At least 35 people are killed and dozens injured in an attack at a mosque in the Pakistani garrison city of Rawalpindi…. From BBC News. Full story

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At least 40 people are killed and dozens injured in an attack at a mosque in the Pakistani garrison city of Rawalpindi…. From BBC News. Full story

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Enter, it says.  And he says, Yes and does as he says.  He doesn’t wait on the stoop.  It is the door that spoke.  It spoke without a tongue, as if the wind blew through it.  And he walks over the threshold inside.  It feels like love to enter and find the furniture arranged as if it, too, awaited a guest to arrive.  Sit, I say.  And sit he does.  And so we talked all night like flames.  The morning opened up the room.  It hadn’t seemed close.  Dark makes everything close seem far away and the far away seems near, like stars.  The dead have come to me at night.  And hate, which had rooted in my heart, unmoored.  I said some of this to the guest.  And some of this in particular he already knew.  Together we arrived at the solution.  Forgiveness is as easy as to ask.  But knowing who should start troubles me still.  Perhaps he keeps a souvenir.  Perhaps.  Perhaps he might never return.  The house regards his departure just the same as it regards the blooming and the blowing of leaves.

Two women are attacked and their car windows smashed after they leave a drive-through McDonald’s in Milton Keynes…. From BBC News. Full story

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Luke 21:25-36

Near

1.  Way In

How was your Thanksgiving?

Did you get enough to eat?

 …nice visit with family and friends?

…enjoy the day your own way?

My family had a nice day at home

started out with the Turkey Trot

… us and more than 400 friends gathered behind the church

4 truck-loads of food for Alpha/Holy Angels

Sarah Steenrod, Darryl Cloud – many other helpers

you did a fantastic job!  Thank you!

home by 10:30

to enjoy the smells of a happy kitchen

1:30 or 2:00 we gathered for a delicious feast

This is the first time we’ve been together since Thanksgiving Dinner at church

last Sunday

delicious food, good crowd

What about before that?

Were you here to decorate the church after worship last Sunday?

Hanging of the Greens

doesn’t it look great?

good job, Worship Committee

be sure to notice the beautiful wall Advent hanging

Marilyn McCarthy made it

you can also see her work featured in the 2010

OPHS (right?) calendar

and we had a nice lunch after that, thanks to Worship Com.

A busy day

on top of all that, we had a congregational meeting after worship

still finished church very close to on-time

So how was this week for you?

Remember the sermon last Sunday?

Were you thinking this past week about who Jesus put in your life?

Did you step outside your comfort level?

I know.  I said maybe this isn’t the week to invite the homeless and poor into your house …

 “I said maybe next year” on that.

but I hope you paid attention

because even if we decide that this isn’t the year

that doesn’t mean Jesus wrote us off

Jesus doesn’t necessarily wait until it’s convenient for us

sometimes…he goes ahead and shows up,

or maybe just shows us something

we need to be watchful – that’s something we hear about at Advent

We sing the carol, Joy to the World, “Prepare him room”

The days are surely coming …

justice and righteousness

there will be signs

be alert

the kingdom of God is near

2.  Tell the Story

Gospel reading, Jesus teaching about the last days

signs

skies: sun, moon, stars

earth: distress among the people

they will see the Son of Man coming in a cloud with power and glory

What to do?

when you see these things:

stand up, raise your head

for your redemption is near

parable of the fig tree

when the leaves sprout, it means summer is already near

connect the lesson

so, when you see these things I am telling you about happening

you know that the kingdom of heaven is near

Prediction

this generation will not pass away until these things happen

heaven and earth will pass away – but my words are permanent

So be ready

be on guard so that your hearts are not burdened

dissipation, drunkenness, worries of life

don’t try to self-medicate or be distracted

don’t fall into that trap, like others who are not prepared

Be alert

at all times

pray that you will have the strength to escape these distractions

and stand before the Son of Man

3.  So What?

Prepare him room – the kingdom of heaven is near

Second Coming has always been a big deal

disciples thought Jesus would come back within their lifetime

when he says “this generation will not pass away…”

but Jesus has always taught that we should not concern ourselves with when that time will be

“Just be ready”

live every day as if the kingdom of heaven is near

not just to save your hide

not just to bide your time until the “sweet by and by”

but live every day in the way God made us to live

abiding in his word

building up the body of Christ

creating a community of faith

that is ruled by the gospel of Christ’s love and reconciliation

not just so we don’t get caught doing something else

but because that is how God created us to live

Jesus isn’t coming back to bust us

but to save us and take us into himself

Don’t worry about the signs

there are always signs in the skies

falling stars, eclipses,

 constellations seeming to move about as the earth orbits the sun

the people will respond

confused by the roaring sea and waves?

these happen all the time

the tide goes in and out daily

waves never stop coming to the shore

storms and natural disasters?

yes, these are tragic

and claim numerous lives

I would never mean to diminish that

but we need not attach some apocalyptic meaning to every event

don’t let yourselves be filled with terror and fear at these signs

instead:  Stand up, raise your heads, your redemption is coming near

don’t get all caught up

Jesus will come again

in fact, the kingdom of heaven is already near

and we get glimpse of it whenever we prepare him room

And when we get ready – when we prepare him room – we see glimpses

we don’t prepare him room because Jesus needs a clean place to sit

sometimes we have to get Pauly to prepare room in the den

his toys are all over the place

there’s not a place to walk or sit where there’s not something underfoot (or under something else)

seems the whole house sometimes is littered with

Transformers, Hot Wheels, balls, and books

although I don’t mind the books – can’t get enough of those

we need Pauly to prepare room in the house so people can get around

We prepare Jesus room when we get rid of the things that keep us from knowing he’s there – or that he’s coming

distractions, desiring our comfort

My family was among the people out in force on “Black Friday”

I didn’t take the earliest shift

it was around 10am before I left the house

that was after Kazy came back to get me

she had been out since….well, much earlier

I suppose we saved a little money

Christmas and Pauly’s birthday

we were preparing for something

Christmas-related if not Christ-related

but I was hardly “Preparing him room”

But there were some moments in the past week that I was aware of “Preparing him room – for the kingdom of heaven is drawing near”

observing people decorating the church for Christmastide

grateful for the Worship Com keeping up with decorations being fresh and current

Marilyn McCarthy’s banner

mostly, enjoyed seeing how y’all work together on that – like you always do

fellowship at lunch after Hanging the Greens

Thanksgiving Dinner last Sunday night

remember the challenge from my sermon last Sunday?

did you invite anybody else?

did you notice somebody you didn’t know?

did you spend time with anybody new?

examples

Thanksgiving Dinner: did anybody else notice the unexpected family who came in about the time everybody else was through eating?

were we hospitable?

did we prepare him room?

was there anything else we could do?

was there still enough left to send food to Jackson Towers?

Did you notice the Jackson Towers folks who came for dinner?

notice how we are building community with them?

did you know they held 2 food drives for Turkey Trot donations?

what can you do for our friends at Jackson Towers?

How can we prepare him room?

Did you know the Deacons still serve dinners regularly at Alpha Center?

Did you now they are also preparing dinners and games

 at Jackson Towers?

Did you know they are also taking dinner to the volunteers at

Compassionate Care?

Did you know you don’t have to be a Deacon to participate in

these?

Ask a Deacon to let you go along next time

How can we prepare him room?

Notice how our relationship with Central School is growing?

now Munch Bunch

how can you help?

How can we prepare him room?

friends we are working on building relationships

first within these walls

then outside – maybe just across the street

what are you doing about it?

how can we prepare him room?

When we prepare Jesus room

we set aside our differences

claim what we have together

unity in the Body of Christ

shared sense of call to reach out

this is how we prepare room for Jesus in our life and in our world

    So may it be with us.  Amen

Pipe Shrine House, Mesa Verde

When I visited Mesa Verde this summer, I noticed a rather odd sandstone block at Pipe Shrine House, one of the mesa-top sites known collectively as the Far View Group.  These sites, like many others in the park, were excavated by Jesse Walter Fewkes in the early twentieth century, and documentation of the work done on them is correspondingly sparse.

Sandstone Block with Spiral Petroglyph at Pipe Shrine House, Mesa Verde

The block in question has a spiral pecked into it.  Not a whole spiral, though; rather, the middle of a spiral, with the upper and lower parts missing, as if the block were cut from a cliff face where a spiral petroglyph had been pecked.  Indeed, the only really plausible way to explain the block is that it was indeed cut from such a cliff face.

Block Incised with Zigzag Lines at Coyote Village, Mesa Verde

This is very odd.  I’ve never seen anything quite like it elsewhere.  There are a few other sites in the Far View Group that have blocks with designs on them, mostly parallel lines, but those are generally incised and they don’t bear much resemblance to common petroglyph designs.  They don’t show any particular evidence of the designs having been present on the stones before they were cut, either.  The spiral, though, is a very common type of petroglyph, and the Pipe Shrine block remains very puzzling.  Who cut that block?  Where?  Why?

Incised Parallel Lines in Building Block at Far View Tower, Mesa Verde

It’s very hard to say.  The fact that the block is at the top of the current wall strongly suggests that it was not originally part of the site.  In sites like this the top stones are generally modern capping put on with cement to protect the original walls beneath.  The spiral block, then, was almost certainly put on in the twentieth century.  It may have been put on by Fewkes himself after he excavated the site; recent dendrochronological research at the Sun Temple, which Fewkes also excavated and stabilized, has shown that he did a substantial amount of rebuilding there, and it’s quite plausible that he did the same at Pipe Shrine House.  If it wasn’t Fewkes, it was probably some later Park Service stabilization crew.

Plaque Describing Work by J. Walter Fewkes at Far View House, Mesa Verde

Regardless of who put the stone where it is now, though, the bigger question is where they got it, and how.  The mystery is amplified by the fact that Mesa Verde is known for having relatively few petroglyphs compared to many other areas with comparable ancient populations.  The stone looks like the same Cliff House Sandstone (Mesa Verde Formation) as the other stones in the wall, although its patina seems to be a slightly different color, which may or may not be relevant to its origin.  There’s no reason to think it comes from anywhere other than Mesa Verde, but that makes it all the more inexplicable that Fewkes or anyone else would have cut into one of the few petroglyph panels on the mesa for building stone when there are few things in the area more plentiful than sandstone.  I’m no expert on Mesa Verde, of course, so it’s quite possible that the story of this stone is well-known or at least published somewhere in the voluminous literature on the archaeology of the area, but if so I haven’t seen any reference to it.  It’s just very puzzling, and I don’t have a clue what the answer is.

Vent at Sun Temple, Mesa Verde

When I am very sick, lying on my bed, I feel like I am leaving my body. I do not feel my legs and my arms. I feel my chest and my head, however. They seem to be the anchors that keep me from levitating, flying, vanishing out of this body. Sometimes I close my eyes and I feel like I see things underneath, in between and beyond the darkness.

When this happens, I appear to travel at very fast speeds in worlds I cannot comprehend or describe. Everything changes its own shape extremely quickly. At some point, aggressive, repeating images keep coming back and I have to open my eyes and rid my mind of this madness.

When I am very sick, lying on my bed, I often feel like I am very skinny or very fat. When I dream, I experience violent and disturbing events. They become so disturbing that they wake me up.

Sometimes, when I think of these moments, I feel like something is desperately trying to use this feeble state of mine in order to do something to me. I have the feeling that some sort of entity, a being, is attempting to do me harm. I cannot explain it even to my own self, but it seems obvious in some way or another. There is something evil that is fueled with envy and hatred towards us.

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This is another shot taken near Ellenborough Falls to the west of Taree in New South Wales, Australia.

This is a view looking down from up near the top of the waterfall.

Little Colorado River from Homol'ovi Ruins State Park

Some of the most important work on the origins of the kachina cult is that done by E. Charles Adams of the Arizona State Museum, particularly his 1991 book focusing specifically on the subject. In this book he summarizes the available evidence for the origin and early development of the kachina cult, and based on the distribution of the archaeological manifestations of the cult that he identifies he concludes that it originated in the Upper Little Colorado River area of east-central Arizona in the period between AD 1275 and 1325.

Wall at Casa Malpais, Springerville, Arizona

Adams’s reasoning for this conclusion is based on his comparison of the distribution of four types of evidence that he presents as reflecting the presence of the cult: rock art, pottery, plaza-oriented village layout, and rectangular kivas. His summaries of the distribution of all these features in space and time are very useful, but his conclusions about the origins of the kachina cult go well beyond the evidence he presents and are not very convincing. His method for determining the origin of the cult is to look at the distribution of the four features he identifies and find where they first overlap. This seems reasonable enough.

Petroglyphs at Puerco Pueblo, Petrified Forest National Park

Unfortunately, there does not turn out to be any place where the features all overlap sufficiently early to be associated with the initial development of the cult, so Adams has to resort to finding a place where three of the elements overlap. The three elements he uses are pottery style, plaza-facing village layout, and rectangular kivas, which he finds present together earliest in the Upper Little Colorado River area in the late thirteenth and early fourteenth century. He therefore concludes that this is when and where the cult originated and proceeds to describe its rapid spread to the north and east over the course of the fourteenth century. Unlike many other researchers, including Polly Schaafsma, he considers the cult to be fundamentally indigenous rather than Mesoamerican in origin, although he concedes that some elements of it were probably subject to influence from groups to the south such as the Hohokam and Salado.

Sign at Puerco Pueblo Showing Plaza-Oriented Layout

Adams theorizes that after its initial spread the cult was greatly elaborated at Hopi, where it acquired its strong association with rainmaking and began to be reflected in elaborate kiva murals, and that it subsequently spread in modified form from Hopi to areas that had already adopted the initial cult directly from the Upper Little Colorado, such as Zuni and the Albuquerque area of the Rio Grande valley. It is only at that point, after AD 1400, that Adams sees any influence from the Jornada Mogollon coming up the Rio Grande, and he sees this influence, reflected in the Jornada rock art style and a similar style in some kiva murals, as secondary to the Upper Little Colorado and Hopi kachina cult influence already present in the Rio Grande valley. He even speculates that the Jornada influence may not have affected the kachina cult itself at all, and that it may have had more to do with other societies present among the Eastern Pueblos having more to do with war.

Warning Sign at Edge of Little Colorado River, Homol'ovi Ruins State Park

This theory is problematic for a number of reasons. For one thing, Adams relies very heavily on the distribution of pottery styles as evidence for the spread of the kachina cult, but he never establishes the association between the cult and the styles he mentions. He focuses on the so-called “Fourmile style” (named after Fourmile Ruin in the Upper Little Colorado area), a style of polychrome decoration that affected pottery types throughout the Southwest in the fourteenth century. Among the features of Fourmile style that Adams emphasizes are its use of asymmetrical decoration on the interiors of bowls, its extensive use of bird and feather imagery, and its occasional use of obvious kachina cult symbolism, particularly masks or whole anthropomorphic masked figures. It is the last aspect of the style that is clearly most associated with the kachina cult, and the presence of this sort of imagery on ceramics is certainly as clear a sign of the presence of the cult in a given area as the presence of similar motifs in rock art, but Adams goes beyond this observation to associate any use of the Fourmile style with the spread of the cult. This is not something that can just be assumed, however. It is important to note that the Fourmile style was very widespread, including in areas without any other evidence of kachina cult imagery, and it is quite possible that the distribution of the style is completely independent of the distribution of the cult. That is, the Fourmile style may just have been the style of decoration that was popular at the time that the kachina cult happened to be spreading throughout the northern Southwest, so that groups that adopted the cult may have used its imagery on their Fourmile-style ceramics without there being any particular association between the style in general and the cult. Thus, while Fourmile ceramics with kachina imagery would clearly be evidence of the distribution and spread of the cult, Fourmile ceramics without it would not necessarily be, and Adams’s extensive use of them undermines his conclusions significantly.

Petroglyph Panel Showing Mask at Puerco Pueblo, Petrified Forest

Another major problem with Adams’s approach is the way he largely disregards the rock art evidence. When he realizes that there is no place where all four of his lines of evidence come together at the proper time, it is the rock art evidence that he ignores. This is why he is able to conclude that the cult originated in the Upper Little Colorado area, where rock art evidence for the presence of the cult is very slim (probably due largely to the limited study of rock art in this area). Rock art, however, is the most straightforward and obvious evidence there is for the presence of the cult. Unlike Fourmile style ceramics, Rio Grande style rock art is full of kachina imagery, and it is very different from earlier rock art styles in the area where it appears. Schaafsma’s theory linking the cult to the Jornada Mogollon depended largely on the rock art evidence. Recall that her argument for transmission of the cult up the Rio Grande via the Jornada depended largely on the lack of rock art evidence for the presence of the cult in the Mogollon Rim and Upper Little Colorado area. Adams, although he argues for the transmission (and, indeed, the origin) of the cult in this area merely assumes that the Rio Grande style originated in the Upper Little Colorado area along with the cult and that it is unrelated to the Jornada style, which he sees as a late introduction to the Eastern Pueblos after the Rio Grande style was firmly established.

Petroglyphs at Casa Malpais, Springerville, Arizona

It is not hard to see why Adams puts so much emphasis on pottery and so little on rock art. He is trying to determine the time as well as the place of origin of the kachina cult, and to do that he needs evidence that can be securely dated. In the Southwest pottery styles are very well dated by association with tree-ring-dated contexts where they appear, and they therefore give quite precise dates even for sites that have note been excavated or dated in any other way. Rock art, on the other hand, is notoriously difficult to date. Pictographs, which are painted onto the rock surface often using some sort of organic paint, can sometimes be carbon-dated by samples of the paint or other associated organic artifacts, but this technique has rarely been used in the Southwest, and the much more common petroglyphs, which are pecked or incised into the rock surface, cannot be directly dated at all and can only be assigned very general dates based on their style and/or proximity to dated sites. Thus, associating the spread of the kachina cult with the spread of the Fourmile style, which does seem to have occurred around the same time, gives Adams much more chronological control than Schaafsma has with her rock art styles, and it even allows him to argue, in direct opposition to Schaafsma’s interpretation, that the Jornada style in the Rio Grande valley is later than the Rio Grande style rather than ancestral to it. His justification for doing so is very shaky, being based on similarities between the Jornada style and the style of kiva mural found at sites such as Kuaua, north of Albuquerque, but it is not possible to prove that he is wrong. Nor, for that matter, is it possible to prove that he is wrong to associate the Fourmile ceramic style with the cult, although he does so on similarly shaky grounds.

Casa Malpais from Above

Nevertheless, despite all these problems with Adams’s theory for the origin and spread of the cult, his model for why the cult was adopted so quickly and easily throughout the Pueblo world is quite convincing and useful. The explanation is basically the same as Schaafsma’s: the kachina cult, being a non-kin-based system with the potential to integrate whole communities easily, was very attractive to the rapidly aggregating villages developing throughout the Southwest at this time, and it was therefore adopted as a way of dealing with and resolving the many conflicts that inevitably develop within diverse and rapidly growing communities. He defines the model more rigorously and in more detail than Schaafsma, however, and presents a four-stage process for adoption of the cult, with corresponding correlates that should be identifiable in the archaeological record:

1. Immigration: Starting around AD 1275, when major environmental changes occurred throughout the Southwest, locations that either maintained their attractiveness for settlement or became newly attractive as a result of the changes saw massive influxes of population from the many areas being abandoned at this time.
2. Aggregation: In the locations seeing large-scale immigration, the new immigrants coalesced into large, aggregated villages, either joining previously existing populations or, in sparsely populated or previously unattractive locations, developing their own aggregated villages. These villages are often but not always plaza-oriented.
3. Appearance of kachina cult imagery: Shortly after initial aggregation, the plaza-oriented villages begin to show signs of kachina cult imagery, either in nearby rock art or on locally produced pottery. This demonstrates the adoption of the cult by the village, perhaps in part to deal with the problems caused by rapid aggregation.
4. Continued aggregation: As a result of the usefulness of the kachina cult in integrating the new communities, new immigrants continue to join them and are able to be successfully integrated. This part is important; previous attempts at forming large, aggregated communities in the Southwest had not lasted for long, probably because existing religious and social systems were not able to successfully integrate populations on that scale.

Adams applies this model to the cluster of sites at Homol’ovi Ruins State Park near Winslow, Arizona, where he has conducted extensive research as part of a long-term project by the Arizona State Museum. He finds that the model fits the history of the sites there quite well. Adams’s model can also be used to evaluate the impact of the kachina cult and the development of plaza-oriented village layouts on aggregation in other parts of the Southwest during this time period, and perhaps during others. Adams sets the beginning for his model at AD 1275 to correspond to the environmental changes in the northern Southwest associated with the so-called “Great Drought” of AD 1276 to 1299, and this does correspond to the onset of major aggregation in many areas, but in other areas aggregation began either earlier or later than this, and the adoption (or, perhaps, development) of the kachina cult may have played a role in these contexts as well.

Masonry at Homol'ovi I

Adams’s model may be an effective way to address the relationship between aggregation and the spread of the kachina cult, but it still leaves open the question of why people were aggregating in the first place. This has been a matter of much dispute and argument over nearly the whole history of southwestern archaeology, and many theories have been proposed. Many of the recent theories revolve around changing environmental conditions and the need for changes in subsistence systems, and they address this idea from varying perspectives, often focusing on the need for more centralized decision-making and/or more efficient land use as the result of less reliable or more difficult conditions for agriculture. In his discussion of this issue, particularly in relation to the case study of Homol’ovi, Adams seems to endorse some version of this idea, with a particular focus on the decisions of community leaders. Unlike many archaeologists who study the ancient Southwest, Adams does not present prehistoric Pueblo society as egalitarian, and he assumes throughout his discussion the presence of a two-tiered society with a small priestly class making decisions at a community level and deriving their authority from their control of ritual knowledge. Importantly, however, he notes that this elite never managed to amass the sort of surplus wealth necessary to transform Pueblo society into a truly stratified society with significant economic inequality. Adams attributes this mainly to the marginal nature of the Southwest for agriculture, but it is likely that another major factor is the communal ideology of the Pueblos, which strongly discourages individual gain and encourages leaders to put the needs of the community above their own desires.

Walls at Homol'ovi II

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Bridge over Rio Puerco of the East, Cuba, New Mexico

One of the more confusing aspects of the geography of the Southwest is the fact that there are two completely different rivers with the exact same name, and they’re quite close to each other.  The name is “Rio Puerco,” meaning “dirty river” in the New Mexico dialect of Spanish.  It’s an apt name, since rivers in the area tend to carry a lot of sediment and the water in them tends to look rather dirty.  Nevertheless, the use of it for both rives can lead to considerable confusion, and while in technical and scholarly contexts they tend to be carefully distinguished, in more accessible public contexts there isn’t much clarification out there.

Rio Puerco of the East, Cuba, New Mexico

One Rio Puerco originates in the Jemez Mountains and flows south through the village of Cuba, then parallels the Rio Grande for a considerable distance before joining it south of Belen.  In contexts where careful disambiguation is necessary this river is generally called the Rio Puerco of the East, on maps and signs where highways like US 550 cross it it’s usually just labeled “Rio Puerco.”  Today the Puerco of the East forms a rough eastern boundary for the Navajo culture area, and the communities along it (especially Cuba) serve as important points of contact between the Navajos and the New Mexico Hispanic culture area.

Rio Puerco of the West and Train Tracks at Petrified Forest

The other Rio Puerco originates on the southern slope of Lobo Mesa near the Continental Divide and flows generally southwest through Gallup and the Red Mesa valley, paralleling the railroad and I-40 into Arizona.  It passes through Petrified Forest National Park before flowing into the Little Colorado River at Holbrook.  This river is generally called the Rio Puerco of the West, and it forms a very rough southern boundary for the Navajo culture area, with the area further south dominated by the Zunis along the eastern portion and by Anglos (largely Mormons) along the western portion.  The towns along the river are mostly nineteenth-century railroad towns.

Sign at Bridge over Rio Puerco of the East, Cuba, New Mexico

Clearly, these two rivers are very different and have nothing to do with each other.  They are on opposite sides of the Continental Divides and belong to completely different drainage systems: the East flows into the Rio Grande and ultimately into the Gulf of Mexico, while the West flows into the Little Colorado, which flows into the Colorado just upstream from the Grand Canyon and ultimately ends up in the Gulf of California.  Confusingly, though, they’re really quite close.  If you drive from Albuquerque to Flagstaff on I-40 you cross both of them, and each is marked only by a sign saying “Rio Puerco.”  They are also both close to Chaco, and both areas were integrated into the Chacoan system, though probably to different degrees.  The only major Chacoan site known from the Puerco of the East is Guadalupe, while the Puerco of the West has a whole string of sites that have been identified relatively recently as Chacoan outliers, including Allentown, Chambers, Sanders, and Navajo Springs.  Unfortunately, the names are so entrenched at this point that there’s little prospect of changing either (or both) to something less confusing, so it looks like this is something we’ll just have to keep dealing with.  Hopefully this post will help reduce the amount of confusion over this issue.

Bridge over Rio Puerco of the West at Petrified Forest

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Perhaps in no other area of personal injury law, can a swimming pool accident attorney be of more importance than in ensuring that a client involved in a near drowning seeks immediate medical attention.

If you or a loved one have been involved in a swimming pool accident, visit our law firm website at http://www.SebastianGibsonLaw.com for more information and call us at any of the numbers easily found on our website.

A condition not often discussed is near-drowning or dry-drowning. This can occur hours after a person has nearly suffocated in water and with a build-up of water in their lungs, they can die after walking around and talking and performing other activities. Seek medical attention for yourself and any member of your family involved in a near drowning, even if you feel fine.

If you or a member of your family has been seriously injured in a swimming pool accident in California, you may also be wondering what steps you should take to provide care or to seek compensation for your injuries or loss.

Drownings don’t just occur to kids and they don’t happen just in swimming pools. A very small amount of water can be fatal to a small child. And an adult or a child who has had a near-drowning can still suffer brain damage, respiratory damage or death hours later.

Depending on the research you read, or the ages involved, drowning is from the fourth to the first cause of deaths to children. For children under the age of 14, drowning in swimming pools is the leading cause of death. Other studies put drowning fourth after guns, car accidents and burns for the leading cause of unnatural death of all children. The fact is, more people die in swimming pool drownings than any other type of activity.

A child however can drown in a beer cooler, a fish pond, another water feature, Jacuzzi, toilet, water bowl, stream, river, drain and any other place where their head can be in the water.
Because of their disproportionate weight of their heads, a toddler can fall into water and find it difficult to lift their head or their body so they can breathe.

For every child that drowns, five are left with permanent brain damage or damage to their respiratory system.

So what can be done to prevent drownings? Vigilance is the word, whenever children are around water. Keep gates to pools closed and locked, and whenever possible keep covers on pools. Many people are unaware of electronic splash sensors that can be employed to sound an alarm whenever a splash is detected. And take a CPR course or take a refresher course.

If you or another member of your family have been involved in a swimming pool accident, visit our law firm website at http://www.SebastianGibsonLaw.com and call the law firm of R. Sebastian Gibson immediately for advice.

How to find approximate Nash equilibrium for sparse games

Constantinos Daskalakis is one of the experts in modern game theory, especially the structure of Nash Equilibrium for non-zero sum games. He has written a wonderful paper with Christos Papadimitriou On oblivious PTAS’s for nash equilibrium. Also see his nice survey for more information.

Today I want to talk about Costis and Christos’ paper as it relates to sparse games. This is another example of the Iceberg Effect: their paper has a beautiful result on game theory, but I missed another of their results.

Constantinos, Costis, was kind enough to point out two things about sparse games after my earlier discussion on games. First, that in his paper with Christos at STOC 2009, they stated a theorem that solves the sparse case of symmetric games. He went on to sketch the proof, which they did not include in their paper: I will give their proof in a moment.

Second, he points out that Shanghua Teng has observed that the uniform distribution is trivially a -Nash equilibrium of a -sparse game—the expected payoff from any row is at most for the row player and similarly for the column player.

His second point is one that I would like to discuss, since it raises an issue by what we mean to approximate a Nash Equilibrium (NE).

Let’s turn to discuss first NE and then their theorem.

Nash Equilibrium: Exact and Approximate

What does it mean to find an approximate NE? I think it will be easier to first explain the main issue involved by an analogy. Anyway I love analogies.

Suppose that you have a polynomial and want to find an so that

of course, we call a root. Usually is not a rational number, so we cannot write it down exactly. Thus, what we do is try to find a so that

where is the required precision and are integers.

There is a fundamental problem: simply because is small does that mean that it is near an actual root of ? It does not, in general. What we want are the stronger statements:

1. The value of is near ;
2. There is a so that and is also small.

In this case we can say that is an approximate root of the polynomial. If there is no such , then is an interesting point, but it is not correct to call it an approximate zero.

This behavior is analogous to what happens with “approximate NE’s.” There are two types of interpretations of what an approximate NE is:

An -near NE: This is a pair of strategies that are within an of an exact NE.

An -NE: This is a pair of strategies such that a player who defects from their strategy can gain at most an .

Costis, in his survey, points out that the first notion is reasonable, but the latter is the one that we usually use: Note also that it is easy for a player to check the approximate optimality of the actions used by her mixed strategy. So the notion of an approximate Nash equilibrium is much more appealing and, in fact, this is the notion most commonly used.

Note, the analogy to the root problem: in the first we are near a root, and in the second we are at a small value. As Costis points out the latter can be checked easily, while checking that a point is near an exact root is not as easy.

Sparse Games

I will now state their theorem:

Theorem: Suppose that is an matrix with entries in , such that each row and column in has at most ’s. Then, for the symmetric game defined by , we can find an -NE in time bounded by

Here is a sketch of their proof:

Proof:

The key insight is that it is enough to consider strategies for the row and column player where the probabilities are integer multiples of . The number of such strategies for either player is at most

This follows since the number of strategies are bounded by the number of ways to place objects into “bins.”

We now have a “small” set of strategies, the following argument will show that one of these strategies contains a pair that is an -near NE. Consider an exact NE say . Notice that there exist strategies such that the following are satisfied:

1. For all : and .
2. For all : if then , and if then .

Consider . If , then set to . Otherwise, set to the nearest multiple of . This almost works: the small issue is that if is not a exact multiple of , then do we round up or down? Either rule will make satisfy the needed conditions above. However, we also need to be a probability vector: it is easy to see that by rounding some up or down we can adjust to satisfy

which will make it a probability vector. The same method works for . Now we need to prove that this strategy pair is an -near NE. The payoff for the row player is and for the column player is . Let denote a unit vector with at -th coordinate. For notational convenience, we omit the transform symbols on the vectors. The usage should be clear from the context.

Notice that the pair of strategies and the NE satisfy:

1. , for all .
2. , for all .

The first claim follows from the fact that

The second claim is analogous. This is where we use that has at most ’s in each row/column. Therefore, the total error from the NE is at most

It follows from the above that is an -near NE of the game.

The above proof shows the existence of an -near NE in the search space formed by the strategies that are multiples of . This strategy pair is near the exact NE . However, because of the difficulty of searching for an -near NE, an exhaustive search in this space can only guarantee that we would find an -NE, and not an -near NE.

Open Problems

An interesting open problem is to try to found an -near NE. The above proof shows that it is in a relatively “small” list of strategies. Is it possible to discriminate and determine which are near exact NE’s?

The above proof gives us a PTAS for games with a bounded number of 1’s in each row and column. However, for matrices with 1’s in all, the problem of finding a PTAS is still, I believe, open.

article from www.eformulacarnews.com

BARRIE, ONT. (October 27, 2009) – With the 2009 Ontario Formula Ford Challenge season now in the books, the Brian Graham Racing/TLM Racing with Team Grote gang wasted little time in preparing for

the 2010 season. With FF1600 rookies Taylor Near, Ayrton Triolo, and Mackenzie Clare all getting behind the wheel, the team recently had a very successful test day at the Mosport Driver Development Track.

While the day started with a damp track, it soon dried and all three drivers logged over 90 laps by days end. Working with data and coaching between sessions, they all steadily improved, ending the day within 4/10th of a second of one another. It was the first outing for Near and Triolo, and they both acquitted themselves very well. Clare who will not be of age until the 2011 season, showed good speed as well, and when he turns 16, he will be more than ready.

“It was a very productive day for all of us,” stated Team Owner Brian Graham. “Both Ayrton and Taylor are products of our ladder system and we hope to have some announcements shortly on their plans for 2010. Mackenzie gets quicker every time out and is progressing nicely. When he turns 16 we will see him on the OFFC grid, and I suspect at the pointy end! We will continue our testing as late as the weather will allow, and then look south to warmer locations.”

Mackenzie will continue with his testing program next season with BGR/TLM, while both Ayrton and Taylor are currently working on deals for the 2010 season.

BGR/TLM will continue to test as long as the weather allows and then will look to the USA for winter testing. Plans for a full Pro F2000 series are also in the works, interested drivers should contact the team through the team website http://www.briangrahamracing.com