## Thursday, February 12, 2009

### Baseball Families and Math Families

Bill James, the baseball statistician, once had an article on measuring Baseball Families. Who was the best baseball family? Would it be ...
1. The Alous: Felipe, Jesus, Matty were brothers. Moses was Felipe's son. All made the major leagues, and some of them were pretty good.
2. The Bonds: Bobby and Barry Bonds. Father/Son- both excellent. While you might rather have them then the four Alou's on your team, having four in a family just seems like a stronger family.
3. The Aarons: Hank and Tommie Aaron. Hank was a great player who hit 755 home runs (without steroids). Tommie, his brother, had a very short career. Even though its a real family, still doesn't seem like the right answer.
4. Babe Ruth alone: Bill James him rates as the best player of all time. Hence the "Ruth family" would seem to be a very good baseball family.
So, how to go about the question of who is the best baseball family ever? First we need a way to assign to a player some number saying how good he is. Bill James has already done this via a method called win shares. The idea is that you assign to a player how much he helped the team win. This is very complicated and I won't explain it here. However I will point out that it can't be negative and it varies quite a bit. For example Hank Aaron had 643 win shares, while his brother Tommie had 15. For some examples of players with high win shares see this.
So, you could just take the sum of the family members win shares. But this makes the family of one, the winner. We want a real family to get some credit for being a real family. Bill James' solution: Say the best person has a1 win shares, the second a2, etc. a1 > a2 > ... > an. Rate the family via a1 + 2a2 + ... + nan. Under this metric the Alou brothers were the best baseball family as of 2003. See here for the numbers.

But I am still bothered. Why the combination a1 + 2a2 + ... + nan? Is there some other way that is more mathematically sound or that can be derived? I doubt it since the question is somewhat subjective.

Clyde Kruskal has brought up another point. What if you had a longer link between relatives? What if you had a great-grandfather, grandfather, father, son. If the father is the best baseball player, start there. People who share half his genes (son and grandfather) count fully. But the great-grandfather counts less. You could even do this if someone in the family does not play baseball. We will see an example below under (what else) the Kruskal Math Family.

Who are the best Math families of all time? Here are some, not in order. I am sure there are more. Corrections and additions welcome! (I may make a website out of it.) I only count a family if it has at least three members and all of the people are related by blood (sorry Blums). Aside from that, I am fairly informal. This list is not meant to be the final word.
1. The Bernoulli Bunch Link. There were eight of them. Jakob-Bernoulli numbers, Nickolaus-Prob theory and Geometry (NOT Bernoulli Dist), Johann- Brachistochrone problem and possibly L'Hopital's rule, Daniel-Bernoulli's principal (also physics and probability), Wikipedia does not have info on the other four, but says they were math folks.
2. The Kruskal Kin: William (Kruskal-Wallace test in statistics), Martin (Solitons), and Joseph (Min Spanning tree, Kruskal Tree Theorem (set of all trees under embedding is a well quasi order), Kruskal-Katona Theorem). They are all brothers. Martin's son is Clyde (Parallel Computation, Coloring the Plane). Clyde's son is Justin (Ramsey Theory, though he's still in High School, so perhaps shouldn't count). William's son is Vincent (Computer Science-IBM research). Rosaly and Molly Kruskal are sisters of Martin/William/Joseph. They do not do math, but Molly has two sons who do math: William Kahn (statistician), and Ted Kahn (Statistical Software); and Rosalie's son is Jeremy Evnine (OR, Math Finance). (Using Clyde's theory these people would count some.) The following does not count as he is not a blood relative: Joe Kruskal's son-in-law is Neal Madras (Math prof at York Univ in Canada).
3. A Nest of Noethers: Father: Max Noether one of the finest mathematicians of the nineteenth century according to Auguste Dick who wrote a book on Emmy Noether. Max's son was Fritz Noether. Fritz Noether. Max's daughter was Emmy Noether the most important woman in the history of mathematics according to Einstein and others. (That was meant as a compliment but sounds so odd nowadays.) A great mathematician independent of her gender. The only father-son-daughter combination that I know of.
4. The Markov Chain: Andrey Markov (Markov Chains), his brother Vladmir Markov (Markov's inequality co-authored with his brother), and Andrey Markov Jr. (logic) son of Andrey Markov.
5. The Browder Brothers: Felix (PDE's), William (Topology and Geometry), and Andrew Browder (Analysis).
6. A Litter of Lenstras: Hendrik (Computational Number Theory), Arjen (Crypto), and Jan Karel.
Interesting misses:
1. A Research of Rabin's: Michael and Tal. A Father-Daughter both in Crypto. Probably the only such.
2. A Manifold of Millars: Terry and Jessica. A Father-Daughter both in Recursive Model Theory. Definitely the only such.
3. A Troop of Tardos': Eva and Gabor. The only other Brother-Sister combo I know of is the Noethers.
4. The Courant Clan: Richard Courant (Math), Hans Courant (son of Richard, Physics), Ernst Courant (son of Richard, Physics) Ted Courant (son of Hans, Math), Jurgen Moser (son-in-law of Richard, Math) Lucy Moser-Jauslin (Jurgen Moser's daughter, Math), Jerry Berkowitz (son-in-law of Richard, Math), Peter Lax (son-in-law of Richard, Math), Carl Runge (Father-in-law of Richard, Physics and Numerical Analysis). Note that Jurgen and Lucy Moser are a father-daughter combination.
5. A Band of Blums: Manuel and Lenore (married) and their son Avrim. All do TCS at CMU. Lenore-Avrim is the only mother-son combo I know.
6. A Geek of Gauss' or A Nerd of Newtons or An Egghead of Eulers or An Ark of Archimedes' are competitive with any of these families. But one person does not a family make.

1. I think that you're missing some families that might be right under your nose.

In the realm of baseball, there are the Ripkens. Cal Ripken Jr. is the #2 short stop in win shares, and his father and Brother, Billy were also in baseball, with a concentration of their activities right near you in Maryland.

In the realm of Math, it definitely could be argues that the Brins should be considered a Math family, Sergey used math in making google, and is an alum of the your department, his father Michael is a prof in the Math department there at UMd, and according to multiple biographies his grandfather was also a mathematician.

Also the mathematical validity of any system of weighting the contributions of a family depends on what you are trying to optimize for.

2. Unlike many math (and other) families, the Milman family is
certainly very functional:
Daniel, (Krein–Milman theorem)
Vitali (concentration of measure),
and also Pierre and Emanuel.

3. Here is a near miss within TCS. Orna Kupferman and Tami Tamir are twin sisters.

Orna's husband, Raz Kupferman is a professor of mathematics at the Hebrew University.

4. How about Valiants (Les, Paul, Greg), Kannans (Ravi, sampath)?

5. Another near miss - a Field of Feffermans: Charles Fefferman was a child prodigy, Professor at U. of Chicago at 22, and has a Fields medal (he is now at Princeton); Robert Fefferman, his brother, is a Professor at U. of Chicago now (actually the Dean of Physical Sciences, maybe this is not a plus in terms of his stature as a mathematician!). Interestingly both of them went to Maryland for undergrad, got their PhD's at Princeton, and were Professors at Chicago.

Making this an even closer near miss is the existence of logician Solomon Feferman, whose last name is spelled differently and is not related.

6. Charles and Robert Fefferman are also academic brothers, in that their advisor was Elias Stein.

A father-mother-son combo: Greg Kuperberg and his parents, Wlodzimierz and Krystyna Kuperberg. They have a paper together, and each pair has a paper without the other; Greg and his mother even have one in the Annals.

7. Friedmans, Cartans

ps. Searching for "is also a mathematician" and "is also a computer scientist" does not work well.

8. Robinsons! (Julia: Hilbert's 10th problem, Abraham: Nonstandard Analysis, Rafael:Robinson Arithmetic Q, John Alan) All in logic!

Julia Robinson was one of the greatest mathematicians of modern times.

9. Don't forget Umesh and Vijay Vazirani

10. what about the naors? at least 4 of them work in theory.

11. The Tauman-Kalais. Adam and Yael, with Adam and Yael's dads both being famous game theorists. (Gil Kalai is unrelated).

Also, are te Naors one family? I don't think so Moni and Seffi are brothers, but Asaf is unrelated.

12. How about a host of Horodeckis? (brothers Michal and Pawel, and father Ryszard, all work in quantum information theory).

13. How about Isaacsons and Kellers in Mathematics?

14. "The Mis-Family Robinson"... unfortunately the husband-wife team of Raphael and Julia are not related to Abraham.

15. This is surely not a mathematical issue, but I have to take issue with your conception (no pun intended) of a family as a collection of people related by blood. Ruling out the Blums seems really peculiar (one parent + Avrim constitutes a legitimate family by your definition, but not both?). And what of families with adopted children -- admittedly, I know of no examples that apply, but can you say with certainty that you have not included any in your list unknowingly?

And for a final bit of flame-bait: From a Christian standpoint, doesn't the Holy Family include Joseph?

16. If I included marriage
then what about living together? What about a divorced couple? I choose blood because I wanted a stable and well defined definition.
Having said that, YES I would
include adaption since it is also well defined and stable.

Is Joseph part of the Holy Family? I agree that he is, and that would count.

17. Ken Griffey and Ken Griffey Jr. Junior will be in the Hall of Fame. Father and son even hit back-to-back homers in a game, the only time it's ever been done.

18. Computer science as a full-fledged academic discipline is roughly beginning its third generation of researchers. (The 40th STOC was last year the 50th FOCS is this year.) We shouldn't expect too many dynasties.

Already twenty years ago at UW we had a distinguished lecture series with five academic computer scientists who were parents of UW Computer Science Ph.D. students. Are there any third generation computer scientists, yet? If not, how long will it take?

19. I was just talking about this same subject with respect to Hockey families: Staal brothers (4); Sutter brothers (6); Hull (father and 2 sons), Hunter brothers (3), Sedin brothers (2, twins).

I'm not sure how many won Stanley cups, but, in this list, the 2 Sedins and all 4 Staals are currently playing in the NHL. (And I think there's still 1 more Staal brother at home...)

Liz (Rodgers) Fraley

20. It seems unreasonable to count married couples. If you do, however, Oded Goldriech and Dana Ron.

- Guy Even in TAU is Shimon Even's son.

- Joram and Naomi Lindenstrauss are a mathematician and a computer scientist (from HUJI), and they have two children who do math - Ayelet and Eylon. This gives us another father-daughter, another mother-son, a mother and a daughter, a brother and a sister, etc.

21. Come on now! Married couples are a dime a dozen. For the Fefferman one, you might also want to include daughter Nina Fefferman, who is an applied mathematician at DIMACS.

22. Bernard Dwork (deceased mathematician) and Cynthia Dwork (CS theorist), father-daughter pair.

Edward Witten and whatever his dad's name is, both physicists.

I think there is a fourth mathematical Lenstra missing from your list.

I think that mathematicians Karl Rubin, Herman Rubin, Vera Rubin, Arthur Rubin and maybe one or two others are all from the same family.

Borwein brothers Jonathan and Peter, and Chudnovsky brothers (I forget their names) all have worked on computing digits of pi.

I think Michael Artin sometimes confirms and sometimes denies being related to Emil Artin. Or maybe I'm thinking of Armand Borel and Emil Borel.

I'm sure there's lots more. Maybe these sets should be restricted to cardinality >= 3 to be considered interesting.

23. Jesus and Musatov 1st in 3rd base. They never played on earth though.

24. Vince, Joe, and Dom DiMaggio!