http://www.siam.org/news/news.php?id=827

Eigenvalues. Fixed points. Stable equilibria. Mathematicians like things that stay put. And if they can't stay put, the objects of study should at least repeat themselves on a regular basis, like orbiting planets or populations of predators and prey. Even in the case of chaotic systems, mathematicians have traditionally gravitated toward invariant features, such as strange attractors, stable manifolds, and periodic points.

What makes this tradition possible is that dynamical systems---at least the ones mathematicians favor---are governed by equations that depend on time either cyclically or not at all. But nature doesn't always oblige. Many phenomena require equations whose coefficients are non-periodic functions of time. Indeed, many---arguably most---phenomena can be described not by equations at all, but only as an amalgam of time-varying data.

http://www.larouchepac.com/news/2007/12/28/larouche-whole-operation-paki...

"People are being idiots," he said, "because they say, well, `You can't say that! Let's concentrate on the facts. Let's concentrate on the facts,' is what they'll say. Now here you have, the fact is, we're in the point of a total breakdown of the international financial and monetary system. This is not a collapse; this is not a depression. It's a disintegration of the very integument upon which the whole civilization has now come to depend. That's the game. And, any developments which don't fit the game, don't explain this kind of thing. It's one thing after the other; it's a chaos operation. The tendency is to create chaos; it's a chaos operation. So, therefore, in a chaos operation,-- don't try to attribute chaos, to some individual who's not chaos.

"We don't know who the culprit is; we don't know which faction, who is the faction," LaRouche concluded. "We can identify the faction by the nature of the faction. But the identity of the faction, we don't have. The guy who's doing this, is doing something. We know what they're doing; we know what the effect is they're playing for. That's clear. WHO that someone is, we don't have."

Most people don't like such alternatives...
Guess you are talking about those less than 5% of the world population that just happen to live in the US ? :)
The same that consume 25% of the world's oil ? Maybe the rest of the world will adapt more easily actually ?

Just Heard this song on NPR: I think that if we are going to choose to listen to someone other than Uncle Dave we will surely end up nude in a cave without food. It's time to take Uncle Dave seriously. He's not a manic depressive, just a freakin realist.

Uncle Dave's Grace: lyrics by Peter Berryman, music by Lou Berryman

"We gather together to ask the Lord's blessing" Thanksgiving day, Uncle Dave was our guest

He reads the Progressive which makes him depressed

We asked Uncle Dave if he'd like to say grace,

A dark desolation crept over his face

"Thanks," he began as he gazed at his knife,

"To poor Mr. Turkey for living his life

All crowded and cramped in a great metal shed

Where life was a drag then they cut off his head"

"Thanks," he went on, "for the grapes in my wine

Picked by sick women of seventy-nine

Scrambling all morning for bunch after bunch

Then brushing the pesticides off of their lunch

Thanks for the stuffing all heaped on my fork

Shiny with sausage descended from pork

I think of the trucks full of full of pigs that I see

And can't help imagine what they think of me"

Continuing, "I'd like to thank if you please

Our salad bowl hacked out of tropical trees

And for this mahogany table and chair

We thank all the jungles that used to be there

For cream in our coffee and milk in our mugs,

We thank all the cows full of hormones and drugs

Whose calves are removed at a very young age

And force-fed as veal in a minuscule cage"

"Oh thanks for the furnace that heats up these rooms

And thanks for the rich fossil fuel it consumes

Corrupting the atmosphere ounce after ounce

But we're warm and toasty and that is what counts

I'm grateful," he said, "for these clothes on my back

Lovely and comfy and cheap off the rack

Fashioned in warehouses noisy and cold

In China by seamstresses seven years old"

"And thanks for my silverware setting that shines

In memory of miners who died in the mines

Worn down by the shovelling of tailings in piles

Whose runoff destroys all the rivers for miles

We thank the reactors for our chandelier

Although the plutonium won't disappear

For hundreds of decades it still will be there

But a few more Chernobyls and who's gonna care?"

Sighed Uncle Dave, "though there's more to be told

The wine's getting warm and the bird's getting cold"

And with that he sat down as he mumbled again

"Thank you for everything, amen"

We felt so guilty when he was all thru

It seemed there was one of two things we could do

Live without food, in the nude, in a cave,

Or next year have someone say grace besides Dave.

http://www.levity.com/eschaton/Why2012.html

Why: Winter Solstice Sun Conjuncts The Sacred Tree in 2012 A.D.
First, the tzolkin count originated among the Olmec at least as early as 679 B.C. (see Edmonson's Book of the Year). We may suspect that astronomical observations were being made from at least that point. The tzolkin count has been followed unbroken since at least that time, up to the present day, demonstrating the high premium placed by the Maya upon continuity of tradition. In this way, star records, horizon positions of the winter solstice sun, and other pertinent observations could also have been accurately preserved. As suggested above, precession can be noticed by way of even simple horizon astronomy in as little time as 100 to 150 years. (Hipparchus, the alleged "discoverer" of precession among the Greeks, compared his own observations with data collected only 170 years before his time.) Following Edmonson, the Long Count system may have appeared as early as 355 B.C. Part of the reason for implementing the Long Count system, as I will show, was probably to calculate future winter solstice dates.

We must assume that even at this early point in Mesoamerican history, the crossing point of ecliptic and Milky Way was understood as the "Sacred Tree". Since the Sacred Tree concept is intrinsically tied into the oldest Mayan Creation Myths, this is not improbable. At the very least, the "dark rift" was already a recognized feature. Early skywatchers of this era (355 B.C.) would then observe the sun to conjunct the dark ridge in the Milky Way on or around November 18th.5 This would be easily observed in the pre-dawn sky as described above: the Milky Way points to the rising sun on this date.

Yes I seem to remember reading in one of Thor Heyerdahl's books that the biggest statue of all was one that was still not completely finished. This means they were in the process of making it when their society collapsed and the work stopped.

I expect we'll do the same. When capitalism doesn't work, the solution will be more capitalism. Environmentalists, government regulations, and NOCs will get the blame for "not letting capitalism work."

Its likely to be the exact opposite: Socialism! When things get tough, politicians promise more handouts and more subsidies as a means to get elected. "Vote for me, and I will give everyone free food/gas/whatever, but you'll need to give me more authority so I can end corruption/other lame excuse for more centralized control"

This usually causes a transition away from free markets into centralized control which can lead to totalitarianism. The countries with the highest levels of socialism and central control are the first candidates to fall into Totalitarianism. I believe at least some of Europe will swing this way. I think the US will become decentralized as Washington remains a quagmire and states are force to pick up more an more responibilty as Washington falls to accomplish anything. Another words I expect the United States to become the Divided States of America.

I wonder if it is likely that any stone age culture would start off building huge statues and progressively build smaller ones.

Not giant stones: new bombs, new missile systems, new surveillance systems, new "detention centers" (what did they used to call them?) Giant stones wouldn't be all that terrible.

DTI--
More like the "Invisible Fist", with the help of the State (capitalism has never existed without a strong state to enforce it's rules, as it emerged in the Italian City States of the 15th century, to the global World Bank and IMF)--
When the State collapses, so will capitalism.
Of course, this probably will be a bit messy.

I agree. high oil prices will slap you in the face and say stop using so much oil. car pool. grow more of your own food. get a PHEV.

if capitalism isn't the solution we have a real big problem.

Bingo. If capitalism was the solution, I doubt many of us would bother hanging out here in the first place.

John--
Let's be blunt:
"We Have a big problem"

Reduced economic activity is a very effective means of reducing oil consumption.

Alan