this is like the thing with pluto, but less understandable, and involves laundry

Dear Fandom,

Okay, granted, xkcd started it, but still. Is the Banach-Tarski Paradox supposed to tap dance on the conservation of matter or am I missing a key point that make this make sense? I mean, fuck Euclidean geometry, I was always terrible at geometry, but this is screwing with how I internalize the universe so stop that shit, mmmkay?

God, this is like when they de-planeted Pluto.

Axiom of Choice is almost like, understandable in comparison.

Note: Admittedly, my reaction to Banach-Tarski and Axiom of Choice may be based on the entire sock construction, being that there's an assumption that socks are paired for choice when experience states the dryer inevitably eats one of every pair. Wait, is the dryer exercising Axiom of Choice in choosing one sock from the pair (bin) with no rule on how to pick and let's face it, sock-eating dryers are in fact infinite? If bin is a pair, socks are--objects? And Axion of Choice is what happens when there's no built-in selection mechanism? Ergo, my dryer performs higher mathematics in set theory every day.

I have no idea what it means that I'm relating my issues with laundry to mathematical theory. I'm honestly not entirely sure what I just wrote. But I am wondering if this can be used to find missing socks. And are they all white socks?

SGA totally destroys people's ability to nod blindly and not google this shit.

--Seperis, with a headache

Context at fandom_wank.

ETA: Melannen uses food coloring to visualize the paradox. I like the part about upper limit sizes. I still have a headache.

Comments

[beachlass]

Somedays I think I need a tshirt that reads:

I learned everything I need to know at FandomWank.
And XKCD.
And porn.

[seperis]

I would buy that shirt.

[dreamatdrew]

I would steal said shirt from you.

[parhelion]

Back when I had to study a tiny dab of advanced physics and math, I decided that the world only made sense to me because the mental tool kit I was evolved to use fit with deceptive neatness at human scales. Therefore dramatically different scales and contexts would always seem weird and could be enjoyed like superhero comics, certain kinds of porn, or ghost stories: lots o' fun if internally consistent within their own genres, but not mattering day to day.

So far that decision has worked, but some of the recent work on getting instantaneous information flow above quantum scales has been hitting it awfully hard. I intend to view all pumpkin carving this year with dark suspicion.

[aivilo_18]

Okay, wait. So, what does this have to do with pumpkin carving?

::sigh:: I don't understand what's going on. I don't even get the point of the comic strip they're wanking on. I mean, this is about the pumpkins, right?

[seperis]

It's a joke that relies on the idea that some kinds of math don't apply to real life because they deal with things that aren't measurable. The paradox mentioned is--roughly speaking--about objects that it is impossible to measure, and so cutting them up into pieces and putting them back together works from the idea that the only true statement is that each piece of the whole object must be equal to or less than the size of the original object.

It took me almost ten minutes to write that. I keep falling down on the idea of an object that exists but there is no way to measure it and length plus width plus height no longer apply. Or physics. *clings to physics*

...this really relies on heavy narcotics, to be honest. Or alcohol.

[beck_liz]

If it makes you feel better, this helped me understand that strip much better. It flew over my head when I initially saw it. *passes the alcohol*

[seperis]

The only way i can deal with it is to pretend I'm in a dark room and I only know the object exists by smell; the only criteria I could give anyone is that it's smaller than the room I'm standing in, and I know the size of the room.

*takes alcohol* My brain hurts.

[dreamatdrew]

Yeah, see, this is why I will never go back and finish the CS degree.... evil math is EVIL!!!

[seperis]

BA in CS requires a lot less math. Lots less. Except some graphing stuff that applies to modeling.

[jenna_thorn]

If it helps any, and it may not, conservation of matter is more physics and many of the paradoxes are pure mathematics, by which I mean that physics is using mathematical models to explain and predict the real world while Mathematics is thinking really hard about numbers.

Never get a mathematician to tutor you for statistics. I loved to hear him talk, but I wouldn't let him balance my checkbook.

[mrshamill]

Jesus I bet you're a riot at parties. What the hell would you do with Zeno's Paradoxes?

Wait, don't answer that.

[seperis]

I do give PhD-studying BFF's husband headaches sometimes. I am so ready to toss the dryer-sock-axiom of choice at him and see what he does with it. Everything my dryer has ever done is explained by that; that axiom is like, the magic bullet for saying everything happens for a reason. There is a reason! It's not random! Each sock chosen had something in common! Even though there is no preset selection criteria to say what that is, the Axiom states there is a reason and it is me! Er, if it could talk.

I think a blood vessel just broke with that. Though now I don't get why we have to have only two pumpkins when there could be infinite pumpkins if we only know each pumpkin piece can be no larger than the original pumpkin and there can be infinite pumpkin pieces.

Ow. Definitely a blood vessel breaking. Ow.

[mrshamill]

Now you're making MY brain hurt, but mostly from rolling my eyes and laughing. It's NOT the dryer, you doofus, it's the WASHER. I proved that years ago when they introduced all those sparkly enzymes into the detergents.

It wouldn't be the AoC if there was a REASON, the AoC is random by definition. The whole point is that there are an infinite number of little pieces of sock that have been blasted into pieces by those enzymes and when they come back together, the washer is designed to delete the extra ones, but it doesn't, because it's made in America, so it deletes too many. It's dirt easy.

Now if you'll excuse me, I have fabric softener to add to the rinse cycle.

[seperis]

Axion is random by definition, which means all the socks have the axiom in common and therefore are no longer random. So it's almost like creating a selection criteria after the fact based on the lack of criteria. Nature, and math, do not cherish a vacuum.

God I hate the existence of wikipedia and Zeno. Though at least Zeno can be easily refuted when you hotwire in a variable with a value is greater than zero and less than or equal to the highest number in the sequence. Or stop treating time and space as independent variables but a single whole.

Febreze fabric softener is deeply awesome.

[mrshamill]

One should never discuss math in conjunction with laundry, especially when one hates both.

Random and choice are the words you're getting wrapped around; you can have both AND you can have neither, it is the nature of the beast and why we have theoretical physicists like Rodney McKay to insult us with his brilliance. Nature abhors a vacuum (and so does my cat) which is also why theoretical physicists are desperately trying to prove the existence of dark matter. Just because something is random and has that in common with something else does not mean it is no longer random. It just means that the random is compounded. Give them down time, as Zebbie said.

I haven't tried Febreze but I'll try anything that isn't what that obnoxious talking teddy bear advertises. shudder

[seperis]

Isn't random considered now to be impossible, that everything works from some kind of predisposed or predetermined pattern in nature? Even Chaos Theory, in some interpretations, is a theory based on method in madness, that there is a pattern, even if we cna't see it.

Which is kind of how I read the Axiom of Choice; there are no selection criteria because Axiom is in itself that criteria, and that criteria has an unknown meaning, but there's a definite meaning. Though it seems to be an argument against deterministic choice, they don't--and deterministic actually did give me a headache--didn't seem contradictory to it.

[mrshamill]

Theories change with the hemlines... but I tend to stay away from the causal determinists. That way lie demons, just ask Laplace. There could be method in the madness but the idea of it is beyond our ken as we're simply not set up to see/think/believe in that dimension or reality (or however you want to phrase it). To us, it will be random because that word works within our limited scope of how reality works. You know this is a no-brainer to the Doctor.

The AoC is, in itself, a belief system. You believe it or you don't. It exists or it doesn't and if you believe it you can warp your specific belief system around it. Are you a determinist? Or are you a devotee of Philippa Foot? You are right in saying it is a criteria in that it asks you to believe it in order to accept that particular set theory. If you do not believe in the AoC, then that set theory is bunk because it can't exist.

Pure mathematics is elegant and beautiful and utterly, completely without practical applications, for the most part. It's why I only adore pure mathematics -- the rest of it can go to hell because I hate it with the hate of a billion hating things. Set theories, number theories and symbolic logic (except sorities) I love because it only exists in the mind and I don't have to pick up a calculator to discover I added the last couple of numbers in the fucking checkbook wrong.

Go buy a copy of Godel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter. That should get you started.

[seperis]

HA!

Infinite number of balls from one ball! Okay, that makes sense. For what value the word sense can be used.

*bounces*

[mrshamill]

Yep, but in the context you were using, it is completely irrelevant. If your dryer (or my washer) were using this model, we'd be up to our eardrums in socks. Instead, we are randomly losing them.

Perhaps the dark matter is socks? That would explain why I've always got enough of Mark's white tube socks but always lose his dark dress socks...

[montanaharper]

Everything my dryer has ever done is explained by that;

Or by this:

On the Experimental Verification of the Nonconservation of Parity and the Quantum Mechanical Tunneling of Macroparticles

*g*

[cathexys]

Oh, that really made my day. Thanks for linking to it!!!(And I kinda love the Theo dude explaining it!)

[seperis]

The argument was hilarious.

[ellixis]

It's all dependent on the space between the parts of the pieces, rather than the pieces themselves. Matter is essentially, on an atomic scale, tiny bits floating in space. If you take certain bits from one part and certain bits from another, using the space between them to move them into another configuration, it seems to create more matter, because it's spaced differently. A bit like moving your peas from a loosely spaced scatter on your plate into two discrete and slightly more densely packed groups, within the same area.

... I could be pulling this totally out of my ass, mind you, but this is how it makes sense to an admittedly amateur mind.

[erika]

No, sorry, you're wrong because the paradox isn't saying it SEEMS to create more matter. They're saying you take a ball, for example, separate it out into a finite number of pieces (which happen to be created of infinite numbers of points) and then create two identical balls with it.

In other words, you're actually creating a ball. Or something. Point is, there was one ball, now there are two, but the two balls are still identical in every respect, including spacing.

[ellixis]

I think I phrased myself wrong in trying to explain what I'm trying to visualize, but you're right that I'm making mistakes as well. Sorry for any confusion caused.

It does make a weird kind of sense, but in a way that requires thinking outside the normal parameters of experience and knowledge. Which, I guess, is why it's called a paradox.

[seperis]

Would that work to explain solid-liquid-gas? because visualizing this as a solid melting and therefor one ice cube of volume X could create two identically volumed post-ice cubs (aka water) then it makes a weird sense. Though I still can't figure out why there can be only two when there are infinite pieces and infinite ways to compress and expand space

[ellixis]

As erika says above, I'm confused about things and not doing a very good job of explaining what I'm thinking. Uh - ignore me, I suppose. Sorry to confuse.

[aurora]

The food coloring mostly makes sense, but the rest of it is making my brain hurt. :(

[fiamaya]

OK, I studied this once upon a time, so here's an explanation of why Banach-Tarski doesn't conflict with conservation of matter. (You may realize this already; sorry for lecturing.) In the real world, there's a smallest possible length -- the Planck length, which is about 1.6 x 10^-35 meters. It literally isn't possible for anything to be smaller than that, thanks to the extreme weirdness that is quantum physics (and everything is some multiple of the Planck length).

To make Banach-Tarski work -- and, btw, I love Melannen's explanation -- you need to be able to cut arbitrarily small bits. In other words, how ever small a piece you're thinking of, you need to be able to cut smaller than that. So the Planck length keeps B-T from working in the real world, and there's no conflict with the conservation of matter.

(Just for a bit of surreality: there's a smoking hot kinky SGA fic that features Banach-Tarski: http://shaenie.livejournal.com/322545.html#cutid1.)

[eponymousanon]

Thanks for linking me to that, if only for the hothot SGA BDSM fic linked partway down the page lol.

[ravyn-09.livejournal.com]

*blink*

uh.....huh? o_O

[rissabby.livejournal.com]

SGA totally destroys people's ability to nod blindly and not google this shit. So true.

In Defense of Dryers:

I once used a lingerie laundry bag (made of mesh with a zippered top) for my socks, hoping that the extra containment would reduce loss. My bag developed a small hole, about the size of a medium blueberry. When transferring the bag from washer to dryer, I often found a sock squeezed halfway out of the hole, leading me to surmise that the sock was desperately trying to escape.

My belief is that the washer and the dryer may be accomplices in the sock's bid for freedom, and that they are not sock-eating villains as they are usually portrayed. Further, when contemplating the life of a sock; kept in a dark drawer until used as a cushion between foot and shoe, surrounded by sweat, bacteria, and fungi; one can easily see that a brave and doughty sock might seek the alternative of flight into the unknown.

[tavella.livejournal.com]

Ooh, thanks to the link to Melannen, that makes me understand it.

[blacksquirrel.livejournal.com]

Woah

[laurele.livejournal.com]

The "thing with Pluto" is not a done deal, and many astronomers continue to view Pluto as a planet. Only four percent of the IAU voted on the controversial demotion, and most are not planetary scientists. Their decision was immediately opposed by hundreds of professional astronomers in a formal petition led by Dr. Alan Stern, Principal Investigator of NASA's New Horizons mission to Pluto. The debate over the planetary status of Pluto and all dwarf planets is very much ongoing. You can find out more from my Pluto Blog at http://laurele.livejournal.com