What were the biggest empires in world history? How long did they last? How much land was under their control?

Now, answer each of those questions and present the results on a single infographic....

That was one of the challenges the Michigan Geographic Alliance has taken on and in 2010, they produced a remarkable visualization to present the ebb and flow of empires over the millenias of human history. Here's the result of their work as featured at Visual Capitalist:

The Michigan Geographic Alliance has a Google Drive site where you can get a PDF versions of the World Geohistogram along with educational material to support lesson plans associated with it.

The visualization contains some surprising insights. For example, many will think of the Roman Empire as having been one of the largest in world history, which is true, but it didn't cover as much territory as Alexander the Great's short-lived Greek empire that preceded it.

The largest empires were those of European nations in the period from 1492 to the 1960s, but this is misleading because they were not under a single power. The British Empire was the world's largest ever, which at its peak, controlled about a quarter of the world's landmass, but it didn't control the 8.5% of the world's land that was controlled by France. Nor did it control territories under the sway of the Dutch, Spanish, Portuguese, Belgians, Germans, Russians, etc.

Meanwhile, the smallest and shortest-lived featured empire belong to the Hittites during the Bronze Age nearly two and a half-centuries ago, which aside from its interactions with other empires, has become overshadowed by them and their successors since its collapse.

Another Visualization

UsefulCharts' Matt Baker also built a chart tracking the rise and fall of empires through history, which is similar but different in significant ways. In the following video, he talks through what his version of much of the same information conveys.

Baker's presentation is more of a "subway map" style of presentation, which focuses on connecting events in time. While the Michigan Geographic Alliance's version shares that characteristic, it also provides visual cues to convey the scale of the empires it features, which we think gives it an edge in communicating vital information about the relative size of the empires it tracks through history.

Reference

Jeff Desjardins. The World’s Biggest Empires of History, on One Epic Visual Timeline. Visual Capitalist. [Online article]. 16 November 2025.

Colin Marshall. A Visual Timeline of World History: Watch the Rise & Fall of Civilizations Over 5,000 Years. OpenCulture. [Online article]. 18 December 2025.

The S&P 500 (Index: SPX) sank in the early part of the third week of December 2025 as fears of whether the returns on investments being placed on AI-technology can overcome the debt that several high-profile firms like Oracle (NASDAQ: ORCL) are taking on to make them.

While the index bottomed at 6,721.43 at the close of trading on Wednesday, 17 December 2025, it went on to recover strongly by the end of the week. The index reached 6,834.50 by the close of trading on Friday, 19 December 2025.

That recovery in the latter part of the week came thanks in no small part to computer chipmaker Micron Technology (NASDAQ: MU) boosting its outlook on the strength of its AI-related order book and because the shutdown-delayed inflation data for November 2025 came in much lower than expected. The news about inflation would seem to clear a path for the Federal Reserve to continue reducing the Federal Funds Rate in 2026.

But that's in question. Because the Senate Democrats' shutdown fiasco affected the collection of a good portion of data for the November consumer price index report, there are questions about how well the Bureau of Labor Statistics was able to capture how prices changed.

If there's one thing Wall Street's bulls and bears can agree on, is that they want better quality data on which to stake their investments. If that's not already on their 2026 wish list for Santa Claus, it should be. 2025 has been a year in which the shortcomings of how government agencies collect and report economic data have been laid bare with much needing to be fixed.

That's enough editorializing! Here's the latest update to the alternative futures chart, in which we've added a new redzone forecast range to project the most likely trajectory stock prices will take through the end of 2025.

We add redzone forecast ranges to the alternative futures chart when we know in advance the dividend futures-based model's projections will be affected by the echoes of past volatility in stock prices. This is a forecasting challenge that arises because the model incorporates historic stock prices as the base reference points from which it projects the potential futures.

The new redzone forecast range bridges across the period in which past volatility in stock prices will cause the model to undershoot the path the S&P 500 will most likely take. One end of the forecast range is anchored on 18 December 2025, while the other will float based on the projections for 23 January 2026. We assume investors will focus their forward-looking attention on 2026-Q2 during this time.

That's because of the how the expectations for how the Fed will set the Federal Funds Rate in 2026 are changing. The timing of the next expected rate cut has been fluctuating in recent weeks and although the CME Group's FedWatch Tool anticipates quarter point rate cuts on 18 March (2026-Q1) and 29 July (2026-Q3), with no other rate cuts projected in 2026, that first rate cut has the potential to slide into 2026-Q2.

How far investors are looking into the future as they make their current day investing decisions can have a large effect on stock prices and often depends on the random onset of new information. Speaking of which, here are the market-moving headlines that influenced those decisions during the third week of December 2025.

Monday, 15 December 2025

• Signs and portents for the U.S. economy:
• Oil prices fall as supply outlook offsets disruptions in Venezuelan flows
• An ounce of silver now buys you a barrel of oil
• Favorites emerging to be next Fed boss:
• Trump says he is leaning toward Warsh or Hassett to lead the Fed, WSJ reports
• JPMorgan's Dimon signals support for Kevin Warsh as Fed chair, FT reports
• Fed minions satisfied after solving all of nation's economic problems with perfect monetary policy execution:
• Williams says Fed policy in good position, sees inflation moderation in 2026
• Fed's Collins says supported rate cut but it was a 'close call'
• Fed's Miran: Current inflation not reflective of supply and demand in the economy
• Fed decisions distorted by ‘phantom inflation’, says Stephen Miran
• Bigger trouble developing in China:
• China's Economy Is Deteriorating on Several Fronts
• China's economy stalls in November as calls grow for reform
• Xi Blasts "Reckless" Projects Exaggerating Growth After China Reveals Dismal Macro Data For November
• EU minions back off plan to ban fossil fuel-powered cars in 2035:
• EU yields to pressure from automakers as it rethinks 2035 combustion car ban
• Wall Street ended lower as investors eye a busy week of economic data
• Wall St closes lower as investors position for busy week of data
• Exclusive: Nasdaq seeks to extend trading hours, as Wall Street gears up for 24/7 move

Tuesday, 16 December 2025

• Signs and portents for the U.S. economy:
• US unemployment rate hits four-year high of 4.6%
• US job growth snaps back in November; shutdown distorts unemployment rate
• US rate futures briefly raise odds of January rate cut after jobs data
• US jobless rate for Blacks and teens surges in November
• U.S. business activity growth hits 6-month low in December
• Oil slips below $60 on Russia-Ukraine talks, weak China data
• Fed minions worried more rate cuts might boost inflation, think their favorite monetary policy tool is becoming ineffective:
• More rate cuts could reignite inflation, hurt Fed credibility, Bostic says
• Dallas Fed paper argues federal funds rate transmission effectiveness waning
• Bigger trouble, but no stimulus developing in China:
• China data dives, but Beijing balks at fiscal splurge
• China accelerates crude stockpiling amid weaker oil price trend
• BOJ minions expect to win game of 'fiscal chicken' with JapanGov minions as they gear up for next rate hike:
• The BOJ will win Takaichi’s game of fiscal chicken
• Bank of Japan to take interest rates to 30-year high
• Bigger trouble developing in the Eurozone:
• Low growth is now Europe’s biggest financial-stability risk
• Wall Street ended mixed after stronger jobs data and a drop in oil prices
• Wall St ends mixed, healthcare and energy stocks weigh on S&P

Wednesday, 17 December 2025

• Signs and portents for the U.S. economy:
• Oil jumps 2% as Trump's Venezuela blockade stokes uncertainty
• https://www.reuters.com/world/americas/trump-orders-blockade-sanctioned-oil-tankers-leaving-entering-venezuela-2025-12-16/
• Fed minions grease financial wheels, say monetary policy is too restrictive:
• Fed liquidity measures calm year-end funding jitters
• Waller says Fed policy still in restrictive territory, sees room to cut rates
• Fed governor Waller says rates could be cut by as much as a full point
• Fed's Waller says he 'absolutely' would defend US central bank's independence
• Growth signs developing in Japan:
• Japan's exports to US post first rebound in 8 months as tariff pain eases
• Japan's premier says country must pursue proactive spending for growth
• Wall Street closed noticeably lower while oil prices popped
• Wall Street falls as AI funding jitters hit tech stocks
• Gold forecast to glitter again next year despite biggest gain since 1979
• US tech stocks slide as Oracle data centre setback reignites AI concerns
• Oracle slides on uncertainity over $10B Michigan data center financing
• Gold forecast to glitter again next year despite biggest gain since 1979

Thursday, 18 December 2025

• Signs and portents for the U.S. economy:
• Expectations before consumer price inflation data:
• US consumer prices likely posted largest annual increase in 1-1/2 years in November
• Consumer price inflation lower than expectations:
• Consumer Price Index: Inflation Cools To 2.7% In November, Lower Than Expected
• US annual consumer inflation slows in November, but report distorted by missing data
• The pain points and bright spots in a patchy US inflation report
• Oil prices settle slightly higher as market assesses mounting supply risks
• Fed minions surprised by lower-than-expected inflation, suggest more rate cuts may be coming:
• Fed's Goolsbee in Fox Business interview welcomes latest inflation data, says more rate cuts may loom
• BOJ minions get another high inflation reading before anticipated rate hike:
• Japan's core inflation steady in November, stays above BOJ target
• ECB minions say they've achieved perfection with Eurozone monetary policy:
• ECB upgrades growth outlook, closing door to more cuts
• ECB policymakers see steady rates next year but cut not off table, sources say
• Lagarde's statement after ECB policy meeting
• Wall St closes higher fueled by tech rally, soft inflation data
• Wall Street ended higher after trimming earlier gains as investors digest CPI data

Friday, 19 December 2025

• Signs and portents for the U.S. economy:
• Oil prices climb as US blocks Venezuelan tankers, eyes on Russia-Ukraine talks
• Surging barrels at sea spook oil markets more than Russia or Venezuela
• US existing home sales edge up in November as mortgage rates ease
• Fed minions say they're in no rush to cut interest rates again:
• Fed's Williams tells CNBC there is no urgent need to cut rates again
• Bigger stimulus surprisingly not developing in China:
• China set to keep rates steady for seventh month despite slowing economy
• BOJ minions hike Japan's interest rates, lose credibility?:
• Bank of Japan raises rates to 30-year high, signals more hikes
• BOJ Governor Ueda's comments at news conference
• Yen weakens across board after BOJ delivers rate hike
• Yen bears emboldened by no-surprises BOJ
• Loss Of Credibility: Yen Craters, Yields Surge After BOJ Hikes Rates To Highest Since 1999
• ECB minions say they have Eurozone inflation right where they want it:
• ECB's Santos Pereira: inflation at target, rate moves to hinge on economy
• ECB's Escriva expects monetary policy to remain steady
• ECB's growth, inflation risks are large but balanced, Sleijpen says
• Eurozone's biggest economy expected to recover slowly next year:
• German economic recovery to get a subdued start next year, Bundesbank says
• Wall Street ended the week on a high note with back-to-back session gains
• Wall St climbs as tech rally continues, led by Micron
• Micron surges on AI demand, 'memory supercycle'; analysts highlight historic margin guidance

The Atlanta Fed's GDPNow tool projection of real GDP growth in the U.S. during the recently ended 2025-Q3 is unchanged at +3.5% this week. The tool won't shift to forecast 2025-Q4's GDP until 23 December 2025, which coincides with when the BEA's official initial estimate of GDP for 2025-Q3 will be released.

On a programming note, this is the last edition of the S&P 500 chaos series for 2025, we'll be back with a new edition on Monday, 5 January 2026.

In between now and then, we'll feature one of the best data visualizations we've seen during the year and will also present the biggest math story of 2025. We'll officially return on Friday, 2 January 2026 with a new tool you can use to see what your paycheck will look like in 2026.

Image credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a Wall Street bull and bear who are both asking for better quality data in 2026 from Santa Claus"

We've run up to the last weekend before the holidays arrive next week. If you haven't yet completed your shopping for gifts, you only have a handful of days left before time runs out.

We were surprised at how many shoppers took advantage of our suggestions for last-minute gifts in 2024. So much so we've asked the Inventions in Everything team to assemble a list of the kinds of gifts they would seriously give to people they know.

Better still, most of the items on the 2025 list can be acquired for about $25 U.S. dollars or less through Amazon, which means you can shop affordably while avoiding the crush of shoppers you will otherwise face at this late date. Here are the suggestions the IIE team recommends:

Bits and Pieces 10-Step Puzzle Box

Giving gift cards, cash, or lottery tickets has become a staple for the last-minute gift shopper. If that's you, you can separate yourself from the pack of all the other like-minded last-minute gift shoppers by packaging your gift in Bits and Pieces' Japanese puzzle box. This particular model requires ten steps for the gift recipient to manipulate the attractive box to receive it.

To be sure, this is really a gift for people who like puzzles and will be happier with the box than they will likely be with whatever gift card you might have placed inside it. While there are several other puzzle boxes out there, the design of this model is what caught our attention. It would not look out of place when kept on a dresser, which gives it an edge over the more rustic-style of puzzle boxes.

Contigo Luxe Stainless Steel Thermal Travel Mug

Thermal travel mugs offer the benefit of being both common and practical. What makes this model stand apart from all the other vacuum-insulated stainless steel travel mugs on the market is its "killer app" feature: it is extremely easy to clean because it is top-rack dishwasher safe!

We're featuring the stainless steel model of Contigo's Luxe series as a last-minute gift idea because we think it's likely the most durable version of the product. There are two other versions that add black or blue coatings, but which consumers who have bought these mugs report can chip. The pure stainless steel version however doesn't have that as a potential drawback.

QAQcew Magnetic Fidget Pen

This is the kind of gift that makes sense for those who have take notes and who fidget a lot. QAQcew's Magnetic Fidget Pens are unique writing implements that can be broken apart into segments, which can be reconnected into a variety of figures with magnets, where what you can make with the segments of each is only limited by your imagination. These pens come in black, blue, purple, and rainbow-hued models, which are also compact enough to work as stocking stuffers.

Escape Aromatics National Park Candles

It's a pretty good bet that at least one of the people you're shopping for are the kind of people who really enjoy candles and their aromas. If they also happen to enjoy the great outdoors and the kind of wilderness that can only be found in America's national parks, Escape Aromatics' soy wax candles incorporate scents that might make them think of the natural wonders of Yosemite, Dry Tortugas, Redwoods, Glacier, Joshua Tree, or Hawai'i Volcanoes.

Before we go any further, we should note that these candles are not meant to represent what these places might smell like if they were burning. The Yosemite model, for example, has the following aromatic profile:

• TOP NOTES: Pine and Green Citrus
• MID NOTES: Jasmine, Rose, and Earthy notes
• BASE NOTES: Vanilla, Cedarwood, and Sweet Spice

If your gift recipient is the kind of person who wants to smell what things would smell like if they're burning, we have an alternative selection that might work for you....

KFC Firelog

This is another gift whose main selling point is the aromas it creates. However, this is a gift that only makes sense if your target recipient has a wood-burning fireplace, also enjoys fried chicken and has a real sense of humor. If they do, this product is "designed to make your home smell like fried chicken and feel as warm as an Extra Crispy drumstick at the bottom of a KFC bucket of fried chicken".

If your potential gift recipient lacks any of these three characteristics, you'll be better off giving them any of the other last-minute gift ideas we've featured. A quick note of warning: this particular gift item is selling for $39.99, making it the most costly on this list.

Previously on Political Calculations

All of the items we featured on our 2024 last minute Xmas gift ideas list are still available and, most surprisingly, the Pudlicki Car Cleaning Gel was the most popular among readers.

Meanwhile, the gift ideas for math lovers we presented back on Black Friday are all still out there. Happy shopping!

Image credit: Two black and white boxes with gold bows photo by Javier Miranda on Unsplash.

The U.S. Bureau of Labor Statistics continued playing catch up with shutdown delayed employment statistics. The BLS has released its employment situation data through November 2025. While that gets them fully caught up, it also means they only reported the data they collected for November 2025 because they didn't collect any data for October.

The bad news is the employment situation for U.S. teens declined after its September 2025 rebound. That pain was highly concentrated among younger teens (Age 16 and 17), which saw their numbers in the workforce drop by 179,000 to a seasonally adjusted 1,936,000 in November 2025. This is similar to how this part of the teen job scene looked in May 2025.

By contrast, the number of older teens dipped by just 2,000 over the same two-month period, with 3,472,000 counted as having jobs in November 2025.

The following chart shows these changes along with the seasonally-adjusted total Age 16-19 employment level:

In this chart, the number of employed Age 16-17 teens and Age 18-19 teens doesn't add up to the combined Age 16-19 figure. That's because each demographic gets its own seasonal adjustment. If you want numbers that do add up within a small margin of error, you'll want to access the BLS' nonseasonally adjusted employment figures.

Sharp-eyed readers will also note the chart is showing an estimate for each teen population group for October 2025. These figures are simply the average (or midpoint) of the recorded employment levels for September and November 2025, which we think are reasonable estimates of what would have been recorded for October 2025 had the household employment survey been performed. This survey is conducted by the U.S. Census Bureau, which was also shuttered by the shutdown because its funding was not authorized by the U.S. Congress.

Overall, November's teen employment figures are within the range they have been during 2025.

Reference

U.S. Bureau of Labor Statistics. Labor Force Statistics (Current Population Survey - CPS). [Online Database]. Accessed: 16 December 2025.

Image Credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a high school student who is having trouble finding a job". We tweaked the image so the Help Wanted sign indicates 'MUST BE 18 OR OLDER'. With the jobs number for younger teens being similar to May 2025's figures, we're re-using our cartoon from that month since it's on point.

The outlook for the S&P 500's dividends through 2026 has improved in the month since we last presented our previous snapshot of their future. For the most part, they have improved with the 2026-Q1 looking to show the biggest jump.

Before we go any farther, we're referring to future quarters as they apply to dividend futures contracts, not regular calendar quarters! For dividend futures contracts, 2026-Q1 begins on Saturday, 20 December 2025 and will end on the third Friday of March 2026.

Here is our summary of how the outlook for the S&P 500's dividends has changed in the past month for the final quarter of 2025 and the upcoming four quarters of 2026:

• 2025-Q4: Decrease of $0.03, declining to $19.91 per share
• 2026-Q1: Increase of $0.57, rising to $21.46 per share
• 2026-Q2: Increase of $0.01, rising to $19.74 per share
• 2026-Q3: Increase of $0.14, rising to $20.01 per share
• 2026-Q4: No change, holding at $19.79 per share

The following animated chart shows how expectations for the S&P 500's quarterly dividends per share changed in the month from 14 November 2025 to 15 December 2025. If you're reading this article on a site that republishes our RSS news feed, you may need to click through to our site to see the animation.

This is our last update for 2025, our next snapshot will be taken in mid-January 2026. Because it will soon be very relevant, be sure to read the "More About Dividend Futures Data" section, which explains why the quarterly dividends Standard and Poor will report for the S&P 500 are different from dividend futures data. We anticipate S&P will report the index' quarterly dividends for the calendar quarter of 2025-Q4 early in 2026.

More About Dividend Futures Data

How changes in the outlook for dividends at specific points of time in the future contribute to changes in stock prices is described by this math.

For this series, we have been taking a snapshot of the CME Group's S&P 500 quarterly dividend futures data shortly after the second or third week of each month.

Dividend futures indicate the amount of dividends per share to be paid out over the period covered by each quarter's dividend futures contracts, which start on the day after the preceding quarter's dividend futures contracts expire and end on the third Friday of the month ending the indicated quarter. So for example, as determined by dividend futures contracts, the now "current" quarter of 2025-Q4 began on Saturday, 20 September 2025 and will end on this Friday, 19 December 2025. From the perspective of dividend futures, 2026-Q1 will become the current quarter on Saturday, 20 December 2025.

Because dividend futures are tied to options contracts that run on this schedule, that makes these figures different from the quarterly dividends per share figures that are reported by Standard and Poor. S&P reports the amount of dividends per share paid out during regular calendar quarters after the end of each quarter. This term mismatch accounts for the differences in dividends reported by both sources, with the biggest differences between the two typically seen in the first and fourth quarters of each year.

Image Credit: Microsoft Copilot Designer. Prompt: "A crystal ball with the word 'SP 500' written inside it". And 'Dividends' written above it, which we added.