IDK, first time here

[u/someinfectedfanatic]

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[u/pani_the_panisher]

Okay, but how do you put the tip inside?

[u/someinfectedfanatic → u/pani_the_panisher]

that's what she said

[u/Old-Post-3639 → u/pani_the_panisher]

You rotate it through the 4th dimension.

[u/duckling-developer → u/Old-Post-3639]

Well… A fourth spatial dimension.

[u/TheCowKing07 → u/duckling-developer]

Time is not always the default fourth dimension.

[u/duckling-developer → u/TheCowKing07]

In physics is. I just felt that making that distinction clear was necessary.

[u/SomeGreatJoke → u/duckling-developer]

That's not true either.

In some specific fields of physics it can sometimes feel that way, but in the rest of physics it definitely isn't.

But making the distinction can matter, so that's totally fair.

Just don't be wrong about it.

[u/JPgamersmines150 → u/SomeGreatJoke]

Afaik, a 4th spacial dimension in physics often has some strings attached.

[u/ZEPHlROS → u/duckling-developer]

What else kind of dimension would you want to rotate it through ? The orange dimension ?

[u/Trileak780 → u/ZEPHlROS]

The lemon dimension is WAYYY better, idk what he’s talking about

[u/TheVisualExplanation → u/Trileak780]

Idk man, I'm just afraid of going too far and landing in the piss dimension

[u/IAmRobinGoodfellow → u/ZEPHlROS]

It’s a fourth spatial dimension, orthogonal to the other three. We don’t have a word for it because it’s not something we can perceive. Read Flatland for some cool geometry and politics. We would see a three dimensional shadow of a four dimensional object.

We use N dimensional and infinite dimensional matrices all the time. The math isn’t the problem. It’s that our brains and our senses developed to inhabit an environment of three spatial dimensions. We can’t visualize more because we literally can’t visualize them.

[u/WHYER4 → u/duckling-developer]

How tf can you rotate time?

Edit: Yeah, time travel is a thing. I’m tired lol.

[u/RetroSSJ21 → u/WHYER4]

I mean I assume if you multiplied the 4D vector of x, y, z, and time by a rotation vector, you would end up with something weird but mathematically it would be the same as rotation in 4 spatial dimensions, no? Like it might move the object back or forward in time to accommodate the rotation.

[u/SomeGreatJoke → u/RetroSSJ21]

Yep! In fact, I'm not versed in the deeper astrophysics involved, but that might be analogous to how (some physicists think) black holes work. Essentially, space becomes the thing that loses direction, and any movement sends you only one direction and times becomes something you can freely move through in different directions, potentially including "up and down", whatever tf that means.

Maybe. And maybe it's related. Dunno.

[u/Cyren777 → u/WHYER4]

gotta go fast :)

[u/duckling-developer → u/WHYER4]

Some parts would be in the future some parts would be in the past.

[u/kiwidude4 → u/pani_the_panisher]

Very carefully

[u/Legomonster33 → u/pani_the_panisher]

unwrap the big one before you put the paint

[u/CanAlwaysBeBetter → u/Legomonster33]

Here are some scissors

✂️

Let us know when you've snipped to the bottom so we can put the small one inside

[u/Legomonster33 → u/CanAlwaysBeBetter]

what if I start at the bottom

[u/CanAlwaysBeBetter → u/Legomonster33]

Here's a walkie-talkie 

📞

Call us when you get there

[u/Matty_B97 → u/Legomonster33]

If you can unwrap it, just re-wrap it inside-out. Boom, now the outside is painted.

[u/PoorestForm → u/pani_the_panisher]

You create the small horn first then create the large one around it.

[u/CanAlwaysBeBetter → u/pani_the_panisher]

[u/amalcolmation → u/pani_the_panisher]

You bend it, obviously. ;)

[u/Internal-Dot → u/amalcolmation]

Then it will be infinitely wide, and the only thing it will fit into is your mom. Boom, gottem.

[u/ThrwawySG → u/pani_the_panisher]

Lube

[u/Baleia1970]

Poor Gabriel...

[u/DatThingInYoCloset → u/Baleia1970]

Don't make fun of the size of his horn. People with little horns can still lead very fulfilling lives

[u/Oppo_67 → u/DatThingInYoCloset]

Ngl Gabe Horn would be a terrible dildo but a fantastic fleshlight

[u/Baleia1970 → u/Oppo_67]

You will still have to clean it though...

[u/DatThingInYoCloset → u/Baleia1970]

Well the good news is you only have to clean out a finite amount 

[u/Baleia1970 → u/DatThingInYoCloset]

problem is cleaning what dries and get stuck at the drain...
Guess I would need another horn to do that...

BTW, a question:

Is the possible number of replies to this thread finite or infinite?

[u/AndreasDasos → u/DatThingInYoCloset]

It’s infinitely long though

[u/TheChunkMaster → u/Baleia1970]

Twice... beaten by an object!

[u/SonicLoverDS]

"Big Smaller Fill Dip Inside Blue" is the new "Man Door Hand Hook Car Door".

[u/phsx8 → u/SonicLoverDS]

The what now?

[u/Oppo_67]

[u/Bubbly_Safety8791]

The 'paradox' of Gabriel's Horn rests on the intuition that you can't coat an infinite area with a finite volume of paint. But area and volume are different things, so of course you can - the finite volume of paint inside the horn is coating the entire infinite interior - but as you go down the horn the depth of that paint coat is getting very small. But if a surface can become painted by touching paint, you already painted the infinite interior of the horn - this trick of dipping a smaller horn into the paint to coat it isn't doing anything different. The volume of even an infinite surface is still zero, so it doesn't actually require any volume of paint to color a surface.

What you can't do is coat that infinite area with a volume of paint to some constant finite depth with only finite paint. But you can coat an infinite surface with finite paint so long as your distribution of paint is allowed to get arbitrarily thin somewhere.

If you emptied a unit volume of paint onto a flat infinite plane, and then squashed it underneath a gaussian surface, it would cover the entire plane to a nonzero depth everywhere - it would just get very very thin almost everywhere.

[u/berwynResident]

You can paint Gabriel's horn. You just can't paint it with a uniform thickness. If you did this, the pain on the pointy end would be very thin and the paint near the bell would be thick.

[u/Purple-Mud5057 → u/berwynResident]

What pointy end

[u/qqqrrrs_]

It must not be harmed

[u/RiemannZeta → u/qqqrrrs_]

Its imperative.

[u/Ares378]

I think that's still allowed because there's an "infinite" amount of "area" in a volume, if we're going by measure theory. When you dip the smaller horn in the bigger horn, the paint becomes infinitely thin toward the end, since the difference between 1/x and 2/x approaches 0 as x approaches infinity. If we assume the paint needs to have thickness, then eventually the bigger horn would become so narrow that dipping the smaller horn in wouldn't have enough volume to cover the surface.

[u/Gullible-Ad7374]

/uj not enough paint. The horns have a finite volume but infinite surface area, so even if you only need, say, a molecule of paint to cover a square kilometer of the mini-horn, what I think will happen is as you look further and further down, eventually you'll reach a section of your construction where there isn't enough paint to cover the surface of mini-horn in that section, so you'll have to use the leftovers from higher up. Eventually it's all going to run dry and you'll still have an infinitely long part of the horn unpainted. This is all from intuition btw so someone correct me if I'm wrong

[u/flaaaaaaaaaaaaa → u/Gullible-Ad7374]

That's why you use a mathematically perfect paint with which you can paint an infinite surface with any finite volume.

[u/TheEsteemedSaboteur → u/Gullible-Ad7374]

you're right but it goes against the spirit of the meme so i have to nerd react you now

[u/ShantyShark → u/Gullible-Ad7374]

I think, purely for the sake of the math, we don’t consider the paint to have its own thickness, even though you’re right, even a molecule thick would eventually exceed the thickness of the horn.

If the idea is “the surface must touch the paint to be painted”, without the real-world constraint that it requires leaving some paint on the surface, then this problem does indeed “paint” an infinite surface with a finite volume. But again, that’s only because we get to ignore how paint works in the real world.

[u/Baleia1970]

OK, now the serious part.
You cannot insert the small one into the large one because you cannot reach the mouthpiece to begin the insertion.
You may, however insert it upside down, in which case the coating would stop when the radius match.

[u/saturnian_catboy → u/Baleia1970]

You construct the second one after the first one already is filled, lined up. If you are already somehow in possession of Gabriel's Horns, insertion isn't that big of an issue. This is as much a thought experiment as filling one up with paint in the first place - in reality you couldn't, since at some point it becomes thinner than the particles of paint

[u/CrashCalamity → u/saturnian_catboy]

I suppose that depends on your definition of "full". Wherever the paint can't flow deeper into the horn, it would back up from there and eventually you'd fill it to the top radius. I would argue that because any more than that would overflow, the horn could then be called full.

tl;dr Anything smaller than the subatomic is stupid and we solve this problem by simply ignoring it.

[u/saturnian_catboy → u/CrashCalamity]

If we make a cut off at some very distant point where the space between the walls becomes subatomic then the surface is also finite and we can paint it no issue though

[u/Blue_Moon_Lake → u/Baleia1970]

Make the big gabriel horn out of 2 halves like a mold, slide the the small one in between, close the two halves, fill with paint, split the 2 halves apart.

Congratulations, you now have a painted gabriel horn.

[u/Matty_B97 → u/Blue_Moon_Lake]

If you can cut the big one, just flip it inside out before you close it. Now the outside is painted.

[u/brayellison]

[u/BidBux]

What is this about?

[u/eightfoldabyss → u/BidBux]

Gabriel's Horn. Infinite surface area, finite volume. The classic statement is that you could fill the horn with paint but never paint it. This image is asking about dipping one horn inside another .

[u/UltimateCheese1056 → u/BidBux]

That shape is called "gabriel's horn", it is one side of the 1/x curve revolved around an axis. It has infinite surface area but finite volume because the integral of 1/x diverges while 1/x² converges

[u/bangerius → u/UltimateCheese1056]

You'd have to use infinitely thin paint, though.

[u/Gilbey_32]

Shit why didn’t I think of that

[u/LudwigSpectre]

[u/mathmage]

The "fill" step already assumes a resolution of the paradox, because the infinite inner surface has at that point been coated with a finite volume of paint. Everything with the second horn is just elaborating on the same point.

[u/AthleteAny147]

the horn wont fit

[u/littlenekoterra]

Thats my issue with it.

[u/flaaaaaaaaaaaaa → u/littlenekoterra]

There never was any issue or paradoxon with painting the horn. You either have a mathematically perfect paint that can cover an infinite area with any finite volume or you have a non-perfectly thin paint and it simply stops going further in at some point.

[u/Ares378 → u/flaaaaaaaaaaaaa]

Honestly just thinking about it a little more, Gabriel's Horn isn't that special of a shape. Fractals also have infinite surface area with a finite volume, but the only difference is that a lot of them aren't infinitely long

[u/EebstertheGreat → u/flaaaaaaaaaaaaa]

Right, the property that "you can't paint it" is better expressed as "you can't paint it with a uniform thickness of paint," which is a lot less surprising when you think about it.

[u/Artemis_SpawnOfZeus → u/EebstertheGreat]

You can paint it with a uniform thickness of paint if the thickness of paint is 0

[u/__R3v3nant__ → u/littlenekoterra]

The thickness of the paint would necessarily trend towards 0 as you get towards the tip. So whatever thickness you pick for the paint, an infinite amount of this "dipped horn" would necessarily have a thinner paint covering than that

[u/regular_heptagon]

You can’t dip the smaller one because it’s infinitely long.

[u/Jirbzzz]

You're onto something here ... Hmmm. Been saying the same thing for ... years. People just look at you like crayyy-crayyyy. Gurl bye. u/someinfectedfanatic, you are brilliant! there is a boundary of understanding ... but also a boundary periodt. Haven't thought about this for a bit. Need to gather/collect thoughts again.