Not a Number

This is the second day in a row that Collin County, TX, has not reported or updated its COVID-19 case or death count (or any other statistics). It is – likely not coincidentally – two days since the State took over the handling of cases from the County. The question is: what is the state doing if not collecting information about new cases, deaths, recoveries, etc.?

I’ve only been able to enter NaN – not a number – into my charting of new cases in Collin County. Once data becomes available again, I will revise these placeholders or let the code interpolate between numbers, as needed. But it’s just not credible that there have been no new cases for two days, since new case counts began climbing late last week. While absence of evidence is not evidence of absence, the timing is terrible; neighboring Dallas County today reported its record high number of new cases and deaths for one day. [1]


The Muon: 1970

In 1970, Hall, Lind, and Ristenen (Univ. of Colorado at Boulder) published a paper in the American Journal of Physics (AJP, vol. 38, No. 10) on “A Simplified Muon Lifetime Experiment for the Instructional Laboratory.” Basically, it articulates precisely the experiment at the heart of a similar instrument at SMU. Muons are produced in cosmic rays raining down on the atmosphere. Some muons make it all the way to sea level. Some of those are moving slowly enough to be stopped when passing through material. If that material gives off light in response to the slowing, stopping, and then decay of the muon, it is possible to use the light to measurement the lifetime of the muon.

An excerpt from the Hall et al. paper, showing their collected data (counts vs. channel, where one channel represents about 100ns of time) and the results of a least-squares fit to the data to extract the lifetime of the muion.

Hall et al. reported on a run of their experiment of 695 hours (about 29 days!). I’ve had nothing but time on my hands, and after discovering the Hall paper when I started playing around with the SMU instrument I was inspired to repeat their experiment.

Data from the SMU muon detector.

As of today, I have 695 hours of data from the muon detector at SMU. Based on a model fitted to the data (an exponential decay function added to a flat background), I find the lifetime of the muon to be 2170 \pm 29 nanoseconds (ns). The accepted lifetime is 2196 ns. The Hall et. al result using a similar but earlier version of the experiment found 2106 \pm 58. (note: they quote the half-life, but that is easily converted to the lifetime [average life of the muon] by dividing the half-life by ln(2)).

In 1970, as now, the lifetime of the muon has not changed within the resolution of two 695h data sets, taken independently and 50 years apart. There is a wonder in the power of scientific investigation to reveal those things that are steady and constant in the cosmos.

Scenes from Collin County, TX

One of my daily activities in the last 20 days (or so) has been to scoop up the COVID-19 case and death data for my county from the Texas Department of Health’s (DSHS) information center [1]. I’m not an epidemiologist; I’m a physicist. I’m not trying to make predictions; I’m making observations, assuming the data from DSHS is accurate (given under-testing and under-reporting, it’s most likely a suppressed count on both cases and deaths, but I can’t correct for that).

COVID-19 reported cases (black) and deaths (red) in Collin County, TX. Data taken from the Texas Department of Health and visualized using open-source tools (Python, Matplotlib, Seaborn, SciPy,NumPy). The green arrow indicates the date on which Collin County imposed social distancing requirements on individuals, but deemed all businesses as “essential” and allowed all to remain open. It was on March 31 (cyan arrow) that this part of the order was rescinded, and businesses were no longer all deemed “essential.”

Collin County began social distancing on March 24, 2020. At the time, we were in the middle of what would become the first major phase of exponential growth of COVID-19 cases in our County. The first case was reported to DSHS 37 days ago; by March 24 (19 days after the first case), our county had about 35 cases. At that time, the doubling time for cases was about 2 days. If we had remained on that climb, which presumably represents a doubling-time scenario before social controls over spread, then…

  • By March 26, 2 days later, we would have had 70 cases;
  • By March 28, 4 days later, we would have had 140 cases;
  • By March 31, 6 days later, we would have had 280 cases;
  • By April 2, 8 days later, we would have had 560 cases;

You get the idea. By today, 38 days after the first reported case, if you run the math we would have had almost 9700 cases. Let that sink in. If the trend that emerged between about March 19 and March 27 (inclusive) had persisted, we would be approaching something in the neighborhood of 10,000 cases alone in Collin County right now.

(Of course, the exact numbers should not be taken strictly literally; there is statistical error on each count, and in addition to that there is an unknown systematic error from under-recording of cases – likely, the above are underestimates, and so can be considered a best-case situation.)

The rapid increase in cases is the direct result of how unchecked diseases spread: exponential growth. However, about one week after social distancing measures went into effect in the county, the doubling rate slowed. Instead of doubling every 2 days, we entered a period (where we still are now) where the doubling rate changed to 7.5 days. It lengthened (a good thing!) by just over a factor of 3. That change in slope began around March 28.

What this meant was that as of April 10, instead of the almost 9700 cases we might have had on the old doubling trend (when we were doing no appreciable social distancing), we instead have reached only 400 cases using limited social distances (businesses were finally not all deemed “essential” on March 31, and we should be expect to see the effects of that in the next weeks).

Social distancing is working. The data backs this up, even in a segment of America like Collin County. But we have not peaked. We have not peaked. We’ve slowed the spread, but we have no stalled nor reversed it. This is no time for complacency.

We are in a world war. The actors are not nations, the prizes are not borders. Every place is vulnerable. The prize is living through this without succumbing to a nasty virus. Every new infection is a victory for the virus. Every person who avoids the virus is a victory for humanity.

We humans are both the soldiers and the battlefield. Each of us is the weapon and the target. Right now, the best medical tactic is to hunker down in our trenches, spread out, and try not to be easy pickings for the respiratory bombs deployed by the Coronavirus.

But we need an offensive plan. We need a coordinated strategy. We need a team of generals to fight a war on multiple fronts: developing tactical weapons against the enemy (vaccines, anti-viral drugs), developing new defensive strategies (deployments of medical equipment), and developing strategic campaigns to cut the enemy off from its supply of resources (e.g. rapid testing, contact tracing, and targeted quarantine).

But we have no leaders. Not really. So for now, we soldiers must run the fight. For us, that means we hunker down in our trenches, isolated and in modest safety. It is a safety threatened if we are suddenly ordered by the loud lunatics to “charge!” without weapons, without armor, without a strategy.

Keep distancing and carry on.



The Joy of the Muon

Muons are a gateway drug. They are just difficult enough to detect that they are really not obvious to humans. They are just easy enough to stop in material that, once you learn to spot them, you want to stop them and watch them do what they do. What do muons do?

They decay.

In about 2 millionths of a second, that muon you just captured is gone – evaporated into a particle spray containing an electron and two neutrinos. This fact allows us to measure the lifetime of the muon. Being captured by an atom resets their quantum clock to zero. What happens after that, and when it happens, tells us the probability that a muon, nearly at rest, will decay after a certain amount of time.

If you can capture all of this in a detector system, you can measure the lifetime of the muon.

Thanks to my colleagues, Tom Coan and Jingbo Ye, we have an awesome little muon detector in the basement of Fondren Science Building. Thanks to our awesome “Internet of Things” developer, Guillermo Vasquez, we have a Raspberry Pi computer connected to the detector that accepts data from it. I had some fun writing python code to read and save the data to disk, and then I used a Jupyter notebook to analyze it.

And here is the joy of the muon: a measurement of its lifetime from an ensemble of >1000 decayed muons and assuming an exponential decay model. The accepted value of the lifetime is 2196.9811(22) nanoseconds, where the numbers in parentheses are the uncertainty on the last two decimal places of the accepted lifetime measurement. Not bad. Not bad at all.

This image is updated every minute or so, representing an updated data sample from the detector (and an updated fit of the model to the data). The rate of “good muons” through the detector is about 3 per 15 minutes, so don’t hold your breath. Reload this page daily to see new results!

P.S. What’s the data coming in from the electronics, you ask? It’s the number of clock cycles between the flash of light that signals muon capture by an atom, and the flash of light that signals the decay of the muon (and the exiting of the electron from the medium). The clock speed is 50MHz, so a period of 20ns. Each clock cycle is thus 20ns of time.