7 July 2009 - 14:58The presidential birthday paradox

It occurred to me back at the time of the inauguration that the number of presidents is such that we ought to have had two who share a birthday. The well known “birthday ‘paradox'” is that once you have as many people in a group as the square root of the number of days in a year there is a good chance of a collision. We have had 43 different presidents, which is just in the right range to see the ‘paradox.’

I tested this when I first learned of the effect back in high school by waiting outside a classroom that was about to let out (my class had already dispersed) with the intention of asking everyone their birthdays. The first person out was the girl I had a crush on at the time (hi Hayley!) and I asked her. She had the same birthday as me. Paradox lost.

Returning to presidents, there is about a 90% chance that two should share a birthday. And in fact two of them do: Warren Harding and James K. Polk (the Napoleon of the stump) were both born on November 2nd.

More interesting are the death days of presidents, which display more surprising results. There are three collisions! Truman and Ford both died on December 26th, Fillmore and Taft both died on March 8th, and Adams, Jefferson, and Monroe all died on (get this) July 4th! Adams and Jefferson even managed to die on the same 4th of July, in 1826.

How anomalous is this? Fairly, but not unbelievably. I figure there’s almost exactly a 25% chance of there being three two-way collisions. Having a three-way collision at all is just under 6%. Without doing the calculation, it can’t be too unlikely that conditioned on a three-way collision you also get two two-ways, since having two two-way collisions is something over 50%. So it’s around 3% likelihood to get a distribution like the one we have. Of course, to have the triple collision on a particular important day you have to divide by another 365. That’s pretty extraordinary.

On the other hand, the presidents’ birthdays are also a little odd. There’s over a 2/3 probability that there should be at least two collisions, and we only have one. Ok, now that I’ve written that it isn’t all that odd.

But what can explain the improbable deaths? I conjecture that the deaths are more likely to be closely correlated than births. December 26th is certainly a special day–it’s easy to imagine old men hanging on to see their grandchildren for one last Christmas. And maybe old presidents are trotted out for Independence day and the fireworks give them heart attacks. I wonder if anyone has the actuarial data and the wherewithal to check on such correlations of births and deaths among the population at large.

In case anyone is interested, I calculated the probabilities using the python program below. I know I could have done this analytically, but I thought it would be a useful exercise for learning a little python, which I’ve been meaning to do for a while. The program illustrates loops, if blocks, function calls, and importing a library. To run it, paste it into the python interpreter then issue a command like:
probability(43,365,10000,2)
This will compute the expectation value of having at least 2 collisions and print out a list of those probabilities for collisions of size zero through 5. It does this by picking 43 birthdays at random, in a year with 365 days. The 10000 is the number of times to run the loop to get more accurate results. I don’t deal with leap years since I’m don’t really need a particularly accurate answer.

def birthdays(births,year):
    a=[0]*year
    for x in range(0,births):
        a[int(random.random()*year)]+=1
    return [a.count(0),a.count(1),a.count(2),a.count(3),a.count(4),a.count(5)]

def probability2(births,year,iters,howmany):
    counts=[0]*6
    probs=[0.]*6
    for x in range(0,iters):
        a=birthdays(births,year)
        for y in range(0,6):
            if a[y]>=howmany:
                counts[y]+=1
    for x in range(0,6):
        probs[x]=float(counts[x])/float(iters)
    return probs

No Comments | Tags: Computers, idea, physics, Uncategorized

22 December 2007 - 19:20Back from India

Taj Mahal with cart

I’m back from India, where I was for QIP2008. (click on the picture to see the full width until I figure out a wordpress setup that is wider)

Aram Harrow had a good bad idea when we were discussing the preference for boy children and the abortion of girls. We had just seen a sign advertising ultrasound imaging, and someone said they thought that had been made illegal in order to prevent such sex-based abortions. This doesn’t make much sense as the procedure is important for many other diagnostic reasons and I don’t think it’s true, based on a quick googling. Though it may be illegal for the doctor to tell you the sex of the fetus, something which is true in Korea anyway, coincidentally coming up in a New York Times article just today on how things are starting to balance out there.

Aram’s idea is to adapt technology used to blur out the naughty bits in airport screening X-rays which can see though your clothes to prenatal ultrasounds. Silly as it sounds, it might actually be a good idea. Though I doubt this could work–any blurring of the image would risk missing important diagnostic information. Of course, it is claimed that the airport security screeners won’t miss any concealed weapons compared to the unblurred images. This also seems unlikely. A penis shaped gun doesn’t seem like much of a stretch.

No Comments | Tags: idea, personal, politics

12 November 2007 - 0:50Just like learning to swim

The confirmation of Michael Mukasey as attorney general gave me an idea. I propose that waterboarding be used as a regular part of the senate confirmation process. Mukasey hardly answered any questions and waterboarding should remedy this situation in the future. Surely if it’s important to get information out of people who may be plotting to take over or destroy our country, it is just as important to get it out of those who already have are plotting to run it.

1 Comment | Tags: idea, politics

20 October 2007 - 13:48Randomized reassignment of children

… and no parent is to know his own child, nor any child his parent. — Plato, 360 B.C.

Ok, when someone pointed out this idea of mine goes back 2400 years to Plato I felt a bit late to the party, but in good company. I had the thought when I had heard one too many times the “conservative” (feel the air quotes) idea that everyone stars off equal and the best rise to the top, while the same people push for elimination of the inheritance tax (the so-call “death tax”).

Obviously in our society (and probably all societies) children born into rich families have a huge leg up on those that aren’t. The true conservative ideal would be for everyone to start out really equal–i.e. a 100% inheritance tax. Thinking further, I had the idea of random reassignment of babies. All babies born in a certain period are simply given to other parents who also had babies during the same period. This has several good effects, to which no conservative should object, and which are universally appealing liberal values:

First, it serves to remove the inherent inequity of the correlation between genetics and inherited wealth. Secondly, it will reduce racist tendencies–any parent can end up with children of any race. Finally, imagine parents who for whatever reason are more interested in the well-being of their genetic offspring than of the children they are charged with raising. Since they cannot find their biological children, all they can do to improve their lot is to promote the general welfare, making sure there are things like good public education and health care.

A modification of this plan could also include parents unable to have children. The randomization also in effect isolating the chance of not having children from the biological inability to produce them. And unwanted children can be placed into the pool as well, automatically taking care of adoption.

I have found, despite the Platonic pedigree of this idea, that it is unpopular among those with children, and that it is quite unwise to try to discuss it with expectant mothers. But then, I am perhaps not wise.

No Comments | Tags: idea, politics

16 October 2007 - 12:12Upside Down Racing League

Ah sigh, another of my brilliant ideas appears to have been had independently, further encouraging me to finally start writing them down.

Modern race cars (Formula 1 and Indy cars in particular) have wings and tunnels providing downforce, to increase traction. In fact, so much downforce that they could actually drive upside down. So why not an upside down racing league, or URL? Probably a big oval track with some kind of half-loops as ramps to get started. Such a track would be expensive to build, but seems to me to be completely plausible. The cars would have to be designed for this of course, as things like oil pumps are not usually built to run upside down. I remember reading in Popular Mechanics years ago about the twin-rotor helicopter that would be able to fly upside down, limited only by the oiling system. And obviously many piston powered airplanes can do it. It would also be hard on the drivers to sit upside down like that lap after lap. Perhaps cars would be designed to have the driver upright with the wheels above him.

I’m sure there would be a market for such racing. One problem is that everyone wants to see crashes at a race. The crashes on this track might be spectacular, but I envision the track being over water or a net or something to reduce deaths. And the crashes wouldn’t multiply–any car losing speed would just fall out of the way, leaving no debris on the track. But I still think it would be really cool to see and be technically challenging to the competitors. Hard to imagine much spin-off technology to street cars though.

And this would be much more feasible than my new idea for upside down sailboat racing….

1 Comment | Tags: idea