/sci/ - Science & Math

[Anonymous No.14823428]

I'm so FUCKING sick of the axiom of choice

[Anonymous No.14823434]

What are you smoking man? God has already planned your life, can i get an AMEN?!

[Anonymous No.14823490]

>>14823428
>if there are things in collections, then you can make a new collection of things in those collections
you have to an actual schizo to think this is somehow dubious, funnily enough it's the finitards that always go muh intuition

[Jealous No.14823542]

>you can do math but abstraction isn't allowed
>apples in a basket or GTFO

[Anonymous No.14823547]

>>14823428
>let's choose to be retarded
okay... why?
>we need jobs and gatekeeping

[Anonymous No.14823549]

I'm pro axiom of life.

[Jealous No.14823559]

Let me clarify my thoughts on the fact of choice (in abstraction.) The problem is that calling it "the axiom of choice" makes it seem like it there is an open question about whether or not the fact of choice is factual. This is not an open question.

[Jealous No.14823567]

>I'm so FUCKING sick of the axiom of the imaginary number

[Anonymous No.14823568]

>>14823428

[Anonymous No.14823595]

>>14823490
If you accept the infinitist schizophrenia, there's 0 reason whatsoever to reject axiom of choice.
By positing infinite sets you must already concede a fundamental disconnect between what can be constructed in the mind/on a computer and what can exist mathematically. The cope that "but you can't actually exhibit the choice function in some cases" falls flat when when you remember that you can't actually exhibit infinite sets either (i.e. encode them in the mind or in a computer).
>it's the finitards that always go muh intuition
Intuition is an undeniable fact of mathematical practice, acknowledged by every mathematician worth their salt. Theories and theorems do not come from juggling formulas according to a well-defined algorithm; if it did, the computer would have replaced the mathematician's job a long time ago. Instead, it involves a pre-verbal judgement, of what is interesting, beautiful and worth pursuing and what is trash.
Alternatively, proofs in mathematics are not written in formal language, but rather in words, where the justification for the intermediate steps comes intuitively. If you ever dealt with formal systems you would know that formalizing a proof is not simply copying the proof you have but instead involves novel problem solving of how to fit your intuitive understanding of how the proof goes into the formal system at hand. This demonstrates as clearly as anything else that the practice of mathematics is not actually done within a formal system but rather heavily relies on intuition.

[Anonymous No.14823626]

>>14823568
I was trying to figure out what the importance of the expression on the bottom was, but then I realized its nonsense and the joke is that they're making fun of mathematical logic.

[Anonymous No.14823642]

>>14823595
>By positing infinite sets you must already concede a fundamental disconnect between what can be constructed in the mind/on a computer and what can exist mathematically.
Nope, the universe is POTENTIALLY (keyword: potentially) infinite in size, likewise the bigbang is thought to be infinite in density, there is no clear disconnect.
Also, english prosed proofs are written in logical language, they just replace the symbols with their english equivalents, e.g for all and such that. Secondly, intuition has no place in a proof, what's being done in between steps is logical inference, and not the author going "it is intuitive to see that..."

[Anonymous No.14823644]

>>14823626
The bottom isn't math it's logic/analytical philosophy, and as we all know, philosophy is a subject for absolute clowns

[Anonymous No.14823665]

>>14823626
>set theory thread
>can't into FOL
You lost?
>>14823642
>Nope, the universe is POTENTIALLY (keyword: potentially) infinite in size, likewise the bigbang is thought to be infinite in density, there is no clear disconnect.
That's finitism, retard.
>>14823644
>The bottom isn't math
Glad you agree, it shouldn't be considered part of rigorous mathematics.

[Jealous No.14823668]

>>14823595
I spent nine years in college pursing a PhD in physics and I had extensive mathematics coursework and research. Nowhere other than 4chan have I ever seen anyone dispute the possibility of imagining an infinite set and then using a symbol to describe that idea. If that's unreasonable, what is reasonable about imagining the square root of a negative unit and using a symbol to describe it? Once you get past that very low intellectual hurdle, everything else follows from the definition of algebra: the study of mathematical symbols and the rules for describing them.
>I'm so FUCKING sick of the axiom of the imaginary number

[Jealous No.14823675]

>>14823626
The bottom says there exists a set containing the empty set and more than one other element.

[Jealous No.14823678]

>>14823668
>the study of mathematical symbols and the rules for describing them.
the study of mathematical symbols and the rules for *manipulating* them.

[Anonymous No.14823690]

>>14823668
>I spent nine years in college pursing a PhD in physics
Why so long? Are you retarded or something?
> I had extensive mathematics coursework and research
Triple integrals are probably the pinnacle of mathematics in your mind. (as a physicist)
>Nowhere other than 4chan have I ever seen anyone dispute the possibility of imagining an infinite set and then using a symbol to describe that idea.
Nobody's disputing that, just like nobody's disputing the possibility of imagining the largest prime number and using a symbol to describe it.
> Once you get past that very low intellectual hurdle, everything else follows from the definition of algebra: the study of mathematical symbols and the rules for describing them.
Good job exposing you know nothing about algebra XD
>wut iz whiteheadz problem

[Anonymous No.14823692]

>>14823665
Logic isn’t math, and math isn’t logic.
Logic is used sometimes to describe math, but philosophy is cringe clown crap

[Anonymous No.14823694]

>>14823668
if you went to college in the 19th century rather than the Jewish century all of your peers would have disputed it

[Anonymous No.14823696]

>>14823694
Kronecker was (((JEW)))) but ok :^)

[Anonymous No.14823701]

>>14823694
It is true, the foundations of math are more accurately described as theology than philosophy.

[Jealous No.14823707]

>>14823690
>Nobody's disputing that, just like nobody's disputing the possibility of imagining the largest prime number and using a symbol to describe it.
I dispute that you have imagined a largest prime number. That leads to a contradiction. To the contrary, the existence of the imaginary number or an infinite does not lead to a contradiction.

[Anonymous No.14823710]

>>14823707
Seek help Tooker

[Anonymous No.14823725]

>>14823701
No. It is more accurately described as computer science than anything else.

> inb4 schizoposting

[Jealous No.14823727]

>>14823694
I don't think so since Euler was using the infinite integer "i" and its fractional parts such as "i/2" in his work and his thesis was titled "Various observations about infinite series." He did that and other work on infinite products in the 18th century and everyone in the 19th centiry thought he was a hotshot, and rightly so.

Interpreting the infinitesimal mathematics of Leibniz and Euler
https://arxiv.org/abs/1605.00455
>pic

[Anonymous No.14823734]

>>14823725
What is the computational meaning of the Continuum Hypothesis?

[Anonymous No.14823746]

>there's a lipschitz discontinuity in my room RIGHT NOW and it's expanding at the rate of 0.05 per second

[Anonymous No.14823750]

>>14823734
See "Forcing as a Program Transformation" by A. Miquel.

[Anonymous No.14823753]

>>14823750
Umm that has already been debunked. See "Random shit I've read some time" by Ben Dover.

[Jealous No.14823757]

>tfw they aren't subject matter experts and they have to ask 3rd party professionals if you are are for real but you're much more for real than 90% of professionals so the 3rd parties just say you're retarded and you should publish in one of the journals the USA blacklisted you from
>they don't say, "Yeah, he did in a couple of weeks there what tens of thousands of the world's best and brightest failed to do in more than a hundred years of sustained collaborative effort"
>otherwise you might get the low-paying post-doc position instead of the person they want to get it

[Anonymous No.14823779]

>>14823750
This seems to describe a computational meaning of the forcing technique, not of the continuum hypothesis. Quote the paper if I'm wrong.

[Anonymous No.14823816]

>>14823568
Bottom should be powerset.

[Anonymous No.14823821]

>>14823675
Wrong, it says there exist containing the empty set and containing the derivative of every set already in the set

[Anonymous No.14823824]

>>14823816
(You)

[Anonymous No.14823839]

>>14823779
Indeed, but that would also give you an interpretation of CH (or its negation) in that model.

[Anonymous No.14823840]

>>14823644
looks like the math bullshit professors sprinkle in when they want to be faggots.
What I understand it saying is that there exist an X, such that the empty set is an element of x and every single y which is an element of x times the derivative of y which is also an element of x. Its just nonsense and not saying anything.

[Anonymous No.14823843]

if the continuum hypothesis were ever to be proven it will induce a hypercomputational hierarchy collapse turning all sentient life in the universe into p-zombies

[Anonymous No.14823845]

>>14823839
>in that model.
In what model? What's the computational meaning of CH?
(hint: there isn't any, and you're retarded)

[Anonymous No.14823856]

>>14823428
>LEMcucks hated him for telling the truth

[Anonymous No.14823862]

>>14823856
Rejection of LEM = rejection of semantics = admitting you're a schizophrenic doing meaningless shit.
At least the infinitards who accept LEM are consistent in their philosophical disposition.

[Anonymous No.14823878]

>>14823862
>Rejection of LEM = rejection of semantics
Interesting, so then what are BHK semantics?

[Anonymous No.14823888]

>>14823668
That's just because it simplifies everything to imagine those things. Plus it works out. When it comes down to it stuff is calculated or simulated on a computer. No completed infinites or non-computable numbers involved.

[Anonymous No.14823924]

>>14823878
>so then what are BHK semantics
They're semantics of proofs not of the underlying math you dipshit.

[Anonymous No.14823929]

>>14823888
>Plus it works out
Proof that ZFC is consistent?
>When it comes down to it stuff is calculated or simulated on a computer. No completed infinites or non-computable numbers involved
Then why assume completed infinities?

[Anonymous No.14823944]

>>14823929
Like I said, it's simpler and it works. The logicians are free to fuck around in their spare time but I don't think physicists are going to care.

[Anonymous No.14823964]

>>14823862
>Rejection of LEM = rejection of semantics
How?

[Anonymous No.14823970]

>>14823964
Because if you have semantics, every statement is meaningful and has a definite truth value, i.e. is either true or false.

[Anonymous No.14824027]

>>14823924
>They're semantics of proofs
Under the assumption that proof is equivalent to truth, i.e. the proof IS the underlying math.

[Anonymous No.14824036]

>>14823970
>because I can't into three-valued logic

[Anonymous No.14824043]

>>14824027
I'm so sorry for your severe mental retardation

[Anonymous No.14824050]

>>14824043
>>14824036

[Anonymous No.14824065]

>>14823642
>Secondly, intuition has no place in a proof, what's being done in between steps is logical inference, and not the author going "it is intuitive to see that..."
What's the difference?

[Anonymous No.14824077]

>>14823668
The imaginary root has spatial and physical intuitions that is connected to. The infinite set does not. Infinity isn't a thing. It's something made up by mathematics schizos.
>>14823642
>the universe is POTENTIALLY (keyword: potentially) infinite in size, likewise the bigbang is thought to be infinite in density
I'd like to see what you meant by that. That's an interesting distinction. Like, was it infinitely dense because of infinite matter, or was it infinitely dense because of infinitesimal space (which can still imply finite matter). It seems like there are two kinds of infinite potentials to consider, one of mass and space, and there has been no experimental data that can show us either way (nobody observed the big bang). So, finitism chads are still on top.

[Jealous No.14824213]

>>14823821
I think you're making a joke but I can't be sure. I read it as "there exists a set x such that the empty set is in x and for any y in x there also exists a y' in x" where it is implicit that y' is a different set than x, y, or the empty set. I think you made a joke but it could say what what you said.

[Jealous No.14824233]

>>14823840
If the lower case Latin letter x is a set, then it follows that y and y' are sets. That pretty much rules out y' being the derivative, I believe. x is a collection of sets, a multiset which is just a set, and I think the elements of x are labelled y_n where we may substitute for simplitcity y_0=y and y_1=y'. Now if y_0 is collection of two sets, there exists another set y' meaning there are more than two sets and the empty set in x. If y_0 is a collection of three sets, there still exists another y' meaning that x has more sets in it still. This goes on an on so the point of the meme is that the top follows from the bottom. Unfortunately, retards say that I can't actually continue to write "If y_0 has 10000000 sets in it and y' is still another set, then x has at least 100000001 non-empty sets in it," forever, and therefore the collection of an infinite number of sets cannot exist because I complete the exercise of writing down something which is not not needed at all. As is the case for induction, I have explained the idea with "2" and "2+1". Simply substitute "n" for "2."

[Jealous No.14824237]

>>14824233
>cannot exist because I *can't* complete the exercise

[Jealous No.14824245]

>>14823888
I see you have made a statement but I'm not sure what point you're making. Are you say it is a deficiency of numerical methods are they are bound to approximate the analytical solutions of continuous problems? Or are you saying that the analytical solutions (and related things) can't exist because we can't always put them on the computer?

[Anonymous No.14824250]

>>14823490
>if there are things in collections
You're painting a strawman.
Choice grants existence for non-empty sets, you don't have an apriori selection of what's in it.

To make that point explicit, let's play a game. The game consists in two steps. The first step consists of me stating the existence fo some set and asserting that it's non-empty. The second part of the game consists in you telling me an element of that set.

Okay then, let's start the game.
He's my part: There exists a set. I guarantee you that its cardinality exceeds that of the powerset of the powersrt of the powerset of the real numbers.

Okay, now for your part: Name me an element in that set.
Thanks for your coorporation

[Jealous No.14824259]

>>14824245
As an aside, let my point out that when I just into analysis with the same definition of R that this paper starts with R=(-INF,INF), I get a new asshole torn with people telling me I can't just jump into it there and if I haven't started by proving that first, then my whole analysis is shit tier. The fact is, this is the accepted definition of R an if you don't already know what it mean, you aren't in the paper's intended audience. It's like knowing what the characters of the Latin alphabet are and how to read English: you're expected to already know that and authors are not expected to to include the dictionary of the English language as a supplemental appendix.

[Jealous No.14824262]

>>14824245
I used this paper from Sun as a loose style guide for my own similar analysis, btw.

[Anonymous No.14824263]

(Note that the situation is different, since the formal statement of the cardinality exceeding PPPR implies I have some injection that one could use. But the spirit is the same. The axiom of chocie is problematic because it postulates input-output existence in a situation where you don't have the information to do so. If it was possible to do it, we people wouldn't need an axiom. And it's different than set existence statements like the powerset axiom where be know elements of it by definition)

[Anonymous No.14824268]

>>14823626
>>14823568
holy fuck, it's Infinity. what do you even do in this thread

[Jealous No.14824271]

>>14824077
If complex numbers are the transverse continuation of R onto the complex plane, then transfinite numbers are the longitudinal continuation beyond the LUB and GLB of R=(-INF,INF). Just call the continued interval T like we call the complex plane C and everything is the same. What is it in your mind that makes transverse continuation reasonable but longitudinal continuation unreasonable?

[Jealous No.14824288]

>>14824263
>The axiom of chocie is problematic because
It's problematic because it suggests there might not exist sets with infinite elements, such as the set of natural numbers. I must say, if one thinks [math]\mathbb{N}[/math] can't exist, then I have a low opinion of one's opinion. N is "the set of all natural numbers." Saying that it isn't is overzealously pedantic in the best case and completely stupid for all practical purposes.

[Jealous No.14824311]

>>14824233
>>14824288
>what does he mean by jealous?

[Anonymous No.14824354]

>>14823568
>>14823626
>>14823816
>>14823821
>>14823840
Lmaoing at these people smugly asserting that this is bullshit or that it has anything to do with derivatives. Go back to Calc 2 or pick up a set theory textbook and actually learn something before criticizing it lol.

>>14824268
This is the only literate person who responded to the pic. Maybe you guys should get a pass since y' is horrendous notation for the successor of y, but the sardonic confidence in your misunderstanding suggests otherwise.

[Anonymous No.14824357]

We have tolerated the Axiom of Choice cultists for far too long. We have, in retrospect quite foolishly, made every effort and gesture to détente, to de-escalation. The Axiom of Choice cultists accepted the proferred olive branch… by biting off the hand. And at every turn they mock us, let loose their slings and errors, all the while bellowing the victim, gaining a feigned crocodile’s sympathy from the scientific press which they control.

Enough is enough. Our patience has its limits. The Axiom of Choice cultists have gone too far this time. And like a spring tightly wound, our indignation is reaching the limits of our capacity to contain it.

[Anonymous No.14824359]

>>14824354
Oh and I should add that the meme is true (if you reject choice but believe in infinite sets then you need to do some thinking), but also infinite sets exist and finitism is believed by like ten actual mathematicians and no one else.

[Anonymous No.14824391]

>>14823757
Don’t worry about them. I left the academy, got an industry job, and research what I want to nights and weekends now. Beats having to follow trends like Academics do where they all literally wind up researching the same topic at once, it’s stupid.

[Anonymous No.14824393]

>>14824271
>imaginary roots are fine because they have physical representations
>BUT BUT WHAT IF I SIMPLY REPEATED MY INFINITY BULLSHIT IN THE COMPLEX PLANE
you would run into the same problems of why "the reals" are bullshit: infinity

now run along schizo

[Jealous No.14824394]

>>14824391
I like university though.

[Anonymous No.14824397]

>>14824394
If it makes you feel better, the odds of a fresh PhD even getting a postdoctoral are approaching 2% these days. I thought it was bad 8 years ago when it was 5%, but man is academician drying up for everyone, even for the nimrods who blacklisted you from certain journals.

[Jealous No.14824401]

>>14824397
I heard that if you solve the Riemann hypothesis, you get tenure anywhere you want.

[Anonymous No.14824424]

>>14824397
>the odds of a fresh PhD even getting a postdoctoral are approaching 2% these days
>man is academician drying up for everyone
Academia has always been competitive, the fact that it's becoming more competitive should suggest that it's anything but dried up

[frenanon No.14824431]

>>14823757
Kek, I don't think you're complete schizo Tooker, but I think "Proving Time Travel" is more of an indication to the failures in the current Models, and isn't actually a cheat-code for reality.

Same thing with Mandlbaur; I don't necessarily think he's "wrong", but I think he has a couple of flawed assumptions based off one of his COAM papers I read a ~month ago.
>picrel

btw, for anyone who hasn't had a chance to check out the thread: >>14806713 there's a handful of topics in there that addresses new possible paradigms to explain observable phenomena that could potentially offer some reasonable explanations.

[frenanon No.14824456]

>>14824065
>What's the difference?
Critical Thinking.
If it's "too easy", then it must be wrong.

[Jealous No.14824462]

Here's one where where I don't use an unproven proposition for "quickness." In this one:
>>14824262
I taken Euclid's Elements as accepted and then show that if Euclidean geometry is valid, then the Riemann hypothesis is necesarily false. That one is not quick.

[Jealous No.14824464]

In this one, I use a level of rigor appropriate for physics and do it very quickly.

[Anonymous No.14824488]

>>14824391
I do enjoy the freedom of studying on my own but the nice thing about being in academia is having colleagues and people to discuss ideas with. Is it really fulfilling to go it alone?

[Anonymous No.14824490]

>>14824424
There’s a lot less funding for new positions than there used to be, so it is indeed accurate to say it’s drying up.

[Anonymous No.14824503]

>>14824488
You have to go out of your way to meet people but I have been successful. I also am lucky to have made a lot of smart PhD friends over the years that we regularly discuss what we’re working on, I’ve found that invaluable for having out my ideas. Though honestly I even get value from discussing my work with non academic types (so long as they’re interested of course) and I have often found that just the act of explaining to an interested audience is fruitful. I also make an effort to go to seminars online and locally. So no I don’t feel starved for colleagues to discuss math with. The only hard thing is that my industry job colleagues are dumber than rocks and punish creativity so I try to spend as little time with them as possible, but they pay the big bucks that make everything else possible so I don’t complain

[frenanon No.14824510]

>>14824077
>and there has been no experimental data that can show us either way
The data is that "we exist".
That should be all the proof necessary to show that there is an infinite potential for the Universe to produce more, uhhh, "stoof 'n jonk".

Like, if we "assume"(I know, I know...) that atoms/molecules and whatever can exist into perpetuity; then you can create a perpetual-energy-generator which will continue to operate until the end of time, while also being able to extract energy that it passively produces.

I actually have a few different types of projects in mind that could accomplish this.
The problem is, I just can't get any serious interest besides people calling me a retarded schizo; only to find News Articles claiming that >""Scientists at ________ have made a major breakthrough in X, Y, Z!""
So yeah, that's pretty much been the story of my life since ~2010 when I started contacting a bunch of uni professors, Gov/Mili Agencies, and anyone else who would possibly be interested. Still waiting to hear back from any of them. Not sure if all of their e-mails listed under their Public Contact Info all just happen to filter @gmail accounts, but I don't exactly have a ton of faith that the people I contacted are some paragons of virtue and nobility...

[Jealous No.14824511]

>>14824488
>the nice thing about being in academia is having colleagues and people to discuss ideas with
I agree.

[frenanon No.14824537]

>>14824397
>but man is academician drying up for everyone, even for the nimrods who blacklisted you from certain journals.
(((Academia))) has never been better...

[frenanon No.14824560]

>>14824424
>Academia has always been competitive
It's not competitive in the "Academic" sense though.
The Globalist pseud's have just paid their way into important Administrative positions in Public/Private Sectors of Business/Academia/Government.

[Anonymous No.14824662]

>>14823727
Leibnizian infinitesimals were definitely criticized by contemporaries on philosophical grounds, most notably by Berkeley.

[Anonymous No.14824668]

>>14824462
>Euclidean space
no such thing. the Greeks did not believe in something called "space." they didn't even have a word for it. how retarded do you have to be to think that you can steal ideas from the past, botch up the translation, and then shove the ideas back in the mouths of the people you stole them from to give it an air of credibility?

[Anonymous No.14824671]

>>14824510
>The data is that "we exist".
And?
>That should be all the proof necessary to show that there is an infinite potential for the Universe to produce more, uhhh, "stoof 'n jonk".
at best, you mean infinite recombinations of finite things. and that assumes an infinite timeline. otherwise we're talking about finite recombinations of finite things.

[Anonymous No.14824672]

>>14824662
>Leibnizian infinitesimals were definitely criticized by contemporaries on philosophical grounds, most notably by Berkeley.
Why? It's also strange considering Berkeley lifted much of his own philosophy from Monadology kek.

[Anonymous No.14824678]

>>14823595
> you can't actually exhibit infinite sets either (i.e. encode them in the mind or in a computer).
Put your hand in front of your face.
Now look at it.
How many exact points are there on your hand?
Now you can slap yourself with the continuum, isn't mathematics great?

[Jealous No.14824745]

>>14824668
I don't recall using that phrase. Who are you quoting?

[Anonymous No.14824801]

>>14824503
Lucky. I feel like I'm working in isolation and lose motivation. I'm a bit of a recluse.

[Anonymous No.14825025]

>>14824678
Space is not made up of points. It's continuous. Points are something we impose upon space.
If you think looking at your hand proves the mathematical theory of completed infinities then you are stupid.