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Missouri Proposition B: Know your algebra!

November 5, 2012 by Matthew Rave

As I was driving to school today, there was a story on NPR about an upcoming ballot initiative in Missouri.  Proponents want to raise the cigarette tax from $0.17 per pack (the lowest rate in the nation) to $0.90 per pack.  The idea is to generate some revenue and at the same time discourage smoking.

Missourians love their cancer sticks.

Now, I’m not going to go into the pros and “cons” of the initiative.  I would be for it, based on some pretty common-sense data, but I don’t live in Missouri so I guess my opinion doesn’t matter.  However, I’d like to comment on some squishy reasoning put forth on the radio by an opponent of the measure.

In a nutshell: “The measure,” the opponent says, “wouldn’t raise money at all.  It would actually lower revenue.  That’s because any gains made by raising the tax would lower the amount of regular sales tax accrued.” [Note: this isn’t a verbatim quote but a recreation based on my imperfect memory]

You see, Missouri has a 4.225% sales tax which also applies to cigarettes.  And, the “logic” goes, if less people are buying cigarettes, the less sales tax revenue would be generated.

Really?  Is this person completely innumerate?  Let’s say that a pack of cigarettes costs $6.00.  Without the ballot initiative, a Missourian would pay $6.00, plus $0.25 in sales tax, plus $0.17 in cigarette tax, for a total of $6.42.  The state gets $0.42 cents a pack.

Under the new plan, a smoker pays $6.00, plus $0.25 in sales tax, plus $0.90 in cigarette tax, for a total of $7.15.  The state gets $1.15 cents a pack, obviously an increase.

To be fair, the state does actually lose money if the gain in revenue per pack is offset by the loss in the number of sales.  But when would this occur?  Let’s use algebra to find out.  Suppose that N1 is the number of packs of cigarettes bought in Missouri in a given year.  Under the current system, and for a $6.00 average price per pack, the yearly intake for the state is just N1 x 0.42.  Now let N2 be the number of packs bought under the new plan.  It’s easy to see that if the proposal passes, the yearly intake for the state is N2 x 1.15.

The problem is that N2 < N1 (presumably).  So the proposal loses money if N1 x 0.42 > N2 x 1.15, which, after one line of 8th-grade algebra, is the same as N1/ N2 > 2.74.  That is, translated into English, the new proposal loses money compared to the current system if state cigarette purchasing goes down by a factor of almost 3.

I don’t know about you, but I seriously doubt this initiative will cut smoking in Missouri by that much.

The numerically savvy will notice that there is a subtlety.  This result is for a $6.00 pack of cigarettes.  What if the price is much different?  This matters, because the cigarette tax is a flat number added to a pack, whereas the sales tax is a percentage.  If cigarettes cost the same as houses the ballot initiative would be ridiculous, since 4.225% of a huge number is much, much greater than a measly $0.90.  No one would buy cigarettes at all, and the state would lose a lot of revenue.

Is there a tipping point?  That is, is there a price for a pack of cigarettes for which the proposal loses money for any decrease in purchasing? Surprisingly, the answer is no.  Mathematically, we would say that N1/ N2 = 1 only when the price of a pack is infinite.

But setting the bar at N1/ N2 = 1 is unrealistic.  Any tax hike will cause some smokers to buy less.  So let’s make an educated guess:  looking at the first graph at this site, I can see that a price hike of $0.73 produced a corresponding decrease in consumption of about 25%.  (The actual drop would probably be less than this, since in the 1980’s and 1990’s $0.73 represented a higher percentage of the cost of one pack).  So we let N1/ N2 = 1/0.75 = 1.33, and solve for the price of cigarettes.

You get $48.33.  For one pack of cigarettes.

Conclusion: the proposed tax increase would increase revenue even with a plausible decrease in sales, unless cigarettes cost around $48 or more per pack.

Yay algebra!

Some close analogue to Mark Twain or E. B. White (with so many misquotes on the web, you can’t be very sure these days) said that analyzing humor is like dissecting a frog: you don’t learn much, and the frog dies.  So why did I dissect this frog, and show all the gory math details?

I wanted to point out that there is a lot more mathematical detail in most stories you hear, most issues you examine, than you suspect.  And I want to emphasize: if you don’t know math, if you are not mathematically literate, then you don’t know much of anything.

There.  I said it.

Go study your algebra.

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Poem (No apologies to Walt Whitman)

November 2, 2012 by Matthew Rave

When I heard the poet talking about hearing the learn’d astronomer,
When the poet mentioned how all the proofs, the figures, were ranged in columns before him,
When the poet described how he was shown the charts and diagrams, and how to add, divide, and measure them,
When I sitting heard the poet where he read with much applause in the lecture-room,
When I realized of a sudden, how the theme of the poem was “ignorance is bliss” and “beauty and science are incompatible,” and [holding hands over ears] “please! O please! don’t tell me how anything in this Cosmos works, since then it would cease to be ‘poetic’!”
How soon very accountable I became tired and sick,
Till rising and gliding out I wander’d off by myself,
In the rational moist night-air, time to time,
Look’d up in perfect silence at the stars,
Thinking about the fascinating Bethe-Weizsäcker-cycle.

(Sept. 25, 2009)

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One Data Point

November 1, 2012 by Matthew Rave

The name of this blog was originally not “Many Worlds Theory”.

I was going to call it, at first, “One Data Point”.  I know: not very exciting.

I still think that’s a good name;  it gets to the heart of what I want to say in this blog, for reasons I’ll discuss in a moment.  But I went with “Many Worlds Theory” for purely selfish, economic reasons.

(Here’s the monologue that went on inside my head: “Man, I bet I could have made some money if I had registered bigbangtheory.com a few years ago.  That TV show is quite clever.  My wife says I’m a bit like Leonard.  Anyway it would be nifty if I could register a name that would show up on Google searches… Let me play a round a bit and see what happens on Google.  Holy crap, no one has registered manyworldstheory.com?  How’d that happen?”)

I know, I know.  The chance of making money off a blog is about the same chance that the Carolina Panthers’ coaching staff makes good coaching decisions this coming week.  (Is this a topic for a future blog?)  But the name “Many Worlds Theory” is too good to pass up.  In some universe, this domain name really pays off for me.

So.  Back to “One Data Point”.  I got the idea from a physics lab I taught a few years back.  The lab was about the simple pendulum.  What variables affect the period of the pendulum’s motion?   The instruction up front was minimal; the students were supposed to design the experiment themselves.  They were to vary things like mass, initial angle, string length, and see which parameters were important.  (If you’re curious about the outcome, why don’t you try the experiment yourself?)

Fast forward about a week.  A student turns in a lab write-up, and I am grading it.  And I notice: their graph of “Period as a Function of Mass” has only one data point.

One data point.

Their conclusion is that period doesn’t depend on mass.  And to their credit, they have actually drawn a horizontal line through that one data point to make their case.

Here’s a reconstruction of the subsequent conversation I had with the student:

ME: [Pointing] So, do you see anything wrong with this graph?

STUDENT:  Uh, no?

ME: Well, there’s only one data point.

STUDENT: So?

ME: So how were you able to draw a line through it?

STUDENT: Well, I knew it had to be a horizontal line—

ME: You were supposed to verify that it was a horizontal line, with data, not assume the line was horizontal to begin with.

STUDENT: But it was horizontal.

ME: Only because you drew it that way!

STUDENT: Well, no, it was horizontal because it went through the data point we had.

ME: [Stifling laughter] But couldn’t you have drawn a line going in any direction you like, with only one data point?

STUDENT: But it was horizontal.

I’ll stop here; you get the idea.  It reminds me of the bit about the volume “going to eleven” in This is Spinal Tap.

This sort of reasoning is much more common that you might imagine.  I call it the “one data point” fallacy because I am not knowledgeable enough to know what it’s really called (or too lazy to look it up).  The idea is this: most people seem to be unaware that it takes two points to define a line.

Examples:

  • “Hurricane Sandy is awful!  Global warming must exist.”
  • “My friend Joe lost his job.  Therefore the economy is getting worse!  ”
  • “The drinking water must cause cancer, because our neighbor’s son got cancer.”
  • “The streets are getting more dangerous!  I know because I got mugged.”
  • “TV is getting worse!  Just look at that Honey Boo Boo show.”

I hope you can see that all of the reasoning here is completely ludicrous.  That doesn’t mean that all of the statements are wrong; I happen to agree with exactly two of the statements.  But in each case a conclusion was drawn from one data point.

You know that you can draw a line in any direction, consistent with a single point?  That basically means that you can draw any conclusion you like from any of the above examples.

For instance:

“My friend Joe lost his job.  Therefore the economy is getting better!”

How so?  Well, what if Joe were the only person in the entire country to lose his job?  Then that one data point would be a sign of 0.0% unemployment!

The “one data point” fallacy is so pernicious that you have to stop yourself from using it.  It crops up everywhere.  Politicians love it: it is reasoning by anecdote.  “North Carolina is hurting.  Alice lost her job at the factory and had to go onto food stamps.  Vote for me.”  This stuff drives me crazy.

It almost makes you think that people can’t reason worth a damn.

But then again, I need more data to draw a definitive conclusion.

Posted in Rant | Tagged , , | 2 Comments »

Hello worlds!

October 31, 2012 by Matthew Rave

I don’t think the general public is aware that, among theoretical physicists, the many-worlds interpretation (MWI) of quantum mechanics has become almost mainstream.  (See, for example, this article by Max Tegmark.)  This means, basically, that there are a large number of very, very smart people who take the idea of “other” universes seriously.

Maybe you are one of these people.  Maybe you found this blog by googling “many worlds theory” and ended up here.

So, you ask, will this blog be devoted to the “Many Worlds Theory”?  Yes and no.  Yes, in the sense that I am a theoretical physicist, who has published work (such as this) on the weirdness of quantum mechanics.  And yes, I will occasionally post on topics that relate to MWI (such as quantum interference, the philosophy of science, the existence of the universe, and whether Jet Li’s performance in The One was Oscar-worthy.)

But also, no, in the sense that I won’t always devote this blog to quantum physics.  After all, the blog is called “Many Worlds Theory”, and not the arguably more correct many-worlds interpretation or Everett’s relative state formulation or universally-valid quantum mechanics.  By “worlds” I mean not only parallel universes, but things that interest me.  Sounds self-centered, right?  Kinda personal?

Well, it is a blog.  Isn’t it supposed to be personal?

My interests include, in no particular order: recreational mathematics, classical music, philosophy, politics, games of all kinds, science fiction, history, the ouvroir de littérature potentielle movement, movies, sports…(I’ll stop before this too closely resembles an ad on a dating website.  Maybe it’s already too late for that.  Anyway, I’m very happily married, thank you very much.)

Ultimately, this blog will be devoted to examining topics using a scientific mindset.  Let’s get one thing clear from the start: I believe that it is only through science that we have learned anything about the world.  My goal is to have this theme come through in all my posts.  Sure, I might discuss the Higgs boson, the Heisenberg uncertainty principle, Berry’s geometric phase, or other physics stuff.  But even when I discuss something non-scientific like Honey Boo Boo or Deepak Chopra or the Carolina Panthers or economics, I hope to stick to facts, and what can be demonstrated through logic.  If I write a blog about how soccer is a boring sport, rest assured that I will give you reasons as to why it is boring, and cite the source(s) of my claims.

Of course, there is another universe in which this blog is devoted to how great soccer is.

Good thing we’re not in that universe.

[Note: my book Why Is There Anything? is now available for download on the Kindle!]

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