Sunday, December 30, 2012

Recreational mathematics

Vihart's videos on mathematics are brilliant and a treat to watch.  Here are a few of my favorite ones:
  • This one is a great use of "fruit by the foot"
  • This is a great Origami proof of the Pythagoras theorem

  • The most innovative story I've seen:

  • This one is a fun binary hand dance for Pi 

  • and one of my favorite ones is this one on fractal fractions (reminded me of some of my schoolteachers who took great pleasure in unnecessarily complicating math)

Check out her posts.

Friday, December 28, 2012

On the US gun culture ...

The recent tragic mass killings in the US have been unfathomable.  It seems beyond belief that a gunman could turn a gun on little children and shoot not just once but multiple times.  The killings have ignited a debate on whether the US needs tighter gun laws.

The chart below shows the gun deaths per 100,000 people for countries with per capita GDP of $30K+.  It shows just how much of an outlier the US is for gun deaths. 

The US has some extraordinarily lax gun laws.  This post at the Wonkblog examines just how permissive US gun laws are.  They also have a post with some facts on guns which show that:
  • Mass shootings are not all that rare in the US with at least 61 mass murders since 1982;
  • In most cases, the gunmen in the shooting obtained the guns legally;
  • 15 of the 25 worst mass shootings in the last 50 years took place in the US;
  • High gun ownership does not always translate into higher gun violence;
  • Of the 11 deadliest shootings in the US, 5 of them occurred since 2007;
  • America is an unusually violent country. But we’re not as violent as we used to be.
  • Gun ownership in the United States is declining overall.
  • More guns tend to mean more homicide.
  • States with stricter gun control laws have fewer deaths from gun-related violence.
  • Gun control, in general, has not been politically popular.  In a separate post, the Wonkblog points out that the lack of popularity can be explained mostly by NRA membership, i.e. gun owners who are not NRA members tend to support stricter gun laws.
What caught my attention are the studies the Wonkblog cites to suggests that there is correlation between high gun ownership and homicide rates which seems interesting to say the least.  

Mother Jones has a fascinating article analyzing mass shootings in the US since 1982.  The most interesting chart they've posted is the following, which does suggest that some types of weapons are significantly more likely to be implicated in a mass shooting. 



None of these conclusively prove that gun control reduces gun violence but it does suggest that the US is a an outlier and that semiautomatic hand guns and assault weapons are the preferred weapons in mass killings.

What is fire?

I was recently explaining to someone what fire is and realized that there are people who have done this already and done so much better than I ever could.

Alan Alda had posed a challenge on NPR to explain what is a flame is to an eleven year old.  This was the winning video.  It's excellent:



I actually also like Feinman's explanation here:


My favorite part of Feinman's explanation is he brings out the wonder and the inter-connectedness of nature in a way that is wonderful!

Tuesday, December 25, 2012

Federal tax contribution by state

In an earlier post, I had posted the net contribution to Federal government by state as sourced from Wikipedia (i.e. how much the state contributes by way of taxes less the benefits they receive from the Federal Government):



There were a number of people who asked me whether this view is being somewhat distorted by the size of the state.  So, here's the same statistic computed per capita:


What appears to be true is that states with larger populations, as one might expect, have a larger positive net contribution to the Federal government (the correlation coefficient of a state's net contribution to its population is 24.48%).

I ran a little regression and what it suggests is there isn't enough data here to conclude anything and if anything, normalized for states' sizes, although states that voted for Obama were more likely to have a net positive contribution, this isn't statistically significant.

Wednesday, December 12, 2012

Roma are from Northern India

A fascinating piece in the New York Times suggests that genetic research appears to confirm that the Roma (Gypsies) originated in Northern India and likely left India around 1500 years ago.

Interesting on many dimensions.

The Roma are the largest minority group in Europe.  Millions of Roma were killed in the holocaust.  They've been persecuted over the ages (Gadjo Dilo is an interesting movie on the topic).  They've also had astonishing impact for a nearly universally despised people, particularly through their music.

Wikipedia has an interesting discussion of the Romani language.

The state tax deduction ...

In a recent post in the Washington Post, Charles Lane argues that the least defensible deduction is the deduction State and Local Taxes.  His rationale is that this is "this one overwhelmingly benefits upper-income households in a handful of upper-income states, while rendering the entire nation’s finances less transparent."   Later in the article, Charles Lane explains his real rationale for picking this as the least defensible deductions: "But because its impact is so heavily concentrated in blue states, the state and local deduction creates an asymmetry: Democrats have an extra reason to insist on raising rates, and Republicans have an extra incentive to demand loophole-cutting. Perhaps it’s just coincidence, but I have noticed that those most skeptical of the loophole-closing approach include Sen. Charles Schumer (D-N.Y.) and House Minority Leader Nancy Pelosi (D-Calif.)."

When I read his analysis I was struck by a number of issues that I thought I should clarify.
  • Is it unfair to tax taxes already paid?
Here's Charles Lane on the subject: "Taxpayers have been allowed to deduct state and local income and property taxes since the federal income tax began in 1913. (Sales taxes have at times been deductible, too, but that’ s a relatively minor issue.) The theory is it’s unfair to make people pay twice for the public services they receive. That’s doubtful, though, since, despite some overlap, federal taxes support different services than state and local."

Hmm ... let's consider a thought experiment.  Let's say state and local taxes were 60% and Federal taxes were also 60%.  At this point, if the State and Local tax deductions were allowed, the effective tax rate would be 84%.  Under Charles Lane's formula, you could not claim the deduction for State and Local taxes and so the effective rate of taxes would be 120%, i.e. more than aggregate gross income.

I am not sure that there is a positive test for a relatively normative issue like "fairness".  However, if something is structurally unsound enough to result in absurd answers like taxes owed being higher than the gross income, it comes pretty close to QED.  

This is why, as Charles Lane himself acknowledges, the deduction for State and Local taxes has been part of the code since 1913 when the Income tax was introduced.

  • Isn't this mostly a deduction for rich people? 
Well, yes.  It is.  However, that isn't unusual.




As you can see, while state and local taxes are somewhat skewed towards the higher income, it is by no means the most skewed - that honor goes to Capital Gains and Dividend Tax reduction.
  • Are Blue states mostly takers and Red states mostly makers - i.e. isn't this a handout to taker Blue states?
In one sense this isn't wrong.  After all, if Blue states have higher effective taxes, the deduction disproportionately benefits them.

In another sense this isn't right.  Here's a view of net contribution to Federal government sourced from Wikipedia (i.e. how much the state contributes by way of taxes less the benefits they receive from the Federal Government):

Of the 24 states that voted for Romney, 19 had a net deficit, i.e. they contribute less to the Federal Government in taxes than they collect in Federal spending.  By contrast, 14 of the 28 states and territories that voted for Obama had a net deficit.  In fact, the aggregate for all the states which voted for Romney was a deficit of $64,911 million, whereas the aggregate for the states that voted for Obama was $206,848 surplus.  Let me restate that, the red states contributed less in taxes than they collected from the Federal government, the Blue states by contrast contributed more in taxes than they collected.

This is important because the argument hinges on the conflation of blue states and high taxes with "moochers".  Turns out that this conflation is probably not right.

Changing topics a bit, as an aside, the chart of the percentage of the deduction that goes to the rich shows that a lot of these deductions are actually designed to assist those with lower incomes.  So, when someone is arguing the removal of deductions to "widen the tax base" they mean a middle to lower income tax hike.  This raises an interesting question:  just how egregious is the tax on the higher income to necessitate such base broadening?  

Well, one way to think about this is to compare the effective tax rate for those at the higher income levels, i.e. with incomes over $100K, to those of other countries.  It just so happens that the Economist has done just that recently:

Strangely, the US' effective tax rate for $100K+ income is among the low end of the spectrum of the selected countries and will likely remain so even if the proposed marginal tax rate hike goes into effect for those with $250K+ income.

Interesting date

If you have not noticed, today is a very unusual date: 12/12/12.

This will be last time that we will be able to abbreviate the date in a way where the day, month and year are the same number for a very long time.  The next time this is going to happen is on 01/01/2101 - which can be abbreviated as 01/01/01.  That's 89 years from now. :)