Apocalypse A Little Bit At A Time

When I was in college, my mathematics professors and graduate student teaching assistants insisted on showing us "tricks" that would convert intractable nonlinear equations with no general solutions into easily solvable linear equations. Most of the tricks involved crossing out the nonlinear portions and pretending they weren't there - essentially turning curves into lines. 


I found this both aesthetically objectionable and logically dishonest. I figured this was just their way of giving up without having to say so: to turn hard messy problems into flimsy but easy cartoon ones. But surely not. Surely, they being so much smarter and well informed than I, had good reason to resort to these tricks. They understood that those inconvenient portions of equations really didn't make that much of a difference, right?


Well, the minute I had access to the clunky mainframe computers of the time, coded up a lot of these systems of nonlinear equations as recursive functions, set them to running under various initial values, and seeing wildly different results from one run to the next, I realized that this was all bullshit. That pesky little nonlinear factor? That x squared? Or that x times y? It made all the difference in the world. This was years before the whole discipline was called Chaos Theory, but obviously that was what was going on there. 


The deal with Chaos Theory, put in one sentence is that a completely deterministic process turns out to be wildly affected by just the smallest numerical change in your starting variable. You've heard of the Butterfly Effect, the idea that a butterfly flapping an errant wing in Brazil causes a hurricane in Texas? Well, that's the dumb media version. The actual interpretation is something more profound, that an equation with no surprises whatsoever, that runs like clockwork, can give you something completely different every time, with just the tiniest of nudges at the start. It's rather like finding a jewel knocked from the helmet of Satan in a battle fought with God at the dawn of time. Rerun the whole thing, and that jewel is sometimes a diamond, others a sapphire.


So, that thing called Fate? That thing called Destiny? Even in a clockwork universe, both are utter fictions. Delusional Fantasy. It shouldn't come as a surprise, given that the universe is a complex open system with many overlapping and interdependent factors. 


Invariably, a peranoscope viewer will be tempted to examine all possible outcomes of his or her own existence. I advise against it.

The most disconcerting aspect of such an investigation is not the fact that your existence makes up just a tiny (and by tiny I mean tiny, like, not even a bug smear on the windshield of life, not even a greasy little paramecium smear on said windshield) little spot of all, on average 10⁵⁰⁰, possible worlds. Given all the absurd events that could have occurred over the past 13.5 billion years, it's a wonder that you and I are here at all. And the creepiest thing isn't that so many possibilities in our lives end up being coin-flip moments, moments that we agonized over and then it turned out that epic decision made spit for a difference. And it wasn't the Hairy Eyeball Effect - the feeling that, as you view all possible worlds through the peranoscope, you in turn are being viewed, which makes you squirm self-consciously and in turn makes you feel the discomfort of phantoms as they squirm self-consciously, all of it rippling through the quantum foam, and all embarrassed by existence itself. Nor is the creepiest thing finding just how little control you have over your life, how chance and contingency make nearly 99.99999% of everything that happens. 

No the absolute creepiest thing is, that very large but finite number of universes with the Earth, and the Sun, and our galaxy, and us in them, that small cross-section of all possible worlds where we exist, our existential étendue can almost be seen, if you squint hard enough, to be visibly shrinking. 

I figure we cease to exist an average of 1.8 universes per hour. 

All of us, dreaming of the past, or living the present, or in anticipation of living in the next civilization after this one, wink out on a regular and, it seems, accelerating basis. Except for the Convergence. That ensemble of universes where we all of us continue to exist seems to be stable and linearly unchanging.

But I could be wrong.

MY Space Invaders Movie

This past Friday evening, for reasons we really need not go into here, I had a powerful urge to get just completely plowed. I also wanted to invest the least amount of effort doing so, and thus hit up the library for some movies, ending up checking out "Battle Los Angeles" for home viewing.

And so, pre-armed with a bottle of well frozen Stolichnaya vodka and a sixpack of Boulevard Pale Ale, and initiated with a few depth charges in the system, I sat down for some dumb-but-stupid manly blow-em-up action movie shit.

And I gotta tell ya, aside from perhaps a bit too much backstory, I enjoyed Battle Los Angeles. It was no blockbuster, but it was adequately entertaining, and I'll tell you why.

First, I enjoy the actor Aaron Eckhart, who did a good turn in Thank You for Smoking. Also the tough chick Michelle Rodriguez, going all the way back to Girlfight. I also enjoyed the movie because it remained consistent throughout. There were no majorly flagrant abuses of my suspension of disbelief (including the fact that we are invaded from Outer Space - more on that in a bit). The action was well-edited, fast paced, the stunts sufficiently baroque without being over the top, and a lot of shit exploded, which, for guys, is important. We do like the warporn. It also had the appropriate appeal to noble self-sacrifice and selfless actions, which, naturally, is part of warporn.

My only objection was the beginning back stories of all the protagonists, which, no doubt the director and screenwriters feel necessary so that you can care when they die, or don't. Personally, I could have been the voice of one the Marine privates, who, once it is determined that we are under extra-terrestrial attack, should have said (but didn't), in exasperation, "Finally!"

Yeah, about that suspension of disbelief. Well, it is a space invader movie, so from the start you have to cut some slack. I mean, the only way you can away with a truly ludicrous premise is if it is a comedy. But I've always wondered how (with the exclusion of, say, War of the Worlds, where humanity was unquestionably outclassed) aliens with star-spanning technologies seem to think that we humans are a big deal. That we are a problem and a challenge that needs to be addressed. I mean, if I move into a house and find it is full of vermin, I don't shoot up the floor boards to get rid of the pests. So, why don't the aliens just hose down the atmosphere with an appropriate vermicide to get rid of us pesky apes?

Or why is it that the alien weaponry is only a decade or so ahead of ours? Why the need to engage in toe-to-toe boots-on-the-ground combat behavior with us? Is it simply a need to generate drama (admittedly, people dropping like flies, and then aliens dropping out of the sky to sweep us into bins, isn't particularly engaging theatrically, but a lot more realistic).

But it occurs to me that this type of action is similar to the masturbatory TV trope theme of Frankenstein versus The Wolfman, or some such related stoned adolescent stupidity. My understanding is the latest incarnation of this is the Reddit phenomenon of Rome Sweet Rome, wherein a modern Marine unit ends up transported back in time to ancient Rome, and an exploration is undertaken about the all-important question of just how much ass would the marines kick? (Realistically? The Marines are doomed).

Well, this is the Trapped in the Past theme, and there are two behaviors, either try to live a normal and quiet life, or Change Things For The Better. Not many choose the former, and not that surprising entertainment wise.

I can think of one fairly mature treatment by Rod Serling, a Twilight Zone episode called "The 7th is Made up of Phantoms", where a modern tank crew ends up at the Battle of Little Bighorn, and naturally is doomed.

Or the granddaddy of them all, Twain's "A Connecticut Yankee in King Arthur's Court" with the hilariously comical slaughter at the climax of the book, involving machine guns and electrocution, if that is your idea of funny.

So, it sure seems like, if you are a technologically advanced group facing a primitive and backward savage culture, best to just lay low and not draw too much attention to yourself. And if you are an interstellar expedition that finds yourself in Earth's Solar System, maybe just harvest what you need from the asteroids or the Moon. Those don't fight back - too much.

Oh, and my Space Invaders movie? How to explain the close similarity of combat technology?

Well, taking a page from Battle Los Angeles, where the humans finally figure out how to "kick ET's Ass" on their own brutish terms. My movie ends with LA in ruins, the aliens calling for a ceasefire with  the humans, striding up to the Marine commander, taking off their bubble space helmets, extending a hand outwards and saying:

"Good game, man! Good game! See you next year!"

"A Great Aridness": A Book Report

"A Great Aridness: Climate Change and the Future of the American Southwest" by William Debuys

I'm sure that anyone living in the proximally near or east of the Mississippi river during March of 2012, with a record breaking streak of record breaking warm temperatures, must have, even for the briefest unguarded moment, had a little thrill of fear thinking:

"Wow, what if this it? What if we went through the phase change and now this is the new normal? What if, come June, the temperatures are a steady 120F? And the month of August never gets below 140F?" Face it, even the most rabid climate change denial type had to have had experienced just the slightest frisson of foreboding. Personally, I have a dollar bet that the arctic becomes permanently ice free during the summer come 2015. I suspect I'm going to collect that dollar.

Well, I do have friends who are going through that particular cognitive dissonance known as global warming denial, despite the fact that the weather is getting weirder, the arctic ice is shrinking, the upper latitudes are warming twice as fast, and getting ready to dump a whole bunch of methane into the atmosphere, they are convinced that anyone who believes in global warming is a fool. So, I guess it is going to take a phase change to convince them otherwise. Naturally, it will be the places that least need it that will experience the worst. The American Southwest is one such place.

Now, if there is any place in the United States of America that ought to serve as an object lesson, a true lesson of history as to how you should be prepared to live, it's got to be the Southwest, with it's ruins of pueblo village such as Mesa Verde, and Chaco Canyon. So naturally, if you are to settle anyplace that is already arid, you'd possess a certain predisposition towards hardship, a ready willingness to ape the ant, to be a tough and fibrous creature that stores up for hard and bleak times. What you wouldn't be is some type of soft, sloppy spendthrift, demanding green lawns, golf courses, the sidewalk-and-gutter, two car garage lifestyle of the more luxuriantly water blessed regions back East, or up North.

But, apparently, we Americans are just as deluded as the Indians and Spaniards that came before us. Build big dams, cut big ditches, make big plans, force Nature to service us, and ignore the whole long past history of the region, which is: fire, dead trees, dust and thirst. So, it won't surprise me not a bit when 30 to 50 million people, some five to ten years down the line, suddenly find themselves with a comical slackjawed "Oh!" of an expression on their fat, stupid faces when they get gut-punched by their hubris.

And the saddest part is, an extended drought, a decades long megadrought, is not going to be the type of hardship that will bring people together. Time and again, during catastrophe, people do have a tendency to be neighborly, to be altruistic and giving, but not during a drought. People compete, people get cranky and selfish, and nothing productive gets done Some inklings of this are already seen in how the states of the region compete for water.

Arizona, it would seem, does a very good job of representing almost everything that is wrong with America. This is not to say that there are not good people living there, or good people that have lived there for several centuries - even including the Anglos, who have modified their behavior to live in the land. Tucson, it would seem, has done well in this regard, as they realize they a desert town.

So, let me modify my statement, and hone it down to the Phoenix metropolitan area, the Sun Corridor, as representative of the worst American characteristics. Take, for example, their self-righteous and mercenary spirit, proudly ignorant of their subsidized condition, ruggedly individualistic and possessed of a manic private property fetish, and all the while convinced of their innate and inherent right to privilege. Defiantly white, Protestant, English-only, anti-immigrant, anti-Latino, devoted fans of right-wing television and talk radio. Zealots, angry, unappreciative, and dementedly entitled, made all the worse by the fact that they, retiree immigrants from places like Milwaukee, Pittsburgh, Little Rock, Duluth, don't seem to realize that they are the alien invaders. They may be frightened and confused by the people they deem foreign in language, looks, values, and behavior, but they just don't seem capable of realizing that these are the centuries-old inhabitants of the region.

Nor do they understand their utter dependance upon the divine grace of the federal government, who provides them with their very existence. Without the vast expenditures and engineering projects that the Bureau of Water Reclamation, their would be no sun Corridor, no Mountain Megacity, no air-conditioned paradise, and, given the long term climatic trends, will there be . They are doomed. Fucked. And probably just as well.
  
This is not to say the region will be abandoned entirely. People will still live there. They'll just live more realistically, and the ones that don't leave. But the ones that leave? What should we do with them? Do we really want these selfish, short-sighted, unpleasant peoples to settle among us?

I wonder, would these refugees develop some sense of empathy for the present plight of a similarly straightened peoples, just south of their border?

"The Stealth of Nations": A Book Report

System D, the second largest economy in the world, is covered in the book "The Stealth of Nations: The Global Rise of the Informal Economy" by Robert Neuwirth. An excerpt of the book can be found in this article at Foreign Policy.

If you are wondering how Neuwirth can be a cheerleader for the black market, well, there's a lot to like in this book. Everyone appreciates the virtues of a constructive life, the struggles, the hustles, the triumphs, the setbacks, the inherent dignity of self-sufficiency (such as it can be for social creatures), and most importantly the ingenuity and clever workarounds that are displayed by the more-than-clever-by-half human animal. And there are stories aplenty in this book of people who have made good*, from Sao Paulo to Lagos, from Shanghai to Mumbai.

My chief complaint is not the extensive use of theft, piracy, smuggling, evasion, graft, bribery, corruption, and venality that is endemic throughout System D. This is, after all, business with a big B as usual on Planet Earth, "building a better world, one deal at a time".

Why, I'd be downright disappointed if the private sector types didn't lie, cheat, and steal. We are talking about Commerce after all, which has it's very foundational social contracts well embedded in the concepts of force and fraud.

No, my chief complaint with Mr. Neuwirth's cheerleading is that he presents this system as perhaps something new, perhaps the next big thing. System D is, in fact, old, terribly old, an old and tested system that I suspect goes back possibly 250,000 years, to the first behaviorally modern humans.

Neuwirth himself is not blind to this, but chooses to consistently gloss over the inconvenient parts.

Take, for example, his recognition that one of the pitfalls of the cash-based economy of System D is that it is cash based. There is a twofold problem here. The first being that cash is subject to exchange rates and their fluctuations. The economic underground is dependent upon national currencies. In short, the State and the Market are not conflict with each other, but wholly interdependent. Thus, cannot exist without nation states. The second problem being that, since everything is cash-based, no system of leveraged debt is available to expand a worthwhile enterprise. Unfortunately, the next step after the market, is, so far, capitalism, which, if System D will evolve into if it manages to go "legit". Which sucks, because we are just now finding out the full consequences of this particular item tucked in the Neolithic cultural package, just as we are only now fully understanding the full impact of the lever and fulcrum, the wheel, the pulley, the screw, and the inclined plane.

Furthering my complaint is the depiction of System D as an open source network. System D certainly opens market opportunities to those traditionally shut out, but it does not, by any stretch of the imagination, operate as science does, with (hopefully) unrestricted information dissemination or any form of egalitarian reward sharing. Merchants in System D rely on arbitrage as surely as your average hedge fund scumbag does. Information is jealously guarded, and scheming is an integral part of the game. And workers in System D still operate under a hierarchical labor structure where the lion's share of the profits go to the traders, and only a small slice ends up at the level of the industrious laborer. There are no discussion about wages in System D business meetings.

Nor does System D seem to be any better at capitalism in learning lessons. Take, for example, copyrights and piracy. And long and noble tradition of piracy and counterfeiting extends well past so-called civilized times to some 40,00 years ago when carved stone and ceramic fake seashells were traded. The problem with this version is the ironic complaint among System D merchants that other merchants can copy your pirated goods and undercut you profit. (Indeed, some companies in China, realizing that a race to the bottom results in increasingly razor-thin profits, have opted for the opposite route of creating quality brands). There is a supposed advantage to having a regulatory agency or institution assuring honest quality. True, for the past 10,000 years, the State has offered just such services to the market - quality assurance, arbitration, and universally equitable transactions, but not everyone shares a complete trust of the State (and who can blame them, with the undue influence of those lucky enough to control wealth?). Still, this certainly presents an entrepreneurial niche to System D merchants to provide for such an agency, but then again, you merely head towards the "modern" institutions of capitalism like Sotheby's and Standard Oil.

And speaking of the State, would some form of System D exist in regions of the world where governments actually worked? Take Nigeria, where there is no water system, little electricity, the roads paved first in front of the homes of the rich and well-connected, the government clearly cannot demonstrate its worthiness to the people. Is it any small wonder that taxes are not paid, if the State will not recognized its smallest responsibilities?

I could go, but let's face it, we in America are in no position to play holier than thou.

In summary I say more power to them, maybe they can forge a new better way, but I ain't seeing it.
I really cannot see the difference between the social and economic setup between System D and life in the developed capitalist world. If anything, when it comes to the most vile business practices, coupled with a legal system crafted for the top parasites, we show the inhabitants of System D to be mere pikers.


* "Ralph Makes Good" by Wally Cox. I could not find a worthwhile link to this short and wonderful book, written in 1965 and long out of print, but here's a great summary from Kirkus reviews:

"Ralph is a self-made man, new in town and so happily stupid that he must have come there straight from an eggshell. On the advice of his barber, Ralph began as a lawn mower, shrewdly shifting to leaf raker with the seasonal decline of grass. One glimpse of Sylvia and a vision of bigger things enthralled him. He ran against the mayor, '...a dependable criminal in the old tradition', and emerged as dogcatcher, a political position threatened by impeachment and lynching before Ralph makes good -- and Sylvia, the dime a dance girl. It is the lightest of featherweight satire on local government, among other things, and this form has a banty-sized audience today. The famous comedian author entry may help counteract some of the reader apathy as well as the delight Cox takes in converting the precise use of words into literary wit."

The Franz Ferdinand Divergences

One of the difficulties of operating a peranoscope is that big changes are never the result of one single cause. Thus, when confronted with a big series of divergences, it can rarely be traced back to a single branch point. To use another analogy, using a peranoscope under the best of conditions is similar in many ways to peering into a Magic Eight Ball.

"Reply hazy, try again".

Take, for example, the First World War. From my perspective, it is not even a century since it's beginning, which was the 28th of July, 1914. Many historians will tell you that WWI was inevitable - that once the first domino was pushed all others would fall. That the entangling alliances of the Great Powers were too closely knotted, the alarm tripwires too taut, the personalities and circumstances all leaning inwards towards war, like the rotted frame of a house.

A Peranoscope

Consider the Franz Ferdinand Divergences. They generally start with Gavrilo Princip, the Serbian terrorist, missing his shot at the Archduke by a millisecond (not inconceivable, a policeman had lunged at Princip's hand). The Archduke and his wife are whisked away to safety. 

As a result, Israel never exists. Israel does not exist without WWII and the Holocaust. The Holocaust does not occur if Hitler never comes to power. Hitler never comes to power if the Germans are not starved throughout the first war, and starved and humiliated in the year following the armistice of 1918. The armistice does not occur if WWI never happens. WWI never happens if the Archduke Franz Ferdinand is not assassinated in Sarajevo.

Oh, bullshit. I wish it all were that simple.

The Emperor Francis Joseph I's hotheaded Chief of Staff, Conrad von Hötzendorf, knowing the assassination plot originated in Serbia, would have demanded war. Ferdinand, a consistent moderate in the past, would have demurred. In fact, Ferdinand, as in prior crises, reminded the Chief of Staff and the Emperor that war with Serbia meant war with Russia. War with Russia would have meant the certain end of the Austro-Hungarian Empire. Ferdinand would have argued this, and Emperor Francis Joseph would have agreed. It is true that friction with Serbia over the Balkans may have continued, but these crises had been going ever since the annexation of Bosnia-Herzgovina since 1908.

So, fast forward to November 21st, 1916, Francis Joseph I is dead. Franz Ferdinand is crowned Emperor.

Oh, wait a minute. Rewind. A few things can occur during those two years. Most imperative, Great Britain is plunged into civil war. Great Britain and Ireland that is, and over Ulster. Without WWI, the Government of Ireland Act of 1914 is enacted, Home Rule comes to Southern Ireland and the insurrection of Northern Ireland breaks out in utter foment. With civil war, dividing even parts of the army, the entire Expeditionary Force, the Special Reserve, and the Territorial Army are required to restore order. The Troubles, as they come to be known, had started.

Had Germany declared war on France, and invaded through Belgium (the cause for Great Britain's entering war), the BEF, pinned down in Ireland, could not possibly aid France. Without the BEF in those first bloody crucial months, the Germans would have marched into Paris.

It's a good thing then, that Germany does not declare war on France (aside from the fact that one million men will still be alive come October 1914). Germany does not declare war on Russia and France because Austria-Hungary does not declare war on Serbia. There are, of course, several ongoing crises throughout Europe, but all are settled diplomatically as had happened with others, such as the Bosnian Crisis of 1908, or the Morocco Crisis of 1911, or the Balkan Wars of 1912, or the... well, you get the picture.

What happens in America? Keep in mind, the mood of the country is that the US economic model is broken (though not spoken of in those terms), the Socialist movement is making great gains in popularity. 1914 is the beginning year of a serious recession. Businesses throughout the country were depressed, farm prices deflated, unemployment serious, heavy industries working far below capacity and bank clearings were off. Without the 1915 war orders from the Allies of WWI, an economic stimulus never occurred and the recession deepened. The Panic of 1916 helped matters not at all, and the public mood became ugly. No polls existed then, but it is estimated some 74% of Americans felt that they were not adequately rewarded for their hard work and skill, and that the idle rich, possessed of  almost all the nation's wealth, truly were living off the backs of the industrious poor. The ruling classes, seeing the country ripe for a number of violent upheavals, were forced to co-opt from the pages of the Progressives as had been done earlier by Teddy Roosevelt during the so-called "reform" movements of his administration. In a handy bit of political ju-jitsu (involving both violent repression and political reform), the ruling classes enacted a series of laws and subsidies to keep the citizens of the United States pacified. The great Social Experiment, as it came to be known, or by others, ironically, as the "New Socialist Paradise", produced the large social assistance programs similar to those enacted by Franklin Roosevelt in the 1930s (in a different reality). There was hardly a choice. The bankers and industrialists would surely have lost everything in the ensuing revolution (which in itself was an interesting - if short-lived - divergence), or at least through government nationalization of the market. But, as it was in prior crises, the shit managed to float on top. What was perhaps unnoticed through the enactment of these laws was the ongoing erosion of the Bill of Rights, through the Securitization Act, the Right to Work Act, and the Militia Act, which put restrictions on first and second amendment rights. These acts were all upheld by the Supreme Court. The foremost liberal of the land, Oliver Wendell Holmes, in a superbly clever and attractive treatment, supplied the rationale to justify these laws. Well, as the old Vulcan saying goes, "Only Nixon could go to China". Of course, the recession turned into a depression which lasted well into the late 1920s, but at least the populace was placated and endured the downturn.

Couple these circumstances with the series of events which made America the military laughingstock of the world, and you have a formula against immediate global influence. The continued disastrous military adventures carried out under the one-term Wilson administration - the inept military adventure into Mexico, the debacle of US troops being slaughtered in Siberia aiding the failed Bolshevik movement during the Russian Civil War, the humiliating retreat from the Philippines in 1917 - all soured the public appetite for foreign adventurism, and solidified the already deep and endemic isolationist streak within the American character. It would take another generation for the United States to move from being a continental to a world power.

And Russia? The one seeming inevitability is the fall of Tsar Nicholas II. The debacle of the 1905 war against Japan and subsequent Revolution of 1905 determined the fate of the Romanovs. Despite continued and ongoing land reforms, the sheer incompetence of the Tsar himself guaranteed his eventual downfall in November 1914. Had it not been for the intervention of his cousin, Kaiser Wilhelm, "Nicky" and his family would surely have perished. They eventually resided in Denmark. The Kaiser also, very conveniently on the advice of his generals, had V.I. Lenin assassinated while in still exile. The loose factions of the Reds never quite congealed, and after a brief turning towards democracy under Kerensky, Russia returned true to form under the dictatorship of President Julius Martov.  Despite modernization programs instituted under Martov, Russia remains relatively backwards well into the 1930s.
 
(An interesting side note, if you will indulge me. Typically, fictional depictions of alternate timelines often make the mistake of using familiar characters from history populating these people scenarios - even though the chances of them even existing are near impossible. Funny then, how many familiar historical characters continue to exist in the Franz Ferdinand Divergences. Indeed, these tightly bound  alternatives do not start to unravel until the early 1940s - as you will see).

The USGA

So, continental Europe tense but peaceful, England heavily involved in internal strife, Franz Ferdinand ascends the thousand-year-old Habsburg throne. As a young man, Franz Ferdinand toured the United States by train. Ferdinand sought an American, a Federalist, solution to the ills of his thousand-year-old empire. Foremost was the Southern Slav question, the annexation of Bosnia-Herzegovinia had burdened Austria with a restive Slav population owing more allegiance to neighboring Serbia. (Indeed, the Serbian Black Hand organization sought the Ferdinand's death to prevent his federalization program). Upon ascension to the throne, Ferdinand immediately implemented the formation of "Die Vereinigten Staaten von Groß-Österreich", or as we know it, the USGA, The United States of Greater Austria. The formation was not without its birth pangs. At one point, Ferdinand requested help from his friend "Willy", Kaiser Wilhelm II of Germany, who sent "Franzi" a division of crack Prussian troops to quell the Magyar Rebellion in Hungary. But once things settled down, the diverse ethnic governments cooperated in a remarkably cohesive and congenial manner. Even Bosnia-Herzegovinia, after a popular referendum favored reuniting with Serbia, was allowed to return, and good riddance. Relations with the Balkans improved dramatically. The Empire was saved from certain implosion.

In fact, conditions both economic and social improved considerably. Despite Ferdinand's reactionary personality, not to mention his loathsome anti-Semitism, he embarked upon a series of social and education reforms which uplifted and improved the conditions of  all segments of the general populace. Major universities were expanded through a program of free education, and valued talents (especially in the areas of mathematics and physics) were attracted to the vibrant atmospheres of cities such as Graz, Vienna, Prague, Cracow, and Budapest for the remainder of 1910s and onward. The whole of Germany and the USGA prospered as industry and academia cooperated to produce a seeming endless series of innovations and inventions. The flowering of Quantum Mechanics results in practical applications such as radio, radar, TV, vacuum tubes, transistors, aviation, jet engines, rocket engines, and the beginnings of the computer age, all created within Central Europe. 

A stellar constellation of talents, among them Albert Einstein, John von Neumann, Leo Szilard, Eugene Wigner, Enrico Fermi, and Hans Bethe flocked to the University of Vienna. Not surprising, then, that the USGA, in cooperation with the German Empire, developed the atomic bomb. The first atomic pile is constructed by Enrico Fermi in Trieste, on January 5th, 1925. The first test occurred in the Kalahari desert, east of the town of Gobabis, on July 23rd, 1928. 

MittelEuropa

By 1930, Germany and the USGA, all but in name unified as one, have been joined by the Kingdoms of Denmark, Sweden, Norway, the Netherlands, Poland, Belgium, etc. to form a loose confederation of mutual economic and political interests. It is the world's preeminent economic powerhouse. The Great Powers of the world now confront the Greater Power of MittelEuropa. The race to play catchup is all consuming, but especially so to the US of A (catchup being that "most American of games"), finally coming out of it's decade long funk.

Which brings us to the Devastation (I told you this was a divergence). Back in the second term of President Charles Evans Hughes, Sr. (Republican three term president 1916-1928), the War Department embarked upon an intensive program of modernization. With the loss of American Pacific possessions to the Japanese Empire, it was felt that, in a modern era of aeroplanes and missiles, the separation of two oceans was no longer a sufficient barrier to threatening powers. In the Pacific, the Empire of Japan had, with no real opposition, engulfed all of EastAsia. The Colossus known as Europe (for at this point, both France and Russia were obliged, hat in hand, to work with Central Europe, which controlled huge swaths of Africa, and almost all of Eurasia. Britain, through culture and circumstance, and the seeming advantageous contingency of her colonial empire, chose to side with America, and together, they could be defined as Oceania. By 1940 all the triggers were in place for a war over resource extraction, and Africa was the prize.

Espionage had transferred the nuclear secrets into the hands of the Americans. By the late 1930s, under a crash program, they had developed their own nuclear weapon, exploded in New Mexico, in 1939, and proceeded to work on their arsenal.

Unbeknownst to the Americans, an engineering team in Vienna led by Edward Teller had developed "Die Super", the H-bomb, the thermonuclear fusion bomb. By 1944, their H-bomb had been miniaturized enough to be delivered via rocket. Unfortunately, through a staged bit of theatrical victimization claiming surprise attack, America declared war on June 6th, 1944. American bombers, loaded with fission bombs, departed air bases in England. Two bombers managed to deliver their cargo - one on Antwerp, the other on Hamburg.

Soon afterwards, dozens of ICBMs equipped with megaton range thermonuclear warheads were launched against the American homeland. Some ninety million people are wiped out in minutes. President Winston Smith vows never surrender, and the sheer horror of the mass slaughter turns the world against Europe. Sufficient nuclear weapons remain on both sides to cause decades long strife, so much so that by early 1984, those few humans left alive, if you can call such specimens human, have been reduced back to the Stone Age. And soon after that, they all perish.

And just as well, don't you think?

The Science of Investment Materials

I have no backup copy of this essay, and I'm worried that the original post at warmglass.com will eventually disappear, so I'm posting the essay here as a precaution.

All of the papers listed were found in the Journal of Dental Research, and I will repost all of the URLs. For those of you unwilling or unable to follow the papers, I’ll do my best with summaries. 

Over the past year, I’ve also bought and read a few more advanced materials science papers on the subject through Science Direct. There are no URLs available for these papers (they are all restricted PDFs). I’ve also found some helpful downloads available at http://www.netzsch-thermal-analysis.com/. These are available under their Literature link, and are free. Just register to look at them. I’ve borrowed and modified a lot of the data from the restricted papers and the Netzsch site into visual graphs, which will hopefully be more helpful than all of the technical jargon. (Be forewarned, there is technical jargon involved in the following text, but I will try to explain it as we go along).

Throughout the literature, the primary material of interest is gypsum. This is as it should be. Gypsum, or calcium sulfate, or the calcium salts of sulfuric acid, chemical formula CaSO4, is the binder of first choice in traditional investments. (I prefer the term gypsum, instead of plaster, as a more general descriptive term for calcium sulfate. Plaster, in my mind, refers only to the form known as calcium sulfate hemihydrate). 

There’s any number of substitute binders available, from magnesia- and phosphate-based binders, through the colloids of silica, alumina, zirconia, etc. Substitute binders are all refractory (can take the heat), and most are relatively chemically inert at high temperatures. But not all are as readily available, as easily frangible (breakable) upon casting completion, and, most importantly, as dirt cheap as gypsum. 

Gypsum shrinks upon heating, so other components – known as fillers or extenders - are added to the investment that will counteract this shrinkage. One such extender is silica – either as powder, sand, clay, grog, etc. Silica is fairly refractory, readily available, and again, dirt cheap. 

(One popular misconception is that silica, or other extenders such as alumina, talc, etc., are added to make the investment more refractory. As you will read later, this is simply not true). 

Let’s start off with the granddaddy of the papers, first published in 1931, “Dental Casting Technic: Theory and Practice”, available at: http://jdr.iadrjournals.org/cgi/reprint/11/5/681.pdf.

This is a good beginning paper describing the behavior of gypsum-bonded investments, especially the thermal expansion behavior and influence of water/powder ratio. It allowed me to produce the following graph:

According to the paper, gypsum shrinks up to 2% in volume when heated. Silica expands when heated.All of the allotropic (solid exhibiting more than one crystalline state) forms of silica (tridymite, cristobalite, quartz, and fused silica) expand.

All of the forms, with the exception of fused silica (amorphous silica, e.g. glass), undergo phase transformations (changes in molecular structure). The transformation of quartz is possibly familiar to you, and is often called the quartz inversion. The quartz inversion occurs between about 500-600C (932-1112F), and results in a rapid expansion of the material. Cristobalite also undergoes a much more drastic expansion in the range 240-275C (490-527F). For silica, these transformations are reversible. Gypsum also undergoes phase transformations, but these are not reversible.

Varying the percentage of gypsum to silica can change the expansion profile of the investment material. This is a very easy way of controlling the thermal expansion of your molds. Here are some examples of the thermal expansion profile of different percentage mixes:

The next paper is “Thermal Behavior of the Gypsum Binder in Dental Casting Investments”, a must read in my opinion, and available here: http://jdr.iadrjournals.org/cgi/reprint/65/6/877.pdf.

Gypsum, or calcium sulfate, going from room to glass casting temperature and beyond, undergoes a number of phase transformations that all result in irreversible contractions. 

Dehydration of investment occurs in a double step process. Let’s start the cast investment at room temperature. The first form of gypsum is plaster – calcium sulfate dihydrate: CaSO4 + 2 H2O.

The idealized structure of pure gypsum consists of lattice planes of calcium sulfate molecules weakly bonded to alternating layers of water. The bond is an ionic one between the oxygen atoms and the hydrogen atoms in water – very easily broken. Water thus weakly bonded is often called the water of crystallization. As gypsum is heated, the water is diffused out of the matrix, and the plaster converts to calcium sulfate hemihydrate: CaSO4 + ½ H2O. (Obviously, there is not half a molecule of water, one water molecule is shared by two calcium sulfate molecules). This conversion is completed at 177C (350F). This is step 1.

Further heating of the investment will release all remaining water. This occurs at 200C (392F). This is step 2. 

In numerous DTA (Differential Thermal Analysis), and DSC (Differential Scanning Calorimetry) experiments, this double step can be seen as two endothermal (heat-releasing) peaks. In other words, as the temperature was increased, the heat capacity of the material jumped, which resulted in less heating required to increase the temperature. What this also means is that 100% dehydration did not magically occur at 200C (392F). It takes time for the water to completely disperse from the matrix. The second endothermal peak does not bottom out – indicating 100% dehydration - until about 300C (572F).

Here’s a fun little graph from Netzsch, that illustrates what I just said: http://www.netzsch-thermal-analysis.com/en/materials-applications/ceramics-glass/gypsum-and-quartz-sand-phase-transitions.html. The graph shows two curves. The first curve shows the TG profile of gypsum over temperature range (TG means “thermogravitic” which is just a fancy term for “as we heated it up, we weighed it"). The TG curve shows the thermal behavior of gypsum over temperature. The second curve is the DSC profile, which shows the heat capacity of the material. For an explaination of what Differential Scanning Calorimetry is and what it means, here is a URL: http://pslc.ws/macrog//dsc.htm. 

Yes, yes. I know its a web page about plastics. Amorphous polymers behave like glass. They have a glass transition range, and can undergo devitrification. In fact, pretty much any material, heated up and cooled correctly, can go through a glass phase - including metals. This has been well-documented since the 1960s. (And if you don't know what a glass transition is, maybe you should do a little googling, or maybe a lot). 

(A popular misconception is that steam can crack a mold if all the water is not removed. It will take some time for a solid block of investment to release all the water. While this is occurring, the varying temperatures within the block of investment will be well below or near the boiling point of water - due to escaping water drawing heat from the mold through evaporation. True, there is a point where the surface and exterior layers of the mold will start to calcine, as the remaining water cannot evaporate quickly enough to cool it. But regardless of the air temperature within the kiln, the mold will remain “cold” while water is within it. Since the water diffuses out of the matrix at about the same pressure as sea level atmosphere, it is impossible for steam pressure to crack the mold – simply because there is no steam within the mold to begin with. This is not to say you can crank the kiln temperature with a wet mold. An unnecessarily fast heating rate can and will crack a mold. As the outer layers dry out, they will undergo a different thermal expansion than the interior layers. This puts tension of the outer layers, which causes cracking. In short, an excessive heating rate will crack a mold – not steam).

Once the mold is completely dehydrated, the hemihydrate has converted to anhydrite: CaSO4 + 0 H2O. (Obviously, each form of gypsum does not convert instantaneously upon hitting a temperature benchmark. It is a continuous conversion, and each phase retains some quantity of the last phase, which slowly converts. So, the dihydrate has some small portion of unreacted hemihydrate, and the anhydrite, some portion of hemihydrate, etc). 

As noted in the above paper, Posnjak (1938) introduced the terminology of naming the three polymorphic forms of anhydrite alpha, beta, and gamma. However, confusion can occur with existing terms used in the gypsum industry for alpha and beta hemihydrate powders (produced by the wet or dry calcining methods, respectively). I therefore use the same terminology in describing anhydrite as is used in the paper, namely III-, II-, and I-CaSO4.

(A quick aside here. As noted above, the hemihydrate of gypsum, plaster, call it what you will, can come in one of two forms - alpha and beta. Alpha hemihydrate is traditionally produced by heating a sized gypsum or lump rock under elevated steam pressure in an autoclave. Beta hemihydrate is produced by heating finely ground gypsum at atmospheric pressure. Beta hemihydrate consists of rough, fractured, fragmented particles, and has the attractive properties of high plasticity, high compressive strength, and high density. Alpha hemihydrate consists of finer, denser, more well-formed and orderly crystals than the beta. Alpha has a higher set strength than the beta, and produces molds and patterns of high accuracy, high surface hardness, and low expansion during drying and curing, and is, to some extent, machinable. Most products are made up of a blend of the alpha and beta forms. Some products, such as mixtures for potter's plaster and gypsum wallboard, contain only the beta. Other products, such as Hydrocal FGR-95 or 115 Gypsum Cement, consist of only the alpha form). 

At 200C (392F) gypsum exists in the form of III-CaSO4 (and increasingly small portions of hemihydrate). III-CaSO4 is also known as soluble anhydrite, which is metastable. This means the III-CaSO4 would convert back to hemihydrate if removed from the kiln and exposed to atmospheric moisture. Paraphrased from the paper: “This is a familiar phenomenon encountered in the manufacture of (gypsum). The freshly calcined material possesses the property of rapidly absorbing moisture from the air with a marked increase in temperature, requires large amounts of water in mixing, product sets too rapidly (“fiery”), but it may set too slowly. The mixing characteristics of (gypsum) improve if the powder is allowed to mature under ambient air in storage (aging)”. In other words, you could, for what arcane reason I know not, remove your dehydrated mold from the kiln, place it in a bucket of water, and return it to a liquid slurry. Or grind it up, let it age in air, and then remix it later with water into another mold. Thus the term soluble anhydrite.

Upon continued heating, the largest shrinkage will occur in the range of 348-400C (658-752F), which is accompanied by an exothermal (heat absorbing) reaction. This marks the conversion of metastable III-CaSO4 into stable II-CaSO4, or soluble anhydrite into insoluble anhydrite. This is a phase transformation in which the “crystalline hexagonal needle shape of III-CaSO4 converts to thicker, shorter needles of orthorhombic crystals of the II-CaSO4”. Under experimental recovery (cooling and rehydration of investment), it was found to reach zero recovery for the temperature of 800C (1472F). In other words, all III-CaSO4 was completely converted to II-CaSO4 by 800C (1472F). Paraphrased from the paper: “This is also a familiar phenomenon in the manufacture of plaster. Gypsum that has been heated to a red heat becomes inert in water and is called ‘dead burnt’”. 

(In a different thread, I investigated a hypothesis that this conversion range, when III-CaSO4 converts to II-CaSO4, might require a more delicate touch in the heating schedule, and that molds were more prone to crack here than in other parts of the ramp-up. The idea being that, with the lowest point of thermal conductivity occurring here, along with the inevitable non-uniform temperature gradient between interior and exterior mold layers, would produce conflicting compressive and tensile tangential forces in the mold wall, resulting in the symptom known as a “crack”. The consequence being that you could put short cuts in the heating schedule – heat faster in other parts of the ramp-up, and just go slow in this “danger zone”. So far, the hypothesis has not been proven, and no danger zone found).

Let’s shoot past the (to me) relatively mild glass casting temperatures, to get to the II-I conversion. II-CaSO4 converts to I-CaSO4 at around 1227C (2240F). This crystal form has been reported as “cubic”, density of gypsum increases slightly, and is the result of crystals sintering together. Not much else to say about it, really, except that you can still cast glass in it if you wanted to - with a few provisos coming up.

Various temperatures have been tossed out for the thermal breakdown temperature for gypsum. By “breakdown” I mean the thermal decomposition of chemical bonds. They have varied wildly, from as low as 700C (1292F) to as high as 1500C (2732F). The reason for the discrepancy is interesting. 

Calcium sulfate breaks down according to the following reactions:

CaSO4 ==> CaO + SO3
SO3 ==> SO2 + ½ O2

The above formulas are as follows: CaSO4 is calcium sulfate (gypsum), CaO is calcium oxide (lime, quicklime, a caustic alkali, refractory up to 2572C (4661F)), SO3 is sulfur trioxide, and SO2 sulfur dioxide. 

Sulfur dioxide is a gas highly corrosive to metals, producing an insoluble sulfide on the surface of castings, making it a bugaboo in the jewelry and dental trades. But sulfur dioxide actually strengthens glass, producing a surface substance known as “bloom”. This is a white deposit that forms on glass and is easily washed off. It improves the durability of glass by removing alkalis such as sodium from the glass matrix – an effect known from the wood, oil and coal-burning days of lehrs and annealers. This "dealkalization" reaction is an ion exchange that is made possible by the removal of the sodium ion as sodium sulfate. The general chemical reaction is:

2Na (glass) + SO2 + ½ O2 + H2O ==> 2H (glass) + Na2SO4

It has been determined – under repeated and rigorous laboratory conditions – that calcium sulfate breakdown commences at about 1240C (2264F) and is practically complete at 1450C (2642F). Melting of a CaO/CaSO4 eutectic mixture occurs at around 1350C (2516F), so we will set the upper usable casting limit of gypsum at 1230C (2246F). That’s a pretty good temperature, but, of course, not really realistic. Gypsum could be used as a casting medium, but as we have seen, it drastically shrinks. If dimensional fidelity (cast piece is the same size as the wax piece – kind of important when making dental inlays) is an issue, then you either scale up the size of the wax, or include a material that expands upon heating, like silica.

The addition of silica (SiO2) produces a different chemical reaction:

CaSO4 + SiO2 ==> CaSiO3 + SO3
SO3 ==> SO2 + ½ O2

CaSiO3 is one variant of calcium silicate, which is highly refractory (up to around 1540C (2804F)), possesses high strength, and is used extensively for high temperature insulation (especially by your friends at ZIRCAR). The energy required for the gypsum/silica decomposition to occur is far less than for pure gypsum. As a result, the beginning of thermal decomposition is lowered to 990C (1814F), and is practically complete at 1260C (2300F).

The following chart graphically demonstrates the difference in decomposition via a TG curve:

(The above graph and information was obtained from the paper “Thermal and Microchemical Characterisations of CaSO4 – SiO2 Investment Materials” by G.M. Ingo et. al).

Being conservative, and using the beginning temperature for thermal decomposition as the maximum, one could soak safely at 989C (1812F) for an indefinite length of time! That’s well beyond normal glass casting temperatures. However, carbon also plays a role. Any burnout of organic materials in a mold will leave a halo of carbon residue embedded around the casting. The presence of carbon will reduce the decomposition temperature, as described in “Decomposition of Gypsum Investment in the Presence of Carbon”, available at: http://jdr.iadrjournals.org/cgi/reprint/38/3/541.pdf.

With carbon present in gypsum-silica investment, the following reaction will occur:

CaSO4 + 4C ==> CaS + 4CO
3 CaSO4 + CaS ==> 4CaO + 4SO2
CaO + SiO2 ==> CaSiO3

CaS is calcium sulfide, which acts as a catalyst causing a chain reaction to occur, rapidly converting calcium sulfate into calcium oxide. Carbon acts as a flux, lowering the temperature of the reaction. This reaction is well known and happily taken advantage of by chemists in the concrete manufacturing and steel industries. Coke and limestone is used to draw silicates out of iron ore, producing calcium silicate slag. The above reaction starts to take place at 700C (1292F). The decomposition is displayed in the following chart:

Is this thermal breakdown necessarily bad news for glass casters? In terms of structural integrity, the effect is almost nil. You have already ruined any structural integrity the mold possessed by dehydrating it. It is probably a good bet that calcium silicate does not react with the glass. And the mold will be just as refractory as when it was composed entirely of gypsum-silica, especially when you consider that calcium silicate is an ingredient in refractory cements and investments used in metal casting, such as Hydroperm. 

However, the thermal expansion, heat capacity, and thermal conductivity characteristics of the mold have changed because of the new compounds created. How much exactly, I’ve not been able to ascertain. But I suspect the thermal expansion of the new mold composition to be much less than the original mold composition. And if some portions of the mold remain unaffected, you are creating thermal strain that is at least different, and quite probably far worse, than a uniform block of material. If you can avoid the introduction of carbon into your mold, I would advise doing so. But it appears gypsum-silica investments are much tougher than we have been led to believe. Prepared and treated properly, it can take the heat, and for long durations.

A quick note on water/powder ratios. Ralph Carter, a chemist at Ransom & Randolph, presented a paper on the subejct which can be found here: 

http://www.ransom-randolph.com/Effect_of_Changing_Water_Powder_Ratio_on_JI.pdf

The water/powder ratio may be the most critical aspect of investment mold making - or it may not be. Varying the water/powder ratio will certainly change the the thermal conductivity of the investment, as well as the expansion profile. The W/P ratio usually varies from .28 (28 parts water to 100 parts investment) to .50 (.50 is 1 part water to 2 parts powder). 

Less water within this range, and the investment paste is too stiff to give a good impression, more water than this range, and the investment may be too weak to stand the ramp up in your firing. W/P ratio also affects the porosity of your investment. Porosity is defined as a percentage, and can be determined by weight. Weigh the investment after setting at room temperature, and again after dehydration (this is called the bulk/matrix ratio). The result will be the percent porosity of your investment. I think you will be surprised to find out that mold porosity is around 60% (give or take). Here’s a visual aid:

The needle shapes are calcium sulfate crystals, the larger conchoidal shapes are silica particles. The black stuff in between is empty space – filled with water when hydrated, air when it is not. That’s definitely porous. Porosity changes the thermal profile of the investment. More porous means less density, and less thermally conductive. On the other hand, highly porous materials reduce crack propagation. The "holes" tend to stop cracks - similar to drilling a hole at the end of a crack in a piece of glass or fatigued metal.

Perhaps the best illustration of the effects of the w/p ratio can be seen Chart 6 of Carter's paper. This chart lists the "fired" compressive strength of various mixtures. 

The terms "green-" and "fired-" strength, borrowed from ceramics, are not particularly helpful. A ceramic material will be stronger after firing. Investment is strongest once it is set - when it is "green". It can be seen that there is a sharp decline in compressive strength from a ratio of .34 (34 parts water to 100 powder, or about 1 part water to 3 parts powder) to .36 and above. This is not to say that a .34 ratio is the optimal or best ratio, merely that, within the constraints of Mr. Carter's test, that ratio showed the highest strength after mold dehydration and cooling. One could infer that the mold material would have a similar compressive strength in the high-end soak of the firing schedule, and that may not be the most dangerous assumption. But unless the assumption is tested, it remains exactly that.

One thing that struck me in reading Carter's paper was the lack of defects in the castings regardless of the w/p ratio. Carter surmised that this was due to the robust nature of the R&R premium investment. To confirm this, he then used a "non-premium brand of investment" (presumably a competitors). The molds held up "for the most part" (Carter downplaying the fact that the non-premium brand worked just as well?). The results are not entirely clear cut. It seems that w/p ratios may not be as important as suggested, and that the investment, regardless of the brand, is fairly forgiving, and can withstand "some mishandling". I would suggest that further tests be done on this metric.

Of course the use of the compressive strength metric in making investment forms doesn't provide any great insight. We are much more interested in the tensile strength of the material. Very few materials have similar compressive and tensile strength profiles, and certainly gypsum does not. But compressive strength is much more easily and consistently measured, and so, I suppose we must make do with this measure, but we should recognize the lack of utility in using it. 

For example, let's say I wish to calculate the hydrostatic pressure to determine mold failure. Actually, since this is glass, the measure would be vitreostatic pressure, but anyways... Let's say, for convenience, that the "fired" crush strength of my mold material is 50 psi. That is considered pretty weak. How much glass can I pile on top of it before it breaks? Well, hydrostatic - or vitreostatic - pressure is calculated simply by density x gravity x height. Better still, specific weight has density and gravity terms in it already, so pressure = specific weight x height. The specific weight of water is 1 gm / centimeter cubed. Most soda-lime glasses are around 2.5 times the specific weight of water, so let's use that number: 2.5 gm per centimeter cubed. Converting to pounds per cubic foot, and then to cubic inches, gives me the specific weight of glass = .09 psi. So we simply multiply that term by height in inches. A casting 8 inches in height will exert .72 psi on the mold surface. That's not much. How much glass do I have to pile up to crush my mold? Well, 50 / .09 = 555.55 inches = around 46 feet of glass! That sounds ridiculous. I'd better double check. Okay, the water pressure at the deepest part of the ocean is around 16,000 psi. That's with seven miles of water on top. 7 miles x 5280 feet x 12 inches = 443,520 inches. 16,000 / 443,520 inches gives me .036 psi for water, times 2.5 is .09 psi for glass, so yeah, the calculation is correct - but it still sounds ridiculous. The compressive strength as a useful metric for investment stength is practically useless. 

What about tensile strength? There are varying reports of tensile strength for gypsum investments, ranging from 1/6 to 1/15th the compressive strength of the material. This will vary according to the thickness of the material and the amount of flexure. Perhaps it is easier to calculate the pressure upon the sides of a form. Lets take 50 lbs of glass in the form of a cube. A cube of 50 lbs of glass is a little over 8 inches on a side, but for convenience sake, we shall use 8 inches. Vertical pressure upon the bottom of the mold is easy to calculate, but pressure on the side is a bit more complicated. Pascal's Law tells us that pressure is equivalent in all directions. Thus, at the top of the mold, the first inch of glass will press upon the side at .09 lbs /square inch, but this pressure progresses linearly until at the bottom of the mold, the glass presses upon the side at .72 lbs / square inch. This is known as a pressure prism, and we would have to integrate over the surface area of the side to get the total pressure. Fortunately, basic mechanics provides a straightforward formula for a vertical rectangle in the form of specific weight * midpoint of the side * area of the side = .09 psi * 4 inches * (8 inches) squared = 22.94 lbs of pressure. That's not much at all. If I assume (and this is just a rank and totally unsupported assumption) that tensile strength increases linearly with thickness, and say, a quarter inch of investment, possessed of 60 psi crush strength, has a tensile strength 1/15th that value (i.e. tensile strength is 4 psi), then the mold wall thickness should be about 1 and 1/2 inches to overcome side pressure at the bottom of the mold. Doesn't mean anything really, but I suspect we are all making our molds much, much thicker than they actually need to be.

The addition of other materials to create an investment composite is well known. The addition of the metal reinforcements, such as steel wire, hardware cloth, chicken wire, etc. have been used. Personally, I find they rarely add any strength to the investment. Given the relatively extreme kiln temperatures and oxidation that they undergo, metals soften and weaken very quickly. The addition of refractory materials, such as coarse ground mullite, perlite, etc., again, from a personal standpoint, add nothing to the strength of the investment. True, mullite will form long needle-like crystals similar to gypsum, but only when ground to a fine particle size, and formation occurs only above around 1000C (1832F). 

The one material which would seem to increase tensile strength is fiberglass or ceramic fiber. 

Fiberglass has been known since ancient Egyptian times, where it was used as reinforcement for ceramic vessels. The "modern" manufacture of fiberglass dates back to 1830s France. The use of fiberglass has been rediscovered again and again by many people, and has been used to reinforce plaster architectural elements since at least the late 1960s-early 70s. Fiberglass strand is, pound for pound, approximately six to ten times as strong as steel wire (depending upon the type). Given its extensive use in the construction industries, the physical properties of glass reinforced gypsum are quite well known. The flexural strength is around 3200-4000 psi, and the tensile strength is around 1200-1400 psi. However, one must be careful to use the right type of fiberglass. The most common fiberglass, E-glass, has a softening point reported around 846C (1555F). S-glass, used in aerospace/military/marine composite materials, has a softening point of around 1055C (1932F). Anyone who has reported success with a fiberglass reinforced shell investment under glass casting temperatures has - wittingly or unwittingly - been using S-glass.

Given the relatively extreme strength of this composite material, compared to traditional gypsum-based investments, very thin investment shells are theoretically possible. However, in practical use, unless the fiberglass is embedded woven and whole within the gypsum investment, no appreciable increase in tensile strength is observed. This is due to the fact that the investment bond between fiberglass strands remains weak. It appears the "old masters" using thick and unmodified gypsum-base block molds, knew what they were doing...

2012 or Bust?

When I was a kid - perhaps nine or ten - our neighbor's dog got loose. Our neighbor was a terrible excuse for a human being. I believe the term my father used for him was "asshole". Given that my father cursed about maybe once a year (and, yes, my frequent use of profanity is my form of rebellion), that was a pretty telling condemnation. Also, his kids turned out to be rotten shits as well,so...

Anyway, the guy had no control over his dog, an empty-headed Irish setter named "Colleen". He kept her in a large cage, completely covered by fence wire. I figured out Colleen had gotten out when I looked out the window, and saw a pack of of around a dozen dogs out on the street. Colleen was in heat.

I went out and shooed the dogs away (surprised now that, though many growled and bared their teeth, none of them took a snap at me, and instead cowered when I raised a hand to cuff them - apparently the brutish inhabitants of the 1960s kept their dogs well-beaten), and went to grab Colleen to take her home. She had no collar on, so I had to grab her by the scruff her neck, and that's when I found that she was completely covered in dog semen.

Well, it's one of those semi-rural moments, like stepping barefoot into chicken shit, when you get grossed out, but there's nothing to be done about it, and you are already committed, so... it's not like you are gonna die from it.

So, to use the above as a metaphor for the 2012 Republican primaries, who is what? Is Colleen, the bitch in heat, the Republican voter? Or are the ardent suitors? I kind of view the bitch in heat as the Republican voter, but an empty-headed Irish setter bitch in heat kind of Republican voter. In which case the candidates are just these frenetic humpers that can seem to find an entry, and so just coat the voter in dog jism. Except Newt Gingrich. I can't imagine him as part of the pack. More like, the soft-served swirl of doggie doo left after the frenzied fuck mêlée.

But Romney, Santorum, Paul? Even Paul is not trying very hard. So, I guess it's just Romney's and Santorum splash-coating the voter's fur.

There is a certain paranoid frenzy to all this. Jonathan Chait chalks it up to a cold realization on the part of Republicans that the population is getting away from them, that the demographics are leaving them all behind. And so, rather than compromise and watch their position steadily weaken, they have decided to make a last stand, and try and jerk the nation as far to the right as they can. Maybe.

Certainly the strategy of sabotage that has been carried out over the past four years has not left them in good stead with the voters. But only if it is a strategy, rather than just a tactic, a temporary rearguard action.

Smart money (as well as the planners and PR flipperlimbs) says that the Republicans give this round to Obama, and let him have the second term. They always have Rubio in 2016. Yeah. Well...

By then, they may have rubbed most of the dog sperm off of their hides.