The Journal of the Noetic Society
Number 63
July 1991


By C. M. Langan

Refilling his maw, he thanked providence for small favors.  Why,  the kid might even have subjected him to some kind of Ph.D. thesis on the mysteries of Bayesian paradox!  Such paradoxes apply mainly to sets of differently-relativized probabilities, not to localized calculations like those involving the die and the box of marbles.  A given subject either has information or not; if so, he either has evidence of its relevance or not.  If not, it's useless.  Beyond  observation, he has only CTMU probability theory and telekinesis.  At least the kid had seemed to understand that probabilities are by definition relative: none of them remain valid in the event of a loss or extension of relevant data.  The only invariants are certainties, and even these finally obey the same logic as probabilities.  You can take the objectivity out of the subject, but you can't take the subjectivity out of objective reality.

Hey, maybe the kid's astronomical IQ had meant a little something after all.  At least the boy wonder had known better than to fabricate the initial probability distribution.  That, mused Jojo as his tongue batted a lump of Haagen-Dazs around his mouth, would have been like speculating on how many angels could do the lambada on the head of a pin.  Where every initial probability distribution has an equal claim to validity, there is no choice but to settle for their average.  Probability distributions are represented by curves plotted against the x and y axes, each curve bounding an equal area of total probability.  The average of the curves is a flat line, and the area beneath it is evenly distributed along the horizontal axis of independent possibilities, discrete or continuous.  The curve isn't bell-shaped, ball-shaped, or banana-shaped, and Jojo was grateful to have been spared the full treatment. 

Then again, even though the term "average" reflects the symmetry obtaining among exclusive possibilities in the total absence of information, it sometimes needs qualification.  Say you have a Markovian system of co-dependent events.  You may want to seek its "attractors" by interpolation and/or extrapolation (which can also be viewed as a kind of "averaging").  There might be a number of different ways to do this; which one is best can be known only by virtue of -- you guessed it -- informative data pertaining to the particular system you're observing.  Assuming that this system is deterministic, the attractor guiding it towards its successive equilibria might be "strange", chaotic, and fractally regressive.  That can complicate things.  But in any case, the amount and nature of your information determines not whether you should symmetrize, but merely how.  No exceptions allowed; by definition, every probabilistic algorithm involves some kind of symmetry, even at the deterministic limit where the "probability" goes to unity!  The kid had also seemed to understand the importance of information, and the necessity to symmetrize when you run out of it.  That was impressive, if only because it isn't clear from the perspective of standard information theory.  Info is more than bits of transmitted signal; it's a dependency relation recognized by an acceptor, and its "transmission" is just lower-order recognition on the part of any acceptor defined to include the source, channel and receiver.  Information thus describes every possible kind of knowledge.  Since objective reality can be known only as knowledge, it must be treated as information. 

Over the centuries, different thinkers have come up with some pretty funny ideas concerning what reality "really is", and have been ridiculed by their children and grandchildren for what they thought.  But defining information on cognition, and cognition as an informative function of information, ensures that whatever else reality turns out to be -- ether, phlogiston, or tapioca pudding -- it can always be consistently treated as information for cognitive purposes.  Since cognition is what science is all about, what's good enough for one is good enough for the other.  So if the equation of reality and information is a "joke", reasoned Jojo, our chuckle-happy descendants will be the butts of it no less than we.  And anyway, they'll probably be too busy crying about the barren, overpopulated, tapped-out ball of toxic sludge they've inherited from us "comedians" to laugh about much of anything. 

The cognitive universality of information implies cognitive symmetry or stasis in its absence.  The counterpart of symmetry, asymmetry ("not of like measure"), obtains among variables which differ; to be used in any computation, this difference must be expressed over the qualitative range of a set of distinct differentiative predicates, or the quantitative range of at least one differentiative predicate.  If you can specify no such differential scale, then no such scale exists for the purpose of your computation.  And with no such scale to aparametrize the function assigning weights to the various possibilities, the function can't assign different weights.  That leaves you with non-asymmetry or symmetry.  As information arrives, this symmetry can be "broken".  But information alone can break it, and you're stuck with it until then. 

Sameness can sometimes be deduced, in which case it has informational value.  But as an effect of symmetrization, sameness means that no differentiative information is available.  Whenever there's no info on hypothetical arguments, the corresponding variables must remain open for computative purposes.  Symmetrizing the object variables themselves -- for instance, by assigning the same content to each of them -- entails the risk of creating false information; these identical values might be wrong.  But symmetrizing on a higher level of induction -- e.g., by equalizing the distributions of possible values of algorithmic parameters -- leaves the variables open.  They remain objectively neutral, unbiased, and free of potentially misleading false information.

This unbiased neutrality is a rock-hard inductive criterion.  If it orders crepes suzette, it had better not get lumpy oatmeal.  And what it craves is the kind of higher-order symmetrization just described.  The distinction between higher-order and lower-order symmetrization is subtle and easy to miss, which explains why many probability theorists don't understand how or why they should symmetrize.  But then again, your average ankle-biter doesn't understand why he shouldn't rape the cookie jar before every meal, either.  And that, concluded the clown, is pretty much the reason why some folks find the "principle of equivalence (or insufficient reason)" hard to swallow, and why they become mired in paradoxes that can't be resolved without it.

Yeah, Jojo knew about Bayesian regression, a paradox generated by a pair of inconsistent assumptions.  One is that each one-place predicate occurring in an n-fold observation of r objects is equally likely; the other is that each n- or r-place predicate involving these one-place predicates is equally likely.  In the first case, you're likely to observe each possible color the same number of times.  In the second, you're as likely to observe any subset of colors more or less often than other subsets.  The question is, which assumption should you make in the absence of definite information regarding either one?  Jojo, who had been kicked out of MIT for pie-facing the chancellor[1], didn't need a degree to unkink that one.  All he had to know was higher-order predicate logic, courtesy of that sidesplitting vaudeville-era comedy team, Russell and Whitehead.  Their act, Principia Mathematica, had played in London, Paris, and Reno, and Jojo had it on the original 78. 

See, the gist of it was, predicate logic is stratified.  Each successive order includes all those below it, but none of those above it.  What that means to probability theorists is as clear as benzene-laced mineral water:  it's impossible to express dependency relationships which violate this rule, known to aficionados as the theory of types.  It was designed to avoid the negative circularities called paradoxes or antinomies.  It manages to accomplish this by "breaking the loop" of language by which such paradoxes are formed.  But here's the sweet part: this same mechanism also prevents artificial tautologies, circular inferences which justify themselves like so many philosophers at a teach-off.  Jojo chuckled inwardly: cogito ergo sum quod cogito quod sum quod cogito quod... I think, therefore I am what I think what I am what I think what...  Somewhere along the line, you've got to admit a little "objective reality" into the deal!  Or, like a snake who lost his coke bottles, you swallow your own metaphysical tail and roll away into the never-never land of fantasy and solipsism, a scaly hula-hoop of empty assumptions powered by a perpetual motion machine. 

On the other hand, it's just as stupid to think you're the Solomon who can meat cleaver a Haitian divorce for the subjective and objective parts of reality.  It takes two to tango, and this pair dances in a crazy-glue lockstep.  Neither one can even be defined without the other.  Kant knew it, Russell knew it, and even that hilarious Austrian Godel knew it.  But quite a few other people didn't seem to know it.  Take, for example, the vast majority of practicing logicians, mathematicians, and empirical scientists.  Sure, a lot of them paid it the "correct" amount of lip service... apparently to apologize for not being able to make any sense out of it.  But it's real clear and real unequivocal, and nobody has anybody but himself to blame if he talks the talk before he can walk the walk.  The whiz kid, who'd started out like some kind of solipsist, had probably been as thoroughly sucked in by modern scientific pseudo-objectivism as all those Joe Average "dummies" he habitually surveyed from on high!

Even type theory itself was in some ways a bust.  It was meant to rid logic and mathematics of paradox, but did so only by shifting paradox into the higher realm of undecidability theory.  When Godel delivered that little punch line, Russell felt like the joke was on him.  That, lamented the clown as he smeared mustard on his next kosher pork delight, was a shame.  Had Jojo been around, he'd have reminded his good pal Bert of a cardinal rule of comedy: you have to learn to tune out the hecklers.  Hecklers frequently knock comedians for telling jokes over their heads, and science is full of critics ready to pounce on any theory they're too dumb, lazy, or preoccupied to understand.  Anybody who comes up with anything really brilliant in this world learns that from Jump Street. 

Type Theory can't eliminate paradox, because paradox is a condition of human mentality.  Every problem on every IQ test ever invented can be formulated as a paradox, and every solution is the resolution of a paradox.  Man is a problem-creating, problem-solving animal.  Eliminate paradox, and you eliminate human mentality.  It was amazing, the lengths that some of these goofs would go to in order to avoid a little common sense!  Russell could have yanked victory from the jaws of defeat merely by reformulating the purpose of his theory.  Instead of claiming that it eliminated all logical paradox, he could simply have claimed that it placed certain logical restrictions on paradox-resolution...and therefore on solving the logico-mathematical and scientific problems that can be expressed in paradoxical terms.  And guess what, whiz-kids of the world, thought Jojo as he horked down a gigantic bolus of garlic and gluten: that just so happens to cover problems like my little box of marbles.  Patting his side, he was answered by the reassuring rattle of ten glass globules.  He silently blessed each and every one of their stony, money-making little hearts. 

Because paradox is a condition of subjective mentality, being the self-referential basis of temporal consciousness, it also applies to whatever is observed by the subject -- in other words, to so-called "objective reality".  And to ice the cupcake, it also applies to the subject's conception of his relationship to objective reality!  That was Godel's insight.  Unfortunately, old Kurt, in his zeal to yank the banana peel out from under old Bert, went light on the scientific ramifications of his undecidability gag.  This left the audience with a bunch of cracked and leaking coconuts where their wise and learned brains had been, and science was able to skate right along like nothing had happened.  But see, something had gone down after all, and Jojo couldn't decide whether to laugh or die about it.  But so what? he thought as he wiped his de-gloved paws on the window curtains next to his table.  At least he knew he'd always be able to make a buck off it. 

But hey, money wasn't everything, even in this city.  There were other important things to remember.  Like the purposive connection between the theories of Types and Relativity.  See, Jojo wasn't the only famous Einstein who shared Russell's concern with logic.  Herr Albert had something very similar in mind when he adopted the principle of locality in order to avoid causal paradoxes in which super-luminal agencies make observations and then change the way they happen.  The basic idea was the same: effects cannot negate their causes.  Causes can negate certain effects by way of promoting others, but not vice versa.  And more to the point at hand, the output of a function or algorithm cannot post hoc tend to negate the function or its parameters...e.g., the initial distribution on which observations depend.  Where the output has already been observed, this forces the symmetrization of all the "causes" (e.g., chromatic likelihoods) from which it may have resulted.  Deduction eliminates possibilities; but whenever an inductive context can be arbitrarily extended relative to a given hypothesis, the inductive process must respect all possibilities by obedience to the theory of types.  

In other words, what type theory said about Bayesian regression was this.  Bayes' rule is an algorithm, or complex logical function ascribing one of a set of predicates (probabilities) to a variable causal argument.  It was designed not only to derive a conditional probability, but to do so without contaminating relevant data with irrelevant assumptions.  The latter amounts to the avoidance or prior resolution of any paradoxical inconsistency between such assumptions and the reality which is being measured: if you assume something that favors any particular outcome representing a fraction 1/n of possible outcomes, you will only be right 1/n of the time.  That amounts to a paradox (n-1)/n of the time, a situation that has to be avoided wherever possible.  

Type theory avoids it by directionalizing the inclusory or attributive dependencies in the formulation.  A variable standing for a color is of higher type than one representing an object.  A variable standing for a chromatic distribution is of higher type than one representing a color.  And a variable standing for a probability distribution (of chromatic distributions of colors over objects) is of higher type than one representing a chromatic distribution.  Each one of these variables gets to determine those beneath it, but not with or above it.  So you can't take an assumption about a chromatic distribution -- say, that each color is or is not equally likely to be observed in sampling -- and try to determine the probability distribution from it.  Since Bayes' rule requires initial information on the probability distribution, you have to forget about the likelihoods of specific colors and start from the probability distribution itself.  That means that where you have no prior information on the probability distribution, you have to symmetrize or flatten it.  Each chromatic distribution is thus equally likely, and the corresponding range of individual chromatic likelihoods is open and unbiased.  See, Ma?  No loops. 

Jojo recalled a related question involving the states of systems in probabilistic contexts.  Prior to extended observation, how do you know how to partition the set of possibilities you intend to symmetrize?  Take an urn containing two marbles.  What's the probability that the marbles have different colors?  Are the possible states enumerated combinatorially: xx, xy, yy?  Or permutatively: xx, xy, yx, yy?  Jojo chuckled, almost choking on a pickled egg.  Probabilities, states, and difference relations compute solely as information.  In CTMU probability theory, information about states is subject to the same constraints as that expressed in terms of states.  There are 3 states in a combinatorial urn.  There are 4 states in a permutative urn.  Since 4 > 3, the permutative state-set has more information.  But just how has this extra permutative info been acquired?  The down and dirty truth of it is, it hasn't  been "acquired".  It's been fabricated.

Most probabilistic algorithms need at least combinatorial info to work.  If you're going to go without observation and fabricate information about states, it has to be at least combinatorial.  But you don't dare help yourself to extra unconfirmed info!  So the urn's states are initially combinatorial, and p = 1/3.  In other words, states defined on individual objects and ordered relations among objects don't get to determine higher-order combinatorial predicates of whole sets.  Only observation is "high enough" to do that.  And that, concluded Jojo as he shoveled ice cream in a last-ditch attempt to quench the egg's fiery -- no, radioactive -- aftertaste, was that.  Glory Be to the CTMU unification of probability theory and higher-order predicate logic!  Trying to get over on the CTMU is sort of like trying to outsmart yourself: you lose if you win, and win if you lose.  The clown wheezed pitifully.  Where the heck could a mere egg-pickler be getting plutonium-239?

The necessity for combinatorial information in purely subjective computations is a demand of our cognitive syntax...the way we see the world and organize it mentally.  Such demands determine all the mathematical models we construct to represent and simulate reality.  Because they inhere in every such model, they are a basic ingredient in all calculations based on such models, "objective probabilities" included.  The fact is, since all probabilities have subjective components, there are no grounds for refusing to recognize subjective probabilities as "real".  Is the above probability highly subjective?  Yeah.  Is it only relatively valid?  You know it.  But while some bananas are strictly by Goodyear, a chimp has to eat.  And the only way to chew this particular bunch is to recognize that all probabilities regress, on data reduction, to statements about the semantical relationship of subjective cognitive syntaxes to that of "objective reality".  Such statements, if extremely general, nonetheless express a real relationship between two realities, you and your environment.  The only way they aren't real is if you aren't real.  And if you're reading this, you're as real as Cheetah, Bonzo and all their offspring combined. 

The Bayes algorithm is formulated in a certain metalanguage, and its variables occupy specific levels within it.  Any universe to which the rule is applicable must conform semantically to its internal stratification.  By virtue of type, the dependency relationships among Bayesian variables are asymmetric and directional.  This also applies to more specialized rules like the Schrodinger equation, which are merely empirical-slash-subjective[2] evolutions of Bayes' rule under given kinds of empirical input.  In this sense, Bayes' rule is the universal first step in scientific inference, and associated at a very deep level with the human mental syntax itself.  That's why Bayesian inference, Bayesian paradox, and Bayesian regression are central issues in reality research, and why anybody who complains that they're bored or irritated with these topics belongs on Monkey Island with the rest of the big time mental heavyweights.  And that, mused Jojo, goes double for anybody unwilling to grasp the topic at even the general level on which he was thinking about it.  He was glad that he could keep his thoughts to himself instead of having to run a hard-sell on some bunch of self-styled "experts".

Jojo, who felt himself converging on an explosive disaster to rival even his Kreemi-Whip nightmare, reflected on the molasses-in-January speed with which the scientific community often seemed to assimilate earthshaking new abstractions.  Hand them a gadget or a preformed mechanical principle, and they treat it like a three-alarm fire in a loaded bank vault.  But hand them a pure, beautiful abstraction, and you might as well indulge in a little suspended animation while you wait for all the "experts" to puzzle and grope their ways through it.  Even so, it's just a heartbeat next to the time it would take them to root it out themselves from beneath the tangled circuitry of fact and supposition that they call "knowledge".  It's a practical world, and the reformer of abstractions had better dress for a long, cold hike to acceptance.  Because people want to face their mistakes and inadequacies about as much as a hundredth-time-virgin bride wants to show hubby that Property of Hell's Angels tattoo on her creamy derriere.  

See, everybody's an expert, and everybody has his or her own ideas about what is or is not "rational", "imaginable" (see Noesis 58, p. 17), "possible" (see Noesis 46), "probable", and so on for every subjective context.  This can apply even to hard, extensional contexts like truth and certainty.  But Jojo had noticed that whenever people bother to justify such opinions, they always fail to come up with anything remotely resembling a formal derivation.  That's because no categorical derivation is possible with respect to anything but the most general features of the human cognitive syntax.  Instead, they offer "plausible arguments" on which there "seems to be a consensus" among like-minded cognoscenti.  Translation: mildly denatured crapola, with 99.9 percent certainty. 

Jojo, not content to settle for any narrow field of expertise, was an expert on experts, and knew that no expert could determine diddley except relative to his own axioms and rules of inference.  That naturally precludes any value judgment on anything involving additional axioms, rules, or data.  Some things are easily recognizable as nonsense because they oppose known facts at identical levels of specificity: if somebody were to claim that the War of 1812 was fought in 1922, he'd plainly be a bag of gas.  But as the situation gets more complex, it rapidly gets very difficult to make this kind of determination.  If a critic isn't extremely careful, he risks becoming just another old curmudgeon with antiquated notions about what rules the universe is "required to obey".  

Take Newcomb's paradox, a generic anomaly designed to cut off the ring on such lamebrain arguments.  Newcomb's paradox is just an arbitrary version of a situation that has arisen, and will no doubt continue to arise, countless times in the always-surprising annals of science: data is received which appears to contradict a currently accepted set of axioms and rules of inference.  That much  is obvious, since otherwise there would be no point to it.  But the clever way in which the formulation evokes the issues of free will, rationality, and megabucks seems to have short-circuited the faculties of many of those who tried to solve it.  They treated it as nothing but a real or phony get-rich-quick scheme instead of as a paradigm for empirical and theoretical induction!  Even when this big bad paradox was finally resolved by Jojo's personal amigo and sometimes-biographer Chris Langan, everybody played ostrich, 'possum, and downright deaf and dumb rather than admit they might have "overlooked" something.  Given the fact that some of them claimed ultrahigh IQ's and had a lot to lose by imitating the furniture, Jojo found this...well, unimaginable, improbable, and incredible. But true.  Langan had belonged to a society of whiz-kids when he resolved Newcomb's paradox and certain other notorious inconsistencies.  The poor guy had been led to believe that he would thus be assured of a fair and insightful hearing for his ideas.  But he'd been in for a minor disappointment.  Jojo recalled a few notable examples: one member had implied that Langan's ideas were less than original because one partial aspect of them had been "proposed" by somebody else who apparently had a limited grasp of the logico-mathematical complexities they entailed...many of which nobody but Langan seems to have even considered.  Another had adopted the computative terminology of Langan's Resolution to undermine the work itself, an exercise in one-man foot-shooting.  And yet another had denigrated Langan's contributions because "others" had expressed disapproval, telling him that his request for an apology amounted to "killing the messenger"!  Instead of presenting their arguments in ways that invited a response, these critics all seemed to dismiss out of hand the idea that any suitable response would be possible.  The fact that none of them offered so much as one unqualified sentence in support of his concise and incisive analyses had sort of bugged Langan.  But it really shouldn't have.  Because if he'd known whiz-kids like Jojo knew whiz-kids, he'd have expected nothing but the kind of meaningless and circular bickering he got.  And he'd have made a laff riot out of it, just like Jojo with his whiz-kid. 

Then again, Langan's critics didn't have to look so bad.  Some of their remarks were relatively insightful.  The problem was, they offered their criticisms after Langan had already answered them!  For example, it was remarked -- after Langan had made it clear that the standard type-theoretic resolution of the Epimenides paradox could be transformed into a resolution based on CTMU many-valued logic upon real time violation -- that this paradox "would really lead to a (CTMU-invalidating) contradiction" if one were forced to assign one of only two truth values to every statement.  One of the main ideas of the CTMU, if Jojo wasn't badly mistaken, was to define a paradox-resolvent stratification of truth functions generating a potential infinity of truth values (top paragraph, page 9, Noesis 44)!  Good thing Langan had a sense of humor. 

Part of the beauty of the CTMU was the way many-valued (modal) logic was so naturally applied to reality in the stratified computational model.  The two-valuedness of the human accepting syntax delineates only that part of global reality constrained by human conceptual and observational limitations.  For each level [gamma]n of [gamma], there is an nth truth value.  Truth values are related according to the inductive and deductive relationships holding within and among the levels of [gamma].  Langan had made this as clear as possible, given limitations in space and reader attention.  

Someone else had made the observation that using the CTMU to resolve Newcomb's paradox was "like using a B-2 for crop dusting"!  Newcomb's paradox, a conundrum relating physics, decision theory, and the philosophy of free will within a metaphysical matrix, had defied resolution for over twenty years by the time Langan wrapped it up.  The reason? Physics, decision theory, and the philosophy of free will is to crop dusting what botanical genetic engineering is to spreading fertilizer.  Along with the other matters to which it was closely related -- e.g., quantum reality -- Newcomb's paradox had all but smothered to death under a two-decade accumulation of "fertilizer" before Chris Langan rescued it with his CTMU.  It was even denied that quantum non-locality confirmed the CTMU, despite the equation of non-locality and metrical violation.  Langan had already explained that metrics, being parts of the computative syntaxes of dynamical transducers, could be computationally relativized to nested transducers in such a way as to resolve these violations while affording an elegant explanation of quantum wave function collapse.  Man oh man, the trials that Chris Langan had been made to endure!  Genius could be a long row to hoe for someone with no fat cat academic "mentors" willing to sponsor his radically superior ideas for a prestigious and potentially lucrative slice of the credit (funny, thought Jojo, how the sacred responsibility of such mentors to "protect the integrity of their disciplines" so often seemed to line up with the protection of their personal funding and reputations).  The clown suffered silently on behalf of his sadly misunderstood buddy, who had foolishly dared to weigh in on the scales of truth with no more than the certainty of being right.  Talk about your Don Quixotes!

Yet Jojo, with benefit of hindsight, knew that Langan's opponents had all been squashed from day one.  Langan's grasp of logic and reality was so advanced that it could be risky even to get an argumentative look on your face where he could see it, and his critics had argued without knowing the real extent of his ability.  For example, their journal Noesis had contained several citations of the notorious four-color problem of graph theory.  In one of these, it was mentioned that a pal of the editor had been working to shorten the computerized proof of the four-color theorem.  First, proofs are informational and must be relativized to the cognitive automata by which the information can be processed.  The proof in question involved millions of logical operations directly unverifiable by any human, and thus proved zilch relative to human cognitive capabilities.  If the four-color conjecture had become a "theorem", it existed only for human-digital cyborgs with split personalities whose two faces had no guarantee that they could trust each other.  Second, what Chris Langan knew about this kind of problem -- and about problems in general -- would ultimately send most four-color theorists and their machine programs straight into the academic fossil pit, there to R.I.P. on their tarred laurels.  

Jojo wondered how all those megamelons, who were aware of many of the paradoxes and inconsistencies riddling science and metaphysics, could by sound or silence reject the most general and necessary model in which "undecidable" mathematical and logico-philosophical conjectures become relativizable and solvable.  The situation had been truly bizarre.  But what goes around has a way of coming around, and the Noetic Society later met with a kind of poetic justice.  Chris Langan, after being criticized half to death by his fellow members, had told them that they risked wearing "a pair of huge floppy shoes, a red rubber nose, and a baggy jumpsuit with outsized polka dots and a big round crinkly collar" for failing to pay adequate attention to his explanations.  Jojo stared at his riotous reflection in the deli window and laughed aloud.  All right, so none of you had a clown suit to wear, he thought.  That's okay.  At least somebody can dress the part.  And tell when he's playing it.

See, a funny kind of game had been played right in front of all their noses, but in such a way that most of them missed it.  Langan had been trying to introduce a new theory, the CTMU.  The trick he had to perform: cram enough detail into an intelligible but maximally abbreviated account of his ideas.  He thought he was doing a pretty good job before a couple of members screamed like wounded peacocks, accusing him of "long-windedness" and other complimentary attributes.  All right, so they didn't care for his way with words.  Facing reality, he bowed out of the editorship like any duly-chastened "windbag" should have.  But then, from the soggy ash heap of rejection, a whole new perception of the situation seems to have arisen.  In effect, the CTMU was criticized for being incomplete and poorly reasoned.  Get a load of that!  Langan was cut off at the mike, and then harangued for not finishing his speech (if not for being a loony, slipshod crackpot to boot). 

Now, if there was some sub-rosa agreement that this was the best way to proceed, Langan was not a signatory.  There was no undertone of cooperation.  These people were simply being unfriendly to him, and it stank.  It was bad enough that he was cut off from conventional avenues; that he had been forced to develop his ideas utterly without support, acknowledgment, or encouragement.  But to give him (or watch him being given) the bum's rush was something like contemptible, particularly after he had donated valid resolutions of major paradoxes that nobody else could handle.  If that's the way science is supposed to work, then Murphy's Law qualifies as a crucial axiom of the scientific method.  While this would have come as no surprise to a long line of intellectual desperados -- guys like Copernicus, Galileo, and Galois -- it falls well short of the promotional hype advantageously used by the shiny, impeccably tailored "front men" of academia. 

According to them, the academic and industrial intelligentsia form a kind of "ecosystem" in which the "Darwinian competition" of ideas results in "survival of the fittest".  The only problem is,  these are fallible humans, not natural forces.  The front men even manage to create an impression that where conventional processes fail to reveal "the fittest" ideas because these ideas are too far out and iconoclastic, there exist "fail safes" sure to prevent them from being lost.  Fail safes like the MacArthur Foundation, which at one time was making a lot of noise about searching for "the new Einstein" in hopes of supporting his research.  Unfortunately, in true catch-22 style, such organizations wouldn't know "the new Einstein" if he walked up and kicked them in the whoopie cushion.  Instead, they rely on the "expert opinions of established authorities" in various fields.  The result? While Langan was crunching paradoxes, they were fixating on clowns.  No, we're not just talking silly people; the MacArthur Prize was once actually awarded to a clown who looked just like Jojo.[3]  Jojo had wanted to kick himself for missing out on that little opportunity, which would have catapulted him and his aging mother straight into a cushy condo in Westchester.  But at least he was in good company: if the MacArthur Foundation had existed in the time of Evariste Galois, the founder of the modern theory of algebraic equations, it would have "encouraged his genius" post mortem by at least half a century! 

Langan recognized all of this, and coped with the situation by doing whatever he had to do to support his own research.  He never kissed up to anybody, and he never made the slightest compromise regarding what he understood to be logico-mathematical certainties.  Knowing that nobody would stick up for the truth if he wouldn't, he tightened up his belt and ate crow until the Noetic Society provided him with a convenient way to introduce it.  No doubt about it, printing his theory in Noesis didn't offer much in the way of amenities.  But it did give him something he might not have been able to get any other way.  That is, no matter who squawked about his presentation, who objected to his personality, or who might have adopted his insight without a word of thanks or credit, he had established his exclusive authorship of what would ultimately prove to be the culmination of post-Aristotelian intellectual evolution.  It wasn't much, but at least it was something.  Langan appreciated the help, even if it had been like pulling teeth.  And he was still willing to cooperate with his fellow eggheads.

Being a realist's realist, Jojo knew that the Noetic Society was no group of dunces.  But it was also no wellsprings of sympathy and understanding where Langan was concerned, and Jojo -- when not hard at work on some gobbler -- was a lover of fair play.  Chris Langan was walking the walk; while the experts exercised their jaws, he dogged truth and meaning with minimal concern for his own personal  welfare.  With so many other birdlings in the nest of science peeping their little beaks off for food and attention, Langan had been nobody's darling.  He was accustomed to paying the price for his "lone-wolf" attitude.  But what really got Jojo's goat was the way the Noetic Society, which in effect billed itself as a mutual appreciation society for lonely geniuses at the pinnacle of human intelligence, had repaid Langan's insight with every particle of personal, political, and conceptually irrelevant chicken manure it could generate.  Like he was some guano-starved bean patch.

If any Noetic Society members had appreciated what Langan gave them, they were so intimidated by the chicken-manure hurricane he encountered that they scurried for cover like so many field mice, thus punctuating the hurricane with long spells of arctic weather.  After all, better to be a one-in-a-million hero than stand with a one-in-five-billion pariah who seemed to have finished last in the Noetic Society Mr. Popularity competition.  The amazing thing about it was, the way Chris Langan continued to voice respect for the intellects of his fellow members as they did their level best to frustrate him spitless while sabotaging the intellectual future of the human race.  How, long after others would have written them off, he refused to abandon them in the desert of ignorance.  Why, if the clown hadn't overeaten, he would have rushed straight back to the flophouse and composed volumes of soaring poetry to celebrate the perseverance of guys like Christopher Michael Chappelle-Langan!

Then the flashbulb of inspiration detonated like a loaded cigar in Jojo's teeming gourd, infusing him with a new and wonderful sense of destiny.  If that kid he'd hustled was really one of the smartest people in the world, then Jojo was in the wrong line of work.  Life as a clown had been good.  But his new life would be even better.  Armed with years of experience as a professional buffoon, Jojo was about to become...a politician!  He gazed serenely out the window.  It was autumn in Manhattan, and the Apple was a fat juicy pearl in the humongous gaping oyster that was the world.

COPYRIGHT 1991 by C.  M.  Langan.  All rights reserved.

[1]Jojo's mother, a gorgeous trapeze artist, had sent him to MIT for a year.  Jojo had been expelled for fleecing the eggheads, no big deal until he accidentally bilked the dean of admissions out of his cab fare one afternoon.  Nor had it helped when he pie-faced the chancellor on his way to the podium for one of those boring inspirational spiels to the student body.  This turned out to be a morale-booster far in excess of anything the highbrow had to offer.  Jojo was already a campus icon for his entertaining dress and behavior, and the students loved this prank so much that he thought they'd give him a medal.  Instead, he learned that good sports are about as plentiful among university administrators as ingenues in massage parlors, teetotalers in drunk tanks, and acrophobes at hang-glider conventions.  Jojo gladly bade the place good riddance, departing for the freer and more down-to-earth existence of street life.  Any drudge with a climate-controlled IQ could plug away at a place like MIT, provided he was willing to trim a few frills off his swinging lifestyle (at the height of his disaffection, Jojo had circulated a petition to change the school song to "M-I-T, K-E-Y, M-O-U-S-E...").  But the college of hard knocks was for the few and the proud, and the razor wit of a clown needed something hard to hone it.  To Jojo's diamondlike intelligence, the street had been a gemcutter's vise, and its harsh lessons the blows of hammer on chisel.


[2]a posteriori/a priori, mathematical


[3]In fairness to this recipient, Jojo seemed to recollect that he had been working with autistic or otherwise disadvantaged children and was therefore deserving...even if he wasn't a "new Einstein".