## Common ancestors

Posted in Statistics with tags , , , , on June 8, 2011 by xi'an

In conjunction with President Obama’s visit to Ireland two weeks ago and in particular to his ancestral Irish town, I happened to glance at his family tree and saw that he shared a common ancestor with George W. Bush. (They are 11th cousins, meaning that a 12th-order ancestor is common to both their  family trees.) This sounds at first amazing, but it is another occurrence of the (von Mises) birthday problem. (The fact that it is not that amazing is demonstrated by the simultaneous presence of [French!] ancestors of Dick Cheney in the same tree.) If we consider President Obama’s mother side, the probability that all of her 11th-order ancestors differ from all of George W. Bush’s 12th-order ancestors is

$p=\dfrac{(M-2^{12})(M-2^{12}-1)\cdots(M-2^{12}-2^{11}+1)}{M(M-1)\cdots(M-2^{11}+1)}$

where M denotes the whole population of potential ancestors at this period. If we consider all those ancestors as coming from the British Isles, then about 1650, the population was about 8 million. This would lead to a probability of p=0.35, i.e. there is a 65% chance that they share a 12th-order ancestor. If instead we consider the whole European population at that time (if only to include German and French ancestors to President Obama), M is about 100 million and the probability increases to p=0.92, so there is then an 8% probability for them to share an ancestor. Obviously, this rough calculation relies on simplifying assumptions, avoiding the issue of inbreeding which means that the potential 2¹¹ ancestors are in fact much less than 2¹¹, and the fact that their ancestors are necessarily emigrants, which reduces the value of M(This post appeared yesterday on the Statistics Forum.)

## Art in Philly

Posted in Kids, Travel with tags , , , on August 22, 2009 by xi'an

Yesterday, while in Philly, we had the privilege of visiting the studio of a friend, Carolyn Rathburn George, who draws paintings in a very personal style of “art naïf”, with links to the Southwest (through recurrent appearances of Spanish missions and flashes of brights colours) but also to byzantine icon paintings (not only because of the Santos series, but also in her use of frames and perspectives).

The use of intense pencil colors in those paintings is quite amazing and very well-mastered, as it multiplies the degrees in the perspectives and translates the brightness of the southern sun. The depth in the paintings is reinforced by the creative use of frames and boxes that reminds me of the ex-voto niches found in the countryside in Italy and Greece. If you have the opportunity to be in Philly on October 10 or 11, you also can visit this studio (and others in the area) and meet the artist, since Carolyn is participating to POST 2009, the Philadelphia Open Studio Tour.

Carolyn then took us to the nearby Magic Garden, an incredible bric-à-brac construction by Isaiah Zagar mostly made of mosaics based on recycled materials. The occupation of the space by the mosaics in what seems more like a vegetal living process than a mineral one is dizzying and the repeated use of mirror pieces makes the mosaics even more alive by their impression of an ever-changing background.

The connection with other “art brut” monumental projects like Cheval‘s is somehow obvious, with the same vegetal feeling and the same reminiscence of Hindu temples like Angkor but there is a universality in the representations that makes Zagar’s work moving if overwhelming at times.