Date of Original Post: Wednesday, March 10, 2021 6:37 PM
> all the reports I have seen have not
> had any sort of correction factor for where that county or state was
> on the curve of development.
This may be due to a small misunderstanding. They were not measuring the
speed of the cars, they were measuring the rate of the change in the
acceleration.
The acceleration is the rate of change in the speed, and the rate of change
in the acceleration is defined by the exponential function.
It did not matter what the "Y" value was on the graph, they were looking at
the slope of the graph, which in an exponential function.
Any exponential function, for example, f(x) = e^x has at every number x ,
the same slope as the value of f(x).
> Take NY for example, its curve is
> completely different in timing than say TX.
Let's apply f(x) = e^x to the above. NY got a "head start" because of those
daily flights from Wuhan arriving at JFK, and a Mayor who was on TV eating
moo goo gai pan, and telling everyone in January 2020 with it was safe to go
out and eat at the restaurants in either of NYC's two "Chinatowns" (lower
east side, and Queens).
So, let's make it a drag race - the cars are capable of constant
acceleration.
So, NY starts out "driving" early. At x = 0, the slope of f(x) = e^x is
f(0) = e^0 = 1. That means when NY started, the odometer read 1 mile, and
its speed was one mph. After 10 hours of this constant acceleration, NY
has gone e^10 miles, and is traveling at a speed of e^10 miles per hour.
(Roughly 22,000 miles, just out to the geosynch orbits for satellites, and
going 22,000 mph)
Now, TX just started 3 hours ago, e^3 = 20, so 20 miles and 20 mph. But the
slope of the curve (the rate of change) is the same, and given 10 hours, TX
will arrive at the same point and velocity as NY did, increasing its speed
exponentially.
(As an aside, I've been heckled fairly often over the years due to similar
misunderstandings of math and statistics as applied to bees. It's all fun
and games until we start taking casualties, and with Covid, we are taking
serious casualties, so I am being so foolish as to bring up math again.)
> Comparing bar openings in FL, with those in AR with drastically
> different population density and climates is a red herring.
AR has 3 million residents, and currently has 325,383 cases, and 5,357
deaths, which is 10% of total population infected, 0.10% (1/10th of a
percent) of total population dying.
FL has 21.5 million residents, 1.95 million cases and 31,888 deaths, so 9%
of total population infected, and 0.10% of total population dying.
I don't see a whole lot of difference there in terms of per-capita impact,
but AR has slightly more cases per capita.
A very close friend was getting a very prestigious math award, and, as his
Division Manager and head of the lab, I flew out with him to sit in the
audience and clap for him. He is a shy type, but he had to give an
acceptance speech. He must have read a book about giving speeches, because
he made opened his talk with a joke - "Did you hear the old one about the
two statisticians?" he asked. I could not control myself. I called out
"Probably!"
It took quite a time for the giggles to settle down, and he did not forgive
me for several weeks.
***********************************************
The BEE-L mailing list is powered by L-Soft's renowned
LISTSERV(R) list management software. For more information, go to:
http://www.lsoft.com/LISTSERV-powered.html
|