How can people adjust spoken language to adapt for the discovery that they live on a non-orientable surface?

Question

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

To quickly summarize the world, their are rightie and leftie people which are mirror opposites of each other. In the past they have generally hated each other. However, it turned out they lived on a projective plane, which has no global notion of mirror opposites (orientation), only a local notion. They did not know this at first, but overtime figured it out for the most part. In particular, as society become global instead of local, the non-orietability of the world started having dramatic and easily observable affects, such as lefties becoming righties and vice versa. More details in the post.

Anyways, there's an issue. Translators have adapted to non-orientability to ensure that it is clear what orientation they are talking about, no matter where you are in the world. (When translating or writing translation dictionaries, they specify very clearly how righty and leftie are translated. If their translations are reversed, the translator using it knows that all other oriented concepts will also be reversed. Sometimes it is not clear whether or not they are reversed (if for example the languages are usually not used in close areas), but it leads to consistent translations.) However, one of the languages is quickly becoming very popular world wide (similar to English in our world). We will call the language Z (not to be confused with Z notation). We will only talk about its vocal variant, since mirror reversed written Z is obviously distinct from regularly written Z.

Linguists developed adaptions to Z to deal with orientation, but most people did not care, considering the issue to be solely a theoretical one. Orientists and orientist sympathizers in particular where very vocal advocates. Things changed, however, after the burger poisoning, where 100 people (43 righties and 57 lefties) died of food poisoning because the orientation of the burgers were confused. Non-orientation played a large factor, which was not caught by translators since all the communications involved took place in language Z, thanks to its global nature. Some negligence on the part of the restaurant and others was also involved, so to deflect blame they made a very big deal about non-orientability, and began a campaign to get the adaptions to Z adapted.

My question is, what were these linguistic adaptions? How could the linguists have adapted Z to prevent orientation misunderstandings?

Also, for context, here are some other reasons for adoption.

• Social Justice, Sociology, and Politics: Lefties and righties have historically been separate social groups, and have frequently oppressed each other. Therefore, even if someone is not an orientist, they need to understand orientation to understand the relationships between individuals and society. A first step for this is being able to talk about orientation. They do not want language errors to hinder this.
• Business: Businesses need to understand non-orientability in order to best serve their orientist customers. For example, airlines need to make sure they do not mirror reverse orientist customers, or make them feel mirror reversed. Although they would not use the adapted language with these customers, they would need to use it internally to ensure optimal customer service.
• Biology: Although being nearly identical, lefties and righties do have some (symmetrical) biological differences. Simple examples include tools; some leftie tools do not fit in a rightie's dominant hand properly. Perfumes and other scents might also smell different. Orientation is also inherited, which is important for genealogical research. Diseases also spread and affect them differently. Most importantly, some rightie delicacies are poisons for lefties. The mirror opposites of such foods have the opposite affects. They usually smell and taste different, but hamburgers are the ultimate counterexample. Rightie hamburgers taste and smell exactly the same to righties and lefties (since the scented and flavored ingredients are achrial), but do not cause health problems for righties in moderation. However, one of the ingredients is extremely lethal poison for lefties. Leftie hamburgers work the opposite way.

Notes:

1. Here is the criteria for solving the problem: Say someone takes an object, and passes it around the world in such a way that it gets mirror reversed. The person them self stays in one place. Each time it is passed, the person passing the object tells the person receiving the object the name of the object. Once it gets back to the original person, the name of the object they are told must reflect the fact that the object has been mirror reversed. Moreover, this must never happen in a similar scenario in which the object is not mirror reversed. Note that this implies that the name of the object must change at least once along the mirror reverse path, but multiple name changes are permitted.
2. Z started out in a small, orientable, region. Thanks to colonization and globalization, it is now commonly used in large, non-orientable region of the world.
3. Sound is symmetric, so you can not mirror reverse the sound waves as part of your solution. (Well, you can, but it won't do anything.)
4. Z is not a particularly good language.
   1. Every noun has a grammatical-orientation, even when this orientation has no physical meaning, even locally. For example, gold is considered a "rightie" noun, and dirt is considered a "leftie" noun, even though mirror reversing them causes no physical change.
   2. Many nouns have "duals", which roughly means that they are mirror reverses, and have opposite orientations. For example, clockwise is dual to counterclockwise, a rightie person is dual to a leftie person, right is dual to left, etc... However, this rule is implied very inconsistently. For example, right is also dual to wrong. Gold is dual to dirt. Even more worryingly, rightie hamburgers are not dual to leftie hamburgers. Rather, the words for them are completely unrelated, grammatically. This is similar to how "brother" and "sister" have no grammatical connection in English. The same goes for many foods unfortunately. This means the linguistic adaption can not rely wholly on grammatical orientation. For example, the word for gold should not become the word for dirt when passed around the world. However, the linguistic adaption should "make sense" as much as possible using the rules of grammatical orientation. Ideally if grammatically dual nouns are in fact mirror reversed, the language adaption will switch them when they get mirror reversed by going around the world, instead of inventing new words for all of the physically mirror reversed objects.
   3. Z also has many other grammatical irregularities, sometimes making it difficult to determine grammatical orientation of a word. This is similar to how "goose"'s plural is "geese", even though you usually make a world plural by adding a "s" to the end. Homophones also cause the usual problems from time to time. It is acceptable if your solution has trouble with homophones, however, since people are used to coping with them.
5. Any orientable subset of the world will leave out at least one densely populated area. That is, every orientation reversing curve crosses a major population.
6. The adaption should be reliable, meaning it is hard to mess up accidentally (intentional errors are fine sense you can't stop people from lying). In particular, if one person uses the adaption, and the other does not, they should not misunderstand each other. Rather, it should be clear that they are using different language conventions, and will have to express themselves differently. It should also be reasonably easy to learn and use, to promote adoption.

Answer 1

If I understand thing correctly, if a righty person carries a box of righty food around the world and back to the same place in a certain way, he will end up a lefty person with a box of lefty food - without the feeling of having changed himself, so the other righties around him will look like lefties to him. I'm not fully with you on the math, so I hope that's right.

In that case, since there is no absolute sense of chirality, what we have to track are changes. What matters is not if an object is lefty or righty, but rather the relation between two objects. Two righties originating in the same place are "even" to each other. A lefty and a righty in the same place are "odd". Travelling a chirality-changing route relative to another object switches your odd/even-relationship to objects not moving, and keeps your relation to objects you take with you.

In each population center, designate one reference object. This object should be something that a person can easily compare themselves to to determine if they are odd or even to the object. I could be something that makes a scent that smells different to people of different orientations, or maybe a medical scanner that determines what side of your heart is bigger. Every person in this place should know their orientation relative to the local reference.

Also build up a reference table that keeps track of the relations between the reference objects. Anytime you need to determine chirality, you can use the refence objects as a go-between. For every two references, have a person travel between them and test themselves at both to see if the path switches you.

Example: Person A has traveled here and wants to eat food F. Can they? Well, A is even to the reference of their home town. The path between here and there is odd. Food F is odd to the local reference object. Two odds cancel each other out, making F even to A. The food is edible!

The benefit is that the odd/even words should not have to interact with the old left/right words at all, minimizing confusion. For translation purposes, you can also pair each reference object with a guide saying that if you're even with the object, you're a righty in the local language. With time, this should preferably be less and less needed though.