This photo is perhaps the most stunning astronomical visual from the Artemis II lunar fly-by mission.

Here's the official caption:

Captured by the Artemis II crew during their lunar flyby on April 6, 2026, this image shows the Moon fully eclipsing the Sun. From the crew’s perspective, the Moon appears large enough to completely block the Sun, creating nearly 54 minutes of totality and extending the view far beyond what is possible from Earth. We see a glowing halo around the dark lunar disk. The science community is investigating whether this effect is due to the corona, zodiacal light, or a combination of the two. Also visible are stars, typically too faint to see when imaging the Moon, but with the Moon in darkness stars are readily imaged. This unique vantage point provides both a striking visual and a valuable opportunity for astronauts to document their observations during humanity’s return to deep space. The faint glow of the nearside of the Moon is visible in this image, having been illuminated by light reflected off the Earth. Editor's note: This caption was updated on April 8, 2026, to reflect ongoing scientific observations and discussion about the image.

What the official caption omits is there are several planets photobombing the shot. If you look at the three brightest dots between the moon and the lower right hand corner of the image, from leftmost to rightmost, those are Saturn, Mars, and Mercury.

But that's not all. Neptune is hiding in between Saturn and Mars, too faint to be very visible at the image's resolution. If the image were slightly zoomed out, Venus would have been visible in the upper left corner, but falls out of the frame in this shot.

Every four years, we celebrate Leap Day as the shortest month of February gets extended by an extra day and we have to cope with the idea that 29 February is just like any other day.

That's an inaccurate statement, because there are years where you would think there might be a 29 February inserted into the calendar, but isn't. Those are years that can be divided evenly by 100 and the next time that 29 February will be left out of the calendar after a four year interval will be in 2100.

But that's not quite right either, because there are plans to insert a 29 February into the calendar for 2400. And every 400 years after that.

It's all very complicated, but fortunately in the leap year of 2016, Matt Parker took the time to not only explain why 29 February keeps getting added to the calendar when it does and why it doesn't when you think it should, but also how to fix it so calendars make more sense.

Glad to have that all sorted! Now if we can just get him working on fixing daylight savings time.

Have you ever really thought about odd numbers? Or what it is that makes them odd?

Vsauce's Michael Stevens has, sharing his thoughts in the following 22 minute video, which goes in directions you might not expect to explain why odd numbers mysteriously show up when gravitational acceleration is involved:

We're still on the fence as to whether the rules should prevent dogs from playing high school basketball, but the universe is an odd and mysterious place. Which is to say it's more entertaining when they can, once. We believe any potential sequels or reboots however should be strictly prohibited and are happy to cite the Beethoven franchise as proof.

The year was 1978. Americans were suffering under the weak leadership of an ineffective president. Inflation was running hot and about to get much worse. And then, as if to put an exclamation point on just how bad things were getting, one of the three broadcast television networks that existed at the time aired The Star Wars Holiday Special.

It's difficult to describe just how crushingly bad this entertainment event was. The year before, the movie Star Wars (as it was popularly known at the time, today it goes by "Star Wars: Epsiode IV - A New Hope") had been a spectacular success, providing a beacon of light in the gathering gloom of the era's popular entertainment. By contrast, The Star Wars Holiday Special has been described as a "cosmic catastrophe" and "infamously terrible". No wonder Star Wars producer George Lucas and the stars of the movies worked hard to bury the memory of the special in the decades since.

But some Star Wars fans, being who they are, couldn't let it go. Not only did they remember it existed, some have worked to improve it in a campaign to bring it back. One fan has even gone so far as to create a two minute 4K video trailer for The Star Wars Holiday Special, employing AI and machine learning to improve a portion of the viewing experience.

The trailer only hints at the badness to which Americans were subjected in 1978. To get the full experience, we need to turn another effort to improve the watchability of The Star Wars Holiday Special, put together by Rifftrax.

If you don't think the jokes in the added soundtrack are an improvement, try watching the special without them. You'll soon see why President Jimmy Carter was sermonizing about malaise to Americans just a matter of months later.

We'll agree with CNet's Gael Fashingbauer Cooper that the best part of the improved viewing experience are the vintage ads.

Previously on Political Calculations

Since we're on the verge of the holiday season, here's a sampling of how we've celebrated the time of year in years past.

• The New Physics of Santa and His Reindeer
• How Much Should You Spend on Gifts this Christmas?
• Air Shark!
• Why There Are Only 12 Days of Christmas
• The Quantum Santa and the Solutions to Other Christmas Conundrums
• Inventions in Everything: The Santa Claus Detector
• 2020's Xmas Bill
• Reworking Overworked Christmas Carols

And for Star Wars fans, do have a happy Life Day!

Once again, for the second year in a row, Mariah Carey's All I Want For Christmas Is You is the top song on the charts this week in the U.S. And just so we're clear, that's Mariah Carey's version of All I Want For Christmas Is You that was originally released in 1994.

We're not quite as tired of it as we are of the dreaded 12 Days of Christmas song, but we're getting there given how overplayed it becomes this time of year. Overplayed enough where we are finding a mashup of it with Radiohead's Creep to be more worthy of a listen, though it takes a while for the lyrics to break through the uptempo introduction.

All in all, it is surprising how well the Radiohead-Mariah Carey mashup works. Now, if someone could deal with the standalone dread that is The Little Drummer Boy, which not even the talents of Bing Crosby and David Bowie or Pentatonix could rescue, we would declare a Christmas miracle!

We got up early this morning to wrap up our Christmas shopping for 2020. We weren't very imaginative this year, in that we decided to go out and get as many things as we could from the dreaded "12 Days of Christmas" song from a local PNC branch, the only place we know that carries all the items listed in the carol.

Or would, if it weren't for the coronavirus pandemic. Some things on the list just aren't available this year, so our gift recipient will get no dancing ladies, no lords-a-leaping, no pipers piping, and no drummers drumming.

Here's the receipt for all the rest....

The good news is that at $16,163.14 before sales tax, the bill this year for the available line items is $22,825.45 cheaper than in 2019. With the state government's lockdown orders, all the ladies, lords, pipers, and drummers are subject to a stay-at-home order and are thus not available in 2020.

Of course, we're really taking the cheap route in only getting one set of each of the items listed in the "12 Days of Christmas" song. If we were to take the cumulative math resulting from all the repetition in the song seriously, the pre-tax bill for 2020 for the items we can buy would be $105,561.80.

Can you use a break? If so, we can recommend visual artist Cristóbal Vila's Infinite Patterns as a marvelous way to contemplate the beauty of infinite patterns, without taking up an infinite amount of time. In fact, it clocks in at just under four minutes, which is just long enough to get the job done.

Previously on Political Calculations

• Beauty Within An Eight Millimeter Square
• Automated Zen
• Accidental Beauty
• Slow Dance

We bring you the following $25,362 video produced by the U.S. Consumer Product Safety Commission on some of the things that can go very wrong should you not handle fireworks safely. While no people or animals were harmed during the making of the 2018 video, by our count, six mannequins and two watermelons didn't fare very well....

According to Pacific Specialty, eight people died as a result of fireworks-related incidents in 2017, while another 12,900 were insured, with about two-thirds occurring from mid-June through mid-July. On average, the CPSC has reported an average of seven fireworks-related deaths per year since 2002.

The modern alternative to fireworks is drones, where Travis Air Force Base featured a show with 500 of Intel's Shooting Star drone fleet:

Our prediction: fireworks will continue to be used to celebrate the Fourth of July, and drones will become part of the show.

What happens when you ask Siri "What's one trillion raised to the 10th power?"

For those willing to lay down a beat, something magical!...

That was from three years ago. Now, for a solo version from earlier this year!

And that can go on for all 120 zeroes! It wouldn't be anywhere near as fun if Siri knew scientific notation!

It's Friday, it's been a long week, and what better way to go into the weekend than with a bit of fun recently featured at Reddit on the intersection of math and cows!

If you want more, we'll point you toward Vincent Pantaloni's twitter feed, where he compares cow math to dance notation.

Previously on Political Calculations

• Learning About Economics From Cows
• Mathematical Formulas With Dance Notation

As seen on Reddit....

Math problem from r/funny

The answer is 5.099 feet per second, or if you want to reference a more precise mathematical representation for the answer, they are moving apart at exactly √26 feet per second. Assuming, of course, that they're moving on a flat plane, which means we're neglecting the curvature of the Earth's surface in calculating their relative separation speed.

It's Okay To Be Smart's Joe Hanson addresses how the troubling physics of Santa Claus can ultimately be resolved by the science of quantum mechanics.

Meanwhile, the question of whether all of Santa's reindeer are female has been raised because while all reindeer grow antlers each year, male reindeer typically lose their antlers a month or more before Christmas comes around, which would mean that if we see Santa's sleigh being pulled by reindeer with antlers, they would have to all be female because they lose their antlers much later.

But at least one reindeer herder has an alternative theory that might explain how at least one of Santa's reindeer could be male. Click the iPlayer symbol in the lower left corner of the picture below for the audio explanation....

Finally, we'll leave you with one last Christmas conundrum - a mathematical puzzle:

You can find the solution presented here.

If you ever wanted to know how fireworks work, the American Chemical Society has you covered!

Have a happy Fourth of July!

Randall Munroe is the author of best-selling (and great gift idea) books like Thing Explainer: Complicated Stuff in Simple Words and our favorite, What If?: Serious Scientific Answers to Absurd Hypothetical Questions, who has just recently come up with a creative way to resolve the decades-old debate on which is the better temperature scale: Fahrenheit or Celsius. Munroe presented his solution at xkcd:

Now, that's the kind of practical genius that we just cannot ignore, so to help facilitate the worldwide adoption of the new Felsius temperature scale, we've built the following tool to convert either degrees Fahrenheit or degrees Celsius into the new degrees Felsius. If you're accessing this article on a site that republishes our RSS news feed, please click here to access a working version of the tool on our site.

Take that, Lord Kelvin!

Are you ready to put all the other houses in your neighborhood to shame this Halloween? If so, you might want to employ some of the latest in digital imaging technology, where you can conjure spectres from the aether on command with the power of downloadable technology! Digital decorations developer AtmosFX explains how in the following video (HT: Core77):

If that's not enough to scare those pesky neighbors, here at Political Calculations, we have a strange tradition where we celebrate the scary in furniture on Halloween.

Except this year, we were stopped in our tracks by one of the more inexplicably disturbing videos that we've seen in quite a while, that redefines what scary in furniture can mean. We don't want to minimize it through understatement, but we would describe it as haunt your dreams stuff, and while it is safe for work, barely, we cannot explain it, nor will we. We will however warn you that you cannot unsee it after you've seen it.

You cannot say that you were not warned. Have a happy Halloween, and good luck forgetting whatever the hell that was.

If you work for a modern American corporation, whether at an office or from home, you have the kind of conference calls that only today's modern Internet technologies make possible: really awful ones.

You know what we mean, and so do the creative minds at I-am-bored, who posted the only possible way to make it through the ordeal of interacting with your professional colleagues in the online world with any shred of your sanity intact: by turning each Skype, Lync or Facetime meeting into a game of Conference Call Bingo!

Here's the basic game card:

Armed with this card, rather than multitasking as most Americans workers might attempt during such an event, you now have an incentive to hang on every word spoken during each conference call so you can catch every one of the typical statements made by the attendees of today's conference calls as they make them, where we encourage you to shout "Bingo" if you get five in a row. Or get all four corners and the center square. Or, for a real challenge, see if you can completely fill your card during the duration of the call!

Of course, you should set your headset or microphone to mute when you announce each victory. Your managers will greatly appreciate your concentrated focus on the matters being discussed during their calls and presentations, but even though they and your company's IT department are the ones who hooked you up to today's online meeting technology, we're afraid that because they did, they're not eligible to play....

Previously on Political Calculations

• Office Survival Skills (Part I)
  
• Office Survival Skills (Part II)
  
• Office Survival Skills (Part III)
  

The business of fireworks in the United States centers around the events of the Fourth of July and New Year's holidays. Since this is the Fourth of July, we thought we'd present data on the fireworks business that was reported by the U.S. Census Bureau and USAToday in recent years!

$296.2 million

The value of fireworks imported from China in 2016, representing the bulk of all U.S. fireworks imported ($307.8 million). U.S. exports of fireworks, by comparison, came to just $10.0 million in the same year.

$368.6 million

The value of fireworks sales by retailers in 2012.

$482.6 million

The value of fireworks and firecrackers sales by wholesalers in 2012. There were 172 wholesalers who sold these items in 2012.

$1.09 billion

The total annual sales of fireworks by all U.S. fireworks sellers. $755 million of those fireworks are sold to regular consumers, while $340 million worth of the really good stuff is sold for professional fireworks displays.

285.3 million pounds

The total amount of fireworks used according to the American Pyrotechnics Association. Of that quantity, 91% are used by regular consumers, while the remaining 9% are used in professional displays.

Have a great Fourth of July holiday, and be sure to enjoy the fireworks!

We're enjoying an extended Fourth of July weekend this week! We'll catch up with the S&P 500 in Week 4 of June 2017 and Week 1 of July 2017 next Monday. In the meantime, the dog's going fishing, and we're with the dog....

Every now and again, a famous economist will say something that not only stands apart from everything else they've said and done, it turns out to be the defining quote of their entire life, regardless of what other achievements they may have had or contributions they may have made in their field. We thought it might be fun to revisit some of the more famous, or really, infamous, things that several famous economists have said that might very well be placed on their tombstones as their final epitaph.

Here's a very famous one about the U.S. stock market....

Stock prices have reached "what looks like a permanently high plateau," Irving Fisher, Yale economist, told members of the Purchasing Agents Association at its monthly dinner meeting....

- Irving Fisher, 16 October 1929, less than two weeks before the U.S. stock market began to crash, marking the unofficial beginning of the Great Depression.

It's been said that if you laid every economist in the world on the ground end-to-end, you would never reach a conclusion. As proof, here's an opposing viewpoint on the U.S. stock market.

It really does now look like President Donald J. Trump, and markets are plunging. When might we expect them to recover?

Frankly, I find it hard to care much, even though this is my specialty. The disaster for America and the world has so many aspects that the economic ramifications are way down my list of things to fear.

Still, I guess people want an answer: If the question is when markets will recover, a first-pass answer is never.

- Paul Krugman, 9 November 2016, after which, the U.S. stock market quickly rose to reach a series of all-time-record highs over the next several months.

Some statements have to do with the health of the U.S. economy.

The Federal Reserve is not currently forecasting a recession.

- Ben Bernanke, 10 January 2008. Some time later, the National Bureau of Economic Research would mark December 2007 as the peak of the U.S. economy's period of expansion before it entered into the "Great Recession", where January 2008 was its first month of economic contraction.

But rest assured, all is well for the U.S. economy now.

"Would I say there will never, ever be another financial crisis?" Yellen said at a question-and-answer event in London.

"You know probably that would be going too far but I do think we're much safer and I hope that it will not be in our lifetimes and I don't believe it will be," she said.

- Janet Yellen, 27 June 2017

It's almost like the Fed Chair is asking for that to be her economic epitaph!

Image Credit: Tombstone Builder

If we go by media reports, there is a very fine line between ho-hum and major fear in the U.S. stock market as it considers the potential outcome of the United Kingdom's popular referendum today on "Brexit", in which the British people will state their preference to either remain part of the European Union or will declare that they no longer wish to remain part of Europe's dominant economic and monetary union.

Here is a case in point from yesterday's headlines, courtesy of Reuters:

Wall Street flat, all eyes on Brexit vote

From that headline, you would expect that Wall Street isn't very emotional at all on the topic of Brexit. If you looked at how U.S. stock prices traded on that day, you would find that they fell by 3.45 points, or 0.165%, on the day before the U.K.'s historic vote.

If you want to use an adjective to describe that level of change from the previous day's close in the market, flat is a pretty good one to choose.

Now, compare that headline with the following one that Reuters produced just over a week ago:

Wall Street falls as Brexit vote becomes major fear

From that headline, you would reasonably expect there to have been major market carnage on Wall Street that day, wouldn't you?

There certainly was, if your threshold for major market carnage in the U.S. stock market involves the S&P 500 plunging downward by 3.74 points, or by 0.180%, from its previous day's closing value.

Clearly, where the the most mainstream of media is concerned, there is a very fine line between ho-hum flatness and outright fear in the markets. It just happens to fall somewhere within the 0.29 point gap between a market index that falls by 0.165% on a day defined by what might be described as mildly watchful apprehension and one that falls by 0.180% from the previous day on a day filled with "major fear"!

Update 24 June 2016, 9:24 AM EDT:

Are you ready for blood running in the streets panic - at least, if we go by Reuters' measure of fear? Via Barry Ritholtz, here are the pre-market futures following the actual Brexit vote:

Barry writes:

We haven’t seen numbers like this since the financial crisis — although to be fair, these numbers bring us in the USA back to where we were on Monday, prior to the rally this past week; Europe seems to be getting punished to a much greater degree.

As a heads up for what's going to happen in today's stock market action, we're about to get a case study on what happens to U.S. stock prices when investors suddenly shift their forward looking focus from one point of time in the future to another. In this case, from the distant future to the much nearer term. This will be evident today as a direct result of the Brexit vote outcome.

Where the U.S. stock market is concerned, nothing has changed with respect to the expectations for the amount of dividends that will be paid out in the future - at least, as yet, and thus, nothing has changed with respect to the alternative trajectories that U.S. stock prices might take, except just how far forward into the futures are looking. If you want to know where stock prices are going to go, figure out how far into the future investors are looking (use the following chart as your guide, in which we've sketched in how the stock price futures for the S&P 500 stand before the market opens.)

We've been through this kind of rodeo with our model's performance before, back when China had its meltdown in August 2015. There will also be a wild card speculative element (noise) in today's trading, but the main shift in the trajectory of stock prices should become pretty apparent over the next several trading days, if not sooner.

As for what to expect, assuming no new unexpected events impact the market, should investors remain focused on either the near term future defined by 2016-Q3 or 2016-Q4, the S&P 500 is likely within 1-2% of where it will end the day. It is certainly possible that an outburst of speculative noise might erupt in the market, which could take it down by an additional 4% from where it looks set to open, but the immediate impact of the Brexit event itself will likely fade during the day, leading stock prices to stabilize.

It is also possible that the world's central banks will take an action that will succeed in refocusing the attention of investors on the more distant future, which would be accompanied by a significant rally.

We'll have fun watching how it all plays out!

Update 24 June 2016, 9:38 AM EDT:

Via Eddy Elfenbein's Twitter feed:

Live update from the currency pits. pic.twitter.com/kvRWc6WzsL

— Eddy Elfenbein (@EddyElfenbein) June 24, 2016