Errors and Creativity

In any deep and complex endeavor, it is easy to make mistakes.  Even after intense scrutiny, errors in logic and reasoning can be difficult to catch.  However, when properly harnessed, errors can lead to new and interesting ideas.

Recently, a bright junior colleague made a mistake in a calculation, and I am sure that he was down on himself over the whole thing;  so, I wrote him the following email (which I have modified slightly for you).  After rereading it, I thought it would be good general advice to all students who are struggling with work at the boundaries of the unknown where mistakes are common.

Dear Student,

Do not be hard on yourself about such errors.  We all make them.  When you have been around long enough to have made all the simple errors, you move on to the more complex ones.  As you mature, you will make these transitions over and over again.  The two of us are similar in the sense that we perhaps make more errors than the average physicist.  This can become a strength if you use it to your advantage.
 
I believe that the tendency to make mistakes is associated with creativity. Mistakes take us into new territories that others may never imagine.  Often, it's a mistake that leads me in new directions that brings me into uncharted domains.  When my colleagues question me about how I ever even thought of doing X, I can't explain it.  Now that I think about it, I should answer that it was a string of errors that led me to X.  These random meanderings avoid the huge walls that block the straighter paths.

The key is to work hard and tirelessly in the pursuit of entertaining lots of new ideas, be slow to publish so that you can catch your mistakes before they become public, and allow yourself times of unrestrained creativity but temper those times with disciplined thought.  And most importantly, do not get caught up in mathematics without thinking about the physical consequences.  It is the physics that is the most fulfilling and the best guide through your intellectual hardships.

Should I get back on Statins?

Next week, I need to make a decision that may strongly impact my health a decade or two down the road.   The million dollar question, "should I get back on statins?" given that a high fat diet worked for me in the past but is a bit slow to lower my risk factor this time around.  This is a long post so for the short summary, you can skip to the end (Section 4).

1. Background - 1996 to 2012

a. Experts were saying that a high fat diet would not result in weight loss, but would raise cholesterol

A short digression will explain how I got to this point.  In 1996, I started the Atkins diet to combat my growing bulge.  At the time, I was warned not to do it because (1) Eating lots of fat can't make you lose weight; and (2) My cholesterol would rise and I would certainly dye of a heart attack.  My doctor also cautioned me about these issues; but, being an open-minded and intelligent individual, he suggested that my cholesterol be monitored periodically.  He also informed me that the best medical advice of the day was that the ratio of total cholesterol to HDL, called the risk factor, should be below 5 -- but the lower the better.

b. The experts were wrong.  My weight plummeted and my health improved while I was eating lots of fat

A couple months after I started the diet, the ratio tested at almost 8 (see green points on the plot to the right) -- so huge that I was truly concerned.  My cholesterol from a year before was inching up to 5, so 8 was a huge increase.  Since my weight was literally dropping exponentially, as you can see from the red points in the diagram to the right, I decided to wait another 3 months (Atkins stated that the cholesterol in his patients dropped in the long term).  The reading was 6 and then three months later, 4, and six months after that down to almost 3.  So, the critics were wrong.  My weight and cholesterol remained low for over 6 years.  As an added benefit, I felt great; my skin cleared to the sheen of a baby's butt, my weekly migraines disappeared, indigestion was gone, blood pressure plummeted, insomnia was cured, and I was full of energy.  I may be confusing correlation with causation; but, all these effects correlated with my weight loss and risk factor decrease.  The bottom line is that getting over 75% of my calories from fat and about 20% from protein did not make me unhealthy according to the metrics used by the medical profession.

c. The diet was tasty and easy to maintain for more than 6 years

The diet was not difficult to maintain because the food was tasty and enjoyable, and I never felt hungry.  What killed my "healthy" lifestyle was traveling overseas.  In Europe, the "healthy foods" and "exercise" did me in.  My wife and I spent a large fraction of one delightful summer in Belgium.  We had no car so we biked or walked everywhere; yet, I gained over 10 pounds.  A few more years of traveling overseas and my weight and cholesterol slowly crept up; so, I eventually took statins and decided that my health was protected, so I went back to eating pasta, bread, fruit, vegetables, and of course meat.  By the time we got back from our trip to Italy last summer, I was nearing my peak weight of 1996, so I decided to once again go on the Atkins diet for good.

2. The present - Summer of 2012 to Now

I started the Atkins diet for the second time at the end of the summer of 2012.  The data appears to the left (the black points represent my weight).  Over the first two weeks of the diet, my weight hovered between 205 and 210.  Back in 1996, I had lost about 10 pounds in the same time interval (for comparison, blue curve from my 1996 data superimposed in the recent data.)

Internet searches revealed articles that claimed statins were responsible for all kinds of evils, from fog brain to fatigue to increased blood sugar to muscle pain.  I had experienced all these same symptoms to varying degrees.  However, these articles did not offer proof.  They were based on lots of anecdotal evidence.  It is not unreasonable for people to experience all these symptoms as they age, and since statins are prescribed to older people, one could easily confuse correlation with causation.

a. Is Ezetimibe/Simvastatin the Culprit?

I was taking Ezetimibe/Simvastatin for my cholesterol, and it did a good job of lowering it to an acceptable level.  Just as I was getting frustrated with my lack of success on my diet, I also read articles suggesting that while Ezetimibe/Simvastatin does indeed reduce cholesterol, some studies showed that this particular combination (ezetimibe is a cholesterol absorption inhibitor and simvastatin a statin that inhibits HMG-CoA) was no better in outcome than a simple statin.  And since statins alone did not lower my cholesterol, I wondered whether I was really being protected from heart disease.

b. Testing the hypothesis that Ezetimibe/Simvastatin interferes with weight loss

While I could not determine the efficacy of the Ezetimibe/Simvastatinin in protecting me from heart disease, I could test its effect on weight loss.  On day 19, I stopped taking my medication and the weight began to consistently drop.  I accept that this may have been a coincidence, but I noticed improvements in my overall well-being - again a subjective observation.

I regularly play floor hockey year round and ice hockey in the winter.  Since starting my Ezetimibe/Simvastatinin prescription, I felt a general degeneration of physical stamina.  After sprinting for 10 seconds, I was exhausted, and needed to rest for longer and longer periods of time between shifts. More depressing was the unpleasant exhaustion I experienced for at least 12 hours after playing.  The nature of my fatigue was not the good feeling after a workout.  It was a diseased feeling.  Hard to explain, but I attributed it to getting older.  Remember, correlation does not imply causation, so I had no reason to believe that Ezetimibe/Simvastatinin was to blame.

About two years after starting to take my medication, I had an unexpected hit of fog brain.  It was very distressing and it resulted in a lasting general fuzziness of my senses.  I was concerned enough to visit my doctor, who did various tests including an MRI of my head.  Nothing showed up.  Again, I attributed this to aging.

After I stopped taking Ezetimibe/Simvastatinin this year, my energy and stamina returned.  I can now sprint in multiple bursts in a shift without fatigue and I once again feel blissful fatigue after each game, which fades after just a couple hours.  The improvements are so extreme that I am certain that the effect is real. And its been this way consistently for five months.  It's harder to say whether or not the termination of medication has impacted my occasional bouts of fog brain. On this front, I would say the results are inconclusive.

c.  Effects of high fat diet on cholesterol

In my diet of 1996, my cholesterol drop lagged my weight loss by about 6 months.  In reading many books on the topic, and even mentioned in Atkins book from the early 70s, the first phase of an Atkins diets is associated with a cholesterol increase due to cholesterol entering the blood stream as fat is metabolized.  Once weight loss levels off, cholesterol drops.  This is indeed what I observed, with more than a factor of 2 drop in my risk factor.

To track my results this time around, I am monitoring my blood (glucose, ketones, triglycerides, HDL, LDL, etc.) on a weekly basis.  My experiment is complicated by the fact that I stopped taking medication during the diet and then only later started doing blood tests.  In the newer figure above, the horizontal dashed red line represents my risk factor (total cholesterol/HDL) when on medication and the red points show my measurements after getting off the meds.  There is a clear increase in risk factor over time, though with sawtooth features.  The horizontal solid red line is the danger level, and I am in very high territory, though not as high as during the initial phase of my 1996 diet.

Because I have changed both my diet and my medications, there is no clear way to deconvolute the two.  However, there is one striking feature;  my weight plateaued between about day 40 and 90, followed by a precipitous increase in the rate of weight loss.  In contrast, the 1996 data shows a steep and steady drop.    Could the plateau be due to my metabolism making an adjustment to me stopping the medication, and I am finally in the state of rapid fat loss, thus the increase in risk factor?  Did the medication change the equilibrium point of my metabolism to a more unfavorable level? Or am I just becoming old?

d. Cholesterol is not the whole story - the size of LDL particles

New research has shown that LDL comes in a distribution of sizes.  The tiny particles are the ones that lodge themselves in the arteries, while the big fluffy ones do no damage.  Sadly, there is no such test available in my area.  However, studies show that the triglyceride/HDL ratio is a proxy for the LDL particle size and levels below 2 are good.  The green squares show my data and the horizontal green line labels a ratio of 2.  In this regard, my numbers during my 2012 are good.

3. The Science

The issue of diet has been highly politicized and much of the research is not science.  I recommend that readers check out the books by Gary Taubs to understand how our society has become so averse to fat even in the face of contrary evidence. There have been many criticisms of his book that he selectively chooses data that supports his views and ignores the other data. To some extent this is true.  However, his explanations ring true based on my experiences.  The problem is that counter arguments also make sense, so how is the patient to decide the best course of action?
 
My intention is to study the scientific literature to develop an understanding of the ideal healthy lifestyle.  Sadly, this is a daunting task given the huge number of studies.  Also, given the complexity of the human body, variations between individuals, and the difficulty in doing clean studies, it is likely that no single strategy exists that applies to all individuals.  If this is the case, it is foolish to come up with a one-size fits all recommendation, yet that is how patients are treated.

a. How can we judge the truth of the matter?

 Here are the facts.

1. Double blind studies are the hallmark of research that involves people but are not are clearly not possible to implement in diet research.  My own study is not blind at all, and therefore not reliable as a test of any hypothesis, though it does confirm that increasing fat intake and decreasing carbohydrates has resulted in weight loss (1996 data and 2012 data), and based on the 1996 diet, cholesterol drops too.  So, high fat diets can do some good, but are there downsides?
2. Epidemiological Observational Studies (EOS) observe diets of large populations in search of correlations between diet and health (this can include whole countries or studies such as the huge one of doctors and nurses who periodically respond to questionnaires). These can be used to generate hypotheses but do not constitute proof of causation.  Other studies are needed to prove anything.  Unfortunately, such studies are often deemed to constitute proof.  EOS studies have good statistics but do not prove anything.
3. Controlled studies, in which individuals are fed strict diets under researcher supervision, or are taught to independently continue with the diet with frequent monitoring are the best comprise.  The degree of intervention required necessarily limits such studies to smaller groups of individuals and therefore have sparser statistics.
4. Studies on one individual, such as mine, give lots of data but suffer from bias and lack of statistics. This approach gives indicators that can be used by the individual to make medical decisions.  It is satisfying when an N=1 experiment correlates with larger studies.  Indeed, my weight loss dats from 1996 is much cleaner than the data in the literature analyzing the Atkins diet.

There are certain statements that can be definitively tested even in small studies.  For example, the statement that people can't loose weight on low carb diets is falsified by evidence to the contrary.  Controlled studies show that some people loose lots of weight on this diet.  Similarly, eating lots of fat does not guarantee that you will have high cholesterol.  We must also acknowledge that there are populations that eat high carbohydrate diets who are healthy, so it would be false to state that such diets always lead to poor health.  However, this observation does not prove that carbohydrates make you healthy.  The problem always comes down to generalizations.  I need to make a decision about me, and what happens in the case of the average population is of no help.

4 What should I do?

Here is the sequence of events:

A. Historically, when I went on low fat diets (including a vegetarian diet), I

1. never lost weight
2. was always hungry
3. suffered from idigestion
4. couldn't sleep
5. had chronic migraines
6. felt miserable

B. On a high fat diet,

1. I lost weight dramatically
2. My cholesterol risk factor dropped by more than a factor of 2
3. The diet was tasty, I ate as much as I wanted and was never hungry
4. Many of my other indicators of health got better
5. I felt great

 C. I slowly drifted off of the high fat diet due to

1. overseas travel were it was impossible to get enough fatty foods
2. pressure to conform when dining out
3. constant bombardment by the media and the medical establishment of the evils of fat
4. slowly losing faith in the wisdom of staying on a low fat diet given all the persistent voices to the contrary

D. After abandoning the diet

1. I tried to stay away from processed carbohydrates and eat less fatty meats
2. my weight drifted upwards
3. my cholesterol got high enough to require a prescription
4. I was prescribed Lipator(R) but it did not lower my cholesterol
5. Vytorin(R) 10/12 dramatically lowered my cholesterol
6. while on Vytorin(R) for 5 years

• I became extremely fatigued after exercise
• my blood pressure increased
• I developed fog brain
• my weight increased to almost its 1996 peak

E. After going back on the diet

1. My weight loss was stalled until I stopped taking Vytorin(R)
2. My weight is now dropping fast
3. My cholesterol levels started rising after going off the Vytorin(R)
4. My fatigue after exercise is gone
5. My doctor is urging me back onto statin

So, should I go back on statins?  I am seeing my doctor on the 12/17/12, and will then have a blood test.  I want to develop talking points with him to bring up the pertinent questions and I also want to have a decision tree ready before we talk so that I can make choices without emotion.

Here is what I am thinking:

1. I do not do well when eating carbs, so my only alternative is to eat lots of fat.  Since I need to continue eating fat, I need to better understand if it is having a negative affect on my health based of my higher cholesterol and C-reactive protein numbers during my recent diet. My CRP was up a few months ago, but still below the recommended value.
   
2. If statins decrease my cholesterol and my C responsive protein (two purported risk factors for heart disease - though a causal link is not definitively established), then I would gladly take statins if they cause no other ill effects.
3. Statins alone did not lower my cholesterol but the combination drug did.  However, it has been shown that the outcomes (i.e. disease or death) for the combination drug is no better than for statins alone.  So will a statin really help me if it does not decrease my cholesterol or CRP?
4. Given that the combination drug reduces my ability to exercise, and may have other side effects, I prefer to avoid them.
5. Given that statins have been shown to have positive outcomes, perhaps acting as anti-inflammatory agents, then maybe I should take them even if they do not lower cholesterol and then check my CRP and decide later if I should quit.
6. What if there are other systemic effects of statins?  Will they interfere with my insulin response and unravel my positive response to the high-fat diet?  Could this lead to an increased chance of diabetes? Given my data, the combination drug seemed to have had an adverse effect.  Are plain statins better?
7. Sometimes no action is better than action if the benefits are not well defined and the risks unknown. If statins will not help with my chances of decreasing heart disease risk, perhaps I should not take them given the potential risks.
8. Large scale drug tests do not take into account individual variability.  What in my medical history can be used to make a more informed decision?

 My plans for now are to go ahead with a blood test next week.  If my numbers are getting better, I'll probably hold out for another 3 months then plan another visit to my physician.  This is the simplest outcome given the fact that I expect a 6 month lag between starting the diet and stabilization of my cholesterol levels.  The complication is that the combination drug may have delayed this effect.  If  my lipid panel is the same or getting worse, should I stay the course to give my diet a chance, or should I take the statins and risk them making me worse off in the long run by interfering with my diet?

There are clearly no clear-cut answers. What do you think?

How do We Know a Black Hole Lives at the Milky Way's Center?

People often wonder how science can get a handle on out-of-this-world things like the properties of the universe many light years away or the small-scale structure of space-time itself.  In 2005, I presented the distinguished faculty address to give my audience a sense of how this is done.  The title of my talk was, "From Black Holes to the Internet:  How We Use The Scientific Method To Understand the Mysteries of Things Unseen."  It was a very enjoyable hour with lots of wonderful audience participation.  Here I summarize one part of my talk on "how we know" that there is a black hole in the center of our galaxy.

Science often proceeds by taking small steps that together build a general understanding. Here I outline how experiments on the earth along with observations of our universe can lead to an amazing understanding of the natural world.

The outline below shows how simple experiments on the earth's surface can be used to detect a massive black hole at the center of our galaxy, the Milky Way.

1.  Establish Newton's Theory of Gravity by measuring forces between hanging masses here on earth.
2. Use Newton's Theory of Gravity to determine the mass of the earth and check if it is consistent with what we know about the earth's composition and size.
3. Predict the orbital shape and period of the moon based on the earth's mass. It is found that the calculated period is consistent with the measured one and the shape of the orbit is accurately predicted (ellipse with the earth at the focus). This evidence suggests that gravity acts on lunar distances.
4. From the orbits of the planets, the mass of the sun is determined. Every planetary orbit gives the same solar mass (with the sun at the focus of every ellipse), so gravity appears to work even on these larger scales. Furthermore, the density of the sun that is determined from its mass is consistent with what we know of the sun's composition from independent spectroscopic measurements.
5. The orbital properties of all bodies in the solar system obey Newton's Theory of Gravity with impeccable precision. This includes comets, asteroids, moons, satellites, and space ships.
6. Mercury's orbit is found to deviate ever so slightly from Newton's predictions. This irks physicists until Einstein formulates the General Theory of Relativity in 1918 which fully accounts for the small deviation. It turns out that Newton's Theory of Gravity is a special case of General Relativity, which predicts the possibility of the existence of black holes.
7. Telescopes that view infrared light are able to penetrate the dust that obscures the center of the Milky Way to visible light to see stars at our galaxy's center.
8. Astronomers measure the orbits of these stars over more than a decade. As predicted by Newton, the orbits of the stars are perfect ellipses. The foci of these ellipses all coincide with an invisible object.
9. Using the orbital data, the calculated mass of the dark object is almost 4 million solar masses.
10. Some of the stars get very close to the dark object, so an upper limit of the object's size is determined from the distance of closest approach.
11. The dark object's mass and density fall in the range predicted by general relativity for a black hole.

The infrared observations of stellar orbits as described above do not prove the existence of a galactic black hole; but provide strong evidence. There are other independent measurements that all point to a black hole (see below). When the pieces of the puzzle are assembled, the picture that emerges is one of a huge black hole at the galactic center.

Incidentally, such massive black holes are found at the centers of other galaxies and even globular clusters. Since evidence of smaller black holes are routinely "observed" in binary star systems, it becomes clear that black holes are out there.

This journey illustrates something fundamental about nature, and about the breadth of physical laws. Richard Feynman said it best, "Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry."

A youtube video shows the motions of the stars around the central black hole that comes from direct telescopic observations.  The data covers over a decade of observations. A more dramatic version can be seen here.

Scientists are slow to accept a new idea or theory unless there are multiple pieces of supporting evidence.

The case for black holes is bolstered by X-ray observations of the hot gas surrounding the galactic black hole at the heart of our Milky Way. The observed X-ray spectrum can be used to determine the gas temperature using the same principles that betray the temperature of glowing orange embers in our fireplaces.

If the gas is to remain stationary, the inward gravitational tug of the black hole must be balanced by the outward pressure of the gas. The calculation is simple enough for a high school physics student, requiring only Newton's Universal Law of Gravity (see below) and the gas laws.

This simple calculation leads to a black hole mass of about 3.4 billion suns, in agreement with the observations of stellar orbits.

Newton's Universal Law of Gravity

Newton's universal law of gravity states that the force of attraction between two objects is proportional to the product of the two masses and inversely proportional to the square of the distance between their centers. The constant of proportionality is G.

G can be determined be measuring the forces between masses that are measured with a torsion balance. This is a common experiment done in most physics departments by students, and even in high schools.

 

---

Kepler's Laws (1571 - 1630) Kepler's laws follow from Newton's theory of gravity.   Kepler's Laws state that: Planets travel in elliptical orbits with the sun at one of the foci (shown above). Equal areas are swept in equal times (see diagram below). The time it takes to complete one orbit is proportional to d3/2 All objects in our solar system are observed to obey Kepler's Laws, and therefore confirm Newton's more general theory. Einstein's Theory of General Relativity is the most general theory that makes small corrections to the orbit of Mercury and is required to make the GPS system work. But don't believe the authorities. Anyone can observe the motion of Jupiter's moons to determine the mass of the gas giant. I took the photo below of Jupiter and three of its moons.

---

 Cutting Through the Dust

Raleigh found that the degree of scattering is proportional to the inverse of the fourth power of the wavelength of light. Blue light has a shorter wavelength than red light, so is more strongly scattered. Rayleigh scattering explains why the sky is blue.

Yellow fog lights work on the same principle. When white light is filtered to remove the blue light, what remains is green and red, which appears yellow. The longer wavelengths pass further through the fog and the scattered glare from the blue light is eliminated, making it easier to see.

The infrared range of the spectrum is made from light of even longer wavelengths, allowing telescopes to see through the muck. Special detectors are used to image the light. The image below is of the center of the Milky Way, taken by researchers at Max-Planck Intitut fur extraterrestrische Physik.

What I expect of my PhD students

Every graduate student needs to be aware of expectations.  Each adviser is unique and operates on different principles.  A small number view their students as a pair of hands to do the dirty work.  In the old days, some advisers expected their grad students to mow their lawn and do housework. A friend of mine from grad school had an old-school adviser who had him come to his place on the weekend for services.  However, most faculty members by that time had already moved into the modern era and this kind of despicable practice is no longer tolerated.

It is important that each student have an understanding of what they are getting into when they join a research group. Here I will explain what I expect.

My highest principle is thinking of a graduate student as a junior-colleague-to-be.  Even the best students start out incapable of doing real research.  They are clumsy in the lab and need lots of hard work to sharpen their analytical skills.  As such, my first criterion is that they be good students who like to learn.  That doesn't mean that they need to be straight-A students.  In fact, many A students make poor researchers because they lack creativity.

On the topic of classes, I believe that the more the better.  I encourage students who are in the middle of their research phase to take classes.  Ironically, the students themselves resist because they feel it interferes with research.  Even some of my colleagues prefer that their students not take courses that are not of direct help to the research at hand.  I strongly disagree with this premise. The process of learning new things sows new ideas.  I myself enjoy learning because these new nuggets of knowledge invariably get incorporated into my research, which leads to totally new and wonderful directions.

Principle 1.  Always keep learning from classes, reading the literature, and just thinking about crazy ideas.  If you feel yourself to be leaving your comfort zone, you are on the right track.  I expect my students to never stop learning and to be constantly pushing themselves.

An important part of being a PhD scientist is independence.  Grants, which support research activities, expect results.  Many advisers thus give their students a very short leash.  The end result is bad for the student's independence.  I prefer to give the student a specific assignment, and let her and him work on it for a year or so without giving them a detailed map of how to get there.  However, I do give lots of course corrections and teach them things they need to know along the way (or send them to the literature) if their struggles are based on missing information.

I once had a PhD student who complained that I seemed to be giving another student lots of attention while neglecting him.  I treat PhD and masters degrees differently.  The individual with a masters degree needs skills to survive in industry, while a PhD scientist is required to come up with new ideas and find ways to tackle a new problem.  Having said that, some of my best and independent students happened to be masters students who were quite capable of getting a PhD.

Principle 2. Learn to be self reliant early on in your research.  Read the literature and talk to others to gain the skills you need to do your work, but don't wait for someone to tell you what to do with those skills.  Constantly try new things in the lab or with paper and pencil to both sharpen your skills and generate new ideas.  You will make lots of mistakes along the way when not given step-by-step instructions, but making these mistakes and getting through them are the most important part of the experience.

I do not yell at my students, ever.  I may tell them when I am displeased with research performance, but if a student does not perform, (s)he will not get a degree.  Passing the Prelim and being in a research group is no guarantee of success.   I disagree with the idea espoused by the administration that we need to help the students along so that we increase our graduation rate.  Graduating a PhD without the proper skills and talents serves nobody.  A PhD degree is not a ticket to a good job.  It's the skills that the individual has mastered and the ability to think independently that makes him or her valuable to society.  A huge pool of unemployed physicists is not what we want to be generating.

It takes lots of hard work and perseverance to finish a PhD degree.  People often ask me how many hours they should work.  My answer is all the time.  If you are not excited by your work and don't enjoy thinking about physics beyond your area of expertise, then you're in the wrong field.  Academic jobs are tough to get, and real research jobs in industry are rare.  However, PhD physicists have lots of success in engineering jobs, which are more plentiful.  If you like to tinker, then engineering may be an excellent way to earn a good living while having fun.

A PhD degree should not only be a guarantee of skills, but of work effort and perseverance.

Principle 3.  Approach your research with a passion.  The benefit of enjoying your work, aside form the direct rush of endorphins, is that you will put in the time required to do a good job.

One of the most important attributes is perseverance.  Watching Star Trek, or other sci-fi shows/movies gives one the impression that scientists apply skills to very easily solve problems.  This is not the case unless a student is super lucky.  I have a long list of stories on the same theme;  students who would spend months trying to get an experiment to run, only to have to start from scratch to try a different approach.  Aside from being good problem solvers, the PhD degree is an imprimatur of a person that does not give up.

In my PhD work, I had spent quite some time building an experiment on a 5' x 10' table optical table, which was filled with all sorts of laser sources and optics, resembling a Borg city.  Each step in the process often required a step backwards.  After completing the construction of the experiment, it still didn't work.  I then figured out the reason, tore the experiment apart and rebuilt the whole thing on another optical table with another laser.  Luckily, it ended up working.  Only then could I start taking the data that was the topic of my thesis.

Principle 4. Don't give up.  When something doesn't work, don't shy away from the problem.  Work twice as hard.  This will serve you well in all aspects of your lives.  When I was a new faculty member, aware of the importance of getting grants, I would write two new proposals for every one that did not get funded.  After my first two years, I built a healthy portfolio of projects.

Many people do not recognize the creativity behind science.  Creativity is part of choosing a scientific problem to study, helps in problem solving, and leads to interesting new science.

Principle 5.  Be creative.  Always think about neat implications of what you are doing or find new ways of looking at old problems.  This skill is particularity important in the career of young scientists who want to make it to the next level.

Principle 6.  Be meticulously careful in your work. Do not publish sloppy results, which will come back to haunt you, and always apply the highest standards to yourself.  You should be more critical of your own work than I am of you as your  adviser.  On the flip side, do not let this attitude prevent you from finishing a project.  In the end, we can never be sure if we are right, and there will always be a mistake somewhere.  If a paper is perfect, it is not science.  When working in the unknown, there are always huge dark shadows in the areas not exposed by your searchlight.

Principle 7.  Be honest with others, but especially with yourself.  Many very good scientists have fallen into the trap of fooling themselves into believing in something that is false.  Consider cold fusion, N-rays. etc.  Design experiments that are resistant to experimenter bias.  Also, do not try to make data fit your adviser's expectations.  I need to know when an experiment contradicts my viewpoint.  And it goes without saying that you should never fudge data in any way or plagiarize the work of others.

Principle 8. Impress me.  When you graduate, I need to make an honest assessment of your strengths and weaknesses in the letter of recommendation, which will determine your success on the job market.  Follow all of the above principles.  Do not come to my office to ask what you should do next.  Tell me the issues you are having, your line of reasoning, possible explanations, and engage me in debate about the possibilities.  You should act as a junior colleague.  Don't worry about offending me.  I am more interested in getting at the truth than being right.  However, that does not give you the right to be caustic.

What I have posted above mentions nothing of the content of the work, which is of central importance.  A short post cannot cover the nuances.  To zeroth-order approximation, I expect the student to add a new piece of physics to the body of knowledge.  This could be a theory that helps us understand a phenomenon or the discovery of a new phenomena.  Fitting data to a mathematical expression is not enough.  The parameters of the theory must have meaning that is independently testable, be interpretable in terms of fundamental processes, and make predictions well beyond the domain of the original results that generated the theory.  Perhaps I will write more on the topic later.

If you approach everything in life with a passion, it will be a fulfilling one.   When you take a break from physics, make it count.  While I may seem one-dimensional in this post, I do find time for other activities.  Though I am not good at it, I play ice hockey with a passion.  I enjoy playing the piano and writing.  Taking a break from work is, in a sense, work.  During times of alternate activities, things percolate in the brain.  I have had the most profound revelations while driving my car in the middle of nowhere or playing the piano.  So, don't hesitate to take a break with intense activities.

I have to run now.  After I finish packing, I will take a short walk around San Diego, then I have to catch a plane back to Pullman.  Until then, get excited about physics.

Perhaps this time it may be right - taking a big chance

I wrote a while back how Shiva's measurements gave 0.29eV as the binding energies in our polymer/dye material (with an experimental uncertainty of 0.02 eV) which is responsible for forming domains that are at the heart of our theory of self-hearing .  I tried to figure out what interactions between molecules and polymer would give this energy and came up with a possibility.  But because I read the data tables incorrectly, I wrongly thought I had solved the problem.

When preparing my talk for SPIE a couple days ago, I drew the PMMA polymer chain with a molecule drawing program and added a few DO11 tautomer molecules to see where they would fit.  Miraculously, as a plopped the DO11 molecules on the page, I immediately saw that the NH from the DO11 tautomer cozies up to one oxygen in the PMMA polymer chain while the OH group naturally attaches itself to another oxygen in the chain, as shown above.  And he energy?  You got it; the sum of the two hydrogen bound energies is 0.30eV, a match.  The table below shows the energies of four types of hydrogen bonds.




There are always other possibilities that we have not yet considered, but this smells right.  Perhaps we are onto something.  Future experimentalists will allow us to test this hypothesis and zero in on what is going on when a molecule self heals.

This project has been one huge puzzle, were each new experiment presents to us a new piece.  It reminds me of how the discovers of the structure of DNA (Crick, Watson, and Wilson  ) pieced together cardboard cutouts of molecules to guess its molecular structure, and confirmed their results using x-ray scattering data from  Rosalind Franklin.  Incidentally, the story behind Franklin's contributions to the discovery of DNA and not being recognized  at the time makes for interesting reading.  I also recommend readers to check out Schrodinger's guess as the structure of DNA using simple physics principles.  The title of his very thin but fascinating book is

"What Is Life?: with 'Mind and Matter' and 'Autobiographical Sketches'"

I can imagine the thrill of discovery experienced by Crick, Wason, Wilson, and Farklin.  From little cardboard pieces and an "X" on a piece of film from an x-ray scattering experiment (shown above), they revolutionized our understanding of the workings of DNA.  Ironically, the forces that hold together the double helix reside in the hydrogen bond, the very forces that seem to be at work in our molecule/polymer system.

I am preparing my talks this morning, and plan to go on a limb proposing stating that the interaction between a DO11 molecule and a polymer chain  through hydrogen bonding underpins the phenomena of self healing.  I am not a chemist and have a naive view of the intricacies of how molecules interact.  But, I hope that my bold proposal will result in good feedback form my audience that will help us fine tune our models of the mechanisms of self healing.

I have been very excited in recent months by all of the discoveries that we are making.   Even if they end up being wrong, the process of the search for the truth is exhilarating.  Gotta run.  Too much to do.  And again, sorry for the typos!

Even teeny weeny discoveries are great fun

This morning, in the process of editing a paper, I made a small discovery. We have developed a new mathematical framework for determining the properties of quantum graphs in terms of the properties of the pieces. This work provides simple identities on the pieces that will allow us to determine general principles form the ground up rather than having to calculate the properties of the full graph.

I have to run because my wife is calling me to lunch.

Here is my email to my collaborators.

Your introduction to edge states was perfect. I liked the physical approach that leads to the formalism. In fact, its clarity was instrumental in allowing me to make a minor discovery (see below).

With regards to the paper, EDGE STATES ARE WONDERFUL! I am taking a break for lunch now, but FYI, I have been working soley on the appendix because I have done what I think is a really neat calculation which uses the power of the edge state. If you recall, in the past, we used the fact that the sum over all of the edges yields the full sum rule. However, it turns out that there are sum rules on each edge! The edge state formalism has allowed me to do this very easily. The result is given by Equation A20 of the geometry. I have pretty much dropped everything to work on this, but I will need to get back to preparing my talks for SPIE since I still have lots to do.

I suggest the following. I still need to reread the appendix because I was making changes while calculating -- never a good thing in terms of introducing typos. I will work on this after lunch. In the meantime, please check the appendix and let me know if I made any errors. The result is so logical that it seams right. I will then alternate between working on my talks and working on the paper.

Most likely, I will not go in to work today so that I can finish the paper in time to be posted on the archives tonight. Even these small discoveries are great fun.

A correspondence with a colleague on our nonlinear topology/geometry project

We are not resting on our laurels, but rather are continuing to work on new ideas and extending our work to more general cases.  In the process, we call get confused about the physics of the system, and try to find ways to picture what is going on that gives insights into how a system may behave under various conditions.

In working on this project, I realize that I spend lots of time writing emails to colleagues and students about various aspects of the work.  An email may come in at 10:30 at night because my collaborator is hot to figure something out and wants insights.  I too write emails at weird hours asking students for more details on something they observed in an effort to test my newest crazy ideas.  This is not a line of work for those who want to sleep soundly.  Being excited about physics is the best stimulant.

Anyway, today I took a two-hour break to play floor hockey and found a series of emails from a collaborator who is very excited (as am I) on the new direction of our work and the new physics that is implied.   Since we are moving into new territories, many things are not well mapped out, so we have to navigate partially by instinct.  I occasionally like to post excerpts from emails to give readers a sense of the kinds of exchanges that we have in the process of working on a project.  Here is my response to an exchange about a new quantum graph that we are working on, as shown above.

An excerpt from my email response (edited for typos and names removed):

First, I think there is a big difference in taking the limit as the prong length goes to zero and actually having a zero prong length.  In the former, I think that you get a broken vertex, because as the wire gets shorter, the end of the wire is getting closer to the vertex, so indeed the wavefunction on the prong must get vanishing small as the prong length goes to zero.  Then, this will look identically to a break in the loop.  Of course, when there is no prong, you get the traveling wave solutions.  So it is interesting that the limiting case yields a very different result than the case without the prong - again a statement about topology.  As long as the prong is there, no matter how short, the topology is of a loop-star.  Get rid of a prong, and then it is just a loop!


I am a little confused about what you are saying with regards to the ground state energy.  So, let me just make a point that may not be related at all to what you are saying.  If I have a prong with zero wavefunction, the loop cannot have a constant wavefunction, i.e. the wavefunction with n=0.  By continuity, the amplitude of the constant wavefunction will be zero, so there is no particle in the system.  So, I believe that in a loop, you have the zero-energy wavefunction but as long as a prong is there, you will not have a zero-energy wave function.


However, you bring up an interesting possibility of a wavefunction in which there is zero wavefunction in the prong and a standing wave in the loop in which there is a node at the prong.  This seems to be alright in terms of the continuity of the wavefunctions, and probability current is certainly conserved.  So unless there is another constraint that I am not seeing, this looks reasonable.


The problem is that this may be a legitimate wavefunction, but not an energy eigenfunction and is therefore not a stationary state.  Forcing this kind of state would be like having a particle in a box wave function, let's say with multiple nodes.  Having the wavefunction oscillate to he left of the node, then zeroing it to the right of the node obeys all the boundary conditions, but, this is not an energy eigenstate.


So, I think I will stick with my original assessment, though now I have thought about this for an additional 10 minutes for a total of 15.  I am not confident in my view because I have not done anything with paper and pencil, just picturing things in my head - a very dangerous activity!


These kinds of discussions do not come out of the graduate students until the point that they are getting ready to graduate.  Only then does a light bulb turn on, which makes them get it.  Once they become very useful and great fun in terms of being intellectually stimulating, they leave for greener pastures.  Then they can start to challenge and stimulate their new advisers.

Not all triangles are the same

Just the other day I wrote about a revelation I had about the self healing process, a hot topic in our lab these days. As often happens, the first impression is simplistic and not quite right, but eventually, we hopefully converge on the truth. However, my fallacy of yesterday gave me insights today, which I continue to pursue.

On another front, we have completed a new paper that we are submitting to Physical Review Letters, the highest impact physics journal. I always have reservations about sending a manuscript to a journal just because it is prestigious. What counts is the quality of the paper. On the other hand, if our work is as significant as we believe, then appearing in a top journal will give it more visibility.

I am excited by the science, and the possibility that we may have started a new branch of study. At the heart of our work are calculations of the optical nonlinearity of quantum wires. This in itself is totally new (to the best of our knowledge), but we are taking the elevator down a level to the realm of fundamental science. For those more practically minded, our work may also have some useful applications.

Science is often focused on a particular thing. While a researcher may be interested in solving the problem of global warming -- a grand problem, the actual work may involve studying the behavior of a particular kind of electrode dipped in a specific chemical. In fact, many groups around the world may be studying exactly the same thing, trying to work out a detail that could make a battery store 5% more energy. Such a leap would indeed be important.

Rather than focusing on details, our work is painting a big picture. I like ideas that have broad influence; views of the world from unique perspectives; and unexpected results on topics that have not crossed anyone's mind, but that resonate with all scientists as being really neat.

Our new work falls beyond the typical boundaries of what others are doing. We are interested in the abstract concept of how the shape (geometry) and topology of an object determine its optical properties. These ideas go beyond specific molecules or materials. To allow us to focus on the basics, we need to remove other complications. To that end, we study what is often called a toy model -- one that brings out the qualities of interest and suppresses the rest. In our case, we are considering structures made of connected wire segments that carry a sole electron.

Consider a continuous loop of wire in the shape of a triangle. If we deform this triangle into other triangles with differing edge lengths and angles, we find that the nonlinearity changes smoothly and not a hell of a lot. In fact, deform the triangle into a quadrangle and then into a quintangle, and nothing much new happens. Any closed loop, independent of the shape, is of the same topology. Thus, we might conclude that the geometry has little effect on the nonlinear response.

A bent wire that does not form a loop is of a different topology. So, consider the simple experiment of a triangle whose nonlinear-optical response is being measured. Now cut a vertex of the triangle so that two of the edges no longer touch. This is still a triangle but its topology has changed. Interestingly, the nonlinear response is found to be profoundly different with the snip of the wire cutters. Thus a change in topology for fixed geometry leads to a dramatic change of the nonlinear-optical response.

This work has applications in the design of better materials because it suggests that taking a molecule (modeled as a wire) and lopping off just a single bond could yield a dramatic improvement. Or, our work could inform nano-technologists on how to make better quantum wires.

We have only evaluated a small number of shapes, including loops made into triangles, quadrangles, quintangles, bent wires, split triangles, and star graphs. Star graphs, which are lines radiating from a central point, represent a topology that yields the larges hyperpolarizability.

To sample the space of all possible shapes, we let the computer randomly pick triangles, quadrangles, quitangles, star graphs, and whatever other shape we can squeeze in. Then we can see what is possible. With enough random tries -- we usually run our simulations over tens of thousands of configurations -- we can test the influence of any parameter, such as topology.

Below is a plot of the first (left) and second (right) hyperpolarizability, which tells us how strongly two and three photons interact with a molecule. Included are triangles (red), simple quadrilaterals (with no crossing edges - green), and all quadrilaterals (blue). Each point (and there are 10,000 here of each color), represents one configuration. A casual glance at the pattern reveals that geometrical effects do not make a big difference. To see the effects of topology, you'll have to read our paper on The Physics Archives.



I find this work really neat (and I hope the reviewers will agree) because we are sampling a very fundamental property of a molecule in terms of some very simple mathematical concepts that go back hundreds to thousands of years. The ancient Greeks heard the music of the spheres in planetary motion using a the metaphorical geometric ear. In our work, we can literally see the effects with light on our eyes when the system's structure changes so ever subtly. And, we get to enjoy a vision of the underlying process with the minds eye as portrayed in very pretty and colorful plots.

A pendent necklace and a new insight about self-healing molecules

In a recent post on our research on self healing, I discussed our new theory, which is posted in the Physics Archives (see it here). The paper has been accepted for publication in the Journal of Chemical Physics and will appear soon.

We used lots of data as input to construct the model, which took years to complete. Data that seemed to support one model initially would later be contradicted by additional data. Over time, the model evolved into a coherent picture as more hypotheses were eliminated by experiments. Finally, we had a model that fit the data AND had as its cornerstone the formation of domains of molecules that together, would help a damaged molecule heal.

There is no direct evidence for domain formation, though the behavior of all the experiments to date are consistent with this model, and only this model. Remove the domains and the predicitve power of the theory is lost. The burning question pertains to the nature of the domains. What are they? Are they clumps of molecules or molecules that are somehow stuck to the same polymer chain? What is the nature of the force that keeps the domains together, and how is it that a domain of healthy molecules acts to promote healing in a damaged one?

We may be closer to an answer.

The lab is in a wonderful buzz of activity with lots of new measurements -- always an exciting time. There are bold new hypotheses based on initial data that generalize our model, followed by letdowns after new data or a more detailed calculation proves us wrong. The process is highly stimulating. I can just smell it; something new and wonderful is brewing.

In the midst of all this activity, I found myself sitting at my computer writing my conference paper for SPIE, where I will give a couple of papers in August. I completed writing the introduction and then explained our new model. What next? I needed something new that did not detract from the presentations of my students. So, I drew the molecular structures of the polymer and the molecules, and started to play with them, rotating this one this way and that one here, etc.

In less than a few minutes, I realized again that a molecule could stick to a polymer through what is called hydrogen bond -- an attractive force between a hydrogen molecule and in this case, an oxygen, very much like the forces found between water molecules. This thought had crossed my mind in the past, and is indeed a motivation for a subset of projects. However, having all this jumbled data running around my head made me realize that Shiva, my coauthor on the theory paper, had already determined the three parameters of our model, one of which is the force that binds the molecule to a domain. If the molecules are sticking to the polymer chain through a hydrogen bond, the hydrogen bond energy should have the same value as the corresponding parameter in the model.

This is an excellent example of a model that we built to explain the data is now guiding us in figuring out what is going on.

I got on the internet and searched for hydrogen boding and found a table of numbers. The energy between a hydrogen and oxygen was one of the first values listed, at 0.3 eV. Then I nervously clicked through the directory tree on my computer to find its measured value. As I scrolled to the table with the results, my eyes focused on the value of the lambda parameter -- 0.29 eV with an uncertainty of 0.01. The two matched!

It is not often that things work out this easily, so I considered the next question, and that was how self-healing is mediated by molecules attached to a chain. A polymer with molecules connected by hydrogen bonding looks a lot like a necklace (polymer) with pendents (molecules) thrown on the night dresser as shown in the figure below.The hypothesis that I proposed is as follows. (a) When a molecule absorbs a photon, (b) it breaks into two fragments that are charged. There is evidence from earlier work that charged species are involved. One of the fragments is fixed in place by the polymer and (c-e) the other hops from molecule to molecule along the chain (f) until it finds its mate and recombines.

An alternative explanation is that the attached fragment attracts a small fragment from a neighboring molecule. The neighboring molecule then attracts a fragment from its neighbor, and so on, which propogates down chain like a wave of fans at a stadium until the original damaged piece combines with an adjacent fragment. The more molecules in the domain (i.e number of molecules attached to a polymer chain), the bigger the chance that there is a contiguous path for the fragment to find a mate.

This is indeed an exciting time. In addition to this work, there are other very exciting developments that I will post in the near future. Breakthroughs can be addictive. I can't wait for the next one!

An excuse for UPS late delivery - Derailment

I just realized that a package I had expected to arrive a few days ago had not yet arrived, so I clicked on my UPS tracking number, and here is a screen shot of what I found. The train with my package got derailed. I never saw this excuse before!

Zeroing in on the cause of self healing

As I have mentioned in the past, one of our biggest projects seeks to develop an understanding of the mysterious self healing process following damage to a molecule by a zap of light. Recently, a former graduate and I developed a model of the healing process that hinges on the formation of domains of molecules. Members of these domains are highly cooperative: they accelerate the healing of a damaged molecule in proportion to the size of the group and they prevent their comrades from being damaged. This behavior is as strange from the sociological perspective as it is from the underlying physics. Why do the molecules aggregate and how does their community enhance healing and prevent physical damage?

We have gone out on a limb and made what I believe is a bold assertion; that there are forces between the molecules that cause them to aggregate, and that these same forces are responsible for healing. Such an assertion would be just a wild guess if it were not for lots of data that we find to be consistent with our model. With only three parameters, our data fits the model as a function of temperature, concentration, time, and intensity. The model also makes predictions beyond our present experimental capabilities, so it will gain acceptance only if it holds up to future scrutiny.

When submitting something this interesting (at least to us) that may go past the present paradigms (Shiva got some lifted eyebrows and jaw dropping during an interview talk, which turned to nods of approval after he presented supporting evidence), one always worries that the work will not be understood. There are many examples of Nobel-prizewinning work being rejected by a journal. In our case, the first journal did not even send the paper out to review, claiming that our work was not appropriate. How can a physics paper not be appropriate to a physics journal?

Of course, I have no illusions that this is a Nobel-prizewinning paper, but if the underlying mechanism is found to be new, it could very well end up being a significant achievement for whoever makes this discovery.

Rather than fight the editor, back in mid May, we sent the paper to a second journal of equal quality. Then we waited. I was still concerned that the reviewers may not see the importance of the work. But alas, they accepted it on the first pass, suggesting only minor revisions. And it was also incredibly fast given the nature of our paper. The first reviewer summarizes the paper as follows,

"This interesting manuscript continues the authors' work aimed at discovering the mechanism behind the observation of self-healing of photoluminescence in chromophore doped polymers. The authors have proposed a phenomenological model for their observations that is able to predict aspects of the time, temperature, concentration and intensity dependence. The model focuses on the formation of dye domains in the polymer and studies the dynamics of these..."

Then (s)he goes on,

"While these are interesting results, the manuscript could be more satisfying if the authors did more to understand the physical mechanisms behind the model. Some well-considered speculation on the materials physics in the conclusions would suffice. "

We tried to hold back on speculation, but this review gives us an opportunity to present what we think is happening. Incidentally, the reviewer is right that we need to work more on the mechanisms, which is exactly what we are doing now. We are already getting data that is pointing at the mechanism, but its still too premature to mention.

The second reviewer made no suggestions for revisions and believes that the paper is in good shape in its present form. (S)he writes,

"In this paper authors present a model on photodegradation/self-healing kinetics of dye molecules doped in a polymer matrix. This investigation is an extension of their previous work. Using phenomenological arguments the authors generalize their model. They allow (implicitly) for association of dye molecules which form correlated domains interacting with the polymer matrix. A healing rate is assumed to be proportional to the number of undamaged molecules in a correlated region and a decay rate is proportional to the intensity normalized to the correlation volume. The model proposed by the authors predicts decay and recovery of the population of doped molecules. The results of the theory are successfully tested with experimental data.

"The paper is generally well written and contains several interesting results. I recommend it to be published as it stands..."

The next step will be to determine the physical significance of these parameters. I am excited by the prospects that we may be looking at some very new physics because this process is like no other that I have ever seen. As I sit at my computer bogged down with lots of administrative tasks, new physics is in the air. I hope to be able to get back with pencil and paper to work on the next set of ideas. But first I need to work on some proposals so that we have the resources to do lots of wonderful work in the future. And as penance for writing proposals, I also have some that I need to review. Similarly, I have a pileup of papers to review.

Hopefully in my next post I will report on even more interesting physics. On another project, something very exciting is brewing. Again, new physics! Until then, ...

The good old days

I had lunch yesterday with a hockey buddy who plays on our Old Geezers team. The discussions, of course, started with hockey, but then went all over the map and eventually ended on our mutual interest in astronomy. This reminded me of the days that I used to enjoy spending under the stars.

As I get older, I find it more difficult to make time for things that I enjoy because work takes up more of my life. Recently, I accepted two editorial posts, which together do not take a whole lot of time, but when combined with my other responsibilities, consumes day and night. I keep on kicking myself for constantly making choices that bring me angst, but I always feel compelled to provide service in my area of expertise.

During our lunch conversation, I recalled one particular night on which I observed a spectacular meteor. Early that evening, long ago, I viewed familiar objects with my new 10" Dobsonian such as the Pleiades and the Andromeda galaxy. Then I focused on M31, M32, and M110. The night was warm and dark, and as midnight approached, the skies got darker as the lights went out one by one all around my neighborhood.

My log book (my memory is too unreliable these days), dated September 26, 2003, reads "Later that night (about midnight) I went up on the upper deck to take in the wonderful sky. I was looking at the Milky Way with its clean dust lane down the center when a meteor shot right along its length through the middle of the dust lane. It started somewhere above 45 degrees from the horizon, maybe near Perseus, and beyond the zenith before it broke up into pieces. It looked like fireworks with maybe 4 obvious fragments. This was one of the brightest meteors I have seen. This wonderful evening made me realize that I want to spend more time under the stars."

Almost 10 years later, I still recall the deep satisfaction of seeing nature at work, the meteor silently streaking across the sky along a smooth arc until it broke up.

In my next entry, dated December 17, 2003, I wrote, "I read my last entry and am ashamed at how long it's been since I went out observing! Though, I did get some nice pictures of Saturn a few nights back (and also the moon)." (See an older post at http://unknownphysicist.blogspot.com/2010/12/nostalgia.html)

Sadly, my last entry in my log book was on 5/8/04, the day after I bought a large 12.5" Dobsonian (I had sold my 10" scope to raise some cash). It ends with "When looking for M81/M82, I found a very dim and broad patch at 50x. At 212x, I could not see it. It was in the vicinity of Caddington Nebula, and it fits the description, so I believe I was looking at IC2574."

Life got too busy to do much observing. I have occasionally (perhaps 5 times in total since 2003) taken out a telescope to show a friend the wonders of the night sky. Though I really enjoy my research, I think I spend much too much time on related service activities to the university and my profession. I continually break promises to myself to take out my telescopes in order to meet my work commitments.

(To the right is a photo I took with my digital camera and telescope back in 2002 of M13, the Great Globular Cluster in Hercules.  This is a spectacular cluster to view in the eyepiece of a telescope, appearing as a scattering of diamonds on black velvet.)

So, next time you visit me, if the skys are clear, ask me to show you the wonders of the heavens. I would appreciate the kick in the butt to take out my telescope. Perhaps such a reboot will get me into the habit of occasionally enjoying some quiet time under the stars.

Clear Skies!

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.