Fame for its own sake

After giving a talk in Milan, my host, another visitor from the US, and I had lunch. Discussions meandered from our work to our profession and then to the topic of how trailblazers often do not get credit for their discoveries. A book that I am now reading, "The Infinity Puzzle," describes this phenomena in the development of the standard model in particle physics.

In 1783, the geologist John Michell wrote a letter to Henry Cavendish proposing the existence of a super-massive body whose gravity was so great that even light could not escape. The letter was published in the Transactions of the Royal Society in 1784, yet this incredible human mind is not generally recognized for the very reason that it should be - it was way ahead of its time.

People who end up getting credit for a discovery usually live at a time when others are around to appreciate the work. Being a good communicator also helps. Our conversation at the outdoor cafe culminated in an interesting question. Would it be better to enjoy fame and fortune in this life for work that is posthumously found to be wrong; or, to make a discovery that is only appreciated long after we are gone?

I would rather play a part in the development of a new paradigm of thought that is right than to get credit for a transient fad that ends up being wrong. What would you prefer?

Expertise is stagnation

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.

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.

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?

After almost a year of waiting, finally some good news!

These are tough times for any programs that are funded by the U.S. government. Last summer I was contacted by NSF for some clarifications on my proposal, which I provided and resulted in the program manager's approval. In my experience, official notification to our university about an award comes no more than a few weeks after this first contact. In this case, we heard nothing for months.

While on an NSF panel in the fall semester, I visited with the program manager to inquire about the disposition of my proposal. He told me that the paperwork had been signed and that the documents "were on the Directors desk" awaiting final signatures. However, congressional battles on funding to NSF put proposals on hold until a resolution was in sight.

I was getting concerned that this proposal would never be funded. However, a couple weeks ago I was contacted by an accountant with questions about a budget issue. It took only a few emails to resolve the issue, so again, I waited. While I have not received official word in the form of a binding award letter, the NSF website now shows my proposal as "awarded." The reviews are also posted.

Excerpts from the panel summary follow.

Objective: The objective of this program is to invent new approaches for manipulating quantum systems in a way that enhances their nonlinear-optical response.

Intellectual Merit:
The intellectual merit of this proposal is very high and may lead to discovery of universal properties that will enable optimization of materials for a given task, such as nonlinear optical response. The PI's approach is to use sum rules in conjunction with numerical optimization and Monte Carlo studies to broadly understand those issues that are most important in making an optimized material. This will include development of fundamental quantum mechanical concepts that build an understanding of the performance limit of optical materials and practical methods for attaining the limit. The knowledge will guide chemists and nanotechnologists in designing new materials and nanostrucutures. The PI is very well qualified to carry out the proposed research. If successful, the proposed effort will lead to transformative paradigms enabling physicists and materials scientists to synthesize novel functional materials and to generate novel photonic devices.

Broader Impacts:
This proposal has the potential to make transformative advancements in the development of novel materials for photonic applications. The fundamental knowledge will serve as a guide in optimizing a material for a given task, such as nonlinear optical response. The work applies to any system based on the interaction between light and matter including molecules, inorganic materials, nanoparticles, smart materials, nanowires, etc. Education and outreach efforts are very strong and will broaden participation of Native American and under-represented groups and undergraduate students in the research program. The PI also plans to promote undergraduate participation and interaction with high school students through online interactive resources. Numerical codes that will be developed as part of the program work will be distributed over the web so that students can participate in research.

Summary:
The panel considers this is an excellent proposal with strong technical and education components. If successful the research will have a transformative impact on development of fundamental quantum mechanical concepts to synthesize novel functional materials.
Reviewer Ratings: E, E, V,

Panel Recommendation:
The proposal was placed in the Highly Recommended [HR]] category by the panel. The Program Directors concur with the panel opinion as expressed in the panel summary with respect to both the Intellectual Merit and the Broader Impacts criteria.

Extreme Physics

In our culture, the word "extreme" has taken on a new meaning because of its use in naming new sports that are dangerous. By "extreme physics," I mean the physics of a phenomena when one of its defining parameters is at an extrema; that is, a minimum, maximum, or point of inflection. Mathematically, an extrema of a function is defined as the point were the first derivative is zero. In many ways, extreme physics can be just as exciting as extreme sports.

It interesting to me that the underpinnings of physics are based on extremes. Surely I am not unique in thinking this way; but, I am excited by the topic because one of my projects is based on the theme of using the limits of the nonlinear-optical response to discover new things about light-matter interactions that in the end may lead to a deeper understanding.

As we have been digging deeper and deeper, new patterns are emerging. This regularity, however, is only observed at the extremes of the nonlinear-optical response. Given how all of known physics manifests itself by an extrema, it is pretty exciting to think that we may be on the verge of discovering truly new physics.

There are other projects that are going well and have potentially very exciting ramifications. For example, we are in the process of fine-tuning a new model of the self-healing process. But this is not just a model in the form of an equation that we use to fit our our data (which we are indeed doing), but the parameters represent new phenomena. If the model fits, we are potentially looking at new theory that may be generally applicable to many things. The more general the applicability of our work, the happier my mood.

I end here by lifting an excerpt from a review article we are writing for Physics Reports. It is a more detailed description of what I have written above.

The extremes of physics are characterized by unique behavior. For example, the second law of thermodynamics states that entropy cannot decrease in a closed system. The special case when entropy change is minimized (i.e. it remains unchanged) defines reversible thermodynamic processes. The maximum efficiency of a heat engine requires a reversible process. Calculations of reversible heat engine efficiencies led to the definition of entropy. While motivated by practical applications, entropy has become one of the most important fundamental concepts in physics.

Quantum mechanics is based on the fact that certain quantities cannot be simultaneously measured to arbitrary precision. To accommodate this observation, variables such as momentum and position are generalized to become operators that do not commute. The mathematical formalism naturally leads to the uncertainty principle, which states that there is a lower bound to the product of the position and momentum uncertainties. The fact that uncertainties are constrained by a lower bound is the basis of quantum mechanics, which describes a vast richness of new phenomena that is inexplicable using classical mechanics.

The principal of energy conservation originates from the more general concept of a Hamiltonian, which yields the equations of motion through a process of finding the extrema of the action. These ideas carry over into the quantum realm in the formulation of path integrals, which bring out the wave nature of matter. The absolute maximum speed limit defined by the speed of light, on the other, leads to non-absolute time, where observers in different coordinate systems view the same phenomena but from the perspective of a rotation in four-dimensional space-time. The marriage of relativity with quantum mechanics as embodied by the Dirac equation led to a natural way of accounting for the electron spin, and as a bonus unexpectedly predicted the existence of antimatter.

Clearly, the extremes are fertile soil from which the most fundamental concepts in physics grow. As we later show, the fact there there is a fundamental limit to the nonlinear-optical response of a quantum system defines an extreme that is characterized by several features. For example, while many states of a quantum system contribute to the nonlinear-optical response, at the upper bound only three states are found to contribute. This was originally postulated as a hypothesis and later confirmed to be true for many quantum systems, though it has not yet been rigorously proven. As such, it is referred to as the three-level ansatz.

We will show that systems with a nonlinear response near the fundamental limit share other properties. Why this is true is not yet understood; but, the fact that certain universal properties appear to be associated with the extremes of the nonlinear response hints at fundamental causes, perhaps grounded in new physics, which become apparent only under scaling rules that follow naturally from these limits.

A sampling of everything that is possible

It is spine tingling to view a two-dimensional representation of everything that is possible given the laws of physics. I had previously written about our work, where Shoresh used Monte Carlo simulations to let the computer randomly sample all possible quantum systems that are compatible with the Schrodinger equation. In my recent report to the National Science Foundation, my awe in Physics and its ability to make such grand and sweeping statements was rekindled. Above is a summary of our work in graphical form. It is aesthetically pleasing in its visual appeal, but more so in its intellectual content.

I cannot explain in the small amount of space here the beauty of these results, nor what they mean in terms of the basic science. Nature is clearly hinting at some deep structure of the quantum world when we probe molecules with light. My summary to NSF states it best:

"The uniqueness of our work is that it provides a new way of thinking, which in the words of a Spotlight on Optics article describes our approach as "reminiscent of the cutting of the Gordian knot by Alexander the Great. (see article)" Rather than focusing on one application, our work provides a new paradigm for understanding the critical material properties that need to be controlled for making better materials for any application that is based upon the interaction of light with matter.

"Technologies that may benefit from this work include high-contrast medical imaging, laser-based cancer therapies that target malignant cells without damaging surrounding cells, all-optical computers that are ultrafast by virtue of new architectures enabled by light, high-speed telecommunications through technologies that eliminate the electronics bottleneck, and high-density reconfigurable optical information storage."

Now I need to get back to the painfully boring task of updating my CV and preparing my annual review materials. I can't wait to finish these inane tasks so that I can get back to thinking about the things that I find most meaningful in life.