Five Rings for the Electoral Kings

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David Byron

David Byron is a software developer working for the military-industrial complex. At Popehat, he writes about art, language, theater (mostly magic), technology, lyrics, and aleatory ephemera. Serious or satirical poetry spontaneously overflows from him while he's recollecting in tranquility. @dcbyron

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9 Responses

  1. CTrees says:

    Great bit of work, David. This makes me miss writing for college – in my industry, we seem to believe words are our most valuable resource, to be doled out as parsimoniously as one is able.

  2. Rich Rostrom says:

    two adherents to a particular subset of a particular religion would have greater chances of successful conflict resolution than members of two mutually exclusive faiths would have

    I disagree strongly here. Members of different faiths are far enough apart that they can agree to disagree. Members of rival sects within a single faith often find it impossible to tolerate one another.

    The heretic is hated worse than the infidel.

  3. David says:

    Maybe. I suppose it varies with circumstance and opportunity.

  4. deadcenter says:

    "Musashi here calls attention to the notion that winning the battle and winning the war are two different and not necessarily concomitant things."

    Our involvement in Afghanistan during the Soviet occupation is a perfect example of this. We spent billions aiding the resistance but not a penny to rebuild the country afterwards and were surprised by the outcome.

  5. IGotBupkis, Sailing the Economic Seas Betwixt Scylla And Charybdis says:

    Two people committed, for example, to the guidance of formal logic, to empirical data (confirmed to a high degree of probability), and to a foundational set of axiomatic principles have a prospect of settling any disagreements that may arise between them. All such disagreements would be, by definition, a consequence of the incorrect application of logic, incorrect evaluation of data, or misapprehension of axioms.

    Mwaaahahahahhaaaa, grasshoppa, you step into my little web, all the better to eat you with, my dear!!!

    Actually, no — Gödel's incompleteness theorems identify that it is actually literally impossible to create a truly complete, fully inclusive system, even in mathematics, much less something as muddy as English.

    More simply, in any given set of Rules, there Must Be An Exception To The Rules. Add in that exception to the Rulebook, and you will find that there is yet another exception which it will not include… lather, rinse, repeat, for as long as we both shall live…. plus a few trillion years

    If it weren't the case, there'd be far less need for lawyers… :D

    God might be able to do it, but He operates outside of our Frame of Reference, and so does so in violation of that rule as a result. Heck, perhaps the reason for the GITs is God. He's the outside component of the universe that completes it… :D

    As a result of this, your assertion, "All such disagreements…" is inherently defective, as it may come down to a differing interpretation of the Exception to the Rules.

    One exception that many who went beyond Algebra in High School is from Geometry… It's usually Euclidian Geometry taught in High School, with its notion of a plane as a "flat" surface projecting in all directions to ininity. Now, if you happen to recall anything at all from waaay back then, you might not have a hard time with the fact that there are "23 definitions, five common notions, and five postulates" — you might recall that four of those five postulates are fairly self-evident "axioms"… they are remarkably easy to grasp, and one has no problem at all with understanding the inherent "truth" of them…

    Well, not so for the fifth of them:
    "The Parallel Postulate"

    This postulate is much more complex and nontrivial to explain. Essentially, it says that, in any given plane, given any three non-collinear points, there is EXACTLY one single pair of parallel lines running through them. That is, any other two lines intersect, if each of them passes through one or two of the points (the "non-collinear" codicil excludes any three points which fit into a single line)… note that this description is actually called "Playfair's axiom", an alternative description derived much, much later.

    Now, it's much more subtle about this axiom but this ties to a whole bunch of other moderately significant concepts — for example, another way to state it is that all three angles of a triangle total 180 degrees (this was Euclid's original description, in fact). The two statements are virtually interchangeable, violating one means violating the other…

    Now, the thing is, that there are at least two other systems which "argue" over this basic exception — either the angles of a triangle add up to less than 180 degrees ("Hyperbolic Geometry") or greater than 180 degrees ("Elliptical/Spherical Geometry")

    In the former, the shape of a plane more closely resembles what one thinks of as a saddle, and there are an infinite number of lines passing through a given set of three points which are parallel to each other.

    In the latter, a plane is basically the surface of a sphere or an ellipsoid, and essentially all lines are "world lines", that is, the intersection of a "classic, Euclidian plane" with the sphere or ellipse, and running through (in the sphere's case) the center… that is, there's no such thing as parallel lines at all.

    A really simple way to look at this is "zero, one, many". That is, either the system breaks down into zero options, one option, or an infinite number of options. This occurs all through mathematics — zero and one have unique properties that make them distinct from other numbers — other numbers do not have such distinctions from one another, for most mathematical purposes, 5 and 100 are indistinguishably nondifferent (yes, there are exceptions, outside the realm of this discussion).

    I mention the zero, one, many choice because it's often a crux point where such "exceptions" lie — usually there's a choice between those three options, and there's no inherent reason why one is "more correct" than the other two… we just choose which one to accept as a rule and then see what happens.

    But, like with the parallel postulate, the other options are fully internally consistent systems with valid real-world applications of their own.

    Spherical trigonometry, an obvious outgrowth of spherical geometry, for example, has a great deal to do with navigating around the world and identifying the relationships to stars in the sky and/or using data about the placement of those to tell you where you are on the earth's surface with a fairly high degree of reliability. Long before Riemann started playing with the parallel postulate in the mid 1800s, European sailors had learned the precepts to navigate reliably all around the earth for a couple centuries while no longer tethered to the sight of land.

    Anyway, end of today's Math & Real World lesson:

    even given a thoroughly competent and well-defined set of axioms, there will always be exceptions to the rules which lie outside the answers which can be derived from those axioms.

    That's why, as much as we want to, even if we DO Kill All The Lawyers, they will, of necessity, spontaneously regenerate, the inherent zombies of the universe.

  6. IGotBupkis, Sailing the Economic Seas Betwixt Scylla And Charybdis says:

    Oops, forgot the closing line:

    That’s why, as much as we want to, even if we DO Kill All The Lawyers, they will, of necessity, spontaneously regenerate, the inherent zombies of the universe. How's that for Job Security?
    :D

  7. David says:

    I appreciate the invocation of the Name of Goedel, which, of course, settles any casual dialectic about provability and completeness!

    Not quite. I've written a little about this elsewhere (ca. 1998), so rather than take us far afield, I'll just note that provability in a logical formalism and conflict resolution among persons are two rather different domains. Ponder that, and you'll grok my point above… grasshopper. ;)

  8. IGotBupkis, Sailing the Economic Seas Betwixt Scylla And Charybdis says:

    I tend to disagree with the very notion that there is any real distinction to be made with regards to mathematics vs. "human knowledge".

    Math is the least fuzzy of all the sciences, solely because it does deal with the most concrete, knowable entities we have access to. To argue that a mathematical proof about completeness says nothing about the possibility of completeness in less well-definable, still more fuzzy entities is relatively absurd.

    Not saying you can't say you know something, only that that claim resides in the realm of Faith and not in the realm of True Knowledge.

    Moreover, the explicit statements you provide, to wit:

    the guidance of formal logic, to empirical data (confirmed to a high degree of probability), and to a foundational set of axiomatic principles have a prospect of settling any disagreements that may arise between them. All such disagreements would be, by definition, a consequence of the incorrect application of logic, incorrect evaluation of data, or misapprehension of axioms.

    expressly derides the presence of any vague "transcendental" knowledge that you are attempting to suddenly add to the mix in order to dodge Gödel. Any such system of reasoning or argumentation will, inevitably, include items where two reasonably distinct and mutually exclusive elements — exceptions to the rules, if you will — may arise and from which contention can and likely will exist, regardless of the intellectual honesty and the devotion of the individuals to conflict resolution and devotion to following the rules… At some point, everyone has to "agree to disagree": discord is inherently built into the universe**.

    A Christian would interpret it, almost certainly, as a sign of Original Sin. That it had to exist before Adam or Eve touched the apple is a discussion for another time.

    ==================

    ** I think the real magic comes when you start applying the Iterated Prisoner's Dilemma to that inherent discordia. You want a subtle proof of God (He won't give you a complete one, merely a suggestion of one), I'd argue that Fits The Bill. To take a dreary, bleak fact of universal discord, like the basic Prisoner's Dilemma, and covert it into a sign of hope and promise requires Real Magic.

  9. David says:

    1. Mathematical entities are abstract, not concrete. Having two rocks is not the same as having the number two. (A nominalistic attitude toward abstracta does not vitiate this point.)

    2. The epistemological question is not reducible to mathematics. To say that Bubba knows X is to say, at least (Gettier notwithstanding), that X is true, that Bubba believes that X is true, and that Bubba has sufficient warrant to believe that X is true.

    One might satisfy the conditions of knowledge while falling far short of mathematical analyticity. There's a "real difference between mathematics and human knowledge", unless you're prepared to exclude all synthetic truths or (denying the analytic/synthetic distinction) to claim that anything not known perfectly is not known at all.

    I cannot join your fantasy that all "True Knowledge" is exclusively "mathematical knowledge". See whether Spinoza or Pythagoras is available.

    3. The assertion you quote does not "deride" (sic) the "presence of any vague 'transcendental' knowledge"; rather, it presupposes transcendental conditions of its own possibility.

    4. You propose "agreeing to disagree" as the alternative to "a prospect of settling any disagreements" where those are, by definition, a consequence of the incorrect application of logic, incorrect evaluation of data, or misapprehension of axioms. But "agreeing to disagree" is simply one means of settling a disagreement, and the initial statement you're trying to criticize entails it as an option.

    Your confusion on this point appears to arise from your failure to distinguish "settling a disagreement by reduction" from "settling a disagreement by recognizing its irreducibility" and your failure to recognize that both were always already in scope.

    5. Your thoughts on irreducibility, presented as "discord", are interesting, but do no damage to the point of the essay.