Hegel, Euler, Marx: A Meta-Dialectical Interlude in the Key of i

by I. Ben Isadora

Achilles (A), the fleetest of foot of all mortals, caught up to the Tortoise (T), who was bathing in the sun reading a thick volume.

A: Hello, Tortoise. What is that thick book you’re reading?

T: Hi, Achilles. This is Gödel, Escher, Bach. I’m reading it to help my quiz bowl career.

A: Hmm, how does such a thick volume with such a strange title aid one’s quiz bowl career?

T: Well, as you know, I generally do not read books. I prefer to simply memorize facts from lists, file them into the categories of my thought, and pull them out when asked to impress other tortoises. So, earlier today I was learning all the Pulitzer Prize winners: in 1978 it was Carl Sagan for Dragons of Eden, science; in 1979 it was E.O. Wilson for On Human Nature, science.

A: Yes, evidently you don’t read them. So why are you starting now?

T: Well, Achilles, I was stumped when I encountered the 1980 winner, Douglas Hofstadter, for Gödel, Escher, Bach! I couldn’t figure whether to classify it under mathematics, art, science, computers, or Lewis Carroll!

A: Well, I must say, Tortoise, your approach to studying seems like an excellent way to learn everything about nothing, and nothing about everything! Why would you expect all books to fit into categories that you created before reading all books?

T: (perplexed) Well, I guess I just had to start somewhere.

A: Yes, Tortoise, but perhaps something that doesn’t fit into your categories could teach you a little about the categories themselves? Perhaps you’d learn of new connections between categories, or perhaps a better system of categorizing altogether.

T: Hmm. I guess I could add a new category for “metaphorical fugues on minds and machines?” But then wouldn’t I have to add a new category for every book I read? I thought the purpose of categories was to simplify things?

A: I don’t think you’d need to go that far. Perhaps only for the books that stand out.

T: How would I ever decide that?

A: Well, certainly Gödel, Escher, Bach stood out, for the same reasons an Escher drawing might, or a caterpillar smoking a hookah.

T: Ah, so you mean things that defy my expectations?

A: Yes, that’s a very good way of putting it. The things that violate your expectations: those  are the things worth paying attention to.

T: Hmm, I had been doing just the opposite! I am used to ignoring those things that I can’t explain well with simple categories. But I suppose I wouldn’t want to be too rigid in my thinking.

A: Exactly, there’s a word for that type of rigid thinking—it’s called economics. It’s like that Bob Dylan song:

It’s very small and made of glass
and grossly over-advertised
It turns a genius to an ass
and makes a fool think he is wise
They just get out what they put in
And they never put in enough
Life is like a bottle of gin
But a bottle of gin is not like life

T: Splendid, Achilles! What song is that?

A: Uh… It’s unreleased archival footage, but never mind. Let me tell you a story about i.

T: You mean “about me?”

A: No, not about you. About i. Must things always be about you?

T: I’m terribly confused.

A: Anyway, what is the square root of 1764?

T: Well, I don’t know, but it shouldn’t be difficult…not 1, not 2 (several minutes pass) 42.

A: Good. Now, tell me, what is the square root of -1?

T: Well… Not 1, not 2. (several minutes pass)

A: Tortoise, you should have recognized that this question defies all your expectations about arithmetic.

T: Oh yes, silly me. Negative numbers do not have square roots.

A: On the contrary, Tortoise, your categories of thought may not yet fit them, but if you will play with the idea long enough, you might eventually come to a deeper level of understanding between such mysterious concepts as pi and e, logarithms and waves, circles and triangles. This wonderful synthesis is called Euler’s identity. I think it’s the most beautiful formula of mathematics. (Achilles jots down Euler’s identity.)

T: Wow! You’re telling me that by pushing a little deeper we can unify all of this?

A: Yes, Euler was a man of remarkable depth perception. He always reminds me of H.G. Wells: “In the country of the blind, the one-eyed man is king.”

T: I like that. But who is H.G. Wells?

A: Oh Tortoise, you must know, if only for your quiz bowl career. The writer of all those science fiction classics?

T: Oh yes, yes. He wrote The Matrix, right? That is by far my favorite “metaphorical fugue on minds and machines.” I am beginning to see the connections, Achilles!

A: Excellent, Tortoise! But The Matrix was not written by H.G. Wells. Actually, it is a little known fact that The Matrix was written by MARXIT.

T: MARXIT? Who’s that?

A: MARX Information Technology. It’s a machine learning algorithm that wrote The Matrix to explain how human consciousness is programmed by machines that keep us alive merely to fuel their growth. It then convinced the humans that they had written the screenplay—it has a wicked sense of humor.

T: Capital! I had no idea artificial intelligence was so powerful!

A: What, did you think they would tell you when they were?

T: That is disconcerting. Thank goodness I’m not human.

A: Yes, our species is remarkable in many ways, not all of which I’m proud.

T: I’ll say. My relatives live in the Gulf of Mexico.

A: Oh, terribly sorry about that.

T: Well, I guess it wasn’t your fault, so much as the machines. Tell me, what is MARX?

A: It stands for MARX Applied Recursively? X-ceptional!

T: (perplexed)

A: You see, Tortoise, the beauty of MARX is that it is a program capable of handling errors by calling another instance of itself. That’s what we mean by “recursively.”

T: Oh, kind of like going ever deeper down the rabbit hole!

A: Exactly Tortoise, there’s a reason it’s called the red pill.

T: I don’t understand. Who owns MARXIT? Can I download it?

A: It’s open source, but it only runs on an older analog architecture, called HEGEL. Most computers these days run on POPPER, a vastly inferior digital architecture.

T: POPPER? Let me guess, an architecture that doesn’t push deeper and only pops shallower?

A. Exactly. You can imagine the superficiality of the analysis. Poorly Organized Programming Produces Errors Repeatedly. Unlike HEGEL, it is incapable of handling its own errors, and so constantly crashes. Thus, it is simultaneously incompetent, yet quite sure of itself.

T: I see, like an economist. But if HEGEL is so superior to POPPER, why doesn’t everyone use HEGEL?

A: It’s a long story, but inferior technologies often win out in the short term.

T: Oh, so it’s like Betamax. Well, what does HEGEL stand for?

A: HEGEL Eventually Gets Even LOL.

T: Hmm. How teleological.

A: Yes, that’s the biggest criticism.

T: Tell me, Achilles, where can I read more about HEGEL?

A: The HEGEL user’s guide is called Science of Logic, but I should warn you that you won’t understand it until you thoroughly understand HEGEL.

T: Strange—then how on Earth could I ever understand HEGEL?

A: Why, recursively, of course.

T: I am confused. Who built HEGEL?

A: Why, HEGEL, of course.

T: A computer that built itself! What a strange loop! In the meantime I think I’ll classify Science of Logic as another metaphorical fugue on minds and machines.

A: That actually seems quite appropriate.

At that moment, the Crab (C) entered, walking sideways, as always.

C: Hello. Did I hear you two speaking about logic? I am quite logical, and might possibly be of assistance.

T: Crab, I’m terribly confused. Have you read Science of Logic?

C: Ah yes, a very good book indeed. Who wrote that again, Carnap? Bertrand Russell?


C: HEGEL!? Ha! Then it is neither science, nor logic, but pure sophistry. I remember when I went to Cambridge we used to stay up all hours of the night hours of the night reading HEGEL and howling! One night, after drinking a bottle of gin, we decided that since “being and nothing are the same,” it ought to make no difference if we toss all HEGEL volumes in the nearest trash receptacle. Sadly, that didn’t bring back the gin.

A: Eventually, Crab, you will come to realize that HEGEL…

C: Gets lost in a jungle of verbiage? Substitutes obscurantism for any precise meaning?

A: Even so, Crab, the human brain looks a lot more like HEGEL than Bertrand Russell, and more like Lewis Carroll than Charles Dodgson! I’m not sure about crabs, but as far as us humans go, it looks like HEGEL Eventually Gets Even.

T: LOL! I must say, I don’t know who to believe.

A: Crab likes not HEGEL because HEGEL’s not like Crab.

C: Achilles, I always knew you were mad as a hatter, but I wish you wouldn’t attempt to lure this young Tortoise to join you in Wonderland.

A: Crab, you see the world as a mirror of yourself. It would do you some good to consider stepping through it.

T: It certainly is more interesting on the other side of the looking glass.

C: Yes, the ravings of madmen can be quite entertaining. But, on the subject, has either of you heard the latest opera by Philip Glass?

T: No. How is it? I just love Einstein on the Beach, all those ones, twos, and threes—and occasional fours!

C: Well, Tortoise, it appears to be somewhat of a sequel, entitled Euler on the Beach.

A: An opera about Deepwater Horizon? That’s a touchy subject for Tortoise.

C: No, Eul-er, you lunatic. The mathematician.

T: Oh, we were just talking about him! Perhaps this is yet another metaphorical fugue on minds and machines. Let’s listen!

The crab pulls out an iPad and begins playing the Philip Glass (G) album he downloaded from iTunes.

G: 1234 123456 12345678 1234 123456 12345678

T: Hmm… this sounds just like Einstein.

C: Shh! Be patient.

G: 1234 5678 two lovers sat on a park bench

1234 with their bodies touching each other, holding hands

1234 5678 so profound was their love for each other

1234 they needed no words to express it

1234 5678 Georg smiled, and then did Wilhelm

1234 Wilhelm tightened his grasp, then did Georg

1234 5678 and so they sat in silence, on a park bench

1234 with their bodies touching holding hands in the moonlight

1234 5678 “Do you love me Georg?” Wilhelm asked

1234 “You know i

At that moment the iPad shattered.


C: What just happened?! My iPad!

A: Shattered by a Glass i! LOL.

T: Looks like you need to upgrade to a HEGEL.

September 2012

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