Range Anxiety

I was talking to some friends (and one cab-driver) about electric and hybrid cars the other day, and the concept of range anxiety came up.  Consumers may very well wish to purchase electric cars, but they are apprehensive about getting stranded on long trips:  auto makers call this range anxiety.

I wonder what the average consumer’s range anxiety is (measured in, say, miles), and I wonder how that compares to the capabilities of a typical electric car.  Consumers are assumed to act with lots of information (provided by commercials and marketing, for example), but perception is often far from reality.  There could be a large gap between someone’s range anxiety and the capability of the car–range dissonance, perhaps?  In order to make sales, car manufacturers need to close that gap, through technology or marketing.

There’s a lot of interesting quantitative analysis to be done here, both of the car’s performance, and the consumer’s perception of performance.  In addition, the government–which seems interested in promoting electric car use–must understand the needs of the cars and consumers as well, as it starts to develop the geometry of “filling” stations.

How Much is Blockbuster Worth?

Blockbuster Video will always have a special place in my heart.  When a store opened up a few blocks from my childhood home, it was a big deal.  We were excited to walk over, browse the rows of VHS (and, for a short time, Beta) cassettes, and bring back a movie or two for three days / two nights.

Oh, how times have changed.  Once valued at nearly $5 billion (in 1996 dollars), Blockbuster stock is currently trading at around 17 cents a share, which means that the company is currently valued at around $37 million.

So where is this $37 million in value?  The company has dropped more than 100-fold in value, but $37 million stills seems like a lot of money.  Does Blockbuster have any significant revenue?  Do they have exclusive agreements with movie studios that have value?  Is the Blockbuster brand worth something?  Can they sell all their old VHS tapes to Panama?

Determining the value of a company is an interesting and complicated problem.  Facebook provides another good example of the complexities involved.  Recent reports suggest Facebook has a value between $10 and $20 billion, even though Facebook’s revenue is on the order of $1 billion.  How does one determine that all the non-revenue-related stuff (brand identity, user base, etc) is worth $9 billion?

One thing is for sure:  Netflix, currently valued at around $5 billion, is definitely 133 times more valuable than Blockbuster.  At least.

Geometry of BBQ

There seemed to be a lot of geometry involved in my grilling this weekend.  The circular grill, the cylindrical chimney starter, the pyramid of coals.  The charcoal briquettes themselves look like solids with mirrored parabolas as vertical cross-sections and squares as horizontal cross-sections.

As I cooked a few times over different coal arrangements, I wondered about the heat distribution on the grill over the perfect pyramid of charcoal.  Obviously the hottest point is the center (nearest the peak of the pyramid), and the temperature drops as you move toward the edge along a radius.  Does it drop linearly?  Like a parabola?  Like a log function?

My guess is it looks like the image below.  I don’t have any evidence for this speculation, but this is a representation of a Gaussian distribution, and when in doubt, go with Gauss.  Gauss seems to have a hand in everything.  Maybe I’ll bring the meat thermometer next time and take some readings.

Real World Problems

I’ve been shopping for a new cell phone (doesn’t yours have an antenna?) and it reminded me about cell phone plans and linear algebra.

Cell phone plans used to be the prototypical real world problem for high school math classes.

Plan A costs $10 a month plus 25 cents a minute, while Plan B costs $30 a month plus 12 cents a minute.  Which plan should Sue Consumer choose?

Figure out the equations of some lines, find the intersection, make some conclusions.  Math in action!

Fast forward to the present, and it’s embarrassing how confused I am by all the options:  a serious multivariable analysis is necessary to figure out which plan is the right one for me.  This was once an exemplar of simple, relevant application, but now it has become ugly with the real real world details.

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