Math and Taxes

There's been quite a lot of news coverage on what Presidential candidates pay in income tax.  This got me to thinking about what I pay in taxes, not because I don't like paying taxes.  I really do enjoy it. My money paves the roads I drive on. It makes the skies safe when I fly (it also pays the salaries of the sometimes surly TSA agents).  It provides affordable education to the nation's students, and it provides a little financial security and healthcare to seniors.  These are a few of my favorite things.

Mitt Romney says that his effective tax rate is about 15% while Newt Gingrich's tax returns shows his is 32%.  Calculating  the effective tax rate is easy, but before I cover that, let's explore the federal tax rates for 2011.  Here are the federal tax rates for 2011.

I remember an urban myth about these tax rates.  I haven't heard it recently so maybe this is one myth that has finally died.  The myth says that if a person was near the top of one tax bracket and got a raise that bumped that person into the next bracket, the person would end up taking home less pay than before.  But that's not how these brackets work.  UPDATE: USA Today published an article on Sept. 2, 2011 that contained this error.

Let me illustrate.  Suppose a single woman earns $34,100 in 2011.  I mean for this amount to represent her taxable income; basically, taxable income is your income minus personal exemptions and deductions.  The first $8,500 is taxed at 10%, so she pays $850 to the IRS.  She is taxed at 15% for only the difference between $34,100 and $8,500.  So, the tax on $25,600 is $3,840.  Her total tax liability is then $4,690.

To find her effective tax rate is really simple.  Take the total amount of taxes paid and divide by her taxable income.  Here, $4,690/$34,100 = 0.138 = 13.8%.

Now suppose she gets a raise (in this economy?), and her 2012 taxable income rises to $35,700.  The 2012 tax brackets have been inflation adjusted.

So next year she can expect to pay $870 (10%) on $8,700, $3,997.50 (15%) on $26,650, and $87.50 on $350.  Her 2012 taxes will then be $4954.50, and her effective tax rate will be $4954.50/$35,700 = 0.139 = 13.9%

According to my 2010 return, my effective tax rate was 19.1%.  

With all the talk about the 99% and the 1%, I wonder where I am.  I earn a 'nice dime.'  I found a % calculator on the Kiplinger website.  Kiplinger is a financial advice and forecast business.  It figures that I'm in the top 10% of American wage earners.

So I played around with it.  To be in the top 5%, you need an income of $175,000.  The 1%?  $350,000.  

When I was much younger, I would tell people that I wanted to earn a comfortable living.  They'd asked what comfortable was.  The smartass that I am replied that if I could lose half of my income and still be comfortable, that was a comfortable living.  If I earned $350,000 and lost half of that, could I still be comfortable?  

Wouldn't I like to try!

[N.B. Here are the tax brackets from 1919 to 2011.]

My Personal Periodic Table

Here are the only elements I need.

The Future Is In Good Hands

Here are two 4-year old girls.  They make me feel good about the future of civilization.

Stella explains the mistakes in this dinosaur toy.

Riley wonders about companies marketing to young children.

Snooki Knows Why The Sea Is Salty

In the Aug. 6, 2011 edition of the New York Post, Snooki Polizzi said, "I don’t really like the beach. I hate sharks, and the water’s all whale sperm. That’s why the ocean’s salty."

Um…

The organization Sense About Science asked oceanographer, Dr. Simon Boxall of the University of Southampton to comment.

Snooki – it would take a lot of whale sperm to make the sea that salty! The salt in the sea comes from many millions of years of water flowing over rocks and minerals. It slowly dissolves them leading to the ‘salty’ nature of the seas – it’s not just salt but every material on the planet including gold. Salt water actually keeps our oceans free from many human pathogens (microorganisms that cause disease) – so why not give the beach another try and get back in the water?

For more celebrities spouting about science, see this pamphlet from Sense About Science.

Some highlights are

• Suzi Quattro (teenage males from the 70s know who she is) thinks that colon cleansers prevent sore throats.
• A former Presidential candidate believes vaccines cause mental retardation.
• Gwyneth Paltrow 'gooping' on detox diets.
• Bill O'Reilly knows that no one can explain the cause of tides.

Everything We Hear, Everything We See

“Everything we hear is an opinion, not a fact. Everything we see is a perspective, not the truth.”  Marcus Aurelius.

Marcus Aurelius was Roman Emperor from 161 to 180 C.E. and is one of the greatest of Stoic philosophers.  Although Stoicism does have a natural philosophy, that is, a physics, this article is not about Stoic science, nor is it a comment on the news media.

I saw this quote and realized how it - unintentionally - emphasizes how little of the universe humans actually experience directly.  We have contact with the universe through our senses.  Historically, the senses consist of sight, hearing, smell, taste, and touch, although we possess many more senses such as balance, temperature, and pain.

The human eye responds to certain frequencies of light. Those frequencies or colors we can see are represented by the rainbow.  How we see other colors like brown, pink, and teal is a cool problem in physics and neurobiology/psychology.  There are other 'colors' though.  Radio waves, microwaves, infrared, ultraviolet, X rays, and gamma rays complete the rainbow (electromagnetic spectrum).

You can visualize (pun intended) an electromagnetic wave as an oscillating electric and magnetic field.  If you've played with a balloon with a static charge, you've played with an electric field.  Same for playing with a magnet.  See Maxwell's Silver Magnet for more on electric and magnetic fields.

Sound on the other hand occurs whenever a substance, usually air, vibrates.  In most science texts, the range of human hearing is given as 20 Hz to 20,000 Hz.  Note that the unit Hz is an abbreviation for Hertz and means the number of vibrations per second.  If you place your hand on a audio speaker you can actually feel these sounds.

However only young 'uns can hear up to 20,000 Hz.  Once people reach the age of 20, their hearing starts to degrade.  I have heard anecdotes that children can be easily annoyed when they hear high frequency sounds that their parents can't hear.  You can purchase ringtones for your phone that only young people can hear.

Are their sounds lower than 20 Hz or higher than 20,000 Hz?  Infrasonic tones are those that are lower than 20 Hz.  Earthquakes are a sound wave (remember sound is a vibration) that have frequencies in the infrasonic region.  The stories of birds and livestock being aware of earthquakes before people are sometimes explained as these creatures being able to detect these low frequencies.  There are studies to suggest that infrasonic sounds can cause people to have feelings of nervousness, fear, and anxiety.

Sounds at the other extreme are called ultrasonic.  Ultrasonic cleansers are a popular and safe way to clean jewelry and golf clubs.  How high can ultrasonic tones go?  There's no theoretical limit.  

In condensed matter physics, the study of nearly everything that's not a gas or plasma, there is a phenomenon called a phonon.  A phonon is a particle of sound the same way a photon is a particle of light.  It's quite common for phonon frequencies to be in the THz region.  That's TeraHertz; 10^15 Hz = 1,000,000,000,000,000 Hz.

What piece of these spectrums to we experience?  A  tiny, tiny, tiny,…, tiny piece.  From the Abstruse Goose comes the graph below.  [WARNING! Notice the axes of the graph.  Each tick mark is a power of 10.  That is, each mark is 10 times bigger than the previous one and 10 times smaller than the next.  I tried to graph this on a regular (linear graph for you math and science folks), but i quickly realized that you wouldn't see anything.]

I feel small.

But on the other hand, everything we know about biology, chemistry, physics, geology, astronomy, and the other fields comes from scientists using their puny senses and rational thought to find ways to not only measure, but to comprehend aspects of nature from the Higgs boson, to my favorite molecule ethanol, to huge molecules like DNA, to cellular structures, to tectonic motion, to extrasolar planets, to galactic motion, and all the way to the Big Bang.

I feel huge.

The Old Testament Universe

Diagram from James L. Christian, Philosophy: An Introduction to the Art of Wondering, 6th ed.,(Harcourt, 1994), p. 512.

I'll just link to the blog that originally posted this figure.  He discusses the relevant biblical passages.

Stupid People Killed This Baby

This is Dana Elizabeth McCaffery.  She lived for 33 days.  She contracted pertussis, also known as whooping cough.  There is no treatment for whooping cough.  

How did this beautiful baby catch pertussis? 

All children should get the series of DTaP shot that protects from diphtheria, tetanus, and pertussis. The first in the series come at 2 months.  Four other shots come later.  There's another vaccine Tdap that's meant for people ages 11  to 64.

What should have protected Dana is herd immunity.  When a sufficient number of people in a community are resistant, the few who are susceptible are protected from the disease, because the probability of a susceptible person coming into contact with an infected person is small.

To be protected from pertussis, at least 94% of the community needs to be vaccinated.  Dana had the poor luck to be born in a community with one of Australia's lowest vaccination rates.

Why are people not being vaccinated?  The only answer I have to that question is - stupidity.

Vaccines may be the second most important advance in medical science, second only to proper sanitation.  Vaccination has eradicated smallpox.  Polio is unheard of.  As a child, I had the measles, mumps, and chicken pox (with the scars to prove it).  What child gets these once common diseases today?  The MMR vaccine was introduced in the United States in 1971, and the varicella (chicken pox) vaccine was developed in 1995.

But thanks to stupid people like Jenny McCarthy, the National Vaccine Information Center, and Andrew Wakefield, there is a decline in the number of vaccinations.  Andrew Wakefield started this nonsense with a paper published in the British medical journal, The Lancet, that has fully retracted the paper and called the paper "false."  The British organization responsible for maintaining medical standards, the General Medical Council, found that Wakefield acted with "callous disregard" toward children and with "dishonesty."

I'm inclined to be a but more tolerant of Jenny McCarthy, because she's a mother who truly has the health of her child in mind.  But my tolerance goes only so far when her anti-scientific opinions endanger the health of an entire community.

The anti-vaccine National Vaccine Information Center's tag line is "Your Health. Your Family.  Your Choice."  I wonder what Dana's parents feel about "your choice."

I encourage anyone to investigate the science of vaccines.  Here's a few recommended sites:

Science-Based Medicine (vaccines),

Science-Based Medicine (herd immunity),

A DTaP pamphlet for the Center for Disease Control,

An Open Letter from Dana's Parents.

If science doesn't convince you, then see if you can watch this video of a 7 week old infant suffering from pertussis.