# Team Kimberlin Post of the Day

Team Kimberlin never lets facts get in the way of their narratives—or math either, as this Math is Hard post from six years ago today demonstrates.

* * * * *

Central Daylight Time (CDT) is 5 hours behind Coordinated Universal Time (UTC).

9 – 5 = 4

10 – 5 = 5

* * * * *

Yes, and two and two are still four.

# Coal Fired Teslas

The electricity flowing from a charging station doesn’t magically appear. It must be generated and transmitted to the charger.

Let’s do a bit of analysis.

Looking around the interwebz, I found that the typical Tesla uses 34 kWh of energy to go 100 miles. I’m more used to dealing with energy calculations in joules. 34 kWh = 122 MJ. That’s megajoules.

The typical charging station has an efficiency of about 90 %. In order to deliver 122 MJ to the Tesla’s battery, it will draw about 136 MJ from the power line. The typical efficiency of the power grid from generating station to end user is about 89 %. Some power station needs to generate 153 MJ to get 122 MJ into the Tesla’s battery.

Let’s assume it’s a modern coal fired plant. The efficiency of the process of burning coal to heat water to make steam to turn a turbine to spin an electrical generator is typically around 32 %. That means we need 472 MJ of energy from the coal.

Burning a ton of coal delivers about 22 GJ (gigaojoules) of energy, so we’d need to burn about 43.4 pounds of coal to charge a Tesla to drive 100 miles. That gives a fuel economy rating of 2.3 miles per pound of coal, and that’s roughly equivalent to 15 mpg for a gasoline vehicle.

YMMV

# Quote of the Day

Randomness, chaos, uncertainty, and chance are all a part of our lives. They reside at the ill-defined boundaries between what we know, what we can know, and what is beyond our knowing. They make life interesting.

—Ivars Peterson

# Quote of the Day

It is known that there are an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so the average population of all the planets in the Universe can be said to be zero. From this it follows that the population of the whole Universe is also zero, and that any people you may meet from time to time are merely the products of a deranged imagination.

# Taxing Unrealized Capital Gains

Lots of folks have seen the value of certain capital assets rise significantly over the past couple of years. One of the reasons my 401k has done so well is that several of the mutual funds in that portfolio have positions in companies such as Tesla, SpaceX, and Apple. I haven’t become a billionaire, but I’ve been along for the ride.

So now, the some of the more economically-challenged on the Left are proposing a “wealth tax” as a way of funding the Build Back Better scam. I saw a tweet this morning suggesting that because Elon Musk had seen his stock portfolio rise \$36 billion recently, he should be hit with an \$8 billion dollar tax bill. Musk seems to be a very savvy enough businessman. I doubt he keeps that kind of cash on hand. I’ll bet he’d have to sell a substantial part of his holdings in order pay up.

If he dumped a large chunk his stock in companies like Tesla and SpaceX, wouldn’t that cause a drop in the prices of those stocks? Supply would suddenly exceed demand in the stock market. What could happen to my 401k? If it suffers an unrealized capital loss, should I get a tax rebate?

If he had to sell so much stock that he lost control of the companies, would the new owners keep him? If not, would they be as well run? Would the value of the holdings in my 401k be further depressed. How many jobs might be lost if the companies’ are as well run?

If destroying the businesses run by one of the richest men on the planet would only provide \$8 billion (less than 0.25 % of the \$3.5 trillion advertised price of Build Back Better), are the enough other fortunes that could be raped to fund the scam? And with so many business trashed and jobs lost, what would happen to income tax revenue?

Inquiring minds want to know.

# Quote of the Day

Our discombobulated lives need to sink some anchors in numerical stability. (I still have not recovered from the rise of a pound of hamburger at the supermarket to more than a buck.)

—Stephen Jay Gould

# Math is Hard—Logic is Harder—and Facts are Stubborn

Today, Joe Xiden said that 350,000,000 Americans have now been vaccinated against the Wuhan virus. Here’s a snapshot of the U.S. Census Bureau’s online population clock taken at 12:18:39 ET this afternoon—His Fraudulency is also encouraging those Americans who haven’t yet been vaccinated to get their shots.

I was going to write a longer post about vaccination records possibly being processed by the people who counted votes last November, but I’ve got real work to do.

Is it 2025 yet?

# The Physics of Filtering

When I was small child, our family lived in house without air-conditioning. We had screens on all the windows and an attic fan to cool the house. The gaps in the screens were small enough to prevent flies and mosquitos from entering the house. It would have been foolish to replace the screens with chain link fencing and expect that the bugs would still be kept out. A housefly has a wing span around 1/2 lnch, and the wires in chain link fencing are a couple of inches apart. The gap is about four times the size of a fly. A fly can easily pass through.

The gap between fibers in a typical cloth face mask is on the order of 2 to 3 micrometers. The coronavirus is on the oder of 0.3 micrometers.

The mathematics of the filtering is left to the Gentle Reader as an exercise.

# Math and Science Are Hard

I was puzzled by the CDC’s recent claim that the Wuhan Virus Pandemic had cased a one year drop in life expectance in the U. S. It turns out that their claim is so screwed up it isn’t even wrong. If life expectancy has dropped because of Covid, the decline is probably less than a week, an amount so small that it’s inside the roundoff error of the statistics. Eugene Volokh has a post up with details from a report by Dr. Peter Bach.

Analysts estimate that, on average, a death from Covid-19 robs its victim of around 12 years of life. Approximately 400,000 Americans died Covid-19 in 2020, meaning about 4.8 million years of life collectively vanished. Spread that ghastly number across the U.S. population of 330 million and it comes out to 0.014 years of life lost per person. That’s 5.3 days. There were other excess deaths in 2020, so maybe the answer is seven days lost per person.

No matter how you look at it, the result is a far cry from what the CDC announced.

It’s not that the agency made a math mistake. I checked the calculations myself, and even went over them with one of the CDC analysts. The error was more problematic in my view: The CDC relied on an assumption it had to know was wrong….

Apparently, 2 + 2 equals whatever the public health establishment needs it to be.

# Quote of the Day

Musica est exercitium arithmeticae occultum nescientis se numerare animi. Music is a hidden arithmetic exercise of the soul, which does not know that it is counting.

—Gottfried Leibniz

# Quote of the Day

There was a young fellow from Trinity,
Who took the square root of infinity.
But the number of digits,
Gave him the fidgets;
He dropped Math and took up Divinity.

—George Gamow

# Solving the Problem of Woke Math

There’s an excellent review of woke math over at Legal Insurrection. Go read it; it does a better job of summarizing the danger to our society.

However, I have a suggestion about how to shutdown woke math education in the schools. Simply calculate the pay of any teacher or education bureaucrat using or promoting woke math on the basis of 2 + 2 = 3.

# Quote of the Day

Thermodynamics is a funny subject. The first time you go through it, you don’t understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don’t understand it, but by that time you are so used to it, it doesn’t bother you any more.

—Arnold Sommerfeld

# A \$15 Dollar an Hour Minimum Wage is Racist

All the arguments that have been presented for increasing the minimum wage to 15 bucks an hour rely on claims that a lesser wage does not provided enough money to a worker. Such claims are based in the use of arithmetic to compute the worker’s financial status and implicitly endorse the proposition that there is such a thing as a “right answer.” However, it now received educational theory that the very idea of a “right answer” is a racist concept. Thus, in order to advance minorities and suppress white supremacy, it is vital that we not only defeat the Fight for Fifteen but also must also repeal the existing minimum wage laws that have been used as tools of oppression for decades.

# Don’t Know Much About Algebra

For those of you who don’t know the Sam Cooke song Wonderful World (the first line of that song is “Don’t know much about history …”), this is a line from the second stanza. I think it makes a good headline for a post about teachers who don’t understand math.

Fox reports that the Oregon Department of Educations is seeking to undo white supremacy in mathematics education. The minicourse being offered to teachers

includes a list of ways “white supremacy culture” allegedly “infiltrates math classrooms.” Those include “the focus is on getting the ‘right’ answer,” students being “required to ‘show their work,'” and other alleged manifestations.

“The concept of mathematics being purely objective is unequivocally false, and teaching it is even much less so,” the document for the “Equitable Math” toolkit reads. “Upholding the idea that there are always right and wrong answers perpetuate objectivity as well as fear of open conflict.”

I wonder how many of the education bureaucrats who are promoting the course would object to the calculations on their paychecks being done on the basis of 2 + 2 = 3.

# Unjust Justice

Rev. William Barber has a post over at In These Times about The Fight for a \$15 Minimum Wage Is a Fight for Racial Justice. He quotes a loose translation of the beginning of the 10th chapter of Isaiah in support of his argument—

Woe unto those who legislate evil and rob the poor of their rights, who make women and children their prey.

I agree with Rev. Barber that those of us who are better off have an obligation to treat the poor justly and to compassionately care for widows and the fatherless. However, I believe the minimum wage increase he supports will hurt rather than help the poor. Indeed, passing such a law will be legislating an evil.

The general effect of increasing the minimum wage is to price workers with marginal skills out of the labor market. Businesses don’t have bottomless funds from which they pay wages. They can only extract so much revenue from their customers, and that money must be divided among paying for inventory, rent, wages, and other expenses. A minimum wage bill doesn’t make expenses like rent disappear, so a business only has so much it can divide among its workers for payroll. When the law artificially increases each worker’s pay, simple arithmetic shows that fewer workers can be paid before the money is gone. Business that survive will keep their best employees and fire marginal workers. Business that grow will hire fewer workers.

Not every worker who loses his job because of a minimum wage increase will remain unemployed. Some will find work off-the-books in the informal economy, but increasing the minimum wage invariably increase unemployment among our poorest citizens.

We Americans generally believe that everyone has a right to work to support himself and family. Is it just to pass a law artificially pricing poor workers out of the labor market? I don’t think so.

# Math is Hard

According to Pennsylvania State Representative Frank Ryan (R-Lebanon), analysis of the November election show 6,962,607 total ballots were reported as being cast, but official system records indicated that only 6,760,230 total voters actually voted. The difference of 202,377 more votes cast than voters voting, together with the 31,547 over- and under-votes in the presidential race, is a discrepancy of 170,830 votes—more than twice the difference between Donald Trump’s and Joe Biden’s vote counts certified.

# Crudely Modeling Herd Immunity

So what is this “herd immunity” that people keep talking about?

It works something like this:

Adam becomes infected with some disease. We’ll call it Batpox for this example. It turns out that the statistics of Batpox’s transmissibility are such that it is about as contagious as measles. Measles has a basic reproduction number (R0) of about 12. When Adam goes to visit his friends Betty and Chuck, the odds are high that they will both become infected as well—unless they are already immune because of a previous encounter with the disease or a vaccine. OTOH, if enough of the people Adam contacts while he’s sick are immune to Batpox, the disease isn’t likely to spread any further. A population has reached herd immunity for a disease when enough of the population is immune to prevent the disease from easily spreading.

The percentage of population required for herd immunity is greater for larger values of R0. The formula for the approximate percentage of immune individuals necessary for herd immunity is

X = (1 – 1/Ro) X 100

For measles X is about 92 %. That’s why it’s important for kids to be vaccinated in order to get the number of immune individuals as high as possible.

The initial estimate of R0 for the Wuhan virus was around 2.7. That would imply that we’d need about 63 % of the population to be immune in order to achieve herd immunity. However, the Real World data for Covid-19 shows much lower values for R0. That’s values, plural, because different places have different factors that affect transmissibility.

Take a look at these charts of how R0 has varied over time in various states. (Source: rt.live) The solid lines represent the calculated values for R0 and the shaded areas around the lines show the confidence intervals for the calculations based on the amount and quality of the data. These plots are for entire states; the New York and Michigan numbers would be even lower with the effects of New York City and Detroit removed.

Note that these states have all achieved an R0 of about 1. Plugging that value into our formula for herd immunity gives a required immunity percentage of … pokes at calculator …  zero.

Now, I’ve been engaged in modeling here, and we know how problematic that can be, but I believe this gives us a hint about why people are ready to get back to their normal lives in large swaths of the country. Certainly, a value of R0 below 1 explains why the death toll hasn’t spiked in Georgia.

There are still places in the country struggling to contain the Wuhan virus outbreak, and they should be supported in their efforts. However, the data support letting the rest of the country get on with our lives.

# Bending the Curve

I went over the the Maryland Department of Health’s coronavirus website and found the daily numbers for confirmed new Wuhan virus cases and deaths. Here’s the data. The green bars are the daily raw numbers. That data is rather noisy. The blue lines are the 5-day moving averages.

First, the confirmed new cases day by day—

Second, the daily deaths—Eamining the case data, it looks as if the number of cases hasn’t diverged far from a linear rising slope. Projecting the trend present around the first of this month onward yields about the same rate as we actually have now. If the was exponential growth, the exponent wasn’t much more than 1. Maryland hasn’t turned the corner on new cases yet, but it appears that we’ve kept the rate of increase from exploding as it did in New York City.

The downward bend in the death rate over the last few days is a hopeful sign.

Maryland’s response to the pandemic hasn’t been perfect, but we have achieved better results than some without having to go to full-tilt, nanny-state fascist as have some jurisdictions. Now comes the hard part. We need to reengage the economy without reinvigorating the virus.

# Time Constants, Half-Lives, and Modeling

My podcasting partner Stacy McCain has a post up, MSNBC’s Doomsday Crisis Theme, that looks at the actual rate of increase in Wuhan virus infections and deaths in North Carolina and notes that they are increasing more slowly than the University of Washington’s Institute for Health Metrics and Evaluation model predicted.

Well, as someone who uses modeling as one of his principal professional tools, I’m not surprised. Mathematical models work well when they accurately describe the Real World system under study and they’re fed with data that represents the Real World system’s actual parameters. They’re like sewer pipes in that if you put garbage in, you’ll get garbage out.

Radioactive decay is a statistical process which is well described for every isotope of every element. Physicists speak of the half-life of an isotope meaning the time it takes for half of the atoms in a given sample of an isotope to undergo radioactive decay. Half-life doesn’t vary between two samples of the same isotope.

Now, consider the discharge of an electrical capacitor. The voltage across a discharging capacitor will drop at an exponential rate, and the value of that exponent is determined by the reciprocal of the product of the capacitance in farads and resistance in ohms. Because farad X ohm = second, engineers refer to that exponent as the circuit’s time constant. If I’m analyzing an electrical network that might have widely varying values of capacitance and resistance, my model will give me a broad range of possible time constants. Knowing the possible range of part tolerances (and how they might vary over time, temperature, phase of the moon, or whatever) is important in predicting how a circuit will perform.

While the models used to predict the spread of viral disease are relatively straightforward and perform reasonably well when driven with good data, the Covid-19 pandemic is too new for sufficiently good data to have been acquired.

Here’s what we do know—1.) The disease is spread by person-to-person contact. 2.) Taking little or no protective measures produced disastrous results in China, Iran, Italy, and Spain. 3.) Thus far, it appears that several protective schemes work well. See, e.g., Taiwan and South Korea. 4.) In the U. S., densely populated areas with more opportunities for person-to-person contact have seen the majority of cases.

So, here’s what I’m doing—I have complicating factors (age and coronary artery disease) that make me high risk. I live in a state (Maryland) that’s under a mandatory stay-at-home order, but I’ve been telecommuting since it became an option. My son does my shopping for me, and if I do go out, it’s at odd hours when I’m likely to see fewer people.

Do I think the lockdown is necessary? I don’t know. There isn’t enough data yet.

Several people have spoken of the response to the Wuhan virus pandemic as if it were a war. It isn’t, but there is one bit of wartime ethics which may be applicable. When we are at war, we know that some people will suffer and some will die in order to save other lives. At some point, shutting down the economy will cause ongoing problems that will weaken our ability to maintain and improve our agricultural, transportation, medical, and other business and infrastructural systems. That impoverishment, in turn, may sentence more people to misery and possible death (in the long term) than might be saved by continuing economic disruption. That will be a difficult choice if it comes.

I hope and pray that the pandemic will not be so severe that we have to face that sort of ethical dilemma. It appears that drugs are being found for treatment, and a vaccine is possible.

Meanwhile, I’m being careful.