2: Tenjou Nanami and Schrödinger's Cat

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Qualia the Purple

Arc 2: 1/1,000,000,000th of a Kiss

Chapter 2: Tenjou Nanami and Schrödinger's Cat

By the way, have you ever heard the word "qualia"?

It's sometimes explained as the "nature of feeling," and in short, it refers to the sensation born in your head when you feel something. The feeling of "red" when you see something red, the feeling of blue, or of purple... people might be looking at the same color, but depending on their circumstances they might interpret that color in various ways. That feeling is referred to as "qualia."

Of course, this definition extends beyond purely visual stimuli like red or blue.

For sound, touch, smell as well... all the subjective experiences born from the five senses, and all sensations in general, had associated qualia.

For instance, even pain had qualia.

When we got hurt, we felt pain. Yes, it is understood that this was a defense mechanism that alerted our bodies to danger. And because of that, there were also various types of pain.

But, exactly why did pain feel the way it did?

When your wounded area felt hot or cold, felt tight or had aches, those feelings were qualia of pain. And if those qualia caused you to feel sadness, or annoyance, or maybe happiness, then those feelings would again be another set of qualia. Qualia also weren't limited to instantaneous feelings like that, and for example you could watch a movie one day and feel happy or sad the entire day, or you could feel your blood boil in fury and just lose yourself in the reverberations of that feeling, and those reverberations would also count as qualia.

The person who taught me about the concept of qualia was one of the few people who knew of Yukari's sight, and one of only two people who had experienced that sight for herself: the honors student from the class next door, Tenjou Nanami.

Nanami had a long history with Yukari, and we would have to go all the way back to kindergarten to trace that history back to its beginning.

As a child, Yukari didn't smile at all.

In fact, she couldn't even will herself to express emotions on her face.

After all, all the other humans looked like robots to Yukari.

And robots normally didn't express any emotions.

At the very least, they couldn't display the bountiful range of diverse emotions that humans had access to.

In other words, Yukari had never seen a human's "facial expression" before. When she said she didn't know if I was a boy of a girl, she wasn't just pulling my leg. She honestly did not understand how to tie facial expressions to subtle changes in someone's emotional state. In fact, she didn't even appreciate that the concept of a "facial expression" could exist in the first place.

Did dogs and cats have emotions? Did they have facial expressions that could express those emotions?

If you were a pet owner, then you'd probably have an instant answer to that. You'd tell me immediately that of course cats and dogs have emotions. And if you've spent a particularly long time with a pet, you could probably read that pet's emotions from his face. If you put a lot of love and a lot of time into a relationship with that dog, then even if it didn't come growling and baring its teeth, even if it didn't start waving its tail back and forth, you might be able to read your dog's emotions from his "facial expression."

But, if you just were shown a dog or cat that you had never seen before, then you probably would have a lot of trouble distinguishing the nuances in the animal's facial expression.

In a similar fashion, Yukari couldn't understand human facial expressions.

If she was around someone for a long time, then just like a cat or a dog, Yukari would be able to guess what someone was feeling based on their facial expression, but if it was someone she was meeting for the first time, someone who she hadn't known for a long time, then she wouldn't be able to judge whether that person was laughing or scowling, whether that person was happy or sad. That was the world Yukari was living in with her purple eyes, and that made Yukari appreciate her friends all the more. Tenjou Nanami was not only the first friend Yukari managed to make, but also the one who, once she figured out that Yukari didn't understand the concept of facial expressions, took it upon herself to teach Yukari how to express her emotions.

Yukari might not be able to make any facial expressions, but of course that didn't mean she didn't have any emotions.

She just couldn't express any of them properly.

Even though Nanami was only a child, she exhausted every idea to try and teach Yukari to smile. She would pinch Yukari's hand, telling her that her face was making the expression for "sad" at that moment, or steal Yukari's lunch, telling her that her face was making the expression for "angry" then. Or she would whack Yukari and make her express surprise, or tickle her, or feed her sweet treats, or watch a movie with her, or go to the zoo with her. Every time an emotion appeared on Yukari's face, Nanami would draw that face down or make Yukari look in a mirror. "You probably didn't even mean to, but that look on your face right now is called an 'expression,'" she would say. "And that 'expression' is by far the best way to tell someone else how you're feeling right now."

Like that, after constant supervision and coaching from Nanami, Yukari finally became able to express her emotions. And oh, what frank, sincere, bountiful emotions they were, to the point where I almost got embarrassed in her presence. And... this might frustrate me to no end to admit, but I have to acknowledge that Nanami deserved the credit for all this.

Until the accident, Nanami and Yukari were best friends.

After the accident, Nanami grew distant and also began to treat Yukari cruelly, taking every opportunity to block Yukari at every step.

However... no matter how much Nanami bullied Yukari, Yukari would still call Nanami her friend, and still continued to wish that they could get along again.

That might've been because her eyes - eyes which were useless for seeing human expression but in return were sharp when it came to reading a situation - allowed Yukari to use the experiences she had cultivated through her long relationship with Nanami to see through Nanami's hostile exterior and understand her complicated state of mind underneath.

And no matter how much Nanami might've hated Yukari from the bottom of her heart (and I truly believed a part of her did feel that way), she was still the one who had taught Yukari how to laugh. For that alone, Yukari would never quit considering herself as Nanami's friend.

Tenjou Nanami had taught me all about "qualia."

She also taught me about a lot of other difficult-sounding concepts - philosophical zombies, inverted qualia, etc. Keep in mind that around that time we had both just started junior high, and Nanami was probably just repeating things she read in a book or saw online, so it was really suspect whether we were talking about these things in the right way or not (for example, at one point Nanami told me that qualia is an "emergent phenomenon," and then at another point she said that qualia is not "emergent." I pointed out to her that she had just contradicted what she said before, but without a single hint of shame on her face she responded that contradictions like this weren't uncommon at all considering science was rapidly advancing each and every day. And all this discussion took place even though I didn't really know what an "emergent phenomenon" was in the first place). But even if we didn't know what we were talking about, Nanami's desire to learn more about these kinds of things was absolutely sincere, and I was also curious about these topics. So even though we were still children, we just continued discussing these things in our own way.

When it came to explaining "qualia," Nanami had this to say:

"To put it simply, qualia is embodied by the phrase 'a picture is worth a thousand words,' I think."

"'A picture is worth a thousand words'? That idiom?"

"Yes. So, for instance, no matter how much you think you know about the color red, there are things you just can't understand about it until you see it in reality. Conversely, if someone has never seen the color red, then no matter how much they might know about it they can't ever say they know what red is. You follow? They can hear thousands of words about what red is without ever being able to understand it, but one look at something red and they do. I think that 'one look' is precisely what qualia is... although, it's not like I really understand what that 'one look' is at a fundamental level."

Even if we didn't really know what we were talking about, we often got into very serious discussions like this.

We just couldn't stop ourselves.

One time, we also discussed the concepts of "quanta" and "Schrödinger's Cat."

"Hatou, do you know what a 'quantum' is?"

"Like, electrons or molecules... they're sorta the smallest unit for things, right?"

"Yes. Humans, planets, everything in this universe are made from quanta. And, those quanta possess both properties of particles and of waves... did you know that? In short, these quanta both possess physical form and yet can be also considered a type of formless energy. And because they are waves, they don't live completely in the concrete world, but exist more in the realm of probability. At their core, quanta are represented by probability densities."

"Probability... densities...?"

"Yes, something that tells us whether the probability of a quantum existing in a certain state is high or low. Did you know that until they are observed, quanta don't exist in any definite state? It's not that we just don't know what state they're in, but rather that this state really hasn't been decided. But the minute they're observed, their existence also becomes definite. Until they are observed, we have no choice but to think of their existence in terms of probabilities... that is the nature of quanta.

This might all sound pretty strange, but this isn't science fiction; this is actually how scientists think reality works. Until you observe a quantum, you don't know its state... and our bodies are composed of many, many of these quanta."

"...... Hmm, I see."

It's not like I could relate to any of this, so I couldn't really come up with anything but a half-assed response. Still, Nanami didn't seem discouraged and just continued. ¬

"So, Hatou, have you heard of 'Schrödinger's Cat'? It's a famous thought experiment."

"... Umm... I have a feeling that I've heard of that somewhere... but maybe not..."

"To put it simply, there's a box with a switch on it and if someone pushes that switch, it releases a lethal poison gas into the box. We put a cat into the box. So, is the cat alive or dead?"

I had no idea where this was going, so I gave a hesitant answer.

"Umm, until someone pushes the button... the cat's alive... but after someone pushes the button it's dead?"

"Yes, that would be what normal logic would lead us to believe. However, for this thought experiment, the agent pushing the switch isn't a 'person,' but rather a quantum system. In other words, there's some kind of machine that can detect quanta, and if it detects a quantum the switch is pushed, but if it doesn't the switch is not.

However, quanta are probabilistic entities, so we can't really be certain whether there is a quantum there or not until we observe it.

That means that, because the on-off state of this switch is controlled by a quantum system, that state itself is probabilistic until we observe it. Until we open the box and check inside, that switch behaves just like the quanta that control it and is simultaneously in a state of being pushed and not pushed with some probabilities assigned to each. Consequently, because that switch determines whether the cat is alive or dead, the cat behaves just like the switch and quantum system and is both alive and dead simultaneously with some probability. Do you see what I'm trying to say?"


"Let me try to summarize the point this thought experiment is trying to make. Quanta are strange things with strange properties. However, one might think those properties only apply to the microscopic world quanta live in, and do not apply to the macroscopic - the real - world. But what I'm trying to say is that this is a huge misconception! Just like this quantum system is linked with this switch, and the switch is linked with the life or death of this cat, it would be utterly strange if the strange things that occur in the microscopic world did not also extend to the macroscopic one. If quanta really behave this way, then until we ourselves are observed, we must exist in a superimposed state of both life and death, in a probabilistic state just like the quanta themselves. That is what the Schrödinger's Cat experiment is telling us."

I chewed over Nanami's words but then couldn't hold in my surprise.

"Ehh? Wait, but look at us, we're definitely alive and exist, don't we?! Not as probabilities, but as concrete, definite things. Like, even if nobody's looking at us, it's not like we're just going to disappear or anything."

"Are you sure?"

"........ Well...... I mean, that's..."

"Well, to be honest, even Schrödinger was using this thought experiment to make the point you're bringing up. He wanted to point out that it's ridiculous to have a cat that's both alive and dead at the same time, so quanta can't be these uncertain entities we're claiming they are.

However, there were physicists from Copenhagen who disagreed with him.

They believed that quanta were indeed probabilistic, and that the only reason nobody had successfully seen a cat that was in a superimposed state of life or death was because that cat had been a thought experiment, and that if you eliminated problems with heat and vibrations and other external sources of interference and conducted a precise experiment, you could recreate Schrödinger's experiment in reality. And this interpretation is currently widely accepted - people say that Schrödinger himself quit physics during the late part of his life because of this. Well, that's a rumor I heard anyways, but wouldn't that really be something? The author of Schrödinger's Equation, which forms the basis of all quantum mechanics, couldn't even accept his theory's validity himself."

Nanami's lips curved upwards, but I interrupted her before she could continue.

"Wait wait. So are you saying we're all probabilistic beings too? That if those external sources of interference you mentioned weren't there, the minute everyone took their eyes off us we'd suddenly be both alive and dead or something?"

Nanami shrugged.

"Who knows."

"... Huh?"

"Well, nobody really knows, right? All we know is that quantum systems behave probabilistically, but nobody really knows why, or how they got to be like that, or why these phenomena are only observed in the microscopic world. There's no perfect answer for these questions.

We don't even really understand what 'observation' means for quantum systems. What does it mean exactly when we say that observing a quantum system puts it into a definite state? Scientists call this 'collapsing the wavefunction,' by the way.

Take Schrödinger's Cat, for example. At what point do we consider the cat 'observed'?

Is it when a human opens the lid of the box and sees the cat inside? Is it when the view of what's in the box travels up his neurons and reaches his brain? Or does just opening the lid count as observation? Or maybe it's when the cat itself feels something? Conversely, what if the human who opens the lid of the box was himself in a larger box? What if there was another human outside this larger box, staring at it? And if that human again was in a larger box, and there was a third human outside it all observing that box, exactly when can we say for sure that the cat is alive or dead? Do we have to wait for the outermost human to open his box? In the microscopic world, the strange truth is that quanta exist as both waves and particles. We can even confirm that molecules, which are made up of many quanta, can exhibit quantum-like behavior. We might be able to confirm similar behavior for viruses too. So, why is it that once we get to the macroscopic world, we can't confirm anything like this anymore? If observation really forces things into a definite state of existence - collapses their wave functions, so to speak - then when, why, and how does that happen? There are many interpretations for all this, but in reality we don't understand it very well. We just can observe the outcome... but there are people who claim that we'll never understand how the system arrives at that outcome no matter how much science progresses."

Long ago, scientists thought that as long as science continues to advance, we'll eventually understand all the universe's mysteries.

But modern scientists now refuted that idea.

After all, in the microscopic world, just observing something would apparently change that thing's state. And that small change could have huge, complicated repercussions in the macroscopic world. There was a limit on the things we could understand, and no matter how much science progressed, it was impossible to perfectly predict the weather every single day - at least, that was true under our current scientific framework.

At any rate, Nanami continued.

"We've been talking for quite a while, but I think what I wanted to make clear is the world is not as definite as you might think. So... for example, some people feel that quanta aren't probabilistic, that they aren't forced into a definite state when they're observed, but there are just infinite parallel worlds and quanta exhibit their strange, seemingly probabilistic behavior because these infinite parallel worlds interact on a microscopic level."

"...... Parallel worlds?"

"Yes, parallel worlds. Worlds that are almost exactly like this one, but with subtle differences. Quanta interact with the versions of themselves in these parallel worlds and through that interaction behave probabilistically, and they are forced into a definite state when they lose this ability to interact with each other. Following this line of reasoning, the cat in the box is definitely either alive or dead from the onset, but there are infinite worlds where the cat is alive and infinite worlds where the cat is dead, and there is a cat that exists in all these worlds. All these cats interact with each other, but each cat can only feel what's going on in its own world.

Can you believe that? This whole parallel worlds business?

This might all sound like science fiction, but it's actually the subject of real scientific research right now.

They call the wave function collapse picture the 'Copenhagen Interpretation,' while the parallel worlds picture is called the 'Many-Worlds Interpretation.' The Many-Worlds Interpretation also ended up forming the basis of quantum computing theory. We really can't be sure which interpretation is the correct one, but both of them are plausible options...

So, it's not science fiction at all. This is how our world works, how our reality works."

For those of you who want to laugh and make fun of us for being junior high students getting in way over their heads talking about things they don't understand, you should see what it feels like to die once. And then to get brought back to life. To have half your broken body fixed using the scraps of a dilapidated jungle gym, or to have your severed left arm healed with parts of a cell phone.

Try going through that, and maybe you'll come to understand a bit how Nanami and I felt.

"... Anyways, this might seem like a bit of a leap in logic, but I was thinking about how Marii's eyes are kind of like this. We all look like robots to her, right? So if we take the Copenhagen Interpretation as true, then you could say that maybe her eyes collapse our wave functions into what she perceives as robots. If you take the Many-Worlds Interpretation as true, then maybe her eyes are just looking at versions of us in another world where we exist as robots. Or, hmm, maybe...

Maybe it's not that qualia is born from what we see, but that qualia itself solidifies what we see into its proper form."

"... That certainly was a sudden leap in logic."

"Well, I agree, but I'm not a scientist, so give me a break. But it's not so far-fetched, is it? When Marii looks at something, like our bodies, that induces change in the microscopic world, or in some other world at some other level, and the thing she's looking at changes itself. We might not be able to see directly what's going on, but quanta aren't really supposed to be visible anyways. For instance, no matter what our bodies are really made of, as long as my own qualia makes me observe my own body as flesh and bone, my body will be forced into that state. In your case, it's like how your left hand is a hand and not a cell phone because you observe it to be so...

Anyways, if we think about it like that, then Marii's 'power' might actually be a pretty natural thing. We just can't perceive what's happening, but what actually is happening is in fact quite normal."

In the past, Tenjou Nanami had been involved in an accident, and was on death's door when Yukari saved her.

In order to save her, Yukari "fixed" her body by using spare parts from a jungle gym.

If Yukari was telling the truth, then that would mean around 40 percent of Nanami's body was being held together by "steel bones" right now.

Not by the normal materials that made up a human body, but by parts from a jungle gym.

Nanami was only a child then. It wasn't too much of a surprise that she ended up fearing Yukari, which then turned into hatred.

In general, Nanami and I didn't like each other very much, and when Yukari was between us we tended to just bicker with each other relentlessly. But when it was just us two, we often talked normally. When a nice breeze was blowing, and the sky above us was clear and blue, and we could just laze around all calm and relaxed, it was almost like Nanami had forgotten I was her sworn enemy and would just lay herself bare to me as she talked at length about philosophy and other things she had learned.

For example, she told me that she was still sometimes jolted awake by nightmares.

That she would sometimes look in the mirror and hallucinate that she wasn't human.

That she would sometimes fear that in the next instant, her body would start to rust from her metal parts and reveal the "robot" underneath.

In reality, Nanami loved Yukari and thought of her as a precious friend.

Nanami also knew that Yukari only meant well when she saved her life.

But, to her, acknowledging Yukari as a friend now would be equivalent to acknowledging that around half her body was now made from a jungle gym - she knew that without the jungle gym she wouldn't be alive right now, but if she acknowledged what had happened, could she really still claim to be human? To be the same as she was before?

Both she and Yukari were dealing with feelings that were difficult to describe, and Nanami was desperately trying to come to terms with reality.

She would find information on things that seemed even tangentially relevant - qualia and quantum mechanics, for example - and would study them as well as a junior high student could, in order to try and come to terms with everything.

And while it might be a bit strange for me to be saying this, I did believe I now played a large role in her life.

After that incident when I was attacked and dismembered by a murderer (thinking about it now, that really was a gruesome, awful thing that had happened), Yukari had fixed my body, and while she didn't use a jungle gym, the way she fixed me was pretty similar to what she had done to Nanami. Yukari had used a complete cell phone to fix my left hand, and she had used a jungle gym to fix Nanami's body; through these horrific experiences, Nanami and I had become birds of a feather, two people who both had "illegal parts" in their bodies and who could mutually understand each other's circumstances and states of mind (granted, I think Nanami was much more traumatized by her experience than I was by mine...).

My connection with Nanami had been formed through Yukari, but through me Nanami had begun the healing process in her relationship with Yukari.

When Nanami saw that I had accepted the reality that Yukari had "fixed" me, she also started to be able to deal with her own reality.

Given just a bit of time, Nanami would've definitely been able to get back onto her feet after that entire affair.

She would've become friends with Yukari again, and they would grow just as close as they had been before.

... If only Yukari didn't transfer out from our school.

After the school year ended, Yukari moved overseas, and these talks between me and Nanami grew less and less frequent.

During the next school year, we were placed in the same class, but I felt some sense of guilt somewhere in my heart (and perhaps Nanami did too), so we ended up avoiding each other and generally ignoring each other.

And so, my relationship with Nanami ended right when Yukari moved away.

Actually, in one particular world, I ended up meeting Nanami again at a class reunion.

It was eleven years later, and I was twenty five. In that world, Nanami had somehow become a popular actress (I was working as a freelance writer), so I never imagined I would meet her again, but she ended up attending our class reunion and gave me a warm greeting when she saw me.

Do you still remember me? she asked.

I ended up skipping the after party and inviting Nanami over to my place.

Nanami (who by the way was known by a stage name now, which was written with different kanji) told me she had work the next morning, but she ended up staying the night with me.

I had stayed overnight with Yukari plenty of times, but this was the first time I was doing this with Nanami.

I turned off the light, and we lay there stretched out in my room side by side, and began to talk.

We hadn't seen each other for a long time, and so we started with how our lives were going, and slowly worked our way back up all the way to junior high.

"By the way, Tenjou, didn't you start dating Kasoku during your third year?"

"Uwah, you knew? I was trying to keep that quiet..."

"Yeah, it was pretty obvious, you know... ah, are you sure you want to be here with me? You probably want to see him, right? He definitely was at the reunion."

By the way, I ended up going out with Kasoku in around exactly the same period as when Nanami had been going out with him. Of course, I don't mean he was two-timing Nanami or anything - it had been a rather serious one-on-one relationship.

"....... Uh, well... that's..."

Nanami sounded rather embarrassed as she fumbled over her words.

The timing seemed right, so I switched topics.

"By the way..." I started. "Tenjou, do you remember anything about Marii-san?"

Nanami seemed to think for a little bit, before letting out an "ahh!" and nodding.

"Yes! I remember her! There was definitely a Marii Yukari back in junior high, wasn't there? She was a strange one, that girl. And she was really cute too."

Nanami continued on, not a care in the world. It was then that I noticed.

Nanami had already forgotten about Yukari... about the girl I had called Marii.

It was as if everything that had happened was just stuff from the distant past, and Nanami had begun to change her perception of that past... change her memories of what had happened.

Yes, humans tended to change their memories all too easily. They would change them into things that were most convenient for themselves... sometimes in order to protect themselves.

Nanami had "re-observed" her past, so to speak.

She had recreated a past that was more acceptable to herself.

Everything about Yukari's eyes, about Nanami's own body being repaired with a jungle gym... all of that was now just a "joke" played by a "strange girl," and not reality...

I was a bit shocked by this, but I didn't really feel annoyed by it.

I didn't really have a right to get angry here.

Because if there was one person in the world who was in no position to blame Nanami for turning her eyes away from reality and recreating the past in her own interest, it was me.

Nanami continued carelessly.

"Actually, that girl didn't come today, did she? Ahh, she transferred out at the end of our second year, right? I wonder what she's been doing these days."

"...... Beats me."

"Now that you mention it, after we got put in the same class we never really hung out, did we? But even though we never talked much back then, isn't it strange we can just lie around here and talk like this now?"

"...... Yeah. I guess it's pretty strange."

It really was.

Back then, I'm sure we could've become good friends.

If only Yukari hadn't moved away.

If only Yukari were still alive.

... I couldn't bring myself to be angry at Nanami for conveniently forgetting about Yukari.

I didn't feel any jealousy, any frustration... actually, I felt quite relieved. That was probably for the best... yes, she was probably happier this way.

In the morning, Nanami wasted no time in heading back.

But just as she was leaving, she hesitated a bit before calling out to me.

"...... Hey, Hatou. Do you think I could call you every once in a while after this? So we can, you know, like today..."

"Yeah, of course."

"Really? That's a relief. To be honest, I don't have anyone I can talk to like this..."

Nanami was showing an openness I would have never expected from her in junior high, and I couldn't help but give her a strained smile.

"Oh my, a rising star like you saying that to little old me? Of course it's alright. Feel free to call me anytime. We're... friends, right?"

Yes, we were friends... friends that had met through Yukari, though.

So Nanami, please call me anytime.

But, please rest assured that I will never, ever forget about Yukari. And so...

I had no need for a world like this.

It seems we've gotten a bit ahead of ourselves.

I'll try to go a bit more in order now so we can all avoid additional confusion.

After a year of knowing Yukari, during the summer break of my second year in junior high, I was involved in an horrific incident that left me gravely wounded, and Yukari had saved (fixed) me.

After that incident, I used that adaptability of mine that Yukari talked about so often to get right back on my feet, and I also sensed I was growing closer to Yukari (and Nanami as well) in the process. But then came the entrance ceremonies right after summer break, on the first day of the new semester.

A transfer student arrived at our class.

She had blonde hair and amber eyes, and a physique that made her look like she had jumped straight out of a work of fiction. Her name was Alice Foyle.

Alice also knew all about Yukari's way of seeing the world.

Oh, actually, I just remembered something else.

Tenjou Nanami had also been the one who had taught me about the strange properties of light.

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