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I want to visualize how worlds with different mathematics and logic could function, as opposed to worlds with different physical laws. For instance, I came up with the following examples.

  • A world where all the observer wants is true.

  • A world where all the observer fears is true

  • A world where all the observer believes is true

  • A world where all the observer believes is false

But it seems some of such worlds can be unstable, for instance, they can quickly degrade into ultimate hell.

Are there any examples of worlds with altered logic which remain stable?

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – L.Dutch - Reinstate Monica Sep 24 at 16:02
  • $\begingroup$ If you wish to read a book which explores this concept, I suggest you read M.K. Joseph's The hole in the Zero . Honestly one of my all time favorites - points to a progression of possible realities where "will" and conflict between characters is the theme - evolving to a final stable state. Limited in it's scientific explanation, but the metaphor is well developed and totally applicable to the "human condition". $\endgroup$ – We are Monica. Sep 28 at 15:00

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Not a world, precisely, but an adventure that I once ran: "The Illusory Castle". It was a puzzle that, once the solution was known, was quite easy. An artifact the party needed had been taken for safe-keeping by a legendary illusionist. When the party tracked down the artifact, they came to a castle with a groundskeeper who confirmed that the artifact was indeed held within the castle. He also told them that the entire place was an illusion, and ONLY the artifact was real. However, banishing the entire illusion would trap the artifact in the illusionist's pocket dimension, so they needed to extract the artifact first.

I had planned on this taking an hour or two to solve, including encounters, but it ended up taking most of a weekend. This was the premise of the puzzle:

  1. The castle was set to "accommodate" its guests. Whatever they looked for, it provided. If they looked for a door, there was one, if they looked for a secret passage, they found it. If they asked if there was a guardian in the next room . . . yep . . .is he a badass? . . . yep . . . wait, are there traps we have to avoid while fighting the guardian? . . . yep.
  2. If the players looked for the artifact, the castle showed them an illusion of the artifact, not the real thing.
  3. Any time they got tpw'd, they woke up back at the groundskeeper's shack with some wounds. Not dead, but worse off than last run.

Solution: There was one constant every time they went through, a sword that always looked the same and, if the players examined their wounds, were the only "real" wounds that the place left on them.

That is the only example I have of something similar to what you ask. A whole world built on a similar concept would be like a dream plane . . . and either a nirvana or nightmare realm . . . or both, depending on how one set up the rules.

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This would only work if there was only one observer and it was God.

Everything would break down as soon as another observer was added.

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    $\begingroup$ Explaining why it would break down would be relevant. We generally discourage answers which presume a reader can "fill in the gaps" themselves, as it were. $\endgroup$ – StephenG Sep 24 at 8:59
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    $\begingroup$ Given the meaning of "God" is very fuzzy, I do not see what this answer is trying to conduct. Maybe worlds with alternate logic indeed would break when another observer is introduced, but this is not evident. Also, it may be the case that a world with standard logic also needs only one observer and do not allow more. $\endgroup$ – Anixx Sep 24 at 10:39
  • $\begingroup$ Perhaps a broken world model could still be built upon. $\endgroup$ – Willem Sep 24 at 19:48
  • $\begingroup$ In our world, I can see a face, but you see the back of a head, and both of our observations can be true under the rules of our universe based on perspective. It is all there, but parts are occluded to each of us. In an alternate reality, I can fear heights, you can fear dogs, but we can both see what we fear (because we are looking at the embodiment of fear from from different angles). This embodiment of fear is a multi-faceted thing who's facets include all things feared, and our perspective is derived from our experiences and how this "thing" turns. $\endgroup$ – Nosajimiki Sep 25 at 20:59
  • $\begingroup$ Best not to smoke that stuff $\endgroup$ – Kilisi Sep 25 at 21:08
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Mathematics (and logic as a branch of mathematics) is an "absolute" science, in the sense that it is not bound to experimental verification. Physicists keep verifying Einstein's relativity theory, no mathematician keeps verifying Pythagoras' theorem.

In physics or any other science one makes an hypothesis, design an experiment to falsify that hypothesis, and based on the outcome accept or reject the hypothesis. This endlessly goes on. I.e. Newtonian gravity works well if it is about throwing stones at your enemy. It fails when it comes to control the timing of GPS satellite signal.

In mathematics one starts from axioms, which are a set of statements which are taken as true (like Euclid's five postulates founding Euclidean geometry), and from them derives/proves a set of theorems. Those theorems are true within the boundaries defined by the axioms, and don't need falsification. I.e. in Euclidean geometry the sum of two sides of a triangle is always bigger than the third one. That's proven and independent from the observer and the precision of the observation. There is no observer in mathematics.

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    $\begingroup$ Mathematics is not a science in any reasonable meaning of the word science -- and this is exactly because mathematics is absolute. Mathematics, just like philosphy, is a search for what's true (within certain well-defined assumptions); science is a search for what's practicable. $\endgroup$ – AlexP Sep 24 at 8:08
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    $\begingroup$ Desagree with absolutisation of mathimatics. It is quite practical and experimental. Arithmetics espacially : lay down 5 apples and then 2 more apples near them and count altogether - you will count 7. But other parts of mathematics, even superabstract, are also verifiable by building and verifing math models. $\endgroup$ – ksbes Sep 24 at 9:04
  • $\begingroup$ Have you heard about experimental mathematics? en.wikipedia.org/wiki/Experimental_mathematics $\endgroup$ – Anixx Sep 24 at 10:36
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    $\begingroup$ @Anixx, do they keep verifying the same conjecture over and over once they have proved it? $\endgroup$ – L.Dutch - Reinstate Monica Sep 24 at 10:49
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    $\begingroup$ @Anixx, verifying is not proving. A proved theorem is true forever. A verified statement is true until the contrary happens. $\endgroup$ – L.Dutch - Reinstate Monica Sep 24 at 10:53
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I can think of two sets of examples.


There is one such kind of world and you go there everyday, even if you don't remember. We call such worlds dreams.

In a dream, you may find yourself light as a feather and yet be stuck to the ground as if by great weight, while everyone around you is moving normally.

In a dream, you may accelerate in the vacuum of space without the need to expel reaction mass.

In a dream, your clothes may quantum-tunnel themselves off of you when you are about to speak to a crowd.

If you wish to see some really creative works related to such worlds, I highly recommend a series of comic books called The Sandman, written by Neil Gaiman and published by Vertigo.

Everybody has a secret world inside of them.

The image above is XKCD #52


Also, .

True magic is different from science, in the sense that it is not some technology which we cannot understand. It is the modification of reality through the mystic/"occult". In many works of fiction, the engine that channels, powers and drives such magic is the mind.

Consider Marvel's House of M, where the Scarlett Witch one day got tired of whole struggle of mankind vs. mutants. On a whim she said "no more mutants", resulting in ~90% of them losing their powers.

In the world of Marvel comics, there are other beings who can reshape the world with their thoughts: Lord Chaos and Master Order, the Living Tribunal, Shuma Gorath, the Beyonder, the Shaper of Worlds. Dr. Strange is usually either dealing with those directly or being consulted by others about those beings.

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  • $\begingroup$ But those worlds (from the second part of the answer) remain logical. One cannot make pi number eual to 4 with a thought. Only in the first part of the answer it is possible. $\endgroup$ – Anixx Sep 24 at 11:15
  • $\begingroup$ @Anixx you haven't read comics enough. I remember a crossover between Marvel and DC where the Joker became omnipotent and he started screwing up reality just like that. $\endgroup$ – Renan Sep 24 at 21:20
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We use Lagrangian mechanics to identify a set of shrewdly chosen coordinate axes on which a seemingly intractable problem becomes static.

Assuming there was some Lagrangian where some extremely cleverly chosen axes of mental state were stable, what might that look like? I'm thinking that things like The Heroes Journey and TV Tropes - libraries of a general "shape" nearly all of humankind's stories take - would probably fit.

What would this look like? It would be a world where bad guys always wear black, are often somehow disfigured. Good guys generally wear white. Good people are beautiful and healthy. The solution to almost every problem requires going on a journey and facing some obstacle. Teachers are wise, but most times impossible to understand. And so on.

In literature, Torg tried to do this explicitly with their pulp reality The Nile Empire. Games Workshop' Chaos has touched on these ideas, but almost exclusively looked at the monsterous aspect of it. Not surprisingly, since GW admits taking a lot of ideas from him - Michael Moorcock's Eternal Champion explores living in a world like this, where you might or might not (hard to tell) be the observer in charge. And in modern theater Inception had semi-stable traversable internal worlds of the mind, that followed externally predictable rules as viewed from a carefully chosen perspective.

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As stated in other answers, some of the ideas from your question are impossible due to the different points of view, beliefs and thoghts of everyone, for example:

  • A world where all the observer wants is true: if I want to be rich and someone feels envy from my wealth, desiring my poverty, the physics of this world would be in conflict.

But... this leds to a new idea for me, where you could complete the "laws" of this universe stablishing some priorities, like some "karma gravity" making the "good" people (in a global moral/ethic way) to get their desires come true prior to the desires of an "evil" man with opposite ideas. "Karma" could be changed by age, weight, etc.

Similar things happen in the following ideas:

  • A world where all the observer fears is true

  • A world where all the observer believes is true

Every universe where everyone can define/created/generate changes, matter, feelings by their minds will (unconsciously or not, represented by fears, desires, ideas, etc.) will suffer by the opposition and the non-coincidence of the different people thinking.

Finally, we left with "the world where all the observer believes is false". In my mind, this option you propose can be perfectly plausible, as René Descartes stated:

"I suppose therefore that all things I see are illusions; I believe that nothing has ever existed of everything my lying memory tells me. I think I have no senses. I believe that body, shape, extension, motion, location are functions. What is there then that can be taken as true? Perhaps only this one thing, that nothing at all is certain.", Meditations on First Philosophy.

In our universe already, we can suppose thet our beliefs are false.

In order to comment an example, we never live the "present itself". We are always reacting to what happened a few microseconds (if we are looking at something a few metter far from us), a few minutes (properly, eight minutes if we look for changes on the Sun surface) or hundred of years (300 years, approximately, if we look at Polaris star in the night sky) back in time. We will never know what happening in "real precised" real time.

We can also asume that our senses are not perfect. Is our blood really red? If nobody tells the colour blind people about our different (and more frequent) perception, they would defend that blood is blue. Are we all colour blind compared to another race? Who is the truth owner?

It should not be difficult for the writer/story designer to make that the reality everyone perceives is wrong (partially at least). Every mistakes/misbeliefs could get assembled all as an entire lie for all. What makes me remember a couple of examples...

Neo wake up from Matrix.

I hope you can find inspiration to create your world with this.

Good luck! And don't let your sense lies to you... to much.

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  • $\begingroup$ "if I want to be rich and someone feels envy from my wealth, desiring my poverty, the physics of this world would be in conflict." This would be allowed even in physical world if we allow the world split on each conflict into two parallel worlds, or if we allow only one person to affect the outcomes. $\endgroup$ – Anixx Sep 24 at 12:34
  • $\begingroup$ @Anixx: That could lead to a logical problem - in both the split worlds, if the two protagonists still exist, then there is still a conflict. You have to somehow suppress one or other's wishes after the split, which will then stop each world being one where every observer gets what they want. Essentially you have set up a logical "unstoppable force vs immovable object" and yes the only resolution is to have one such deity-like being in each universe, with hard limits on power - e.g. an observer could not wish to undo splits or travel to another universe because they wished harm to someone $\endgroup$ – Neil Slater Sep 24 at 15:25
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We alredy live in a world with different logics. Logic depends upon the worldview of the person using it (see Radek Chlup, Introduction to Proclus). Something that is madness and ilogical to a person will be perfectly reasonable, logic and correct to another. Take for example that part of the bible where it is written that the logic/knowledge of the wise man is foolishness to the kingdom of God. Christian (for example, but any worldview would do) logic, if consistently applied, is madness and irrationality to the modern man. So, there isn't something called Logic, but many different logics, each derived from a different worldview, and each of them mutually incompatible beyond trivial statements. For example, you can't understand ancient egyptian logic using modern, industrial-iluminist logic, to understand what the egyptians were really saying, instead of what you think they were saying, you must acquire their worldview first.

Also, your examples make no sense, unless human will creates Reality, and, in that case you should not ask for different logics but how to resolve opposing wills creating conflicting Realities.

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Logic and Mathematics are absolute sciences which are often misused and misapplied to justify outcomes that different people want.

I think that you can find mulch for your Gedanken experiments by focusing on a range of cultural expectations of people's decisions.

Rather than pursuing some form of Einstein's Dreams and postulating how relativity will impact people and society, turn the idea on its head.

If Culture A instills that values that you, an individual, should always make decisions based on the best outcome for everyone you know, how would that shape peoples behavior? Would groups of people surround and social insulate a few people at their center so that center-folk make decisions that benefit this small group at the expense of the world they don't know? Consider Culture B that values making fast decisions based on logic and science, but isn't considered with consistency. What would that world look like?

They all use identical logic and mathematics, but how they assess virtual and outcomes is varied, and how their people's behavior adapts to the social construct.

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Math and Logic are what might be called analytic fields in that you start from a set of premises and they build from there.

For a few of these premises, you could imagine something different. An example of that might be a case where parallel lines converge or diverge (and there you have non-Euclidean space).

But much of math and all of logic would be true for all possible worlds. In other words, you can't really have it be the case that a thing (say a rock or the number 1) isn't itself (aka, the identity principle).

And therein lies the general problem: You're looking for a different case for something that's true in all cases on all possible worlds.

That said, I think you might have something with a people's collapse of their model of the world. And you could also work in an unreliable narrator. But I don't think you could work in different math or logic and have it pass the sniff-test.

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TL:DR;

One of Einstein's students at Princeton (Kurt Godel- he's kinda famous) showed that every system of logical, well defined rules has truths about it that can't be proven using its own logic. Every system of math and logic needs a different system to fully describe itself according to Godel's Incompleteness Theorem. There's an infinite number of worlds that have made these different systems, and thus different discoveries about these systems.

I'm going to be brutally honest and say your examples make no sense to me, but in terms of mathematics it's been formally proven that you can define an infinite number of unique worlds with different (but totally valid) logic and ways of doing math because none of them will be a complete description of all logic.

If you're a maths junkie, there's actually a great example of this in the real world. A renaissance mathematician (Gerolamo Cardano) was competing for a place as a mathematics professor at the University of Pavia (it was the Harvard of the time). To get this special place, you had to best the current professor in a geek-off of mathematical problems. To win, Cardano invented a whole new system of numbers so he could solve 'previously impossible' cubic equations- imaginary numbers.

enter image description here

Anyway, my point is that this development led us to understand so much more about 'normal numbers' (0.7, 1, 5/2, etc.) that we would be decades behind today if we hadn't. Imagine if we'd started off with complex numbers, and used different systems to describe them- what world would we be living in now? Logic is surprisingly subjective.

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  • $\begingroup$ Complex numbers is not a special kind of math or logic. $\endgroup$ – Anixx Sep 24 at 12:15
  • $\begingroup$ Well firstly complex numbers are a kind of math and logic, and moreover the point is that it's an extension of real numbers. The incompleteness theorem shows that there's always stuff we're not going to know due to our system, so different systems reveal things we don't (and could never otherwise) know. $\endgroup$ – mcRobusta Sep 24 at 12:33
  • $\begingroup$ AFAIK, Godel was not Einstein's student. They were good friends at Princeton (Einstein and Von Neumann helped Godel for his immigration interview). Godel published his incompletude theorems before moving to the USA (so before meeting Einstein). Also, as explained above, complex numbers work with the same logic than real numbers. They are basically points (or vectors) of the real plane with special addition and multiplication to give them a structure of a field. They are used daily in physics, and are as much "real" as the real numbers. $\endgroup$ – Taladris Sep 25 at 4:41
  • $\begingroup$ And the invention of complex numbers is usually attributed to Bombelli. Cardano's work is more related to cubic equations. $\endgroup$ – Taladris Sep 25 at 4:45

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