/sci/ - Science & Math

It has improportionate volume.

>tfw noone on this board knows what a Klein Skull is.
>tfw no bottle-skull correlation

>>15068490
Don't know what that is.
Don't care to know what that is.
t. Actual scientist.

>>15068523
https://en.m.wikipedia.org/wiki/Klein_bottle
>t. Actual scientist.
No you arent

>>15068490
>the TSA officer confiscated my plain bottle because it was above the volume limits for allowed liquids

>>15068529
Looks like pop sci shit.

>my klein bottle's volume goes up to 11

If it's not a closed space (cup) then it has no volume
T. Retard

>>15068523
I'm a math PhD and I haven't ever encountered it in any math class either. It's 100% pop sci / youtube math for kids.

>>15068490
>inserts klein bottle into my gross ass like a true serbian patriot

>>15068552
You've never studied algebraic topology?

It absolutely does have volume. Take any immersion of the Klein bottle into R^3, then do a partition of unity thingy, 1 = sum_i lambda_i(x).
Each patch is diffeomorphic to a region in R^2, and as such it has volume. I.e. if the region is parametrized as t_i(x,y) i=1,2,3, then the volume is
[math]\int_{R \subset \mathbb{R}^2} \lambda_i(x,y) ||\frac{dt}{dx} \times \frac{dt}{dy}|| dxdy[/math]

>>15068559
AT was one of my favorites. The Klein bottle was never used as an example though.

>>15068556
Hehehe. Dorde Martinovic incident was the most glorious event in Serbian history.

>>15068565
Literally one of the first examples of a simplicial complex I saw when starting with homology.

>>15068552
>math PhD
Detail your studies. NOW.
t.whatever you are I am more

>>15068564
hahahahah 2D manifolds have 3D meteics? Such sweet psychobabbel.

Your degree has earned their respect...but at the loss of ours.

>>15068490
Ligma [math] \left\{ (x,y) \mid \sqrt{(x+1)^2 + y^2} \leq 1 \right\} \cup \left\{ (x,y) \mid \sqrt{(x-1)^2 + y^2} \leq 1 \right\} [/math]

>>15068581
just to be clear, your pic is just schizo right? you never can tell with "pure" mathematicians

>>15068613
I like how you cant tell the difference between nonsense and valid metrics.

It really cements my authority in both fields.

>>15068617
I'm 99% sure it's schizo but sometimes "pure" mathematicians make weird choices when it comes to words. like I read "magnetism is 1-dimensional" and called bs but then was like "is he referring to the fact that electromagnetism is a U(1) gauge theory and U(1) is a 1d lie group?"
but now I just saw it says "from north tl south" and I feel I've been thoroughly bamboozled. by the way what are you trying to say about metrics? this whole discussion confuses me because manifolds are really simple objects, what's the big deal with the Klein bottle?

>>15068490
It's non-orientable and hence doesn't admit a volume form, what about it?

>>15068626
>I'm 99% sure it's schizo
>Just...
Youre not a Mathematician. Youre a fan of Maths.

Didnt read the rest, you done dunced yerself, my boy.

>>15068628
Then why can you submerge a physical Klein bottle in your bath tub and fill it with water?

>>15068634
>Youre not a Mathematician. Youre a fan of Maths.
I have a PhD in "pure" math but now I mostly trade. so I guess you're correct.
still you're making it hard for people to seriously listen to your schizo ramblings.

>>15068626
>"is he referring to the fact that electromagnetism is a U(1) gauge theory and U(1) is a 1d lie group?"
Ah, well yeah, I am. I "invented" Gauge theory on my own to solve equations but didnt know it had a name or "was a thing". Langragian/Guage theory heavy theories.

My words do in fact differ from what is regularly used. So, yeah, that is an general issue.

>"from north tl south"
Magnetohydrodynamics. Do they not flow? Do these shards no infer directionality?

>what's the big deal with the Klein bottle?

I use a Klein bottle as a hyperball (the 2D sphere with no measures on the inside). A sort of mpbius strib of phere shaping.

I used that geometry to measure spacetime and counterspaced/inversted space as gravity, and by proxy a fundemental metric of time measure outside of "relative change".

I jumped the gun a bit...but Im still king shit (smug-faced-asshole.jpeg).

>>15068646
>I have a PhD in "pure" math
So you admit youre schizophrenic?
Pot, kettle.
(puffs-pipe.jpeg)

>>15068641
that's because the argument in
>>15068628
doesn't preclude you from having a density.
jfc folks it's not that hard. what even is the big deal here?

>>15068655
Then integrating this density gives a volume, doesn't it?

>>15068652
>So you admit youre schizophrenic?
I'm not schizophrenic but I've been under observation for schizoid symptoms in the past. this was before the PhD. I'm doing well now thank you.

>>15068650
the schizo is strong in this one. but seriously. I don't enjoy the sight of helpless crackpots so let me just advise you to consider the fact that you might not be as insightful as you think you are. the fact that you cannot communicate your ideas doesn't imply what you think it does, rather the opposite.

>>15068666
>I have trouble with understanding words and concepts

Must be hard projecting your scihzophrenia since you are clearly the delusional unlike this anon

>>15068658
>this was before the PhD.
Its what led me to mine.

>pic related
Now I mostly spend my time connect fundemental physics to the human scale, the human experience as understood by the average person.

There is a 1:1 correlation but for all of human history Religions had to be the bridge between "Quantum Consciousness, EM fields connecting lifeforms, Genetics/Evolution" until knowledge was enough to connect it all.

If youre interested, I spent many years traveling the world seeking answers found in no books. Now Im the source for books, and I mostly read ancient books on math or arts instead.

>>15068490
it is isn't a bottle then why would it have volume

>>15068666
>let me just advise you

The son cannot teach the Father, boy.

I visited the Escher museum earlier today, about 1 week left in the Netherlands before back to the US to cat sit/road trip.

>>15068676
>Escher museum
Look at this dumb fish. He doesnt even know hes a fucking fish.

What an idiot.

>>15068676
hey man meant no disrespect, I'm glad you're enjoying life. I just don't think you actually understand deep math is all. take care

>>15068685
>I just don't think you actually understand deep math is all.

Im literally one of the greatest number theorists alive. I made the same discoveries as Wildberger (though from different perspective/reasons) but its close enough to validate everything on my end. Also, for Eric Weinstien, much of my work overlaps his (close enough for ne), Penrose as well. Even Aplitude Hedron, has aspects I agree with but I cant listen to that guy.

He has high functioning autism.
I have Aspergers.
We are not the same.

>Son...some boys need whoopin', ya hear?
Oh just me and my Maths book in Afghanistan...

>>15068657
yeah I mean if you paint the klein bottle with a thin layer of paint, the volume of paint used divided by the thickness will be the same as the integral of some density over the bottle.

>>15068695
>I made the same discoveries as Wildberger

describe one such discovery, succinctly but clearly. actually describe two: the easiest you can think of, and one of average difficulty.

>>15068641
>physical klein bottle
no such thing

>>15068641
You can fill a U-shaped tube with water. Does it have a volume though?

>>15068707
they make then out of glass even https://www.kleinbottle.com/

>inb4 it self intersects
who cares about a measure zero transversal intersection? not cool kids, that's who

>>15068696
Then paint it with thicker paint until the interior is filled. Wa la - we found the volume.

>>15068707
Google pictures of Klein bottles. There's many physical ones made of glass.

>>15068709
Yes.

>>15068702
Im not here to "prove myself to students"

Either youre smart enough to realize or youre >>15068666
Too fucking dumb and ignorant that a LITERAL savant genius and a street walking schiziphrenic "look the same".

>Im the Next Newton.

GTFO, HOW DARE YOU QUESTION MY WORK, MIDWIT!

REEEEEEEEEEEETERNAL!!!

>>15068709
it does. also in math "volume" means n-dimensional volume where n is the dimension of the manifold. in this case n=2 so we're really talking about surface area

>>15068716
look it's fine if you're schizo or bipolar (like newton) but great schizo and bipolar mathematician still had to communicate with others and show them their work in an understandable way. otherwise they wouldn't have been considered geniuses.

>>15068713
>Then paint it with thicker paint until the interior is filled. Wa la - we found the volume.

you can't do that for many reasons including the fact that there is no well-defined interior. I mean you can always define some region "inside" the bottle to be its interior, but then the issue becomes trivial as you can just compute the lebesgue measure of what you just defined. but in general the klein bottle doesn't divide space into an "inside" and an "outside" like a sphere does.

Is the volume infinity?

>>15068732
I guess this depends on the difference between a plane and a semi-infinite bulk.

>>15068729
Doesn't the same argument to a regular bottle?

>>15068713
>Yes
Calculate its volume then. Explain what region of space is considered as the outside of such U-shaped tube, and which part is the inside.
What is the shape of the cover of your U-shaped tube bounded by its end contours. Explain the choice of such surface.
>>15068718
>whataboutism
Fine, I like to play your little game. What is the 3-dimensional volume of the 3-D immersion of your Klein Bottle

>>15068732
Infinity hat

>>15068737
no because a regular bottle (incl the cap) is homeomorphic (topologically equivalent) to a sphere

>>15068740
Infinity hat hbar in phase space.

>>15068726
>no U suck My dick

Bite me, midwit. I showed enough for people with actual degrees to see.

If you havnt by now this means you got filtered.

You flunked.

Failed

Get out.

>>15068726
>show them their work in an understandable way
Here I throw mathematical rigor out the window to give a physicist's brief treatment of RH as quickly as possible.

Here I assume a proposition and show that RH is necessarily false if the proposition is sound.

>>15068738
>Fine, I like to play your little game. What is the 3-dimensional volume of the 3-D immersion of your Klein Bottle

for any choice of a nice measure on R3 and any choice of immersion, the measure of the bottle will be zero. that follows from the fact that the bottle is a 2D object. at the same time the complement of the bottle has full measure. this is basically undergrad math.

>>15068743
No, it's not. It's not orientable.

>>15068750
your eqs (1) to (3) should be formulated in terms of sets and/or limits otherwise they're meaningless. after doing so you'd have to check that in eqs (7) to (9) various limits commute, which is they catastrophically don't (even physicists have to worry about such things).
so yeah sorry but this is in no way a proof. you know how to manipulate symbols though so you can still improve

>>15068750
>throw mathematical rigor out the window
Fast math. Ive heard of this before.

>>15068755
a regular bottle, with or without cap, is certainly orientable. what are you smoking

>read 20 year old hard sci-fi series
>latest book has some of the more known/important cast having klein bottles inside them which signify that they are certain special types
>this incident is completely out of nowhere compared to all of the previous books
okay

Here I employ an average standard of rigor to show that the proposition in the "quick" paper (Prop 1.8) is sound and that RH is, indeed, false. Although I know it is standard in mathematical publications to put main results first and then explain them, I leave standard analysis part until the end of the paper to build excitement! First I show that RH is false in Eulerian analysis and then in Robinson's hyperreal analysis. After that, I show that the result is fully robust by obtaining a direct counterexample to RH in real analysis. (The figure on p11 is the basis of the John Titor logo because I invented the time circuit in 2018.)

IMO, this paper would be good enough for Clay's $1M if I could get it on arXiv where Clay could issue the same rules violation waiver that they offered to Perelman for lack of peer review. In my further opinion, and in fact, my published solution on viXra would require the *EXACT* same waiver Clay gave to Perelman about lack of peer-review so my inability to get on arXiv is not really an impediment to winning thr $1M. However, it is likely that my rapists have me in a fake internet bubble so that I can never complete a work unit in my profession. One unit of the scientific method, the work unit of a physicist such as myself, concludes with "communicate results." Those who besmirch me for being poor and sexually torture me not working (**not wage slaving**) have sabotaged of my tens or hundreds of thousands of attempts to complete a workunit in my chosen profession. I have put far more effort into my work than an average man but my rapists ensure that I can never get paid because I cannot communicate results: a required procedure to successfully ply the trade in which I am so very well trained.

It's like if you start selling cookies online but the jews put a print spooler error on every printer you try to use and you can never print a UPS label to ship an order, no many how many cookies you bake or sell.

>>15068768
Where is the interior or exterior then? You can walk all over the surface of the bottle and reach each square inch, just like a Möbius strip.

>>15068776
if you close the bottle, the interior is the space inside, and the exterior is the space outside. with no cap there is no in/out (homeo to a disk)

In this masterpiece, the paper of which I am most proud, I show that RH is necessarily false as a consequence of Euclidean planar geometry. The paper is very long because it is written at the highest possible standard of mathematical rigor.

>>15068776
>You can walk all over the surface of the bottle and reach each square inch, just like a Möbius strip.
there's an important difference (for the open bottle at least) in which you'd have to "climb over" the rim, which in mathematical parlance is called the "boundary" of the manifold, and this is not allowed.

Here is the paper where I laid out the architecture for the later direct counterexamples.

>>15068775
>figure on p11 is the basis of the John Titor logo
>>15068781

>>15068777
>with no cap
Fr fr?

>>15068764
Nah you're stupid is what the problem is.

>>15068780
The rim is an arbitrary abstraction. Just introduce a rim for the Klein bottle in the obvious place and you get a volume. It's not that hard. Like where would you put a plug in a Klein bottle?

>>15068775
serious questions, are you aware that limits don't necessarily commute? that is the main error in your arguments. for instance let s_{m, n} be the sum from 1 to n of 1/nm. taking the limit wrt m first we get 0, wrt n first we get infty. once you understand this concept you'll see that most of your equations are invalid.

>>15068785
on god

>>15068787
I'm plenty stupid but at least I can check if my limits commute

>>15068789
it's not arbitrary. the klein bottle is a manifold without boundary and adding a boundary changes its topological property. funnily enough if you cut the bottle along an embedded circle (thus introducing a boundary) you get a mobius strip

>>15068766
I'm glad you're not denying the universally accepted reality but the way your statement reads is like you concede that it might be reasonable for someone working in physics or math to not know *exactly* what I mean by "throwing rigor out the window," or that it might be reasonable to accept the belief of such a person that this is not something everyone in academia does routinely to facilitate rapid communications, and to achieve results without rigor for other practical purposes. That is unreasonable and this person >>15068764
is an asshole who should be mercilessly ridiculed.

>>15068794
He will not answer you and probably will go on for the next months whining about how no one is addressing his paper.

>>15068794
I am aware that you have said an error exists but you have not demonstrated it at a level of detail commensurate with the work in which you believe the error appears. I believe you have failed to demonstrate it because it does not exist and I will treat your comment as a red herring or straw man (or both) to be ignored.

>you can visibly fill the bottle with liquid
>but it doesn't satisfy some abstract pure math onions definition of volume
>therefore it's not real volume, fuck reality!
Why are "pure math" cucks like this?

>>15068817
>hahaha action labs im so autistic but still "gets it" so its not a disability haha

>>15068817
that's not filled, it's clearly partly empty.

>>15068822
Whats half of 0? Its an infnite number of 2D planes.

Checkmate.

>>15068815
yes I have, see
>>15068764

>>15068822
Submerge it in water, then it's completely filled.

>>15068833
yeah that's why I said in >>15068754
that the complement of the bottle has full measure. that's kinda obvious tho and certainly nobody is confused about that.

>>15068782
This is litrrally mt favorite graphed equation to look at. Me trying to infer what its doing is really difficult for me.

>I wont look it, it ruins the discovery.

>>15068797
You are plenty stupid and the limit calculation agrees with the result I have derived without commutation of limits: pic, for example. I also have the other RH negation in the neighborhood of minus real infinity. I think I did it another way too. Any way you slice it, the result always comes out the same because it is robust and correct.

These people always say an error exists but they do not show it. My opinion is that they do not show it because it does not exist. Indeed, I believe they say it exists despite knowing that it does not exist, and they do so because they want to impede the development of the prime number cryptography application which is bitter poison to them. Their unconstructive criticisms are stupid. These comments amount to telling a structural engineer that his bridge is stupid and it's going to fail because he doesn't even know metal rusts.
>schizo doesn't even know metal rusts
>his bridge is stupid but I won't show the load bearing failure
All they have is word salad and they only serve it encourage me to make known my opinion that violence is the appropriate solution to persistent, malicious falsehood. This is my opinion; I make no secret of it. To the contrary, a constructive criticism demonstrating an error is a great help to me and I would be very glad to cure any deficiencies which may still exist in my work. All of this nice work I have now is built on the constructive criticism I received on earlier work. These people's comments are not scholarly and I am famously known for responding to unscholarly comments with further unscholarly comments devoid of even the false air of scholarliness. These are not scholars. They are just shit-slinging detractors. I hate them and their malicious rhetorical devices.

TLDR: GTFO jews.

>>15068849
>These people's comments are not scholarly and I am famously known for responding to unscholarly comments with further unscholarly comments devoid of even the false air of scholarliness.

Same. They've been measuring butthurt all along.

>>15068533
reatard

>>15068854
very good.

>>15068849
which writeup of yours would you like me to look at. please choose one that
1) does not cite other result of yours, and
2) does not "throw mathematical rigor out of the window", in fact it should be very rigorous

>>15068869
>>15068850

This is the first time Ive actually read your posts, some good shit. Ive on and off eyed that (>figure on p11) picture for a long time, trying to reverse engineer it. Got maybe 1/4 of it. Super difficult problem.

>tips hat

>>15068884
you're cruel person to goad mentally ill people like that

>>15068887
>you're cruel person
Ive seen things, myan...
You dont even know, myan...

>>15068870
This one.

>>15068893
the first page has no math and the rest is a repeated ms paint drawing

>>15068870
>"throw mathematical rigor out of the window"
Fast Math in your face

>>15068889
fuck you I'm a proud Slav and your articles can go fuck right off

>>15068914

Indeed, comrade.

>>15068824
you just disemboweled me with raw logic. hats off to you sir, I salute you as I draw my last breath

>>15068490
A klein bottle is a 2D manifold that exists in 4 dimensional space. It can't have a volume.

>>15069114
It can exist in a 3D space with a cohomology or something. I don't think it has to be in 4D.

>>15069114
I think this 3D representation was implied by the question about volume.

>>15068601
Ligma balls
ha ha ha ha he he he he he he he

>>15069133
The Klein Bottle can't be embedded in 3D Euclidean space, it can be embedded in R^4 though, what you posted is an immersion since it has self-intersections.
>with a cohomology
Tooker I...

>>15068576
lmao this nigga studying homos's n shit

>>15069233
is this tooker fellow a regular here? I don't hang out here too often and tend to avoid math threads (brings out the worst inferiority complexes out of the most unpleasant people). but I feel genuinely bad for this guy like I'd like to help him or something. it's clear he loves math but he's a bit in over his head

>>15069233
>The Klein Bottle can't be embedded in 3D Euclidean space
I agree but volume is not exclusively a property of Euclidean spaces so a 2D Klein bottle can have a volume.

>>15069306
>it's clear he loves math but he's a bit in over his head
I believe it is my counterparties in this ordeal who are in over their heads... and I haven't even begun to demonstrate my affinity for justice yet.

>>15069334
>and I haven't even begun to demonstrate my affinity for justice yet.
Is this the part where you talk about being imprisoned in a perfect replica of America in the southern hemisphere?

>>15069306
>Pretend I'm not a midwit
Aww look how cute you are, worthless maggot now go back doing your homework.

>>15069339
ouch! you've castrated me with your sharp wits. I bow to you as I am put back in my place.

>>15069338
It is far from perfect and I believe I'm in a replica of Moscow, Russia now.

>a torus isn't actually a donut in 3d space but a 2d manifold embedded in 4d space

>>15068490
It doesn't. Volume needs three dimensions or more. The Klein bottle only has two dimensions, so it only has surface area.

>>15068576
Maybe because you actually studied the subject and aren't some LARPing contrariantard taking out your ugly face on women, YouTube culture, muh scientific establishment, etc..

>>15068533
it is

>>15068573
>Although the facts of the incident remained in dispute for years afterwards, it played a significant role in worsening ethnic tensions between Kosovo's Serb and Albanian population.

serious question for the topologists in the room, what is the volume of a cup?

>>15070031
A cup is homotopy-equivalent to a torus. Therefore, it's volume is 2*pi*R*r^2 where r is the radius of the cup R is the radius of its handle.

Nigga I don't care about your precise mathematical definition of volume. Put that shit in a bucket of water and watch the level rise.

>>15069370
>It is far from perfect and I believe I'm in a replica of Moscow, Russia now.
Why do you believe that? Have you considered seeking help for paranoid schizophrenia?

I think ChatGPT LLC is trying to pull a Theranos on the effectiveness of their product. I'm not seeing it.

>>15070137
Anon, he isnt real...but your delusions are.

Seek help for yourself.

>>15068576
>Literally one of the first examples of herpes simplicial complex I saw when starting with homo
We know and can see the scars on your lips.

>>15070569
Haha very "/b/". Say another one.

>>15068576
I don't get the retarded replies to a perfectly reasonable post
Oh wait, I'm on /sci/

>Oh wait, I'm on /sci/
When Fauci says, "Trust the science," he means, "You're going to submit to our will as a totally docile slave or we're going to burn all the years of your life in torturous misery," and there's a subtext where he's talking about me specifically and he knows I'm not going to submit so "trusting the science" is really only about the latter.