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Visualizing Large Numbers with Pennies

The MegaPennyProject

When we start discussing topics with very large numbers, for instance the finance worksheets from earlier this week, or atomic dimensions in chemistry, it’s helpful for kids to relate it to something familiar and physical. In a more adult context, I heard someone asked in an interview to estimate the number of pennies it would take to span the Golden Gate Bridge, which in case you were wondering…

4,200 feet
1
×
12 inches
1 foot
×
1 penny
0.75 inches
= 67,200 pennies

Imagining physical sizes of things is a great tool, even for adults. And if you can take those thought experiments beyond the usual “how many jellybeans in the jar” questions that can be demonstrated in real life, into the realms of “how big would a million pennies be?” it helps make these millions, billions and zillions all a bit more meaningful. The illustrations at the MegaPenny project are a fun place to start.

Math Riff: The Cruel Math of Weight Loss Multiplication

Raise your hand if one or more of your new year’s resolutions are “get in shape” or “lose weight” or “By Halloween, look just like Gerard Butler for that Spartan warrior costume I’ve twice now skipped in favor of the Energizer Bunny suit.” What? No?

The sad news from the scale this morning is that I’m 16 pounds away from my resolution goal weight, and while I’m making progress already, it’s slow. I saw a Science Channel program where a guy lost something like 12 pounds in one day. By swimming the English Channel. Still, I can do this.

To get motivated, I decided to do a little math. The Mayo Clinic says there are 3500 calories in a pound of body fat, and the elliptical machine is reporting that I’m burning calories at a rate of 800 per hour, so a little unit conversion math would surely tell me I could work this weight off with a couple of days of serious commitment…

16 pounds
1
 ×
3,500 calories
1 pound
 × 
1 hour
800 calories
 =  70 hours

Ouch. These are not the results you were looking for, Obiwan. In fact, my left calf just developed a cramp I think to make darn sure my brain was on the same page with the the muscular/skeletal system’s assessment of these figures.

And, you know, thinking more about it, that Energizer Bunny suit was awfully slimming.

Probability and the Evil Tweep of No Sleep

As I type this, the calm clicks of the keys are punctuated once a minute by a sound I can most accurately ascribe to an evil, mutant cricket. It is the smoke detector at the top of the stairs, warning me that its battery is low. It has, in fact, been warning me quite urgently and persistently since 3:22AM this morning. I do not believe the timing is random, and I suspect it is actually, motive unknown, part of a sinister plan to do me in.

Having invested our full share to inflate the housing bubble, our home meets all of the recent building codes pertaining to fire safety. This includes a full complement of hard-wired smoke detectors — one in each bedroom, at the top and bottom of any stair way and in locations within hallways whose precise specification eludes me. The net result of this is that we have no fewer than nine smoke detectors in the house. I discern at a minimum that the authors of the current building code possess significant stock holdings in smoke detector companies, even if they are not fully complicit in the threats against my life.

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Math Riff: The Supercomputer Brain Part 1

There are all sorts of interesting supercomputer news out there recently. Los Alamos National Laboratory’s Roadrunner supercomputer narrowly edged out Oak Ridge National Laboratory’s Jaguar to take the title of the world’s most powerful with a score of 1.1 petaflops of computational power. Not to be outdone, Lawrence Livermore National Laboratory announced they were contracting with IBM to deliver a 20 petaflop machine in 2009. That would actually create a machine more powerful than the 500 fastest supercomputers on the planet and represents a significant leap forward.

Naturally, all of us are looking for faster computers these days. Ray Kurzweil’s hope is for computers fast enough to deliver full blown supra-human artificial intelligence. As in brain-in-a-jar, download your head and live forever stuff. You can read all about it in his book The Singularity Is Near. Be forewarned… If you’re the least bit apprehensive about computers inside your skull, Ray’s train of thought may have you pricing cabins in Montana. Ray pegs the arrival of the Singularity as circa 2040.

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Math Riff: The Supercomputer Brain Part 2

In the previous post we set out to talk about the comparison between brains and computers, looking specifically at whether Ray Kurzweil’s prediction for human-level artificial intelligence is likely in the next few decades. Our main conclusion based on looking at the structure of a brain is that we’d need roughly 32 petabytes of space to accurately model what the brain looks like. This post delves into what kind of silicon-based infrastructure you would need to process a data structure that size.

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2008 Electoral College Ball… Go Team!

It’s officially two weeks until Election Day, and we’re already gearing up here for an evening of popcorn in front of the TV. With Dad not being a big sports fan, election night is something like the Super Bowl around here, and this is the first election where the kids realize there’s something like “teams” we root for throughout the night.

That said, if we learned anything in the last two elections, it’s that score keeping is hard. Seriously, if football had scoring rules like the Electoral College I think we’d be looking at a lot more hockey fans out there. Let’s take a closer look!

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Math Riff: Flipping Coins for Lucky Numbers $7 Billion and $700 Billion

Big numbers starting with seven are in the news this week, and it’s worth a Math Riff to try to get a handle on just how much tax payer contribution our elected leaders are asking us to sign up for. It’s those billion dollar figures again that boggle the mind. Did you know a billion dollars worth of pennies weighs 312,000 tons, and would make a cube 126 feet on a side? Or that there are over 2 billion pennies in circulation today?

The $7 billion dollar amount is the current revenue short fall in California. Governor Schwarzenegger is getting ready to hit up Uncle Sam to cover the gap until the credit markets loosen up and the state can go back to conventional lending sources to cover its cash needs. That should get California through this fiscal year, but what the state will do next time around is anybody’s guess… Unless the California tax payers can find two million pounds of pennies in between their couch cushions or car seats, there could be an even bigger crunch come next year.

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Math Riff: Why the Dow Jones Industrial Average is Almost Entirely Meaningless

Oooh boy. It’s been a wild week in the stock market. With the Dow Jones Industrial Average (the DJIA or the “Dow”) swinging madly up and down several hundred points at a day, 100 year old companies biting the dust and comparisons to 1929 in the wind, a number of family and friends around here grew a healthy crop of gray hair. So while everyone had the daily change in the Dow right on the tip of their tongue, it turns out almost nobody could actually describe what a change in that number really means.

People associate up moves on the Dow with healthy markets, a strong economy, sunny days, bumper farm crops, and who knows what else. Investors assume the Dow is a reliable market indicator, but in reality, the Dow is poorly constructed, tells little and should never be used as a benchmark. I haven’t used the Dow in decades […]. My advice to you is you will see markets better if you train yourself to ignore the Dow for the rest of your life as well.

– Ken Fisher, #271 on the Forbes 400, from his book “The Only Three Questions That Count”

As you might guess from Ken’s opinion, the Dow itself isn’t exactly a straightforward number, and even the components from which the big number is derived don’t match measure value the way people generally expect. To find out what a change in the Dow means in real dollar terms, you need to understand how it is calculated… And that will lead you directly to Ken Fisher’s conclusion that the Dow is pretty much useless.

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Math Riff: Hurricane Ike versus T. Boone Pickens… Fight!

Part of the fun with math is just playing with numbers, but the numbers have to actually mean something to make it interesting. I call these “Math Riffs” as in many respects they’re just stream-of-consciousness runs of calculations, and while thought provoking, meant mostly for entertainment value. They’re the kind of things that I hope provoke a “Wow!” response from my kids, but sometimes I’m sure they’re thinking “Oh no… My Dad’s a geek!” or something similar.  Oh well.

There’s a lot of numbers in my professional field, but they’re nothing like playing with big scary government sized numbers… the National Debt, the Federal Budget, the Gross Domestic Product, the Annual Energy Consumption… What? Last one didn’t ring a bell? Okay, fine… Let’s play!

According to the Annual Energy Outlook, the United States used approximately 73 quadrillion BTU’s worth of energy in 2006.

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