There has been quite a bit of debate about the “dire” predictions that COVID-19 models have made and are making for infections and, especially, deaths, and how those predictions are being used to scare people.  I can say with a great deal of certainty that scientists making these models and doing the simulations are not intentionally trying to scare anyone.  (The only “scientists” I am skeptical of are the ones trying to sell books or market themselves for something.  The “Plandemic” woman is in this category.  She’s been peddling false hope to people with chronic illnesses for a long time.)  On the other hand, in the hands of the media and politicians the predictions can be used in many different ways.  I think many of the early models used a few different scenarios:  we do nothing, we socially distance and/or shutdown, we discover a vaccine, etc.  If you want to scare people, the predictions from the models in which we do nothing can certainly be used, and I believe that if we had done nothing we would be in a very serious situation.

I’ve spent most of the last 30 years developing and analyzing models, mostly trying to predict how physical systems will respond.  Physical system models are not hard to develop if you understand the physical laws that govern them (and the mathematics needed to study them).  There have been very few advances in modeling physical systems at scales visible to humans in nearly a century.  That is why physicists rightly say that most of what engineers do is classical physics.  One nice thing about physical systems is they are not alive to change their behaviors to something not included in the model.  (Note, “smart” materials on which I did a lot of research are not actually smart. [1])  Another nice thing is you can do controlled experiments to validate your model.  Finally, you have a lifetime of experience and intuition to use to see if the results make physical sense.  However, I think the best results are the ones that do not initially make intuitive sense and require you to adjust your intuition.  See footnote [2] for a great example of this and footnote [3] for my experience trying to get engineering students to use their intuition and common sense.

The basic model for disease spread is what’s called the SIR (susceptible/infected/recovered) model; there are many variations and extensions of this.  There are also many good explanations of this model online so I won’t go into details about it here.  I would recommend watching the YouTube video I’ve embedded at the end.  One thing to know about these models is that they are statistical and have many parameters that people can “tweak” and many “features” that can be added.  Being statistical, they will only give you an “average” sense of what might happen.  Likewise, you can adjust the parameters to get almost any prediction.  This is where so-called fitting comes in.  Scientists will tweak the parameters until they fit known cases and hope those parameters will predict what will happen in the future.  When scientists share these models they usually provide the parameters they’ve used and what “ingredients” have been included.  Although some people want to keep their models proprietary, and I would be skeptical of them.  The problem here is that by the time the predictions hit the media and politicians all those details have been stripped away to make it more digestible for the general public.

Statistical models have been used in physics for over a century, and from basically the time we realized matter was made of atoms but we could still measure properties of matter without having to keep track of every atom.  For example, the temperature of something basically measures on average the energy contained in the atoms/molecules comprising the material.  We don’t need to track every atom to get this average.  Likewise, the pressure from the air you feel is the forces of all the molecules in the air hitting you.  If the wind hits you from one side you notice a net force acting to push you in the direction the wind is blowing.  This is simply because more molecules are hitting you on one side than the other creating a net force that wants to move you.  Again, we do not need to keep track of every molecule/atom to determine what this force is.

Statistical models in physics (a subject called statistical mechanics) work extremely well and are used extensively.  Like SIR models statistical mechanics models can be more or less complicated by adding or removing ingredients.  For example, the “ideal gas law” that relates pressure, temperature, and volume was known long before we understood anything about atoms, and we now know that it can be completely derived by averaging the motion of atoms and molecules modeled as balls bouncing around.  However, there are cases when the ideal gas law doesn’t work well.  For example if the gas is made from molecules you can include the rotation of the molecule as an ingredient.  It turns out that under “normal” conditions this ingredient isn’t needed, but under extreme conditions it helps explain why the ideal gas law fails.  The other time statistical models don’t work well is when you don’t have enough particles (i.e. atoms or molecules) to average over.  If you only have, say, one thousand atoms bouncing around in a box, statistical averaging starts to not work so well.  Fortunately, with modern computing power, we can model billions of atoms moving around using molecular dynamic simulations.

One reason statistical models and molecular dynamic simulation work so well is that atoms do not have free will, i.e. under the same situation they will all act the same.  People on the other hand are very different.  It’s this behavior and the feedback causing that behavior that makes modeling populations so hard.  If you have millions of people you can try to estimate how the average person will behave and include that in a statistical model.  Most of the variations of the SIR are doing just that, but modeling behavior even on average is very difficult.  While we could theoretically model every person in the United States acting in an average way, we know this would provide the same results as the statistical model.  We could include some randomness in the every-person model, but again with enough people you’re still going to get the average result.  What an every-person model may help predict is how a very non-uniform population density plays a role.  However, SIR models can be adjusted for this too.

To help explain the SIR model, the creator of the two videos below basically does molecular dynamics simulations with people replacing the atoms and behaving in different random ways.  Note the Twitter screenshot he includes around the 2:14 mark with someone responding to him, “Im not a gas in a box :'(”  Because he is only using around one thousand people walking basically randomly he makes many runs and averages the results.  To try to model the variation in people’s behavior he uses various percentages and looks at how these percentages change the results.  For example, he varies the percentage of people infected that get quarantined or the percentage of people traveling from one community to another.

When you’re modeling things with algorithms instead of equations you can play around with all kinds of probable behaviors and actions.  Things can get extremely complicated and often you have no idea what the result might be.  There is actually a scientific/mathematical buzzword for this called “emergent behavior.”  According to Wikipedia, “emergence occurs when an entity is observed to have properties its parts do not have on their own.”  You can think of your body as the emergence of all the individual cells doing their own thing.  Scientists and mathematicians are enamored with emergent behavior because you often see very interesting and realistic behaviors emerge from very simple models of how the parts interact.

While I am certainly biased, I believe the scientific community is doing a great job simply trying to keep people informed.  Unfortunately, their messages can get distorted and used politically.  Plus, scientists usually avoid words like “never” and “always” so when someone asks them if it’s possible 10 million people will die, they’ll simply answer, “Yes.  It’s possible.”



[1]  Playing with a dielectric elastomer “smart” material water balloon in the lab of my former student Nakhiah Goulbourne at the University of Michigan during the summer of 2010.  What makes this material “smart” is a crazy-stupid 5,000V being applied across the membrane, although there is very little current so not much power.


Wrinkled mylar balloon.

[2] A great example of needing to adjust your intuition based on strange results from a model is a model/simulation I worked on with Elaine Serina when we were graduate students.  Elaine wanted to understand how forces on your fingertip get transferred to tension in the skin and stresses on the bone as part of a larger study on carpal tunnel syndrome.  As a simple first step, we decided to model the fingertip as an ellipsoid (think of a plain M&M) inflated by water and then compressed between two plates.  We wanted the initial inflation because there is usually tension in your skin (unless you’ve been soaking in water and are all “pruney”).  However, when Elaine took the equations I derived and wrote code to solve them she kept getting strange results that we were both convinced couldn’t be correct.  The simulations were showing that when you inflated the skin membrane you would get compressive stresses.  Our intuition said, “You can’t inflate something and get compression.”  We spent at least a month trying to figure out what was wrong with the model and/or the code to no avail.  After a meeting with our thesis adviser in which he concurred with our intuition that something must be wrong, we were walking back to our lab through the student union and noticed the inflated mylar balloons.  One of us (likely me because I was the one studying wrinkling caused by membrane compression) realized that all the mylar balloons were wrinkled around the edges, just where our model was predicting compressive stresses.  The only way you get wrinkles is when you have compressive stresses.  Thus, we realized our intuition was wrong!  As you inflate a mylar balloon the edges want to pull in towards the center.  This creates the compression.  If you have a rubber balloon of this shape, adding more pressure will eventually cause the wrinkles to disappear.  However, because mylar is so stiff you can’t pressurize it enough to remove the wrinkles without it rupturing.

[3] I was always a bit disheartened with how many mechanical engineering students did not seem to have this intuition when they got to the junior-level class I regularly taught.  To address this, part of every homework problem was a statement about why they felt their answer was correct or incorrect.  Early in the semester I would get answers like, “Because I followed all the steps and checked the math.”  I was constantly shocked at how many mechanical engineering students did not come into the class with the skill of looking at the result they got and evaluating if it made physical sense.  Every semester I talked a lot about “sanity checks.”  Plus, I wanted to know if they suspected their answer was not correct, as it’s much better in the real world to know a result is likely not correct than to think it is.

I have asked many colleagues why it matters to them to be promoted to ‘full’ professor (from associate professor) because, at this point in my life, it just does not matter that much to me.  The vast majority of full professors I have talked to really could not give me a concrete reason for what motivated them but said that I should be striving for this promotion.  A few suggested that I not worry about being promoted and do what I enjoy.  The main reasons I have been given for why I should feel this is important are:  prestige, salary, accomplishment, and respect.  Ultimately, while no one came out and said it explicitly, I think most are interested in the power and influence that it affords them.

And this is also why it just does not matter that much to me.  Sure, a more prestigious title might be nice but I doubt anyone in my extended family even knows the difference between an assistant, an associate, and a full professor.  Thus, I would essentially have more prestige in a small community that I do not really feel a part of anyway.  Having a larger salary would be nice but I make more than my parents combined ever did (adjusting for inflation).  My kids pretty much have everything they need.  In fact, I worry that they have too much.  The sense of accomplishment that comes with a promotion would probably make me feel good for a few months but then I would just be back to feeling terrible about getting proposals rejected.  I suppose having more respect from my peers would be nice but it’s the kind of respect I really don’t want, i.e. respect for a title not accomplishments, contributions, or opinions.

While all of these benefits would be nice, I have to think of the cost of the time and happiness I would need to sacrifice to get them.  At this point in my life I just do not think the benefits, which I do not see as all that important, are worth the stress, my time with my family, my mental health, etc.

I am quite worried about the state of this country’s graduate education system.  While I am sure we are cranking out record numbers of students with advanced degrees, I think the quality of education has been severely eroded.  This stems primarily from the desire of many universities to build large, well funded research programs.

Unfortunately it seems that over the years a ‘large, well funded program’ has essentially become synonymous with running a consulting company.  To understand why this is you have to understand the different types of funding engineering faculty can get.  One can split it into government funding and industry funding with the vast majority of the money coming from the government.

Let us consider the smaller industry funding first.  This money comes as either a grant or a gift.  Gift money is essentially unrestricted and companies give it for a couple of reasons.  First is to build relationships with academic research groups which helps in preparing and recruiting students.  The second reason is that gift money goes farther because universities typically do not charge overhead on it.  Grant money on the other hand is charged overhead (typically around 50%) but there is a contract in place and deliverables expected.  Thus, the company has much more say in what research should be conducted and what results should be delivered.  Gift money is probably the best type of money someone can get because it is essentially unrestricted.  However, unless a faculty member has had a very long relationship with a business, gifts are usually very small (tens of thousands of dollars) and are hard to rely on because of natural business cycles.  Grant money from industry is probably the worst type of money you can get because there are usually many deliverables.  I.e. companies are looking for tangible results from their investment.

Government money makes up the vast majority of funding.  As an engineer there are two primary sources of government funding, the Department of Defense (DoD) and the National Science Foundation (NSF).  Depending on the specific type of work, engineers also get funding from the Department of Energy (DoE), the National Institutes of Health (NIH), and NASA.  Funding from NSF is arguably the best because it is largely unrestricted, allowing the faculty member and the supported students freedom to explore interesting ideas that may not have been explicitly proposed.  DoE and NIH funding can also be fairly unrestricted.  NASA funding was always relatively small and it is almost completely gone now.  The vast majority of engineering research funds come from the various DoD agencies.  This is probably the worst type of funding there is from an academic freedom perspective because DoD wants specific results and will not continue funding a program unless they get them.

While I am not suggesting that having deliverables and expecting results from a funded research project is bad, I do think it diminishes the academic experience and the education of the students supported by the funds.  If a faculty member is being pressured by a funding agency to deliver results (or lose the funds) that faculty member will pressure the students working on the project.  The faculty member then becomes a manager, the students employees, and the research group a small consulting company.

Putting pressure on graduate students to get research done is not necessarily a bad thing.  However, it seems to always results in the student spending less time on their courses/education and more time on their research.  If the work is truly graduate level research the students should need to spend at least a year doing mostly coursework to build a deeper understanding to perform the research.  The pressure to get immediate results distracts students from learning anything besides what is directly needed to get the results.

This pressure also affects how faculty members advise their students.  Students are frequently directed to take the minimum number of classes required and steered towards easier classes requiring less work.  A light course load will mean there is more time for research.  I was shocked to hear that students in one lab are actually told not to do schoolwork from 9:00 to 5:00 because that is when they are ‘working’.  This environment is really the same as they would have working in industry and taking courses towards an advanced degree in the evenings.

In fact, it seems like in many situations the students would be better off doing just that.  Even if you consider the tuition the students do not have to pay, the money they make is much less than the money they would be making in industry.  The only reason I can tell for students not opting for this is the necessary classes are not offered in the evenings.  Maybe as more and more classes are offered online we will start seeing students take this route.

Thus, one has to wonder why companies are still willing to hire graduate students.  This is likely because these students are usually the smartest and hardest workers.  Going to graduate school does not change that, and the classes they do take and the research they perform do likely better prepare them.  Unless they are doing the exact same type of research as they did for their thesis (which is highly unlikely) the lack of focusing on courses, learning, and broadening and deepening their knowledge will make them less prepared than they could have been.

While a previous post explains why I do not enjoying advising (graduate) students, that should not be interpreted as not wanting to have any graduate students.  In fact, I would like to have a graduate student or two.  While I will not like the managerial aspects of having the students, the energy required to manage two graduate students will not overwhelm the joy of teaching them.

I will now try to explain why then I do not have any graduate students.  The reason is essentially all about funding.  I have written many proposals over the past few years (mostly in collaboration with other people).  The vast majority of the funding I have requested in these proposals is to support graduate students.  Unfortunately, none of them have been funded.

The last grant I received (about four years ago from NSF) requested funds to hire two graduate students, one in physics and one in ME.  Unfortunately, while the grant was funded, the funds provided were about half of what was requested.  With such a limited budget for the work proposed the co-PI and I decided to hire a post-doctoral researcher.  (Note that with the exceedingly high tuition at PSU and the fact that the full amount must be paid for supported students, it actually costs about the same to hire a post-doctoral researcher as it does a graduate student.)  Even if the grant had been fully funded, the funding period was only three years (typical for NSF).  With it taking (on average) five years for a student to finish a Ph.D., there would more than likely be at least two years during which the student would not have funding unless another grant was awarded.  With funding rates so low and my success rate not that encouraging it was hard for me to be comfortable telling a student they would be supported as a research assistant for the entire time.

In many regards it is much easier to manage post-doctoral researchers because they can be let go (and are expected to be let go) once the funding runs out.  Making sure students have funding whether it is from a research assistantship or a teaching assistantship generates a great deal of stress.  I realize that it should not be overly stressful on me but it is.  I feel obligated to make sure a student has support for their entire stay at PSU.

Another benefit to hiring a post-doc for me in particular is that I can readily find someone with a strong background in theoretical mechanics (needed to do the research I propose).  The reason this is so important, especially at PSU, is that our graduate curriculum in theoretical mechanics (at least in engineering) is in shambles.  I will discuss this further in future posts.  Thus, for me to get someone up to speed in all the fundamentals means that I either need to find a student willing to learn a whole lot on his/her own, or I have to spend a tremendous amount of energy teaching them.  While I would expect students to have to teach any graduate student (or post-doc) quite a lot, having to teach them everything is a huge added burden.

All that said, I will continue to request funding to hire graduate students, and will do so when that funding is awarded.  I will also continue to look for the rare student that has his/her own funding and is interested in doing research that requires a deep understanding of physics and mathematics.  Unfortunately, the intersection of these two sets is very small.  Almost all the students that might have their own funding are domestic ones.  Almost all the students interested in the necessary physics and mathematics are foreign.

Maybe as China and India become wealthier nations I will start to see well-prepared foreign students coming to the US for graduate school with their own funding or fellowships from their government.

I was pretty shocked when my boss recently came to the conclusion that I do not like teaching students.  That is actually one of the things I like most about my job.  In the end I think she took my dislike for advising to mean I dislike teaching.  I can understand the connection but it forced me to think about the differences between teaching and advising students and how someone could enjoy one but dislike the other.

It basically comes down to the fact that I utterly hate managing people, and while advising consists of a great deal of teaching it also requires a great deal of managing.  Thus, the thing I enjoy most is actually teaching/helping other people’s students (or co-advising students).  I think this is also why post-docs are attractive.  They usually do not require much less teaching than graduate students (since their background does not usually match their current project) but they seem to require a whole lot less managing.

Loathing managing is not something I discovered later in my life; I remember feeling this way in high school. In fact, a big reason I decided to go to graduate school was to be able to have a job in which promotions did not mean managing more and more people.  (Although I realize now that is not necessarily the case in academia.)  The structure I saw at a Ford plastics plant (where everyone had a BS) and an IBM research lab (where everyone had a PhD) made me realize I needed an advanced degree to avoid the managerial track.

I am not sure why I hate managing so much.  Part of it is obviously that I am not very good at it.  However, that is more of a result of disliking it so much, i.e. I loathed managing before I realized I am terrible at it.  It is likely just a personality trait and similar to why many great athletes do not make good coaches.  While I enjoy helping people and giving them advice, I dislike telling them what they should do.  Everyone should just think for themselves.

This personality trait is also probably why I am a terrible recruiter and promoter.  I recall reading an article about the, so called, Fab Five who began their college basketball careers at Michigan while I was there.  In the article they mentioned how Juwan Howard and Chris Weber had very different personalities when it came to helping recruit new players.  The coaches would always have recruits spend a lot of time with Juwan because he thought Michigan was the best place in the world and would tell them they should play at Michigan.  Recruits spent very little time with Chris even though he was the best player because he was not a good recruiter.  He would basically tell them they should make up their own minds and go to college wherever they wanted.  I am much more like Chris in this regard.  While I never tell students they should not come to Penn State, I also do not pretend to think it is the greatest university.  There are a lot of reason students should want to come here, but I could say that about almost any university.

This seems to have a lot to do with ‘sales’, another thing I hate and am terrible at.  Managing is essentially very much like sales in that you are selling people tasks.  My terrible ability to sell myself and my research will the the topic of a future post.