COVID Day 50 New Cases Data

COVID-19 Death Rates

A basic characteristic of epidemics is that, until a significant percentage of the population is infected, the number of infected persons is an exponential function of time, N(t)=N0 2^{t/d}, where d is the doubling time and N0 is the initial population. In order to slow down the rate of infections, it is desirable to make d as large as possible by, for example, social distancing as we are currently doing in the COVID-19 pandemic.

      To monitor progress in social distancing, one can monitor the fractional daily increase in the number of cases \Delta ln(N) =\Delta N/N, from which the doubling time becomes d=ln(2)/\Delta ln(N).  Because the daily numbers fluctuate, the fractional daily increases are noisy and it is convenient to average a few days together to see what the trends are. Here are recent US COVID data plotted this way:

The data clearly show that, since serious distancing began being practiced in mid-March, the doubling times have greatly increased.  Equivalently, the daily percentage increases have fallen substantially.

     The total cases data are always suspect due to testing problems.  Data on deaths should be more reliable  (though not infallible as some people, particularly in NYC, have chosen to die uncounted at home.  This should not be a large fraction of the totals, though.) What is encouraging is that the daily deaths data are also showing substantial decreases in the percentages as a function of time, again starting in late March.

Rather than increasing exponentially, the death rates have been quite steady at about 2,000/day.  Again, this suggests that the social distancing efforts implemented in most of the states are effective and managing to keep our death rates at a manageable level (NYC being the notable exception).  Had the death rates continued to climb at 25% per day, as they were doing in late March,  the death rates would be over 5000/day on April 10.

The Science-free Eclipse

Note (March 2020).  This post was composed in 2018, but never posted.  But I still agree with it, so better now than never!

A little confession to start this post.  I've hated virtually every planetarium show I've ever attended.  What?  Why would a science type hate a planetarium show?  Because they typically spend 90% of the time talking about constellations.  There is no science in constellations!  The operator goes into great detail identifying the constellations, naming the various stars and drawing lines between them to show the bear or whatever.  Content free.  The big exception was the night an amateur astronomer friend of mine put on a planetarium show for our Cub Scout troop.  He quickly went through the requisite constellation stuff, then showed us photographs he had taken of the rings of Saturn.  In addition to the spectacular photos, he explained how he took them, and described many features I had never known about.  I enjoyed that immensely.

The recent eclipse mania was, alas, reduced to a outside planetarium show.  As an example, check out CNN's "The Solar Eclipse, in Pictures".  It is mostly pictures of people viewing the eclipse!  There is a nice picture of the corona, which can only be seen by eye during an eclipse, without even mentioning it.

In the various discussions of the eclipse, if anything scientific is discussed, it is an explanation of why eclipses happen so rarely.  That's great, I like that.  But what is rarely discussed is that the eclipse is only possible due to the nearly identical angular sizes of the moon and sun.  And what is the nature of that corona?  What do we know about the fields and charged particles that are only so rarely revealed to the naked eye?  How do scientists learn about them without waiting for rare eclipses?  The soul hungering for some science starves with the media coverage of this supposedly scientifically important event!

COVID-19 Progress

A look at the COVID data: Here is the March US data of daily new cases. It is better to look at that data rather than the total number of cases because the daily number tells you how you are doing now, information that takes a while to show up in the totals. Furthermore, the plot is on a logarithmic scale. On such a scale, exponential growth shows up as a straight line. The slope of the line tells the doubling time for new cases, how long it takes for the number of daily cases to double.

You can see that from March 1 to about March 21 the US new cases followed the straight line very well, with a doubling time of about 2.3 days. However, my daughter and I noticed early this week that that the new cases were now doubling only every 5-6 days. This is significant; today the US had about 19,000 new cases but if we had continued on last week's curve there would have been 73,000 new cases today! I think this is encouraging news. We're still on an apocalyptic trend, but it will take us twice as long to get there now!

Data from worldometers.info, updated April 3, 2020.

The $15 Minimum Wage

A doubling of the U.S. minimum wage to $15/hr was recently proposed by Sen. Bernie Sanders, who is running for the Democratic presidential nomination.  It is also being put into place, somewhat bizarrely, for New York fast food chain workers.  No question that the current rate is too low; at 40 hrs/week the annual income of $15,600 is only somewhat above the poverty line for a single individual and is below if that person has even one dependent.  Can we really justify wages for honest work that do not allow a person to escape poverty?

The bloviators proclaim that such a move would be inflationary, would cause businesses to reduce the number of workers, thus pushing more people into unemployment, reduce our competitiveness etc etc.  A simple anecdote will suffice to illustrate the nonsense of such arguments.  

My daughter used to work retail, at minimum wage or barely above, at a well-known clothing store at the local mall.  As a reward for her industry and reliability, she began to be given fairly substantial responsibilities (but no pay raise of any significance, of course).  One day she got to tally the sales for her store, about $15,000.   For fun and illumination, we estimated what the labor costs were for that day.  They had, in addition to the manager, typically 3 minimum wage workers for the 11 hours the store was open.  33 hours at $7.50/hour is $250 total cost for those workers.  This is 1.6% of the sales for that day.  

So, how much would they have to raise prices in order to maintain the same profit levels with double the labor cost?  1.6%.  Not even noticeable.

Or, consider the cashier at the local fast food hamburger joint.  That person is, I estimate, probably processing 1 order per minute at what I would guess is a typical $10 per order.  How much would prices have to increase to cover a doubling of the cashier's salary?  $7.50/$600=1.3%.  No one would notice.

Various calculations like this suggest that labor costs represent an insignificant fraction of service and retail industry costs.  Only irrational greed keeps the wages at such unconscionably low levels.

Sudoku Logic III

I noticed an interesting twist of logic in today's Sudoku puzzle that enabled quick solution of the rest of the puzzle.  Here's the situation:

Our focus concerns the contents of F6, but our considerations will lead us to learn what goes in F5, after which the rest of the puzzle is not hard.

A little thought shows that A8-A9 must contain 1 and 6, so A5-A6 must contain 2 and 5.  A slightly more involved sequence--(The 5s in D1 and E9 imply that 5 must go somewhere in F4-F6.  5 is forbidden in G5, so it must go in H4-I4, thus eliminating F4)--shows that either F5 or F6 must contain a 5. Now comes the key point:  F5-F6 cannot have a 2, since if it did both A5-A6 and F5-F6 would hold 2 and 5, and there would be duplicate solutions to the puzzle.  Therefore F6 cannot be a 2.

Now let's try to find what does go in F6.  Looking at row 6, remembering F6 cannot be 2, leads to F6 being 5, 7 or 9.  Now 9 can only go in F6 or F8 in the F column.  So let's try 9 in F8, hoping to eliminate either 5 or 7 from consideration in F6.  A 9 in F8 requires that 7 goes in D8.  But in row 6 the 7 can only go in D6 or F6.  The only remaining possibility is F6.  Thus we have learned that F6 can only be 9 or 7, not 5.  But since either F5 or F6 must be 5, the only possibility is that F5 is a 5.  By studying F6, we have the collateral result that F5=5.

Knowing F5=5,  the puzzle solves easily.  (One possible sequence of deductions is A6=5, A5=2, G5=4, F4=3...)

Gas is Too Cheap

A favorite topic of mine--the low price of gas--was covered by Click and Clack this week.  They came to the same conclusion I did in my first blog post: gas costs represent about 25% of the total cost of operating a vehicle.  That's too little, and here are some reasons why.

• Low gas prices distort decision making, and encourage frivolous driving.  I'm guilty of this.  It takes me a half-dozen trips to the hardware store to complete even the simplest household repair.  But I don't care--the gas adds a trivial cost to the project.  At twice the price, I might try a bit harder to be more efficient.
• Low gas prices discourage efficient public transportation.  The higher the price of gas, the more we are likely to take buses, trains, etc. when we need to move from place to place.  These alternates use dramatically less fuels, per person-mile, than personal automobiles.  All over the U.S., people commute 10, 30, even 50 miles each way to work.  This is wasteful and unnecessary, and a huge human cost in wasted time.
• Wars in the Middle East.  We supposedly fight these wars for various reasons, but do you really think we would care so much about that region of the world were it not for the fact that it contains the largest fraction of the world's petroleum reserves?  It really bothers me that we fight war after war there, sending our young men and women to die (not to mention killing their people along the way) without asking for any sacrifice on the part of us who stay at home.  If we had to pay for our military directly from the gas pump, it might help us reassess whether or not we really need to to do all that fighting and killing.
• Petroleum is the ultimate non-renewable resource.  The time scale for it to be replenished by natural processes is millions of years.  We are going to run out in less than a hundred.

There are other arguments, (economics, pollution, global warming...) for why a massive gas tax would be good for us.  But when it comes right down to it, our current practices encourage a wasteful and destructive style of life that our grandchildren will one day condemn us for.