Thread: Dump bad equations. They lead to bad decisions.
On May 10, Mr. @BorisJohnson proposed a simple equation to determine #COVID Alert Level. He then explained how the reopening policy could be shaped based on this "Threat Level".
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On May 10, Mr. @BorisJohnson proposed a simple equation to determine #COVID Alert Level. He then explained how the reopening policy could be shaped based on this "Threat Level".
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In this thread, I will explain why this equation is not only wrong, but is also completely unnecessary — especially when we have clear alternative measures that can guide #COVID policies and decisions.
* Fast forward to tweet # 11 if you already know Dimensional Analysis.
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* Fast forward to tweet # 11 if you already know Dimensional Analysis.
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One of the first subjects in physics is "Dimensional Analysis". It needs to be emphasized more in high school and college physics courses.
See this @wikipedia article for a technical description:
en.wikipedia.org/wiki/Dimension…
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See this @wikipedia article for a technical description:
en.wikipedia.org/wiki/Dimension…
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Dimensional analysis ensures that you don't add "apples and oranges". In other words, UNITS of different terms in an equation must be compatible.
In physics, there are seven fundamental dimensions. The most commonly used dimensions are Mass (M), Length (L), and Time (T).
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In physics, there are seven fundamental dimensions. The most commonly used dimensions are Mass (M), Length (L), and Time (T).
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A couple of examples.
Newton's second law is often written as F = ma, or Force = mass × acceleration. Acceleration is the rate of change of velocity:
a = v/t.
Velocity = distance / time, so:
[v] = L/T,
where [ ] denotes dimension (or physical unit) of a variable.
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Newton's second law is often written as F = ma, or Force = mass × acceleration. Acceleration is the rate of change of velocity:
a = v/t.
Velocity = distance / time, so:
[v] = L/T,
where [ ] denotes dimension (or physical unit) of a variable.
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Since [a] = [v] / [t], we get:
[a] = (L/T)/T=L/T^2.
Therefore, F = ma tells us that:
[F] = ML/T^2.
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[a] = (L/T)/T=L/T^2.
Therefore, F = ma tells us that:
[F] = ML/T^2.
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Similarly, for @AlbertEinstein's famous E = mc^2, we get:
[E] = M (L/T)^2 = ML^2/T^2,
Note that c is the speed of light, which means it has the same dimension as velocity:
[c] = [v] = L/T.
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[E] = M (L/T)^2 = ML^2/T^2,
Note that c is the speed of light, which means it has the same dimension as velocity:
[c] = [v] = L/T.
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One of my specialties as an Applied Mathematician is modeling dynamic systems, as I explain in the thread below:
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A very important "sanity check" for models that we build is compatibility of all dimensions (units) in a model, regardless of how complex the system is.
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An equation with compatible units is not necessarily correct, since equations should realistically represent the [natural, physical, biological, viral, social, economic] systems that they attempt to model.
However, an equation with incompatible dimensions CANNOT be correct.
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However, an equation with incompatible dimensions CANNOT be correct.
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For this reason, Mr. @BorisJohnson's equation is fundamentally incorrect.
Covid Alert Level (C) is dimensionless, i.e., it has the dimension of a pure number:
[C] = 1.
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Covid Alert Level (C) is dimensionless, i.e., it has the dimension of a pure number:
[C] = 1.
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Number of daily infections, i, has units of people (P) per day.
[day] = [time] = T, so:
[i] = P/T.
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[day] = [time] = T, so:
[i] = P/T.
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Rate of daily infections, R, has units of people infected per day per each person:
[R] = (P/T)/P = 1/T.
For details, see:
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[R] = (P/T)/P = 1/T.
For details, see:
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So, Mr. Johnson's equation, C = R + i, rewritten in dimensions becomes:
[C] = [R] + [i],
or
1 = 1/T + P/T.
This is mathematically impossible for the same reason that one cannot write the following equation:
Wall = Snake + Oil.
3 variables with 3 different units!
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[C] = [R] + [i],
or
1 = 1/T + P/T.
This is mathematically impossible for the same reason that one cannot write the following equation:
Wall = Snake + Oil.
3 variables with 3 different units!
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Modelers sometimes propose a simple "indicator" variable in complex systems to easily describe some behavior of the system.
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For example, I introduced a simple "indicator" called Carrying Capacity in HANDY, which models dynamics of pre-industrial civilizations:
doi.org/10.1016/j.ecol…
This indicator combines many variables to determine the sustainability state of a society.
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doi.org/10.1016/j.ecol…
This indicator combines many variables to determine the sustainability state of a society.
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But @BorisJohnson's COVID Alert Level is wrong, vague, & confusing.
It is also unnecessary, because in the epidemic system, we have simple, clear variables that can guide the reopening policy/decisions: DAILY NEW CASES & DAILY DEATHS.
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It is also unnecessary, because in the epidemic system, we have simple, clear variables that can guide the reopening policy/decisions: DAILY NEW CASES & DAILY DEATHS.
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The transmission rate (R) is, however, much more complicated to define and calculate:
hindawi.com/journals/cmmm/…
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hindawi.com/journals/cmmm/…
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Many countries have successfully used daily new cases as an indicator for reopening.
Below, I will provide examples of countries that are past the rapid transmission phase of #coronavirus, countries that are close to success, & countries that are far from ready to reopen.
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Below, I will provide examples of countries that are past the rapid transmission phase of #coronavirus, countries that are close to success, & countries that are far from ready to reopen.
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#Taiwan never even had to lock down the country because they successfully controlled the spread of #coronavirus through thoughtful, early response. They have a few daily new cases that they can CONTAIN by testing, contact tracing, and isolating patients.
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#Iceland & #NewZealand have decreased daily new cases to just a few, which means they are now as good as #Taiwan.
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#Australia, #Austria, #Norway are down to a couple dozens of daily new cases. This is a manageable level of daily new infections in order to implement a successful test & trace program.
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However, reopening should not be mistaken with going back to "business as usual", as Mr. Johnson implies in Step 3. We cannot afford to have big outdoor events and crowded indoor spaces (e.g., movie theaters) until a vaccine becomes available.
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#SouthKorea had a few daily cases for ~3 weeks, until a silent #coronavirus carrier went bar-hopping last weekend in #Seoul, exposing over 7,000 people to the virus. Seoul and some other cities have decided to shut down bars & clubs indefinitely.
dw.com/en/spike-in-so…
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dw.com/en/spike-in-so…
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#Canada has ~1,200 daily new cases. But these new cases mainly appear in #Quebec, and to a much smaller extent in #Ontario & #Alberta.
#BritishColumbia #Vancouver can safely reopen as it has ~10 daily new cases.
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#BritishColumbia #Vancouver can safely reopen as it has ~10 daily new cases.
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Therefore, it is clear which countries are FAR FROM READY to reopen: US, Brazil, Russia, UK. (Any similarity between these four?)
Politicians should not confuse people with incorrect equations & ad hoc indicators when daily new cases can show our safety status so clearly.
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Politicians should not confuse people with incorrect equations & ad hoc indicators when daily new cases can show our safety status so clearly.
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The key to success against #COVID is in-depth understanding of its transmission mechanisms. We need effective education (eg, on correctly wearing a mask) to attain this knowledge: via TV/media for adults & K–12 for children. That would be the best use of this lockdown time.
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SUMMARY: Observe daily data trends to decide when it is safe to reopen. Forget bad equations, politicians' orders, & complex models that you cannot understand.
A big thank you to @bing for the plots and datasets. And thank you all for reading my thread!
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A big thank you to @bing for the plots and datasets. And thank you all for reading my thread!
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