Archive for the ‘Science’ Category

Wherefore Pop Art Thou?It’s time for another look at the kind of CSD you’ve been drinking lately when you toss down a sweet LRB. And the results may be scarier than than you expect. (But hang on — the charts are better than ever!)

Beverage Digest has brought out their yearly summary, leading off with the ominous words, “2013 Was A Challenging Year for U.S. Beverage Business.” Among other things, note that this capitalizes “Was” and even “A” but not “for” in that spooky opening line. That may give you some idea that there’s trouble ahead.

First some terminology you need to know when discussing this topic as though you know what you’re talking about:

  • BD = Beverage Digest
  • LRB = Liquid Refreshment Beverage
  • CSD = Carbonated Soft Drink

I think insiders pronounce those bud, lurb, and cussed, as in, “Bud says the cussed lurbs are losing market share again.”


US CSD sales were down a bit to a mere $76 billion in 2013. That’s a big number even if you’re a billionaire, so to give it some perspective: If a country only made, bought/sold and drank that much CSDs and did nothing else, it would have a GDP of about the 85th largest country in the world. Imagine everyone in the country of Jordan doing nothing but buying and selling that much Coke and Pepsi all year long. They’d be as much of an economic powerhouse as they are now, except the people would probably burp a lot more.

On the other hand, that much money is only enough to give everyone on the planet a $10 bill. Once. So maybe it’s not so much after all. But on the third hand, it’s still comfortably above the comparatively meager $56 billion that Americans spent on their pets last year.

Per Capita Consumption

Things start to get scary with this factoid: BD says that US consumption per person was down in 2013 but still equivalent to just shy of two drinks each day for every man, woman, and newborn baby in the country. This could help to explain many, many things. But we won’t try.

 Soft Drink Pie

If you’re the kind of person who can’t help but go to the Google or Bing image search page and type in oddball search terms like “soft drink pie chart”, then for the last few years you will have seen the 2010 pie chart near the top of the results list. So obviously it’s time to provide another pie chart, for 2013, to try to get more of these images in the top of those searches. Because … well, because of some important reason that has temporarily slipped our mind.

These pie charts may show up for other image searches like the slightly more reasonable “soft drink market share” although performance is sporadic for such reasonable search terms.


2103 approximate relative market share for the top 10 soft drinks (CSDs)


CSD Market Share Can

The pie chart can be somewhat disorienting to the excessively logical types, who are disturbed by a food-based diagram used to depict drinks. So in yet another hopeless effort to appease such folks, here’s another look at 2013 CSD market. If you were a person with super-typical tastes who…

  • bought soft drinks in exact proportion to the rest of the country
  • selected the top ten most common flavors
  • mixed those all together well
  • and then poured the mixture back into all the empty cans

.. then each of the combo-cans that you drank would be composed as shown in the following picture. Bottoms up!We are what we drinkAnd if you’re not feeling good after drinking all that, go see the doctor and mention you suspect it’s cussed lurbs.


Data presentation tip: strive for charts and graphs that (a) communicate with a zing, or at least (b) make people hungry or thirsty. If a 6-year old can quickly grasp the message, you’re on the right track. In this case, the little tyke will soon be asking for some sugary drinks. Anyway send in requests for new ways to depict these things so we can help people to just get it. Finally.



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Recent evidence indicates that Earth may unexpectedly be orbiting a pair of stars, instead of just the one that most people call the ‘sun.’ And since we exist on this planet, there’s a reasonable chance that such orbits can yield habitable planets. The picture below was taken at the Charlotte, NC airport and appears to clearly show the two stars out on the morning horizon. This is an un-retouched photo — it’s just as it came out of the iPhone camera. (OK, the bottom part was cropped out.)

When will the textbooks start including our other sun?

Morning photo over downtown Charlotte, NC

Binary stars — with two suns orbiting each other — were first discovered (in public consciousness) in 1977 in the first Star Wars movie, as Luke Skywalker gazed out from the planet Tatooine at the two stars in his solar(s) system. Since then, scientists have discovered that binary stars are actually fairly common in the universe.

Luke and his two legitimate suns

Many stars are in binary (dual) or larger systems — perhaps one-third of star systems are binary (or more), meaning (do the math) about half of the stars are in these systems. But there is some controversy, that lots of little, harder to see stars are singles and thus binary stars are not quite as high a percentage. (Pretend to care about that for a moment … OK, done.) A visible-to-the-eye case is the second star in the handle of the Big Dipper, which has in the past been used as an eye test. It also turns out that the North Star is part of a triple star system (but two of them can’t be seen with the naked eye). Here’s how that works, using the Alaska flag for convenience.

Alaska flag with Big Dipper and North Star

Alaska flag with Big Dipper and North Star

There has been a fair amount of calculating going on, trying to figure out if a planet can orbit a binary star system in a stable, life-friendly way. A quick survey of the literature indicates that the definitive answer is: maybe yes, maybe no.

Some folks claim that if things are just right, like if two closely placed stars are about 80% as big as our sun (the one you read about, not the other one in the first picture above), then there could be some places where a planet could sneak in and orbit stably and comfortably for life to exist. There are, unfortunately, a lot of ways a planet in a binary system could try to orbit that would alternately freeze its local residents to death, followed a little later by cooking them to death, due to odd shaped or perturbed orbits (such as ones that eject the planet from the star system). Try this link for the hopeful story. Some other pictures here.

But another article studied this problem and, not to give things away or anything, they put the word ‘pulverized’ in their title, as in “Planets Pulverized in Double-Star Systems.” If you want to live there, at least housing should be affordable, and you should ignore any analysis of the planet’s orbit that includes the phrase, “Something chaotic is very likely going on.” Why worry about things you can’t affect?

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I was on a recent flight from San Francisco to Seattle that took off just as the sun was about to sink below the horizon. From a window seat on the left side, I faced over the ocean to the west. As the plane climbed, the setting sun actually began to rise further and further above the horizon. This occurred since our climbing into the sky allowed us to see further over the horizon. The sun rose from just the tip top showing, to about 40% above the ever-changing horizon line. So instead of disappearing quickly, it was nearly frozen (a challenging adjective to use for the sun) in that position for maybe 15 minutes, and then it ever so slowly finally set. For a while the scene was like the following picture, taken from the window from my phone – the actual sun was a lot sharper partly-below-the-horizon view.

Rising sunset from exit row seat

There is a reported green flash that can occur just after a sunset (or before a sunrise) if atmospheric conditions are just right. I hoped to see it – perhaps several times in this case – but whether due to clouds along the horizon or whatnot, it didn’t occur. More on that later.

Curiously, on the flight I was reading the book The Light Between Oceans, a novel set around a lighthouse on an island southwest of Australia. As I watched the reverse sunset, I was reminded of this line in that book, about the perspective from up at the top of the lighthouse tower: “Because it’s this high above sea level, the light reaches over the curve of the earth – beyond the horizon.” One character notes the light is like “seeing into the future,” looking ahead to save a ship before it knows it needs help. For my case, it was like looking slightly into the past, pulling the sun back up above the horizon after it had nearly disappeared.

That book features a live baby that washes up on the island, with a dead man on board the boat. This is not much of a spoiler because you learn this after about page two. It reminds me of a curiously similar plot point in CS Lewis’ Narnia book, The Horse and His Boy, in which (page 5 spoiler alert) a living baby washes ashore in a boat that also contains a dead man. In that case, the child had been sent off by someone trying to stop a prophecy that the boy would lead to a kingdom’s downfall. This attempt to block the prophecy was the necessary ingredient to make it come true.

Which echoes, curiously enough, a theme in the previous book I had read, Terry Pratchett’s The Last Continent, which also took place on Australia. Well, as Australia-like as can occur in a ‘Discworld’ novel, complete with kangaroos. In this novel, the wizard Rincewind is selected to solve a particular problem, and such scenarios always mean pain for him. So he flees, as it turns out, in the proper direction to allow him to eventually save the day. In a sense.

And speaking of the Narnia series, the book The Voyage of the “Dawn Treader” ends (spoiler alert) with a few humans and a mouse sailing off, to beyond the end of the world, toward a spectacularish sunrise. That suspended rising sunset that I saw gave a small yearning for this Narnia event, which included this bit, with several details omitted:

And suddenly there came a breeze from the east … It lasted only a second or so but what it brought them in that second none of those three children will ever forget. It brought both a smell and a sound, a musical sound. Edmund and Eustace would never talk about it afterwards. Lucy could only say, “It would break your heart.” Why,” said I, “was it so sad?” “Sad! No,” said Lucy.

And back to that lighthouse book: As it turns out, the boat that serviced the lighthouse island was named Windward Spirit. Which is a bit curious since this turned out to be within one vowel of an almost appropriate title for the guy sitting next to me in the exit row of the plane; he leads an organization called Windword Ministries. He had just been doing some ministry work in Mexico and was heading back to B.C. via Seattle.

And curiously, while watching the sun hang on the horizon, I was listening at the time to one of my favorite songs, Beautiful by Shawn McDonald. Here were the lyrics playing into my ears, giving an apt description of what I saw with my eyes at the time:

As I look off into the distance
Watching the sun roll on by
Beautiful colors all around me, oh
Painted all over the sky
The same hands that created all of this
They created you and I
What a beautiful God

The green flash that can appear after sunset or before sunrise is elusive and some of us have yet to see one. You need a good view of the horizon and some favorable atmospheric conditions. A good explanation of it (along with rainbows and mirages) can be found here. [Bonus points for seeing the error in the 7th-to-last figure.] And I wouldn’t suggest that pictures of the green flash are ever faked, but if you click on the ‘source‘ for the final green flash picture in that rainbow post, you’ll see at least one serious skeptic concerned about its genuineness. I’d never make that claim, just as I’d never suspect that the super elusive tricolor-flash picture below (must have been taken from the exit row of a low flying airplane) could be fake — could it? Just curious. (Click on picture to spot the supposedly real flash.)

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A rather fascinating animation of, well, the whole universe can be found by clicking here or on the picture above. It’s a rare day when you can learn so much by just scrolling your mouse wheel or sliding the slider button at the bottom of the picture you’ll see there. This will take you from the teensy tiny (more accurately, the teensy teensy teensy and then some tiny) to the far reaches of the universe (more accurately, the place where it would be handy to have read this book if you’re hungry at the time because yelp doesn’t cover this area — yet).

Here are a few highlights among many things you can learn.

Yoctometers are the smallest unit of measurement that folks have bothered to define, at 10-24 meters (yocto is a trillionth of a trillionth). That’s roughly the size of a neutrino (the low energy ones) although that may be wildly off and they may actually be two or three yoctometers across. If you’re not familiar with these tiny particles, they are: super small, super lightweight, uncharged, and therefore super reluctant (in a human sense) to interact with anything. And just as you should not worry when you hear a pilot say, “There is no cause for alarm,” so you should not worry about the following fact. If you stand up straight and face the sun (the source of most of the neutrinos around here), there will be about 500 trillion neutrinos zipping through your body every second. Actually it doesn’t matter if you’re facing the sun, the same is true if you do this at night since the neutrinos zip right through the earth to get to you even in the dark. If this bothers you, then roll up in a ball and then only about half that many neutrinos will be flying through you every second.

At the other extreme, the ‘yotta’ prefix in yottameter means there are 1024 of them (a trillion trillion). A yottameter is about 100 million light years long, and don’t forget that a light year is a distance, not a time (it’s how far light travels in a year if it doesn’t stop off for a smoke now and then). The universe passed the yottameter mark a long time ago and is now closer to 500 yottameters across. While we don’t really know quite where it all ends, we have a good idea that the universe is expanding at a faster and faster rate. We are living in a good time to be able to see it all; in the distant distant future, we would not be able to see as far across the universe anymore because of this increasing expansion rate.

If you can’t remember whether yoctometer or yottameter is the big one, just use this handy rhyme: Yotta is a lotta. In other words, it’s the big one. Simple.

Rotten Egg Nebula

There is plenty of interesting things sized between a yoctometer and a yottameter — such as most everything you can think of. Including shrews, thankfully. And the rotten egg nebula. If you look closely at a picture of the rotten egg nebula, you will quickly be amazed at how anyone could ever be crazy enough to select such a name for it. But as it turns out, it’s not named for its shape, it’s named for its smell (from the sulfur). Ah, that makes more sense. Astronomers smelled it even though it’s 5000 light years away.

Remember: There is yada yada yada between yocto and yotta.

Scaled so the ring is 1/25 of an inch across;
the gray circle is as small as the unaided eye can see.

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The male passenger pigeon

I’ve been pondering a rather remarkable fact lately, since learning that passenger pigeons — extinct for about 100 years now — used to number in the several billions. The remarkable thing is that they used to fly around in flocks which were estimated at more than a billion, perhaps over three billion. ‘Flock’ may be too small of a term for that size group.

The bird’s name comes from the French word passager, to pass by. Which these birds could do at a blazing 60 mph.

Here’s an entertaining essay that describes the scene in the U.S. a couple hundred years ago (LINK). Try to imagine being outside one day when a billion birds fly over. For hours and hours. I think it’d be fascinating, and I’d be tempted to lie down on the grass and watch. But it wouldn’t take long to decide that it’s wiser to watch from under some protection, like a tree.

Here’s a curious observation about passenger pigeons that helped lead to their demise once hunting limited their population: “This was a highly gregarious species—the flock could initiate courtship and reproduction only when they were gathered in large numbers; it was realized only too late that smaller groups of Passenger Pigeons could not breed successfully, and the surviving numbers proved too few to re-establish the species.” [a],[b]

In other words, this species took the concept of group-dating to a whole new level (or, to new heights). And it raises an interesting variation on the chicken-or-egg problem: Which came first, 1 billion passenger pigeons or a billion eggs? These critters didn’t seem inclined to populate from small numbers.


All this got me to wondering: how often, if ever, do I encounter things that number into the billions? There are several billion people on the planet, but on a normal day I probably encounter a thousand or less. Going to an event like a ball game or concert could push that up to tens of thousands.

If you want to find a billion of something one day, it needs to be small sized. It’s easy enough to be around billions of molecules, although they’re a bit hard to see. Grains of sand is a good choice. I estimate that in a moderate sized sandy beach, there are probably more than a trillion grains of sand, and about a billion of them lying on the surface so in a sense you can more or less see them all at once. (For the curious, see calculations below.)

Tree leaves are a candidate for encountering a billion in a day. I live on a greenbelt and so I spent some time estimating leaf count per tree. This varies widely with tree type and size, of course. I estimated perhaps 5,000 to 10,000 per moderate sized tree, and maybe 10 – 20 times more, up to 200,000 on the big trees. Here’s a panoramic shot out back, with the world curving the wrong way due to the panorama stitching effect.

There are a lot of trees in this greenbelt, as shown in the satellite picture of the area, below. It would take more than 10,000 trees at these (wild) estimates to make the billion — might be possible. So a day of strolling through such forested areas should put one in the presence of a billion leaves. Not bad for finding a billion of something that big.

Rule of thumb: People, Ants, Stars

Critter wise, there are a lot more ants on the earth than there were ever passenger pigeons — many quadrillions, but you’re not going to find a billion in one day (hopefully). But here’s a very handy rule of thumb. With about 7 billion people on earth, something in the vicinity of 100 quadrillion ants, and something in the (very large) ballpark of 70 sextillion stars (70,000,000,000,000,000,000,000) in the universe, a handy (and very approximate) way to relate these is:

For every person on earth, there are about 10 million ants.
For every ant, there are about 10 million stars.

It’s simple to remember: just imagine each person covered by 10 million ants, and then each ant associated with 10 million stars.

Estimates: Red tree, 5000 leaves. Big tree, 150,000 leaves.

By the way: remember that Carl Sagan, famous for the phrase “billions and billions” didn’t actually use this phrase (link). This reminds me of a time when Logitech discovered, through customer surveys, that they were thought to be #2 or #3 in the world in keyboards, before they had actually entered that market. This is a good strategy — whenever possible, dominate a market before entering it.

Also, this post is dealing with the “true” billion, the one with 9 zeros (1,000,000,000). Some of the Europeans have developed a bad habit of sneaking in a few extra zeros for a billion (1,000,000,000,000) — see this article (which also includes the important misinformation about Sagan’s billions and billions phrase). Maybe this has something to do with the debt crises there.

Have a favorite thing that you encounter in the billions? Leave a note so we can go looking for more billions and billions.


Calculations: Taking an average sand grain as having diameter = 1 mm. On a beach that’s about 100 yd (or meters) by 25 yards by 8 inches deep with sand:

# grains of sand total = Volume of beach / Volume of sand grain = (100 * 25 * 0.2 m3 * 109 mm3/m3) / ((4*pi/3)*(0.5mm)3) = approx 1 trillion.

# grains on beach surface = Area of beach / Area of grain = (100 * 25 m2 * 106 mm2/m2) / ((pi * 0.5mm)2) = 3 billion

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Flying slightly below the radar of most normal people is a raging mathematical controversy with serious implications (for raging mathematicians, anyway). So it’s time to jump in to enlighten the general public and contribute to the discussion. And along the way, we’ll introduce the solution to this whole mess in a bold ploy for personal fame and glory.

The controversy involves some people’s favorite number, pi. That’s the 3.14 etc etc number that’s also written as π. This number is featured in one of the possibly three most famous equations known to the masses (note that it’s good to have something “squared” if you want to invent a famous equation):

1. E = mc2 (Einstein’s big winner about energy, mass, and the speed of light)
2. a2 + b2 = c2 (Pythagorean theorem for right triangles)
3. A = πr2 (Area of a circle in terms of its radius)

Some upstart folks have starting lobbying that it’s better to talk about a number “tau” (written as τ) instead of our lifelong friend π. All this for a number that is simply equal to 2*pi. That’s it. So tau is about 6.28 while pi is about 3.14. These upstarts want to replace π in equations with τ (well, with τ/2 to keep things accurate).

This might not be a captivating matter to all readers. And that’s OK because this post is actually about a number better than either π or τ. So hang on a moment.

First of all, the tau advocates are passionate that circle size (circumference) should be thought about in terms of its radius (C=τr) instead of its diameter (C=πd). And they claim that this also makes some equations a little simpler. Their full case can be read at this LINK. Take some tranquilizers before reading that so you won’t get too worked up about suggestions that we relegate π to second class citizen status. This is almost as unthinkable as deciding that Pluto is no longer to be considered a planet. As with Pluto, it will never happen. In any case, a rebuttal to the τ manifesto can be found HERE.

Ending the pain: e-volve

Enough of that. It’s time to end all that numerical saber rattling by moving those two numbers aside for the number that actually deserves top honors. It’s known as ‘e’, and like π its value is written by an endless string of decimal place numbers that doesn’t repeat: 2.718281828459 … and so on forever.

This number is at the heart of an exponential equation that has the following curious characteristic: at any point, the value of the equation is equal to the rate at which the equation is changing. Yes I know, that’s profound and at least 75% life-changing. The rather simple equation is: y = ex, as shown in the picture.

So here are approximately 3*e (8) reasons to go with ‘e’ over its competitors.

1. It’s used in equations relating to exponential growth or decay, such as population growth or compound interest. People do not use pi when analyzing how bacteria can multiply to take over the world, or how many years it will be after they’ve died before they can actually afford to retire. It can even be used solving ‘derangements‘ which is obviously a cool word even though we don’t know what it means.

2. We are living in exponential times, the theme of this video, and e is all about exponential. We are not living in pi or tau times.

3. Its name has a nice history, involving other letters.

While the concept of e has existed in the universe from way back (since the times when people could count to almost 3), it only started to be used and written down in the 1600’s. An early reference comes from work of one John Napier. He forgot to name it, and later in the century Jacob Bernoulli ‘discovered’ the constant explicitly and it was named ‘b’ for a while.

But in 1727 or 1728, the 21-year old Leonhard Euler came along and figured out a number of important properties about e. But mainly he started calling it ‘e’ in an act of extreme humbleness. There are reports that it was also briefly called ‘c.’

4. As a number, e is both irrational and transcendental. Like most of our bosses. Admittedly, π and τ also have these properties, but who’s counting. And transcendental is another nice sounding word that we don’t understand but will use freely.

5. e is involved in two of the easiest possible math questions that can make you look smart even if you aren’t. Here’s a tidbit from calculus: It turns out that the derivative of ex is ex, and also the integral of ex is ex (ignoring the inevitable constant that comes along with integration). So if someone asks what the derivative or integral of ex is, you don’t have to remember the details, just confidently mimic back the answer: ex (pronounced “e to the x”).

Let’s see π or τ be such an easy answer to a complicated sounding question.

6. Because of the previous point, e is involved in an excellent gimmick that a math teacher can play on students.

Teacher: What’s the derivative of ex?

Student: ex?

Teacher: Yes, that’s what I’m asking, ex. What’s the derivative of ex?

Student: ex

Teacher: Are you deaf?? Yes, I want the derivative of ex. Now tell me the answer!

Student (emphatically): ex!

Teacher: All right, if you’re not going to answer, let’s try a different one: What’s the integral of ex? Ignore the constant in the answer.

Student: ex

Teacher: Yes I’d like you to tell me the integral of ex.

Student: ex

Teacher: [etc. etc.]

After a while, the teacher expresses exasperation, rolls eyes, and says with resigned drama: OK, let’s switch gears. What’s the 4th derivative of sine of x?

Student: sine of x

Teacher: Yes, tell me its 4th derivative

Student: sine of x


7. Google’s IPO in 2004 sought to earn e-billion dollars, or $2,718,281,828 (and some change). If Google likes e, it must be good. I verified that with Bing.

8. Smaller is bigger

While 2.718… is smaller than 3.14… which in turn is smaller than 6.28…, this discussion on ranking allows us to accurately but paradoxically write,

e > π > τ

This is illustrated vertically in the figure above. Click on that figure to see how e feels about that.


Teaser for future post: an easy way to quickly remember and recite more digits of e than even 99.9% of mathematicians can recite. Can’t wait.

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In the previous post, we discussed the deep philosophical question of whether the glass is half full or half empty or several other choices. This time we tackle a philosophical riddle:

When is nothing stronger than something?

Well, one answer is: when the nothing is something that isn’t there any more.

Consider for example something that is nearly nothing: Air. Imagine the amount of air in a decent sized balloon. It’s hard to appreciate how powerful that air is until you take it away. Thanks to gravity (that fundamental force that’s always getting us down) pulling on the little invisible air molecules, the Earth’s atmosphere weighs in at about 11 trillion-trillion pounds. At the surface, that’s about 14.7 pounds per square inch. That adds up, so that an open newspaper has a few tons of air pushing down on it.

Fortunately this air pressure pushes on things in all directions, so we don’t notice it so much until it gets removed. Suck the air out of a pop can and it would collapse from the surrounding pressure. But if you make a strong enough container that won’t collapse, you can earn a small place in the history books.

In the 1650’s the mayor of the German city of Magdeburg, one Otto von Guericke, figured out how to make a vacuum pump. With the flair of a modern-day infomercial producer, he sought a demonstration to dazzle the crowds with the power of the nothingness that his pump could produce.

He fashioned two bronze balloon-sized hollow hemispheres (about 1.5 ft across). When placed together, they could be easily separated. But with the air between them pumped out, the resulting vacuum held the two hemispheres tightly. So tightly that in various showings he was able to take 8 to 30 horses, split into two teams pulling the resulting sphere in opposite directions, without separation. Once the air was let back in, the hemispheres fell apart.

And so nothing proved to be stronger than at least several horses.

Nothing like Search Trivia

As you may know, searching in Google or Bing using “double quotes” forces the search engine to find the exact phrase, instead of variations that change the word order or may use less than all of the words. Before this post was posted, if you searched for “nothing is stronger than something” with those double quotes, Google gave only one hit (here) and Bing found zero matches. In the modern world, this is nearly impossible and means that this phrase must be Special. If you don’t use the double quotes, you’ll get hits for things like ‘nothing is stronger than love’ and other non-Special things like that.

Should we conclude that Bing has figured out the power of the vacuum since it had zero hits? Maybe. And if you know other cases of strong nothingness, please comment.

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