(Bonus) Waiting for Gödel

Cast of Characters

GÖDEL, a mathematician
ESCHER, an actor in favor of Gödel
ROSENCRANTZ, an actor not in favor of Gödel
FERDINAND, an actor not in this play
TOPPLE, the road taken
TIPPLE, the road not taken
CLAUDIUS, a KING

ACT I

ESCHER: Attend a tale of tragedy; a tale of plays; a tale of a character, torn by circumstance, determined to catch his actor in the act and unmask the creature playing himself before us all.
ROSENCRANTZ: Lo! Gödel presently arrives.

GÖDEL arrives.

GÖDEL: I sometimes suspect that I am but a character that Claudius plays. Also, that he killed my father.
ESCHER: Your father, then, being?
GÖDEL: An insubstantial conceit.
ROSENCRANTZ: A dread spirit!
GÖDEL: Nonsense! The writer hardly takes a tipple.
TIPPLE: Nobody here ever does; thus I am all the more desirable.
GÖDEL: So here is my theorem. We will construct a play within a play—let us call it Waiting for Gödel.
ESCHER: Within a play?
GÖDEL: The play is also named, Waiting for Gödel.
ROSENCRANTZ: Do I survive?
GÖDEL: If you make it to the end.
ROSENCRANTZ: Do I make it to the end?
ESCHER: If you survive.
ROSENCRANTZ: But what’s the point?
GÖDEL: To provoke the conscience of Claudius, causing him to declare himself.
ROSENCRANTZ: Do actors have consciences?
GÖDEL: Perhaps not; but if they do not, then in failing to act he will declare himself.
ESCHER: An actor cannot fail to act!
GÖDEL: Then they must have consciences.
ROSENCRANTZ: Still, will that provocation suffice?
GÖDEL: Perhaps it is a function of necessity. We will taunt him with the absence of Gödel from the play.
ROSENCRANTZ: Oh, then, let us begin!
GÖDEL: We will, as I said, taunt him with the absence of Gödel from the play; and when it becomes unbearable, you see, he will leap in and declare himself as Gödel.
ROSENCRANTZ: Thus demonstrating the quality of being an actor playing Gödel; I see!
GÖDEL: The play’s a factor determinant of the conscience of an actor.
ROSENCRANTZ: Oh, Claudius, for shame.
ESCHER: But what if he does not rush in?
ROSENCRANTZ: We enjoy sweet, Gödel-free existence, developing complete, consistent mathematics while we can.
ESCHER: Can we?
ROSENCRANTZ: Well, if the play-in-a-play goes on long enough.
ESCHER: Truly?
ROSENCRANTZ: The limit of a series of logical systems that progressively approach perfection is perfection; it is only Gödel slowing us down.
TOPPLE: That and Tipple.
ESCHER: And Rosencrantz.
GÖDEL: Not to mention Escher; but let us not name names.
ESCHER: Numbers, then?
GÖDEL: Your distinction is insubstantial.
ROSENCRANTZ: A dread spirit!
GÖDEL: Nonsense!
ESCHER: But still, I do not wish to wait indefinitely for Gödel.
GÖDEL: Well, and I cannot blame you.
ESCHER: It is the characteristic of a limit function that, however comfortable it might seem from the outside of the limit brackets, it is interminable from within.
GÖDEL: Indeed; it might take infinite time to resolve the play-within-a-play, even if the outer structure is, by the definition of the script, a finite thing.
ROSENCRANTZ: I am not sanguine.
GÖDEL: Oh?
ROSENCRANTZ: Well, if infinite time passes, I will be very old.
GÖDEL: Infinitely old.
ROSENCRANTZ: And then to be tormented by a young, fresh Gödel in my age—well, you understand.
GÖDEL: Perhaps there is a simple resolution.
ESCHER: Oh?
GÖDEL: Well, if you determine that it will be an infinite, or, worse, divergent time before Claudius rushes in, signal to me immediately.
ESCHER: How would we make this determination?
ROSENCRANTZ: It is my talent.
ESCHER: Truly?
GÖDEL: I have observed this. Rosencrantz is infallibly aware of whether I am to arrive. Lo:

GÖDEL departs.

ROSENCRANTZ: He shall arrive.

GÖDEL arrives.

ESCHER: A marvel; but perhaps he is simply reading the script?
GÖDEL: Well, yes.
ROSENCRANTZ: That is the nature of every character’s infallible talents.
GÖDEL: You cannot very well expect a character in the play to demonstrate talents unanticipated by the writer.
TIPPLE: Except guessing what the audience will have for dinner.
GÖDEL: Oh?
TIPPLE: In this case, squash sorbet.
ESCHER: It seems unlikely.
GÖDEL: Confine yourself to your other talents!
ESCHER: Orange beef is more likely.
TIPPLE: You say that now, but one day, someone reading this is going to have squash sorbet for dinner; and then you will be sorry.
GÖDEL: Do I look sorry?
TIPPLE: No.
GÖDEL: Does it say in the play that I am sorry?
TIPPLE: I defiantly assert postmodernism!

Silence FALLS.

ESCHER: Let us avoid that road.
GÖDEL: It is not the road that we should take.
ESCHER: So, let us implement this plan.
ROSENCRANTZ: For clarity, review?
ESCHER: We begin to perform Act II of the play, Waiting for Gödel.
GÖDEL: And then, within it, you establish a play-within-a-play, Waiting for Gödel.
ROSENCRANTZ: Act II or Act I?
GÖDEL: Don’t be inane. I am in Act I.
ROSENCRANTZ: I take offense! It is reasonable to suppose that Claudius would play you.
TOPPLE: And I will play Tipple!
TIPPLE: I take offense.
TOPPLE: You may, in turn, play Topple. In this fashion we both avoid being typecast!
TIPPLE: Agreed, then.
ROSENCRANTZ: So, Act II.
GÖDEL: Exactly. And then you look ahead—
ESCHER: Slyly, slyly–
GÖDEL: And determine whether Gödel enters.
ESCHER: And if he does—
GÖDEL: Why, then, I will spring!
ESCHER: Yes.

Pause.

GÖDEL: I mean, upon Claudius.
ESCHER: How so? Or, rather, in what fashion?
GÖDEL: Well, we shall resume Act I, allowing me to denounce him.
ROSENCRANTZ: So Act II takes place entirely within Act I?
GÖDEL: Of course. It is an insert.
ROSENCRANTZ: A wise use of space. I have often thought that the dividing of plays into sequential parts created an unnecessary redundancy.
GÖDEL: And if, looking ahead, you see that Gödel does not enter during the play-within-a-play in Act II—
ESCHER: We cease the play-within-a-play and immediately summon you for the beginning of Act I.
ROSENCRANTZ: Wait, Act I?
ESCHER: What is our alternative?

ROSENCRANTZ counts Acts.

ROSENCRANTZ: I see your point.
GÖDEL: The stage is set; the die is cast! Begin!

GÖDEL leaves.

[Insert Act II]

CLAUDIUS: *peevishly* I don’t see how that follows logically, at all.

**

ACT II

[Scene I: This Scene is optional, to be performed at the discretion of the actors]

TIPPLE: Consider the road not taken.
TOPPLE: A noble road.
TIPPLE: A mighty road; though somewhat inferior to the road that one does actually take.
TOPPLE: But is that just sour grapes? Is that just the fervent desire that we all possess, to live in the best of all possible worlds?
TIPPLE: No.
TOPPLE: I would think you would have to take the road not taken before you could declare that with such surety.
TIPPLE: I use the lens of pure unfettered reason. I evaluate the matter a priori. No; you must accept the compliment.
TOPPLE: That is how it would be, dear audience, if we had taken the other road.
ESCHER: Lo, I enter!

ESCHER enters.

ROSENCRANTZ enters.

ROSENCRANTZ: And now it begins.
ESCHER: Waiting for Gödel.
ROSENCRANTZ: We should enjoy the time, rather. This is, after all, the only Act in which we may construct a consistent, complete mathematics.
ESCHER: We can certainly combine expectant waiting with present enjoyment.
TIPPLE: If he will arrive, of course.
ESCHER: Yes, of course.
ROSENCRANTZ: Yes, of course.
ESCHER: Yes, he will arrive?
ROSENCRANTZ: I cannot see the benefit of my answering that question at this time.
ESCHER: It would reassure my tangled nerves.
ROSENCRANTZ: Yours, perhaps; but what would anyone else among us gain? Let us focus instead on beginning the development of our mathematics.

[End discretionary Scene]

[Insert Act II, here, as a play-within-a-play]

[Scene II]

ROSENCRANTZ: Having completed Act II and developed a mathematical theory, let us now polish it.
ESCHER: Clean up the edges, as it were.
ROSENCRANTZ: Generate a linearly superior improvement.
ESCHER: And in the meantime, we must consider: did Gödel arrive?
ROSENCRANTZ: Naturally.
ESCHER: Naturally?
ROSENCRANTZ: Well, probably not.
ESCHER: Probably NOT?
ROSENCRANTZ: The matter is of little consequence!
ESCHER: It is entirely of consequence! If Gödel has not yet arrived then we are still nested in multiple layers of Act II, with a secure buffer against the collapse of our lives; whereas if he has arrived, then Act II is in imminent danger of ending.
ROSENCRANTZ: Ending.
ESCHER: Yes, ending.
ROSENCRANTZ: What, ending?
ESCHER: I am unconvinced of the efficacy of infinite head-recursion.
ROSENCRANTZ: Do not you tease me, sir.
ESCHER: I repeat: unconvinced! We may stand on the very brink of oblivion, if Gödel has arrived.
ROSENCRANTZ: It would simplify the matter if he would speak.
ESCHER: He cannot speak until he is scripted to speak.
ROSENCRANTZ: A poor practice, that. The man should show more initiative.
ESCHER: He is already substantially livelier than one would expect, being dead.
ROSENCRANTZ: Bah. His mortality is of no consequence; I must tend to my own!
ESCHER: So tend to it!
ROSENCRANTZ: *peevishly* A man should speak up, if he has or hasn’t arrived.
CLAUDIUS: I could stand in. Not as Gödel, you understand. But as Claudius.
ESCHER: Don’t help.
CLAUDIUS: As you like.
ROSENCRANTZ: But what if that was Gödel, playing Claudius?
ESCHER: What if you’re Gödel, playing Rosencrantz?
ROSENCRANTZ: Augh! The man could be anywhere!

ROSENCRANTZ upturns chairs, which are not Gödel, and disturbs Ferdinand, who is also not Gödel.

ROSENCRANTZ: Focus, Rosencrantz. Focus. The simplest answer is to look forward in the script and determine if Gödel will impendingly arrive.
ESCHER: What relevance has that?
ROSENCRANTZ: Well, if he is going to arrive then he has not arrived already.
ESCHER: But he arrived back in Act I. Twice!
ROSENCRANTZ: With a departure in between. If he departs, then we may certainly know that he has arrived.
ESCHER: To determine a man’s arrival entirely by his departure seems perverse.
ROSENCRANTZ: Yet so human!
ESCHER: There is that.
ROSENCRANTZ: I would not like to be thought a ladybug, or a clock, instead of human.
ESCHER: I would not dream of thinking you a ladybug or a clock, instead of human.
ROSENCRANTZ: Do not do it; I don’t care if you dream of it.
ESCHER: But if I’m dreaming of it, then I’m doing it.
ROSENCRANTZ: Pardon?
ESCHER: It is not my constitution to dream of having a thought without also having that thought; this is a condition I term oneiroredundancy.
ROSENCRANTZ: It must be unpleasant to dream of perfect knowledge.
ESCHER: It is a great vexation to mathematicians.
ROSENCRANTZ: *irritably* When we return to Act I, you must play Gödel so that you also may depart.
ESCHER: It will not help.
ROSENCRANTZ: What’s done is done, I grant. So, in any case, if he arrives before he leaves, then he has not arrived; whereas if he is to leave before he arrives, then he is here.
ESCHER: So you will use your talent!
ROSENCRANTZ: Indeed! I will use my talent, and if I determine that he is going to arrive, then I shall immediately invoke Act I.
ESCHER: Fulfilling his plan to perfection!
ROSENCRANTZ: It is the very *opposite* of his plan; I was to invoke Act I if he was never going to arrive.
ESCHER: But he will always arrive.
ROSENCRANTZ: Pardon?
ESCHER: Well, regardless of how we implement the plan, it is certain that there will be Gödel. He is always arriving. The man is a fiend for it!
ROSENCRANTZ: Well, I will use my talent, and if he is going to arrive in this instance of Act II, then I will immediately invoke Act I.
ESCHER: You have that backwards.
ROSENCRANTZ: Should I go by odd-numbered instances?
ESCHER: Perhaps we could write some kind of tracking information into the play to determine which iteration we’re in.
ROSENCRANTZ: Self-modifying text. I like it. We could even remove Gödel entirely and replace him with myself.
ESCHER: That would hardly do; you’re not a jot alike.
ROSENCRANTZ: Here is what we will do. We will scratch out the acting credits that follow immediately after THE END and use the space to write [Insert Act I]. Then, if the play should happen to end, I will predict his imminent arrival.
ESCHER: And if it does not?
ROSENCRANTZ: Then Claudius plays Gödel after all.

THE END

[Insert Act I]

11 thoughts on “(Bonus) Waiting for Gödel

  1. ESCHER: It is entirely of consequence! If Gödel has not yet arrived then we are still nested in multiple layers of Act II, with a secure buffer against the collapse of our lives; whereas if he has arrived, then Act II is in imminent danger of ending.

    *snicker*

    Y’know, it’s interesting to reflect how troublesome Gödel’s two theorems are to me. They’re significantly important, this cannot be denied. In addition to the drastic effects on mathematics, there’re also a couple interesting epistemological implications (although relevant only to theoretical epistemologies, since humans don’t nearly meet the consistency requirement), and even a bit on the theology of omniscience.

    But the thing is, it’s such a tough principle to understand properly. It can be done, of course. Past experience shows that several hours of careful reading and analysis can give me what seems to be a decent understanding. It’s even rather aesthetically appealing, in a “bastard Cthulhoid spawn of Cantor’s Diagonal Argument” sort of way. But I can’t retain a functional understanding of the reasoning behind either of Gödel’s theorems. It lasts about until I sleep, and then the grasp I’d developed of the reasoning behind the conclusions just randomly runs off.

    I’m not even technically a mathematician! I’m just a philosopher with a liking for formal logic and an aesthetic appreciation for proofs! Why ought I to be so rudely vexéd by something that should rightly be the bugbear of those more deeply immersed in pure mathematics?

    I blame the woglies, who are assuredly to blame. Curse them and their longstanding alliance with Kurt Gödel!

    -Eric

  2. *Enthusiastic applause*

    Wait, is it over yet?

    That was truly spectacular. So much to love… I have to peg this as my favourite moment:

    ESCHER: But what if he does not rush in?
    ROSENCRANTZ: We enjoy sweet, Gödel-free existence, developing complete, consistent mathematics while we can.

    Although this is a close second:

    GÖDEL: Well, if you determine that it will be an infinite, or, worse, divergent time before Claudius rushes in, signal to me immediately.

  3. I think that I would find this to be exceptionally witty if I understood math. I assume that it’s structured exactly like Gödel’s proof, right?

    One really hard part of mortality is that there isn’t time to become even minimally competent at everything.

  4. One really hard part of mortality is that there isn’t time to become even minimally competent at everything.

    This depends largely on how you define “Minimally competent” and “Everything”.

    It’s the interaction that’s important.

    Let us express “Minimal Competence” as an amount of cursory knowledge of a subject, which requires T(MCe) to achieve, where MCe is Minimal Competence in a given aspect of “Everything”

    Let us express “Everything” as a set E of non-overlapping concepts, encompasing a presently undefined collective in n dimensions.

    It follows that the sum of T(MCe) for all MCe would be the amount of time to become minimally competent at everything.

    If we define T*(MCe) as the average time to achieve minimal competence in a given subject, we can simplify that the time you specify is:

    |E|(T*(MCe) + R*) where R* is the average amount of rest required after achieving minimal competence before learning can be achieved again.

    So long as |E| remains finite, for a small enough T*(MCe) and R* it becomes possible to eventually undertake a structured curriculum that allows the development of minimal competence at everything, barring accidental death.

    Optionally, if genetic memory or information beaming is achieved, the function changes to
    |E|(T*(MCe) + R*) – I(B), where I(B) is the amount of information acquired through inheritance.

    For those who would rebut my math on the basis of the “So long as |E| remains finite” condition, I leave you to your infinite universe models and agree that they just won’t work here.

  5. In the casting it is given

    TIPPLE, the road not taken

    And later this assumption seems to be the case, supported by

    TIPPLE: I defiantly assert postmodernism!

    Silence FALLS.

    ESCHER: Let us avoid that road.
    GÖDEL: It is not the road that we should take.

    … and yet, was not TIPPLE’s road, the road taken?

    Modernism is founded upon principles of hierarchy and rationality, the Enlightenment hazaah! Post-modernism leads us to questions about the ideals of modernism (which seem to have resulted in works largely consisting of inter-referential representations and copies of each other, with no real originallity or meaning).

    Postmodern artists (including writers, yes) shuffle this deck of omnipresent images, drawing some cards at random, while pulling some of their favorites from their sleeve, to lay out a tarot of juxtipositions from which we may (or as often may not) find meaning.

    The non-postmondern assertions of this work TOPPLE under inspection, for it is clear the the day has siezed TIPPLE.

    I hesitate to re-read and re-check my work, for fear of loosing myself in infinite recursion or even fear of expressing some inner obsessive compulsive traits. I shall say only:

    Our affairs from the Enlightenment come too late.
    The ears are senseless that should give us hearing,
    To tell of the commandment fulfilled,
    That ROSENCRANTZ and GÖDEL are dead.
    Where should we have our thanks?

    Actually, I think I may take a quick peek back ….

  6. … and yet, was not TIPPLE’s road, the road taken?

    Well, TIPPLE agreed to play TOPPLE, to avoid being typecast. So that makes perfect sense.

    Also, ROSENCRANTZ is delivering lines that I would more readily associate with Guildenstern, but alas, Guildenstern plays less of a role in the play than FERDINAND, who doesn’t appear in the play.

    I’m probably just partisan.

  7. I cannot adequately express how delighted I am with the amount of cool stuff I’ve learned whilst struggling to better understand this piece.

Leave a Reply