Political Calculations
Unexpectedly Intriguing!
11 June 2021

Cuneiform is the world's oldest known writing system. It's also one of the most successful, because its use spans two-thirds of recorded human history. In the following 11 minute Numberphile video, Alex Bellos explains how to write numbers the way the Sumerians, Akkadians, Babylonians, Elamites, Hittites, Assyrians, and Hurrians did!

Be sure to check out The Biggest Math Story of 2020, in which we featured Matt Parker's video describing the world's first known math mistake, which also involves techniques for recording numbers that pre-date cuneiform writing. Just scroll down to the section on "A Year Defined by Mistakes".


10 June 2021

What percentage of the population needs to be vaccinated to usefully reduce the risk of dying from COVID-19?

We're going to do a back-of-the-envelope calculation to estimate the answer to that question using Arizona's high quality COVID data in general, and the state's data for COVID-related hospital admissions and deaths in particular.

We're also going to build off our previous analysis that synchronized Arizona's figures for the number of positive COVID infection test results, hospitalizations, and deaths according to the approximate date of initial SARS-CoV-2 coronavirus exposure for the Arizonans who became infected and experienced these pandemic-related events. The following chart shows these three streams of data using a logarithmic scale, covering the period from 15 March 2020 through 30 April 2021.

Arizona's Coronavirus Pandemic Experience, Rolling 7-Day Moving Averages of Cases, Hospital Admissions, and Deaths Indexed to Approximate Date of Initial SARS-CoV-2 Coronavirus Exposure, 15 March 2020 through 30 April 2021

We've annotated the chart to indicate two periods of "noise" in the data for deaths, which came into play when the daily number of COVID-related deaths of Arizonans dropped into the single digits. Because of the small numbers involved, having a relatively small change in the daily number can have an outsize effect on the appearance of the overall trend, which accounts for the "noisy" short-term trough that was recorded in mid-September 2020 and the short-term spike in late March 2021. We've added the dotted lines to these areas of the chart to indicate what the overall pattern would look like without the short term noise in the data.

Now to the bigger question. We're going to focus on the ratio of deaths to hospital admissions because these events represent the most serious classes of COVID infections. In Arizona, 75% of COVID-related deaths have occurred among the state's senior population, Age 65 or older. This same demographic has accounted for 46% of COVID-related hospital admissions in the state.

These figures confirm seniors are disproportionately vulnerable to both these outcomes if they become infected by the SARS-CoV-2 coronavirus. This fact is why this portion of the state's population was targeted for early COVID vaccinations once the vaccines became available.

Because the incidence of COVID-related deaths in concentrated in Arizona's senior population, we should see a sustained decline in the ratio of COVID deaths to hospital admissions corresponding to roughly when the population Age 65 or older achieved effective herd immunity. We can then identify what percentage of the state's elderly population had been received at least one vaccine dose at that point in time, which in turn, will give us a reasonable indication of what percentage of the population needs to be vaccinated for COVID to reduce its risk of death.

The next chart graphically shows the results when we combine these points of data together.

Arizona Ratio of Rolling 7-Day Moving Averages Deaths to Hospitalizations Indexed to Approximate Date of Initial SARS-CoV-2 Coronavirus Exposure, 15 March 2020 through 30 April 2021

We find at least 55% of the population would need to have received at least one dose of the COVID-19 vaccines to provide the benefit of reduced risk of death from becoming infected by the coronavirus. That's the percentage of the Age 65 and older population of Arizonans who had been vaccinated as of 28 February 2021, which marks the point in time at which COVID-related deaths in the state began to plunge as a result of the Operation Warp Speed vaccination programs.

That's the low end for our estimate, because it does not consider the portion of the senior population who would have obtained natural immunity from having become infected with the SARS-CoV-2 coronavirus and who recovered from it. As of 28 February 2021, Arizona's senior population accounted for 109,897 known COVID infections, about 13.4% of the state's total at that time. Added to the 696,559 Age 65 or older Arizonans who had received at least one COVID vaccination dose at that date would put the high end of the estimate at 64%.

That upper level figure would explain why public health officials have set a target of 70% of the population for COVID vaccinations, but it seems strange they are not giving more weight to the potential contribution of natural immunity in achieving that goal. If they did, they could focus their limited resources for providing COVID vaccination more effectively.

Looking at Arizona's data, we would say the magic percentage for vaccinations to achieve useful COVID herd immunity is somewhere between 55% and 64% of the population. That's because there is almost certainly a good amount of overlap between those who have recovered from COVID and those who have been vaccinated. It would be more beneficial and less wasteful for public health officials to target the COVID vaccines to those who have not developed any antibodies to SARS-CoV-2 coronavirus infections.


Arizona Department of Health Services. COVID-19 Data Dashboard: Vaccine Administration. [Online Database]. Accessed 10 June 2021.

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09 June 2021

Consumer prices are rising rapidly these days. Just last month, we found the discounted sale price of Campbell's Condensed Tomato Soup had risen to $0.96 per can, a rise of 13% above pre-pandemic levels.

One reason we track the price of Campbell's iconic tomato soup because the product itself has proven to be remarkably stable over time. If you stepped into a time machine and traveled back to nearly any point in time from January 1898 to the present, you could likely find the same 10.75 ounce size can of condensed tomato soup stocked for sale in American grocery stores.

That makes Campbell's iconic soup unlike other products, whose producers engage in a market tactic called shrinkflation, where they keep the sale prices the same, but shrink the size of the goods they sell. If the phrase sounds familiar, it is because the topic is increasingly popping up in the news.

There are lots of reasons for companies to engage in shrinkflation, but the end result is the same. You get less stuff for the same amount of spending. Whether its toilet paper, cat food, or packages of Hershey's chocolate kisses.

Things that don't change don't have that option. Unlike these other kinds of products, they cannot get away with shrinking the amount of goods inside their packaging. Because these goods cannot get smaller, producers are forced to pass along their higher costs from the escalating prices of the things they have to buy, which consumers see as rising prices. That difference makes these goods very useful for keeping track of how inflation is affecting your personal finances.

Speaking of which, keeping track of those price changes can be a time intensive activity. When we track Campbell's tomato soup prices, we review dozens of weekly ads to identify the prices at which retailers are selling them each time we update our database of monthly price data for the product. Our price database for Campbell's tomato soup extends back to January 1898.

With prices now escalating rapidly enough to become a regularly featured news topic, we were excited to find that Microsoft has introduced a new capability into its Edge web browser, which makes it easy to track the recent price history of products like Campbell's Condensed Tomato Soup. Here's the announcement from the rollout of Microsoft Edge's price history tracking capability:

Before making a purchase, I like to make sure that I’m getting the best deal possible. Because prices on certain items fluctuate over time, knowing when to buy can make all the difference. This is why I’m excited to share that, this month, Microsoft Edge is releasing a new feature called price history.  It shows me historical online prices to help me decide if I should wait a few days before making a purchase. To see an item’s price history, all you have to do is click on the blue tag in the address bar. Learn more about which retailers are supported. This is just another way we’re helping you save time and money.

In our case, it provides a very easy way to track recent price trends for our favorite inflation-tracking product! Here are two snapshots of what we found when we looked at its price history on 28 May 2021 and again, 10 days later, on 7 June 2021.

Shopping in Microsoft Edge: Campbell's Condensed Tomato Soup Price History, Snapshots on 28 May 2021 and 7 June 2021

Recognizing that we're looking at a limited sample of just three large retailers (Amazon, Wal-Mart, and Target), it's interesting to see the historical prices that MS Edge reports over the past month generally agree with what we've documented using our well-established tracking methods.

Obviously, there are more consumer goods than just Campbell's Tomato Soup to consider in assessing how fast inflation is growing in the U.S. At this writing, Microsoft Edge's price history tool pulls its data from products sold at eight large retailers, including Amazon, Wal-Mart, Etsy, Macy's, Nordstrom, Home Depot, Target, and Best Buy.

If you have Microsoft Edge, check out its price history tracking capability out for yourself by picking out a basket of goods and watching their price changes over time. If nothing else, you might get a very good idea of how today's inflation is directly affecting you and your quality of life.

Bonus update! Campbell Soup (NYSE: CPB) is reporting its previously projected profits will be negatively impacted by rising material and transportation costs. That confirmed upward cost pressure will make it less likely for significant discounting of tomato soup prices in the next several months, even as demand declines to its seasonal low.

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08 June 2021

Median new home sale prices continued rising faster than median household income in April 2021.

We can see that trend in the latest update to our chart tracking the ratio of the trailing twelve month averages of median new home sale prices to median household income. Through April 2021's preliminary estimates, we find the typical new home sold in the U.S. now costs 5.24 times the typical household income.

Ratio of Trailing Twelve Month Averages of Median New Home Sale Prices and Median Household Income | Annual: 1967-2019 | Monthly: December 2000-April 2021

We're introducing a new chart today to more clearly communicate the trends for the relative affordability of new homes sold in the U.S. Here, a rising trend corresponds with new homes becoming relatively more affordable, while a falling trend indicates new homes are becoming less affordable.

Relative Affordability of New Homes in U.S. | Annual: 1967-2019 | Monthly: December 2000-April 2021

Mathematically, the chart simply expresses the inverse of the data indicated in our chart showing the ratio of median new home sale prices to median household income as a percentage.

Since 1971, we find the relative affordability of new homes sold in the U.S. have been generally falling over time, which has periodically been punctated by short term periods where either fell faster than median household income, such as during the housing bust of 2006-2009, or when median household incomes rose much faster than new home prices, as in the period from late 2017 to early 2020.

The latest short term downtrend coincides with rapidly escalating prices combined with stagnant income growth. That combination is contributing to the fastest decline in the relative affordability of new homes recorded during the 21st century.


U.S. Census Bureau. Median and Average Sales Prices of New Homes Sold in the United States. [Excel Spreadsheet]. Accessed 5 June 2021.

Political Calculations. Median Household Income in April 2021. [Online Article]. 2 June 2021.

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07 June 2021

With the trading week shortened by the Memorial Day holiday, the S&P 500 (Index: SPX) mostly drifted sideways in the unofficial start of summer for the U.S. stock market.

Alternative Futures - S&P 500 - 2021Q2 - Standard Model (m=-5.0 from 11 May 2021) - Snapshot on 4 Jun 2021

Investors were therefore left with all the same unanswered questions they had coming into the week, although the weaker-than-expected jobs report on Friday, 4 June 2021 provided a signal the Fed is unlikely to begin pulling back its stimulative bond-buying activities until sometime later this year.

That was enough to bid stock prices up to close the week, but not to definitively resolve the questions investors have for the future. Meanwhile, the market moving headlines of the week that was reveal other factors investors were focusing upon.

Tuesday, 1 June 2021
Wednesday, 2 June 2021
Thursday, 3 June 2021
Friday, 4 June 2021

Barry Ritholtz succinctly summarized the positives and negatives he found in the markets and economy news of the holiday-shortened trading week!

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04 June 2021

The purpose of patent illustrations is very straightforward. They are intended to visually convey the novel features of an invention. Consequently, they tend to make for pretty dull, static presentations, even for inventions that themselves are dynamic in operation.

That's why the Inventions in Everything team gets excited whenever we come across a patent with illustrations that tell how an inventor conceives their invention will function through a sequence of illustrations. Or as we're about to see with U.S. Patent Number 5,781,936, which was issued to Jacob Alaloof on 21 July 1998, where a single figure from a patent tells an entire story. In this case, how the invention of an airbag suit for motorcyclists would function to protect their lives in an accident. The story is told from right to left....

U.S. Patent 5,781,936: Figure 1

Here is the background of the invention describing the problem the invention is intended to solve:

It is generally recognized that there is a greater risk of serious injury to motorcyclists in the case of an accident than to automobile passengers. This is due, inter alia, to the fact that, unlike automobiles, motorcycles are not equipped wiht protective systems which enclose users thereof. Accordingly, apart from injuries that may be caused to a motorcyclists by his colliding directly with a moving vehicle or stationary object, there is also a very high risk that, in the event of a collision between a motorcycle and either another vehicle or a stationary object, he will be thrown from the motorcycle. When this happens, the motorcyclist is liable to sustain fatal injuries or, at least, very serious damage to vital parts of the body, especially to the back, spine, neck and pelvis. This can result in very serious injurty thereto, if not paralysis or death.

And here's the description of the invention itself:

The present invention seeks to provide a protective system for riders of nonenclosed vehicles. The protective system is in the form of a garment which is automatically inflated to a force dissipating or deflecting shape in response to unintentional separation of the rider from his vehicle.

We would say the patent illustration ably captures both the scenario of the problem the invention is intended to solve and the solution.

Motorcyclist airbag suits are a real thing, which though not yet widely in use, have become more so during the past two decades as the technology has evolved toward greater practicality. FortNine's Ryan Kluftinger does a fantastic job of explaining the physics and the psychology of using an inflatable airbag suit while riding a motorcycle in the following under 10 minute video, which also provides a nice survey of today's state of the art in this invention category:

From the Inventions in Everything Archives

Here's a selection of previous inventions the IIE team has covered involving related technologies:

"Fishing for Boats" presents our animation of the patent illustrations provided in U.S. Patent 7,744,313.


03 June 2021

May 2021 continued the strong environment of the last few months for the U.S. stock market's dividend payers.

The easiest way we've found to measure the relative health of the U.S. stock market is to simply count the number of dividend cuts each month. Since 2012, with the arrival of a large number of variable dividend payers, we've found that if the number of dividend cuts and omissions is below 50 per month, the business environment for the firms listed on the U.S. stock market can be considered relatively healthy. If the monthly number of dividend cut declarations rises above 50, that's a very good indication that recessionary conditions are present within the U.S. economy. We can then can identify which industries are seeing the most distress during those periods by seeing which companies are announcing dividend cuts.

With that threshold in mind, we're now seeing perhaps the strongest environment for dividend paying stocks in the last 10 years, as defined by the relative absence of dividend cuts.

Number of Public U.S. Firms Increasing or Decreasing Their Dividends Each Month, January 2004 - May 2021

Here's the rest of May 2021's dividend metadata, complete with comparison to April 2021 and the year-over-year change from May 2020, which marked the bottom of the coronavirus recession for dividend cuts.

  • 1,853 U.S. firms declared dividends in May 2021, a decline of 166 from the 2,019 recorded in April 2021. That figure is also a decrease of 1,265 from the 3,118 recorded in May 2020.
  • Some 47 U.S. firms announced they would pay a special (or extra) dividend to their shareholders in May 2021, an increase of 8 over the number recorded in April 2021 and an increase of 25 over the 22 recorded in May 2020.
  • Standard and Poor counted 148 U.S. firms announcing dividend rises in May 2021, a decline of 7 from the 155 recorded in April 2021, and an increase of 83 over the 65 recorded in May 2020.
  • A total of 6 publicly traded companies cut their dividends in May 2021, a decline of 10 from the 16 recorded in April 2021 and also a decrease of 108 from the 114 recorded in May 2020.
  • One U.S. firm omitted paying their dividends in May 2021, the same as the number recorded in April 2021. That figure is also a decrease of 152 from the 152 recorded in May 2020.

Our sampling of dividend cuts from our real-time sources of dividend declarations for May 2021 captured 67% of all the cuts announced during the month. Which is to say four of the six:

We note that two of the four in our sample are oil royalty trusts that pay variable dividends from month to month, which falls well within the typical level of noise we see for these firms during periods of relative health for the U.S. economy. In this case, that comparative health is driven mainly by the lifting of coronavirus pandemic lockdown mandates in much of the country.

Update 6 June 2021: A reader alerts us the article reporting a 75% dividend cut for Mosaic (also linked above) is in error. We've confirmed that Mosaic increased its regular dividend from its previous level of $0.050 per share to $0.075 per share in June 2021.


Standard and Poor. S&P Market Attributes Web File. [Excel Spreadsheet]. 28 May 2021.

Seeking Alpha Market Currents. Filtered for Dividends. [Online Database].

Wall Street Journal. Dividend Declarations. [Online Database when searched on the Internet Archive].


02 June 2021

Political Calculations' initial estimate of median household income in April 2021 is $67,788, an increase of $1,542 (or 2.3%) from the initial estimate of $66,248 for March 2021.

The latest update to the chart tracking Median Household Income in the 21st Century shows the nominal (red) and inflation-adjusted (blue) trends for median household income in the United States from January 2000 through April 2021. The inflation-adjusted figures are presented in terms of constant April 2021 U.S. dollars.

Median Household Income in the 21st Century: Nominal and Real Modeled Estimates, January 2000 to April 2021

April 2021's jump in median household income is being accompanied with rapidly rising inflation, which is eroding the purchasing power of American households. That observation is brought home in the following chart, where we find that while the year-over-year growth rate of nominal median household income has turned positive, when adjusted for inflation, it is continuing the recessionary decline.

Median Household Income in the 21st Century: Year Over Year Growth Rates, January 2000 to April 2021

Analyst's Notes

The BEA's estimates for aggregate wage and salary data in October 2020 through March 2021 were revised significantly upward from the Bureau's previous estimates. The upward revisions ranged from a low of an increase of 1.1% for October 2020 to a high of 2.2% for February 2021, with March 2021's estimate increased by 2.1%. The revisions suggest a stronger economy in the U.S. than previously reported during this period.


U.S. Bureau of Economic Analysis. Table 2.6. Personal Income and Its Disposition, Monthly, Personal Income and Outlays, Not Seasonally Adjusted, Monthly, Middle of Month. Population. [Online Database (via Federal Reserve Economic Data)]. Last Updated: 28 May 2021. Accessed: 28 May 2021.

U.S. Bureau of Economic Analysis. Table 2.6. Personal Income and Its Disposition, Monthly, Personal Income and Outlays, Not Seasonally Adjusted, Monthly, Middle of Month. Compensation of Employees, Received: Wage and Salary Disbursements. [Online Database (via Federal Reserve Economic Data)]. Last Updated: 28 May 2021. Accessed: 28 May 2021.

U.S. Department of Labor Bureau of Labor Statistics. Consumer Price Index, All Urban Consumers - (CPI-U), U.S. City Average, All Items, 1982-84=100. [Online Database (via Federal Reserve Economic Data)]. Last Updated: 12 May 2021. Accessed: 12 May 2021.


01 June 2021

The Fed's minions worked overtime early last week to convince investors the surge of inflation confronting U.S. consumers won't cause them to prematurely take away their proverbial stimulus bond-buying punch bowl.

That was enough to prompt investors to bid up the value of the S&P 500 (Index: SPX) up toward the 4,200 level.

Alternative Futures - S&P 500 - 2021Q2 - Standard Model (m=-5.0 from 11 May 2021) - Snapshot on 28 May 2021

But the closer it got, and especially once it crossed that line, the Fed's minions started really talking up how they want to talk about how and when they'll take away their proverbial punch bowl.

There was more stuff that happened in the past week, but as you'll read in the summary of market moving headlines below, that description that the Fed has started talking about talking about tapering its stimulus bond buys pretty much summarizes all the U.S. stock market's action ahead of the Memorial Day holiday weekend.

Monday, 24 May 2021
Tuesday, 25 May 2021
Wednesday, 26 May 2021
Thursday, 27 May 2021
Friday, 28 May 2021

What positives and negatives did Barry Ritholtz see in the markets and economy news heading into the Memorial Day holiday weekend? Click through to find out!

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