A PhD degree in Physics represents a new contribution to the body of scientific knowledge; but, it is more than that. The power of new physics is not in the generation of new information, though that is one important side effect. It is the new or deeper understanding of the nature of how how things work that are its treasures. It is not a process in which a student goes through steps 1, 2, 3, 4, 5, and then is done, but a journey of exploration that often can come up empty handed. Putting in lots of time and effort is not enough. There needs to be a tangible result that adds to the corpus of Physics.
The dissertation documents the contribution a PhD student has made to science. The process of writing up ones work and results inevitably uncovers errors, weakness in logic, and oversights that need to be addressed. As such, the period of writing prior to submitting the dissertation to the examining committee is filled with stress. One never knows if the errors that are uncovered will be fatal to the thesis. Many students are unaware of the magnitude of the demands. In the end, it has to be right (internally self consistent and in accord with the rest of Physics) and the dissertation committee needs to be convinced that the work is significant enough to be worthy of a PhD.
I write this as Shiva is finishing up his dissertation and getting ready to defend. The work is excellent and I believe that it will be a major contribution to the body of Physics. We have proposed a novel model based on experimental observations that pass the test of simplicity - with only three parameters all of the data is explained over a huge range of conditions; and, it suggests new physics, namely, that a polymer mediates the interaction between molecules in a way that coerces them into healing after they are damaged by powerful laser pulses. This phenomena is new and its explanation is bound to be controversial; and it may end up being wrong...
In the process of writing his dissertation, Shiva had to make major changes to the analysis of the data, needed to take additional data, and had to take into account complications that had slipped by our attention. Each time he thought he was done, there always seemed to be one more thing to check, one more experiment to do or one more calculation to correct. I can imagine the ups and downs associated with the relief of being done followed by the anxiety over a potential error that could mean the downfall of the dissertation.
As I write this post, I believe that his dissertation is finally done, and I am comfortable with the scrutiny that is to come from the committee. There are certainly loose ends that will be addressed, but those can be completed prior to the oral or as minor revisions after the defense.
I have advised dozens of graduate students over the years. Many have vocalized the childhood question asked of parents during a long road trip, "are we there yet?" Others think about their progress quietly while some may assume that they will get a degree as a result of making an effort. In the end, only students who persevere after what appears to be endless failure and hardships will make it through to the end. The process includes hard work, independence, cleverness, deep thinking, and extreme grit. As a result, the future employer of a PhD physicist is not getting just an expert. If that is what they think, the employers miss the best part. They are getting an individual who is fearless in the face of new challenges that require a nonexistent expertise.
Expertise is stagnation. Dealing with the unknown is wrought with fear, insecurity, and doubt; but, there is an air of exhilaration from the possibility of successes. The PhD student builds problem-solving skills and the ability to think beyond his or her knowledge base and to thrive in a world of uncertainty. It is character not just expertise that the PhD represents.
The beauty of nature is that she is consistent and filled with rich and wondrous phenomena. On the downside, she holds the highest standards and is intolerant of contradiction. I am glad to have a job that allows me to be continually confused, insecure and humbled. Every new piece of knowledge or expertise gained drives me into a new unknown realm. I am simultaneously frustrated and ecstatic, perhaps a required blend of opposites that lead to fulfillment and happiness.
Having acquired a taste for this life, I wish the same for my students. As Shiva is finishing up, I look to the next generation of students coming up through the ranks in the hopes that they too will succeed.
Saturday, April 28, 2012
Saturday, April 21, 2012
Quantity, quality and language
I write more for myself than for an audience. The act of writing flushes out ideas and provides a record of what I was thinking so that I do not spend time reinventing the wheel (by wheel, I mean my personal wheel, not new ideas to the world, which I am sure are few). Sadly, I often get hot about an idea, start writing about it, and then get too busy with other things to finish. As a result, my ideas are lost.
I spend a few minutes every few months erasing incomplete posts. Today, while I was clearing several such posts, I pondered about the wasted effort of the process and the added entropy to the universe each time I hit "delete." So, I decided to share this one with myself and anyone else who cares to read it.
To place the state of my mind in perspective, I was writing this post in the first half of August, 2011, just before the start of the semester, when I was slated to teach Classical Mechanics. I recall being excited about my insights on the topic, but sadly, I no longer recall the punchline. Perhaps one of you can help me out.
Here it is:
Language is often inadequate to describe what we are feeling. A far greater problem is that language permits imprecision and inconstancy. As a result, we are falsely lulled into a sense of meaning when there is none.
The classic example of self contradiction is the sentence: "This sentence is false." We can reject this construction for obvious reasons. However, consider the statement, "His action was immoral." The first three words are well defined, but the last is not.
At issue is the fact that many concepts in language are based on subjective feelings, that when assigned a word, may be imprecise or nonsensical yet carry an absolute sense of its existence. When analyzed dispassionately, we can surmise that the sense of morality is an inbred feeling that was shaped by evolution, and helped the survival of our species. Thus, when someone cheats, our sense of distaste stems from our collective disapproval of behaviors that weaken the group.
However, our gut assigns to the concept of morality a sense of absoluteness of "right" and "wrong" of actions - two additional words of the same ilk. Morality is thus elevated to an absolute standard that cannot be questioned. It is wrong for women to vote. Why? Because it is an absolute, and absolutes cannot be questioned. Thus, the sense of morality can lead to concepts such as women being mere property to serve at the pleasure of men, homosexuality as an evil, drawing a cartoon of certain individuals an objectionable action deserving of death, etc.
One may argue that without an absolute morality, humans would be lost and unable to decide what is right. Humans have been making the "right" decisions for ages without religion; but, this is not the point of this post. Instead, I want to speak about a different kind of language that does not suffer through the same pitfalls; but ironically, is responsible for the development of imprecise language; and that is, mathematics.
One of the earliest incarnations of mathematics was counting. Shepherds wanted to make sure that all their flock was accounted for by the end of the day. The simple act of counting may seem trivial and lack meaning. As it turns out, it is the basis for everything.
Mathematics became more sophisticated with the introduction of multiplication, which is the act of counting groups of groups of things. Three families of four make twelve people. Division is then the inverse of multiplication as is subtraction to addition. Aside from keeping track of cattle and assigning value to property, mathematics in this guise appears devoid of any deep meaning.
But, mathematics progressed. Variables were introduced to assign unknown quantities, functions to describe relationships between variables, etc. The growth of mathematical structure grew hand in hand with applications. Exponential functions could be used to describe the growth of livestock, the degree of hotness was associated with temperature, etc.
Then operations on functions were introduced. Derivatives gave slopes of curves and integration, the reverse of a derivative, yields the area under the curve. It was a stroke of intense insight when someone recognized that numbers associated with various physical quantities behaved in correspondence with what the operations predicted. This is a subtle point that deserves more - later.
Then came abstract mathematics that deals with groups theory, linear algebra, differential geometry. Even these seemingly non-practical concepts describe things such as the curvature of space-time, that governs the the motion of spacecraft and makes the GPS system possible, and predicts the groupings of elementary particles.
All of this leads to the obvious conclusion that there is no dichotomy between quantity and quality. Quality is in fact described in terms of quantity.
For example, we may say that gold has the qualities of being soft, yellowish, and shiny. Silver, on the other hand, is harder, greyish or some would say colorless, is shiny and half as dense as gold. As it turns out, the difference between the two atoms is in the numbers of protons, neutrons and electrons. Silver has 47 protons in a tiny nucleus and 47 orbiting electrons Gold, on the other hand, has 79 protons and 79 electrons (we ignore the neutrons since they don't affect an atom's chemical properties). It is the number of electrons and protons that determines the quality of the material. Thus quantity determines quality.
The numbers of various atoms in a molecule determine its properties. As we go up the later and make complex molecules, cells, organs, people, communities, and the universe, the properties of each object is determined by numbers that quantify the underlying things.
I have failed to mention forces, which determine how matter "sticks" together. The forces, which behave according to simple laws, determine the structures of molecules, galaxies, and nuclei. The simple laws that describe forces are formulated in terms of equations that represent numbers. So there are numbers everywhere that determine the quality of things.
However, the macroscopic universe is so complex, that it is difficult on human scales to express its properties in terms of the numbers that quantify the smallest units. This is where it is easier to think in terms of quality. You would prefer to think of your winter coat as warm and cozy rather than describe it in terms of the thermal conductivity of its parts, the chemical reactions in your body that create heat, etc.
-- This is where my post ends, with typos and incomplete thoughts. Perhaps someone can figure out what I had in mind. If so, please send me a note.
I spend a few minutes every few months erasing incomplete posts. Today, while I was clearing several such posts, I pondered about the wasted effort of the process and the added entropy to the universe each time I hit "delete." So, I decided to share this one with myself and anyone else who cares to read it.
To place the state of my mind in perspective, I was writing this post in the first half of August, 2011, just before the start of the semester, when I was slated to teach Classical Mechanics. I recall being excited about my insights on the topic, but sadly, I no longer recall the punchline. Perhaps one of you can help me out.
Here it is:
Language is often inadequate to describe what we are feeling. A far greater problem is that language permits imprecision and inconstancy. As a result, we are falsely lulled into a sense of meaning when there is none.
The classic example of self contradiction is the sentence: "This sentence is false." We can reject this construction for obvious reasons. However, consider the statement, "His action was immoral." The first three words are well defined, but the last is not.
At issue is the fact that many concepts in language are based on subjective feelings, that when assigned a word, may be imprecise or nonsensical yet carry an absolute sense of its existence. When analyzed dispassionately, we can surmise that the sense of morality is an inbred feeling that was shaped by evolution, and helped the survival of our species. Thus, when someone cheats, our sense of distaste stems from our collective disapproval of behaviors that weaken the group.
However, our gut assigns to the concept of morality a sense of absoluteness of "right" and "wrong" of actions - two additional words of the same ilk. Morality is thus elevated to an absolute standard that cannot be questioned. It is wrong for women to vote. Why? Because it is an absolute, and absolutes cannot be questioned. Thus, the sense of morality can lead to concepts such as women being mere property to serve at the pleasure of men, homosexuality as an evil, drawing a cartoon of certain individuals an objectionable action deserving of death, etc.
One may argue that without an absolute morality, humans would be lost and unable to decide what is right. Humans have been making the "right" decisions for ages without religion; but, this is not the point of this post. Instead, I want to speak about a different kind of language that does not suffer through the same pitfalls; but ironically, is responsible for the development of imprecise language; and that is, mathematics.
One of the earliest incarnations of mathematics was counting. Shepherds wanted to make sure that all their flock was accounted for by the end of the day. The simple act of counting may seem trivial and lack meaning. As it turns out, it is the basis for everything.
Mathematics became more sophisticated with the introduction of multiplication, which is the act of counting groups of groups of things. Three families of four make twelve people. Division is then the inverse of multiplication as is subtraction to addition. Aside from keeping track of cattle and assigning value to property, mathematics in this guise appears devoid of any deep meaning.
But, mathematics progressed. Variables were introduced to assign unknown quantities, functions to describe relationships between variables, etc. The growth of mathematical structure grew hand in hand with applications. Exponential functions could be used to describe the growth of livestock, the degree of hotness was associated with temperature, etc.
Then operations on functions were introduced. Derivatives gave slopes of curves and integration, the reverse of a derivative, yields the area under the curve. It was a stroke of intense insight when someone recognized that numbers associated with various physical quantities behaved in correspondence with what the operations predicted. This is a subtle point that deserves more - later.
Then came abstract mathematics that deals with groups theory, linear algebra, differential geometry. Even these seemingly non-practical concepts describe things such as the curvature of space-time, that governs the the motion of spacecraft and makes the GPS system possible, and predicts the groupings of elementary particles.
All of this leads to the obvious conclusion that there is no dichotomy between quantity and quality. Quality is in fact described in terms of quantity.
For example, we may say that gold has the qualities of being soft, yellowish, and shiny. Silver, on the other hand, is harder, greyish or some would say colorless, is shiny and half as dense as gold. As it turns out, the difference between the two atoms is in the numbers of protons, neutrons and electrons. Silver has 47 protons in a tiny nucleus and 47 orbiting electrons Gold, on the other hand, has 79 protons and 79 electrons (we ignore the neutrons since they don't affect an atom's chemical properties). It is the number of electrons and protons that determines the quality of the material. Thus quantity determines quality.
The numbers of various atoms in a molecule determine its properties. As we go up the later and make complex molecules, cells, organs, people, communities, and the universe, the properties of each object is determined by numbers that quantify the underlying things.
I have failed to mention forces, which determine how matter "sticks" together. The forces, which behave according to simple laws, determine the structures of molecules, galaxies, and nuclei. The simple laws that describe forces are formulated in terms of equations that represent numbers. So there are numbers everywhere that determine the quality of things.
However, the macroscopic universe is so complex, that it is difficult on human scales to express its properties in terms of the numbers that quantify the smallest units. This is where it is easier to think in terms of quality. You would prefer to think of your winter coat as warm and cozy rather than describe it in terms of the thermal conductivity of its parts, the chemical reactions in your body that create heat, etc.
-- This is where my post ends, with typos and incomplete thoughts. Perhaps someone can figure out what I had in mind. If so, please send me a note.
Sunday, April 15, 2012
The dark side of the internet
Bill Andrews writes in the August issue of Astronomy Magazine, "People confuse their inalienable right to their opinion with a fictitious right to be right, and it's growing increasingly acceptable. The level of science education in this country has apparently sunk so low that a significant portion of the population doesn't even know how to distinguish verified data from personal opinion, and no one seems to care. It doesn't get get more basic, or scary, than that."
Is the internet, with websites such as Reddit - which elevates popularity and opinion over fact, part of the problem?
Is the internet, with websites such as Reddit - which elevates popularity and opinion over fact, part of the problem?
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