1100 to 13?!?!?

I've been reflecting a lot on the basic mathematics of the Israel/Palestine/Gaza situation. The Arab birthrates in Gaza are among the highest in the Middle East. Even within the borders of Israel, the Arab birthrate is higher than that of Israeli Jews. In other words, in a peaceful democratic Israel, the Arabs will become a majority and the Zionist project would eventually, organically, naturally, evaporate in the long term. So if the Jewish character of the state is to be maintained, Israel almost "has to" commit genocide. And in that context, the continual atrocities and illegal actions... bulldozing Palestinian homes, illegal Jewish settlements, the humanitarian crisis in Gaza and the West Bank, etc. should not be surprising.

Now, in the current Gaza situation, the numerical discrepancies in the casualties are huge, but also shouldn't be surprising. Since the conflict in Gaza began, nearly 1,1000 Palestinians have been killed in Gaza, about half of them civilians, many of them women and children. On the other hand 13 Israelis have died, almost all of them soldiers, and almost half of them due to friendly fire! (i.e. the Israeli forces themselves have almost killed as many Israelis as Hamas)

There is no way this conflict makes sense in terms of Israel merely defending itself from Hamas. It makes much more "sense" as a low-level genocide against the Palestinians.

Al-Jazeera: The president of the UN General Assembly has condemned Israel's killings of Palestinians in its Gaza offensive as "genocide"
Al-Jazeera: Israel breaking law with Gaza war
BBC: Strike at Gaza school 'kills 40'
Jewish Congress Says World Jewish Population Shrinking

"do your math..." (part two)

There is within the spiritual universe of Islam a dimension which may be called "Abrahamic Pythagoreanism" or a way of seeing numbers and figures as keys to the structure of the cosmos and as symbols of the archetypal world and also a world which is viewed as the creation of God in the sense of the Abrahamic monotheisms. It is this possibility within the intellectual universe of Islam and not any external influences that enabled Islam to develop a philosophy of mathematics akin to the Pythagorean-Platonic tradition of antiquity [...]

-Seyyid Hossein Nasr, from the Forward of Islamic Patterns by Keith Critchlow

So I recently picked up the book Islamic Patterns. I've owned it for a while, what I'm saying is that I'm making another attempt to get through it. It contains some interesting discussions of the philosophical principles which lay behind much of the geometric artwork in the Islamic world. To be honest, it is taking some effort to get through. What I'm finding is that my own mathematical training makes it hard for me to really see where Critchlow is coming from. There is definitely a gap between the typical academic concept of what a number is or what geometry is about and the Pythagorean notion of the same.

"do your math..."

Recently I've been thinking in general terms about different kinds of mathematics: partly with the hopes of developing an innovative curriculum for my students next year, partly for my curiosity and edification, partly with hopes of putting together some kind of article or document, and possibly in order to develop a career as not just a mathematician but a numerologist of sorts.

One route (exemplefied by the song "Mathematics") is to extract the mathematical content of our everyday lives with an eye towards social relevance. Another route would be to take a more metaphysical path (through the I Ching, sacred geometry, enneagrams, and similar constructions). We'll see how it goes.

[Mos Def]
Booka-booka-booka-booka-booka-booka
Ha hah
You know the deal
It's just me yo
Beats by Su-Primo for all of my peoples, negroes and latinos
and even the gringos

Yo, check it one for Charlie Hustle, two for Steady Rock
Three for the fourth comin live, future shock
It's five dimensions, six senses
Seven firmaments of heaven to hell, 8 Million Stories to tell
Nine planets faithfully keep in orbit
with the probable tenth, the universe expands length
The body of my text posess extra strength
Power-liftin powerless up, out of this, towerin inferno
My ink so hot it burn through the journal
I'm blacker than midnight on Broadway and Myrtle
Hip-Hop past all your tall social hurdles
like the nationwide projects, prison-industry complex
Broken glass wall better keep your alarm set
Streets too loud to ever hear freedom sing
Say evacuate your sleep, it's dangerous to dream
but you chain cats get they CHA-POW, who dead now
Killin fields need blood to graze the cash cow
It's a number game, but shit don't add up somehow
Like I got, sixteen to thirty-two bars to rock it
but only 15% of profits, ever see my pockets like
sixty-nine billion in the last twenty years
spent on national defense but folks still live in fear like
nearly half of America's largest cities is one-quarter black
That's why they gave Ricky Ross all the crack
Sixteen ounces to a pound, twenty more to a ki
A five minute sentence hearing and you no longer free
40% of Americans own a cell phone
so they can hear, everything that you say when you ain't home
I guess, Michael Jackson was right, "You Are Not Alone"
Rock your hardhat black cause you in the Terrordome
full of hard niggaz, large niggaz, dice tumblers
Young teens and prison greens facin life numbers
Crack mothers, crack babies and AIDS patients
Young bloods can't spell but they could rock you in PlayStation
This new math is whippin motherfuckers ass
You wanna know how to rhyme you better learn how to add
It's mathematics

Chorus: scratched by DJ Premier (repeat 2X)

"The Mighty Mos Def.."
"It's simple mathematics" -> Fat Joe
"Check it out!"
"I revolve around science.."
"What are we talking about here?"

.. "Do your math" -> Erykah Badu (2X) ..
.. "One.. t-t-two.. three, four" -> James Brown ..
.. "What are we talking about here?" ..

[Mos Def]
Yo, it's one universal law but two sides to every story
Three strikes and you be in for life, manditory
Four MC's murdered in the last four years
I ain't tryin to be the fifth one, the millenium is here
Yo it's 6 Million Ways to Die, from the seven deadly thrills
Eight-year olds gettin found with 9 mill's
It's 10 P.M., where your seeds at? What's the deal
He on the hill puffin krill to keep they belly filled
Light in the ass with heavy steel, sights on the pretty shit in life
Young soldiers tryin to earn they next stripe
When the average minimum wage is $5.15
You best believe you gotta find a new ground to get cream
The white unemployment rate, is nearly more than triple for black
so frontliners got they gun in your back
Bubblin crack, jewel theft and robbery to combat poverty
and end up in the global jail economy
Stiffer stipulations attached to each sentence
Budget cutbacks but increased police presence
And even if you get out of prison still livin
join the other five million under state supervision
This is business, no faces just lines and statistics
from your phone, your zip code, to S-S-I digits
The system break man child and women into figures
Two columns for who is, and who ain't niggaz
Numbers is hardly real and they never have feelings
but you push too hard, even numbers got limits
Why did one straw break the camel's back? Here's the secret:
the million other straws underneath it - it's all mathematics

Chorus

{closing scratch} "Mathematics.."

we are family

From time to time I like to reflect on the mathematics of genealogy, but I quickly get overwhelmed. Barring virgin births, everyone has 2 parents. Barring, incest, everyone has 4 grandparents, 8 great- grandparents, 16 great- great- grandparents, 32 great- great- great- grandparents`and so on, doubling with every generation. If you know anything about geometric progressions you would realize that the number of ancestors a person has in any given generation will get very very large, very very quickly as we move into the past.

Now, in order for two people to NOT be related what is necessary is the near-impossible requirement that their two respective geometrically increasing clouds of ancestors not overlap. But eventually, if you go far back enough, each person's theoretical number of ancestors in a generation will exceed the total population on the planet. In other words, there doesn't seem to be enough room on the planet for two people to really be from different "tribes". We are all at least distant cousins.

A special corrollary of the realization that we are all related is the fact that we are all related to royalty (or any sufficiently prolific historical figure). For example, everyone today of European descent is apparently descended from Charlemagne. A good discussion of this idea can be found in an old article which appeared in The Atlantic entitled The Royal We by Steve Olson

Last year, in a surprising turn, it was discovered that Barack Obama and Dick Cheney are cousins. And more recently, last month, Juan Cole over at Informed Comment wrote about how: Queen Elizabeth II was Descended from the Prophet Muhammad (saaws). (although this has been known among professional genealogists for a long time.)

See also:
britney spears may convert to islam
kerry descended from the prophet muhammad?
i'm back...
al sharpton and strom thurmond

mancala

For reasons I don't want to get into right now I've been thinking a lot about mathematics education, especially in the Black community. In that vein, I want to make a plug for using mancala games (sowing games or count-and-capture games) as a tool in the classroom and elsewhere to stimulate greater interest in mathematics, logical reasoning and strategy among Black youth.

Firstly, many of the games in this category are Afican in origin and are commonly played in Africa or the diaspora so the the games would be able synergize well with any other Afrocentric content which was part of the school curriculum. (Some of these games are also popular in Asia. E.g, recently a friend of mine sent me a picture of a Malaysian coin which has the image of one of these games on one of its sides.)

Secondly, the games are almost purely "mathematical" in the sense that they are based on keeping track of the number of stones or seeds contained in various "pits" on a game board and so they will provide a certain amount of practice in counting, doing arithmetic, and certain kinds of mathematical reasoning.

To be honest, I'm still trying to figure out which particular mancala-game is the most mathematically rich for the purposes of teaching. Oware is one of the more "serious" versions and seems to be the most respected in terms of adult-play (e.g. The Oware Society holds international tournaments and keeps track of rankings.) Kalah is the most widely-marketed version in the U.S. (It was one of the games included on my first cell-phone and it is also the game included in the links below.) I've met a group of Haitian-American students who like to play a version of mancala which is basically a race to clear their side of the board. But there are literally dozens of variations. If anyone out there takes my plug for mancala games seriously, you might even consider starting clubs or organizations where young people could come together to become familiar with several different games instead of just focusing on one.

Mancala (Kalah):
Mancala (3 stones per pit)
Mancala (4 stones per pit)

Planet Grenada on games:
submachine games
pencak silat
weeping and nashing of teeth aka he got game