I don't like this new policy change tbh

[OzyWho]

I think there used to be pages of angry posts before closing a 'serious discussion & debate' thread was considered. (Other than Voss sometimes closing a thread after a few off topic posts. But for as long as they were semi on topic..)
It used to be a last resort type of deal.
I don't remember mods ever editing posts either tbh.

Now a few angry posts and an entire thread is closed?
Go follow the site rules and give people infractions for not following the subforums or sites rules if you must, but please stop closing threads unless absolutely necessary?

[Renegade]

Agree

[DJarJar]

okay, infractions given and thread re-opened. Good call ozy.

[OzyWho]

okay, infractions given and thread re-opened. Good call ozy.

What infractions were oberon and rumox given for comparison? This "good call ozy" sounds like a mockery due to it looks like a double standard to me.

Edit: it's possible I exhibit double standard as well.

[DJarJar]

oberon was infracted on 3 posts for personal attacks, oops was infracted on 1 post for pure trolling. I did not see anything from rumox

[SuperJack]

Hi I'm aamirus and impersonating admins is what I do.

[Voss]

the good call ozy is not sarcastic. thanks for being brave enough to bring this up. staff does try and listen to the community, and there are many examples of this (particularly in the forum mafia side).

[Helz]

I like the idea of moderating individuals more than topics. A part of me was sad when I saw the topic was closed and I felt like the conversation was just starting in some regards.

Its upsetting to me when the Admins mess with my secret master plan to corrupt everyone on the site and seduce them to the dark side : (

[NightmareFrIEND7]

oberon was infracted on 3 posts for personal attacks, oops was infracted on 1 post for pure trolling. I did not see anything from rumox

You guys (you, rumox, Voss) are all idiots btw. You guys can take turns fucking each other. And when you're done you can hop on my dick. That is number 1.
Number 2. I actually wrote this post before but you promptly banned my smurf before the post got 'approved'. How can you even claim you are any different than MU? You ban me and I'm unable to even appeal anything. You just don't like me lol, you're better off admitting that. You're just a trio of sick fucks that enjoy others' suffering. Why else would you infract me for 'toxicity' when the cunt that started the toxicity was rumox? Oh yes, the reason is because he did not personally insult me directly! Also how funny it is to infract the guy that overreacts. Kinda like slapping the kid that takes offense cuz he doesn't get jokes instead of the guy that makes the joke KNOWING FULL WELL that the dude doesn't get jokes. That doesn't even make sense lol

Number 3. You infracted oops... for trolling? LOL, since when is trolling that bad? That's retarded. You should also infract Voss for trolling based on that logic for the post he made about 'goofy'
So, you infract me THRICE, without even warning me ONCE (the warning Voss posted was meaningless. I got infracted after the warning lol), for different posts? You're just a control freak retard. How small is your cock? @aamirus . Because, let's not pretend you're a woman. You just say that so people will put up with your passive aggressive soul-stealing bullshit you fucking cunt. How small does your cock have to be for you to derive enjoyment from belittling a guy living on a different continent, when said guy is assaulted relentlessly by your dumbfuck friends?

Number 4. I deleted my discord account. I'm done with you fucks. I had an exam, I was clearly under extreme amounts of duress. It's not enough that the fucking chef at the place I work at has me working EVEN WHEN I HAVE school; one week I literally had one exam and 2 deadlines within 3 days of one another, so I asked, can I please stay home so I can study? Nope, of course not. I had to work 6-8 hour days that week and I barely had any time for school lol. And of course because his dumbfuckery is constant and consistent, this is still happening. I literally had an exam today and I asked to stay home, but what did he say? Nope just start as you can. Fucking bitch! Even after all I do for them lol, show up when I don't even have to and work so hard.

And yeah, after all this? Mag, you're too aggressive! Mag, you get angry too easily! Yeah, you know what? I'm fucking done with trying to have understanding for people. I have more than enough. It's about damn fucking time someone gives ME some understanding. How about you do that and not add yourself to the fucking problem?

Btw I hope you ban this smurf again so everyone sees how much of a loser you, Voss and rumox are

[Stealthbomber16]

You guys (you, rumox, Voss) are all idiots btw. You guys can take turns fucking each other. And when you're done you can hop on my dick. That is number 1.
Number 2. I actually wrote this post before but you promptly banned my smurf before the post got 'approved'. How can you even claim you are any different than MU? You ban me and I'm unable to even appeal anything. You just don't like me lol, you're better off admitting that. You're just a trio of sick fucks that enjoy others' suffering. Why else would you infract me for 'toxicity' when the cunt that started the toxicity was rumox? Oh yes, the reason is because he did not personally insult me directly! Also how funny it is to infract the guy that overreacts. Kinda like slapping the kid that takes offense cuz he doesn't get jokes instead of the guy that makes the joke KNOWING FULL WELL that the dude doesn't get jokes. That doesn't even make sense lol

Number 3. You infracted oops... for trolling? LOL, since when is trolling that bad? That's retarded. You should also infract Voss for trolling based on that logic for the post he made about 'goofy'
So, you infract me THRICE, without even warning me ONCE (the warning Voss posted was meaningless. I got infracted after the warning lol), for different posts? You're just a control freak retard. How small is your cock? @aamirus . Because, let's not pretend you're a woman. You just say that so people will put up with your passive aggressive soul-stealing bullshit you fucking cunt. How small does your cock have to be for you to derive enjoyment from belittling a guy living on a different continent, when said guy is assaulted relentlessly by your dumbfuck friends?

Number 4. I deleted my discord account. I'm done with you fucks. I had an exam, I was clearly under extreme amounts of duress. It's not enough that the fucking chef at the place I work at has me working EVEN WHEN I HAVE school; one week I literally had one exam and 2 deadlines within 3 days of one another, so I asked, can I please stay home so I can study? Nope, of course not. I had to work 6-8 hour days that week and I barely had any time for school lol. And of course because his dumbfuckery is constant and consistent, this is still happening. I literally had an exam today and I asked to stay home, but what did he say? Nope just start as you can. Fucking bitch! Even after all I do for them lol, show up when I don't even have to and work so hard.

And yeah, after all this? Mag, you're too aggressive! Mag, you get angry too easily! Yeah, you know what? I'm fucking done with trying to have understanding for people. I have more than enough. It's about damn fucking time someone gives ME some understanding. How about you do that and not add yourself to the fucking problem?

Btw I hope you ban this smurf again so everyone sees how much of a loser you, Voss and rumox are

I think you need to take a step back and reanalyze how much a random topic about politics on a website means to you. These discussions literally do not matter and will not ever matter. You are under a lot of stress right now (#4 shows it). Try not to let that stress get into every facet of your life.

Wish you the best.

[NightmareFrIEND7]

I hope to cause you three cunts as much pain as you fucks have caused me. If any of you DARES to so much as ATTACK me for what I said, I swear to God I will make you suffer. I will literally post BS about how Voss belittles people constantly, about how aamirus does it, etc, until I am satisfied you fucks are freaking out over it as much as I am. I hope you 3 (especially aamirus) go to hell. You guys don't deserve forgiveness. Best fate for you is pure death. You better hope there's no afterlife.

[NightmareFrIEND7]

I think you need to take a step back and reanalyze how much a random topic about politics on a website means to you. These discussions literally do not matter and will not ever matter. You are under a lot of stress right now (#4 shows it). Try not to let that stress get into every facet of your life.

Wish you the best.

It's not the discussion that matters... it's the way I get fucking treated in them. Like the issue isn't that there was disagreement, the issue is that I got infracted AND BANNED. I feel personally attacked for that. That's fucking unacceptable.

[Renegade]

I think the ban is automatic and expires after the points go off the record.

[NightmareFrIEND7]

They have literally given me a headache IRL. I hope they burn in hell.

[NightmareFrIEND7]

the good call ozy is not sarcastic. thanks for being brave enough to bring this up. staff does try and listen to the community, and there are many examples of this (particularly in the forum mafia side).

Fuck off you fucking bitch. Don't you dare fucking talk about how "staff listens to the community". Do you even have a moral compass? Fuck you. What else do you do other than tell others how they're brave for bringing something random up? Last time you infracted me and retracted the infraction you didn't even fucking apologise btw, I only realised that now.

[Stealthbomber16]

It's not the discussion that matters... it's the way I get fucking treated in them. Like the issue isn't that there was disagreement, the issue is that I got infracted AND BANNED. I feel personally attacked for that. That's fucking unacceptable.

The issue is how you handled the disagreement. Somebody disagreed with you and asked you to elaborate on your points. You took that as a personal slight against you.

You know whats also beyond me? Your reaction whenever I put forward an argument you do not agree with. :shrug:

I don't see how his post warranted a response like that. The staff team clearly agrees with me. You then proceeded to double down.

You’re extremely aggressive *especially* towards me to the point where I’m wondering if you’re just disagreeing because you don’t like me or something instead of actually believing what you say

Rumox then did respond dismissively and out of turn. The fact of the matter is that you responded to his dismissal with aggression and negativity. I've seen the original post.

The way that I, a neutral observer with absolutely no stake in the argument, see it is that you reacted disproportionately three separate times to rumox questioning your beliefs. You were infracted for it and that infraction lead to an automatic ban.

[Voss]

Fuck off you fucking bitch. Don't you dare fucking talk about how "staff listens to the community". Do you even have a moral compass? Fuck you. What else do you do other than tell others how they're brave for bringing something random up? Last time you infracted me and retracted the infraction you didn't even fucking apologise btw, I only realised that now.

I never retracted the infraction. We gave the other person posting personal insults an infraction too.

[Stealthbomber16]

They have literally given me a headache IRL. I hope they burn in hell.

A good example of what I mean. This is a disproportionate reaction.

[FM Belgium]

Rumox simply doesn't like me. He never has. He's always been a prick. He ALWAYS targets me (without mentioning me directly usually) in these types of debates. I do not believe my thoughts are that hard to follow so I think he's just a douchebag that likes trolling me because he knows I react strongly. In fact I believe this is exactly what happened here and why rumox didn't get infracted. Aamirus, Voss and Rumox just don't like me.

Btw, you guys can keep banning my smurfs but fact of the matter is, I'm not using them to "access the website" or whatever. I'm trying to talk about my ban and why I don't think I should be banned. You can keep banning my smurfs for sure, but I don't think it'll look good for seeing as you're literally denying me the opportunity to appeal my ban.

[Voss]

you may open up an answer hall request if you wish to talk to the staff.

[FM Belgium]

No, I talk here. here or nowhere else. I want others to weigh in. I'm claiming bias against me. I wonder how other people will feel.

[Stealthbomber16]

IDK call me simplistic but I tend to not do things I don't enjoy doing. If I find myself not enjoying a game, I don't play. If I find myself not enjoying forum mafia, I don't play. If I find myself not enjoying a discussion, I stop participating. If I find myself not enjoying the company of people around me, I find new company. I've realized I enjoy my life a lot more when I surround myself with people who are positive and genuine. I make my own groups of collections of those people to be around.

I mean, correct me if I'm wrong here, but you never seem to be enjoying these conversations. I always wonder why you come back over and over again.

I feel like I can make these posts to you because I know you're still reading them. If this is a continual issue... why do you keep putting yourself in the position to be in it?

Anyway, thread got derailed. Sorry everyone. This will be my last post on the topic.

Mag if you want to have a discussion about this you can reach out to me over discord. You probably know my handle but my discord tag is #1256.

[Renegade]

What I will say is Mag you seem extremely stressed and maybe take some time to cool off and come back later.

[FM Belgium]

I think I have said all that there is to be said. I do not possibly see how I could talk "to the staff" after what has transpired so I'll do it through a third party. and thank you sb16, I appreciate it. its nice of you.

[rumox]

For what it's worth.

It's clearly evident, but it's true I do not like you. I quit moderation because of this awhile ago because I felt like I couldn't in good faith moderate fairly knowing this. I'm sorry that my blunt comment about saying your logic is incomprehensible to me has lead to this, I could have definitely worded that better. Even though I dislike you I have always tried to engage neutrally with you in these topics because what's the fun in talking about them without an opposing position?

[Marshmallow Marshall]

To address the topic of the thread (the original post), even though I'm a little late and the issue has already been solved: I agree with your line of thought, Ozy, and think straight up closing a thread for good (not just to take a forced break of an overly heated discussion) should not be a common practice when the discussion remains kinda on topic. What ended up happening reflects this position among staff, as do the messages in this thread, so I think it was just a reaction to a heated situation and not a new standard of moderation policy at all. I would oppose such a standard, for the record. Thanks for bringing it up.

[Helz]

For what it’s worth Mag, I do think your treated differently. But I also think there is a sort of feedback loop involved.
Someone says something and you anticipate hostility so you treat it as hostile even if it’s not which creates hostility.
You say something to someone you don’t get along with in good faith but they see hostility and treat it as such creating hostility.
Moderators expect toxic interactions with you so they treat comments as toxic even if they are not.

Confirmation bias is a bitch. It effects us all and it hurts our personal interactions and relationships. I think for years I didn’t get along with oops because I just could not understand the reasoning for his voice in opposition to mine or understand it was simply a genuine opinion. Fast forward like 10 fucking years and I respect his words over most here simply because I have come to understand he is genuine and will say what I need to hear over what I want to hear.

That said, I do think you have a point that there is bias against you but I also think you can take a moment to understand that bias and learn to interact better within a community.
Sure this is some video game website but mafia and the macro social interactions hold value well outside of this game or this website.

Maybe my words will hold value to you?
Or maybe I’m seen as part of the institution you now hate..

[NotPaopan]

I deleted my discord account. I'm done with you fucks. I had an exam, I was clearly under extreme amounts of duress. It's not enough that the fucking chef at the place I work at has me working EVEN WHEN I HAVE school; one week I literally had one exam and 2 deadlines within 3 days of one another, so I asked, can I please stay home so I can study? Nope, of course not. I had to work 6-8 hour days that week and I barely had any time for school lol. And of course because his dumbfuckery is constant and consistent, this is still happening. I literally had an exam today and I asked to stay home, but what did he say? Nope just start as you can. Fucking bitch! Even after all I do for them lol, show up when I don't even have to and work so hard.

Hey man. If you are reading this. You need to separate your personal, work, and virtual personas.

Everyone one of us had our personal problems. A good example here is a parent who came home from work, greets her daughter cheerfully and enthusiastically asked her to come to play with her. But before that, in the workplace... He made a huge mistake that cost $$$, got scolded by his superior, and got fired. But he never brings that up and threw some hissy fits at home.

Eyy bro. Hit me up if you want to troll at town of salem. All you need is 5 bucks and we can have fun as much as we want. We'll get permabanned after a day or two, but 5 bucks are worth it for the joy it brings to us. I play even while at meetings, spamming doesn't usually require you to read and analyze. Anarchy is fun.

[HentaiManOfPeacesGhost]

(i got myself into an orgy with 10 different people including some transexuals, overdosed on v14gr4, and am now posting this from the afterlife)

For once, I'm very pleased that this LOSER got banned! I give credit when it's due and it's pretty obvious here that sometimes broken clocks (the admins) can still be right two times a day.

Also might want to get your head checked by a shrink, Oberon. You seem like the type of outstanding member of society to stalk and kill a woman you were interested in and then get psychopathic when she told you she had a boyfriend. Or maybe berate a fast food worker just if they made a small mistake.

LOL! As I said before, this community needs to do a better job thinning out the undesirable filth like Oberon from this community. A "man" who doesn't even lift and has more anger issues than my drunk father having a bad day at work.

BTW can we also get rid of Helz? He's a sick being trying to normalize his fetishes subtly in all his posts. See here:

I have done lots of things with my meat

https://www.sc2mafia.com/forum/showt...l=1#post948531

BTW thanks aamirus for sending in the infraction report so I can copy and paste my original message everywhere without Voss censoring me.

[Stealthbomber16]

I have come to understand he is genuine and will say what I need to hear over what I want to hear.

Oops will say what he wants to say over what literally anyone wants him to say/what oops should probably say (nothing at all).

[Light_Yagami]

[BananaCucho]

lol

[Helz]

Oops will say what he wants to say over what literally anyone wants him to say/what oops should probably say (nothing at all).

Honesty holds value even when its someone looking you dead in the eye and telling you that you are an idiot.

Has Rev ever been less real? I remember the time I sorted like 900 bug reports to come to a hand full that actually still existed and when I brought them up his response to some Bus Driver issue was "Fuck your BDSM orgies."

[oops_ur_dead]

I have no idea why I got infracted for trolling.

I feel bad for Mag. Whether it's fact or not homie genuinely feels like he's being attacked. I suspect this is also the core reason for some of his other beliefs but that's none of my business.

[rumox]

Wrong place at wrong time bruh. Causality of proximity.

Could be argued that your post isn't befitting of "serious discussion" what with asserting a position then saying it's impossible to refute your position so do not engage with you, but then I should be infracted for this then.

Seriously though I don't see a problem with minor trolling in serious discussion. If it's repeated behavior that's different, but this was a one off post. Up to aamirus to address.

[oops_ur_dead]

I was ready to elaborate on my stance. I said my mind won't be changed which was absolutely true, same how nobody will change my mind on 1+1=2.

[rumox]

Nah what the fuck start a "Does 1+1=2?" thread right now we are debating.

[HentaiManOfPeacesGhost]

Nah what the fuck start a "Does 1+1=2?" thread right now we are debating.

I read this in my head like seven times and I'm convinced you're having a stroke.

People start this 1+1=2 bullshit when they're 100% convinced they're right and apply a fucking kindergarten math equation to a sociologically complex issue as if they're Einsteins of that field. It's fucking ridiculous because anyone who's completed a proper post-secondary education knows how complicated the world is and the dangers of oversimplifying views and analyses to supergeneralize conclusions to major issues.

That being said, the admins should definitely move to SUPPORT topics instead of HIJACKING other people's threads. For example, I've created many threads on wanting to ban ZZOrange, but I repeatedly got ask how stuff like eugenics was related and got my topics locked. A moderator's job is to facilitate discussion, not keep discussions limited to only the OP and lock threads whenever they don't like the direction it's going in.

[SuperJack]

*54⋅43. ⊢:.α,βϵ1.⊃:α∩β=Λ.≡.α∪βϵ2

Dem.

⊢.∗54⋅26.⊃⊢:.α=⍳'x.β=⍳'y.⊃:α∪βϵ2.≡.x≠ y.

[∗51⋅231]≡.⍳'x∩⍳'y=Λ.

[∗13⋅12]≡.α∩β=Λ (1)

⊢.(1).∗11⋅11⋅35.⊃⊢:.(∃x,y).α=⍳'x.β=⍳'y.⊃:α∪βϵ2.≡.α ∩β=Λ (2)

⊢.(2).∗11⋅54.∗52⋅1.⊃⊢. Prop


@yzb25

[SuperJack]

No need to debate 1+1=2 it's already been resolved the
Proof is above.

[Helz]

I was ready to elaborate on my stance. I said my mind won't be changed which was absolutely true, same how nobody will change my mind on 1+1=2.

I duno. Banach–Tarski paradox strongly suggests that 1+0= >2. I could regurgitate the proof to you or you could see it here https://en.wikipedia.org/wiki/Banach...h_of_the_proof but either way there is a very substantial argument that 1+1 does not equal 2 assuming mathematics is a language that reflects reality and is not just abstract nonsense that just lines up well (although thats a debate in itself)

[oops_ur_dead]

I duno. Banach–Tarski paradox strongly suggests that 1+0= >2. I could regurgitate the proof to you or you could see it here https://en.wikipedia.org/wiki/Banach...h_of_the_proof but either way there is a very substantial argument that 1+1 does not equal 2 assuming mathematics is a language that reflects reality and is not just abstract nonsense that just lines up well (although thats a debate in itself)

I am firmly of the belief that math is abstract nonsense that lines up with reality sometimes. Hence, 1+1=2 because that is what we have defined it to be.

[yzb25]

Through the use of the Axiom of Choice, we can cut a sphere into finitely many pieces that can be rearranged and put back together as two balls, yes. However, this does not in any way imply 1+1=1. The difference is you're taking an infinite set of points (the points of a sphere), cutting them up in some fucked way and rearranging them to make two infinite sets that are the same as the prior set, rather than finding a way to literally make one single item into two.

That, of course, still may not sound logical - like you're taking something of 1 volume and producing something with 2 volume. But the key thing to note is that these smaller pieces are unmeasurable. That effectively means it's not possible to apply traditional notions of volume or mass to these broken up pieces. Axiom of Choice gives us the power to make constructions that can't exist in reality, and one type of construction is these weird, fractal-y fucked up partitions that lack a well defined notion of volume.

This does mean people have to be a little cautious when applying results that use AOC to the real world. But in practice things work out much more conveniently than we might initially expect. And it turns out AOC is necessary to attain several results mathematicians consider fundamental.

[Helz]

I am firmly of the belief that math is abstract nonsense that lines up with reality sometimes. Hence, 1+1=2 because that is what we have defined it to be.

We have also defined complex mathematical concepts to be every much as valid as simple mathematical concepts (such as 1+1=2) so invalidating math as abstract nonsense and then referencing math is a severe contradiction. We must either question the nature of mathematics at its core or disregard it entirely- but in either situation 1+1=2 is no longer an acceptable premise with that reasoning.

[Helz]

Through the use of the Axiom of Choice, we can cut a sphere into finitely many pieces that can be rearranged and put back together as two balls, yes. However, this does not in any way imply 1+1>4. The difference is you're taking an infinite set of points (the points of a sphere), cutting them up in some fucked way and rearranging them to make two infinite sets that are the same as the prior set, rather than finding a way to literally make one single item into two.

I did not expect to go down this rabbit hole yet again. But I very much enjoy doing so (made a small edit in red to rephrase my argument correctly). One lesson I have been chewing on for the last month or so is how ideology is the enemy of free thinking. With that in mind I feel like I can phrase this argument differently than I ever have before.

That, of course, still may not sound logical - like you're taking something of 1 volume and producing something with 2 volume. But the key thing to note is that these smaller pieces are unmeasurable. That effectively means it's not possible to apply traditional notions of volume or mass to these broken up pieces. Axiom of Choice gives us the power to make constructions that can't exist in reality, and one type of construction is these weird, fractal-y fucked up partitions that lack a well defined notion of volume.

The fact you see them as unmeasurable does not mean that they are. Sure we are diving deep into the theoretical side of math but we are very ignorant of our reality. For example- What is 1 divided by 3? Unmeasurable. Take that same number in a number scale of twelve and what is a third of a foot? 4". Change the model from base 10 to base 12 and it can be solved perfectly.

Sure, the way we use math right now we can not explain this proof but it is a proof and the only way to invalidate it is to invalidate math itself. My argument here is just a slightly more complex version of my response to Oops but with much deeper reasoning. Consider my premise that ideology is the enemy of free thinking. What we have to dismantle here is the idea that math as we understand it is encompassing.

Think about the concept of 0. It took a long time to come up with and its implications were huge. I am sure people then thought they understood math but something so simple was a huge mind bend to them. So why should we think we are different? We understand reality in 3 dimensions with general exploration of the potentials of 4 dimensions but we have no clue how many there are. We understand the periodic table of elements as we have discovered and measured it and we have even stretched it pretty far creating things in labs that did not exist naturally but who is to say we do not understand the equivalent of the concept of 0 when it comes to chemistry when we have little understanding about 95 - 27% of matter that exists as 'dark matter.'

Then theres the two accepted models of physics from Newtonian to Quantum which do not seem to line up. Both seem valid although the Quantum is newer and less understood. Diving into it something as simple as the exact position of a particle is considered unmeasurable. Schrodinger's cat was considered blathering nonsense until Quantum physics was accepted so it brings up a question of where you want to draw a line. Its cute to say its as simple as 1+1=2 but that is not anywhere close to the whole story and we are honestly so ignorant of our ignorance its tough to accept what 'could be.'

I personally hope there is some parallel between wavelengths of particles and cognitive connections so science is validated but everything in me tells me we are hardly scratching the surface of what we don't know. For the most basic answer I would point out some base level of quantum physics could be the equivalent of what 0 once was.

The understanding of our ignorance is the beginning of knowledge.

[oops_ur_dead]

I'm not sure what your point is. I'm not "invalidating" math by calling it abstract nonsense, I'm describing it. Chemistry and physics are also abstract, though a bit less so.

I'm not as smart or good at math as yzb but per my understanding the reason that one can definitively say 1+1=2 is because it's a conclusion that's derived from a fixed set of axioms that (pretty much) every mathematician takes as true to form the basis of what defines a natural number. Considering situations where 1+1=2 is false by looking at dubious examples concerning concepts that parallel the concepts tied to the symbols "1", "2", "+", and "=", like your paradox example or other examples in physics and chemistry (e.g. mixing solvents often results in a lower volume than the sum of the original volumes) is intellectual masturbation that serves no purpose.

1+1=2 is true simply because that comes directly from the rules that I use to define what that sentence even means. You can say that one infinite set of points plus another infinite set of points equals a third set of infinite points but that's not the same as saying 1+1 does not equal 2 because those symbols and their meanings are not defined in terms of infinite sets of points.

What you are saying is conceptually the same as someone saying "actually 1+1=4 because to me, 1 is what you call 2". They're not necessarily wrong (although perhaps less practical) but it has no bearing on my conclusion because we hold different things to be true.

[yzb25]

Spoiler : original response :

It should be emphasized that this theorem is quite old and in fact reasonably well understood. We have quite closely identified how this "paradox" arises. It can be arguably seen as some kind of ghost or triviality created by our subtle choice of axioms. If we switch AOC for something similiar like axiom of dependent choice, the "paradox" vanishes, because we lose the ability to even access these niche sets. The proof of Banach-Tarski itself is a bit involved for me at least, but there are similar results which are less fancy but use much simpler reasoning that illustrate the core of the problem. I don't know much about your competency in proof-reading, but if you can half-follow that proof, I'd recommend the "Example" on this page:

https://en.wikipedia.org/wiki/Non-measurable_set

In summary, AOC is used to divide a circle into countably infinitely many identical pieces. Summing these pieces up like a series gives us a problem - if the length of each piece is 0 then the sum, the length of the circle, is 0. But if each piece has a constant positive length, the circle's length becomes infinite. The description in the example uses complex numbers and group theory (unnecessarily, tbh) which makes it seem a lot more esoteric than it is. In reality, it is something that can be understood without much background - assuming one understands AOC. If you're interested, I can try writing a more fleshed out description which assumes less background.

Maybe I'm speaking more assertively than necessary - you certainly could resolve this "paradox" in a different way. I guess you could alter the definition of volume so that it does not demand volume is invariant under rotations / partitions / etc. Or maybe you could even keep volume the same and alter arithmetic itself, though I honestly can't even imagine such a thing. Nonetheless, from what I know, ppl typically just don't bother attempting to assign these sets a volume, in the same way we typically don't bother trying to assign a literal value to 1/0. Running away from our problems or pretending they don't exist is an unreasonably effective strategy lol.

I shouldn't really say much about the science because I'm sure you know a lot more about that than me. Nonetheless, I at least agree with the sentiment that we should try to be humble and alert for errors in our thinking and that common sense assumptions about reality, even if they seem reasonable initially, may run contrary to future observations.

p;edit Meh, idk if just puking more words is helping us reach a common understanding here. It might be better to say specifically what you understand this theorem to be and how exactly it breaks math / arithmetic. I don't think these analogies with physics are helping.

[Helz]

Lots of good points. And to be fair I only made the argument I did because it tickled my brain and I felt like it could make for an interesting discussion.

I suppose as pointed out the question has to be clarified. When saying 1+1=2 do the numbers refer to an abstract designation of quantity or are they talking about 2 physical things? And past that even if they are physical things the most prominent model of quantum physics (to my very limited understanding) is string theory and its variations which speaks to the smallest particles being 2 dimensional strings so with that thought cutting up the 3 dimensional sphere would invalidate my entire line of thinking even if we were to say that the 1s refers to real physical objects.

Yxb also gave me some brain candy I had never considered in refuards to how to pick apart this problem. I do love a good rabbit hole.

[yzb25]

Lots of good points. And to be fair I only made the argument I did because it tickled my brain and I felt like it could make for an interesting discussion.

I suppose as pointed out the question has to be clarified. When saying 1+1=2 do the numbers refer to an abstract designation of quantity or are they talking about 2 physical things? And past that even if they are physical things the most prominent model of quantum physics (to my very limited understanding) is string theory and its variations which speaks to the smallest particles being 2 dimensional strings so with that thought cutting up the 3 dimensional sphere would invalidate my entire line of thinking even if we were to say that the 1s refers to real physical objects.

Yxb also gave me some brain candy I had never considered in refuards to how to pick apart this problem. I do love a good rabbit hole.

Only saw this just now, but I'm glad you got a kick out of it! I thought I might have gotten a bit carried away there

I am not sure of the extent to which this theorem can be applied to reality. If real life could cut things into these kinds of unmeasurable sets, that would effectively allow one to violate conservation of mass. That would be some crazy shit. My kneejerk instinct is to view this as some kind of pure, idealistic form humans have created that can't be found in reality, but idk.