The Trillion-Dollar Question

Trillions of Trillions

This meme appeared on Facebook accompanied by the caption: Share with as many as you can!!!  People need to understand

I’m not sure what the author wants people to understand, but the only message I’m taking away from this meme is that the author doesn’t know how numbers work.

When it comes to naming huge numbers, there are two scales.  If you were educated in an English-speaking country, you most likely learned the short scale.  In the short scale, a one followed by six zeroes is called a million, like this:

1,000,000 = 1 million

Multiply 1 million by 1000, and you’ve got a billion:

1,000,000,000 = 1 thousand million = 1 billion

Every three zeroes that you tack onto the end of the number causes it to get a new name, like this:

1,000,000,000,000 = 1 trillion

1,000,000,000,000,000 = 1 quadrillion

1,000,000,000,000,000,000 = 1 quintillion

1,000,000,000,000,000,000,000 = 1 sextillion

If you were educated in a Continental European nation, you probably learned the long scale.  On the long scale, 1,000,000 is still called a million, but there the similarities end.  Numbers don’t get a new name until they have accumulated six more zeroes, so a billion on the long scale is 1 million million, or 1,000,000,000,000.  This is what we short scale users would call a trillion.  And the number that long scalers call a trillion is equal to what we would call a quintillion (with 18 zeroes).

1,000,000,000 = 1 thousand million (sometimes called 1 milliard)

1,000,000,000,000 = 1 billion

1,000,000,000,000,000 = 1 thousand billion (or 1 billiard)

1,000,000,000,000,000,000 = 1 trillion

1,000,000,000,000,000,000,000 = 1 thousand trillion (or 1 trilliard)

And so on…

This meme starts with the number $1,000,000,000,000,000,000 (18 zeroes), which the author refers to as a trillion.  That would be correct if the author were using the long scale.  But the author is clearly a proficient English user, and his meme seems to be directed toward an American audience (since the United States National Debt now stands at just over 18 trillion dollars, according to The Concord Coalition).  I’m at a loss to explain how this combination of numbers and words could wind up on the same meme!

Regardless of what the author calls $1 x 1024, he’s just wrong.  That’s more than the combined value of all the money on Earth; many times more, in fact.  The United States’ debt isn’t anywhere near that value, nor could it be, unless the government decided to build a Death Star after all and didn’t tell anybody about it.  From the outset this meme contains faulty – some might say ludicrous – information, and it just goes downhill from there.

In order to demonstrate how much a trillion (or quintillion) dollars really is, he decides to break it down to minute-by-minute spending.  Now this is a noble effort if you want to impress your audience with the hugeness of a number, but why does he start counting 2015 years ago, during the time of Christ?  The United States wasn’t around to accrue debt back then!  It’s a completely arbitrary start date, unless the author is one of those people who mistakenly believes that the United States is 2015 years old.

Still, let’s go with it.  The author’s first task, which he spells out for us in plain English, is to divide one trillion (whatever you hold that to be) by 2015.  Because why not, I guess.

The author comes up with the following quotient: $496,277,915,632.77 – about 500 billion dollars.  But when I divide 1,000,000,000,000,000,000 by 2015, I get a substantially larger result: about 500 (short scale) trillion dollars!  I started with the same two numbers he did, but somehow my answer came out 1000 times larger than his.  Huh.

Okay, I thought, let’s give this guy the benefit of the doubt.  Maybe he really does know what a short scale trillion looks like, and he mistakenly typed too many zeroes in the numerical representation at the top of the meme.

But that doesn’t work either.  If we assume that he meant to divide $1,000,000,000,000 (1 short scale trillion) by 2015, we get about $500 million, or one one-thousandth of the quotient he listed.  So depending on which version of a trillion he started with, he either overshot or undershot the correct answer by a factor of 1000.

This guy is trying to make a statement about the size of the national debt, but he doesn’t seem to have the mathematical chops to process the numbers involved.  Call me cynical, but I am not hopeful that this will improve as we go on.

Next, our intrepid numbersmith divides by 365 since, as we all know, there are 365 days in each and every year, right?  Interestingly enough, the author manages to get this calculation correct; or I should say, the answer would be correct if the number from which he started were correct.  If you divide $496,277,915,632.77, the author’s solution to his first self-imposed math problem, by 365, you do get about $1.36 billion.  But remember, his first calculation was off by a three orders of magnitude, so this tiny mathematical victory isn’t really anything to celebrate.

The author competently divides his result by 24, then once again by 60, to conclude that you would have to spend about 1 million dollars per minute for 2015 years in order to spend $1 trillion.  But since the author’s initial error has continued unchecked into the final calculation, we know that’s wrong.  If you were trying to spend a short scale trillion in 2015 years (accounting for leap years), you would only have to spend about $944 per minute in order to do so.

After his mathematical gymnastics, the author’s dismount is a stunning non sequitur from a large national debt to an imminent crash.  We’re left to ponder whether the author really is crazy (his word, not mine!).  Personally, I don’t think he’s crazy.  Ignorant, perhaps.  Unwilling to think critically, maybe.  But crazy?  No.

The sad thing is: he’s right about the national debt being huge, and it is a topic worth discussing.  But the author does himself no favors by couching his argument in numerical misconceptions and mathematical blunders.  I’ve said this before: a meme is just about the worst way to communicate important ideas.  It would be much wiser to link to a scholarly article about the national debt, and about its looming implications, than to try to condense an entire debate into a half-assed meme.  When you try to push an agenda in meme form, you don’t convince the opposition.  You simply paint a target on your back that is irresistible to pedantic assholes like me.

Quick Memes, Part 3

It’s time to take a look at a few memes that are Stupid and Bad, but which don’t warrant an entire post.  Enjoy! (Here are parts 1 and 2, if you missed them.)

is it legal

The mind of a smart man asks “Is it legal and right, and if it’s not legal, does the rightness of it outweigh the possible legal ramifications?  Is right for me the same as right for everybody else?  Is my right more important than other folks’ right?  If I think that something illegal is nevertheless right, should I try to reform the laws concerning that thing, or should I just do as I wish and damn the consequences?”  And then the smart man starts to realize that ethical decisions are far more complicated than the simple dichotomy suggested by this meme.

Be aware: if anybody has ever called you a slave because you concerned yourself with questions of legality, that person is a fool, and he’s no friend to you.  A real friend would not offer a false dilemma like this one in order to goad you into making potentially life-altering decisions.  A friend would encourage you to consider all aspects of an ethical decision – legality, fairness, long-term consequences, and so on – before making an informed decision.  And if, in the end, you decide that the rightness of an act is more important than its legality (or lack thereof), then so be it.  But at least you’ll have considered all the relevant details and will have made your decision accordingly, and you’ll know that you’ve made your decision not just as a free person, but as a wise person.


Several things wrong here:

  • Just because some “rednecks” enjoy watching NASCAR doesn’t mean that rednecks contracted, designed, or built the fences the surround NASCAR tracks.
  • Even if they did, there’s a huge difference between building a fence that will stop a 190-mile-per-hour stock car (and the flying debris inevitably associated with it) and building a fence that will stop a nimble person determined to get past it.  People trying to cross the United States-Mexico border – let’s be honest…when you said illegal aliens, you weren’t talking about Canadians, were you? – are seldom (probably never) driving 190-mile-per-hour stock cars.
  • There is currently a “wall” along the United States’ southern border, but it’s an incomplete hodgepodge of various fence types.  There have been political pushes to complete it – especially during election years – but the price tag for this project is uncertain and unpredictable.

So, yeah.  Building a 2000-mile-long fence across various types of terrain is altogether a different task than building a 2-mile-long fence around a NASCAR track.  This meme’s author is trying to compare apples to oranges, and probably feels terribly clever for doing so.  To the author:  Stop it.  You’re not clever.

Also, stop calling them illegal aliens, you racist prick.


This is a personal quibble and I understand if you disagree, but I hate these little “math” puzzles posing as intelligence tests.  It’s not that I don’t get it.  I get it.  I see the pattern, and given any pair of numbers, I could generate the expected “solution”.  For example:

55,500,000 + 55,611,111 = 111,111,111,111,111


228,333 + 228,456 = 123,456,789

Now that’s clever.  But I digress.  The problem with these “math” puzzles, besides the fact that they use non-standard definitions for the plus and equal signs, is that they aren’t intelligence tests at all.  They’re nothing but sharebait.  The “puzzles” presented in these memes are generally trivial in order to maximize the number of people who solve them and pass them along.  Why?  Because a challenging puzzle – a puzzle that really makes you work for that shot of self-satisfaction when you solve it – would hardly get any exposure at all.  These stupid math puzzles give you the impression that you’ve done something smart, when all you’ve done is cleared the minimum hurdle necessary to share somebody else’s meme.

Gays and Guns

Capital idea!   Our approach to gun ownership should exactly mirror our approach to marriage: it’s only legal with the state’s consent and it must be thoroughly documented!

Or would you rather just acknowledge that marriage rights and gun rights are separate issues, and that supporting one doesn’t obligate you to support the other?

Your call.

Privileged Earned

I’d say you’re wrong, Morpheus.  You might be successful because of your education and hard work, but you’re privileged because of the station into which you were born, and because of society’s reaction to that station.  Ignoring privilege doesn’t make it go away.

Facebook Feeds The Hungry

No it doesn’t.  Facebook’s charitable donations are not affected by the number of people that share a meme.  Just like the math puzzle above, this is sharebait.  Its only purpose is to reward you with a false sense of self-satisfaction in exchange for a minimum amount of effort.

If you want to make a real difference, donate real money to real organizations that are working to alleviate hunger and sickness in developing nations.  If you’re a genuine activist, leave the comfort of your home and nation to volunteer in the regions struck by famine, war, and poverty.  Real change takes real effort; clicking “Share” on Facebook isn’t going to do it.

Stand Up and Be Men

Did you ever read something so blatantly sexist that you have to read it twice because you’re certain you misread it the first time?  For me, that’s this meme.  Yowza, what a load of sexist bullshit!  I didn’t even realize they had memes back in the 1950s!

Pennies from Heaven

“When an angel misses you”?  Are you operating under the misconception that angels are the departed souls of our loved ones?  Because if you are, I have to tell you: that flies contrary to your own religious dogma.  I researched the topic briefly, and here’s the theological consensus, as best as I can tell: angels are not humans, nor have they ever been.  According to most religious scholars, angels were created by God specifically to be his right hand not-men; humans, on the other hand, are spiritual beings in physical bodies.  Death is not some kind of graduation from human to angel; it’s merely a passage from physical human to non-physical human.  Or so the Scripture goes.

I’m not trying to tell you what to believe, but those who are telling you what to believe say that people don’t become angels when they die.

If we take this meme at face value, it raises all sorts of interesting questions:

  • Do angels materialize pennies themselves, or do they take already-minted pennies from somewhere else?
  • If they create coins ex nihilo, could they destabilize the economy by injecting enough money into the system?  Do angels have to be careful about that, keeping close tabs on how much money they’ve given away?
  • If angels get their coins from somewhere else on Earth, where?  A fountain, perhaps?  Do angels routinely search between peoples’ couch cushions for loose change, which they redistribute to people who are feeling glum?
  • If angels are the messengers of God, does God direct them to drop pennies?  How do they decide who gets a penny and who doesn’t?
  • Is there a way for people who are really upset to get larger values of money – say, quarters?
  • Do angels deliver pennies only to Christians, or can people of other faiths – and atheists – benefit as well?
  • Do people living in other countries also get US pennies, or do they get coins from their own currency?  Given the abysmal buying power of a single penny, it wouldn’t seem to matter much.  But still, if I lived in Uruguay, being given a useless US penny by an angel would almost seem like an insult.

I eagerly await the advisement of learned theologians on these queries.

Quick Memes

I’ve had a few memes sitting around for a while that just didn’t seem to merit an entire post.  Enjoy!

Being Offended

Actually, we have to stop this recent culture of people not giving a f*** when somebody else is offended.  You might not understand why somebody is offended, or if you do, you might not agree with their indignation, but the least you could do – the most basic acknowledgement you could afford somebody – is to recognize that they are offended, and perhaps to offer your condolences.  Don’t worry…you can still maintain your tough guy individualist persona without being a total jerk to everybody.

Child and Gun Control

Either this meme is a complete non sequitur, or it’s suggesting that many of the societal issues which are frequently blamed on guns (and the public’s easy access thereto) could instead be solved by a liberal application of parental strictness.  It’s hard to imagine how we might test this hypothesis in the United States, so let’s look to other nations.  A 2010 study assessed the relative toughness of parents in Canada, France, and Italy.  The results showed that Italian parents are the most strict, French are moderate, and Canadians are fairly laid back.  If I’m correctly interpreting this meme’s implied hypothesis, gun violence should therefore be most pervasive in our neighbor to the north, and least common in Italy.  But is that the case?

In a word: no.  A 2012 tally of firearm-related deaths per 100,000 population per year lists 0.51 for Canada, 0.06 for France, and 0.71 for Italy.  There doesn’t seem to be a strong correlation between parental strictness and gun-related deaths, at least among those three nations.

The firearm-related death rates of all three nations pale in comparison to that of the United States: about 2.97 of every 100,000 people in the United States are killed by guns each year.  Instead of blaming lax parenting for the United States’ relatively high rate of gun-related violence, maybe there’s another explanation.  If you sort the list in terms of gun ownership, the United States is at the top of the list for which data is available: there are 88.8 guns for every 100 people in the United States.  Let me put that into perspective: there were only about 83 registered passenger vehicles per 100 people in the United States in 2009.

Now I’m not going to preach about gun control this time: you may make of these statistics whatever you like.  But know this: there’s no reason to think that stricter parents will lead to a decrease in gun violence.


Although the Bible never explicitly states that all Angels are male, it always refers to them in masculine terms, and they always seem to appear as men.  Some argue that Angels are genderless.  While I suppose it wouldn’t be beyond the power of an Angel to assume a feminine form, this picture is not, strictly speaking, Biblically-based.  That’s not a point against the picture, by the way.

Also, here we see another example of the awesome power of Facebook to bend the will of the Immortals.  Zuckerberg be praised!


Perhaps you remember learning the Order of Operations in elementary school.  You may have learned Please Excuse My Dear Aunt Sally, or PEMDAS, which tells you that when you evaluate a sequence of mathematical operations, you should first heed anything in parentheses, followed by exponents, multiplication and division (left to right), and addition and subtraction (left to right).  If you’re a PEMDAS purist, you get 7 as the answer:

6 – 1 x 0 + 2 / 2

6 – 0 + 1

6 + 1


Here’s the trouble: contrary to what you may have been taught, there is no single correct Order of Operations, as this video demonstrates.  In fact, the Order of Operations we’re taught in school is quite arbitrary.  This problem could be correctly evaluated to give several different answers, which means it is ambiguous and therefore useless.  Writing intentionally vague math problems and then demanding that your audience use one particular Order of Operations to get a prescribed answer does not show how smart or dumb your audience is; it shows how much of a pedant you are.

Two Different Bands

Ah, so the message is: Throw your money around and you’ve got a dance partner, but put a ring on it and you’ve got a slave!  Classy.

Now I know there are women who happily make their living as housewives, cooking and cleaning and so on, and that’s okay.  I’m just really uncomfortable with the idea that a marriage band mandates a woman to that kind of life.  I just can’t get rid of this idea that a marriage should be an equal partnership, with each partner able to pursue his or her ambitions.  The view of marriage expressed in this meme is…well, it’s kind of Medieval.

It’s 601.3952191 O’Clock Somewhere

Clock of Nines

Points for the idea; not so much for the execution.

I know this isn’t offensive like some (most) of the memes I cover, but there is a problem. If you’re going to make a clock wherein the numbers of the hours are written as mathematical expressions using only the digit 9, you probably want to check your math. Look at the 5 o’clock slot. You see that exclamation mark beside the first nine? No, the clockmaker is not expressing his enthusiasm about the number nine. I mean, it’s obvious that the designer really likes the number nine, but that’s not the purpose of the exclamation mark. In math, that bit of punctuation indicates a factorial. Since the name factorial does absolutely nothing to tell you what it is, I’ll elaborate.

To find the factorial of any positive whole number, you simply multiply all the whole numbers up to and including the number itself. So for example, 2! (read as “two factorial”) is equal to 1 x 2, or 2. Five factorial is 1 x 2 x 3 x 4 x 5, or 120. As you may well imagine, factorials get pretty huge pretty quick.

If you look closely, you’ll see that the factorial symbol is clearly beneath the square root (or radical). Following any logical order of operations, you should evaluate 9! first, then take the square root. Nine factorial is equal to 362,880, and the square root of 362,880 is approximately 602.4. (It’s actually irrational, which means the digits run on forever after the decimal point without repeating or terminating. Sort of like pi.)

If you subtract 9/9, which is the same as 1, you get about 601.4, which is clearly not what the clockmaker was going for. He or she should have placed the factorial symbol outside the radical…maybe like this:


Or better yet, like this:


In either case, one would find the square root of nine first (which is 3), then evaluate the factorial. 3! = 1 x 2 x 3 = 6. And of course 6 – 1 = 5.

I have seen versions of this clock that had the factorial correctly placed, so I’m not sure whether the “wrong” version is the original or a copy-cat. In any case, it seems mildly ironic to make a clock that would appeal to math nerds, then make a mathematical mistake on it.

Kudos, though, for understanding that 0.9 repeating is exactly the same as 1.

A Slice of Infinity Pi

Pi Worlds

Remember pi from your high school math classes? Well just in case you’ve forgotten, pi is the ratio between the distance around a circle (its circumference) and the distance across a circle (its diameter). A perfectly round, perfectly planar circle is about 3.14 times farther around than it is across. But it’s not exactly 3.14 times longer. In fact, there’s no way to write the exact relationship, because pi is irrational.

I don’t mean to say that pi isn’t logical or reasonable; I mean that pi cannot be expressed as the ratio of two integers. The numbers 18, 5/9, and -54.5 are all rational because they can all be written as fractions with whole numbers (positive or negative) in the numerator and the denominator. All rational numbers have a few traits in common: when written in decimal form, the digits after the decimal either come to an end (as in -54.5) or repeat the same pattern infinitely (as in 5/9, which is the same as 0.555555…).

Pi isn’t like that. There are no two integers you can think of that, when written as a fraction, will be exactly equal to pi. The fraction 22/7 is fairly close to pi, but not exactly equal.

And it’s not just that mathematicians have not yet been successful in finding the magic fraction that precisely captures the value of pi; it is utterly impossible to do so. The absolute irrationality of pi was first proved in 1761 by Johann Heinrich Lambert. But I digress.

What about the rest of this meme? Is it really possible to find every picture, every word, every social security number buried within the digits of pi? To be honest…nobody really knows.

Imagine that you had a random number generator – I mean a truly random number generator (you get them at the same place you buy frictionless pulleys and absolute zero meat lockers). Let’s say you set the generator to run day and night, churning out digits to fill the decimal places of a number that is to be infinitely long. In other words, eighty squillion years from now, when the last proton decays into a burst of energy and all other matter is gone, this random number generator will still be cranking out digits (having somehow avoided decaying itself…I’m still working out the logistics on that one). Invoke your God-like powers to travel to the end of space and time, where existence is an abstraction, and examine the infinite sequence of random digits. Yes, in this infinitely long sequence of randomly generated digits, you will truly find every conceivable series of digits. Want to find the telephone number of your first crush? Got it. All of Shakespeare’s plays, translated into Klingon and then represented in binary? Got it. A digital recreation of the Mona Lisa as it would look if it were painted by Andy Warhol? Got it. It’s all there, hidden somewhere within the infinite possibilities, if you know where to look.

Although the digits in pi are not randomly generated, the digits are expected to turn up in about the same manner as if they were randomly generated. In other words, in the first million digits of pi, you’d expect to see approximately 100,000 ones, 100,000 twos, 100,000 threes, and so on. And so far, that has held true, but we cannot claim to know that it will always be true. That’s the nature of infinity; even if we know one googol of pi’s digits, we still know essentially zero percent of them. There is always some possibility that, for reasons yet unknown (and perhaps unknowable), the digit seven will suddenly stop appearing in pi somewhere after the 44 quadrillionth digit. And if it does, then any sequence containing the digit seven that has not yet appeared…will never appear. In fact, it’s possible that all but two digits could stop occurring in pi, and pi could still go on forever without repeating. And although these may sound like mathematical abstractions – outcomes that will never occur – we cannot say for sure.

I would like this meme better if it contained some hedge words like “probably” or “maybe”, but it doesn’t. It’s presented as a sexy math fact – a quotably nifty truth that might not actually be true. It has that “gee whiz” appeal, but it does little to prepare one for the brain-busting unknowableness of the infinite, with its endless possibilities. And for my money, it’s aimed in the wrong direction. To me, it’s a far less interesting possibility that pi might contain every imaginable number sequence, and a far more interesting possibility that it might not.

Minimum Rage

Minimum Wage

I’m not sure whether this meme is taking a shot at people who think minimum wage is too low, or at untrained workers who refuse to work for minimum wage, despite having no skills that would qualify them for a higher-paying job. In any case, I dislike the implication that anybody earning minimum wage is a shiftless, stupid slacker, incapable of making a meaningful contribution to society. In fact, many minimum wage workers are students who are in the process of getting the very education that will one day, hopefully, allow them to work for more than minimum wage.

Now that I’ve said my piece about this meme, let’s talk some more about minimum wage. It is surely one of the most hotly debated topics among political junkies. I thought it would be helpful to compare the buying ability of a minimum wage worker from 1950 to one from 2013. Stand back: I’m going to try MATH!

Let’s start in 1950. The minimum wage in 1950 was seventy-five cents an hour, but of course you didn’t get the full six bits to do with as you pleased. After Uncle Sam and your state government got in on the action, you’d wind up doling out about 22% of your income as taxes, if I’m reading this graph right. So you’d really only bring home about $0.51 an hour. Now let’s take a look at how long you’d have to work to buy things at 1950 prices if you were making minimum wage.

If you netted fifty-one cents an hour in 1950, it would take you:

  • 7 hours 51 minutes to buy a Monopoly board game.
  • 1 hour 4 minutes to buy a bottle of aspirin.
  • About 245 days (straight) to buy a Chevy Corvette (assuming you had no other expenses, of course).
  • 1 hour 33 minutes to buy a pound of coffee.
  • 24 minutes to buy a gallon of gas.
  • 1 hour 36 minutes to buy a gallon of milk.
  • 16 minutes to buy a loaf of bread.
  • 1 hour 16 minutes to buy a dozen eggs.

I could go on and on, but this gives us a good enough idea of how much it cost to live in 1950. Now let’s fast-forward to 2013, when the federal minimum wage is seven and a quarter. We’re still paying the IRS its due, which means the minimum wage worker is really only walking away with $4.93 an hour. What kind of buying power does this uneducated slob have? Surely a minimum-wage worker must be able to buy a Chevy Corvette after only a fortnight’s labor, to hear some people gripe about it.

In 2013, a minimum wage worker must work:

  • 2 hours 38 minutes to buy a Monopoly board game. (-66%)
  • 1 hour 25 minutes to buy a bottle of aspirin. (+33%)
  • About 419 days (straight) to buy a Chevy Corvette, and that’s assuming you don’t want heated seats. (+71%)
  • About 1 hour 13 minutes to buy a pound of coffee. (-22%)
  • 44 minutes to buy a gallon of gasoline (as of today). (+83%)
  • 43 minutes to buy a gallon of milk. (-55%)
  • 17 minutes to buy a loaf of bread. (+6%)
  • 24 minutes to buy a dozen eggs. (-68%)

So what can we make of all this? The buying power of the minimum wage worker in 2013 is not significantly greater than the buying power of the minimum wage worker in 1950. Sure, the modern worker may be able to enjoy an extra serving of milk, eggs, and coffee while playing Monopoly, but the cost of other items, particularly gasoline, has risen to compensate. A household doesn’t need a Monopoly game, but almost every household must purchase gasoline…and in much greater weekly quantities than they would purchase of milk, coffee, bread, or eggs. In any case, the minimum wage worker of 2013 is not wealthy, and certainly isn’t asking for a handout.

My trusty calculator