Can you shoot down a Chinese balloon with a rifle from the ground?

The recent passage of a Chinese balloon at 60,000 ft (20km) altitude over US soil made headlines. One question many Americans are wondering is: would it be possible to shoot down the balloon with a rifle?

To answer this question, I made some assumptions, and then a simulation in Mathematica using available information on bullet trajectories.

For the bullet, I assumed an AR-15, a common rifle in the USA, was used with a muzzle velocity of 1000 m/s. I further assumed a 5.56 NATO round (I'm not a gun expert so I assume this fits together?) and that bullet has a mass of 4 grams, and drag coefficient of around 0.3 (see https://apps.dtic.mil/sti/pdfs/ADA530895.pdf). So then we can plug and chug:

mbullet = 4*10^-3; (* bullet mass in kg *)
dragCoefficient =0.3; 
airDensity = 1.29; (* kg/m^3 *)
bulletDiameter =5.70*10^-3 ;(* diameter in meters *)
g=9.81; (* graviational acceleration in m/s *)
sumF=-g*mbullet-(1/2)*dragCoefficient*airDensity*(\[Pi]*bulletDiameter^2 / 4 )* (y'[t]*Abs[y'[t]]); (* note: need to account for the sign of the deceleration *)
eq1=Simplify[{y''[t]==sumF/mbullet}]; (* Newton's law *)
eq2= {y[0]==0};(* Initial condition, bullet fired from the ground *)
eq3 = {y'[0]==1000};(* Initial condition, bullet at 1000 m/s *)
system =Join[{eq1, eq2, eq3}];
tmax = 40;
s=NDSolve[system,y,{t,0,tmax}];
Plot[y[t]/.s,{t,0,tmax},Frame->True, FrameLabel->{"Time [s]", "Height [m]"}]

  

The result:

So the bullet only gets to 2km altitude, not even close to the 20km altitude of the balloon! 

We can further plot the velocity of the bullet over the trajectory using:

Plot[y'[t] /. s, {t, 0, tmax}, Frame -> True, 

 FrameLabel -> {"Time [s]", "Velocity [m/s]"}]

This gives us:

 

Solving for the end of the trajectory gets us -88 m/s. Since energy scales with v^2, it has less than 1% of the initial energy. For reference, a paintball travels at approximately 90m/s. Still, you don't want to get one of those in the eye, so that's why you should not fire guns into the air to try to shoot down Chinese balloons.

Are the Nobel Prize winners racist against Neanderthals?

I watched the recent 2022 Nobel Prize Winner round-table discussion, and couldn't help but be offended at the lack of scientific rigor and the poor communication to the public when it came to discussing the recent insights into Neanderthal remains. 

What are the logical mistakes that these Nobel Prize winners are making? Here are the logical fallacies that I have identified that are being propagated by the discussion:

1. modern humans existed 60,000 years ago
2. there exists a hominid sub-species that lived 60,000 years ago that we are genetically identical to
3. Neanderthals are "other" and are to be reviled

The three primary participants in the discussion were the host, Zeinab Badawi, Carolyn Bertozzi, and of course Svante Pääbo. So who did the worst job in communicating to the public?

First of all, the host: Zeinab Badawi, in her question "we set sail from Africa 60 to 70,000 years ago to populate other parts of the world with no idea of what layout there" uses the word "we" so as to distinguish "us" from "them" (the Neanderthals). This propagates fallacy#1 that I identified above. It would have been more correct to say "a homonid subspecies left the African continent 70,000 years ago and started interbreeding with the Neanderthals, another homonid subspecies." We give Ms. Badawi 2 angry skulls for her comment. 

Secondly, Carolyn Bertozzi chimed in with her question "you don't know your percent Neanderthal but I do know mine I've had that analyzed so I'm 2.3 percent Neanderthal. Is that something I can be proud of?" On the one hand, a great trolling comment that rebukes Ms. Badawi's poorly phrased statement. On the other hand, it propagates the logical fallacy #2: that there exists a homonid sub-species that lived during the Neanderthal times that we are 100% identical to. Dr. Bertozzi did not explicitly state this, and since her question was somewhat of a trolling comment, we only give her one angry skull:

Finally, Dr. Pääbo answered the question with this gem "Neanderthals don't often have a very good reputation". This joke comment propagates myth #3. We give Dr.Pääbo two angry skulls for this comment:

Then Zeinab Badawi chimed in again with "because they're known for having a very broad muscular you know slightly brutish kind of I mean nothing thuggish about you" which propagates myth #3 and gets three angry skulls:

Finally, Dr. Pääbo could have taken this opportunity to express that there is no ancient homonid subspecies that is 100% identical to modern humans. We are the product of our ancestors. The Denosovians are only 6% similar to modern humans. It would be worth explaining which (if any) subspecies of homonoid that lived 60,000 years ago is most similar to modern humans. For failing to take the opportunity to educate the public, Dr. Pääbo gets two angry skulls:

Some interesting questions that I was unable to find answers to in my brief google searching: there were skeletons discovered such as Oase-1. How similar are these genomes to modern humans? e.g. if Neanderthals are 1-3% similar to some modern humans, how similar is Oase-1 to modern humans? Is it 1-3%? Is it 10%? Is it 95%. That would be interesting to know, yet, I could not find this key statistic. Which homonoid subspecies is most genetically similar to modern humans, and how similar are they?

Could Trump invoke Emergency Use Authorization for a COVID vaccine?

In my previous post, I discussed the likely timing for a COVID vaccine as being March 2021. However, there is a backdoor to the usual FDA safety studies called "Emergency Use Authorization" (EUA).

So what would be the logistics involved in EUA? Interestingly, it's basically just one person (the Secretary of Human Health Services Alex Azar) that could declare a public health emergency that could justify skipping the usual FDA pathways https://www.law.cornell.edu/uscode/text/21/360bbb-3

Mr. Azar has already used EUA to get some vaccines going into Phase I and II trials. However, some groups are already starting to make noise against EUA for a widely deployed vaccine, such as Public Citizen, a consumer health advocacy group, who feel that EUA could undermine the credibility of the FDA and the trust in vaccines in general, if the usual safety steps are skipped for the full safety study after Phase III. I do not believe that an argument based on long-term credibility will be convincing to President Trump, who is now an underdog to win a second term and is desperate for some easy answers to the COVID19 problem.

So basically, there are a bunch of FDA rules, but they can all be waived if the Secretary of Human Health Services Alex Azar feels like it. Of note is that the Secretary of Human Health Services is nominated by the President, and because Human Health Services is a branch of the Executive, he can actually be fired by President Trump. 

Based on the above, I am changing my prediction: I predict that Emergency Use Authorization will be taken by President Trump on an untested COVID19 vaccine that is part-way through trials, in October 2020. If Alex Azar doesn't go along with the EUA plan, I believe he will be fired.

It's easy to be critical, but if you were Alex Azar, what would you do? You have two options: either you stick with the usual FDA rules and wait until March 2021, and as as results thousands of people will die from COVID19 in the meantime, or you use EUA and you risk deploying a vaccine that has harmful side-effects that could harm millions. It's certainly not an easy decision even in the absence of political elections.

When will a COVID-19 vaccine be ready in the USA?

There are a bunch of vaccines being developed against COVID-19. Focusing on the US-based vaccines, the one leading the race at this time is Moderna. There is also Astrozeneca (AZD1222) but they are not registered on clinicaltrials.gov and are being pretty shady about their US clinical trial, and so I will ignore them for now.

So how soon might the Moderna vaccine be available, if everything goes well?

According to FDA guidelines, for a vaccine to be deemed safe and effective, the vaccine must first be observed to not have "Serious and other medically attended adverse events in all study participants for at least 6 months after completion of all study vaccinations. Longer safety monitoring may be warranted for certain vaccine platforms (e.g., those that include novel adjuvants)."

So basically, the Moderna vaccine will have to wait at least 6 months after the last of the 30,000 shots are administered before the FDA will approve it as "safe and effective." As of July 31, 2020, the vaccine clinical trial was still recruiting participants. According to the CEO of Moderna, it will be challenging to recruit the 30,000 patients necessary. Therefore, optimistically, the Moderna vaccine could be ready for commercialization as early as March 1, 2021 (assuming that all 30,000 patients were recruited as of Aug 1, 2020), but realistically it will be much later than that. I will be keeping an eye on the clinical trial, to see when the status switches from "recruiting" to "active, not recruiting" to know when to start the six month clock.

The FDA is an arm of Human Health Services, which is an arm of the Executive Branch of the US Federal Government. Therefore, I believe there will be immense pressure on Moderna and other companies to "release the vaccine" before the clinical trials have completed the six-month safety study, or perhaps there will be large-scale misinformation about when they will be ready. For example, Dr. Fauci has suggested that "We may be able to at least know whether we are dealing with a safe and effective vaccine by the early winter, late winter, beginning of 2021." That is bullshit, the earliest a Moderna vaccine would be deemed "safe and effective" by the FDA would be March 2021. I think Dr. Fauci is muddying the waters by confusing "FDA approved" with "we may be able to at least know", which is some undefined standard of vaccine goodness. I think this type of imprecision may lead to large-scale repercussions such as the White House trying to over-rule the FDA and get a vaccine released earlier, specifically before the upcoming US Presidential election. If Dr. Fauci thinks a vaccine will be ready in 2020, he should tell us which vaccine he is talking about and when the 30,000 patient recruitment was completed.

Note: other countries may have lower standards for safety than the US and therefore release a vaccine much sooner.

Some hope in the US

After a frustrating week of stagnant daily tests, the number of daily tests performed in the US took a jump from 103,000 two days ago up to 216,000 today. Even better news, was that even though testing increased, the number of new positive cases held steady at around 33,000. The positive test ratio is back down to 16%, from a high of 26% two days ago. This gives some hope that the number of tests is starting to outpace the spread of the virus, a good first step towards getting things back under control.

data from: https://covidtracking.com/data/us-daily/

COVID-19's exponential growth

I came across a neat video https://www.youtube.com/watch?v=54XLXg4fYsc&t=362s and thought I would summarize the results in a quick-to-digest format. Skip ahead to see the math behind this plot.

I find it very remarkable how, despite our cultural differences, all people of the world can be fit to this universal exponential curve. When it comes to this virus, we are all the same.

The next thing to note is that once the virus is contained, the exponential growth comes to a grinding halt and the number of new cases per day plummets. Each data point represents one day, so you can see that within a week or two, new cases can plummet relative to exponential growth.

What is clear is that China has done the best job in tackling the virus quickly, South Korea is a close second. The USA and Italy still have some work to do before they contain the virus. I hope they don't get to x=1 (everyone infected). Rather, I would like to see the daily new infections plummet well before we get to that point! 

The point of no return?

China and South Korea performed large efforts to contain the virus, and were successful. For the US or Italy to contain the virus will taken a proportionately even larger effort at this point, since they have already outgrown the Asian case numbers. It may be past the point of no return, where the efforts required to contain the virus (millions of daily tests and even more strict lockdown) are not possible anymore. If that's true, I have a hard time seeing what will stop the virus from hitting x~=1 (we are all infected). I hope it will stop before it gets there, but without a full lockdown I don't see how that will happen. Maybe the virus will just lose steam once enough people properly implement social distancing. It is not the kind of experiment that I would voluntarily sign up to be a part of, that's for sure!

The math

On the x-axis is cumulative cases, normalized by population, and on the y-axis is daily new cases, normalized by population.

Because exponential growth has the property that:

We get the funny property that when plotted on a log-log plot, the daily new number of cases (the derivative of cumulative cases vs time) as compared to the cumulative number of cases will be equal to a constant:

When we eyeball the world countries on the above graph, we see that 1/τ is equal to approximately 0.18. Thus, the virus is growing by a factor of e, every 1/0.18 = τ = 5.4 days. Or equivalently, the number of infections is doubling every τ*ln(2) = 3.8 days. That seems like a universal number for all humans.

data from here:

https://www.ecdc.europa.eu/en/publications-data/download-todays-data-geographic-distribution-covid-19-cases-worldwide

New York

I included New York in the same graph as the nations above, and it's clear that they are proportionately getting hit the hardest. New York is approaching a population-wide 1% infection rate, approximately 10x the national average, although it also fits the universal COVID-19 line, just like all the nations do. The only thing that makes nations different is at what point they break the exponential growth curve.

The big question still remains: will the virus get close to 100% in any nation or city's population? I am worried that it will, but I hope not!

What it would take to cure the world of COVID19

We are currently in the worst possible time in the USA for COVID19 infections. Every day, the number of daily infections is climbing at an exponential rate. However, I want to try to be optimistic. What are some of the best possible scenarios? Well, let's start with reality, then look at the worst-case, and then claw our way back to an optimistic scenario.

Reality is: China and South Korea have contained the virus. The US and many other countries have not, and as a result, the virus is running rampant. Due to the infection now being present in most countries, some of whose leaders (such as Bolsanaro of Brazil) are promoting public interactions and not even attempting containment, the possibility of worldwide containment is a near impossibility.  So based on this, I believe that the COVID19 virus will be around on planet Earth for a while, at least until a vaccine has been made. Within the US, the disease is now so prevalent, that containment seems impossible (https://jamanetwork.com/journals/jama/fullarticle/2763187). However, it is difficult to accept this reality. The difficulty in abandoning the idea of containment was expressed by a comment on the above article: "No! While mitigation must be done also, containment must not be abandoned! China has already shown that containment can be done at scale, with aggressive tracking, testing and isolation."


So that brings us to:

Optimistic scenario #1: the US aggressively pursues containment

The idea that we can start testing everyone, implement contact tracing, and the other steps of containment in the USA, when there are already 100,000 positive cases (and growing with 20,000 new cases per day), and currently little to no contact tracing infrastructure, seems unrealistic to me. However, let's try to stay positive. To get this done, President Trump would need to mobilize a WW2 level of effort and come out and say something like:

"America and the rest of the world are under attack by the COVID19 virus. In World War 2, American troops battled around the world to stop the Nazis. Now, we are going to fight around the world to stop the Coronavirus. We are going to lead the world in containment efforts. First, we are going to beat the virus in America, and then we are going to beat the virus in the rest of the world. Starting today, I am authorizing the FBI, CIA, and local police forces to have 5 experienced officers on every new COVID19 case, to find out everyone that they have been in contact with for the past 14 days, and they will all be on self-quarantine for 30 days. There will be a $10,000 fine for with-holding information, and possibly a one year prison sentence, or both. Those that participate in the self-quarantine program will receive their normal salary and any losses up to $10,000 covered by the federal government. Next, under the Wartime Production Act, and starting immediately, the Department of Defence is placing an order for 1 million rapid COVID-19 tests per day, provided by Abbott and other large biotech companies, which we will distribute to the states that are most in need. Finally, I am urging every American to stay at home for the next 60 days. If we work together, we can beat this virus. Once we beat the virus in America, we will beat the virus overseas also"

Then after the virus is beaten back and normalcy restored to the US, trade can be re-opened with countries that have taken similar measures. Then, to normalize trade relations, the US can send the cavalry (millions of tests and support with contact tracing) to countries in need.

Do I think the above containment scenario is realistic? No. But I like to dream big.

If we execute optimistic scenario #1 above, then we can keep the containment train running with allied countries, sending aid in the form of medical equipment and diagnostic tests, and possible contact-tracing support. Once a country has gotten rid of COVID-19, we can again have normal travel between the countries. There is this weird scenario possible where one country has contained the virus while another has not. For example, if South Korea has contained the virus but Brazil has not, I don't see how South Korea can let Brazilians into their country. They will effectively have to be an entire country in a plastic bubble.

Optimistic Scenario 2: In the long-run we will rid the world of COVID-19

For the next 18 months, we will have to deal with COVID19, until a vaccine is developed. Then, after many years of effort from some dedicated individuals and groups who makes it their mission to eradicate COVID19, hunting down every last pocket of infection, I believe it will eventually be eradicated, just like two strains of Polio have been (https://www.vox.com/2019/10/24/20930553/polio-outbreak-2019-eradication-who)

So in the long-term, we will beat this damned virus.

Optimistic Scenario 3: We can do local containment in the USA while other areas do mitigation.

The most recent modelling suggests that COVID19 will infect most of the population is left unchecked:

https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-Global-Impact-26-03-2020.pdf

In the paper (not peer-reviewed), they show that if left unchecked, we will get 2.9 million deaths in the USA. However, if we do a triggered suppression (engage in a lockdown and extensive contact tracing) when the death rate increases above some threshold value, we can limit the damage to only 520,000 deaths.

There is another paper (single author, also not peer-reviewed) that is making the rounds that touts a very optimistic scenario of only 81,000 deaths in the USA:
http://www.healthdata.org/sites/default/files/files/research_articles/2020/covid_paper_MEDRXIV-2020-043752v1-Murray.pdf
However, in the paper they model the growth rate as an error function (with no justification), and an arbitrary inflection point beta is chosen, based on empirical fitting. Seems suspect to me.

There seems to be a lot of uncertainty in the number of deaths. Lower-end is 81,000, higher end is 2.9 million.

So what is the optimistic scenario in the medium term? Well, I think it is suppression (as indicated in the paper https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-Global-Impact-26-03-2020.pdf), but instead of triggering local lockdowns and contact tracing based on death rate, I propose that we can do better if we perform local lockdowns based on infection rate. In that case, I think we can get even further below the 520,000 deaths that are predicted. I'll take a wild guess and say only 200,000 (made up number). In this scenario, individual States would be placed under Federal Lockdown once infections climbed above a certain threshold. Until then, infections would be allowed to grow at the exponential doubling rate of 3 days. So a state with only 1 case, would turn into the threshold of 1000 within a matter of 3 weeks. Then the state would be locked down for 3 months. Hmm.. now that I think about it, this strategy sucks. So the idea of a middle-ground, where we just beat down pockets of infection when they arise, is basically equivalent to a permanent lockdown for 18 months. In comparison, (optimistic scenario #1) would be easier than this. So basically, option 3 is a shitty option.

Conclusion

The optimistic scenario is: we rapidly scale up testing, and implement containment and contact-tracing in the USA. If watching American movies growing up has taught me anything, beating the odds with a last-minute hail-mary is what the USA is all about. The US has done it before, being one of the last countries to enter WW2, and going for a hail-mary with developing nuclear weapons, but it paid off then, and it can pay off now. The alternative I see is that we spend the next 18 months doing a dance of releasing restrictions and then getting infections until a vaccine is developed. It would be easier to just go all-in now and get the damned virus contained.