21 KiB
[RT] [BST] A story where every mathematical topic has their guardian
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Author: u/MysteryLolznation Dark Flame Master*
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URL: https://www.reddit.com/r/rational/comments/5qc42b/rt_bst_a_story_where_every_mathematical_topic_has/
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Score: 2
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Created: 2017-01-26T19:09:45
Post:
Concept:
The laws of mathematics are moderated and regulated by human beings. Each topic of mathematics have a single appointed human being or guardian to moderate the topic as they manifest. When the first quantity was counted by a human for whatever reason, the numbers king was born. He would be the leader of all of the guardians, and had ultimate power over his guardians in terms of what they can or cannot do.
The highest power would be the God of Logic. This is the embodiment of humanity in all of its facets. The good, the bad, the intelligent, and the ignorant, the evil, and the good, and everything else combined into a single, statue-like, unmoving being which only serves as the universal glue of all things human in nature.
More guardians other than the numbers king showed up as mathematics became more and more complex, and more topics began arising. When the first computers arose, the Computer mathematics guardian came into play. When probability and chance was first discovered, the guardian of Probability and statistics manifested. All these guardians were once human beings, but were appointed by the God of Logic to become the representative of a certain mathematical topic. Should a guardian grow weary of moderating their mathematical topic, they can resign and appoint their own guardian of their own choosing.
The only reason why mathematical topics need moderators are because mathematics was injected into the context of humanity. The collective complexity of all human beings is enough to disrupt the balance of mathematics, which is why guardians needed to be appointed in order to rectify any and all chips they see in their given topic. Further out into space and guardians wouldn't be needed as the wavelength of complex intelligence emitted by human beings would fade. All intelligent civilizations across do have their own mathematical guardians, though.
Environment:
The world at large have little to no knowledge on these guardians for a large part of history. The old ones felt no need to expose themselves, and they spent little time in the output realm, (which is basically earth). They chose to simply stay in the Input realm, where they moderated mathematical topics around earth. After a complete change in management in the present day time, a new set off prodigies were appointed to becoming guardians, but they did expose the existence of mathematical guardians as they didn't see a reason not to, which nearly lead to a global upheaval, but was curbed. Now mathematical guardians are almost seen as god-like figures, but not by everyone. There are still disbelievers in the world. Also, the simpler and more elementary the topic of mathematics is, the more powerful the guardian is.
Characters:
The Numbers King - Guardian of all numbers. Keeps track of all numbers
Guardian of arithmetics
Guardian of Probability and statistics
Guardian of Algebra
Guardian of Calculus
Guardian of Geometry
Guardian of Computation
The list goes on depending on which mathematical topics had been discovered and categorized at the time. For simplicity's sake, assume that all the mathematical topics that have been already categorized in the present time have their own guardian.
Powers and Abilities:
The Numbers king is charged with keeping track of all numbers within a reasonable and calculable sphere. This also means decimal numbers within a certain amount of decimals that has any chance of being used. Failure to do his job would result in worldwide catastrophe fraught with non-existence of logic. Shit would go down, basically. Other than that, the Numbers King has complete jurisdiction over what a guardian can and cannot do. If a guardian, say, wants to increase probability of good fortune world-wide, he can choose to deny it if he wishes. Every other guardian has abilities based on their given mathematical topic. A primary ability would be being able to alter the rules of their given topic, while a secondary ability would be near-perfect mastery over their given topic.
The God of Logic has laid out some ground rules for all guardians to follow. One isn't allowed to harm a human being. The whole point of being a guardian is protecting their world from mathematics imploding on them, fucking everything up. Although the God of Logic isn't capable of enforcing his laws, the Numbers King, the right hand of the GoL, is tasked to do so.
Comments:
u/narfanator [+11] (8 minutes later)
Two things come to mind:
Math is math because it's inalterable. I don't think you can change how a math concept functions - A square is (AFAIK) a shape with four equal sides; how would you twiddle that? And then - math is mostly derived from other math. If you change how numbers work, you change a helluva lot of other math concepts.
Math is not actually provable without axiom's - see Godel's incompleteness theorem.
I imagine the first would hinder your story, while the second would aide it - the only things possibly more powerful than the Number King are the Axioms. Or, all guardians are masks that the Axioms wear, and any alteration the "guardian" does is actually an alteration by the Axiom...
u/696e6372656469626c65 [+7] I think, therefore I am pretentious. (6 hours later)
- Math is math because it's inalterable. I don't think you can change how a math concept functions - A square is (AFAIK) a shape with four equal sides; how would you twiddle that? And then - math is mostly derived from other math. If you change how numbers work, you change a helluva lot of other math concepts.
I think the best way of putting it is this: math is the study of which conclusions follow from which premises. In short, it's a bit like a game: if you play here, I can play there; if you assume this, I can prove that, etc. Of course, this means that it's ridiculously hard to use math as an actual power--at least, not one that makes sense. Gravity powers, for instance, might mean I can change the shape of the local gravitational field. Sound manipulation might mean I can create and alter existing pressure waves in mediums around me. But "math" powers? It's hard to see how you can change the logical conclusion of a series of steps starting from certain axioms, after all. The best I can think of is that the "Guardians" in the OP might be able to change which axioms are true in the "real world". Of course, then it's less "math manipulation" and more just straight-up reality warping, but...
Math is not actually provable without axiom's - see Godel's incompleteness theorem.
Well... uh. It's true that math can't be done without axioms (just like you can't build a tower of blocks without a floor to place the bottom blocks on), but this has very little to do with Godel's Incompleteness Theorem, which states that any formal system whose set of axioms is recursively enumerable cannot be both consistent and complete--or, equivalently, that any such formal system, if consistent, cannot prove its own consistency. (Yes, it's complicated. A more intuitive--if not entirely accurate--way to think about is that there are certain statements in math which, given the axioms we have, cannot be proven or disproven. Such statements are referred to as "independent" by mathematicians and "undecidable" by computer scientists; one example you might be familiar with is Euclid's fifth postulate, the "parallel postulate".) Just a brief lesson there, because I am physically incapable of seeing a mathematical inaccuracy without correcting it. ;)
I imagine the first would hinder your story, while the second would aide it - the only things possibly more powerful than the Number King are the Axioms. Or, all guardians are masks that the Axioms wear, and any alteration the "guardian" does is actually an alteration by the Axiom...
Well, again, it doesn't really make sense for axioms--that is to say, definitions--to be characters, but I think I see what you're getting at here, which is basically something functionally identical to what I said above about the Guardians being able to change which axioms apply to reality. If I'm wrong, feel free to correct me on that.
u/Chronophilia [+7] sci-fi ≠ futurology (57 minutes later)
The rule that "Mathematics doesn't exist until human minds invent it" is clear enough. It's not my own philosophy - I go for "Mathematics is eternal and beyond the universe, and humans can only discover it" - but it's acceptable for a fictional setting. That said, you may still want to make it an explicit rule of the setting.
What does it mean for guardians to change the way their domain works? Can the Numbers King change the value of 413+612 from 1025 to 1024? How does this affect the physical world? What does it do to theorems like "an odd number plus an even number is an odd number"?
u/696e6372656469626c65 [+2] I think, therefore I am pretentious. (7 hours later)
Mathematics is eternal and beyond the universe, and humans can only discover it
...All right, I'll bite. I'm in the mood for some philosophical discussion anyway. What does it mean for mathematics to be "eternal"? And what does it mean for anything to be "beyond the universe"?
u/LiteralHeadCannon [+2] (11 hours later)
This feels like a theist strawman of an atheist position.
u/696e6372656469626c65 [+6] I think, therefore I am pretentious. (12 hours later)
Hm. Could you elaborate on that?
EDIT: Incidentally, are you the one who downvoted my comment? If so, I'd appreciate an explanation as to why.
u/Chronophilia [+2] sci-fi ≠ futurology (16 hours later)
It means that a mathematical theorem like Fermat's Last Theorem is true everywhere and everywhen. Without reference to any particular physical context. It was true before life on Earth began, and it will be true after everyone has forgotten it. If other universes exist, it is true in them as well. If everyone believed it was false, it would still be true.
... I mean, it's conceivable that the proof I've heard of is wrong (due to human error) and Fermat's Last Theorem is actually false. But in that case, it's false everywhere and everywhen, without reference to any physical context.
Scott Alexander once said that 25% of philosophical problems can be solved by drawing a picture of two pentagons. This is one of them.
If a basket contained 2 apples before another 3 apples were put in it, it now has 5 apples. If I walk 2 metres north and then 3 metres north, I will be 5 metres north of where I started. A solar system with 2 stars and 3 planets contains 5 bodies in total. A cake mix made of 2 pounds of milk and 3 pounds of flour weighs 5 pounds. If a bank account that contained $2 receives a credit of $3, it now contains $5. A particle that decayed into two particles massing 2 GeV and 3 GeV originally massed 5GeV.
Either these diverse situations reflect some deeper truth about 2, 3 and 5, or it's just a coincidence. Either "2+3=5" is true without reservation or limitation, or "2+3=5" doesn't really mean anything at all.
u/696e6372656469626c65 [+2] I think, therefore I am pretentious. (a day later)
All right, I'm with you so far. I'd like to ask you a few more questions, though (if you don't mind):
If it's true that mathematical propositions are either true or false without reservation or regard for the physical universe, then how is it that humans--who are very much part of the physical universe--able to obtain knowledge regarding mathematical objects? For that matter, I noticed that all the examples you used when discussing "2+3=5" directly involved things existing in the physical universe--so is there any reason to say that there's something additional about the statement "2+3=5", beyond whatever physical phenomena it happens to describe? And if there is, what is that something?
I should note at this point that I'm actually partially playing devil's advocate here: although I'm fairly sure your position is actually fairly close to my own, I'm still interested to hear what you have to say in response to my questions.
u/CreationBlues [+3] (a day later)
I think this is an interesting question. 2+3=5 is a relationship between integers. This relationship's truth is independent of the behavior of anything you describe, because it's impossible to find a counter example of integer quantities not following this relationship.
To provide an exception that proves the rule, let's define addition with speed. If you stand on a train moving 3 mph and start walking forward at 2 mph, your speed will be 5mph, as far as you can tell. Then, you might think "I have found a phenomenon which follows the laws of integers! Walking on this train, I can add the speed of the train to my speed by going forward, and subtract my speed from the train's speed by going backward!" One day you are going about your business when you hear about some kind of absolute speed limit. Confused, you ask a friend knowledgeable about such thing the question "If I stand on a train going 2/5c, and run forward at 3/5c, shouldn't my resulting speed be 5/5c?" In response, you learn that you cannot merely add speeds together, and must do a bit of math to find the real resulting speed. Is math wrong? Have you found somewhere where 2+3!=5? In short, no. It turns out speeds aren't like integers, but rather like something called a tensor(? Vector? I don't know the actual proper term for what velocities are in relativity, feel free to correct me on this,) and in fact to be able to describe the addition of velocities 2+3 must still equal 5, always and forever.
So it seems that there is something more to 2+3=5, that it only applies to "integery" things, and if it doesn't then by definition you are working in a place where that relationship doesn't directly apply. However, for example in velocities under relativity, this relationship must hold in the background, through linear transformations. I think this gets to the heart of your question. Even if we lived in a world where there were no "integery" phenomena and there were only velocity like phenomena, the relationship between 2,3 and 5 could still be proven and would still hold, even though nobody would be able to produce a physical example of such a relationship.
u/throwaway234f32423df [+1] (2 days later)
413+612
/r/mildlyhomestuck/
u/None [+4] (2 hours later)
[deleted]
u/MysteryLolznation [+1] Dark Flame Master (3 hours later)
I'm sorry if I'm bothering, but I don't seem to get what your issue was.
How exactly did I force connotations of respect for the things I value?
u/696e6372656469626c65 [+1] I think, therefore I am pretentious. (6 hours later)
I... disagree? There are plenty of characters in fiction who hold Impressive Titles with Capital Letters and Important Roles. Even if we exclude all those characters who do not explicitly embody a particular idea or concept, that still leaves stuff like Mother Nature, Father Time, "capital-G" God, "capital-D" Death, etc. I mean, I don't think the idea of having sentient beings guard the foundations of mathematics itself is a very well-thought-out premise, but I can't say I understand the nature of your particular objection.
u/696e6372656469626c65 [+4] I think, therefore I am pretentious. (6 hours later)
You have an interesting seed of a concept here, but I can't help but feel that this isn't even fleshed out enough to have a productive discussion about, much less write a story around. I mean, what do these "Guardians" do, exactly? What can they do? You've said, for instance, that if the "Numbers King" fails to do his job, there'd be a "worldwide catastrophe fraught with non-existence of logic", but what does that mean? It sounds bad, sure, but that's about it. Why does math need "Guardians"? Apparently, because mathematics was "injected into the context of humanity". Again, what does that mean? Without knowing more, it's literally impossible to talk about your idea.
u/Nuero3187 [+2] (3 hours later)
Honestly the only thing I'd kind of be interested in in this universe would be how different gods of mathematics would react to different alien gods. What if we're the only species that uses base 10, what would be the larger universe's reaction to that and vice versa? What if there was a more war oriented race that would have a god that's more focused on quick off the cuff mathematics that could be done during the last second during a battle? Would there be a sort of elitism that occurs between certain branches? I'd kind of like to see these interactions, but not much else.
u/None [+2] (8 hours later)
I've been writing something similar (math powers in a rational universe). This is interesting. Maybe we can chat at some point?
u/MysteryLolznation [+1] Dark Flame Master (11 hours later)
Sounds interesting. Link?
u/None [+1] (19 hours later)
Story is here
I'll be making some edits and then posting it to this subreddit officially in a few weeks.
u/ABZB [+1] Count of Real Numbers (4 days later)
I once read a quite good short story wherein mathematical statement's truth-values were linked (via hand-waving) to the equivalent computations having been carried out by particle interactions at some point since the BB. The plot was that some mathematicians figured out a way to 'wiggle' the truth values of statements at the boundary of our mathematics, uncomputed theorems, and the negations of our mathematics (and there were beings on the 'other side'. There was a whole thing about how if either side made all of math conform to their side, it would destroy the other utterly. It made more sense in context. Can't remember the title, or author, sadly....
Anywaywho, I've been The Count of Real Numbers for years! :)
u/Sparkwitch [+1] (7 days later)
In a game of Nobilis I ran, the Baroness of Arithmetic was more of a zookeeper than a sorcerer. Axioms and postulates were Lovecraftian horrors: incomprehensible beasts of great power and strange motive. She could command them, and they would exercise that command, but she could not change their nature... nor even could she fully grasp it.
She had established the Commutative Property of Addition as guardian to one of the gateways to Heaven. The player characters needed to get through and the terrible singularity of the thing proved implacable to all their reality-warping powers. So one of the most memorable moments of the campaign is when the Duke of Friction (who had, in his previous life, been a stage magician) cowed the beast with a corny sponge ball routine.
u/MysteryLolznation [+1] Dark Flame Master (7 days later)
I guess the Guardians could very well be the keepers of axioms, and the axioms generally being rules written in an absolute language without homonyms/double meanings in order to keep absolute clarity.
The need for guardians would generally arise in the case that there is a force which is obliterating/obscuring these axioms, and the guardians would basically be glorified janitors/caretakers who rewrite and restore the axioms.
I'm having issues coming up with a feasible "force" which has the power to shake the fundamentals of mathematics, and I've got a feeling that my already established reason "Human beings emit a wavelength which is obscuring the axioms and basic rules of maths".
This Nobilis game sounds fun.
u/Sparkwitch [+1] (7 days later)
Maths are pure but abstract. Three apples, for example, can vary quite a bit even though they share the same unit so that what you're left with when you subtract two could be as tough and sour as a Granny Smith or as crisp and sweet as a Cripps Pink.
Humans care about quality and fairness in ways that are actually rather hard to model mathematically... and maths are, as they interact with the world at a human scale, almost always models. Measuring errors and definition conflicts are everywhere.
Not that any of those concepts is particularly epic. The Guardians of such things would wind up being petty bureaucrats rather than crusading heroes.
u/MysteryLolznation [+1] Dark Flame Master (8 days later)
Actually, I did have it in my mind that they wouldn't be anything heroic. Think Urag-Gro-Shub from skyrim (If you've played the game). He's a grumpy librarian who has no sense of humor. It's only fitting that the Guardians would all be ultra-prudent and no-nonsense-y.