Dess(e)ins d’Enfants: the Meno Upgrade for a Constructivist Genesis

This step-by-step construction about the natural implications of our direct experience of reality was written spontaneously in response to yet another article on quantum physicists “proving” something in an overly complex way. I realized that I could explain the basic mechanics underlying what also inevitably leads to their conclusion in a way a third grader could understand using the format of Plato’s Meno dialogue.

A key element to watch for is the simple step that avoids the self-referential gridlock of Russell’s set theory in Part III. We head the Russell car pile-up off at the pass through a single step that accomplishes both reification of and reflexivity within the pair. You can see exactly where the logicians encountered the self-referential hall of mirrors and thought backing away was their only option. Reification by way of reflexivity using orientation is the natural solution.

The following dialogue unifies epistemology and metaphysics through a radical, constructivist genesis on an elementary school floor mirroring Alexandre Grothendieck’s dessin d’enfant. We construct a space with no axes, no coordinates, and no numbers mirroring Hamilton’s Icosian Calculus (itself the first recorded dessin d’enfant!).

PART 1: Lefty Loose-y, Righty Tight-y

EXT. ELEMENTARY SCHOOL – 11:44 A.M.

RACHEL stands before the blackboard a classroom of elementary school children.

RACHEL: "Okay class. Today we're talking about reasoning and how we know things. Because we don't want to just memorize facts, we want to be able to learn things ourselves! Sometimes grownups make mistakes too about what they think.

Now. If a person wanted to tell you which side of this rectangle divided into to two equal squares this dot is on..."

RACHEL uses chalk to place dot inside right square of rectangle.

RACHEL: "What would they have to do to decide if it's on the left or on the right?"

PATRICK: "I KNOW!!!!! I KNOW!!!!!!!"

JANIE—the teacher's pet — and PATRICK— the life-ruining-level-if-not-guided ADHD x dyslexia disruptor kid —both raise their hands.

RACHEL: "Patrick, I love the enthusiasm but we need to take turns and let other people talk too. Yes, Janie?"

JANIE: "They would have to use the angles to measure the lengths of the lines and then plot where the point fell on the graph to see where it was."

RACHEL: "That's good thinking Janie, and that will be VERY useful for the next question I ask so hold onto that thought. But there's something a little more simple underneath that we need to know whether it's on the left side, or the right side."

PATRICK squirms in his chair trying to hold back an outburst.

RACHEL: "Okay Patrick, let's hear it. How do you know if it's on the left or the right?"

PATRICK leaps up from chair, holds up hands in front of face staring at 90 degree angles of thumbs and index fingers like he's an auteur capturing a shot.

PATRICK: "Lefty loose-y, righty tight-y!!!!!!! It's a righty tight-y!!!!"

RACHEL: "That's RIGHT, Patrick."

JANIE looks aghast and the whole class confused at the world shakeup of PATRICK scoring a point over JANIE.

RACHEL: "See, we can only decide if something is on the left or the right if we are looking at it from a perspective. Everyone try something. Join Patrick in standing up."

The class is doubly shook by PATRICK being used asa n example to imitate.

RACHEL: "Okay, everyone hold up your hands like lefty loose-y, righty tight-y. What's something in this room on everyone's right side just like this dot in the rectangle."

PATRICK: "THE DOOR!!!! THE DOOR!!!! WE ALL HAVE THE DOOR..."

RACHEL: "Okay Patrick, yes, we all have the classroom door on the right side. But we need to let others talk too, remember? Okay now everyone keep your hands held up and turn around facing the back of the class. Now, what's something we all have on the left?"

CLASS MUMBLING IN UNISON EXCEPT A MIFFED JANIE: "The...door... "

RACHEL: "Yes! Okay, can you see how…"

PATRICK, who had already lost the thread continuity between following instructions to turn around, turns back around to the front to address RACHEL..

PATRICK: "NO THE DOOR IS ON THE RIGHT LEFTY LOOSE-Y RIGHTY TIGHT-Y WE SAID IT'S..."

RACHEL: "Okay Patrick, I'm actually glad you said that right now because that highlights the main point. Hold your hands up again and do lefty loose-y righty tight-y."

JANIE smirks. World continuity is restored to the classroom collective consciousness. PATRICK regroups his auteur stance with his two hands making 90 degree angles between the thumb and index finger.

RACHEL: "Okay but turn around again."

PATRICK turns around.

RACHEL: "Alright, now what is something righty tight-y that you see right now?"

PATRICK squints into his hands.

PATRICK: "The window?"

RACHEL: "Yes! Now turn around again and tell me something you see that's righty tight-y there."

PATRICK: "The door. WOAHHHHHHHH."

RACHEL smiles. She wants him to still feel the energy of that initial win.

RACHEL: "Uh huh! Okay, you all can sit down now."

THE CLASS takes their seats.

RACHEL: “So you can see that when we say something is on the left or the right, it depends on where we are looking at it from. The geometry like Janie suggested can tell us where a point is on a graph in terms of number coordinates on a graph, but it can't tell us if it is objectively on the left or the right. Because that requires a reference frame and perspective from an observer looking at it."

PATRICK is already lost in his own geometry world, drawing the 'Universal S' onto the wood of his desk.

RACHEL: "So now, knowing this... what would happen if this chalk dot WE see on the right side of the rectangle was drawn in marker on transparent glass. And another class on the other side of the glass looked at it, and was asked to say what side of the rectangle it was on for them?"

Some kids glaze over, and some turn their heads and hands toward the back of the classroom trying to calculate the answer with their bodies.

RACHEL: "Yes, Justine."

JUSTINE answers timidly.

JUSTINE: "It would be on the...left?"

RACHEL: "YES! And I saw you turned around to figure that out. But you can remember as a rule that if someone is facing you and you see something on the right, that person is seeing it on their left. That's why, because 90% of us are right handed, when we shake hands with someone using our right hand it creates a diagonal with the other person's right hand. Everyone find a partner."

The kids in THE CLASS rise to their feet and partner up.

RACHEL: "Okay, face one another. Now shake hands with your right hand, notice the diagonal, and say the universal Peter the dolphin constructivist greeting: ‘Hello. One, two, three.’"

THE CLASS giggles and shakes hands reciting the line. JANIE blushes at the un-seriousness occurring in SCHOOL.

RACHEL: "Now everyone take righty tight-y and point and look to the right."

THE CLASS follows this injunctive prompting.

RACHEL: "Now take lefty loose-y and point and look to the left."

THE CLASS again follows the instructions.

RACHEL: "What do you notice?"

THE CLASS mumbles in unison.

THE CLASS: "We look the opposite ways."

PART II: Inside-Out Distributed Axes Emerge

RACHEL: "That's true. Now notice there are two types of pairings happening here. Some of you are facing each other with one partner's back to the window with the other partner's back to the door. And some of you are facing each other with one partner's back to the blackboard, and the other partner's back to the coat rack in the back of the classroom.

So some of you you probably noticed that when you turned your head and pointed one way maybe depending on how you existed in space compared to your other friends you weren't just pointing to the right, but to another pair of people!

And maybe it was even a pair of people who had a different configuration than yours – say a pair of back-to-blackboard and back-to-coat-rack people, whereas your pair had one of you with their back to the window and another with their back to the door. So can I get four volunteers to come to the front of the class."

PATRICK beelines for the front, abandoning his partner. AETHAN and BODHI, just underneath PATRICK in the ADHD pyramid, also hustle to the front.

RACHEL: "Patrick, we don't just abandon our friends like that. Please ask Ava if she wants to come to the front too."

PATRICK: "Ava!!!! Come on!!!"

AVA blushes and walks to the front of the class.

RACHEL: "Okay now Bodhi, Aethan. Face one another and one of you stand with your back to the window and the other with your back to the door. Move a little closer to the desks, next to the overhead projector."

BODHI and AETHAN reposition themselves.

RACHEL: "Patrick and Ava? You two face each other and, um... Patrick, how about YOU put your back to the class so you're just focusing on Ava and Ava put your back to the blackboard."

PATRICK and AVA find their stance.

RACHEL: "Okay. Now that we're all set up like this, everyone point and look to the left. Note what you see."

THE CLASS all point to left.

RACHEL: "Now everyone point and look to the right and note what you see."

THE CLASS all point to right.

RACHEL: "Alright, Patrick and Ava. What did you see."

PATRICK: "Ava."

RACHEL: "Well, that's not what I was going for but this is indeed the proper orientation of things and that attitude will go far with the ladies and in life, Patrick. Ava, what did you see."

AVA: "First I saw the door, then I saw the window."

RACHEL: "Good. Did you see anyone else, any other pairs when you were pointing and looking left and right."

AVA: "No!"

RACHEL: "You're tracking things perfectly. Okay, Bodhi and Aethan."

BODHI and AETHAN snap to attention from their emerging slap fight.

RACHEL: "Guys, what did you see?"

BODHI has clearly already lost the thread.

BODHI: "Ummmmm..."

JANIE raises her hand.

RACHEL: "Yes, Janie."

JANIE: "When Bodhi looked to the left he saw the class and the coat rack at the back of the room, and when Aethan looked to the left HE saw the blackboard side where he ALSO saw Ava and Patrick.

When Bodhi looked to the right he saw Ava and Patrick and the blackboard, and when Aethan looked to the right he saw the coat rack behind the class."

RACHEL: "Amazing. Let's leave the class out of it for now as we're not part of the experiment, but you've demonstrated that even though YOU are not standing up with a partner doing the movements yourself you were able to track the reference frame and perspectives of Bodhi and Aethan AS IF you were them from a higher vantage point by imagining their perspectives and relations.

Alright class, this one's a hard one so I'll just tell you the first part. Ava, Patrick, look and point to the right."

AVA points to the right.PATRICK startles to attention and points the same way as her to the window with his left hand.

RACHEL sighs.

RACHEL: "Okay Patrick, hands up. Lefty loose-y, righty tight-y. Find your RIGHT hand and point to the right..."

AVA impatiently grabs PATRICK’s right hand with her left and pulls his arm into position. She then drops her left hand while maintaining her point to the right.

RACHEL: "Great, I'm gonna eyeball measure this, ballpark... looks like the length of their arms like this is three and a half feet. Okay you two, switch to the other arm and flip pointing directions please."

PATRICK and AVA point each left.

RACHEL: "Still about three and a half feet no matter pointing left or pointing right because each partner-facing-partner's side is using the opposite arm, making for a continuous length. Whether..."

RACHEL notices BODHI and AETHAN have resumed their slap fight, and chooses not to pick the battle.

RACHEL: "Whether Bodhi and Aethan have their turn seeing Ava and Patrick first or second as they take turns looking to the blackboard direction, they always perceive a continuous length of them as a unit.

And they see Ava and Patrick one at a time as a unit in their turns pointing, but Ava and Patrick never see them when they point! That's because of their orthogonal orientation to one another in space, which is the classroom itself. Okay, two more volunteers please."

A COUPLE KIDS raise their hands.

RACHEL: "Oliver, Georgia. Okay, you two come riiiight up against the door. Face each other in the same pairing as Bodhi and Aethan with one of your backs to the door, and one of you facing the other. Then hold up opposite arms out wide."

OLIVER and GEORGIA arrange themselves.

RACHEL: "Okay, now Ava, point and look to the left aaaaaand..."

RACHEL rushes over to intercept an emergent PATRICK fumble to keep flow and pulls his left arm out as he giggles.

RACHEL: "What do you see?"

AVA: "Oliver and Georgia!"

RACHEL: "Yes! And when you flip arms, Patrick would see Oliver and Georgia on his turn. So now YOU can see someone, who can't see YOU. And because they're waaaaay over there in space and not lined up with you like Bodhi and Aethan are, they can't see Bodhi and Aethan either.

So the line from Bodhi and Aethan's pointing intersects with the continuous three and a half foot long line segment relative to them that Patrick and Ava make.

Thus, their point can ‘see’ Bodhi and Aethan which they perceive as having length from the edge of one hand to the edge of the partner's hand... no matter if Patrick and Ava are pointing left or right. Which it doesn't seem like Bodhi and Aethan can tell if they are on left or on right! It's an illusion of the same thing from that vantage point.

Because Oliver and Georgia are lined up with the line of Patrick and Ava's pointing– even though they're in the same opposite configuration like Bodhi and Aethan are – they are able to see them in the same way Bodhi and Aethan saw Patrick and Ava: as a singular line segment. With no ability to tell which partner is using which arm, or if they are both on pointing left or pointing right.”

PART III: Reifying Reflexivity in the Primitive Solves Russell’s Paradox& Generates Contagious Noncommutativity

RACHEL turns and points to JANIE.

RACHEL: “Janie.You were already thinking like 10 steps ahead when you gave that very good answer when I first asked how to tell if the dot inside the rectangle is on the left or on the right."

JANIE blushes, vindicated. Classroom world continuity has never been better.

RACHEL: "Come be my partner in the aisle of the classroom."

JANIE stands up chin up, chest out, like she's balancing books on the top of her head and proudly strolls to the center aisle.

RACHEL: "We're gonna do something different here. So let's line up exactly on the line with Bodhi and Aethan. I’ll face the door, you face the window.”



RACHEL and JANIE take their positions in the aisle behind BODHI and AETHAN.

RACHEL: “Okay, everyone, everywhere, point left.”



BODHI points to RACHEL pointing at BODHI/RACHEL points to BODHI pointing at RACHEL on the handshake diagonal type arrangement.

RACHEL: “Now everyone point right!”



AETHAN points to JANIE pointing at AETHAN/JANIE points to AETHAN pointing at JANIE creating the opposite diagonal.

RACHEL: “Bodhi, Aethan, and Janie. On the count of three everyone call out if it was right or left when we pointed at each other. One, two, THREE!”



BODHI, AETHAN, and RACHEL shout in unison, with JANIE’s response emerging in the trail of theirs.

BODHI: “Left!”

AETHAN: “Right!”

RACHEL: “Left!”


JANIE: “Right… but not really.” 



JANIE smirks
. She’s getting the hang of this game.

RACHEL: “Excellent, Janie. But me and the boys weren’t totally wrong either. That’s how we experienced it! And since we are lined up exactly on the line with Bodhi and Aethan, unlike how pairs perceive one another when intersecting orthogonally it seems like we can kind of get some type of information from this.

Let’s call Aethan ‘A’ for Aethan, and Bodhi ‘B’ for Bodhi. Since your handedness is tracking with Aethan, you can be ‘A’ in our pair and I’ll be ‘B’. 



This part’s gonna be confusing, so don’t worry if you don’t get it. In fact, you shouldn’t. Cover your ears unless you’re Janie or… maybe, weirdly, Patrick.

Let’s spread out a little to where WE as a unit are on a diagonal to one another and not perfectly overlapped. It still looks like a solid wall to an orthogonal intersecting perspective, but now we have a new dimension emerging.

Bodhi, Janie? Stay where you are.

Aethan? Follow my lead and move a few feet toward the front of the classroom.”

BODHI and AETHAN spread out, now overlapping only on their fingertips.

RACHEL: “Since we can’t agree about whether it’s right or left when we point to one another, we are going to make something like a constructed consensus handedness here between the two of us in this same configuration on the same line.



So everyone point right.”



EVERYONE points to the right.

RACHEL: “Now since we have staggered, we can count pointing right as pointing to ourselves as a unit, via ‘A’ and ‘B’ inside our pair pointing to one another on a diagonal just like how it seemed like we were pointing to one another on a diagonal both times before we spread out!

Now, everyone point to the left.”



EVERYONE points to the left.

RACHEL: “Okay, Janie. Now we see that our pairing as a unit is pointing to the Bodhi/Aethan pairing as a unit. But not both times like before, just when we each point left. You don’t have anything in your line, so you’re just pointing to the coat rack. The boys are blocking the blackboard and Ava and Patrick from my line of pointing, so I’m just pointing to them as a unit.

Since now that we have consolidated our parings like this I no longer have any way or reason to distinguish who of them is pointing. I just know that they are pointing to me, and I am pointing to them. I can’t tell that they’re pointing to Ava and Patrick, but I know that they could be pointing to some other entity or, like you, just pointing to one of the four edges of our space.



Class, you can pull out your coloring books by the way. Don’t worry about this part. Really.”

BODHI and AETHAN start to move.

RACHEL: “Not you guys though. Everyone standing, remain in your positions. You bought the ticket, now you gotta take the ride. Play patty cake or something.”



BODHI and AETHAN resume their positions (and their slap fight).

PART IV: Idempotent (Anonymous,Relational) Identity

RACHEL: “Alright, Janie. Swap spots with me.”

JANIE and RACHEL switch positions.

RACHEL: “Now point to the right. Boys, you too.”



EVERYONE points to the right.

RACHEL: “Same deal right? We’re pointing to the right, so we are pointing to one another and not to anyone else as are the boys.

Even though you’re now over there on what we previously decided was the ‘A side’ — since everyone on this side was named ‘A’ and all ‘A’s scooted a little to the front when we made our new pointing to one another in our pair when pointing right, and pointing outside to other things when pointing left rule. So it seems that since you are now on the ‘A side’, you would be ‘A’ now, right?”

JANIE: “Yes, I am on the ‘A side’ now so I’m ‘A’.”



RACHEL: “But are you really gonna let going somewhere else change your IDENTITY though? If I asked you to swap desks with Patrick, would you be Patrick?”



A few EAVESDROPPING COLORERS snicker.



RACHEL raises her voice as she addresses THE CLASS.

RACHEL: “We’ve got just a few minutes before the bell, kids. All partners stay where you are, but I want everyone else to push the desks to the corners of the room to show one last thing to Janie before recess.”

THE KIDS put their coloring books in their desks and push the desks out of the way, forming a circle around BODHI, AETHAN, JANIE, and RACHEL. PATRICK abandons AVA to join the flurry of movement.

RACHEL: “Let’s have us go back to how we were before. I’m on the ‘A side’, and you’re on the ‘B side’. We point to one another when we point right either way, just like before.”



JANIE and RACHEL switch positions again.

RACHEL: “Now grab my right hand with your right hand, and start to spin by walking backwards until your back is facing the blackboard instead of the door.”



JANIE and RACHEL rotate in unison.

RACHEL: “Great, that’s good. K, stop. Now what’s happened? We’re now in an orthogonal position to how we were in the same configuration as Ava and Patrick are!

Here, after rotating, we are not just limited to where Bodhi and Aethan or anything that showed up along the line to the coat rack were our only options. Now neither of us are on the ‘A side’ or ‘B side’ technically, at least relative to where we were before, because we are on a totally different axis.

We could each point to the left and refer to things along this line if we wanted to. So it seems we aren’t defined by where our backs are facing if we can rotate like this. We can point to a different range of things!

Keep grabbing my hand and walk backwards again until your back is facing the window, like how you were when we swapped positions for a minute earlier.”



JANIE and RACHEL rotate in unison again.

RACHEL: “Wow! Look what’s happened here. You were back on the ‘B side’ like how we started all this, where your name was ‘B’. But me and you NEVER SWITCHED SIDES like we did the first time, and yet now here we are where you seem to be on the A side’ and I’m on the ‘B side’.

But we didn’t switch positions, or change names. If we HAD changed names and switched positions — where you were ‘A’ after the switch, and I was ‘B’ — and then done the same rotation after the switch… then you’d be my side, the ‘B side’ right now, but you would have taken on the name ‘A’!”

JANIE gulps. PATRICK barges into the scene.

PATRICK: “So I was right? Righty tight-y’s always the same no matter what happens? I told you the door was always righty tight-y.”



RACHEL: “Actually Patrick, in a weird way, you’re kinda right. But that rule ONLY applies when it comes to your partner, who for all intents and purposes is 1/2 of your SELF. And you can’t experience right in two different ways, can you? It’s always only just righty tight-y with your same hand.

If you somehow strapped the door onto a cart with wheels, said the top was right and the bottom was left, and made the door your counterpart and the center of your world then never let go of it whenever you rotated… then yes. Righty tight-y would always be the same no matter if you were looking at the blackboard, the coat rack, the window, or… ummmm…. the hole where the door used to be.”



The bell rings. PATRICK beelines for his door. JANIE’s only comfort is the fact that the buzzing anticipation in the lead up to recess meant that nobody except her and PATRICK heard ANY of that. She tries to manually execute a force wipe of the events of the last two minutes from her mind, PERMANENTLY. RACHEL senses her discomfort and moves in as the class clears out.

RACHEL: “Hey, Janie. Look at me. Your first answer is the one they’re gonna ask you to write down on your geometry tests for the next 10 years. Just think of the pairs we all were as singular points on a graph, and don’t give any mind to the whole door-on-the-wheel-cart thing.

Your answer that you swapped to the ‘A side’ and became ‘A’ by moving is technically right too! That’s how all computers work. You had the right answer. But…”

RACHEL laughs.

RACHEL: “Weirdly enough, Patrick did too. But only contextually ‘right’ within this last step, in a way that would never actually happen, right? Go play. I’ll see ya tomorrow.” 


JANIE lets out a small exhale as her shoulders visibly drop. The classroom world snaps safely back into alignment. Her signature poise returns as she grabs her backpack and runs out the door into the sunshine and crisp spring air.

RACHEL shakes her head and her face twists into its own JANIE smirk as she realizes that JANIE was actually originally named 'A' when identity was assigned by the mapping of handedness relative to another set of twins. Both teacher and student were momentarily faked out by the concept of 'the A side' during the step where 'the same side' staggered to reify uniform identity of the twin unit.

Slippery, all of this is! One can see why Russell got tripped up. And yet the problem itself demonstrates the inevitability of its solution. It is an eigenform. The one-step reflexivity and reification solution also implicitly births a third element: recursion. This trifecta — in combination with primordial difference — combines to encompass all of the elements required for computer science.

PART V: Dasein d’Enfants

RACHEL walks over to the window, watching the clusters of kids and their various activities. JANIE has instantly snapped into the rules of the playground grid as she directs the setup for a game of four-square with a group of girls. When you’re managing a room full of people who need the walls to stay still, compassion means meeting them exactly where their coordinate system is. You stretch their capacity, but ultimately you give them the map they need to survive the day.

Movement catches her eye, and RACHEL tracks the path of this lone variable.

It’s PATRICK. He isn’t playing four-square. He isn’t in a group talking about gossip or grades. He’s sprinting through the clusters of groups with a huge grin on his face and without any discernible goal in mind. She envisions his left loose-y, righty tight-y hands framing his face like an auteur getting a shot, building a brand new horizon on the fly with every stride.

RACHEL smiles, leaning her forehead against the cool glass which offers contrast with the stuffy centrally heated room. She’d just told JANIE that PATRICK’s world was a glitch, something that could never actually happen in real life. But looking at him now she knows the absolute reverse is true.

When you decide the door is always on the right you extract the boundary from the cave, mount it on wheels, and take it with you. Maybe that helps reduce everything down to where no matter what is actually on the left or the right it always reduces to whichever “Ava” is standing directly in front of you in a given moment.

Of course, PATRICK doesn’t know any of this consciously. And yet he’s the only one out there who simply lives by the premise that if you aren’t afraid to ask a stupid question or punch a hole through the space you’ve been given... you can step right through the puncture and see the whole machine from the inside out.

Note:

1. All pointing-out happens in synchrony between twins. Pointing-in and pointing-out are a state that mutually toggles. There is no “pointing out on one side only”.
2. I used the filled-in vs. outline-only arrows to clearly show where one side of a twin set is pointing to another twin set vs. the other side not (highlight emergent noncommutativity).
3. I kept all twins in a state of pointing-out to demonstrate how relationships begin to make directed patterns.

The Genesis of Form: Computation Didn't Just Drop from a Coconut Tree

"I don't know what's wrong with you young people. You think you just fell out of a coconut tree? You exist in the context of all in which you live and what came before you."
- Kamala Harris, certified noncommutativity & deixis respecter

Mainstream computer science treats the foundational primitives of code as if they were invented in a vacuum by mid-century academics. But if you back up the tape and track what actually happens when distinction is enacted in the wild you discover a precise, natural embryology. Computation doesn't start with arbitrary syntax; it spawns organically the exact moment a primordial difference (א/ת <—> ת/א) undergoes a localized, 720-degree orientation flip as in Section III of this dialogue.

This diagram maps the inescapable, space-like sequence that is paradoxically experienced as a one-step solution and yet establishes reflexivity & reification as prior to recursion which generates reality's native operating system.

Reflexivity (the observer's double-pointer flip) and Reification (the structural snapping of relational identity) acting upon a Primordial Difference generates Recursion.

Recursion is not an independent actor; it is the stabilizing byproduct born of the tripod.

🕯️ In memory of Richard Tieszen, who directly facilitated so much of the foundations of my present work. In 2012 I wrote a paper for his wonderful “Epistemology or Metaphysics?” seminar on Plato’s Meno dialogue, phenomenology, quantum virtual states, and the XOR function. It all comes full circle and what was then but an exploration now finds its conclusion.