# How can orientation-discriminating people keep their views when it turns out they live on a non-orientable surface?

In my world, there are two types of people, lefties and righties. They have opposite orientations, which means they are mirror images of each (they are Enantiomers of each other essentially). Throughout much of history, most people have been "orientist", or "handist" (since lefties are left-handed and righties are right-handed), meaning that they hate those of the opposite orientation. In each country, usually either the lefties or the righties were in power, oppressing harshly those of the opposite orientation (usually enslaving, but sometimes killing them, and sometimes letting them be mostly free but limiting their rights).

In my country, for example, the righties are in power. Most of our neighbors are also pro-rightie, but one of our neighbors was taken over by a foreign leftie civilization 150 years ago. We have only recently established a tenuous peace with them.

The idea of orientation has an interesting history. About 300 years ago, a foreign leftie astronomer actually came up with the idea that there is no absolute notion of orientation in our world (i.e. it was non-orientable). He was promptly put to death by his government for such an absurd notion.

About 200 years ago, a number of linguists from different countries found a rather odd linguistic paradox. If you translate "rightie" from English, through seven different languages, and then back to English, it comes out "leftie". If you start with "leftie", you get "rightie". The linguists were quick to point out that language is a very fuzzy thing, but some suspect them of non-orientist sensibilities.

Nowadays, very odd things have started happening. The world now has a global economy, so people and goods travel around the world. World travel has the disastrous effect of sometimes corrupting the orientation of goods, or even people, to the opposite orientation! Some scientists are even asserting that the astronomer was actually right, and our world is topologically a Projective Plane!

How should we respond? Everyone knows that lefties are inferior. How can we justify oppressing them if orientation is non-stable? How should we treat world travelers, when we don't know their original orientation? (That is, how can orientists react and adapt to globalization in this world? Is there a way they can keep their prejudice?)

Notes:

• Non-orientability means that you can only compare the orientation of objects that are near each other. There is no consistent way to define orientation globally. It also means that if you travel around the world in a certain way, you become mirror reversed (compared to, say, a sculpture someone made of you before you took the journey which didn't move). See this picture to see what that looks like.
• Orientation (locally) is very easy to tell. Besides handiness, there are also very distinctive biological differences in appearance that are very hard to cover up. (Attempting to cover them up is considered taboo.) There are few other physical differences though. (One of them is that are a couple of foods that only righties or only lefties can eat. This has led to unfortunate effects in the more genocidal nations.)
• There are many equivalent ways to define the projective plane, but one way is the hemisphere model. In this, the projective plane is a hemisphere, in which opposite points on the rim are glued together. This means that if you walk of the rim, you pop up on the other side, but with your orientation reversed. (You might be tempted to say that this is the answer to my question. Just define someone's orientation as what their orientation is at birth, in the hemisphere model! There are two problems with this: (1) For a given projective plane, there are infinitely many different hemisphere models. The orientists would have to pick one, and justify why that one is the best. (2) Perhaps even bigger, orientists near the "rim" of the chosen hemisphere model would regularly change orientation (according to the model). They probably wouldn't accept such a model.)
• Orientation is inherited from the parents. This means that if your parents have the same orientation at the time of conception, you will have the same orientation as your mother at birth. If you parents have different orientations at the time of conception, you will have a random orientation when you are born. (Also, you will probably be killed.)
• So, I've only described the topology of the world. Allow me to now describe the geometry: Establish a 3D coordinate system, where the planet's center is at (0,0,0). Points (x,y,z) and (-x,-y,-z) are the same point, and otherwise physics is mostly normal (except for how the sun works). This means that the planet's surface will topologically be a projective plane. It is also about as round as the earth. There is a star which goes around the planet. It cycles between light and dark every 12 hours (don't ask me how). (The reason this is necessary is the equator only has 180 degrees. This means the sun is always visible. If the sun was always light, there would be no night.)

EDIT: In the comments, many people are suggesting that a solution would to simply "ignore" the issue. (Note: Before globalization, ignoring the problem was a valid solution, and what the people did.) Although for some social issues that works, it doesn't in this case. Here are some scenarios where the ignoring it won't work:

• A prominent foreign person comes to town for some reason (business, politics, acting, etc...). They appear to be a rightie, but there are rumors that they where born a leftie. How do you decide whether or not to hate them?
• The rightie association of this country is having a video chat with the rightie association of some far away foreign country. To their great surprise, when the chat starts, they appear to have opposite orientation (i.e. they appear to be lefties to each other). One of the IT people fiddles in the settings, saying "okay, I swapped the video orientation". They now appear to be the same orientation, but both associations stare at each other suspiciously for a couple minutes, wondering if they are actually the same orientation or not.
• A rightie sends his rightie kid away to college. When they come back for Christmas, they are leftie. They did not decide to be leftie; it was just a side effect of the route their plane chose.

As you can see, this is very different from the flat v.s. round earth issue. This can actually affect people personally (if they care about orientation, that is).

• Comments are not for extended discussion; this conversation has been moved to chat. – Monica Cellio Jan 17 '18 at 3:32
• See also: Wind and Mr. Ug, a world essentially like this one. – PyRulez May 3 '18 at 23:35
• Note that the person travelling to the "mirror side" would feel no difference, but would see the entire world having been mirrored. So the person would still be leftie or rightie from their own point of view - they would also have to re-learn to read and write and drive in mirror unless they want to come back the long way home. – Eth May 4 '18 at 11:27
• What happens when you run the Wu experiment in this world? – eyeballfrog Jan 20 at 21:59
• @eyeballfrog parity would need to be conserved, I think. Except that if you do it on a big enough scale, parity would no longer be well defined. It would have to be huge though. Also, stating the parity is conserved would probably get you killed. – PyRulez Jan 20 at 22:20

## The Spherical World Society and Evil Twins

There is a model of the projective plane known as the projective sphere. It has the following properties:

• Since it is based on a sphere, which is orientable, you can consistently assign objects orientations which do not change as you move along it.
• Unlike the hemisphere model, the sphere model is basically unique.
• Also unlike the hemisphere model, its continuous. There is no point where things, according to the sphere model, randomly change orientation.

Therefore, the orientists can form the Spherical$$^*$$ World Society, which asserts that the world is actually a sphere!

So what's the catch? Every point in the projective plane actually occurs twice on the sphere (one for each orientation). That means that for each actual person, the Spherical world society believes there are two (one leftie and one rightie)! This is known as the Evil Twin Theory.

This actually has economic advantages. Want to trade with an enemy nation? Trade with their evil twin instead! (This only works if they also subscribe to the evil twin theory, of course.)

This has an interesting applications, both comedic and dramatic. For a comedic application, the Mayor of Rightlandia decides to send a spy to aidandlthgiR, which is controlled by lefties, and in particular by the Mayor's evil twin. There is word that they are going to hold a leftie pride parade (which they call a "edarap edirp eithgir") to rival the upcoming rightie pride parade, and the spy is to disrupt it. The spy successfully partially disrupts the parade. At the same time, a leftie spy tries to disrupt Rightlandia's parade, but is only partially successfully. The spy and the Mayor rejoice in each other's partial success.

In a dramatic application, the Rightlandians capture the evil twin of the Mayor's son, and want to kill him, since all lefties are killed in Rightlandia. The Mayor knows that the evil twin of his son is actually his son (since he only "believes" in orientism so he could get a sick hand tattoo), so he has to find a way to stop the town from executing the evil twin, at least until he finds a way to "rescue" his son from aidandlthgiR.

The evil twin theory is sort of a self-fulling prophecy. If someone from Rightlandia goes to aidandlthgiR, he will naturally be hostile to the people there, since from his point of view their orientation's have changed.

It also is an interesting way to mess with the audience. By translating everything to English (for example translating Rightlandia to "Great Mother Country" and aidandlthgiR to "Bear Running Green"), the audience won't realize that your actually talking about the same people. After the big reveal, the audience will have to rethink the role of prejudice and topology in their own world.

The idea of digital communications is also interesting with this. To avoid connecting to the evil twins of your video chat partner, you could use circularly polarized radio (assuming that those in power know what's actually going on, they could allow the radios to connect to the evil twins' radio stations, but make "modifications" if you do). If you want to have a secret communication, you would need a guarded physical connection, since your evil twin will have the same encryption key as you.

$$^*$$Not to be confused with the Flat World Society (which also believes in the evil twin theory, but doesn't believe the world is round) or the Mobius Strip Society (which doesn't believe in orientation, but is mathematically misguided).

See Also: Wind and Mr. Ug, a misguided triangle that falls in love with her evil twin.

You would get tattoos which would be recognizable as mirror images of themselves.

Rightie-pride people would get tattoos depicting their pride and belief. These would vary from person to person but have similar themes, and be publically viewable to greater or lesser extent. Likewise leftie-pride people (but different tattoos, of course!)

A rightie who got switched would still have all his or her recognizable right-pride tattoos, but in mirror image. Letters would be backwards. That is fine; they are still rightie pride tattoos and so this person would still be viewed as a true blood rightie. The fact that the tattoos are mirrored means an unavoidable switch happened. These things do happen.

A leftie could fake it, by getting switched to rightie and getting the tattoos then. A leftie like this would be giving up on any leftyism because lefty-pride people would hate on that person after seeing rightie-pride tattoos. You could not go back and forth with these tattoos.

Persons who did not care enough about their heritage to get the tattoos would be viewed with suspicion by pride people of both sides.

• How will the ones who care about everyone's heritage respond? I've heard there is such a thing as tattoo removal. Probably invented by one of the ambidextrous folks. – N2ition Jan 9 '18 at 0:34
• How would this work with the different languages, keeping in mind the translation "issue"? – PyRulez Jan 9 '18 at 0:49
• @PyRulez: I have "Lucky Lefty" written on my hand in English. You can translate it 7 times and put your result on a Tshirt if you like, but what is on my hand does not change because of your efforts. – Willk Jan 9 '18 at 2:45
• @Will Sure, but it won't help you if you go to France (especially if there is controversy as to how "Lefty" should be translated into French). You also won't be able to understand the tattoos of your fellow lefties. (If it doesn't work with foreign countries, this is still a good answer though.) – PyRulez Jan 9 '18 at 4:24
• just remember that from the traveler's POV, it's not him who changed, it's the whole city. – Mołot Jan 9 '18 at 12:11

The natural way to ensure that orientists can keep the validity of their hatred is to forbid the use of any path which alters orientation. The orientists define a subset of the topology of their world in which they will operate, which preserves orientation globally. Of course, not everybody will go along with this. The orientists will simply have to declare "We hold the true sacred geometry, in which all things are right (or all things are left, depending on the cultural orientation). If you aren't with us, you're against us." Thus they do not have to hate the cis-hands who take these sinful paths, but they can react viciously towards them while reserving their true hatred for trans-hands, who are the true abominations.

• Hmm, this could work. The only issue would be people who are outside the sacred subset, but ah well. – PyRulez Jan 9 '18 at 0:53
• @PyRulez Yeah, it's not perfect. But if I'm reading between the lines correctly, this is intended for social commentary. I think this particular imperfection lines it up even better with actual society, so I'm decently happy with it. – Cort Ammon - Reinstate Monica Jan 9 '18 at 1:19
• Its kind of like the concept of an international date line, actually. – PyRulez Jan 11 '18 at 18:52
• Its also interesting how orientists following this answer would naturally be in conflict with those following this other answer. "Hey, that's leftie Joe! He crossed the forbidden region." "Nay man, that's just Joe's good twin." – PyRulez Jan 11 '18 at 19:15

Orientists could react and adapt to globalization in this world much the same as any-ists do in our world: along a gradient depending on their individual experiences and character traits.

Our world presents a constantly changing environment, to which people observe the changes and choose to react in innumerable ways. Some responses to exposure to new concepts include:

•Not noticing at all. Some people will not even be able to notice a concept that is beyond their ability to perceive or understand. This would be similar to a very young blind child noticing the light switch turns on and off electrical lights. They hear the sound possibly, but cannot notice the light and dark changes in the visible spectrum directly correlate with the flip of a switch. Indeed, they cannot very well even comprehend the light itself, much less the switch's role.

•Noticing, but more subconsciously than consciously. These folks will retain current views, but the potential for another possibility to exist will niggle at their periphery until a time perhaps will come that they are better able to contemplate the issue at hand.

•Noting, considering, then consciously choosing to either retain current steadfast belief, or begin to assimilate some of new information, or wholeheartedly adopt a new way of being. This will depend heavily on individual mind constructs of personal belief systems along with past experiences. There is a lot of play along this string of responses.

•Noticing, considering, and choosing to enter a sort of limbo as they decide to continue to observe and analyze additional data on the subject. This is akin to scientist's method of hypothesis and experimentation. They will delay making any conscious response, sometimes without any definite conclusion at all.

•Noting consciously, contemplating, then deciding they prefer to be either ambidextrous, quit using their hands all together, or find a way to build and implement an orientation system that also includes forward and back, up and down, internal and external, proximal and distal, and on and on. These folks realize they couldn't care less that everyone else wants only two choices. They are excited by the new knowledge that another idea is possible, and some will go on to expand the idea as far as they possibly can. These are fun people, by the way.

Even in a case where the person themselves has re-oriented unintentionally and the change has affected their own self, anyone can still be able to belong to any of the groups above. The power of their own mind will allow them to know themselves outside of any external manipulation of the physical, and spatial orientation is clearly defined here as physical.

I think you answered your own question: people who want to hate someone for not being the same as they are will always find some justification for it. There will be personal, less universal justifications and more generally accepted ones, depending on the charisma and exposition of the person who touts it.

Ultimately, I think true globalisation is not achievable without reaching a level of tolerance. Especially if there is money to be made of it. Those who will not adapt and constrain themselves to (the "right" subset of) people in their vicinity not only in their private lives but also in their professional one, will soon find themselves to be in the minority, and possibly losing opportunities because of it. (They can still cause a lot of damage, though, if someone gathers them into some radical group.) Those who experience changes in their orientation will likely become more tolerant towards different orientations. Besides, on the internet, you can't tell other people's orientation if you only see an avatar. The trait of caring overly much about orientation will soon be lost or constrained to niche environments in the process of social evolution because it's not a winning strategy on a global scale.

So the only way for your orientists to keep their bias is either to move to such niche environments or do away with globalisation.

• As I understand the question, the people want to hate those of the opposite orientation, and don't need justification. The problem that they're encountering is that they cannot tell what a person's original orientation is (only their current orientation) so they don't know whether or not to discriminate. – PunctualEmoticon Jan 9 '18 at 12:02
• @PunctualEmoticon which is why they will not decide based on any sort of logic. They will decide on gut feelings and find a justification for it later. – Real Subtle Jan 9 '18 at 12:35
• Indeed, but how can they know what gut feeling to have when righties and mirrored lefties look identical? – PunctualEmoticon Jan 10 '18 at 22:54
• You see an image of a person (on tinder or wherever) how do you decide whether you like the first impression or not? You just do. It's not a question of conscious decision based on logical clues; your subconscious decides for you and doesn't tell you how. You may later try to go back consciously and find out why you must have liked/disliked this person but that's just guessing because you can't just pull an activity log from your own brain. – Real Subtle Jan 11 '18 at 7:23

In the days of globalization you have technology which will solve these problems. We simply make a government database of all persons and include a field for handedness, which is measured and assigned by doctors on behalf of the government. Note this category will be binary only allowing an R or L, anyone not fitting clearly into either categories is clearly evil and will be assigned the negative handedness of choice.

Once assigned by the government handedness cannot by definition change. If someone appears to change this is clearly either an obvious deception or an illusion and should be ignored. If it is too difficult to identify the objects of hate, or too many of them are able to pass as normal, a government mandated patch could be assigned to clearly mark the individual. If there is any question of course their paper should be checked to verify their status (Lack of papers is of course illegal).

For interesting parallels consider past treatment of groups such as Blacks in the USA, the Jews in Nazi Germany, and the recent bathroom gender laws in the USA. In many cases people from the disenfranchised group are visibly no different from the general population, but were still hated and discriminated against.

• How do you treat foreigners? – PyRulez Jan 11 '18 at 23:46