# Can the existence of an orthogonal reality be proven to those who cannot experience it?

In the following I consider "reality" to be "all the sensorial evidence a living being can obtain by interacting with its surrounding world".

I am setting up a world where two realities exist, but they are mutually orthogonal. To clarify this concept, look at the image:

The thing A, projected on reality Y is different from a dot, therefore it exist in that reality and can interact with it. In reality X instead its projection is a point, meaning it cannot interact in any way with that reality and its entities. To make a long story short, reality X is non existent for A.

The thing B has the same, but with reversed outcome.

The thing C is a very rare case (1 in a billion or so) of something that can interact with both realities.

Now my question is: if A, B and C are sentient creatures, is there any way that C can prove the universe is structured in this way, or will he always be treated as a lunatic from both A and B? (The universe is not limited to the only A, B and C)

For the sake of clarity, reality X and Y are not geometrical directions. You may name them as "physical world" and "spiritual world" if it makes easier to grasp what I mean.

• If C can interact with both, can they grab something from A and rotate it 90 degrees? – Draconis Feb 3 '17 at 6:30
• You might find this answer interesting. – JDługosz Feb 3 '17 at 6:38
• You should read Greg Egan's Luminous which touches on something similar. If the two realities truly cannot interact at all it is hard to see how C can experience both let alone prove he is not just interestingly mad. – nigel222 Feb 3 '17 at 8:46
• Is there any significance to C's projection overlapping A's but not overlapping B's in your diagram? – theonlygusti Feb 3 '17 at 17:15
• What are the limits (or not) of C's physical interactions with either reality? If C is hurt in X, is the wound visible in Y? If C climbs onto something in Y, is she flying in X? That is, is C one mind with two (half?) bodies or a single body that interacts with both realities at the same time? – Matthieu M. Feb 3 '17 at 18:33

You ask a very deep philosophical question whose answer, over millennia of study by the likes of Aristotle, Pascal, and Popper is "dunno."

You'll have to forgive me for this, but those who know me on WorldBuilding know "ask a deep philosophical question, get a wall of text from me in return," so forgive the length. It's so easy for world building to cover great swaths of philosophy in a single stride.

Your question is a very generalized one, in the language of mathematics. However, it turns out even the specific examples are hard. You mention the "physical" and "spiritual" dimensions as one example of this structure. This is the source of one of the golden unanswered questions of philosophy: physicalism or dualism? The question is one of consciousness. Do you need some non-physical substance to be conscious? Typically this is given the name "mind" rather than "spirit," leading to the following definitions:

• Physicalism - Matter is the only substance in the universe. The mind is just an illusion.
• Dualism - Mind and matter are different substances. You cannot have consciousness without mind.
• Idealism - Mind is the only substance in the universe. Matter and the physical realm are just an illusion -- a shared dream.

I put idealism in the list to line up better with your A B and C groups, even though it is currently less popular than the other two. This particular trio of ideas has existed for thousands of years, without resolution. Philosophers cannot seem to figure out how a dualist can convince a physicalist that there's "mind," and a physicalist cannot convince a dualist that there is no "mind." They've been locked in disagreement for almost as long as we can remember.

One of the critical concepts for understanding why this disagreement is so difficult is the concept of something "supervening on another." "Supervene" is a great philosophical word which is used to describe behaviors which are completely explained by underlying behaviors. For example, "the boiling point of water" supervenes on lower level electrostatic attractions and molecular structures. If you understand the electrostatics and the shape of water molecules, you can perfectly predict the boiling point of water. In fact, you can explain what "boiling" is in general.

Physicalists claim consciousness supervenes on matter. They claim that consciousness can be completely explained by the physical state of the brain. Dualists disagree and say that there is something that cannot be explained by brain states, but they haven't been able to pin down what it is in a language which the physicalists can agree with. This inability to distinguish between the positions has lead to even a fourth category of thinking called compatabailism, which suggests that we can never know whether the universe is made of one substance or two!

Another great problem of the same nature is the problem of Many Minds. If you assume you are conscious (either by the phisicalist or dualist concept of the word), how can you be sure other conscious entities exist? It turns out to be surprisingly difficult. One of the major challenges is the concept of qualia, which is your subjective experience of the world around you. Take the concept of "red." Are you certain what you perceive as "red" is the same as what everyone else experiences as "red?" Maybe you were born with "red" and "green" flipped, but then you were taught English and flipped the words as well. You'd never know that you'd flipped both the words and the qualia themselves unless you could somehow experience someone else's qualia. This takes your concept of orthogonal realities to an extreme. This would suggest one separate reality for every conscious being in the world! It's also an unsolved problem in philosophy. Nobody knows how to resolve the question of many minds.

Next on the great list of philosophical questions is what does it mean to "prove" something. You always prove something within a system of proof. For example, you may prove "2+1=3" using First Order Logic and the Peano axioms, which are the basis for arithmetic. This concept of proof is tricky because it is incredibly more precise than the day-to-day intuitive meaning of the word. For example, science never actually proves anything by the philosophical definition. All it does is try to reject hypotheses which seem false, until they are left with hypotheses that work so well that you assume they must be true (a process called abduction). Without a definition of "prove," you cannot answer such existence questions.

However, what you can do is unsettle existing theories of reality. Let's say we get really lucky and two individuals fit into group C. Science of type A could run experiments on them by separating then, feeding knowledge to one individual, letting them communicate through B, and the other individual repeating that same bit of knowledge. Do this enough times and you would demonstrate that either there is another orthogonal existence or the reality of A is non-local, permitting the two individuals to have telepathy. That's as close as it gets.

However, an alternative is that the realities may not be perfectly orthogonal. Given that some individuals do fit into group C, it seems very likely that the world of A has some connection to the world of B. It may be terribly terribly faint, but it's there. The world of A may be able to communicate with B, just weakly.

Of course, if this isn't true, then you have created another interesting problem: a demarcation problem. If you have an individual in group C, you now have to define what an "individual" is. It turns out that this is famously difficult. The line between one person and another is not all that clear when you get down to the molecular level. Your people in A now need to be able to explain why this person (in group C) suddenly has access to all this content that nobody in the rest of the world has, and more importantly, you as an author need to conceptualize where that boundary is.

If a person in group C forms a religion in world A, and people begin to truly believe in world B, what happens? Can C start "giving" them insight into world B? If I am a worshiper in world A, believing that world B exists, can some of the group C individual's abilities "wear off" on me? If the person in group C "dies," and we eat his body and drink his blood, do those atoms connect to world B? What about just breathing the same air as he breathes?

There's a good reason religious wars are fought over these complications. They're not easy questions to answer.

• It's a shame that this isn't a discussion forum as there're a lot of comments I'd otherwise make! I like the broad presentation of topics, though the ideas aren't quite fully developed. For example, dualism is a subset of non-dualism, derivable by making the simplifying assumption that the physical universe can't affect consciousness (and then refutable by noting, say, beer). Also, I'd say that physicalists are compatablists by default; non-compatablist physicalists are a fringe minority at best. – Nat Feb 6 '17 at 15:29
• @ChemicalEngineer I agree there's much more than the three philosophies I mentioned; there's a whole palette of options out there to use! However, three paragraphs in to trying to give them justice, I realized it wasn't helping the answer at all, so I had to condense. – Cort Ammon Feb 6 '17 at 16:18
• As for combatablists being the default, I disagree. Compatabalism requires an acceptance of a quantity of unknown that never goes away, and that bothers some people greatly. While my anecdotes are not a scientific poll, I find I spend about as much time debating with physicalists that disagree with compatabalism as I spend with dualists that disagree with it. We, as a society, really like certainty, and that's one thing compatabalism is in short supply of. – Cort Ammon Feb 6 '17 at 16:19

Esse est percipi: to be is to be perceived. An "alternate reality" which has no interaction whatsoever with "our" reality has no existence.

If the special entity C can take objects from reality A and make them perceivable in reality B then yes, the existence of reality A can be proven to those who live in reality B -- and A and B form one single universe, and physics will have to be restarted from scatch, yay! (Because taking objects from reality A and making them available in reality B implies that energy is conserved only in the "total reality" A + B.)

If C cannot do it, then reality A does not exist for those who live in reality B.

• I don't think I agree. Some of us belive in god even if there is no proof about it/him/her. How do you perceive god? – Noldor130884 Feb 3 '17 at 11:41
• @Noldor130884 That is totally different thing. Gods have a possibility to interact. Belief is not that there is some completely irrelevant being somewhere else that is completely independent on us and vice versa, and that really has nothing to do with us. – user3644640 Feb 3 '17 at 12:16
• @user3644640 "Gods have the possibility to interact" if you believe in them. Where did you see that one dimention is completely irrelevant to the other? The two can be absolutely entwined, but still completely indipendent one from another (and I don't want to start a discussion on religion, but the sentence "Gods are not completely indipendent from us" doesn't sound that you're talking about a divine being. – Noldor130884 Feb 3 '17 at 13:44
• @MarkGardner There you go: you are Universe A and I am Universe B. That is exactly what I meant. How do you convince me that God exists/how do I convince you that it/he/she doesn't? One of us should choose to believe, which at this point I find to be the only possible solution. – Noldor130884 Feb 3 '17 at 13:47
• @Noldor130884: A god who does not interact with this world is devoid of existence; such a god makes a poor subject of devotion. In particular, the Christian religion firmly maintains that Yehowah actively interacts with our sublunar world: give us this day our daily bread, [...], lead us not into temptation; but deliver us from evil. – AlexP Feb 3 '17 at 14:05

Yes, to some degree, if he can find and cooperate with another such rare person, D.

Have B relay messages between C and D. After ruling out other explanations, A will have to either believe in the existence of reality X or telepathy. Since A has been convinced that something implausible is going on, he's likely to believe in reality X, assuming he can't see any reason for C and D to lie about telepathy vs. reality X.

Another possibility: If C can interact with objects in both realities, just take a table from either reality and stand on it. Either people in the other reality will have to swallow your explanation for it or believe that you can levitate. (Though if this were the case, this "demonstration" would presumably have happened automatically soon after C was born or gained his "powers", since the layouts of the realities are probably significantly different, and would pose interesting challenges, as mentioned in another answer wrt. cars)

This scenario also presents interesting challenges in interacting with the realities. Any time you interact with people in one reality, you will seem insane in one. I'd imagine it'd presumably be very hard to hold a job in both realities... (Which raises questions about food, which was touched upon by another answer)

• If the odds is 1 in a billion finding another person with the same capability is going to be extremely difficult. – Taemyr Feb 3 '17 at 12:06
• ...take a table from either reality and stand on it. Might be difficult. If you transported from some other reality into this one, what would you figure odds are that you appeared within, say, 100,000 light-years of any galaxy at all? Much less anywhere near a 'table'. – user2338816 Feb 3 '17 at 12:25
• @user2338816 Why use a table? If the worlds are different then he can just stand on different ground since they will most likely not be aligned. – user31746 Feb 3 '17 at 12:49
• Actually, C and D can directly interact with one another in reality X without needing B to act as intermediary. C can arrange to have D call A on the phone, directing A to write words on paper, make various gestures at objects in the room. C then communicates with D in reality X, and D tells A what C said there. This won't prove that X exists, but will prove C and D have a secret communications path. – Monty Harder Feb 3 '17 at 17:14
• @MontyHarder Simplest explanation is that C & D are next to each other in reality Z and that X doesn't exist. – user2338816 Feb 4 '17 at 9:51

I'm not sure the picture is helpful, but I think I get your concept.

Could a team from persons in A, B, and C create a scientific experiment to support the "orthogonal reality" hypothesis? This would be complicated that only people from C can talk with the entire team.

• Have a person in C demonstrate something to observers in B which is best explained by "having gone through" A.
• Have an experimental subject in C stay healthy on food and air from A, while interacting with B.

This would not prove alternate realities, but perhaps researchers from B will start to think of experiments consistent with the many realities. If all work, the theory will get support.

That won't be proof, because science does not work that way.

• that sounds like establishing a religion... – L.Dutch - Reinstate Monica Feb 3 '17 at 8:01
• @L.Dutch I disagree completely. The purpose of multiple experiments is to build evidence. B can verify/rely on (to a reasonable degree) certain properties of C. For example, that C has a normal-ish body that needs to consume food. If they can show that these rules can be violated, it's evidence of something else going on. Perhaps the rules don't apply to C for some reason, but also perhaps C is drawing resources from A, as it claims. The more B is able to choose and set up the tests, the stronger the evidence base becomes. – Samthere Feb 3 '17 at 13:25

What you do, is get two Cs. A tells something to C1, who then tells B. B then tells C2, who has had no contact with C1(and so no way of knowing the original message) who then relays the original message to A. You then repeat the experiment with A's and B's roles reversed.

It is probably similar to a test for long-range telepathy (10-1000 m).

• your answer is the same as Aleksi Torhamo's which was posted 2 hours before yours. It also happens to be the idea that I was intending to post now (which is 2 hours after yours). I won't be posting because this one excellent answer has already made the list at least twice. I'm commenting here just so you understand why your great answer is not getting as many up votes as it deserves. – Henry Taylor Feb 3 '17 at 15:23

If A can interact with C and C can interact with B, then just by the transitive property A can interact with B.

Photons only interact with things that couple to the electromagnetic field, but we've learned virtually everything we know about the strong, weak, and gravitational forces of the universe by seeing things with our eyes. Whether it's from seeing a ball fly through the air, seeing something in a telescope, seeing the readout of some sensor in a particle accelerator, it's all come to us only via a particle that doesn't directly interact with the other fields.

Since there exist things that can physically interact with both worlds, they aren't actually separate. Not only would there be experiments to prove to A or B that the other exists, I would expect there to be technology made of C type material that could let A or B directly see or manipulate matter in the other "reality".

All you have to do is have A throw a rock at C's head while B is watching and it will quickly become clear something weird is going on.

tl;dr- By saying that $$\text{A}$$ and $$\text{B}$$ are orthogonal, you've explicitly defined them as being unable to meaningfully interact. This question seems to be if this situation is even possible if we allow a mutually interactive $$\text{C}$$ between them. The answer is that, yes, $$\text{C}$$ can exist while $$\text{A}$$ and $$\text{B}$$ maintain complete orthogonality.

## Understanding an orthogonal reality is impossible by definition

No entity in $$\text{A}$$ could ever understand, know of, or meaningfully interact with an entity in $$\text{B}$$, even if an entity in $$\text{C}$$ attempts to serve as a bridge. If $$\text{C}$$ attempted to tell If $$\text{A}$$ or $$\text{B}$$ about the other, it'd be meaningless gibberish to their ear.

The issue is that minds are themselves physical entities, and cannot have any congruence with a fully orthogonal externality. Therefore, it is impossible for any mind in $$\text{A}$$ to reason about anything in $$\text{B}$$.

### Example: Orthogonal beings can't understand $$1+1=2$$

For a concrete example, consider $$1+1=2$$. Really easy, right? Your brain solves this question in two ways:

1. Memorization: You've seen $$1+1=2$$ a million times; so much so that, even if you didn't know what it actually meant, you could recite it.
2. Understanding: You know how numbers and addition work, and $$1+1=2$$ is really easy for your brain to reason out.

It's possible for $$\text{C}$$ to get $$\text{A}$$ or $$\text{B}$$ to memorize $$1+1=2$$, in the sense that $$\text{C}$$ can teach them to reproduce symbols that $$\text{C}$$ would recognize as representing $$1+1=2$$. But, if that fact's orthogonal to their reality, then they're unable to understand it, even if they've memorized the symbols that $$\text{C}$$ can interpret as that fact.

If $$\text{C}$$ could eventually teach $$\text{A}$$ or $$\text{B}$$ what $$1+1=2$$ means, i.e. addition, then they weren't fully orthogonal in the first place, violating the premise of the question.

### Note: $$\text{C}$$ is underdefined

In the question statement, $$\text{C}$$ is defined as not being fully orthogonal to either $$\text{A}$$ or $$\text{B}$$, enabling it to act as a mediator. However, this description could be true in several ways. For example, $$\text{C}$$ could be a strict superset of $$\text{A}$$ and $$\text{B}$$. In this case, $$\text{C}$$ can fully understand everything in both $$\text{A}$$ and $$\text{B}$$.

However, it's possible that $$\text{C}$$ only shares a single aspect in common with $$\text{A}$$, and a different, single commonality with $$\text{B}$$. In this case, while $$\text{C}$$ isn't fully orthogonal to either $$\text{A}$$ or $$\text{B}$$, it would be pretty close.

This isn't a problem for the question because $$\text{A}$$ and $$\text{B}$$ will never see each other as more than pure, random, senseless noise, regardless of $$\text{C}$$'s exact nature.

You might consider them to be more spacial dimensions, but that doesn’t work as I explained in this earlier answer.

If the “realities” are different, then even if they intersect it won’t make any difference as they will ignore each other. A candidate for what that “reality” might be is a D-Brane. If you posit that different branes don’t interfere with each other, we could still feel gravity from objects in other nearby branes.

It's good. But for psycological answer you can look to the "Flatland", sure, it's a bit dated, but human minds didn't changed that much about another dimensions. Also, it seems obvious that C live in its own realm (Z?), which at some point intersect X and Y. So, Z-aborigens have hard time with avoiding objects from X and Y realms, while their own buildings should take places in both realms.
Just to demonstrate, imagine you see a man, who walking down the street. He has hard time to cross the street, as he see both the cars you see, some other cars, invisible to you, he can't pass some empty spaces you see, as there are buildings, or other objects, in alternate realms. The only way they could prove the other realm — their inability to pass the objects from other realm. Try to drag him through the wall of another realm, it's painfull, but solid, as the wall, proof. Another way for C-creature — to realize there could be realm, which is not intersects any other realm, true Z axes in your diagram, where C is not intersects X and Y at all. With such a life I'm sure C's will escape ASAP to it.

• Perhaps a good start. If C can interact, then C can be interacted with. And if C can be interacted with, then there should be "objects" from C that C can make available to A and that can interact with B. A should be able to use a C-object to implicate B. – user2338816 Feb 3 '17 at 12:30
• See this comment. It refutes this answer a bit. – wizzwizz4 Feb 4 '17 at 9:39
• @user2338816, nice one! So C-object should be visible both for A and B observers, and can be interacted with all 3 sides, so, it's just a matter of organizing a meeting with three sides. But, there is a problem, A or B could more easily believe it's some kind of a trick, and demand for another place of demonstration, there other side could not come by some reasons (eg, A has an ocean where B build a city). Which gives me an option - C can walk in the air and on the water! – mr4eshir Feb 6 '17 at 11:18

tl;dr There are multiple problems about defining the various parts of this question (like what a proof means in this scenario) and how the claims of the being existing in both realities might be interpreted by a sceptical person. But my personal verdict would be you can get the other being to believe in the other reality but you cannot proof it.

(I hope this post is not too long but I was a bit interested in these kinds of questions for world building myself so my answers are a bit lengthy.)

I think the task of getting A to believe that reality X of B exists gives C multiple different problems and as we are already talking about different realities the solutions might in the end depend heavily on properties of those realities and their inhabitants, that are fundamentally different from our own or even your views on what can be seen as a proof or what exactly needs to be proven.

There is the problem of how a physicist A would have to solve the task in getting information about this other reality by proxy of C. But there is also the problem of how a philosopher A would interpret it and actually say the claim of C "there exists another reality from this one" is true or false or any other claim of C about this other reality of B for that matter because C wanted to prove not only certain properties but the actual "structure" of the reality.

The problem with the philosopher A interacting and communicating with C and interpreting the findings of physicist A is the following. When do I say a "reality" "exists"? For example no matter what you tell me about our actual universe with planet earth and everything I could argue, that it is just made up in the back of my mind and none of the persons I see really exist. But if I form the will in my head to stomp my foot on the ground and my foot and leg move as if I had a foot and a leg and they stomp on what looks like there is a ground that belongs to the planet earth as if such a thing exists maybe you could say reality exists but there is no actual proof of reality existing. There is just the interpretation, that the things that I perceive are part of a reality. This might sound like a non-issue for most of us but depending on what kind of philosopher A is it might come to different conclusions about these kind of claims especially because there already is a reality that it calls its own so everything else is either part of this reality anyway and is perceivable anyway or its perception behaves as if it does not exist, so that might be important if you think of A actually arguing with C about the reality of B.

I think what we should say is that this task of C to persuade A of another reality can probably not solved by mere communication, because all that would prove is that C talks to A as if there would be another world for C to perceive but A would just tell C that it should stop all this world-building in its head and get a real hobby.

But now to what would actually be the basis of all this philosophical arguing about what might be non-sense or not. Physicist A has to start its work and its object of interest is C. Now C has to be very cooperative about all of this. Basically to get the best kind of argument about the reality of B that A can only perceive "through" C A has to analyze C in every conceivable way possible with the scientific method.

The other answers speak about for example taking an object from the other reality, but that would look to A only as if C can materialize objects from thin air, which depending on the universe they live in might be impressive or not but not a proof for a different reality actually existing. Even if it would have properties that only things in the other reality can have, A would not know that those properties exist on the other reality. This would also have to be proven to A by C. I guess you see the problem here, the properties would also just be seen as being new in this world and created out of thin air, so there still is no proof.

Now lets think about all the ways A could analyze C to figure stuff out about the other reality of B. A could try to push C but if B stands behind C and does not let C move A would be confused about that. If B would heat up C so that energy seems to just come into existence another thing about the laws of physics that A believed in might have been just proven false. But A would as a physicist only think of those things as things that it did not know before about its own reality and it would think that C is a thing with special properties, but only in this reality.

So the problem is, if A believes, that it can still figure out new stuff about the world it will through C only find out more properties about how C interacts with its own reality, everything as if C would have its own rules but maybe not its own reality where there are things like B that communicate with it in some way. Every form of communication can just be seen as made up or popping into existence from nowhere.

So A can use C to scan the other reality of B like a blind man scans his surroundings with a stick, but the interpretation of its findings might just be something scientifically sounding like:

"C reacts to some field that we cannot interact with directly, and this field does not let C through as if the claim of C that there is another person that I am trying to push C through is standing behind C were true. And the field disappears sometimes as if the claim of C that the person has gone away were true. But we cannot catch that person that C is talking about because nothing in our reality except C interacts with it, so the thing does not really act like a person, more like a magical field, that sometimes pops up and sometimes goes away, with some other rules i could find out about it that make its behavior somewhat predictable. I will call this field the dark field (because we can only perceive it indirectly like dark matter) and get a nobel price for the weird properties I have found out about C and some field that interacts with C. Maybe we will figure out more stuff about that in the future"

So C cannot prove A that anything that is able to communicate with him exists in a different reality, and for everything that does happen with C in the other reality, A might interpret it in the simplest way possible like "it just appeared out of thin air" but not like "it appeared, so it must belong to a different reality and the people C is talking to are real".

But A could also just call that a different world "the world of C" or something like that. Or A could just stop being a sceptic and just believe in the claims C is making as we do all the time in the "real" world with our believes, but there would never be absolute proof for a being communicating with C because even if as in a different answer two things of the type of C would know something because B helped would probably be interpreted as a direct form of communication between the to C-like things but not as something like B being here. That might just be the interpretation of C of what is happening because C is hallucinating.

However if for some reason A knows with absolute certainty that some things just are not possible in its world, because maybe A created this reality and knows everything about it and its consistent logic, then that axiomatic truth might be used to deduce that something different must exist. But as far as I know at least we as humans have no proof of anything existing at all we just take this fact as given because it seems obvious.

So either A needs special information, that we cannot have or C needs to be able to basically bullshit A into believing its lies. At least other people in the reality of A would not know the difference between the other reality existing or A just being really gullible and C making stuff up.

But this is a weird topic to think about. I guess because of the nature of thinking about alternate realities a lot of this stuff depends on how something would be interpreted philosophically or what type of assumption you could make about the basic logic of different realities. So you maybe had to define what the consciousness of a different being is and how it works together with things that are objectively perceivable and maybe you could prove the existence of communication with a different being that nobody else can perceive. Although I myself would not be THAT sceptical if you would only want to prove to me that somebody on the other side of the world exists and we can communicate with that over the Internet with a computer. So maybe talking about what a REAL proof is might be a bit unnecessary. I believe things, that I have no REAL ABSOLUTE proof for all the time. The medias I consume ARE my reality, if the things they talk about exist or not and I behave as if those things exist, even if the maybe don't. Maybe C would say that is proof enough, that I believe in them and C should focus on making A behave as if the other reality is existing. If A would have an incentive to believe the claims of C, then A and maybe all other beings would act like that, but now we are debating as what counts as "proof" if there is no other absolute proof.

So to wrap up, there would through the scientific method and logical deduction in a reality with the same logical rules as ours be no way to absolutely proof the structure of the universe with two realities existing and beings with consciousnesses and the ability to communicate in both realities.

But I tried to include some possibilities for "alternative facts" in other realities and some alternative ways of interpreting the claims of somebody as "truth" then the scientific method and logical deduction. I hope this helps and I did not go way too overboard with my explanations.

I assume person A trying to persuade person B, and only person A can perceive the orthogonal reality and interact with it (but can't take any material objects or energy back except for memories).

A can still try to prove the orthogonal reality by asking 1000 people in orthogonal reality to factorize big numbers given to him by B and answering in seconds without any devices available to him.

• C is the one who can percieve / is in both realities. A and B are in realities X and Y respectively, but not both. – wizzwizz4 Feb 4 '17 at 9:44
• Well, then C can be the middle-man. Still possible. – ajuc Feb 7 '17 at 14:38

If he can touch both realities then how does he choose which reality to touch. For example if his body is physically touching reality X then he might be going through a wall in reality Y which he could use to prove the existence of both realities. If you want him to touch both realities then both would have to look exactly the same (mountains, houses and other beings all in the same place), however there would be no point in having those realities.

If you however choose to limit his interaction in one of the worlds, like not being able to touch things in reality Y, then I think you'd have to go with Aleksi Torhamo's answer and find someone else with the same perception and relay a message like (A > D > B > C) proving to A that there is a being B. This could be relatively easy if the world you're creating is similar to ours. Both people could meet up accidentally on a paranormal internet group or meet up at a paranormal investigation society.

• If the realities are orthogonal then moving in one doesn't necessitate moving in the other. (e.g. no matter how long A is it is still a point in X) – Seeds Feb 3 '17 at 19:35
• @Seeds Since A isn't the one moving in X, it's irrelevant if A manifests as a 'point'. And even though it doesn't necessitate moving in the other, nor does it eliminate it as a possibility, especially for C; again, A is irrelevant to what C can do. – user2338816 Feb 6 '17 at 11:56
• The real point, ha ha, is that if C walks back and forth along A, what does it look like to B, as C isn't moving at all in X, but IS moving in Y. – Seeds Feb 6 '17 at 15:33

Is this a similar concept to the Apprentice Adept series by Piers Anthony?

The series takes place on Phaze and Proton, two worlds occupying the same space in two different dimensional planes. Phaze is a lush planet of magic, where Proton is a barren mining planet of science. As the series opens, each person born on Phaze and Proton has an alternate self living on the other world. But if a person on either world lacks a duplicate (for instance if a Proton citizen immigrated there from another planet, or a counterpart from the opposite frame died), he can cross to the other through an energy "curtain" that circumscribes each frame.

As I pointed out in some comments, let belief do the trick.

Your question pretty much implies that creature C has to provide A & B in both their universes a tangible/perceivable proof (which sounds to me a lot like scientific method), but since the dimensions are orthogonal, each inhabitant of these planes would not have the possibility to glimpse the existance of "the others".

Let C be a creature A e B look up to (God?) in both worlds. Through belief of C's words, A could believe in B and vice versa.

Let me write an example: suppose my terrestrial life and the hell are orthogonal. Through religion I believe in the existence of hell, therefore I don't commit crimes or such in order to preserve my soul in the afterlife. By acting like I do, I am altering what happens/will happen in hell (I am wildly assuming that hell has no time). The two dimensions are entwined, but I never had the possibility to experience any proof about it being real.

The question answers itself. Its premise is that a proof can be communicated; its restriction is only that the proof must be convincing. Therefore, since the question contains sufficient data regarding mutually orthogonal universes to convince beings in its own frame of reference, the conclusion must be that any being in any frame of reference would be convinced by the same data.

Because C can interact with both X and Y, if C can determine a constant in X that is a variable in Y, and manipulates the variable within Y while A observes it in X, A will observe a constant become variable against all known laws of X, thus proving a property from Y, outside of X, exists. Vice versa for having B observe an effect from X.

Alternatively, have reality Z, perhaps called "quantum world" existing interactively in both X and Y and relationships are proven indirectly. What A does to affect Z by acting on N, changes things in Z that B in Y can observe, even though B cannot observe A or N. C, able to observe A and N, knows what will happen and tells B to watch for the observable change in Z before it happens. Thus A is proven to B.