (390 to 345 million years ago)” (5). They base this conclusion on evidence found in other organisms. They use the assumptions that vertebrates evolve from pikaia, an invertebrate that is ancestor to other organisms that do not have the tapetum. Also, both hagfish and lampreys do not have a tapetum and they separated from an ancestor fish in the period before the Devonian.

The tapetum allows nocturnal creatures to see better in the darkness, and through dissecting, we can see what it looks like up close, as opposed to viewing it in a live animal. In doing this, we must dissect the organ and view it piece by piece. Understanding all of the functions of the eye, as well as the positions and purposes of each individual part of the eye is also important in understanding the tapetum. The cornea protects the eye, the iris expands and contracts to let specific amounts of light in, and the retina captures the image and sends it to the brain for processing. The tapetum is important in this process in that is reflects light back onto the photoreceptors of the retina for a second viewing. The tapetum is a fascinating aspect of the animal world. So many artistic endeavors have been based around the glow of an animal’s eyes. We see pictures and paintings of wolves and other large mammals where the glow of their eyes is the focal point of the picture over and over again. The tapetum is an important structure of the eye, and it is of great interest to humans in many aspects of biology, evolution, and even art. Not only does the tapetum have a scientific value, the impression that it leaves on humans, who are without it, is everlasting.

Endnotes:


1) Stafford, Barbara, Body Criticism: Imagining the Unseen in Enlightenment Art and Medicine (Cambridge, Massachusetts: Massachusetts Institute of Technology, 1991), 54.


2) F.J. Ollivier et al., “Comparative morphology of the tapetum lucidum (among selected species).” Veterinary Ophthalmology 7, no. 1 (2004): 12.


3) Ivan Schwab et al., “Evolution of the Tapetum.” Transactions of the American Ophthalmological Society 100 (2002): 197.


4) F.J. Ollivier et al., 12.


5) Ivan Schwab et al., 197.


Bibliography:


Goethe, Johann Wolfgang. Goethe’s Theory of Colors. New York: Van Nostrand Reinhold Company, 1971.


Ollivier, F.J. et al. “Comparative morphology of the tapetum lucidum (among selected species).” Veterinary Ophthalmology 7, no. 1 (2004): 11-22.


Schwab, Ivan, et al. “Evolution of the Tapetum.” Transactions of the American Ophthalmological Society 100 (2002): 187-200.


Sepper, Dennis. “Goethe, colour and the science of seeing,” in Romanticism and the Sciences, edited by Andrew Cunningham and Nicholas Jardine, 189-198. Cambridge: Cambridge University Press, 1990.


Stafford, Barbara. Body Criticism: Imagining the Unseen in Enlightenment Art and Medicine. Cambridge, Massachusetts: Massachusetts Institute of Technology, 1991.

Going Beyond Hermann von Helmholtz: The Octave Illusion with Respect to Handedness


Introduction
The octave illusion was initially produced by the stimulus configuration that is depicted in Figure 1a. Here there two tones that are spaced an octave apart, which are then repeated in alternation. This sequence was presented to both ears simultaneously, however, when the right ear received the high tone, the left ear received the low tone and vice versa with each ear receiving opposite tones. This presents the listener with a single continuous two-tone chord, but the ear in which each input is received switches repeatedly (Deutsch, 1981).
This sequence provokes various illusions. The most common illusion that arises from this sequence is illustrated in Figure 1b. This shows a single tone switched from ear to ear, whose pitch simultaneously switched back and forth from high to low. Thus, the listeners heard a single high tone in one ear, which alternated with a single low tone in the other ear (Deutsch, 1981).




The illusion is tried further when various subjects attempt to alter the ear in which the high and low tones are perceived by simply reversing the headphones. Most people still hear exactly the same thing; that is, the tone that was received in the right ear is still perceived in the right ear and the tone that was received in the left ear is still perceived in the left ear. The listener originally associated the difference in right versus left ear perception to the earphone, but the reversal of the headphones proves to the listener that it is not the headphones, but indeed the ears that perceive the different tones. This percept is illustrated in Figure 2. Figure 2 provides a written report by someone with absolute pitch (Deutsch, 1981).



The octave illusion was shown to be based on two factors: (1) the perception of the frequencies presented to a single ear (those presented to the other ear being suppressed), and (2) the localization of each tone to the ear receiving the high frequency signal. This is regardless to whether the higher or lower frequency was actually perceived (Deutsch, 1974). More recently, the octave illusion is explained on the foundation of selective attention.

Selective attention is expressed as the ability to selectively attend to certain stimulus; blocking out unimportant stimulus. Selective attention also explains how an individual in a room full of people can focus on only one conversation. The auditory system contains many centrifugal pathways, which extend from the auditory cortex, Brodmann’s areas 41 and 42 (Andorn, 1989), through the medial geniculate body, colliculi, olivary regions, and back to cochlea. Some of these structures are proposed to play a role in selective attention by modulating midbrain and auditory nerve responses or possibly the activity of the cochlear hair cells (Chambers, 2002).

In general, it was found that among the right-handers who obtained the percept that there was a single high tone in one ear, which alternated with a single low tone in the other ear, had a highly significant tendency to hear the higher tone on the right and the lower tone on the left. This observation did not hold true for left-handers (Deutsch, 1974). This is in accordance with the literature showing that although most right-handers have clear left-hemisphere dominance, the pattern of cerebral dominance among left-handers varies considerably (Deutsch, 2009). This helps explain why the proportion of listeners obtaining complex percepts was much higher in left-handers than in the right-handers (Deutsch, 1981). Furthermore, these results are consistent with neurological evidence.

Neurological evidence suggests that the majority of right-handers are left-hemisphere dominant; meaning their speech is represented in the left cerebral hemisphere. However, this is only true for approximately two-thirds of left-handers as opposed to the overwhelming majority of right-handers. The remaining one-third are right-hemisphere dominant, which means that although most left-handers have speech represented in the left cerebral hemisphere, a substantial amount of left-handers have speech in both hemispheres (Deutsch, 1981). The variation of the hemispheres may help account for the variation of tone localization that can be present in some left-handed populations. Since the brain exhibits contralateral tendencies, it would come as no surprise that right-handers would tend to strongly follow the information presented to their right side (the auditory cortex is on the left side of the brain; right-handed people have stronger pathways to the left hemisphere because of their right-handed dominance to the contralateral left hemisphere) (Deutsch, 1981).

The result of a substantial right-ear advantage for a sequence that is nonverbal is seemingly contradictory according to the widely held belief that the dominant hemisphere is used for verbal functions, while the non-dominant hemisphere is used for nonverbal or musical functions. Left-ear advantages have been obtained in dichotic listening tasks involving musical composition. Thus, it would then be the left ear that would perceive the higher tone in the sequence. Although, a left-ear dominance has been obtained for nonverbal sequences, right-ear advantages have also been obtained. It was found that when subjects were required to recognize two frequencies, dichotically, the ear advantage was purely right (Deutsch, 1981).

In short, this research in its current form focuses on repeating the octave illusion experiment. Based upon previous experiments, it is believed that the majority of right-handed subjects will perceive a high tone on the right alternating with a low tone on the left, while left-handed subjects will vary more in perception, but nonetheless, the majority of left-handed subjects will perceive a high tone on the left alternating with a low tone on the right. Additionally, musical training of the subjects will be assessed for a positive correlation in the ability to correctly establish the differences between the frequencies.


Methods

The current research was performed on 51 undergraduate students of varying degree study programs at the University of Michigan. Of the students that underwent the research, 28 students were female (54.9%) and 23 students were male (45.1%). The ages varied within a range of six years. The minimum age of the students was 17 with a maximum age of 22 and a mean of 19.08 years of age, with a standard deviation of 1.354 years. For a further breakdown of the ages of the participants please see Appendix A, Table 1. 32 of the 51 students were right handed (62.7%), 16 were left handed (31.4%) and 3 students were assessed as both handed (5.9%). Handed was assessed by the questionnaire in Table 1 (Varney, 1975). Answering eight or more in either the left or right category designated a participant to that respective category. Less than eight selections in either the left or right category alone designated a participant to both handed.

Of the right-handed participants, 14 were male (43.8%) and 18 were female (56.3%). From the left-handed participants, 7 participants were male (43.8%) and 9 were female (56.3%).

Furthermore, it was noted whether these 51 students had musical training, which was defined at three years or more learning or playing a musical instrument (Deutsch, 1981). 23 students did not have musical training (45.1%), while the remaining 28 students responded as having musical training (54.9%).

Each subject was tested individually. They were explained that they would hear a sequence of tones that would repeat. Upon the conclusion of the tones they were asked to indicate on a forced choice questionnaire which description best fit their perception of the tone(s), they had just heard (Deutsch, 1981).

The set-up for the testing was quite simple. JVC Gumy Ear Bud Headphones, HA-F150A stereo speaker headphones, with a frequency response of 16-20,000 Hz (JVC, 2010), was plugged into a MacBook Pro. The tone sequence was accessed and played back for the participant from an online source (Philomel Records). The tone consisted of an alternating pattern of 400 (G4) and 800 (G5) Hz (Deutsch, 1974). The clip was 30 seconds in length.


Figure 3



Screen Shot of the embedded music that the participants listened to.



At the conclusion of the clip, each participant was asked to pick one of the following options that best described their individual percept: (A) A high tone on the right alternating with a low tone on the left; (B) A high tone on the left alternating with a low tone on the right; (C) A tone switching from ear to ear with no change in pitch; (D) None of the above (explain) (Deutsch, 1981).

All data and statistics were processed by PASW, Predictive Analytics SoftWare, SPSS, Statistical Package for the Social Sciences, 18.0.


Results and Discussion

Of the 51 students who participated, 32 responded (A) a high tone on the right alternating with a low tone on the left (62.7%); 17 responded (B) a high tone on the left alternating with a low tone on the right (33.3%); 2 responded (C) a tone switching ear to ear with no change in pitch (3.9%). The data was then stratified for various variables. The first of the stratifications was handedness. The following is based from if the participant was right-handed. Of the students who were right-handed, it was found that 18 participants had musical training (56.3 %), while 14 did not (43.8%). Out of the right-handed participants (N=32), 30 participants responded with (A) a high tone on the right alternating with a low tone on the left (93.8%) and 2 participants responded with (B) a high tone on the left alternating with a low tone on the right (6.3%). The following is based from if the participant was left-handed. Of the students who were left-handed, it was found that 7 students had musical training (43.8%), while 9 did not (56.3%). Out of the left-handed participants (N=16), 0 students responded with (A) (0%), 15 students responded with (B) (93.8%) and 1 participant responded with (C) (6.3%). In general, this follows very well with the established trend; right-handed people hear the high tone on the right, while left-handed people are a bit more varied, but generally hear the high tone on the left.

The musical trend of this data set does not follow the pre-conceived notion that left-handed people are more likely to have musical training. Traditionally, the right hemisphere is viewed as the musical hemisphere, thus with the contralateral nature of the brain, left-handed people would stimulate the right hemisphere of the brain more often than right-handed people invoking musical tendencies. (Tramo, 2001). Further stratification of the data was performed to assess the trend in the data. It was found from the data set that if the participant was musical, he or she was more likely to be right-handed. But, due to the greater abundance of right-handed versus left-handed people in the study, it was also found that if a person was non-musical, he or she was more likely to be right-handed. For the complete statistical breakdown regarding handedness and musical training refer to Appendix A, Table 2 and Table 3.

The last set of data stratifications were performed with respect to each tone choice (A-C) perceived. 32 participants responded with having heard a high tone on the right, alternating with a low tone on the left, option A. Of these students, 20 students indicated having musical training (62.5%), while 12 did not (37.5%). Additionally, 30 of the 32 students who perceived the tone sequence associated with choice A were right-handed (93.8%) and 2 students were both-handed (6.3%). 17 students responded with having heard a high tone on the left, alternating with a low tone on the left, option B. Of these students, 6 indicated having musical training (35.3%), while the majority of this subset indicated not having musical training (N=11, 64.7%). Furthermore, 15 of the 17 students were left-handed (88.2%) and 2 were right-handed (11.8%). Lastly were those who perceived a tone switching from ear to ear with no change in pitch (C). Option (C) represented a very small portion of the data (N=2). Of these 2 students, both indicated having musical training, although one was left-handed and one was right-handed.


Conclusions and Recommendations

In general the results of the subjects from this experiment correlated well with those of previously published results. The majority of right-handed subjects responded by perceiving a high tone on the right alternating with a low tone on the left, while the results of the left-handed indicated that the majority of the left-handed subjects perceived a high tone on the left alternating with a low tone on the right. The most substantial difference between these results and previously published studies include the lack of variation within the left-handed participants. According to published findings, the perception of left-handed people should be more varied. The lack of variance in this current study can be attributed to a small sample size.

Additionally, the demographic statistics proved interesting. According to the data, musical training does not affect the tone that is perceived. Again, this could be attributed either to a lack of a relationship or a small sample size. To efficiently test this, a larger sample size is needed of both musically and non-musically trained participants that are equally divided with left- and right- handed subjects.

Overall, this research should be completed with more subjects that equally represent the left- and right-handed population. This would improve the sample and should, in theory, provide data that is more representative of the population.


References

Andorn, A.C., Vittorio, J.A., Bellflower, J.. “3H-spiroperidol binding in human temporal cortex (Brodmann areas 41-42) occurs at multiple high affinity states with serotonergic selectivity,” Psychopharmacology (Berl.), (1989:90), 4, 520-525.


Chambers, C. D., Mattingley, J. B., & Moss, S. A. “The octave illusion revisited: Suppression or fusion between ears?,” Journal of Experimental Psychology: Human Perception and Performance, (2002) 28(6), 1288-1302.

Deutsch, D. “An auditory illusion,” Nature (1974) 251, 307–309.

Deutsch, D. "An auditory illusion". Journal of the Acoustical Society of America (1974) 55, s18-s19.

Deutsch, D. “The Octave Illusion and Auditory Perceptual Integration,” Hearing Research and Theory, Volume 1 (1981), 1, 99-142, New York: Academic Press.

Deutsch, D. “The octave illusion in relation to handedness and familial handedness background,” Neuropsychologia (1983) 21 (3), 289–293

Deutsch, D. “Musical Illusions,” Encyclopedia of Neuroscience, (2009), 5, 1159-1167, Academic Press, Oxford.

JVC. 2010. HA-F150A Specifications. http://av.jvc.com/product.jsp?modelId=MODL028884&pathId=162&page=3

Philomel Records. Diana Deutsch’s Auditory Illusions. http://philomel.com/musical_illusions/example_octave_illusion.php

Tramo, M. J. “Music of the hemispheres,” Science. (2001), 5.

Varney, N. R. and Benton, A. L. “Tactile perception of direction in relation to handedness and familial handedness,” Neuropsychologia (1975), 13, 449-454.


Appendix A

Table 1

Age

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

17

6

11.8

11.8

11.8

18

14

27.5

27.5

39.2

19

11

21.6

21.6

60.8

20

12

23.5

23.5

84.3

21

6

11.8

11.8

96.1

22

2

3.9

3.9

100.0

Total

51

100.0

100.0

Ages of the participants


Table 2

Musical

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

Y

18

56.3

56.3

56.3

N

14

43.8

43.8

100.0

Total

32

100.0

100.0

Whether the participant had musical training (Y=Yes, N=No) with respect to the right-handed participants.


Table 3

Musical

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

Y

7

43.8

43.8

43.8

N

9

56.3

56.3

100.0

Total

16

100.0

100.0

Whether the participant had musical training (Y=Yes, N=No) with respect to the left-handed participants.