Moebius strip, a definition:
The Möbius strip or Möbius band (UK // or US //; German: [ˈmøːbi̯ʊs]), also Mobius or Moebius, is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.
Background: Two sentient beings, Dey and Ray, were affixed to the same region of a Moebius strip, but opposite one another. Despite being separated by the band, they could communicate through the strip. This communication was accomplished by the organism pressing his face into the surface of the Moebius strip, which is elastic, so the other organism can see the expression on the other's face, and the sound vibrates through the surface of the strip. Obviously, in their language, each being speaks of their side of the strip, and that the other organism is on the other side of the strip. Each being is inside their side, and the other being is on the outside.
Dey: Ray, I have been thinking. All I really know is my side of the strip, as I have never seen nor experienced your side of the strip. I have heard you talk about it, but I cannot know what you mean as I only know what is on my side.
Ray: Dey, I don't know what you mean. You can see the expressions on my face, you can know what I feel.
Dey: No Ray, I don't see the real you, I only see what is happening on my side of the strip. How do I know that what I see corresponds to the real expression on your face. I see your behavior, not what you are feeling, not what it on your inner face. In fact, I don't even really know that you have an inner face, that there is anything on the other side. For all I know, this side which I experience may be the only side of the strip.
Ray: What you see Dey is the expression of my being. It is not a sign of my feeling, it is their manifestation.
Dey: But Rey, you can lie about your feelings. Just because you say something, or behave a certain way, I don't know what you are really feeling. Your behavior just stands for your feeling, which only exists on your side of the strip. I can never know what is on your side.
Ray: But if my feelings were not connected with my behavior (which you observe) then our words wouldn't have any meaning. Its not that you wouldn't know that I was in pain, it would be that the concept of pain would be meaningless.
Dey: Nonsense. I can point to my pain, even if you can't see it. I can frown to myself, and I don't have to communicate that to you.
Ray: It is not that you don't have to communicate it to me, its that you can't communicate it to me. I can't ever know what you mean, unless I can connect it to something in my experience.
Dey: Aren't you saying that all there is is behavior? We both agree that the strip exists, and that we can see the strip, but I can't see your side, and you can't see my side, so the strip really has no sides, and there is nothing on either side at all.
Ray: Are you saying that I don't exist, that I am like a character in a philosophical dialogue or something?
Dey: Exactly, we are both characters in a philosophical dialogue.
Ray: But who's dialogue?
Dey: That's the point, if we are fiction, then we don't exist, and there can be no question of where a fiction really exists, or who is writing the dialogue. The dialogue exists, but we are not the dialogue.
Ray: But aren't we part of the dialogue?
Dey: No, we are fictions, so we can't be part of anything.
Ray: But how can fictions communicate? Doesn't there need to be a fictional dialogue, at least?
Dey: No, there is only the strip, only the strip exists, because we agree that the strip exists. I see you in the strip, but there is nothing beyond the strip. You see me in the strip, but there is nothing beyond the strip. It has no sides.
Ray: But how can the strip have no sides? How can we even call it a strip then? If you and I both perceive the strip, then how can you talk about a strip at all if no one perceives it?
Dey: We both happen, by accident, to exist, but if we did not, this strip would still be this strip.
Ray: How do you know?
Dey: Because the strip has always been here, and neither you nor I can cause the strip to disappear. We can adjust or manipulate the structure in the strip, but the strip simply exists, without any sides.
Ray: Isn't that simply a picture? You have a picture of the strip, and you imagine that the strip exists timelessly, but you don't know anything of the sort. You know that the strip is here now, and that the strip has responded in certain ways through the course of your life, but you certainly cannot say what the strip will do in the future.
Dey: I can measure parts of the strip, and observe changes in the strip which precede my existence.
Ray: But you don't know what the strip will be like in the future.
Dey: I can feel pretty confident based on the regularities I am aware of in the past as to what the status of the strip in the future will be.
Ray: But what do you mean by the strip? I see your face in the strip, I can see the gestures your hands make in the strip sometimes, but all I know about the other side is in the strip.
Dey: That's right, the other side doesn't exist, only the strip exists.
Ray: But all I can refer to is what exists on the other side. I can refer to your face, your hands, etc. I can never refer to the strip. The strip contains everything I can refer to, and if only the strip exists, then I don't know how you or I could know the strip. I believe the other side exists, that your side exists, and on your side is your essence, and your activities are manifest in the strip. Thus, I ascertain your essence from your activities.
Dey: But how can we speak of an invisible essence here if all we can know is the activity?
Ray: Well, as you say, sometimes what the activity reveals is false, and sometimes there is no activity, but something is going on on your side.
Dey: What if we were both part of the strip itself? That only the strip exists, and we exist as parts of the strip? Different sides of the strip as it were.
Ray: Sometimes the light is carried through to the other side, and sometimes, it was too weak, or hidden or disguised? The strip is divided into two sides, and each side of the strip communicates to each other by physically manipulating the strip?
Dey: Exactly. But then my side of the strip must be capable of manipulating your side of the strip, and vice versa. But my side is my side, and your side is your side, and only I can know what is on my side. So how could I even know if I were manipulating your side? I can only know what the strip says. There is another problem, I don't see how something on my side can physically interact with the strip. I can see something in the strip, and I can correlate a future state of the strip based on a prior state of the strip, but I can't see how something outside the strip could affect the strip.
Ray: Exactly, if a structure suddenly appears in the strip, I don't know why I shouldn't just say it is random, rather than some manipulation of the strip from the other side. You may say that you caused the change, but you don't exist, all I have is a correlation between an observable speech act and change in the strip. All we can know is the change in the strip, and the only way we can know it is by determining regularities in the changes in the pattern. We merely use the language of a "side" of the strip as a mean term to predict changes in the pattern. For example, if you say you are hungry, then I may subsequently be likely to observe you eating in the strip. But there is no one eating, no one observing, and nothing beyond the changes in the strip, which we can predict with certain regularities.
Dey: But how can we say that we see the same strip? I see my strip from my side, you see your strip from your side. Why should we say it is the same strip?
Ray: Well, we do say it is the same strip, we agree, so there must be some real strip that exists independently of what we see.
Dey: But we can never know the strip that exists independently from what I observe, and what you observe. You are suggesting, not one, not two, but three strips. The one I see, the one you see, and the one that really exists. But how does it help reconcile the contradiction of the fact that we see two different strips, yet we agree about what we see? How does postulating the existence of a strip that neither one of us can see help explain our agreement?
Ray: But we say that the strip exists, and it exists independently of our seeing it. Why should we say that if it does not exist?
Dey: What if the strip were nothing more than the boundary between the two sides?
Ray: What do you mean?
Dey: The strip seems to be the boundary of our activity and experience, and we agree at that boundary. If I could cross the boundary, I would really be on your side, and not stuck on my side. If the boundary did not exist, there would be no sides, no differentiation. But we both exist in each other at the boundary, so to speak.
Ray: Well, I imagine that there would have to be a third strip, and even if it could not exist independently, I imagine that God sees it at all times, and it resembles the strip that you see, and the strip that I see.
Dey: But how does that solve the problem of our agreement? We agree that there is a strip, but whether God agrees with us or not, what we see is different.
Ray: No, what we see is the same, if it wasn't, we wouldn't agree.
Dey: But it can't be the same, because I don't see what you see, and vice versa, we only say that we see the same thing. To say God agrees with us too (or would agree with us if he could see the strip) does not explain our agreement. In this case, there would have to be something above us and God to explain the agreement of the three. There must be a cause of the agreement, and the cause cannot be present in the seeing, because the seeings are different, even if what they see is reckoned to be the same.
Ray: Why can't the agreement just be the ground of meaning?
Dey: But something has to cause the agreement.
Ray: Why? We can't say anything about the cause of the agreement. If we did not agree, then we could have no conventions, and if we had no conventions, then we could have no descriptions. The agreement just is, or perhaps God is the agreement itself, what unifies our lives, which makes meaning possible.
Dey: Then what is God? He would have to be present in both of us, in order for us to agree. He would also have to be present everywhere, because we could only agree where he is present. But God can't be me, because then he would not be you. He could not be on my side, because he couldn't be on your side. He could not be in the strip, because, as we determined, the strip had no sides, and God would have to be on both sides of the strip. Moreover, the strip lacks consciousness, it is simply matter that we both observe. Further, we can't say anything about God, because he is the source of agreement, the source of meaning. Only through the operations of God could my side be unified with your side, and we can only talk intersubjectively about a side-less strip that we can agree on. So this God-talk is ultimately nonsense, and all we can talk about is this strip which we can both observe and which clearly has no sides and is not conscious.
Ray: Agreed. What's on TV?