The Trip Wonker

There are a lot of optical illusion sites on the web. My favorite optical illusion, however, is The Trip Wonker from the Very Low Sodium site. The cool thing about this illusion is that it temporarily distorts how you see things in the real world. Give it a try.

Once you finish with that, you might want to check out the Irrational Exuberance flash animation, which is based off of a bit of Japanese pop called "Yatta" by a group named Green Leaves. If you don't get it, don't worry... I don't think that anyone really does.

Warning: the Irrational Exuberance flash contains some mild adult content.

Movie Review: Modern Times

I sometimes feel that the aficionados for a given thing are often its worst enemy in terms of popularizing it. It is impossible, for instance, to mention Star Trek to a typical person without immediately conjuring images of screaming convention geeks and Klingon weddings. I think that classic cinema suffers from this phenomenon.

In too many people's minds, classical cinema (a.k.a. old movies) is viewed as being opaque, boring and confusing because people who are particularly interested in the art of film have a tendency to point their friends at directors like Bergman, Fellini and Kurosawa. I will be the first to admit that their films are high art but, at the same time, I would be very hesitant to suggest that someone who isn't deeply into the subject should run out and rent themselves a copy of The Seventh Seal.

The unfortunate thing about this is that a lot of classic movies are not only accessible to a typical audience but are, in fact, entertaining. You don't have to be a total movie geek to love Dr. Strangelove or Casablanca. Such movies of these have popular appeal and are enjoyable even if you aren't interested in dissecting their political subtext or interested in the director's use of light and shadow to convey a message (or whatnot).

Silent movies have particularly suffered from this sort of automatic rejection by association. The simple truth of the matter is that a lot of silent movies aren't really that interesting to most people in a modern audience even if dedicated enthusiasts can get a lot out of them. There are exceptions, however. One such exception is Charlie Chaplin's 1936 movie Modern Times.

If you look around for reviews of the movie you come across such statements as

Modern Times is a social critique of the new technology that dehumanizes people, and a powerful statement against the technology and rules that inhibit progress.

Forget all that. This is a movie that you can sit down in front up, with a bag of microwave popcorn and some soda, and laugh. I want to be clear that when I say that this film is funny I am not using the term in the same way that English Literature enthusiasts will try to insist that Shakespeare's plays are brimming with hilarity (just so long as you read this carefully annotated explanation of the social context of the early reign of King James). I mean that you will laugh.

In spite of being made nearly seventy years ago, and being in black and white and being (yes) mostly silent, the movie doesn't have any difficulty speaking to modern audiences, nor does it seem particularly quaint. In addition to a lot of pratfalls and some really amazing stunt work, there's a sly bit of nipple humor and even a little bit of judicious drug humor (Charlie accidentally eats some "nose powder").

The plot of the movie is fairly basic. Charlie is working in a factory when he has a nervous breakdown. Although he gets cured, he's lost his job and has to find new work. Along the way he ends up hooking up with a beautiful young woman who's living on the streets. Together, they try to find happiness and the American Dream having various adventures along the way.

It is true that one can look beyond the basic humor of the movie for deeper messages and subtext. I found myself, for instance, noticing the pervasiveness of police in the movie. The police weren't portrayed as either brutal or bumbling (rather, as guys just doing their jobs) but their overall presence was menacing. You may also take note of Chaplin's portrayal of the plight of the unemployed.

The important thing, however, is that you don't need to do any of that. You can, if you like, simply enjoy it as a fun movie. I can promise that when you're watching him struggle with a berserk automatic feeding machine, you won't need to be taking notes on the relationship between the proletariat and the bourgeois. You will be far too busy laughing your ass off.

Administrivia

Blogger has added a neat bit of functionality that I've decided to incorporate into my blog. If you look to the right of the "Permanent URL" link at the bottom of each post, you'll notice a little mail icon. If you click on this, you'll go to a page that will allow you to automatically email a copy of the article's link to another person.

I think that's pretty nifty, myself.

Rainbow

Lightning struck the rainbow,
And it burst.

Jagged fragments of the spectrum
Rained across the ground
With deadly festivity.

I saw an old lady
Impaled upon a shard of indigo.

I, myself, was almost struck
By a bolt of blue.

They say that the streets ran red.

It is not known how much of that
Was merely chromatic.

They Fight Crime

"He's an otherworldly chivalrous paramedic with acid for blood. She's an artistic foul-mouthed lawyer from a secret island of warrior women. They fight crime!"

"He's a bookish moralistic boxer with a mysterious suitcase handcuffed to his arm. She's a cosmopolitan cigar-chomping schoolgirl who hides her beauty behind a pair of thick-framed spectacles. They fight crime!"

"He's a world-famous Jewish shaman searching for his wife's true killer. She's a supernatural snooty nun prone to fits of savage, blood-crazed rage. They fight crime!"

These and other amusing team-ups can be randomly produced at They Fight Crime.

Is Mathematics a Science?

Today's article is a guest article written by my good friend Arturo Magidin who was kind enough to write the following essay at my request.

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Is mathematics a science? Well, the answer depends on what one means by "mathematics", and what one means by "science". There are well known and respected philosophers of science that will tell you the answer is 'no', while others are just as emphatic that the answer is 'yes'.

So before we can provide an answer to the question, we must agree on what we are talking about.


WHAT IS SCIENCE?

This is in itself a rather tricky question. People bandy about the words "science" (with or without first or last names) and "scientific" quite easily, but most would be hard pressed to provide a coherent answer to the question of what qualifies something as science and what does not.

Since I am writing at the behest of Andrew, I asked him that question when he asked if I was interested in writing this essay. So I will quote his answer and use that as a general guide.

Science is a form of epistemology that, like any good epistemology, attempts to distinguish true statements from false statements thereby leading to an accumulation of knowledge. One of the primary things that distinguishes science from other epistemologies is that it is a) systematic and b) nondogmatic. A proper science must have a means of validating its claims as well as a means of identifying and rejecting false claims. This, too, ought to be systematic.

Let us agree to this definition, and also agree that here "true" and "false" refers to an objective agreement with the 'outside' world.

Mathematics seems to have the deck stacked against her: the axioms are very close to dogma, and it seems not to care about truth or falseness, or even the outside world for that matter. There are proofs, but there seems to be no experimentation; mathematics does not follow the scientific method. Is that really the case?

SOME HISTORY

Most people are never exposed to modern research mathematics. They either know mathematics as a collection of recipes, algorithms, and rules (e.g. the formula for solving a quadratic equation, the rules of differentiation, how to multiply two numbers together, etc), or perhaps know the axiomatic model of Euclid (lemma, proof, theorem, proof, corollary, proof, all based on abstract notions and 'self-evident truths' known as axioms). Or both. The truth is that it is in reality neither, though at one time it (sort of) was close to those impressions.

Up until the 19th century, people who did "abstract mathematics" were called Geometers; they were usually either philosophers, amateurs, or physicist/mathematicians in their spare time. Major mathematical works dealt either with the sort of development similar to Euclid, or were collections of recipes and algorithms to solve problems (e.g., the works of Diophantus and Fibonacci). Almost everyone else who did mathematics was also doing physics. In fact, the most famous mathematical names up to the early 1800's were connected with physics in one way or another: Newton, the Bernoullis, Fourier, even Fermat; Gauss, the Prince of Mathematicians, officially held a post as Astronomer, and did much work in physics. That kind of mathematics was intermingled with physics.

About the only kind of mathematics that did not fit in either one of the above molds was number theory, which was, until Gauss's landmark Disquisitiones Arithmeticae, considered recreational mathematics, and in particular, not a subject of serious study but of play.

Then, during the 19th century, something happened. Mathematics began to develop as an independent field. In part, this had to do with a number of problems that had been accumulating: the foundational problems in calculus, the constructions of monsters that highlighted the problems with naive and intuitive notions being used in proofs, and the discovery of non-Euclidean geometry. Another part was the explosion of new ideas and methods: the beginnings of group theory, complex analysis, and algebra; in the final years of the century, the development of naive set theory (later replaced with an axiomatic variant) and the appearance of non-constructive existence proofs (most notably, Hilbert's finite basis proof). [Please follow this link for a discussion of some of the relevant issues of this proof]

During this crisis, a break developed between physics and mathematics. While most mathematicians still engaged in solving problems derived from physics, and most physicists still solved mathematical problems, the emphasis became different. Physicists were, by and large, not very concerned with the foundational problems, since calculus and its derivations obviously worked. The monsters, paradoxes, and antinomies might be interesting to philosophers, but they were not things that one was likely to encounter in "real" problems. On the other hand, Mathematicians were very concerned with the problems, and struggled to try to place their edifices on solid grounding.

Out of this crisis, there arose two main schools of mathematical thought. Both agreed that mathematics needed to be placed on a more solid foundational footing. On the one hand there were those, led by Kronecker, who believed in an emphasis on algorithms and recipes that followed from clearly defined concepts which were based on some empirical reality; "empirical" here must be taken loosely: Kronecker's famous dictum was "God gave us the integers; the rest is the work of Man", meaning that he considered the (potentially infinite) set of integers to be an 'empirical reality', for example. They were called 'constructivists' or 'intuitionists'. On the other hand there was the school led by David Hilbert, sometimes known as the 'formalists'. To the Hilbert school, the ultimate arbiter was self-consistency and interest. A mathematical theory should be based on clearly stated axioms and rules, but it makes no sense to ask whether the axioms are "true" or "false". The only questions that one must ask are: (i) Is it possible to use the axioms and rules to prove both a proposition and its negation?; and (ii) Is the resulting theory interesting? Upon an answer of "no" and "yes" (respectively), the theory would be deemed acceptable. (The reason for asking the first question is that, under the rules of classical logic, if it is possible to prove both a proposition and its negation, then it is possible to prove anything. Such a theory, needless to say, is both uninteresting and useless.)

However, the axioms need not have any relation to "reality". Here again we have a famous dictum, this time attributed to Hilbert: "It must always be possible to substitute 'table', chair' and 'beer mug' for 'point', line' and 'plane' in a system of geometrical axioms." That is, the actual meaning of the axioms is immaterial; their semantic content plays no role in mathematics.

In the end, it was the Hilbert school that triumphed among most mathematicians (with come caveats). As a result, most mathematicians will describe mathematics as following the classic Euclidean axiomatic model. Perhaps the quintessential example is found in the works of Bourbaki. It has also strongly influenced the way in which mathematics papers are written and advanced mathematics is presented. More on this below.

These days, mathematics tends to be divided into two: applied mathematics and pure mathematics. Applied mathematics are the parts of mathematics that deal with problems that arise out of empirical concerns: statistics, differential equations, and the like. Pure mathematics deal with problems that arise out of theoretical frameworks, often purely mathematical. The distinction, however, is in large part artificial. For example, at one time Number Theory was considered the most pure of pure mathematics, a branch of mathematics that had absolutely no possible practical application. In recent years, however, it has become the cornerstone of modern cryptography and developed a very robust applied side.


WHY THE HISTORY?

What is the point of all of the above? Well, the point is that the Hilbert School exercised a very strong influence in mathematics in the 20th century and through today. This influence in turn helped to produce and enshrine a particular style of writing when one deals with mathematical research. This is the dry definition-lemma-theorem-corollary style that many are aware of.

The "problem" with this style is that it obscures how mathematics is done. A professional mathematician engaging in research does not produce a definition, then write a theorem and its proof, perhaps separating some crucial step as a lemma. The way in which mathematics is reported in research articles and books is very different from the way in which mathematics is done. (I should point out that it is my impression that there has been a slow but steady shift towards a more engaging style in mathematics articles in the past two or three decades; a style that allows the reader a look at some of the process the writer went through to produce the proof; there have always been gifted mathematical writers who did this anyway, such as Gauss, Dedekind, or Paul Halmos, for example, but it seems to me to be becoming more widespread.)

The effect of this prevalent style is that everyone but the professional mathematical researcher tends to get a skewed and inaccurate view of how mathematical research is done. This in turn has led some philosophers to conclude that mathematics is not a science, because its methods are (apparently) so different from those of other empirical sciences. I will argue below that, once we go past the facade provided by the writing style and into the way mathematics is done, that this conclusion is in fact quite unwarranted.

Another effect is that the Hilbert School, from its beginnings and especially in the wake of the work of Goedel, Turing, Church, and others, abandoned the ideas of "true" and "false" in favor of the ideas of "provable", "disprovable", and "undecidable". Our working definition of science places a strong emphasis on truth, and so it would also seem to follow that, insofar as mathematics seems unconcerned with truth and falsity anyway, it could not be considered a science or a scientific pursuit.


BUT IS IT SCIENCE?

Gauss called mathematics "the Queen and Servant to Science". Pretty much everyone agrees at least to the "servant" clause: it is undeniable that mathematics plays a major support role in science. And no longer just in physics, or chemistry, but increasingly in other sciences as well. Statistics was the cornerstone of the change in medicine from art to science. And most social sciences seem to feel that the more math they can put in, the more robust and scientific they will be. It is the claim that mathematics is a science (let alone the "Queen of Science") that seems to lack support.

For starters, does mathematics even follow the scientific method? Observation, hypothesis, experimentation, testing, verification?

In what may come as a surprise to some, yes, it does. This is where the prevalent style does a disservice to an accurate perception of research mathematics. A mathematician engaging in research does not produce a statement for a theorem and proceed to prove it. She is usually feeling her way in the unknown as much as any scientist. She will consider some specific examples (observations), and try to see if they have a property or not. She will formulate some questions, both general and specific, and try to see how she can answer them for specific cases. She may then attempt a general statement (hypothesis), and proceed to attempt a proof (experimentation); sometimes, if that fails, she will attempt to construct a counterexample (falsification and testing). This process continues until the mathematician finally obtains an argument establishing her hypothesis, or she manages to disprove it (or, finding herself unable to do either, sets it aside and tries something else...)

For particularly troublesome problems, working out specific examples is considered a worthwhile pursuit, akin to experimental confirmation of details of difficult theories. Checking all odd numbers up to a large bound to see if any of them are perfect may not be considered mathematical evidence that no perfect odd number exists, but it still helps. Proving that the ABC Conjecture implies certain results which are known to be true does not establish the conjectures, but it lends them some "street cred" (and makes people more interested in trying to establish them as true or false). And so on.

On the other hand, there are some notable differences with sciences like physics: while there is observation, there seems to be no observation of the "real world". And mathematicians always demand "proof", a far more stringent standard than is met by any other science! Take, for example, Newton's Law of Universal Gravitation. The claim that this law applies everywhere (the "universality" of it) would never satisfy a mathematician. The fact that it has never been contradicted is not enough for such a claim. Only proof, meeting mathematical standards, would be. Compare this, for example, with Fermat's Last Theorem: 350 years of being unable to find a counterexample or proof was not considered (mathematical) evidence of truth or falsity. It was merely annoying. Only when a proof was produced (and checked and verified) was this accepted. Or the Goldbach Conjecture, which has been verified to very large numbers; such verification, while indicative, is not enough. Likewise with the existence of an odd perfect number. (As an illuminating aside, a joke has a mathematician, a physicist, and an engineer traveling on a train through Scotland, when they see a black sheep in the distance. The engineer promptly asserts "In Scotland, sheeps are black." To which the physicist replies "No, in Scotland, some sheeps are black." The mathematician then gently corrects him: "In Scotland, there is at least one sheep which is black... on at least one side.")

So: how do we deal with the apparent lack of observation, and the demand for "proof"?

Taking the last point first, I would argue that the demand for mathematical proof does not seriously distinguish mathematics from other sciences. It is merely that the standards which a mathematical result must meet are more stringent than those of, say, physics. But other sciences also set up their own thresholds for acceptance: no more than a certain amount of error, statistical significance to a certain degree of confidence, sufficiently varied observations, predictions, etc. The standards of math are merely quantitatively different (in that they appear to be stronger and with higher thresholds), not qualitatively different.

On to the first point, then. Aren't axioms arbitrary statements? Aren't they dogmatically followed, never questioned or modified? Is there any concern for "truth" and "falsity"? For the outside world?

The idealized model of mathematics presented by the Hilbert School would argue that the answers are, respectively, "Yes, they are", "Yes, but they are arbitrary and we can change to some other system at will", "no", and "no". But like all idealized models, this is not an accurate presentation.

Axioms can be arbitrary statements, but they almost never are. There is usually some reason for presenting a particular set of axioms over some other. They represent not so much "arbitrary statements" as they represent the "ground rules" for a particular development, the minimum agreed-upon assertions from which we will proceed. Often, these are distillation of actual observations, or attempts at abstracting real world situations in a way that makes it amenable for mathematical treatment. The ideas of differential calculus (an eminently empirical development, made for the express purpose of providing the tools to study motion) have been distilled into a series of "axioms" for the real numbers from which we proceed, based on centuries of work and observation. They represent the compromise between avoiding the paradoxes, contradictions, and antinomies which faces mathematicians in the 18th and 19th century, and keeping the properties that allows calculus to be practical and useful.

The axioms of group theory were developed from the study of equations; they represented the minimum conditions on which the arguments would follow. And while one works with groups, these axioms are not changed. On the other hand, people are free to drop, discard, add, or remove axioms at will to produce other systems with which they can also work: this is the case of semigroups (obtained by removing one axiom), or ring theory (obtained by adding a number of axioms).

The axioms are, to some extent, "unquestioned", because from the mathematical side there really is little concern on whether they are "true" in an empirical sense. On the other hand, when a mathematical theory derives from a real world situation it is attempting to abstract and study, the axioms seldom go unquestioned or unmodified, as people attempt to make sure the abstract theory stays as close as possible to the situation it is attempting to model. There is continual feedback and fine tuning between the mathematical theory and the real world.

And while it is true that mathematics usually refrains from saying "true" and "false", and instead talks about "provable" and "disprovable", this does not mean there is no contact or application with the outside world. Mathematical theorems are never simple declarative statements; rather, they are always implications. All mathematical theorems are of the form "If (some conditions are met), then (this conclusion will follow)." Moreover, this will hold true whenver we interpret the theory in a specific model.

As Hilbert noted with his comment on geometry, an axiomatic system should not depend on any specific meaning given to the undefined terms or the axioms. What this means, however, is that any mathematically correct conclusions we draw from those axioms will be true in any interpretation. If we take a theorem of geometry, and interpret "point" to mean "table", "line" to mean "chair", and "plane" to mean "beer mug", then the theorem will provide us with a true statement about tables, chairs, and beer mugs (assuming that the Axioms, when thus interpreted, are also true). In this respect, there most certainly is a connection to the real world and an ability to test and check the validity of the interpretation. In addition, even though we recognize that the semantic meaning we might give to undefined terms like "points", "lines", and "planes" should play no role in a proof, nonetheless these semantic meanings are often used to inspire proofs and theorems. We will make a drawing of a circle and a line to help fix ideas or inspire a proof, even though "circle" and "line" are terms that should carry no semantic content in the proof itself.

The standards of proof that mathematics requires in fact ensure that the conclusion will be true whenever the premises (including the axioms) are also true; and that at least one premise will be false if the conclusion can be seen to be false. What the reliance on provability instead of truth gives us is flexibility and certainty. By relying on abstract rather than concrete considerations, we ensure (or at least, attempt to ensure) that our deductions will indeed follow for any particular interpretation.

Most mathematicians will usually have some specific interpretation in mind when doing mathematics. The danger is that we may use specific properties of that interpretation inadvertedly in a proof, and thereby obtain a result which will not be valid in other interpretations. This was the pitfall into which Euclid himself fell, for example. Proposition 1 of Book 1 relies on the obvious fact that two particular circle segments have a point in common. However, this "obvious" fact does not in fact follow from the axioms. It takes an enriched set of axioms before the theorems of Euclid become actual theorems that will be true whenver all the axioms (both classical and new) are true.

It is because this danger is present that mathematics has developed its standards of proof; just as other sciences have developed their own based on their own experiences. In this it is also that mathematics presents the characteristics of a science.


CONCLUSIONS

Is mathematics a science? I believe so. It follows the scientific method (though this fact is sadly obscured by the prevalent writing style). And while it seems (and sometimes claims) to live in its own little world, cast adrift from concerns about reality, the truth is that, even in its "purest" guise, it keeps an eye out to reality for both applications and inspirations. In its "applied" guise there can be no doubt that it sticks close to reality, and that its assumptions, problems, and conclusions are continually tested and refined against that backdrop. Nonetheless, it is also different from other sciences in that its standards are a bit higher and a bit more certain. But this part of its strength as a science, not a disqualifying property.

So, coming back to our working definition of science, does mathematics meet the requirements? It attempts to distinguish true statements from false statements. However, we must understand here that a "true statement" does not refer to a theorem or lemma in isolation, but rather to the implicit statement given by a theorem, that whenever all axioms and hypothesis are interpreted in such a way as to make them true, then the corresponding interpretation of the conclusion from the theorem will also be true. Likewise, "false statement" would mean that there is at least one interpretation of the axioms and hypothesis which makes them true, while at the same time making the conclusion false.

It is certainly true that mathematics accomplishes this in a systematic manner, through the use of proof. The proofs are open to scrutiny by any and all investigators, who are encouraged to "repeat the experiments", as it were, by going over the proofs line by line and agreeing to their validity (or requesting clarification, or even pointing out mistakes). It is not unheard of that results that had been considered correct are suddenly cast into doubt by a mathematician pointing out a flaw in the argument; sometimes this damns the entire original enterprise, sometimes it merely requires a "fix".

And mathematics has a very systematic way of validating its claims, again through the use of proofs; false claims may be identified by presenting counterexamples or pointing out gaps in proofs. This is done in a systematic and commonly accepted way.

It should then be clear that mathematics does meet the requirements; its particular interepretation of the scientific method, its particular thresholds, may be quantitatively different from other sciences, but they are qualitatively the same. It plays, moreover, a singular role among sciences, being an indispensable tool to so many other facets of science.

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Dr. Magidin is a professor of mathematics who teaches at the University of Montana.

Administrivia: Hiatus

Blogger was having issues this weekend. As a consequence, I wasn't able to publish the regular Sunday essay.

Since I have my posts set up on advanced schedule, I've decided to simply put the blog on hiatus for this week. Regular posts will resume on Sunday.

My apologies for any disappointments this may cause.

Final Exit

I missed my final exit
And forget how to die.

It's not such a bad thing
To be an immortal.

To be sure,
There are days where I wonder
"When did that mountain range appear,
And where did that other one go?"

It is always a bit of a disappointment
When some favorite continent of mine
Crashes into another.

Sometimes I find myself feeling nostalgic
For all the species that I've known
Who have fallen into extinction,
Including my own,
Modulo me.

Often it can be lonely:
Sentience doesn't evolve
All that often
And when it does,
I'm too often out of touch
With the new biologies
To make much sense of them.

But it has its benefits.
I have learned the patience
To watch the slow, slow march
Of the stars across the sky,
As they play cat's cradle
With the constellations.

When the sun expands,
I will look forward to swimming
In its ruby red seas.

Unstructured Cthulhu

I have long been a fan of the Cthulhu Mythos of H.P Lovecraft. Lovecraft posited a universe that was fundamentally inimical and, for the most part, incomprehensible to humanity and which was populated by a host of sanity-warping entities. His most famous story is The Call of Cthulhu which documents the existence and discovery of a gigantic, monsterous entity known as Cthulhu. Many consider it a classic of the genre and a perfect representation of Lovecraft's cosmology.

That being the case, I suspect that even Lovecraft never anticipated that his writings would ultimately lead to the horror that is The Tales of the Plush Cthulhu.

The Buddha in the Bathroom

If you meet the Buddha on the road, kill him. — Buddhist proverb

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It had been a long week. The skies were gray and the air was thick. I was sitting back in the recliner thinking about the upcoming game between the Metas and the Pseudos when the phone rang.

Sarah got it.

"Sam and Sarah's existential exterminators — if it can be, we can do! — may I help you?"

It was that season again. Last year it was an outbreak of solipsists and the year before that it was sophists. Sometimes I wonder what motivated me to get into this business. If you pinned me to the ground, I might be willing to admit that Sarah had something to do with it. Just don't tell her, okay? She's into it for the thrill of it. Go figure.

"Hey Sam!"

"What?"

"We've got a Buddha."

This was great. Just fantastic. In this business, there's a couple of words that you really don't want to hear and one of them is Buddha.

"Tell him we'll be right there."

Sarah hung up the phone and I finished my coffee. Slowly. Ten minutes slowly. Sarah glared at me.

"What's the matter, babe?"

Her scowl threatened to burn tiny holes into the backs of my retinas.

"What do you mean what's the matter? You keep bitching that Reality Plus gets more business than us and now that we've got a call you just sit there like a chunk of lard."

That hurt.

"Listen, you said it yourself. He's got a Buddha in the house. It ain't worth the effort."

"She's willing to pay triple rate for us to get rid of the damned thing!"

I jumped up, got my coat on, checked my gear and was out of the door in a matter of milliseconds.

"Well, what are you waiting for," I shouted into the pressure vacuum that I left behind me, "we've got a job to do!"

Sarah drove. We hit sixty down Tao Way, hung a right at Dharma Drive and went half way around Karmic Circle before we got to the house.

Two things struck me. The first thing was wealth. This house was big, white and clean. To call it a mansion would have been technically accurate but I think that calling it a palace would give you a more accurate impression of the place. The other thing that hit me was a bit more ominous: bo trees. Dozens of them. In my opinion, the things should be banned. I just hoped that we'd arrived in time. Once a Buddha gets under a bo tree, there ain't nothing you can do to get it out.

Sarah was, as usual, one step ahead of me and peering into the ontological analyzer.

"Got anything," I asked.

"Yeah. There's a heavy potential for transmigration. The entire area's on the verge of collapsing into Nirvana."

This was bad. Worse than I had thought. There used to be a place called California. Don't bother looking for it on a map, tough. It ain't there, anymore. It was the worst case of philosophical infestation since India blipped off of the map. Some people say that Nirvana's nothing to worry about. In my line of work that just ain't a very funny thing to say.

I wasted no time in heavily lacing the area with Doubt.

"Okay Sam, it looks like it's stabilizing. Let's get inside and hit the root."

I had a feeling that it wasn't going to be that easy.

I paused just long enough to add some Empiricism to the Doubt and to post a "WARNING: PHILOSOPHICALLY UNSTABLE AREA" sign. It was standard procedure following the kinds of standards that should never have to be invoked.

I pounded on the door. A frenzied woman in her mid-sixties opened the door. She look at me, grabbed my arms and shrilled, "Oh thank heavens, you're here! I thought that you'd never arrive! Where were you! Come in, come in! It's got Harold!"

She then buried her head into my shoulder and started to wail like a Banshee. Trust me, I know how Banshees wail.

Sarah took over. Wrenching her away from me, she turned her around and asked Mrs. Walden to get ahold of herself. Eventually she got her calmed down to the point where she could tell us what in the nine hells was going on.

"What happened to Harold?"

"He, he… he went after it. With a baseball bat. A Louiseville Slugger, I think."

"Get on with it," I grumbled impatiently.

Sarah threw a viciously nasty look at me and asked Mrs. Walden to please go on.

"Anyway, he went to get it and then…"

We both knew what was coming next.

"Well, he went in so mad! I was just certain there was going to be smashing sounds, but there weren't. Just silence and some mumbling through the door."

She was trembling slightly and her hands were twisting around like a can full of copulating worms.

"So, I opened the door and all I can see was… it. It and this big cockroach. So I yelled and demanded to know where my Harold was. Then the cockroach answered and said that it was Harold. I'm married to a cockroach!"

I made a mental note: spontaneous degenerative reincarnation. Type 7, if I'm not mistaken. That's the problem with amatures, of course. They don't realize that a Buddha isn't something you want to mess around with.

Mrs. Walden was still babbling.

"He's a very happy cockroach, you know. He stays out of sight and just eats some sugar here and there. It's just that I know that he's seeing another roach! A woman knows these things!"

"Get a grip on yourself," I interrupted, "we need to know where it's at."

"Oh, probably in the back of the cupboard with all of the other roaches, having their roach parties."

"The Buddha, Mrs. Walden, not your husband."

"Oh! It's in the upstairs bathroom. Just get rid of it and I'll pay you anything!"

In my opinion, this was a good time to renegotiate our fee but Sarah caught my eye, shook her head and told Mrs. Walden that we'd get rid of it in no time.

We decided to do a preliminary search before hitting the bathroom. At the very worst, we expected to find a few lower level koans scurrying around. The worst was far worse than that. Oh, there were koans. Thousands of them. I sprayed them with some Zeno to keep them in place. Koans are annoying but, essentially, harmless, so I figured that we could deal with them later.

The real magnitude of the problem surfaced when Sarah buzzed me from one of the upper rooms.

"Sam, get up here! We've got a Vishnu in a closet."

I hit the stairs running. In the final analysis, we found sixteen Vishnus, twelve Brahmas and a Kali. What's worse was that one of the Vishnus was about to pupate into a Shiva. Once you get a Shiva, you might as well forget the exterminators and call out the National Guard. Literally.

I cut away the Vishnus and the Kali with an Occam's razor and dissolved the Brahmas with ReduxoAdAbsurdium ™. The real bad part was that all of the evidence indicated that this wasn't a recent infestation. We went downstairs to have a chat with our client.

"Mrs. Walden," Sarah begin politely, "how long have you had a Buddha in your bathroom?"

"Well, let me see… it was before Aunt Mertie got divorced but after Johnny was caught with a succubus. It was about the time that Cynthia weren't to the hospital to get exorcised. All in all, I'd say about sixteen months."

"Sixteen months," I screamed, "are you insane?"

Sarah told me to shut up. I didn't care.

"Why didn't you give us a call back then, you crazy old hag?"

I stopped when I noticed her expression. It was the hurt look that a dog gives a sadistic master. I suddenly felt the slick feeling of guilt climbing up my throat.

Verging on tears, Mrs. Walden said that, at first, the Buddha seemed harmless.

"After all," she explained, "it said such cute things about trees and ponds and shapes. We even invited our neighbors over to see it. By the time it got to be a nuisance, we were too embarrassed to call an exterminator. Harold said that he would take care of it himself. And now… now… now Harold's gone! I had no one else to turn to. I'm sorry, I really am!"

"Does that answer your question, Sam?"

Sarah's voice was ice. I suppose that I deserved that. How was I to know that, to a bunch of tired, old people, a Buddha would seem like a fun thing to have? Something to break up the tedium. A novelty.

"Come on, Sarah. Let's get rid of Mrs. Walden's Buddha."

After finishing our preliminary search, we went up to the infected bathroom. Cautiously opening the door, I snuck a peek inside. A portly, bald figure in a saffron robe sat complacently upon the toilet as if it were an emperor on a throne. Its face was a study in serenity. It appeared to be studying a role of toilet paper with unfocused eyes.

Sarah already had the ontological analyzer set up.

"Bad. It's at least a Level 12 Bodhisattva."

I decided that a direct frontal assault was best. I shoved the fumigator under the door and pumped six liters of Descartes. The residual fumes that escaped the bathroom filled us with a profound sense of self-existence.

I once heard of one guy who tried this trick on an enclave of solipsists. Worst idea in the world. He had to subcontract out to another firm before he could control the population explosion of the egotistic buggers. A Buddha is an entirely different matter. A Buddha that believes in its own existence is one less Buddha to deal with.

After waiting five minutes for the Descartes to take effect, I opened the door. Fat boy was still on its throne. It looked over to me and said, in a voice as mellow as sunlight on a pond, "It is unbecoming to become."

I slammed the door shut. Five more second and my partner might have been working with a wombat.

We spent the next five hours pumping in various chemical combinations. We sprayed it with Sartre and Aristotle, wasted twelve cans of Kant and even tried a mixture of Galileo, Newton and Einstein with a chaser of Logical Positivism. In the meanwhile, it's contemplations remained undisturbed.

Frustrated and tired, and still feeling guilty for snapping at Mrs. Walden, I turned to Sarah and said, "There's only one thing left to do. I've got to go in there and face it directly, man to archetypal incarnation."

Sarah had a strange look in her eyes. It almost seemed like respect. With a whisper, she replied, "Let me help you with your gear."

After suiting up, putting in my ontological nose filters, and taking a very deep breath of Descartes, I slammed the door open and burst into the bathroom.

"Okay, Buddha, I want to talk to you!"

Tilting its head, it replied with morning dew calm, "But what is you and what is I?"

"You're a nuisance and I'm the guy who's going to get rid of you!"

"To get rid of, there must be self and direction. There are neither."

I was sweating. Like The Little Train that Was, I started chanting to myself, over and over, I think; therefore I am… I think; therefore I am… I think; therefore I am.

Reality solidified a bit.

"Why don't you leave Mrs. Walden alone?"

"One must always be alone within the self until there is no self to be alone with. This is the only freedom from suffering and rebirth."

I think; therefore I am...

"If that's true, what are you doing sitting in a bathroom?"

"Was it a bathroom before you realized it was a bathroom?"

I think; therefore… I think, um, damn, how does that go?

"Why can't you give me a straight answer?"

"Why do you give me crooked questions that have no answer?"

I think; therefore I'm… not? No, no, no, no!

"Bullshit! All questions have answers."

"What is the sound of one hand clapping?"

I… shit, what was it?

He almost had me. Dimly, I heard another voice. Sarah's voice.

"The tape, Sam! Play the tape!"

Suddenly I realized that I had the Buddha exactly where I wanted it. It took years of study, thousands of volunteer amputees and the most sophisticated synthesizers on the market, but it was worth it. Teeth gritted, I pulled out a special loop-tape from my kit and played the extremely disturbing sound of one hand clapping.

The Buddha's eye's focused. It tilted its head to one side, sat motionless for a minute and said, "Oh."

With a faint pop, it disappeared.

I think that I must have passed out right after that. The next thing that I remember is having my head in Sarah's lap, which felt very nice, and hearing her say, "Good job, Sam! You did it."

That felt even nicer.

Later on, we went downstairs. Harold was back to normal. The Waldens insisted that we stay for dinner which was a proposition that neither of us choose to argue against. After dinner, he wrote out a check for six times the original amount.

"Son, life as a cockroach only has so many pleasures. I'm glad to be a man, again."

When we got back into the office, I poured myself into the recliner. I intended to stay there for a few thousands millennia. The phone rang. Summoning all of my energy, I yelled at Sarah not to pick up the…

"Sam and Sarah's Existential Exterminators — if it can be, we can do! — how may I help you?"

I groaned.

"Hey, Sam!"

"Yeah?"

"We got a Messiah on Maple Street."

I'll say this much: the hours are long and the pay is low but, at least, life is exciting.

A Novel Accomplishment

I was just looking over my Blogger profile when I noticed that I have published somewhat over forty-two thousand words on this little blog of mine.

The typical definition of a novella (which is a mid-length story shorter than a novel) is that it has between seventeen thousand and forty thousand words. Anything longer is considered a novel.

I must say that I'm rather surprised that I've already published a novel's worth of material to here in just a bit over four months of time, especially since it really hasn't seemed like I've been writing all that much.

So, how does one celebrate a thing like this, I wonder?

Heaven's Ledge

Heaven has become
Infested by humans.

It's God's fault --
That whole salvation and redemption thing,

But you know how God is.

It is not so much
That they trod upon
The Untouched Ground,

Nor is it the litter they spew from themselves
Like an angry hive of filthy bees,

Nor even the fact
That they continue to fight about religion
Even here.

No.

It is because I can not go
To any of Heaven's ledges
Without finding one of them

Pissing into Hell,
Pissing on the damned,

Just to add
Their own, personal contribution
To an already infinite misery.

Blogpulse

I have long been interested in the zeitgeist, which is a word meaning the spirit of the times. With the advent of the web, more and more tools have been made available to get a pulse of our times. One of the coolest I've found is the BlogPulse Trend Tool.

The way it words is that you enter up to three search phrases that look for words that show up in people's blogs. The tool then graphs the results as a percentage of blogs that use the phrase graphed over time. Here are a few examples.



I realize that may sound a bit dry but give it a try. If you're like me, you'll have a hard time pulling yourself away from it.

The Bleak Universe, part IV

This is part four of a four part essay. In this part, I will discuss two important time limits that will constrain our exploration of the universe as well as bringing the essay to a conclusion by addressing the question of whether or not we live in a bleak universe.

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Last week I stated that there was a time limit to our explorations of the universe and that the clock is already ticking. Actually, there are two clocks that we are racing against, one of which is thermodynamic and the other of which is cosmological. I shall first discuss the thermodynamic clock.

We tend to think of the universe as being something that's ancient. Current estimates place it's age at around twelve billion years (give or take a billion). That's certainly old enough in human terms and even in geological terms. In cosmic terms, however, the universe is frighteningly young. Measured against the whole of the universes expected existence, we're practically still in the Big Bang.

The current epoch of the universe has been called the stelliferous era, meaning the era that is filled with stars. Indeed, when we look up at the sky, tend to think of the universe in terms of stars: a vast blackness punctuated by bright points of light. In truth, stars represent a minute fraction of the mass and energy of the universe. Never the less, we are not wrong to think that the stars are special given that they are engines of life.

If order for life to exist, there must be an energy gradient. That means, in simple terms, that heat must flow from a higher point to a low point. Such a system allows for the existence of so-called "heat engines". Life is one such engine. Not only do stars create such a gradient, but they are central to the formation of planets and they allow for the existence of such crucial materials as liquid water.

We tend to think that stars are eternal, like mountains. They are enduring than mountains (which rise and fall live shivers on the skin of the planet) but stars do not live for ever. Like people, stars are born, age, grow old and, ultimately, die (they do not, however, reproduce). Fortunately, when stars die, they return some of their mass back to the universe either by shedding layers of their outer mass as their central reserves of fuel diminish or, more spectacularly, by exploding. Unfortunate, they always take a fair amount of their mass to the gave locking it away in the form of white dwarfs, neutron stars and black holes.

The mass that is returned to the galaxy can be recycled into new stars (with heavier elements than the previous generation, but that's another story). The era of star formation, however, will not last forever. Eventually, the material to make new stars will be used up and no more stars will come into existence to decorate the universe and to provide havens for life. Ultimately, the oldest stars will all burn out leaving the universe a darker, colder place.

The stelliferous era started as early as a million years after the Big Bang and will continue for another hundred trillion, or so. This may seem like a long time (certainly much longer than the current age of the universe), but time is deep.

Once the stars burn out, any chance for us to explore the universe will have to give way to an increasingly challenging effort to survive a universe that becomes progressively more hostile. After the stelliferous age, there is a so-called degenerate era (referring to degenerate matter and not degenerate people) where we may try to scrounge energy from white dwarfs and neutron stars. This era will end at ten to the 39^th years. Past that, we may try to salvage a trickle of energy from the evaporation of black holes. If we can manage to do that, we may be able to hold on to some form of existence for a full googol of
years.

Ultimately, even matter itself is likely to betray us since protons are, in the very, very long term, believed to be unstable. Unless we can do something miraculous such as finding a way to reach some other younger, more vital universe, our universe shall become our tomb and the graveyard of any other life that might exist.

Still, even if we are bound to only survive the stelliferous era, a hundred trillion years is not an inconsequential span in terms of human endeavors. As I've noted before, the farthest portion of the universe that we can currently see is only about 10 billion light years away. With a hundred trillion years of leeway, we could get from here to there at a meager 1/10,000^th the speed of light (about 67,000 miles per hour). You're probably not surprised that I'm about to tell you that there's a hitch and that it has to do with that second clock, the cosmological one.

The universe is expanding. This was discovered in the early part of the 20^th century as the first generation of modern telescopes was brought to bear upon the universe. Spectrographic analysis of the stars showed that distant stars (that is, stars in other galaxies) were shifted towards the red. This is an aspect of a phenomenon known as Doppler shift (actually, it's more complex than that but this will do for our purposes). In a nutshell, this meant that much of the universe was moving away from us. Even more curiously, the more distant stars were receding more rapidly. This was, to say the least, unexpected and puzzling.

The solution to this weird behavior is that space, itself, is expanding. In fact, Albert Einstein almost predicted this. When he developed the Theory of Relativity, he found that seemed to require a universe that was either expanding or contracting. He naturally thought that was ridiculous so he included a fudge factor into his calculations, called the Cosmological Constant, in order to eliminate this counter-intuitive behavior. He would later say that this was his greatest mistake.

Counterbalancing the expansion of the universe is gravity which is "trying" to slow the universe down. For a very long time, cosmologists have wondered whether gravity would eventually win – slowing, stopping and, ultimately, reversing the expansion into a collapse – or whether the universal slow but never quite come to a stop.

In the mid to late nineties, various research groups were making observations of distant supernovae in order to try and pin down a critical value known as Hubble's Constant. In the process of doing this, their data showed that universe not only isn't slowing down enough to stop expansion but that it is, in fact, accelerating.

To say that this was unexpected would have been the understatement of the century. It would be like pushing a bolder down a steep incline only to have it stop midway and start rolling back uphill.

The universe hasn't always been accelerating. Until relatively recently, the universe has been behaving according to theory. The acceleration we're now observing is a relatively new phenomenon (remember, of course, that, to an astronomer, a billion years ago is recent). The reason for this acceleration is still being debated but there is a growing consensus that Einstein wasn't entirely wrong in postulating a cosmological constant. However, instead of holding the universe in a static state, the constant drives it towards expansion and acceleration.

Gravity, on the scale of the other forces that govern the universe, is extremely weak (about 1 over 10 to the 33^rd of the strength of the next weakest). It is, however, an important force on the cosmic scale because it acts over an unlimited range and because it only comes in a positive variety (unlike magnetism) so it never cancels itself out. The Cosmological Constant also works over long distance working against gravity by providing a kind of "pressure" that pushes the universe outward. There is one very important difference, though: gravity becomes weaker with distance but the Cosmological Constant exerts a constant force no matter how far apart things are.

In the early universe, gravity was dominant. The universe was expanding but gravity was hitting the brakes fairly hard. Sheer inertia (with a little help from Inflation) kept the universe from immediately imploding. The Constant, by contrast, was fairly feeble. As the universe has grown older and larger, however, gravities grip on the universe has been growing weaker while the Cosmological Constant's influence has remained appropriately constant. At some point, we seem to have crossed over a threshold. Where gravity was ruled, the Constant drives the expansion. The end result of this is that the universe will not only continue to expand forever but that the expansion will go faster and faster, accelerating without end.

What does this mean to us? In a word, it means loneliness. The farthest galaxies we can currently see at the farthest we will ever see. As time moves on, the furthest objects from us will actually disappear over the cosmic horizon forever invisible and inaccessible to us. This process will continue until we left in a universe where only those objects that are gravitationally bound to us will remain with us. It is expected that that will mean the local cluster of galaxies, which is small collection of nearby galaxies numbering about thirty. The rest of the universe will seem vast and empty.

How long this will take is not known, but it is expected to be fairly rapid. It is unlikely that we will have our hundred trillion years of exploration time. Instead, we will be stranded in our small patch of the universe surrounded by an impenetrable and empty darkness.

Do we live in a bleak universe? We must come to terms with the realization that the universe does not have an obligation to be friendly to life. The Copernican Principle may well have instilled an unreasonable sense of optimism in us. Even if there is intelligence out there (and we have cause to suppose that it's out there somewhere), there is no reason to expect that it will be close enough for us to ever meet it or even to signal it. We may well be alone in the only sense that matters.

Shall we despair? Although we may be denied our fondest dreams, I think that we need not despair. If there are no alien intelligences available to us, we always have the possibility of creating new intelligences, either cybernetically or biologically (The science fiction author David Brin suggests that we might decide to "uplift" certain animals to sapience via genetic engineering and selective breeding). We might even decide to be cultivators of intelligence in our galaxy by going out and seeding promising worlds with life and sheparding them through the hazards posed by a dangerous universe. If the galaxy is now a hostile jungle, we might turn it into a garden.

Even if the economics and physics of interstellar travel consign us to live and die in the neighborhood of our own star, I think that we have cause for happiness. If life is uncommon and intelligence is rare that only means that it is precious and special. We can look out at the universe and rejoice that we are, in fact, privileged for the very reason that we can look out at the universe in wonderment and awe. The Copernican Principle to the contrary, we are not mediocre and any universe that can contain beings such as ourselves is not truly bleak.

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This concludes this essay. I would like to acknowledge Fred Adams and Greg Laughlin for coining the term stelliferous as well as for providing a detailed description of the ages of the universe in their book The Five Ages of the Universe which I heartily recommend.