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Magnitude and Precision September 14, 2009

Posted by Chuck Musciano in Leadership.
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A quick math test:

Paula Programmer has been assigned to write a new interface for a web-based application.  She estimates that the task will take seven days.  After one day of hard work, how much of the task has Paula completed?

  1. About one-seventh
  2. 14%
  3. 14.28571%
  4. Not enough information to answer.

Optimists might answer A, on the assumption that Paula estimates well and works consistently.  Pessimists will always answer D, believing that until Paula delivers some code that works, she’s done nothing but shop on eBay all day. An optimist that can do math in their head might come up with B.  Finally, a compulsive optimist with a calculator will answer C.

Why?  Why are people instinctively drawn to numbers with more digits?

I’ll tell you why: more digits imply more precision.  Many years ago, right around the time that schools stopped teaching kids how to use slide rules, they stopped teaching kids the difference between magnitude and precision.  Instead, armed with calculators, kids can rattle off an answer to 8 digits, blissfully unaware that digits 2 through 7 are meaningless.

To review: the result of any computation is only as accurate as the least accurate of all the values used in the computation.  If you divide a one-digit number by another one-digit number, your answer is accurate to a single digit.  In Paula’s case, when you divide “about a day” by “about seven days,” you get A, “about one-seventh,” her inline shopping habits notwithstanding.

Why does this matter?  We deal with numbers all the time in our jobs.  As leaders, we constantly request estimates from our people, and ask them to compute cost ratios, return on investment, completion percentages, and the like.  The resulting numbers are often used to justify projects, allocate resources, and make important business decisions.  Often, the false precision in these numbers gives them a credibility they do not deserve, and our decisions suffer as a result.

Just as distressingly, people often do a lot of extra work to create precision where it isn’t needed.  That extra precision doesn’t help, and the time wasted making the number that accurate can’t be recovered.  I sometimes ask for numbers “to the nearest x zeroes” so that my people know not to waste their time creating useless precision.  Thus, a request “to the nearest four zeroes” should be rounded to the nearest $10,000, and so forth.  They save time, I get the answer I need, and we all move forward.

Given that the public school system long ago ceded their responsibility for effective mathematics education, we must take on that task.  Effective delegation includes expectation management, and that includes defining the precision of any numerical results we request.  Make sure your people know what you want and how precise you want it.  You will get better answers and they’ll save time.  My estimate? At least 4.32675%.  Maybe more!

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My Dear Aunt Sally August 7, 2009

Posted by Chuck Musciano in Random Musings.
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The recent Cash For Clunkers program neatly demonstrates a grave problem facing this country.  No, not the auto industry, global warming, or appropriate levels of government intervention in free markets.  I’m talking about something much more important: simple arithmetic.

Cash For Clunkers set aside a billion dollars to buy back certain vehicles in trade for newer, more efficient ones.  Each trade-in would qualify for either $3,500 or $4,500 in credit, depending on the model.  The program began in late July and was expected to run through November.  It lasted all of a week before running out of funds.  How could that happen?

Easy.  No one can do math in their heads anymore.

Let’s run the numbers. To make things simple, say each trade-in gets $4,000 from the fund.  With a billion dollars available, that allows for 250,000 trade-ins.  There are 23,000 car dealers in the US, each anxious to sell as many cars as possible.  That’s an average of 11 cars for each dealer.  Now ask yourself, how long would it take for each car dealer in the US to sell 11 cars that offer an additional $4,000 discount?

If you guessed “four months,” you have a potential career in Congress.  If you guessed “four days,” you are demonstrating a good grasp of basic market analysis.  In fact, some dealerships sold more than 11 cars in just one day; the only thing that slowed their pace was that the government web site for registering all these sales collapsed under the load, clearly designed with a “four month” mind set.

I’m not presenting this to start a political discussion. I’m here to lament that the average person can no longer solve this problem in their head. (Some people cannot solve it with pencil and paper, either.)

If you seek to run a successful business, or an organization within a business, you’ll need to make many rapid decisions based on numerical analysis.  If you cannot run those numbers in your head, you will not make good decisions.  Pricing, licensing, system loads, capacity planning, leasing terms, scheduling, manpower loading, you name it: quick, accurate math skills are the cornerstone of effective management.

I have sat in many presentations where outlandish claims were made without a murmur of dissent by those attending.  Running the numbers in my head allowed me to question the claim and get a better answer.  We see advertisements every day that cannot stand the scrutiny of simple math, yet many people take them as verbatim truth.  Why won’t people do the math?

In many cases, doing the math leads you to a result that strains your credulity.  In the Cash For Clunkers analysis, you’re left wondering if it would take four months to sell eleven cars.  More typically, you may instead be looking at outrageous monthly lease payments, or unrealistic average network latency, or some other metric that makes no sense.  But if you didn’t do the math, you’d never get to the simple number that makes you say “Wait a minute!”

A big part of leadership is knowing when to say “Wait a minute!” Quick arithmetic skills can play a big part in honing that skill.  Almost all of us can do simple arithmetic, but how many of us use those skills every day to increase our odds of success?

The Circle of (IT) Life June 3, 2008

Posted by Chuck Musciano in Leadership.
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For years, computers have been touted as offering limitless capability, with some fabulous new feature just around the corner.  Unfortunately, we’ve been delivering on that promise, over and over.  Mainframes begat minicomputers.  We then offered up personal computers.  Then we created local areas networks, which grew into wide area networks, which grew into the internet.  We offered simple file transmission, which turned into text-based email, which became multimedia email with attachments and embedded content of every flavor.  We developed FTP sites and bulletin boards that turned into web sites that exploded into the web as we know it.  Now we’re layering all sorts of services atop the web, making computers even more indispensible to an ever-increasing user community.

The problem is that all of the new stuff did not replace the old stuff.  It simply extended it, which means that we have to keep most of the old stuff running.  Even worse, we’re getting better and better at running all this technology, so users naively think it is getting easier and easier.  Email and internet connectivity used to be an amazing capability that astounded previously unconnected users.  Now, these services are expected to just be there, like electricity and running water.  Trust me, it is no less complicated to keep these services running now than it was ten years ago, but we are expected to do so with smaller and more focused staffs.

Think of IT as an expanding circle.  The new stuff is at the edge, where users see and appreciate cool new capabilities.  The infrastructure is everything in the circle, hidden from users but crucial to maintaining the edge.  Our job is to expand the circle.  Each time we grow the circumference (adding a new service of some sort) the area inside grows in proportion to the square of the change, so that the amount of interior stuff grows much faster than the visible stuff.  If each IT person can only cover so much area in your circle, you’ll soon be unable to keep up.  And as the circle gets bigger, each incremental change makes it that much worse.

Consider one of my favorite numerical illusions: if you stretch a band around the equator and add exactly one foot to that band, how far off the surface of the Earth will the band rise?  Most people think of the size of the Earth, compare it to just one foot, and answer with a tiny number.  The real answer is about 1.9 inches.  Since the circumference of a circle equals the diameter times π, and you just added 12 inches to the diameter, you added 12/π (3.82) inches to the diameter of the band.  The band lifts up by half that amount (since the radius of the circle is half the diameter) or 1.91 inches.

That number is the same, by the way, if you add 12 inches to a band wrapped around an orange.  The difference in the surface area?  Adding one foot to the band around a 3-inch orange increases the area inside the band by about 29 square inches.  Adding that same foot to the band around the Earth increases the area by almost half of a square mile! 

Which size circle would you rather support?

A Slide What? May 15, 2008

Posted by Chuck Musciano in Random Musings.
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My son and I were driving home from an errand last night, engaged in a typical Guy Discussion: the mechanics of building a nuclear weapon.  My son observed, correctly, that building an atomic bomb was easy; it was getting it to explode that was really hard.  The trick, I pointed out, was getting the right material in the right shape at the right time.1

My son asked how the first bomb designers did this.  I replied that while current designers use extensive computer simulation (which is why we design and build ever faster computers: bomb design and weather prediction), the original designers did it all by hand, with slide rules.

My son looked at me and asked, in all seriousness, “What’s that?”  I gave him an incredulous stare, completely at a loss for words.2 “No, really.  What is that?”  My son, 13, is an outstanding student, way ahead of the curve in math and science and currently fascinated with computer-aided bridge design.  He was asking an honest question.

“Umm, well, it’s a computing device.  It has three wooden sticks with numbers, and you slide them back and forth to line them up so that you can multiply and divide.  Nicer ones have extra scales for trig functions.”  To help bring this detailed description to life, I used my fingers to simulate the mechanical action of a slide rule.

I may as well have tried to describe some medieval leather tanning contraption or a turn-of-the-century gadget that trimmed lamp wicks.  For a teenager with his own cell phone, laptop, iPod Touch, and game console, the idea of a wooden calculator is either pathetic or hilarious.  I half-believe he thought I was making it all up just to tease him.

Sigh. Another cultural touch point has been reached.  Slide rules are officially ancient and unknown to the current generation.  Close on its heels are tape in any form (cassette, 8-track, reel-to-reel), followed by analog video.  Phones with cords aren’t far behind, either.  Time marches on.  Does it matter?  Yes and no.

In terms of the actual device, it doesn’t matter.  I have my father’s K&E Log Log Decitrig slide rule, a beautiful device that was given to him when he graduated college with a degree in Mechanical Engineering.  It was his most important tool on a daily basis and no practicing engineer could work without one.  It still works, although the slide sticks a bit.  Still, it has been completely replaced by calculators of all stripes and for good reason: slides rules are only accurate to a few digits and are slower to use.

In terms of how it works, the loss of “slide rule awareness” is devastating.  General math abilities in the US are at an all-time low.  No one knows how logarithms work, or why this might be important.  No one understands precision, accuracy, or error ranges any more.  As a result, people cannot interpret numerical data, understand relationships, or make informed decisions.  Even worse, it has become apparent that most people cannot compute percentages or interest rates on a loan.  A disturbing number of cashiers cannot compute the change from $20 in their head.

Not everyone should be able to use a slide rule.  But maybe if we tried to teach everyone to use one, a pleasant side effect might be that everyone would at least learn percentages, and subtraction, and the ability to discern “bad” numbers from “good.”  Such an education will never happen; we’d wind up with lots of people who feel bad about themselves because they failed the slide rule test, and that’s just not acceptable these days.  Instead, we’re building a nation full of happy idiots, lacking the basic skills to survive in a modern world but certainly feeling very good about themselves.

1How like life itself. See my next blog post for more on this.
2Those who know me can attest how shocking this situation is: I am never at a loss for words.