## Visualizing Large Numbers with Pennies

It’s an oldie, but a goodie and one we’ve used a few times here before…

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. 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

Not All Brains Have Equal Processing Capacity

There’s 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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