2025-04-09 NARRATION FOR FLATLAND

revision 2025-08-25 13:44:55

### Music: preshow music mix

### Music: overture, leads into DEB's operatic rendition of the Flatland dedication

PROLOGUE

Good evening. I'm going to tell you the story of Mr. A Square, based in part on his memoir, and largely on my own recollections; I knew him as well as anyone could, after all.

---

Mr A. Square, who is a four-sided square in the country of Flatland, is now a grizzled old shape of a man. A long and difficult life has brought him here, to this disreputable tavern here in Northern Port.

### Sound of the busy tavern fades in.

Oh! This is quite evocative already!

We see him now, surrounded by workers, irregulars, the fallen and the merely curious. Perhaps he is interesting, or inspiring. At any rate, he's bought the whole house a round of flatbeer, and perhaps there's more where that came from.

"Let me tell you about my land and its inhabitants," he begins.

The heckling begins as usual.

Taverner 1: "What? Again? We live here."

Taverner 2: "So I'm an irregular polygon, what of it?"

"Aye, well, yes, but humor me and let me restate these axioms. There may be unseen listeners to, aah, educate. Another round! And also, today, I may just have a proposition for thems of ye that might be brave or curious."

Taverner 3: "Or hungry!"

"Ye-essss."

My name is A Square, and I live in Flatland. I'm a mathematician by trade, and a geometer by inclination. I am a square, with four equal sides and four equal angles. My father, A Triangle, was but a humble dock foreman. I have several sons, all pentagons obviously. One of them A Pentagon, has children, a boy little H. Oh, and a girl, perhaps her name is Eta, I should have to ask my wife to be sure.

II. A. Square Explains The Natural Order

As your own mathematicians have taught you, so we know as well, that the Natural Numbers N comprise the integers beginning at 1, and ascending ever higher. And so here the Natural Numbers correspond to the Natural Social Order, which is obvious, undeniable and true. One who has more and finely-formed sides is of a higher class and rank than one with fewer or less-equal sides.

Each generation ascends a bit towards perfection. Our low-IQ Isosceles triangles do menial and dangerous work, construction and fishing and police work. And each generation may beget perhaps a degree or two to their pointiest angle until the blessed day comes when the proud family begets a perfect equilateral triangle!

Their happiness is, alas, short-lived, as this new primogenitor will be taken away from the low isosceles by the State to be raised by a family of better circumstance.

And so we have Triangles -- crew foremen and shopkeepers

Squares and Pentagons -- teachers and professionals

Hexagons through Octagons -- Scientists and Technocrats and Local Leaders

And beyond that, we have our gurus, priests, judges, governors, kings, CEOs ... Some have so many sides as to claim they are true circles.

Sadly some of our citizens are born with irregular angles or sides. In some cases these abnormalities can be surgically restored to conformity. In a few cases, they are irredeemable and the wretch must be destroyed. Some abominations are retained as specimens to be shown in our lower educational institutions, and truly the majority find usefulness as civil servants.

[SONG: Albert]

III. Of Women

(And here, please forgive me, these are A Square's words, not mine. A man of his world you know.) Ah yes you Spacelanders probably want to know about our females. They are all lines. Just one side or two depending how you count I suppose. No angle at all, and so not very intelligent. They just run our households and the like. Very pointy! Hard to see end-on of course, quite dangerous. We don't let them go to school. They have to sing at all times when in public. Just a matter of common sense safety of course. And sway their tail-points. Just to increase visibility you understand. Hah. Really there's nothing more to say.

[SONG: Deb "The Yodeling Song"]

And that is how the two ladies, Quee and Queg, decided to pose as an isosceles to try to make it in a Man's World. They became quite skilled with the harpoon.

IV. On Recognition And Social Intercourse

You begin to understand our world a little bit. We move about on our Plane of Flatland. All we can see ahead of us is in one line, light and dark. Our buildings are rigid and move little if at all -- I'll leave it to our physicists to ponder how that is. To recognize shapes we learn to interpret the subtle interplay of light and shadow in our world.

### Explanatory projections

A square seen diagonally may appear as two brightnesses, but from the side as just one. And if the light isn't good, every object looks about the same.

And so we are also taught to discern angles by "touch"; a typical bit of etiquette goes like, "Mr B, please allow me to introduce you to Mr C. Mr C, please feel and be felt by Mr B."

For a time, until it was forbidden, it was in fashion to paint our sides with colors, and our homes as well, and with a standard chromatic lexicon visual understanding was greatly improved. But no good idea remains uncorrupted; certain irregulars of a low moral standard would use paint to disguise their atrocity. Even worse, some women would color-wise disguise themselves as men of several, or even many sides. Although what cunning instinct led them to that accidental discovery remains of course a mystery.

[SONG: Julianne colors]

V. My, and Little H's, Introduction To The Third Dimension

On the last day of the year Nine Hundred Ninety Nine, I was at home with my family, discussing the year past and years to come with my sons and grandson, and my wife. And on to little games with my grandson Little H who certainly seemed bright enough.

scene with A. Square and Little H

### Overhead projector images

A: "What is this dot?"

H: "That's zero dimensions, zero, nothing!"

A: "Suppose I take three of these one-inch sticks end to end, what have we?"

B: "Why, gramps, that's three inches! (Quit poking me.)"

A: "Aha! Yes! Good! And if we take nine of these 1-inch-square leaves and arrange them, like so... ?"

H: "That's nine square inches!"

A: "Why?"

H: "Three to the first power is three, and three times three, three to the second power, three squared makes nine!"

A: "Good! And that, you see, is Geometry! The rest is, of course, commentary."

### Narrator whispers to H.

H: "(Cut it out! Ok ok ok I'll ask him.) Grampa? If three to the zeroth power is a point, and three to the first power is a line, and three to the second power is a square, what is three to the third power?"

A: "Aha! Ha ha! Nothing at all! Silly boy, Geometry is the world of two dimensions and it's late we must go to bed."

---

I lay in bed, somehow troubled by what Little H had said. My dreams were troubled, I felt on the verge of connecting to something larger. I dreamed... music?

[Song: Craig's "flatland!" ends with bells]

### Sound: midnight bells

I was awakened by midnight bells from the Capitol ushering in the New Millennium,

Scene with A, Mrs Square, and Sphere

A: [half asleep] "He is a fool."

Mrs: "Don't talk about your grandson that way! He's very clever."

Sphere: (offstage) "He's right you know."

Mrs: Who's that!

[they dash about the room looking]

Mrs: Who are you! How did you get into in our room? A! You promised to seal all the pinholes! And this... this lady shows up??

A: "I did, I did."

Sphere: "Fear not, I am no woman."

Mrs: (very agitated) "A Straight Line to the touch is worth a Circle to the sight,"

Mrs: "Feeling is believing!"

[ She touches the sphere ]

Mrs: "Oh my, Not a single angle! I'm so sorry, dear honored circle visitor! What brings you... can I get you a... I should have swept..."

Sphere: "I am in a certain sense a circle. Dear madam, please excuse us, as your husband and I require a 'conversation' on the nature of Geometry."

[ Mrs leaves the room ]

A: "Aha?"

Sphere: "The boy is no fool! You will see! Once, twice, thrice, 'tis done!"

[SONG: Martin "Into space"]

---

### Projection -- sphere in plane from original book

And oh I can tell you so little, but you unseen listeners will understand it all. The Visitor told me he was a circle of many circles, a Point at one end, much bigger in the middle, and a Point at the other end. That he, a "Sphere", touched into our plane and grew as he passed through it. Then he pulled me out of Flatland!

### Projection -- UPWARD NOT NORTHWARD

Upward, not NorthwarId!

As we whirled about in... "Space"... I had visions of my home, my family, the insides of houses and the insides of people!

I began to understand... "A Ha!!" I would understand what three times three times three... could mean. Yes... A cube! A. Cube?

I felt giddy. I begged of my new friend the sphere, What about a circle of four dimensions, or even five or six? A circle of circles of circleses of circlenia...

My guide The Sphere grew angry. "Foolish heretic!" And thrust me back to Flatland.

"A ha," I lamented.

[SONG: Steve "Back down"]

VI. On The Authoring Of A Manifesto

In the Year One Thousand, I went a little mad. I spent all my time in my study, writing and calculating and drawing what I could to explain the true Geometry of not two but THREE dimensions.

[SONG: Jay, style guide for a Manifesto]

### dvb Interruption 1 -- very brief

/ah, ah david maybe you could do this later, maybe ... at page 7 after "we persisted"? ("oh sorry") Where were we. Ok./

I cannot explain it (A. Square writes) but I believed the Sphere's vapors were still with me there, and tantalized my understanding.

I'm afraid I may have neglected my work and family obligations somewhat. No matter. The truth is the most important thing. I scribbled furiously, at times I ate nothing, or a little flatbread.

In the past, there were always stories of "Dimensional Reverts", though I did not name this connection to myself until much later. But around that time, apparently the problem had been growing, reports of "Dimensional Intrusion" had been coming in and the Authorities felt threatened, and were clamping down. Isosceles clusters marched through the streets, their Equilateral Leader demanding that heretics present themselves for reeducation. I did not realize it could be me.

One day, invigorated with the clarity of my proofs, I summoned my grandson Little H, who came in. His sister as usual tagged along but that's not important. (really now.)

Scene with A and H, and 2 Isosceles guards offstage

A: "Do you remember when you asked what does three times three times three mean?"

H: "Yes grampa!"

A: "Well, I suppose you may have been on to something when you said that perhaps it --"

H: "Oh no, grampa! That was just silly! I'm going back outside to play now goodbye!"

A: "Wait... oh."

[a beat passes, and isosceles guards arrive]

I: Are you Mr A Square?

A: Yes...

I: You're under arrest

[leads off stage]

VII. The Trial

[Song: david, The Trial]

I was sentenced to twenty five years in prison. Oh, I had the occasional visit; for the first few years I even tried to convince them, or anyone who would listen, that the third dimension was real, or at least imaginable. But then I stopped. I tried to unlearn, to forget. But then in a dream it would all come back, tumbling squares, cubes, spheres, and heresy of heresies spheres of spheres! It may or may not have been real, but it was all of it true.

And yet, true or no, real or no, in my heart of hearts I wish I had never met that circle of circles.

[Song: kristin, doing your time]

VIII. The Beginning

### Sound: TAVERN AMBIENCE returns

That was 25 years of misery. But here I am. Which brings us to now, to here, to this tavern. I have some considerable resources, let's just attribute it to exponential interest.

You've come to know me these past months, and I know some of you. We are preparing a great expedition. It will be dangerous.. but we must do this ..

"For knowledge!"

TAVERNER 1: "Who cares?"

"To prove the hypocrisy of the circles, the oppressive status quo, we're all equal!"

TAVERNER 2: "yeah um, we're fine here"

TAVERNER 3: "we've all got color tattoos, nobody cares"

TAVERNER 1: "i don't even know what shape i am"

I pondered. It was a last gambit, but not untrue.

"Well, then I've heard the angle-fishing isn't what it used to be --"

TAVERNER 2:"Now he's gonna tell us about edge warming"

TAVERNER 3:"you can't deny the catch is getting smaller"

"And the best source of blubber. the blobfish, are all but gone."

TAVERNER 1:"Daddy triangle got one once, but i've never seen one"

"Well this Spherefish I'm after... it's the biggest fish that... you literally can't imagine."

"ohhhhhhhhh!"

And that did the trick, said Mr A. Square to himself.

SEGUE

### Media: The Building Of The Flatship, repetitious music and overhead, creating the PQ. (stylized as pq-vector)

And that's how Mr A Square, my grandfather, came to be leading a perilous adventure across and beyond the Flat Sea. Our lengths were so small when he was arrested, and saw him so little in that interval.

It was a time of terrible social and political dimen-sha.

My brother H, just an inch or two then, was caught up in that twisted patriotism. Two words. Just two words was all he needed to say to the triangle leader... and our own grandfather A was arrested and taken from us for half a lifetime. I wish I could say I tried to stop him.

We never spoke of it, not once. Yet... Little H became a lead physicist at Flat National Labs. That vector was of course not available to me, a "lady". But I helped where I could. Growing up, we spent so much time with grandma, and in A Square's old office. I read his notes obsessively. And... I think there was something in the air left over from that Sphere.

My brother's grand project to build a Flatship able to move in direction Z was, of course shut down by the authorities. Nevertheless... we persisted.

And our ship the PQ did get built.

### dvb interruption 2 -- on the original show's duration

/Yes, david, thanks for that, very interesting./ so anyway

We did assemble a crew of derelicts and irregulars from that tavern. But I will mention especially our Harponeer Quee Queg, the most important crew mate on any blob fish mission. Her... their benevolent duplicity saved us all.

ACT TWO

I. A Voyage Extended

Once, twice, thrice, 'Twas done! Our Flatship eventually became a SPACE ship. But we'll come to that.

The rest of this story comes from Quee Queg's voyage diary of the 64 day journey.

WEEK 1

[Entry by QQ.]

It was a jolly beginning. Captain Aha obscured for a day or two, but by midweek he was drinking flatrum with the rest of us. One night he did launch into a confusing monologue. Something like: "So you see we can dissect a square into a circle... but only if the edges are of fractional dimension... my granddaughter Eta made some childish nonsense about it, so foolish, really, but it got me thinking it was possible. But Damn! and Alas! By that self-same reasoning, a sphere could be dissected into two spheres both equal in volume to the original." I put these fanciful nonsense words, sphere and volume, exactly as he spoke them.

WEEK 2

[Entry by Quee Queg.]

Captain Aha has continued with his benign but eccentric behavior. He has been formulating a duty roster by which he aims to reduce repetition and therefore boredom. He speaks of our watch bill as having been reformulated as an aperiodic tiling based on diagonalized transcendentals. Well it has certainly reduced boredom this much we do confirm.

[SONG: deb sea shanty]

WEEK 3

[Entry by QQ.]

Today I share the work of some of our crew members who have devoted considerable time studying & enumerating the varieties of angle fish and other ocean life to be found.

[SONG: Hothousers]

WEEK 4

[Entry by QQ.]

Beginning to run low on stores, we hunted for food. It was a merry chase but we bagged an exceptional blubber, high angle and filling. In the midst of our celebrating and catching us an unusually agreeable mood, Captain Aha told us that the true nature of our journey was to leave Flatsea entirely, and pursue, here he used that strange word again, the sphere. And something about a new frontier called space. I, Quee Guess, was supremely excited. There is no target in the Flat that I cannot harpoon. Am mightily inspired to try something new. Space, let's try it.

WEEK 5

[Entry by QQ.]

We have now been in space -- yes I use the word freely now! -- for exactly one week, for 8 days. These last four days we have survived a storm, a terrible vortex, a three dimensional vortex which took us to strange lands. We came upon LINELAND, whose king could never meet his neighbors. Then further down the vortex we came to POINTLAND, whose only inhabitant was GOD and knew of no other.

[SONG: Virginia, lines and points]

WEEK 6

[Entry by QQ.]

After we escaped the vortex, we had a most curious encounter. We came alongside another vessel, a flatship like ours, also a spaceship. But its people! They were profoundly irregular, soft sided and uncountable, like tiny blubbers. They knew of our Flatland! They said they had met some of our circles, and had nothing nice to say about them. I believe the words "stupid" and "pompous" may have been used.

[Song: jason, the chromatists]

This other flatship. They... they have seen the sphere. They told us it was near our own home, past the straight of triangles.

### dvb interruption 3 -- on etymology and Theron Dramus's interest in the Banach-Tarski paradox

WEEK 7

[Entry by QQ.]

I can't. We just can't. We've come full circle as it were. From "space" we could SEE FLATLAND! I saw inside their houses, I saw what happens in the circle's mansions. The depravity. Here is the truth and we tell it to you. Circles die and break apart leaving a brood of tiny isosceles triangles. High and low. They hide this. They hide this.

[Song: Jay & Co]

WEEK 8

[Entry by QQ.]

We have found the straight of triangles. The sphere is near. We begin.

[Song: Final Battle]

The rest were on their way home to Flatland. Captain A-ha and Quee Queg were adrift on a fragment of their boat.

Aha: How ever is your harpoon so sharp? The others, they got home ok. I'm sure.

Quee Queg: We are drifting parallel to the plane. / This is our end

Aha: Yes. No. I'll crack this timber right here, and you will go down to flatland. And I... will see more of spaceland.

Quee Queg: I need to tell you something / We are not an icosceles.

Quee: I am Quee

Queg: And I am Queg.

Aha: You're... you both are... I thought we were having a bromance!

Quee: we were, captain

Aha: But the two of you...? Hm. Aha.

Queg: It was fun

Aha: and with a twist like this, Downward, not Southward you go!

all: good bye good bye

Aha: ...you could still find husbands...

Sphere: They can't hear you.

[Song finale]

And with that, once, twice, thrice, Tis Done.