Political Calculations
Unexpectedly Intriguing!
29 January 2021

Modern humans (Homo sapiens) and Neanderthals (Homo neanderthalensis) were very similar. So similar, in fact, that modern human DNA contains portions of Neanderthal DNA from interbreeding, which in a sense, has allowed the otherwise extinct Neanderthal species to survive into the present day.

And yet, despite sharing 99.5% of modern human DNA, if you were to run into a time-traveling Neanderthal today, you couldn't help but notice some very large differences between them and modern humans like yourself.

We've been working on a fun project to quantify some of those differences. To do that, we've adapted the math that some models and cosmetic surgeons use to measure how close the proportions of their facial features come to matching the so-called "golden ratio" of 1.62, which, for whatever reason, is held up as an ideal standard for quantifying beauty.

How well do you think a Neanderthal man might measure up by that standard?

Wonder no more, because we've built a tool to do the math! The only thing we're missing is a representative Neanderthal man whose facial features we can measure, which may be difficult to come by because Neanderthals have been extinct for tens of thousands of years.

That's where the modern anthropological reconstructions from phyiscal Neanderthal remains comes in very handy. Speaking of which, it's time to meet Mr. N.

Mr. N, with facial dimension measurement points added

Mr. N represents the hard work of the anthopologists of the Neanderthal Museum in Mettmann, Germany to reconstruct the physical features of a Neanderthal man from their remains. We've added the numbered dots to the image to provide a reference for taking the measurements indicated in the following tool, which we're going to use to compare with modern humans. If you're reading this article on a site that republishes our RSS news feed, please click here to access a working version of the tool!

Facial Proportion Data
Input Data Values
A: Top-of-Head to Chin (Point 1 to Point 2)
B: Top-of-Head to Pupil (Point 1 to Point 3)
C: Pupil to Nose-tip (Point 3 to Point 4)
D: Pupil to Lip (Point 3 to Point 5)
E: Width of Nose (Point 6 to Point 7)
F: Outside Distance between Eyes (Point 8 to Point 9)
G: Width of Head (Point 10 to Point 11)
H: Hairline to Pupil (Point 3 to Point 12)
I: Nose-tip to Chin (Point 2 to Point 4)
J: Lips to Chin (Point 2 to Point 5)
K: Length of Lips (Point 13 to Point 14)
L: Nose-tip to Lips (Point 4 to Point 5)

Facial Proportion Ratios
Calculated Ratios Values
A (Top-of-Head to Chin) to G (Width of Head)
B (Top-of-Head to Pupil) to D (Pupil to Lip)
I (Nose-tip to Chin) to J (Lips to Chin)
I (Nose-tip to Chin) to C (Pupil to Nose-tip)
E (Width of Nose) to L (Nose-tip to Lips)
F (Outside Distance between Eyes) to H (Hairline to Pupil)
K (Length of Lips) to E (Width of Nose)
Overall Average

In the tool, we've used pixels as our basic unit of measure, but you can substitute other units provided you use them consistently. If you wanted to hold a ruler up to the screen to measure in millimeters or inches, or if you simply printed a copy of Mr. N's picture or used the picture of another reconstructed Neanderthal individual to take measurements offline with your preferred measuring device, you can!

For modern humans, each of the indicated ratios should, "ideally" (we're putting it in quotes because its very arbitrary), come pretty close to the golden ratio of 1.62. As you can see from the results from our default data, Mr. N's data varies quite a lot away from the golden ratio, where the average of all seven ratios of facial parameters comes in at 1.23.

If an overall average score of 1.62 defines "perfect" modern human facial proportions for all these features, Mr. N's difference of 0.39 from this value would mean he misses the "perfect modern human" mark by 24%. And for what it's worth, while using the golden ratio to assess the 'beauty' of a modern human is a really dicey proposition, we can use it as an arbitrary reference for quantifying differences in facial features between modern humans and Neanderthals. But only if we know what range of values would apply for these ratios for all modern humans, not just the "perfect" ones.

Facial features are far from the only physical difference between Neanderthals and modern humans. We'll leave you with a short clip from a 2009 BBC documentary, in which a talented voice actor works to mimic what vocal experts believe Neanderthals would have sounded like based on the physiology of their remains. It's also one of the funniest things we've ever seen or heard that's based on the best available scientific evidence of the day.

HT: Adam Rutherford.

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28 January 2021

Our experiment using the relationship between a company's market cap and its forward year aggregate dividends is overdue for an update. When we last left off, we had narrowed in on where we expected the market cap for General Electric (NYSE: GE) would range based only on the historic relationship between GE's market cap and its aggregate dividends established in the period from 12 June 2009 through 8 December 2017. The idea being to project where GE's market cap might go if it were to slash its dividend, which it ultimately did. The following chart shows what that looks like, but updated with data through the end of 2020, with a bonus data point for where GE's market cap stood as of the end of trading on Monday, 26 January 2021.

GE Market Cap vs Forward Year Aggregate Dividends at Dividend Declaration Dates, 12 June 2009 - 11 December 2020

As modeled relationships go, that's pretty clunky. And since we have collected a lot more data points in the period since GE's 2018 dividend cut, we updated the model to include all the data from 12 June 2009 through 11 December 2020. The next chart shows what the updated model now looks like:

GE Market Cap vs Forward Year Aggregate Dividends at Dividend Declaration Dates, 12 June 2009 - 11 December 2020

We're also using some basic statistics to show the upper and lower level of what the variation in the historic data indicates is the 'typical' range in which the observations will fall. We've set those levels to be two standard deviations away from the main trend line, within which we would expect the data to fall 95% of the time, assuming the variation can be described by a normal distribution.

As of 27 January 2021, GE's market cap was just above where it was when it last declared dividends on 11 December 2020, which falls within the upper end of the expected range. Should GE's stock price rise above the indicated upper level, unless it is accompanied by the serious prospect of a dividend increase, it could indicate that the company's stock has become relatively overvalued, which would be a strong signal to sell.

So how do you read GE's announcement of its improving cash flow from 26 January 2021? Since a firm's ability to pay dividends depends both on its earnings and cash flow, the rise of GE's cash flow during 2020-Q4 marks a potential turnaround for the long-troubled company. If sustained, GE will be able to afford a dividend rise.

Is that what's going on here? Because if it isn't, the argument that shares of GE are becoming overvalued and its nearing time to sell becomes stronger if its shares are really trading within the vertical range they have since 2018.

Considering this information, if you were an investor holding shares of GE, how would you make your investment decisions?

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27 January 2021

The average discounted sale price of a Number 1 can of Campbell's Condensed Tomato Soup jumped 13 cents per can during 2020, rising from $0.86 to $0.99 from March through December as the coronavirus pandemic worked its way to, then through the U.S.

For the latest in our coverage of Campbell's Tomato Soup prices, follow this link!

In essence, what happened is that increased consumer demand for Campbell's Tomato Soup during the pandemic led grocers to stop discounting their sale prices for the product as reflected in their weekly ads. Here's the latest update to our chart tracking the average discounted sale price of Campbell's iconic cans of tomato soup from January 1898 through January 2021.

Unit Price per Can of Campbell's Condensed Tomato Soup at Discounted Sale Pricing, January 1898 - January 2021

That situation may be starting to change in 2021, but in a way we think is very specifically attributable to the pandemic. In January 2021, we noted weekly ad circulars putting Campbell's tomato soup on sale at a 50% discount compared to their shelf pricing, with the 10.75-ounce cans carrying a unit price of 50 cents.

Winter months typically represent the peak season for purchases of Campbell's tomato soup, so these sales represent a very atypical event. We quickly found the reason for the discounts after visiting several grocery stores in a region that has been greatly affected by the winter surge in COVID-19 cases, where we found the coronavirus pandemic has prompted a shift in consumer demand:

Political Calculations: Relative Supply of Campbell's Condensed Tomato and Chicken Noodle Soups, January 2021

As you can see in the this picture, Campbell's Chicken Noodle is sold out, while there are ample supplies of Campbell's Tomato Soup. What this indicates is that consumers in this coronavirus-hit area have developed a strong preference for Chicken Noodle soup, which many perceive help relieve cold and flu symptoms.

The pandemic-influenced shift in consumer preference accounts for the relative oversupply of tomato soup with respect to chicken noodle soup, and thus, the atypical sale prices for Campbell's Tomato Soup at this point of the pandemic.

Altogether, all this means is that the pandemic has not changed the laws of supply and demand.

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26 January 2021

From time to time, we take on the challenge of telling a very big story with a single chart. Today, we're taking on the economic story of the coronavirus recession in the United States, as seen through the lens of the relationship between the S&P 500 (Index: SPX) and its trailing year dividends per share. Here's the chart.

S&P 500 Index Value vs Trailing Year Dividends per Share, 30 September 2019 through 22 January 2021

For the chart, we've arbitrarily picked up the story from the end of the third quarter of 2019 to illustrate that the story of the coronavirus pandemic in the United States began during a relative period of order for the U.S. stock market. The current period of disorder began shortly after the market peaked on 19 February 2020, when investors began shifting their forward-looking focus from the distant future quarter of 2020-Q4 toward the nearer term future of 2020-Q2. This shift in the forward time horizon of investors was prompted by expectations the Federal Reserve would soon be forced to slash short term interest rates in response to the developing global economic slowdown caused by the coronavirus pandemic.

After 23 March 2020, the market underwent a regime change caused by the Fed's aggressive response and the U.S. government's fiscal stimulus to provide relief for the pandemic's economic disruption, in which the Fed would employ its quantitative easing tools to underwrite and finance nearly all the U.S. government's deficit spending at near-zero interest rates. That regime change effectively reset the relationship between stock prices and their underlying fundamentals, making it possible for stock prices to rise while dividends have fallen.

How long that state of affairs might be sustained remains to be seen.

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25 January 2021

The S&P 500 (Index: SPX) popped to new highs in the third week of January 2021, before tailing off on Friday, 22 January 2021 to close 11.60 points below its new high mark of 3,853.07.

The news that caused the new record high came from Netflix (NASDAQ: NFLX). The company reported outstanding quarterly results and announced they had surpassed over 200 million subscribers. More significantly, with so many paying customers, the firm announced it will no longer need to borrow to finance its development of new programming. That change will boost the company's profitability going forward, with the news sending its stock price 10.6% higher because of the associated change in its future expectations. The company's market capitalization likewise surged to 0.8% of the entire value of the S&P 500, contributing a significant portion of the index' gains during the week.

Here is the latest update to the alternative futures chart.

Alternative Futures - S&P 500 – 2021Q1 - Standard Model (m=+1.5 from 22 September 2020) - Snapshot on 22 Jan 2021

We think investors are still mostly focusing on 2021-Q2 as they set current day stock prices, although it's possible they may have shifted some their focus toward a more distant time horizon in conjunction with Netflix' change in future expectations. We'll find out over the next two weeks how things settle out for the S&P 500, where the onset of new information will set the tune to which index dances.

Speaking of which, here are the past week's more notable market-moving headlines.

Tuesday, 19 January 2021
Wednesday, 20 January 2021
Thursday, 21 January 2021
Friday, 22 January 2021

Elsewhere, Barry Ritholtz outlines the positives and negatives he found in the markets and economics news of the market holiday-shortened week that was!

Update 27 January 2021 9:56 PM Eastern: Things settled out in the markets more quickly than we anticipated. According to the dividend futures-based model, today's 2.6% drop in the value of the S&P 500 directly coincides with what would be expected if investors had previously set their forward looking focus on 2021-Q4, then suddenly refocused it on the much nearer term of 2021-Q2. Here's what that looks like on a mid-week update to our alternative futures spaghetti forecast chart:

Alternative Futures - S&P 500 – 2021Q1 - Standard Model (m=+1.5 from 22 September 2020) - Snapshot on 27 Jan 2021

According to the news, it was the worst day for stock prices since October 2020. From our perspective, had investors reset their investment horizons on 2021-Q1 instead of 2021-Q2, the S&P 500 could have fallen another 5%, which would be a more impressive Lévy flight event than the relatively small one we saw today.

But what new information might compel investors to become so myopic?

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22 January 2021

You know what quantum tunneling is, right? That physical phenomenon that makes it possible for electronic components like semiconductors, transistors and diodes to work and also for the sun to shine?

You don't? What if you could get up to speed with what it is in just three minutes? Would you want to know more?

If so, we'll point you to the work of Maryam Tsegaye, a high school senior in Fort McMurray, Alberta, who has become the first Canadian to win the International Breakthrough Junior Challenge with her short video explaining what quantum tunneling is. Here's the video, where the math of probability plays a prominent role:

Here's some of the backstory for how she came up with her presentation:

Tsegaye said her original plan was to make a video about entropy, but she stumbled upon quantum tunnelling and thought she could tell a "much better story" about it.

The tricky part was finding a story that would make the theory digestible.

"I knew that I couldn't just throw some mathematical equation at you or a bunch of scientific jargon you wouldn't understand," Tsegaye said.

"That's how the dice came along, because quantum mechanics has to do a lot with probability."

Now, if you want a simple introduction to probability, that will take an 11-and-a-half-minute video to get you going (the dice show up after the 2:45 mark):

There are a lot of useful things you can do with probability math. Here's a sampling of where we've used it here on Political Calculations:


21 January 2021

The last two weeks of COVID-19 data from Arizona suggests the state's second wave of cases has peaked and has begun receding.

The origins of that second wave can be traced back to political campaign activities held throughout the political swing state during the two weekends prior to the 3 November 2020 election. These events triggered an explosion in new coronavirus infections well above and beyond what had previously been a slow and steady rise in the number of coronavirus infections following the September 2020 reopening of high exposure risk businesses in the state.

Arizona's COVID-19 cases grew rapidly as new infections spread beyond the participants in these activities. But that began to change after news reports began focusing on the surge of COVID-19 patients at Arizona Intensive Care Units in early December 2020. We think those reports prompted Arizonans to resume social distancing and good hygiene practices they had previously adopted during the state's first COVID-19 wave in the early summer of 2020, which succeeded in slowing the rate of growth of new cases.

But it wasn't until Christmas came and went, and with it, the period where holiday-related shopping activities and social gatherings contributed to the ongoing spread of COVID-19 cases, that the second wave of COVID-19 cases in Arizona crested and began to recede. At least, that's what the data reported over the last two weeks indicates, which the charts showing Arizona's data for newly confirmed cases by sample collection date, daily ICU bed usage, deaths by death certificate date, and new hospital admissions, covering the period from 3 March 2020 through 19 January 2021. Although the lag from exposure to change in trend for each chart is different, the back calculation method for each confirms the timing of significant events for the progression of SARS-CoV-2 coronavirus infections in Arizona. [Please click on the preceding links or the following images to access full size versions of the charts.]

Arizona COVID-19 Confirmed Cases by Sample Collection Date, 3 March 2020 - 19 January 2021
Arizona COVID-19 ICU Bed Usage, 3 March 2020 - 19 January 2021
Arizona COVID-19 Deaths by Death Certificate Date, 3 March 2020 - 19 January 2021
Arizona COVID-19 New Hospital Admissions, 3 March 2020 - 19 January 2021

Of these charts, only the chart showing Arizona's ICU Bed Usage is fully current. Data for the other three charts are incomplete, where the most recent three weeks shown will be subject to revision during the next few weeks, especially for the most recent dates indicated on the charts.

Notes of Interest

Readers following this series will catch that we're no longer indicating "Event J" on these latest charts. Event J refers to Arizona Governor Doug Ducey's 3 December 2020 restriction on high-attendance events, which proved to have little-to-no impact on the trends for COVID-19 cases in the state.

We are however showing T* to indicate the timing of the Thanksgiving holiday and X* to indicate the Christmas holiday. These events, in and of themselves, had a very noticeable impact on whether Arizonan's sought to be tested for coronavirus infections, which shows up in the chart for confirmed cases. Here, it appears many Arizonans who became sick during these periods delayed seeking COVID-19 tests during the holidays and subsequent weekends, waiting until the following Mondays to be tested.

By contrast, there are slight dips in the data for new hospital admissions and for deaths in the lagging periods associated with the holidays, but these don't greatly deviate from the overall trends.

We've attributed the deceleration and peak in Arizona's second COVID-19 wave to increased social distancing and hygiene practices (standing apart in public, washing hands, etc.). Reports indicate Arizonans have generally maintained a high level of face mask-wearing since the state's first surge in cases in the early summer of 2020, while social distancing and hygiene practices waned. Overall, the evidence suggests social distancing and good hygiene are more effective in avoiding new COVID-19 infections than face masks alone. But we have to emphasize again, the best way to avoid COVID-19 is to avoid contact with political activists.

Unless something changes, we anticipate the next update to this series will confirm Arizona has entered a downward trend for coronavirus infections.

Previously on Political Calculations

We've been covering Arizona's experience with the coronavirus pandemic since the state first became a national hotspot early in the summer of 2020. Here's our previous Arizona coronavirus coverage presented in reverse chronological order, with a sampling of some of our other COVID analysis!


We've continued following Arizona's experience during the coronavirus pandemic because the state's Department of Health Services makes detailed, high quality time series data available, which makes it easy to apply the back calculation method to identify the timing and events that caused changes in the state's COVID-19 trends. This section links that that resource and many of the others we've found useful throughout the coronavirus pandemic.

Arizona Department of Health Services. COVID-19 Data Dashboard. [Online Application/Database].

Maricopa County Coronavirus Disease (COVID-19). COVID-19 Data Archive. Maricopa County Daily Data Reports. [PDF Document Directory, Daily Dashboard].

Stephen A. Lauer, Kyra H. Grantz, Qifang Bi, Forrest K. Jones, Qulu Zheng, Hannah R. Meredith, Andrew S. Azman, Nicholas G. Reich, Justin Lessler. The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application. Annals of Internal Medicine, 5 May 2020. https://doi.org/10.7326/M20-0504.

U.S. Centers for Disease Control and Prevention. COVID-19 Pandemic Planning Scenarios. [PDF Document]. Updated 10 September 2020.

COVID Tracking Project. Most Recent Data. [Online Database]. Accessed 15 December 2020.

More or Less: Behind the Stats. Ethnic minority deaths, climate change and lockdown. Interview with Kit Yates discussing back calculation. BBC Radio 4. [Podcast: 8:18 to 14:07]. 29 April 2020.

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20 January 2021

From time to time, we like to present a snapshot of what the future for the S&P 500's quarterly dividends per share looks like. Here is what investors were expecting as of the close of trading on Friday, 15 January 2021, just ahead of the presidential transition in the United States.

Past and Projected Quarterly Dividends Futures for the S&P 500, 2019-Q4 through 2021-Q4, Snapshot on  15 January 2021

As the Operation Warp Speed rollout of the SARS-CoV-2 coronavirus vaccines continues, and as several state and local governments come to recognize their lockdown policies are not beneficial, we would anticipate the projections of future quarterly dividends will increase as the business outlook improves. But we'll see what happens as the year progresses!


CME Group. S&P 500 Quarterly Dividend Index Futures. [Online database]. Accessed 15 January 2021.


The CME Group's S&P 500 dividend futures are based on futures contracts that cover the period of time through the third Friday of the month ending their indicated quarter, when they expire. By contrast, Standard & Poor reports the amount of dividends paid out per share over the course of a calendar quarter, which is why these two sources often indicate different values.

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19 January 2021

Two weeks ago, the U.S. stock market seemed taken with the idea of the Biden administration's promise of trillions in new spending for coronavirus pandemic relief, sending the S&P 500 (Index: SPX) to a new record high.

But that changed last week, after the incoming Biden admininstration announced its stimulus package would total $1.9 trillion, which requires rounding upward to count as "trillions". Worse, the details of the proposal indicate that much of these funds will be spent wastefully. The measure also aims to boost the federal minimum wage to $15 per hour, which while expected to benefit 1.0 million Americans, would contribute to a projected loss of 1.3 million jobs.

Overall, investors were left with the disappointing impression that the Biden stimulus will do little to improve the nation's economic situation, which increases the uncertainty that it can pass in its current form.

That increase in uncertainty led investors to shift a portion of their forward looking focus of investors from 2021-Q2 inward to the current quarter of 2021-Q1, sending stock prices down from the previous week after the details of the Biden stimulus were announced. The latest update to the alternative futures chart based on the dividend futures-based model shows that shift.

Alternative Futures - S&P 500 - 2020Q4 - Standard Model (m=+1.5 from 22 September 2020) - Snapshot on 15 Jan 2021

In other news, the minions of the Federal Reserve were especially active in trying to shape future expectations, which for them, means little-to-no change in monetary policy in 2021. Here are the headlines we noted for their market-moving potential during the second week of January 2021.

Monday, 11 January 2021
Tuesday, 12 January 2021
Wednesday, 13 January 2021
Thursday, 14 January 2021
Friday, 15 January 2021

Want a second opinion on what the big news items of the past week were? Barry Ritholtz delivers the positives and negatives he found in the markets and economics news the way only he can!

Also, if you ever need to put a picture together of events that influenced the U.S. stock market, check out the earlier entries of our S&P 500 chaos series. Political Calculations is your curated resource for market history in near-real time!

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15 January 2021

What do modern superheroes wear under their costumes?

We know that's an odd question, seeing as many superheroes in the comics follow the tradition of wearing their underwear on the outside of their outfits. However, Katherine P. Rutherford's 2004 invention of a Ballistic Resistant Body Covering would appear to provide a new reason to reconsider the question.

At least, that's what the IIE team cannot help but think after reading the description of the preferred embodiment in U.S. Patent 6,745,394, which we also canot help but think is clearly meant to appeal to any current day superhero (wink, wink):

In use, the device 10 is worn on the body of the user and the various portions coupled together. The device protects the body from ballistic missiles over a large portion of the body including the torso, groin and neck area.

As to a further discussion of the manner of usage and operation of the present invention, the same should be apparent from the above description. Accordingly, no further discussion relating to the manner of usage and operation will be provided.

Of course, the thing that really sells Rutherford's invention can be found in Figure 1 of the patent, where our well-protected prospective superhero oozes with enough superconfidence to project the phrase: "Well, hello there!"

U.S. Patent Number 6,745,394 Figure 1

Rutherford leaves it to the prospective wearer to determine how her invention should be worn. Whether that's over or under your regular costume is entirely up to you.

Inventions in Everything: The Archives

Ready to sample more of the most creative designs and patents the Inventions in Everything team has explored? Our archives celebrate inventions ranging from the whimsical to the inspired in reverse chronological order!


About Political Calculations

Welcome to the blogosphere's toolchest! Here, unlike other blogs dedicated to analyzing current events, we create easy-to-use, simple tools to do the math related to them so you can get in on the action too! If you would like to learn more about these tools, or if you would like to contribute ideas to develop for this blog, please e-mail us at:

ironman at politicalcalculations

Thanks in advance!

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