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Category: Financial / Topics: Ethics Information Management Management

Those Pesky Zeros, Part 1

Moving the Decimal Point

by Stu Johnson

Posted: June 19, 2015


The point of this blog is the significance of smaller numbers buried inside the overwhelming mountain of very large ones, especially when dealing with financial matters.  Allow me a brief diversion as a way of introduction....

Numbers far beyond comprehension

Sometimes numbers get so big, they’re hard to comprehend or even display, so we move the decimal point or call it a “gazillion.”    

“Astronomical!” is the best description of the numbers describing the universe, where distances are so vast they are measured in light years.  Light is the fastest thing we know...traveling at 186,000 miles per second (a shade under 300 kilometers per second). In a year light travels 5.99 trillion miles ( 9.5 million kilometers). In “long-form” that would be 5,990,000,000,000 miles.  Since that is such a big number, and the universe is so big, distances in space are typically measured in other units, the light year being the most familiar to the average non-scientist.

Traveling at light speed would propel you at 670 million miles an hour!  At that speed you could circle the earth seven and a half times in 1 second; it would take 8 minutes to reach the sun, but years to reach most of the stars you see in the night sky.

The Milky Way galaxy in which earth resides (image at top of page) spans 100,000 light years from one end to the other. With recorded human history at roughly 5,000 years, it would take 20 times that long to travel the length of our galaxy at the speed of light.

Now, with the Hubble Space Telescope giving us a view not obscured by the earth’s atmosphere, astronomers can see further than ever (much of what is seen is not visible light, requiring radar, ultraviolet and other types of detection. The age of the universe has been established more definitively than previously possible—at 14 billion years.  Translated from light years and accounting for the continued expansion of the universe since the Big Bang, that means “the edge of our vision spans a distance of approximately 276,000,000,000,000,000,000,000 miles.” [1] 

Because such numbers are so hard to grasp...and cumbersome to visualize with all those zeros, we usually resort to short-hand expressions. That distance is 2.7623 in scientific notation or 276 sextillion (trillions of millions)...a very long way!. [For the proper list of term for large numbers, see the reference in note 2]

Mountains inside mountains

Trying to wrap your head around numbers in space makes the national debt of the United States look tiny– it is 18.3 trillion dollars (more precisely, it was $18,272,836,000,000  at some split-second on the afternoon of June 18 around 3:30 pm CDT as I finished this piece – it takes less than 10 seconds to watch it grow another $100,000).  [3]   

Here is one way of visualizing a trillion dollars (source of original illustration unknown):

Now, let’s try counting all that cash.  I’ll stick to the $100 bills used in the illustration and assume you can count two per second. (Multiple the times by 100 to count $1 bills).

It would take 5 seconds to count $1,000.  That’s a snap, you say, give me more!

Okay, up the amount to $1-million ($1,000,000).  This pile now represents that magical “millionaire" level that is still only a dream of the vast majority of people, yet reached by more people than ever—more on that later. That will take you about an hour and 24 minutes—without pausing to pick up your coffee mug.

At $1-billion ($1,000,000,000), we start getting into the budgets of most states and our largest cities and corporations.  Better get help, because by yourself it would take 174 8-hour days (7 days a week, no breaks).  Speed it up a bit with 24-hour days or getting the help of two other people and it would still take 58 days going at it 24-7.

Moving up to $1-trillion ($1,000,000,000,000), we find the world’s largest governments, or Apple and other companies that are beginning to join the trillion-dollar club, it is going to take a very long time to count those dollars now, even in $100 bills. It will take nearly 476 years of 8-hour workdays seven days a week, or 158 years counting around the clock.  If you wanted to get the job done faster—say closer to a year—you’d have to use 150 counters working 24-7.

Such comparisons may be considered silly, but when you’re dealing with real money, I think it does matter and we need to maintain a sense of perspective, for practical and ethical reasons.  There are indeed, mountains of significance inside the mountain we see. If we (a government or business or household) have stewardship for the resources we manage, ALL the zeros should matter.

Shifting the decimal point

As the numbers we have to deal with grow and we have to place them in spreadsheets, tables and narratives, it is simply too unwieldy to show full numbers.  In many organizations, it is common to find columns of numbers reduced to thousands or millions, rounded to one or two decimal points.   As the numbers get even bigger, the decimal point shifts at each thousand-fold jump, to billions and now more commonly at the federal level to trillions.

The problem I see is the relative ease with which we relegate the missing zeros to insignificance.

The myth of insignificance

There is a too-common technique of trying to deflect the impact of smaller segments of really big numbers. When complaints are raised about fraud and waste in the millions of dollars, how many times do you hear a bureaucrat, politician or even a CEO discount it as such a tiny percentage of the whole. But consider this. While $1-miillion out of $3.6-trillion in federal spending is insignificant as a percentage (0.00033% - 33 ten-thousandths of a percent), even that miniscule percentage, means that tax revenue from 72 households in a year was essentially trashed. [4] 

In the news today was the report of a Justice Department operation that resulted in the arrest of 243 people, including 46 doctors and other medical professional, in 17 cities across America, accused of submitting fake billing to Medicare totaling $712-million.  Again, a small ripple out of Medicare’s $949-billion expenditures (0.0196% of federal spending, 0.07% of Medicare spending). But that represents the tax revenues from nearly 51,000 households—the equivalent of a city the size of Naperville, Illinois, with a total population estimated at 141,000 in 2014 (it is the largest city in DuPage County, Illinois, where I live).

Furthermore, what may be invisible when looking at the very large whole, may be exposed as significant when seen in its smaller context way down the branches of the organization chart.  Perhaps my interest in looking at the details comes from years of working with data and looking for significance by “drilling down” into mountains of data. 

An interesting way to envision this is through the concept of fractals, a type of math that was foundational in high-definition computer animation.  It is the ultimate in drilling down. 

I don’t recall the source anymore, but I heard fractals described this way:  Imagine a map of an island on your desk.  Measure the coastline (perhaps by using a piece of string).  Now, do the same thing on a larger version of the map.  More detail is revealed, so the string must follow more curves and the result will be a longer coastline.  This will continue as you zoom in right up to literally walking around the island yourself with a measuring device. And each time you “zoom in” the more detail is revealed and the longer becomes your measurement of the length of the coastline. 

With data, the difference is we know the “length of the coastline” to begin with, but the details are obscured until we zoom in, or “shift the decimal point” to see more and more detail.

For a short example of a “fractal zoom” see www.hpdz.net/videos/CubicBurningShip2/CubicBurningShip2-tiny.mp4.  For more examples and technical details see www.hpdz.net or search “fractal zoom nature” in YouTube for more extraordinary examples.

Are millionaires becoming commonplace?

From 2001 through 2012 I was involved in a project tracking the weekly lists of bestselling books.  In the spring of 2010 I began to notice a shift in titles for some of the mass market (small paperback) romance novels on the lists, upping the ante from millionaires to billionaires, with titles like “The Billionaire’s Housekeeper Mistress,” “At the Billionaire’s Beck and Call,” “The Billionaire’s Baby Plan,” and “Have Baby, Need Billionaire.”

That shift seems to be part of a pop culture tendency to blow things out of proportion to reality, or forecasting a trend far ahead of time.  This trend made it seem that being a millionaire is no longer an adequate conquest, so let’s shift not 10 times to a multi-millionaire, but 1,000 times, all the way to a billionaire.  So, are millionaires becoming commonplace?
In the spring of 2014 a number of news outlets reported on a Spectrem Group study on millionaire households in the United States. Spectrem started keeping track in 1997, when it found 5.3 million households with $1 million or more in investible assets, or 5.2% of the 101 million households at that time.  By 2006 and 2007, the years immediately before the Great Recession hit, the proportion reached a then-record high of 7.9% (9.2 million out of 116 million total households in 2007).  The proportion dipped to 5.7% in 2008 before slowly recovering, reaching 7.8% in 2013, and then setting a new record of 8.2% in 2014 (10.1 million of 123.2 million households).   

The number of millionaire households is steadily growing, but it is hardly a rush toward becoming billionaires (consider the earlier examples of counting money).  Yet, as the headline in a New York Post online story announced, “A millionaire on nearly every block in US.”  [3]

The number of multi-millionaires ($5-million or more) has also grown as the economy expands, but remains small—from 230-thousand households in 1997 (0.2%) to 1.3-millon households in 2014 (1.1%).   Think about that. In 2014 getting into the infamous and oft-derided one percent took just over $5-million in assets, while in 1997 that level (in real dollars) would have put you in the top of the top one percent.

Billionaires are literally a drop in the bucket—not as readily available as those romance novels would have us imagine. The Forbes magazine list in May 2015 reported 1,826 of them worldwide, with 290 newcomers.[4]  Still, out of more than seven billion people—that translates to roughly 250 per billion people (two-ten thousandths of a percent).

Getting in the millionaire club is getting easier

The mystique of being a millionaire has been around for a very long time, but on the scale of things, it is far easier to achieve in real terms today than a hundred years ago. To equal the purchasing power of the 1915 millionaire would require $23.4-million today, well into the 1% level.

Even in more recent years, it would take $2.2-million today to equal the millionaire entry point 30 years ago.  Looking at it another way – the value of those dollars in 1985 is the equivalent of $452,471 today.  [5]  Obviously, inflation has devalued entry to millionaire club, but it’s still a long, long way to being a billionaire!

The takeaway

Through the ramblings of this blog, the point I want to leave with you is this:  as the universe of numbers gets larger and larger, and we have to move the decimal point to get rid of those pesky zeros, don’t lose sight of the significance found in those hidden zeros. Appreciate them. Be good stewards of them.

Notes:

  1. earthsky.org/space/what-is-a-light-year
  2. A real time “US Debt Clock” can be found at www.usdebtclock.org – it shows a host of information with real time estimates.
  3. For a listing of official “dictionary” terms for large numbers, see www.unc.edu/~rowlett/units/large.html
  4. The analysis here was derived by dividing individual income tax revenue of $1.72-trillion by the number of households in the US, estimated at 123.2-million in 2014—a figure that most people can relate to. That amounts to $13,985 per household. Total tax revenue, including “social insurance taxes” (individual and employer share) and corporate federal taxes totaled $2.8-trillion in 2014, or $23,048 per household.  Sources: census.gov,  www.usgovernmentrevenue.com
  5. Among the numerous sources reporting this story were PBS (www.npr.org/sections/thetwo-way/2015/06/19/415762173/doctors-nurses-among-243-charged-in-million-dollar-medicare-schemes?ft=nprml&f=1001) and Fox Business (www.foxbusiness.com/economy-policy/2015/06/19/feds-announce-largest-ever-healthcare-fraud-takedown)
  6. nypost.com/2014/06/11/number-of-millionaire-households-in-us-rises-again
  7. www.forbes.com/billionaires
  8. Comparison figures calculated at www.usinflationcalculator.com

 In Part 2, next week, we'll look at what happens on the other side of the decimal point


Stu Johnson is owner of Stuart Johnson & Associates, a communications consultancy in Wheaton, Illinois focused on "making information make sense."

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Posted: June 19, 2015   Accessed 1,247 times

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