/sci/ - Science & Math

ok. let's see your model.

Right is all of modern academics

>>16222984
It's fine, I can fix the theory by adding another dimension!

[It's really small and curled up though so don't try to observe it]

>>16223048
The extra dimensions reveal themselves at very high energy levels. Trust me bro. Just one more collider for another trillion dollars please.

>>16222984
>DARK MATTER IS BULLSHIT!!! NOT REAL SCIENCE!!!!
>no I can't offer any alternative explanation that doesn't contradict the rest of physics, but that doesn't mean that dark matter exists!!!!

>>16223055
You are Homer...
https://www.youtube.com/watch?v=xSVqLHghLpw

>>16223067
Please provide an alternative to dark matter to explain all the evidence we have of its existence.
Note that this alternative MUST be consistent with observed and established physics. So no MOND.

>>16223070
NTA but where exactly is the problem with it not being consistent? Physics isn't an exact discipline with consistency anywhere else, why would adding one more source of inconsistency suddenly cause problems?

>>16223109
If in an attempt to solve one inconsistency you introduce a dozen more that contradict observed phenomenon, your theory is worthless.

>>16222984

>>16223034
Non sequitur argument.

>>16223038
Ad hominem and non sequitur.

>>16223048
Non sequitur and strawman.

>>16223052
Strawman and Red Herring.

>>16223055
Ad hominem and a cheeky Texas Sharpshooter to boot.

>>16223067
Not an argument.

>>16223070
No True Scotsman fallacy. Poorly formed prose.

>>16223130
Ad hominem.

>>16223133
Another ad hominem photo.

Do any of you know how to properly have scientific discource?

>>16223160

>>16223169
Calling me a Redditor does not form a valid argument nor does it negate any of your prior logical fallacies. Learn to have an IQ higher than 85 or hang yourself please.

>>16223172
now post your argument

>>16223172
ok.
redditor.

>>16223160
Fallacy fallacy and ad hominem.

>>16223183
Are you asking me to divulge a high-quality intellectual argument in spite of the horribly bad quality of the replies here? I will not sully my intellect by doing so.

Clean up your arguments first, then I will reply to you.

>>16223130
Maybe I'm jaded because I'm an engineer rather than a physicist, but it's always struck me as odd when physicists pretend that their theoretical models aren't basically a form of "best fit" approximations. Even the fundamental equations like "F = ma" are approximations because the distribution of mass and moment are never consistent either in time or space.

I understand that you don't want to introduce new theoretical modeling which seemingly contradicts previous findings, but the contradiction of previous findings and development of special cases literally forms the foundation of modern physics.

>>16222984
Either there is something we cannot detect or the physics is wrong. LARPing as if you are about to invent MOND and nobody has thought about it before isn't smart. Distant binary systems have been found to behave as expected, as have some galaxies, making new physics especially difficult to explain.

>>16222984
anon, dark matter is an adjustment, an adjustment to the expected mass present in a galaxy.

>>16223195
>Maybe I'm jaded because I'm an engineer rather than a physicist, but it's always struck me as odd when physicists pretend that their theoretical models aren't basically a form of "best fit" approximations. Even the fundamental equations like "F = ma" are approximations because the distribution of mass and moment are never consistent either in time or space.
Yes, that's why they are called "models" in the first place.
>I understand that you don't want to introduce new theoretical modeling which seemingly contradicts previous findings,
The thing is that our current theories such as general relativity and the standard model of particle physics match many observations with astounding precision. For instance, the standard model made incredibly accurate predictions of the mass of many particles, predictions that are continually proven to increasing precision.
This indicates that, while the theories may be incomplete, they are very much onto something. Obviously physicists are reluctant to completely throw away these models when they seem to be on the right track. So when something is observed that doesn't match the model, rather than throwing the model away, they try to figure out how the model could be altered to fit the new observations.
Dark matter is exactly that, an alteration to the Standard Model to account for the odd properties of large-scale structures like the rotation of galaxies.
>but the contradiction of previous findings and development of special cases literally forms the foundation of modern physics.
Because that's how science works. You create a theory, test the theory, and find out whether or not the predictions the theory makes match up with reality. If they do, that doesn't mean you stop experimenting. It means you keep experimenting, because you may find out there are cases where the model does not make accurate predictions. Then the model can be altered to better fit with observed reality, making new testable predictions in the process.

Do you think illustrations were made like this in 1800? "Thermometers don't work the way I want them to, therefore dark light is real"

>>16223191
>no argument

>>16223169
>ad redditam
Nice fallacy, cuck.

I think our measurements of galaxies, and the expansion of the universe, is wrong. We've been measuring it for what, a few decades, a hundred years tops?

Maybe we are doing something wrong, and they are not moving like that? Has anyone independently started measuring?

>>16223287
>Has anyone independently started measuring?
What does this even mean? Plenty of people have measured the expansion of the universe and the movement of galaxies.

Musk could fix the dark matter problem if he wanted to, probably wouldn't take him longer than a week to figure it out

>>16223293
Yeah, all the Ivy League big wigs with special connections and long histories. Has anyone gone out with telescopes and measured these themselves?

>Nonono anon, you must trust us, we all agree, this is what we see, nothing for you to check yourselves.

>>16222984
Dark matter are advanced civilizations hiding themselves from even more advanced predators, the true cosmic horrors.

>>16223387
Unless you can afford to build yourself a whole ass observatory, then you're not going to be able to measure the expansion of the universe. Amateur telescopes are not anywhere near sensitive enough for that.

>>16222984
Scientist, broadly, don't believe in spirits. Wherein, whereabouts, whereupon did they definitively falsify the existence of spirits?

>>16223423
shut up with your Russel's teapot retardation

>>16223423
Sorry. I forgot I was on /sci/ and not /x/. I been drinking.

>>16223431
On the real though, saying "It's false" without rigorous falsification process or otherwise rightly seeing to the heart of the matter (and both is probably something that is possible) is essential irrational, dogmatic, and non-scientific (at least with reference to science's reputation of being logical, rational, and upright).

>>16222984
Ok I’m
The biggest science denier here and I have to call bullshit on this post.

Astronomy is how we discovered computers.

Astronomy is how we sailed the seas (celestial navigation)
The very concept of gps derived from this.

Calculating the tides comes from timing of celestial mechanics.

It’s how we measure time and create clocks.

Out of all the dumb post here I think
This one takes the cake.

>>16223438
This. Astronomy is one of the oldest sciences on the planet.
It's kind of hilarious how many people hate on it nowadays, when their ancestors were likely obsessed with the stars as so many ancient people were.

>>16223443
I think people confuse it with modern astrophysics, which consists of black holes and other nonsense like dark Matter.

I mean I know people like discovery and I don’t think mordern astrophysicist are malevolent in their intentions. I just think they focus way too much beyond what is realistically observable with the constraints of current technology. And they just get “lost in the sauce”

>>16223248
> Yes, that's why they are called "models" in the first place.

I like you. This is the right mind-set. Yes, the models we have now are astoundingly good for what they are. I will agree with that. I just get a little confused when people pretend as if these are not models and are in fact some sort of "source code of reality" or something.

Never forget the number one rule, "all models are wrong but some models are useful."

Btw, I don't think that we should throw away "dark matter" as a theory just because we have an incomplete understanding of what's actually happening there. I don't know enough about the subject to really have much of a strong opinion either way. It could very well be the case that there is some sort of matter which has no EM interactions by some mechanism by which we don't fully understand, or it could be some property of rotating incomprehensibly massive body which itself interacts with EM in ways that produce the appearance of dark matter (via distorting our measurements or some other mechanism). Who knows? Certainly I don't.

>>16223513
>Btw, I don't think that we should throw away "dark matter" as a theory just because we have an incomplete understanding of what's actually happening there.

Pop sci fantasy nerd spotted

>>16223522
> Pop sci fantasy nerd spotted

I'm saying "I don't know whether it's right or not." It could be right and I don't understand it, or it could be wrong and there's something else happening that causes the phenomenon we observe and physicists assume dark matter is causing. I don't know enough to know either way.

>>16223070
>Note that this alternative MUST be consistent with observed and established physics.
There is no reason why it should be consistent with established physics. That's a nonsensical requirement.

Reminder OP has made thousands of threads
Reminder OP spends all his waking hours seething on /sci/

>>/sci/?task=search2&search_filename=science%20vs%20astronosoy.jpg

>>16223708
>10 threads
Are you okay?

>>16223710
You're easy to recognize

>>16223712
>In Science & Math, 10 > 1,000
Retard.

>>16223325
he doesn't waste his time on stupid garbage like that

>>16223187
Fallacy fallacy fallacy

>>16223654
>there is no reason why a theory should fit with observations

>>16223250
A similar thing cropped up in black-body radiation, where everyone expected energy to be continuous but the first explanation to work ended up with discrete levels of it. Thus was quantum physics born, trying to explain the spectra coming out of holes cut in ovens.

>>16224001
It needs to fit with observations, but not with previously established theories. In fact what you want is impossible - it can't fit observation any better while still agreeing with the old theories.

>>16223443
>its good because its old
>oooga boooga
the rest of us have long since evolved past junk that was figured out 5000 years ago

>>16222984
I made a similar post here on /sci/ 5 years ago and got a 3 day ban for trolling outside /b/

>>16224942
Dark Matter jannies are the worst. So sensitive. It's not real matter dummies.

>>16222984
>>16223160
>You can't see air, there for it's not there

>>16222984
>You can't see air, therefore it's not there

>>16225086
>You can't see air
yes you can, its visible the same way water is

>>16223133

>>16222984
>dark matter isnt real
Popsci and its consequences has been a disaster for the media landscape.
Dark matter huh? I have plenty to stuff down your throat here, monkey.
*beats chest and flings poop at you*

>>16226134
>like a mathematician
Like a physicist you idealism nigger

>>16223232
>Either there is something we cannot detect
Yes, nothing is the thing that is undetectable, you just have to indirectly assume it as a point of logic since the only way two things can possibly be in direct contact is if nothing is inbetween them.

>>16226134
There’s no such thing as a dark number in mathematics, this meme doesn’t make sense (besides even the fact it’s too wordy to be a meme)

>>16223034
God rotates galaxies for fun

>>16224931
No, modern man still needs to know when the next eclipse will occur and makes a big deal out of it when it does.

>>16226466
He literally just told you what a "dark number" is, its the ... nonsense you might call something else.

>>16226576
Mutation/Evolution

>>16226576
After starting by discussing .999… = 1 he then jumped to Cantor’s diagonalization argument to show the set of numbers that can be defined to arbitrary precision in binary notation aren’t countable. He then says the fact there are always numbers definable to arbitrary precision in binary notation outside of any countable set containing them means those numbers are “dark numbers” which obviously isn’t the case since the Cantor diagonalization argument explicitly constructs an example that can be analyzed just as precisely as any other number in the set.
It seems like a failed attempt to make mathematics seem as arbitrary as physics while also tying together some recognizable but unconnected /sci/ memes. Maybe if they were more focused on their goal of making math seem arbitrary and less focused on shoving irrelevant memes in their then maybe they could try to make a point, but as it is now it’s just a mix of nonsense that would embarrass any self-respecting mathematician.

>>16226597
Could you show me one of these dark numbers to spread light on them and to show we have nothing to fear. I want you to be Hawking penetrating the depths of the darkest black hole. I am going to need that in an expression or equation obviously; hand waiving paragraphs, laden with semantic baggage, just pushes the onus onto the readers. You are way too confident for that.

>>16222984
Astronomy is fine as long as it sticks to empiricism and abandons theoretical physics.

>>16223195
It’s the application of Occam’s Razor to scientific inquiry: You develop models, refine them, and when you discover inconsistencies you try looking at simple explanations that modify existing models that already work before throwing the existing models out altogether. To use your example, F = ma works pretty goddamned well, it’s a model that fits nearly all of our observations and so when we find cases that don’t fit we look at explanations that alter F, m, or a, rather than throw out the model altogether (is there a force we haven’t accounted for? are we in an accelerating frame? etc.)

We do know, now, that F = ma is only the model that fits observations in certain limits (nonrelativistic, nonquantum, etc.) but those new models all still have to yield the same result as F = ma in the limits where it applies.

So we come to gravity. Newton’s Law of Gravitation worked and worked well for everything we could observe a few hundred years ago, and made fairly precise predictions. But then we discovered observations that didn’t fit Newton. Attempts were made to modify the existing model, but ultimately a new theory was needed. General Relativity helped explain those observations, but in the limit of less extreme masses or motions far from gravitating bodies, Einstein’s Field Equations reduce back to Newton’s Law of Gravitation. Similarly, GR can now explain 99% of the observations we make, but there’s a few points where it breaks down. Astronomers are trying to modify other parts of the model (is there mass we didn’t account for) before going back to the drawing board and trying to come up with a new qualitative explanation of gravity that can fit these new observations while still recovering all the results from Einstein.

>>16226666
>Our empirical results show that y=mx+b and that f=ny+c.
>Interesting, these empirical results would seem to necessarily imply that f=mnx+nb+c.
>SHUT UP YOU FUCKING WORTHLESS THEORY FAGGOT THERES’S NO BASIS FOR THAT!

>>16226730
If you had a genius in the 21st century to push things forward you wouldn't need so much theoretical but you don't so average people need to rely on excessive amounts of theoretical physics.

>>16226740
Experiments give theorists observations to model.
Theorists give experimentalists models to test.
This has been the synergy in science for the last four centuries and the people who consistently bitch about it tend to be neither and also tend to be ill-informed about the work of both.

>>16226767
The criticism isn't in the theorising of models synergising with scientific experiments to prove or disprove hypotheses, which has always happened, but in producing untestable hypotheses (untestable not because of technology but because of their nature) mainly to lower the standard of hypotheses to produce as many papers as possible, because science now operates under a publish or die model.

>>16226814
Untestable models are crap, I don’t disagree. String theory is a good example, where I can’t think of a single testable condition they’ve come up with.

But dark matter *does* have testable conditions. We can search for new particles that fit the predicted behavior or dark matter, we can look for evidence of other observations consistent with the gravitational influence of more than the visible matter we can see, etc. we’ve already tested and ruled out several dark matter candidates in this way, and if we rule them all out then we can start looking to expand the inquiry to include modifications to GR.

>>16223160
Declaring some heuristics fallacies and some valid is pseud shit for people that don't actually understand formal logic and have never thought about epistemology.

>>16227076
Enough jargon speak English like normal people.

>>16227085
You think Ug no prove badder than you no prove because you bad brain. You no know what prove is or why prove.

>>16226574
Modern astronomy doesn't do things like that, its devolved to idiocy and insane fantasies.

>>16226714
Thank you for your detailed response. You've given me some things to think about.

To be honest, I don't think we'll get a better deterministic model for most of these systems. It seems to me, (again as an engineer who works on information theory, not a physicist) that the "truth of the matter" will almost always require some amount of stochastic process noise to deal with the intractable imperfections in the dynamical modeling process and our inability to get precise information about static parameters.

>>16226466
there's irrational numbers that you can't describe in any way.

>>16227192
NTA, but this is somewhat of a misnomer as far as I'm aware that most comes from the strange translations that happen between computer science and real analysis.

As far as I'm aware, almost all of what we call "indescribable numbers" are describable via either algorithmic descriptions or infinite degree polynomial equations.

As an example, every one of the Cantor numbers that are involved in the diagonalization argument for uncountability are "describable" provided you allow for an infinite length recursive description. You just can't describe them as the solution to some finite degree polynomial equation.

>>16227192
>>16227202
read about computable numbers and non-computable numbers

>>16227202
I've never heard "indescribable numbers" as some specific formally defined set. But there's a general argument people make that shows the set of real numbers is (much) bigger than the set of all numbers you can define using strings of characters, which is what I assume anon was talking about. The argument is just that if you take any list of characters you can then take all finite strings of characters in that list, and the set of all such strings is the same size as the set of natural numbers.

You're probably thinking about the fact that all the real numbers humans practically care about are possible to define using language. Which is pretty inevitable since humans do most of their objective thought and communication using finite languages, in finite time. It's not really a fact of mathematics as much as a fact about humans and the physical universe they live in. And there's not actually any proof some guy won't come up with an objective system of thought that can't be reduced to finite symbol manipulation. Most people just think it's unlikely.

>>16227225
Maybe I wasn't clear enough but I'm explicitly referring to a kind of non-computable number.

This response here
> The argument is just that if you take any list of characters you can then take all finite strings of characters in that list, and the set of all such strings is the same size as the set of natural numbers.

Is exactly the language confusion I was referring to. A Cantor diagonal number is explicitly non-computable because it requires an infinite number of bits to define due to the sequence itself of bits being a result of a recursive algorithm (bit N is the opposite of the Nth place bit in the N+1th place in a set of infinite bit binary expansions).

This is a non-computable number that is definable in the sense that there is a finite instruction recursive algorithm by which you can define what the "next bit" will be despite never being able to terminate the number in finite time. This is specifically because the recursive algorithm is operating on a set of infinite length binary strings.

In general computability is a pretty bad way to look at really anything mathematically except for search/sorting algorithms. Almost all useful mathematics happens on continuous sets, and computability is a basically useless framework for continuous function analysis. A number being definable (in that it is the result of a finite set of steps you recursively repeat) says nothing about whether it will be computable.

>>16227437
Oops, meant to also quote >>16227244

>>16222984
You're confusing astronomy with astroLogy.
They're 2 completely different things

>>16227437
Computable numbers are an objectively defined set. For instance all possible outputs of the set of Turing machines which indefinitely return 1 or 0. There are equivalent definitions and encodings, but on some level you can pick any definition you want and get the same set. In the sense that if someone points at a Turing machine that endlessly spits out 0s and 1s, then you can always point at a Python program (on a computer with infinite memory) that spits out the same sequence, and vice versa.

To make 'definable number' a rigorous definition that has some objective connection to computable numbers, you would have to explain formally what
>A number being definable (in that it is the result of a finite set of steps you recursively repeat)
means. That's not a definition yet because I don't know what a "step" is. But I will say it seems unlikely to me that you are physically capable of creating any device or formally defined system that will eventually output a non-computable number.

You explained how a non-computable number can be derived from a certain ordering of Turing machines/programs/whatever. But you haven't shown that you're actually capable of producing such an ordering, and as far as I know no other human has ever managed to do that either.

>>16227437
I'll rephrase this >>16227740 slightly. Obviously you're not capable of producing a device that would output a non-computable number because non-computable numbers are infinite strings. But I don't think you're capable of producing a device or objectively defined system that can infinitely output 0s and 1s such that no Turing machine outputs the same infinite sequence.

>>16227745
Why do you need a device to output the number for it to be a number that we can analytically interact with? There are computable numbers that are only possible to define via an infinite series (e.g., e or the output of the Gamma function at a particular value), why would it be any different in mathematically for non-computable numbers that are defined in terms of repeated sequences of finite arithmetic steps?

Obviously it's a more abstract concept and these numbers would need to be approximated when you implement them on a computer, but this would be the case regardless of whether they were computable and precise beyond floating point precision (as in e or π or the output of a non-elementary function) or non-computable. That doesn't matter at all to whether the number is definable in terms of arithmetic/sets.

>>16227749
Making a device was just an example of something you could do in order to 'point at' a sequence of numbers that you're claiming isn't computable. I don't think you're capable of pointing at a number in any sufficiently objective way that we can prove it isn't computable.

You have to explain what "analytically interacting with a number" or 'defining in terms of repeated sequences of finite arithmetic steps' means or you're not actually making a mathematical claim. Like, the way you were talking I thought you were saying there was some provable incomparability between 'computable numbers' and 'definable numbers'. You haven't even defined "definable number" so obviously you can't have proven anything about them or their relationship with computable numbers.

>>16227770
A number being arithmetically definable is about as simple as the name implies. If you want a more formal description you can read here:
https://en.m.wikipedia.org/wiki/Definable_real_number#Definability_in_arithmetic

The basic jist is that a number is "definable" in a quantitative sense if the number is completely described by either a finite number of basic arithmetic steps (in which case the number is arithmetically definable) or a finite number of second order arithmetic steps (in which case the number is usually called analytic, which is a type of arithmetically definable).

Every number that is computable is both arithmetic and analytic, but not every number that is analytic is computable. For example, the Cantor diagonal numbers are defined via a finite number of second order arithmetic steps. It's basically a for loop with a single bit-wise not operation. Because these numbers are definable in a finite number of second order arithmetic steps, they are definable in terms of second order arithmetic despite not being computable.

>>16227437
>This is a non-computable number that is definable in the sense that there is a finite instruction recursive algorithm by which you can define what the "next bit" will be despite never being able to terminate the number in finite time.
you just said this is a non-computable, and that its given by an algorithm

you cannot define what the next bit will be at a certain point, after a certain point determining the next bit will be independent from your axioms
look up Chaitins Incompleteness Theorem

this number is not definable, there is not a finite list of instructions to make it, the list of all possible strings which determine a valid number cannot be enumerated in the theory, if you work over the collection of all those, then the instructions are not finite.

any non-computable number can only be determined up to an interval of computables with non-zero width.
So it doesnt make any sense to take a limit of a non-computable cauchy sequence, and so the reals are fake, a figment of imagination and wrong assumptions.

>In general computability is a pretty bad way to look at really anything mathematically except for search/sorting algorithms. Almost all useful mathematics happens on continuous sets, and computability is a basically useless framework for continuous function analysis. A number being definable (in that it is the result of a finite set of steps you recursively repeat) says nothing about whether it will be computable.
you are literally retarded.

>>16227823
Here you go.
https://en.m.wikipedia.org/wiki/Computable_number

Take a look at the "other properties" section:
> Every computable number is arithmetically definable, but not vice versa. There are many arithmetically definable, noncomputable real numbers, including...

Cantor's diagonal numbers are a great example of these arithmetically definable but not computable numbers. Every Cantor diagonal number can be defined by exactly 1 second order arithmetic instruction (for all n in N, S_0,n = ~S_{n,n}, where {S_n} is any countable set of unique infinite length binary strings) and yet they are not computable because this single second order arithmetic instructions will never halt.

Computable numbers are only a small subset of arithmetically definable numbers.

>>16227840
I know how the computables work, faggot
you literally didnt acknowledge a single thing i said
More importantly, in order to get to the first non-trivial rung of the arithmetic hierarchy, you have to assume the existence of a fucking oracle.
just because you gave them a name like "arithmetically definable" doesnt actually mean you can work with them or show they exist.
If you assume the existence of an oracle, then you can prove P = NP, so wheres your million dollars?

>Computable numbers are only a small subset of arithmetically definable numbers.
arithmetically definable numbers are a subset of the set of intervals over the computables.
meaning you cant actually get "in between" the computables

>>16227850
> I know how the computables work, faggot

Apparently not given that you've been tripped up on one of the first things you learn about computability on the reals (namely that there are uncomputable real numbers when words in your language are allowed to grow to a countable length).

> you literally didnt acknowledge a single thing i said

Nothing you said was worth acknowledging. If it makes you feel any better I will respond to some points now, but in general you are confused about how this works.

As an example, the "you cannot define what the next bit will be at a certain point," is completely incorrect. The whole point of the diagonalization argument is that you can explicitly define in a single second order arithmetic instruction every single bit in this number, which has to be between [0,1], but it cannot be included in any countable set of binary expansions of [0,1].

> this number is not definable, there is not a finite list of instructions to make it, the list of all possible strings which determine a valid number cannot be enumerated in the theory, if you work over the collection of all those, then the instructions are not finite.

Do you think that the rationals are uncountable then? This stands at odds with your statement about the reals not existing because the rationals in [0,1] are exactly this sort of countable enumeration which is used for the diagonalization argument. Why is this the part you trip up on when the enumeration is the countable/computable part?

> arithmetically definable numbers are a subset of the set of intervals over the computables.

Incorrect, you have this exactly backwards. All computable numbers are arithmetically definable, but not every arithmetically definable (and in fact almost every arithmetically definable number) is computable. Once you allow second order arithmetic (which is included in arithmetically definable) computability is not tied to definability.

>>16227860
>when words in your language are allowed to grow to a countable length
why the fuck are you assuming that?
words in a language are assumed to be finite
your constructions are so poorly behaved you have to go down and change the foundations?
where did you even make that assumption before just now

>As an example, the "you cannot define what the next bit will be at a certain point," is completely incorrect.
crazy how i wasnt even talking about diagonalization and youre still wrong
given any uncomputable sequence, you literally cannot determine what its bits will be past a certain point
Chaitins Incompleteness Theorem, like i already said

>The whole point of the diagonalization argument is that you can explicitly define
you cant explicitly define it, the stuff youre diagonalizing over cannot be explicitly given unless you assume that you can solve the halting problem.
or unless you make your wrong assumption that logical statements can be countable
i guess not not not not not ... exists in your retarded system then

>Do you think that the rationals are uncountable then?
what the fuck are you talking about?
the collection of all rationals is given by { m/n for m, n integers }
i was able to specify every rational with a finite number of words
thats a complete enumeration of every rational

the collection "every possible real number" cannot be realized in a finite number of mathematical symbols
there are only countably many proofs, so theres reals that cant be proven to be in the collection
you would need to specify all the uncountably many reals that you missed out
even if you assume your statements can be countable thats not enough

>Incorrect, you have this exactly backwards.
i dont have anything backwards
if you could read you would have noticed this

the arithmetically definable numbers are a subset of the set of INTERVALS over the computables.
i didnt say the arithmetically definable numbers are a subset of the computables you illiterate fuck

>>16227596
they're not all that different, both are equally rational and reality based

>>16227890
> Why the fuck are you assuming that? Words in a language are assumed to be finite.

This is not in general true. The alphabet of a language is assumed to be finite in general, but the words need not be. Their length needs to be either finite or countable.

Take, for example, the sequence 010000000...

We can truncate this to a length 2 word with the alphabet {0,1}, but a word made up of indexed {0,1} letters has absolutely no need to be of finite length in general. It needs to be able to be represented as a finite length word to be directly engaged with by a computer without approximation, but that doesn't mean the words in general need to be of finite length to be meaningful words.

Every single number in the interval [0,1] can be uniquely assigned some sequence of {0,1} values corresponding to coefficients of the power series on s_n (1/2)^n, n in N. There's absolutely no reason to believe we have to limit these expansions to be finite length to be meaningful as numbers.

They just need to be finite length to be computable, not definable or meaningful numbers we can define within a range.

>>16228439
words are always finite
there is no meaning with an infinite word

>Thread discussing astronomy
>Half the thread is two faggots arguing about the definitions of sets and shit.

>>16228453
None of this matters for the countability of these diagonal numbers. They could be finite length of n+1 bits and truncatable then and it would still produce the same outcome.

You could form a countable set {S_n} where each S_n is a sequence of binary digits which has a minimum truncated length of n+1 (effectively meaning the n+1-th bit is always a 1) and you'd get exactly the same proof. It cannot contain the diagonal number despite being a countable enumeration of unique elements in [0,1]

>>16222984
Astronomy is the study of celestial movement and events, such as predicting eclipses and whatnot, which is a respectable science.
Cosmology on the other hand is why science is called a religion.

>>16228518
The point is that the diagonal number cannot even be constructed
it requires an infinite amount of data to determine, it can't just be truncated

If you take that diagonalization, and then assume the diagonal element has length n
And we know there are certain expressions for bits with arbitrarily large minimum length
So there's a sequence, all of whose bits have length strictly greater than n
But from the diagonal element, we were able to determine such a bit with length n
Contradiction

>>16228567
if you diagonalize on the naturals
you don't get a natural

if you diagonalize on the rationals
you don't get a rational

if you diagonalize on the computables
you don't get a computable

if you diagonalize on all finite expressions
you don't get a finite expression

>>16223961
Fallacy fallacy fallacy fallacy

>>16222984
That picrel really spells out how fake and gay astronomy is. They don't care about the scientific method even slightly, all they care about is being pretentious know it alls

>>16228604
False. If the fallacy fallacy had had further supporting suppositions, then it would be correct to call the fallacy fallacy fallacy fallacy fallacy fallacy fallacy. Here, we have the opposing case where it is incorrect to call the fallacy fallacy fallacy fallacy fallacy fallacy fallacy.
Nice try xian.

>>16228567
I think I wasn't clear enough in my wording in >>16228518

The diagonal can't be truncated (meaning it can't be stored in a finite number of bits) but the elements of {S_n} can be truncatable numbers so long as the minimum truncated length is n+1 or larger.

The diagonals themselves are not representable by finite length bit strings (meaning they aren't computable or defined by a finite sequence of first order arithmetic steps) but they are analytic (meaning they are defined by a finite number of second order arithmetic steps, namely 1). Thus these non-computable numbers are arithmetically definable.

>>16228833
Yes, they're arithmetically defineable and yet they cannot be expressed in the same theory which is used to define arithmetic definability.
Remember, the very first nontrivial rung of the arithmetic hierarchy assumes the existence of something which doesn't exist, an oracle.

>>16223034
https://en.wikipedia.org/wiki/Plasma_cosmology

>>16228956

>>16228883
I like this image. It reminds me of Bernardo Kastrup's objections to scientific materialism.

Can you explain what you mean by
> Remember, the very first nontrivial rung of the arithmetic hierarchy assumes the existence of something which doesn't exist, an oracle.

I am not a logician so pardon my ignorance if it is something that I have not seen in my adventures in analysis/set theory.

>>16229455
The arithmetic hierarchy determines the complexity of sets.
If we take dedekind cuts to be at particular places in the hierarchy, we get different collections of numbers.

If the dedekind cuts are given by the lowest level of the hierarchy, the decidable sets, then the numbers we get are the computable numbers.

The next level above the decidable sets, are those sets which are decidable if we have an Oracle for the lower levels.
That is, if we have something which can solve the halting problem on the decidable sets.
This oracle cant determine the halting problem on itself, so then they say to assume the existence of another oracle for determining the halting problem on the first one. etc etc

Set theory is unnecessarily plagued with undecidability and the halting problem, so analysts just ignore the issues and pretend like there are ways around them.

>>16229650
> Set theory is unnecessarily plagued with undecidability and the halting problem, so analysts just ignore the issues and pretend like there are ways around them.

Analysis isn't particularly concerned with decidability or computability. An analytic number is itself something that you can perform valid set theoretic operations on even if the specific number is not computable.

Non-elementary integrals (which often show up in functional analysis, physics, probability and electrical engineering) very often have non-computable exact solutions and require approximation in order to deal with on any level (even with analog computing). Yet, we can use basic numerical analysis techniques to approximate the output of these non-computable numbers to any specified degree of accuracy via sums of elementary integrals (i.e., approximation of non-computable quantities by computable and quantities). Yet many of these non-elementary integrals would require a solution to the halting problem in order to actually compute.

Basically, we don't care if the number isn't explicitly definable if we can establish a recursive process (either first or second order arithmetic) by which we can approximate it. This is especially true in integration theory where we are often only able to produce solutions to difficult Lebesgue integrals via the limit of some sequence of more well behaved measurable functions with respect to the same measure.

Essentially, if there is a way of defining the number with respect to the limit of a recursive process, we don't particularly care if it's directly decidable because we can always approximate via decideable numbers to any specified degree of precision (even if you cannot know exactly when or if this recursive approximation will halt for all degrees of precision).

>>16229674
>Non-elementary integrals very often have non-computable exact solutions
the integral is a computable operation, the antiderivative of the gaussian is a computable function
non-elementary integrals are basically always computable

>because we can always approximate via decideable numbers to any specified degree of precision
this is the definition of a computable number

>>16227777
Do you have a formula which refers to a definable, non-computable number? Can you tell me what any arbitrary digit of that number is?

>>16223160
I use the /pol/ methodology: Anything that contradicts my beliefs is false.

>>16229899
Cantor's diagonal binaries are an example of this.

s_0 = {s_0,n: n in N, s_0,n = S_n,n^c} where {S_n} is any countable collection of unique binary expansions of numbers between [0,1] and the minimum truncated length of S_n is n+1 or greater.

This is exactly a non-computable number that is arithmetically definable with second order arithmetic.

You can't tell what any arbitrary digit of the decimal expansion will be, but you can tell what any arbitrary bit in the binary expansion will be, so you can define it to within a margin of error based on the power series of 1/2 starting at the bit you've just defined (e.g., if you've defined the nth bit, your error can be no greater than the geometric series of 1/2 starting from n+1 and going to infinity).

>>16229753
> this is the definition of a computable number.

Sort of, but not quite (unless I'm misunderstanding computability, which is possible as I'm not someone who has done courses specifically on TOC, but rather looked at what algebraists and analysts have done in TOC).

The Cantor diagonal example which I've given an explicit second order arithmetic formulation for in >>16229899 can specify the binary expansion such that the equivalent rational number will be correct up to some arbitrary degree (the margin of error is at most the geometric series of 1/2 from n+1 to infinity) but the number is still non-computable because the algorithm for computing it is not formally a computable function (there is no function for which a k-tuple of {0,1} values can give you exactly this number as an output).

Diagonalization has NOTHING to do with infinites ... If X is any set There is no surjective map from X to {0,1}^X, since if f: X -> {0,1}^X is any map, by putting g(a):= 1 - f(a)(a) for every a in X, we'd have f(u)(u) = 1 - f(u)(u) for every u such that g(t) = f(u)(t) for every t (so there is no such u in X).

Where did I mention that X was "infinite" (whatever that means)? Brainlets on tje loose again.

>>16227192
okay but irrationals don't even enter the picture in 0.9 + 0.09 + 0.009 + ... = 1

>>16222984
I don’t believe anyone said it was. Are you a boomer? Only stupid fucking nigger boomer faggots make these kinds of retarded strawmen and find these ugly ass cartoons funny. Fuck you nigger and die

>>16230173
>can specify the binary expansion such that the equivalent rational number will be correct up to some arbitrary degree
even if you think you have some non-computable method for obtaining such information, it is literally unprovable that the bits of an uncomputable take a certain value
that's completely independent from the method by which you think you can obtain them

given an uncomputable, past a certain point you cannot prove that the nth bit is 0 and you can't prove the nth bit is 1
it doesn't matter what set theoretic argument is used, set theory cannot get you arbitrary bits of an uncomputable
this is a consequence of Chaitins Incompleteness Theorem

But yeah, I was being somewhat facetious by saying that's the definition of a computable.
If you only allow yourself to do things which exist within the theory, then that's computable

but the issue of talking about "within the theory" and computability, is that computability must also be required in the meta theory as well. On no level can humans ever hope to abstract away from the concept of needing to work things out

>>16230133
I don't think the description you gave in your post
>s_0 = {s_0,n: n in N, s_0,n = S_n,n^c} where {S_n} is any countable collection of unique binary expansions of numbers between [0,1] and the minimum truncated length of S_n is n+1 or greater.
>This is exactly a non-computable number
is correct as is. I hereby declare that S_n is a collection of strings which are 0 everywhere except with a single 1 at some point past n^c. So if I'm interpreting what you posted correctly, s_0 is all 0s, which is clearly computable. At a minimum you need more conditions on S_n.

I know what Cantor's diagonal argument is. I've never heard of "Cantor's diagonal binaries" or heard of the argument being used in relation to computability, and a couple of search engines have shown no results for the phrase in quotes. Is there some specific non-wikipedia source you're getting this from? Wikipedia does mention Specker sequences so I need to look into that, but I'm wondering if there's another source that more directly addresses what we're talking about.

>>16230396
I think you are right that I made a mistake. I think the {S_n} set needs a stricter definition such that it covers the rationals in [0,1].

The basic idea is given in Baby Rudin, Theorem 2.14 and the remark afterwards relating this to binary representation of the real numbers. I don't know if there's a better term for the binary representation of Cantor's diagonal numbers than the one I've used (which truthfully is something I've come up with trying to find a shortened name for something I'm not sure is named succinctly elsewhere).

You can read a bit more about this idea on
https://math.stackexchange.com/questions/28393/why-does-cantors-diagonal-argument-yield-uncomputable-numbers

In Baby Rudin Theorem 2.14 they imply that the length of the sequences in A must be infinite. This isn't strictly true, they just need to be long enough that the diagonal is not possibly an entry in A and that A "covers" the equivalent countable rationals in [0,1].

Definability and computability are not exactly the same thing, especially when you include second order arithmetic definitions. There are many proper second order arithmetic definitions which don't correspond to computable functions (like the Cantor diagonalization process).

>>16222984
If you have an argument against astronomy, what are you going to replace it with?

>>16228956
>electric universe theory
Sigh.

>>16226655
There are no dark numbers, that’s precisely my point. Also Hawking was a moron

>>16227225
Computable numbers are still definable you just can’t calculate arbitrary small bounds around it with a single algorithm. But you can try to discover new algorithms for further calculating them to even more tighter bounds.

>>16230612
>I think the {S_n} set needs a stricter definition such that it covers the rationals in [0,1].
If we're sticking with your restriction that s_n has to have a nonzero entry after the nth spot (which is what I assume you meant by having a minimum truncated length) then such a list isn't possible. There are 2^n rationals that have to be covered by only n-1 sequences.

And without that condition, you can take any computable mapping of N onto Q and compute s_0 with it. In general the only way you can make this work is if S_n isn't computable, so to produce a non-computable number with the kind of diagonal construction you're doing, you have to start with a non-computable list. You're not indicating any specific object, just saying that if you're given a non-computable object, then you could.

If you're just saying that you can express the property of being non-computable using a finite formula, then fine, that sounds right. But back here >>16227777, anon seems to be claiming that there are finite formulas satisfied by exactly one non-computable number, and I haven't seen any of those.

I think you guys are misunderstanding what minimum truncated length means.
It's not referring to the length of the digit or the bit expansion.
It's the smallest number of symbols needed to give the number to arbitrary precision.
10^10^100 has a huge length but a puny complexity
pi can be expressed in the leibniz series

it seems to me you guys are trying to diagonalize on the set of finite sequences
which just gives you an infinite sequence. See my earlier
>>16228578
diagonalization never works

>>16230979
That still sounds like S_n isn't covering every computable number, which means the diagonal isn't proved non-computable.

>>16231008
the computables are not computably enumerable
there is no computable bijection from N to the computables
the diagonal is noncomputable

>>16223477
Interesting pic, you work at the Smithsonian Astrophysical Observatory? There's no palm trees in Boston though.

>>16231030
>the diagonal of a noncomputable bijection which no one was talking about is noncomputable
So what? What are you arguing, exactly?

This conversation was anon claiming there's some kind of peano arithmetic formula that defines an individual non-computable number, and that such a formula would involve the diagonal of some kind of table. So far I have seen no table which both
>can be defined with a peano arithmetic expression
>has a diagonal which is proven to not be computable

Random tables aren't relevant unless you're claiming one has both those properties.

>>16231105
>So what? What are you arguing, exactly?
any bijection from computable to N must be uncomputable

he isn't talking about peano arithmetic, he's talking about second order arithmetic
which is basically irrelevant, since that allows sets which aren't computable from the get-go
but he seems to like the idea of them

>>16226597
They are "dark numbers" though, even if they're just rebranded transcendentals. The overwhelming majority of transcendentals are unknown (besides the famous ones like multiples/powers of pi, e, etc).
Stretching the analogy, similar to dark matter, "dark numbers" make up the overwhelming majority of real numbers (since they're uncountably infinite)

>>16231132
>he isn't talking about peano arithmetic
The picture is the wikipedia article he linked to define "definable [arithmetical] number". It says that there are first order peano arithmetic formulas which define non-computable numbers.

The example it gives is a 'Specker sequence'.
>In computability theory, a Specker sequence is a computable, monotonically increasing, bounded sequence of rational numbers whose supremum is not a computable real number. The first example of such a sequence was constructed by Ernst Specker (1949).
The original Specker sequence was apparently just embedding progressively better partial solutions to the halting problem into binary sequences.

Actually I don't see the problem with this, assuming there's a first order formula which takes x and y, and returns whether the x-th Turing machines halts after y steps. And iirc there is one.

A lot of the other shit said in this thread doesn't seem right to me, but he could be correct about a finite, first order formula defining the solution to the halting problem. Not in a way that actually gives you the number, obviously. So it's philosophically arguable whether this really counts as 'defining'. But I didn't think it was possible to do even this much.

>>16231349
The construction has no connection to any diagonal argument, by the way. It's just a monotone increasing sequence of rational numbers. You can stick them in a table if you feel like it for some reason, but the diagonal isn't important.

>>16231349
my bad, he kept mentioning second order so thought he was talking about analytic

>but he could be correct about a finite, first order formula defining the solution to the halting problem.
I don't even think he or wikipedia are right on that.
considering programs or the halting problem absolutely shouldnt be called first order
if that's standard terminology, it sucks

>>16231343
There are no dark numbers. Remember what was the whole reason for making up dark matter: observable matter doesn’t follow physicist predictions so dark matter is invented to explain why the physics theory doesn’t work. There’s nothing similar in mathematics because the theories work by definition

>>16231482
retard
there are apparently uncountably many real numbers and only countably many names
so 100% of real numbers don't even have a name, much less a way of determining them

if I make a theory where ur ghey, then does that work by definition?

>I can't see air, but I can feel it, smell it and interact with it. Therefore it's probably real
>NOOOO YOU HAVE TO SEE PHYSICALLY OR IT DOESN'T EXIST!!

>Play Peekaboo with a Anti-Dark Matter schizos
>"I can't physically see his eyes, therefore there's not a proof that they are there"

>>16231718
ESL
and theres no proof of anything in the physical world, the egocentric predicament is a thing
theres only evidence of things irl

but dark matter is just a wrong equation and bad measurements

>>16231812
You're just retarded. Just because to can't see a window, doesn't mean it's not there. The proof is that there is extra matter which is obvious as weighing something you can't see or possibly even feel.

>>16231812
>>but dark matter is just a wrong equation and bad measurements
>There are no proofs only evidence, but I yes I know this for certain. Jesus told me.
lel.

>>16232049
just because you measure extra weight than what you expect doesn't mean there's actually something there
Your scale may be calibrated incorrectly
There is no **proof** in reality
it's a retarded example, but if you're in the matrix, then everything you thought you proved is wrong
this is why empiricism is the only valid method of studying the physical world
and why thought experiments arent trustworthy

>>16232061
>>There are no proofs only evidence, but I yes I know this for certain.
I said no proof of anything in the physical world
a formal statement is not physical
the only other thing that is completely true are honest descriptions of sensory perception
even if you can't prove that there's more weight there, it's true that you believe there is more weight there

>>16232498
>I said no proof of anything in the physical world
And yet you state DM is wrong with absolute certainty. Not "perhaps wrong" or "in my opinion". Your scientific philosophy contradicts your baseless unconditional claim.

>>16232793
THATS what you meant?
That's even more retarded than what I had assumed you meant.
Why would you correct me?

I thought you meant
how can you know the statement "you can't know things"

>Your scientific philosophy contradicts your baseless unconditional claim.
Epistemology is not a scientific philosophy you moronic pseud
I specifically said empiricism was the best scientific philosophy
the egocentric predicament has literally 0 impact on the effectiveness of empiricism

>>16232875
>Why would you correct me?
You are being a complete hypocrite. At least practice what you preach. It's not difficult to not talk out your ass about things you clearly don't understand.

>>16232929
>You are being a complete hypocrite
I wasn't making a scientific claim
I was saying something obviously true on a Chinese underwater basket weaving forum
seethe

>>16232929
if I said "it's hot out"
would you yell at me to pull out a thermometer and compare against the average temperature of something before I make a scientific claim
If I say the food looks good, are you going to ask for an analysis of how the brain reacts to seeing food with an understanding of how evolutionary biology plays into it

Or can you stop being an autistic retard?

>>16233026
Painful strawman. Try harder.
Remarking on the weather is not the same as claiming to know a scientific hypothesis is wrong.
Maybe instead of inventing these stupid analogies you could justify what you actually said? What a crazy idea.

>>16233023
>I was saying something obviously true
If it's obviously true then it must be scientific.

>>16233056
>you could justify what you actually said?
if you could give a particle that was dark matter, then we could justify if it exists or not
inb4 bigger collider

I'm not the one who needs to prove that Russel's teapot doesn't exist
it doesn't exist until proven otherwise

>>16233095
>it doesn't exist until proven otherwise
Hang on. You're saying that this teapot definitely doesn't exist. But then suddenly it would miraculously spring into existence after someone's opinion changed, having never existed before. Is this logical or scientific? No. Clearly if something can be proven to exist then you cannot say it doesn't exist. You're just talking shit.
It's funny you fellated yourself over proofs and evidence, and here you are tying yourself in knots to justify something you know is horseshit.

>if you could give a particle that was dark matter, then we could justify if it exists or not
Neutrinos are a type of dark matter as it was originally defined, they're just not the dominant species.
So you're saying that speculating about something means you must have a definite answer? Then justify these:
>but dark matter is just a wrong equation and bad measurements
Please point out the correct equations and the measurement errors. Thanks.

>>16228956
Observations support the existence of dark matter, not plasma cosmology. Plus it does a poor job of explaining the distribution of galaxies into filaments and superstructures. This is not how plasma cosmology explains the formation of the universe and yet that's easily explained by the distribution of a dark matter universe.

Sounds like a piece of shit theory. Why would anyone try and argue for this as opposed to the existence of dark matter?

>>16233130
>Plus it does a poor job of explaining the distribution of galaxies into filaments and superstructures.
dark matter does a poor job explaining satellite galaxies, early galaxy formation, and the BAOs

you can't just point out the strengths of a theory to justify it, you have to compare it's strengths to a control theory before you can try and argue that it's a good theory
otherwise that's just cherry picking

>>16233115
malding cuz I called your imaginary friend fake

>>16233178
>dark matter does a poor job explaining satellite galaxies
MOND can predict dynamics. It does not predict structure, distributions, planes...
>early galaxy formation
There are no quantitative predictions from any alternate model.
>BAOs
BAOs existing at all is a prediction of standard cosmology with dark matter. They're not explained at all in any true alternative like plasma cosmology. There is no evidence from BAOs of issues with DM specifically.

>>16233181
Nice rebuttal.

>hay guys I know everything about the entire universe!!!
>what, differentiate between a picture of a star and a picture of sausage?
>no, sorry I can't do that

Dark matter is made out of unicorns

>>16223070
Tired light
Flowing aether

>>16234144
Post actual evidence these can quantitatively explain all that dark matter does.

>>16234164
Tired light negates the hubble constant.
Flowing aether is frame dragging which accounts for the apparently incorrect mass in rotating galaxies.

>>16234177

>>16234208
>quantitatively

>>16222984
The funniest shit is that if you moved your fat nigger ass for a second to a scientific paper you would know that dark energy and dark matter are full of outcasts who find bullshit the concept of explaining your calculation errors in your theory with shit that you can't even see, measure, interact with or check if it exists.
The only reality is that physics works like

>Being Albert Einstein
>Have an absolutely smoked idea of physics(he smoked something)
>Coincidentally the calculations agree with your ideas
>It turns out that experimentally you are right.
>You become famous.

Physics is full of guys who I don't know are stoned as fuck but proceed to try to prove their most intricate and weird shit with calculations and sometimes they make the biggest bullshit or something that is good.

>>16223387
One reason to believe in the expansion is that it is found that the light from measured galaxies tends to become more reddish in color over time or not to be seen again.
Light waves can be "compressed" (higher energy/blue bias) or more "stretched" (less energy/red bias).
Light travels at a maximum of 300 km/s and this speed is very low for the distances of the universe, so it takes a long time for the light to reach planet Earth and in the process the light wave loses energy and the wave "stretches" and tends. red, so you can judge the distance of galaxies through their color trend.
Previously measured galaxies were seen to have increasingly reddish colors.
Most of them move farther and farther away at speeds that seem to violate the speed of light mostly because space and time expand faster than the speed of light because the laws of special relativity when they tried to explain That the speed limit is 300km/s does not speak about space but only about matter.
There is no law in general relativity that says space cannot expand faster than the speed of light.
In fact, the measure of expansion is in units that are the inverse of time. It is usually given an average value that is between 68 and 72 kilometers per second per megaparsec. The parsec is a measurement used in astronomy and is equivalent to 3.26 light years (or what would be the same: almost 40,000 billion meters).

If you don't believe in fucking expansion give at least and idea of how shit works instead of your /pol/ ass jew theory of Ivy Leagues with special connections.

>>16223387

>>16234294
>or not to be seen again.
Good shit. According to expansion tards there should be galaxies at the edge who becomes invisible to us one day suddenly.
None observed so far.
Therefore its bullshit.

>>16223070
Flawed calculation of mass or energy that violate the conservation of mass and energy

>>16223438
>Astronomy is how we discovered computers.
QRD?

>>16235793
>According to expansion tards there should be galaxies at the edge who becomes invisible to us one day suddenly.
Nope. Anything beyond the horizon would be redshifted and time dilated to infinity. It would never just disappear because there are photons which are already traveling here. Even if new photons cannot travel between galaxies it won't disappear.

>>16236044
Staying a hypothesis is not demonstrating it can explain the observations.
>Please provide an alternative to dark matter to explain all the evidence we have of its existence.

>>16236059
Computers were an invention of the Lyonnaise textile industry, scientists had nothing whatsoever to do with that invention.

>>16223055
excuse me, but that's bullshit. why should I bring you an alternative hypothesis when I point out that this one is bullshit? we just don't know why galaxies don't twirl the expected way.

>>16223240
with a lot of properties fine-tuned to fit the explanation as to why can't we observe it. it's "the cosmic aether being solid and hard to allow fast transversal waves but ethereal to let planets pass without observable friction" all over again.

>>16236212
>all the evidence
we have no evidence. the concept is designed to provide no evidence, as its properties were proposed with the explicit goal of explaining why does it not interact with anything i.e. why there is no evidence.

What is dark matter? Is it just a fill in? Because arguing its an actual form of matter or energy is different than saying we don't know..

>>16233130
is this "dark matter" with us in the room right now?
general relativity explains the behavior of only 5% of the universe. Come on.
Just imagine if Newton's law was F= 0.05ma and you were hell bent on convincing me that it is correct because it works if you add a mysterious F0 to explain reality.

>>16236774
False. Just because it doesn't have other interactions doesn't make it non-predictive. For example, cold dark matter predicted the statistics of the fluctuations in the Cosmic Microwave Background. Before anyone measured it. Even now there is no alternative explanation that doesn't have some matter-like field/particle.

>>16236768
What properties? CDM has one parameter, the overall density of DM.

>>16236762
>we just don't know why galaxies don't twirl the expected way.
Because that is not a scientific hypothesis. You can test a model, falsify it. You cannot falsify a shrug. If you want to better understand the dynamics of galaxies you have to make some models.

>>16236798
People have tied modifying gravity to fix the issue. The result is models like MOND, which work in their regime but fall apart on larger scales. On the other hand dark matter models are simple and don't have this limited range of applicability.
>is this "dark matter" with us in the room right now?
Yes. When DM got it's name neutrinos hadn't been proposed much less detected.

>>16236780
yes, it's just a fill in. It's "something that has mass but we can't detect it and the only evidence of its existence is its gravitational effect", either it's literally matter we can't detect or our understanding of physics is wrong, but nobody can find any actual problem with the physics (especially the shitposters in this thread) so.. dark matter

>>16236874
>or our understanding of physics is wrong, but nobody can find any actual problem with the physics
Maybe that's because nobody actually has a ship to fly out there to conduct physics and chemical experiments to verify if anything is or is not in-line with known sciences.
With no way to verify experimentally what's actually out there for all we know our entire understanding of cosmology is dead wrong.

>>16236873
I don't care for MOND or dark matter, we're clearly going in the wrong direction with both.

>>16236904
but observations of the universe favor both. So why say it's the wrong direction? Because you don't like it?

>>16236887
>for all we know it COULD be wrong
that's not compelling evidence that it is wrong

>>16236874
>but nobody can find any actual problem with the physics
The evidence proved that the physics is wrong. It also proved that not only is the physics wrong, but also that the physicists' unwillingness to admit that their physics is wrong is the biggest problem with physics.

>>16223034
>>16223055
Pay me and I'll come up with a new model.

>>16222984
dark matter is a problem isn't it? It's an inconsistency between hypothesis and observation. Dark matter theories are people's attempts to change the hypothesis. A hypothesis is really just a description or prediction about reality right? So changing your hypothesis isn't changing reality. It's just adjusting your explanation. What say are astronomers doing wrong here? If i were to wager a guess, I'd say scientific communication to the general public

>>16223034
that's a fucking rare pepe

>>16226880
NTA, but the issue i have with astrophysicists is this: that whole "rule out every alternative" should have been the step BEFORE the entire field congealed around a single interpretation of the data like LCDM. that's not what happened, for sociological reasons.

the field widely adopted a single map of the territory and largely refused to invest in other maps of the territory (or dismissed them as 'disproven' via issues much less severe or numerous than LCDM has accumulated at this point), and appears determined to continue until they've run out of ways to wrinkle the paper so the map fits the territory better. there are a LOT of ways to wrinkle a map.

fields like astrophysics, where direct experiment and even sometimes observation are difficult and infeasible, are very prone to creating a false equivalence where "model that maths (mostly) good = empirical observations and proof." low cost and high publication output of theory incentivizes this behavior for entirely non-science reasons, especially at the institutional level.

>>16237426
They're not allowed to form other ideas because any other new idea would necessarily include denigrating the legacy of St. Einstein the infallible sacred jew god of the soiyence atheists.

>>16236950
because GR doesn't work without adding 20x the amount of matter/energy that we can actually observe and explain.
MOND doesn't work on bullet cluster or ultra diffuse galaxies.
I don't like them because they're not scientific.
Now your turn to explain why they're the correct direction exactly.

>>16237517
>Now your turn to explain why they're the correct direction exactly
They don't and can't have another direction; the entire field rests on extrapolating known physics and hoping to God things works the same out there and everything clicks into place.

Cosmofags are already getting thrashed for been a field that have no way to experimentally verify any claims. Imagine the outrage if they just start to straight up invent new physics to better explain what can't be interacted with. Might as well just say it's greek gods out there moving things about at that point.

>>16237426
> that whole "rule out every alternative" should have been the step BEFORE the entire field congealed around a single interpretation of the data like LCDM
That did happen. None of the "alternatives" was ever really viable, they away had obvious problems. People did consider alternative models of dark matter, it took decades for the discussion to settle on CDM. You are ignorant of the history of the field, and confusing that ignorance with a lack to exploration.
And there are still people working on alternative models now, there is a whole field of modified gravity trying to replace Lambda. The issue is that lambda is a simple model, whereas there are basically infinite ways to modify GR. All this complexity to replace one number. Also remember that people have been working on going beyond GR for a century, and they have found nothing. This is far longer than people have been studying dark matter as a model.

>dismissed them as 'disproven' via issues much less severe or numerous than LCDM has accumulated at this point
Give an example of one of these alternatives being discarded for less.

>>16237517
>that we can actually observe and explain.
And why do assume this knowledge is correct? How can it be unscientific to scrutinize both sides of the equation?

>>16237311
what evidence, anon?

>>16237555
> None of the "alternatives" was ever really viable, they away had obvious problems.
so did LCDM, from the start - one of the first modifications that had to be made to it (which was a courtesy largely not afforded to other models, because it was itself an "obvious problem") is right there in the second letter, which also defined it as unobservable remotely outside of the very discrepancy that led to its proposal (and thus defined its parameters; looking at galactic rotation curves as observational evidence is epistemologically the same as simply using the discrepancy between your hypothesis and observation to define an exactly corrective new term to your original hypothesis)
>inb4 lensing
requires a great deal of assumptions and doesn't have unique solutions; we're using interpolation in 2D and limited fidelity distance measures to tease out 3D lens morphology. all the DM gravitational lensing i'm aware of doesn't create rings, so you need to essentially guess the 2D morphology of the lensed sources. could be explained by DM, but the morphology of the lenses is fundamentally unknown, meaning all you can do is provide one possible morphology - it's not a measurement or observation, just an interpretation.
>inb4 modeling
simulation focus is something like an epistemological poison to theoretical studies like cosmology. the degree to which theoretical assumptions are baked into the model's structure and constraints is difficult to overstate. even in areas like CFD where we have easy experiments to directly compare model output to, the models are categorically insufficient to replace those experiments, and it's not just a resolution issue. the middling but still extant feasibility of experimental tests of results in fields like computational chemistry and economics are perfect examples of the trend, sitting somewhere between CFD and cosmology on the ladder of experimental difficulty, and having correspondingly poorer congruence with experimental results.

>>16236978
>i see no compelling evidence that our unverifiable shot in the dark guesses are not perfect descriptions of reality
not how logic works

>>16238019
You seem to have missed this bit:
>Give an example of one of these alternatives being discarded for less.
Please cite an example.

> looking at galactic rotation curves as observational evidence
Which is why no one does. But then you can test CDM with lensing, galaxy clustering, CMB fluctuations, clusters, light element abundances... Rotation curves are however a test of the model. If dark matter is really the cause then simulations should be consistent with real galaxies. CDM didn't get it's start from rotation curves, it was actually theorists trying to understand structure formation. Nobody defined it as unobservable, hence why people are trying to detect it.

>requires a great deal of assumptions and doesn't have unique solutions; we're using interpolation in 2D and limited fidelity distance measures to tease out 3D lens morphology.
What nonsense. You don't need to do it in 3D. Projection is just fine, it is sensitive to the projected mass distribution. Note that rotation curves are also in projection. Pretty much everything ever done is in projection. A model should be able to predict the lensing, and CDM does.

>simulation focus is something like an epistemological poison to theoretical studies like cosmology.
Good luck trying to understand how galaxies form in any model without simulations. Note hydrodynamics isn't even necessarily to simulate DM, only the normal matter.

>>16238037
Not what he said.

>>16238132
>You seem to have missed this bit:
character limit.
easy example here is Brans-Dicke, which was discarded largely in response to its coupling constant being a tunable parameter, despite the fact lambda is also a tunable parameter

>simulations ... consistent with real galaxies
this has genuinely never been the case for any of these frameworks. ALL of them have serious inconsistencies with observed galactic structure and distribution.

>it was actually theorists
nope. just fucking factually, historically incorrect. even if you pretend Zwicky's incorrect result was more influential than it was at the time, and ignore that Kelvin was looking at local stars in the late 1800s (if you want to go back to the true first claims) Zwicky was using the virial theorem, not a structural argument; it literally asserts a bound system (i.e. structure) from the beginning. later developments that formalized dark matter were driven by (and defined 'missing mass' by) rotation curves. at no point in the history of dark matter was it a consequence of large-scale structure formation theories; those came much later.

also, the virial theorem still applies to orbits - the rotation curves weren't technically an independent verification, just an easier way to describe the same thing. Zwicky was, in a sense, looking at the rotation curve of a galactic cluster - just not using the shape of the resulting plot as a way to simplify things.

>Projection is just fine
ONLY if you're working with an object of known distance as the lens (though you still need to make assumptions about lensed source morphology); i'm referring to dark matter mapping there, which attempts to extrapolate collections of entirely non-visible mass from lensing alone

>hydrodynamics isn't even necessarily to simulate DM
and ignoring it leads to simulations that have been demonstrated to be inferior to including the baryonic matter in terms of matching observations (though those, again, still have serious problems)

>>16237556
you're right, but I assume this was already being done seriously

>>16223169
ad hominem lmao

>>16238285
>this has genuinely never been the case for any of these frameworks. ALL of them have serious inconsistencies with observed galactic structure and distribution.
Such as? There are lots of claims about discrepancies in low mass galaxies, but there is always an implicit assumption in the claim about how the baryons behave.

>nope. just fucking factually, historically incorrect. even if you pretend Zwicky's incorrect result was more influential than it was at the time
Zwicky is irrelevant because we're talking about CDM, specifically. As you said "one of the first modifications that had to be made to it is right there in the second letter". Not just any dark matter but why it should specifically be cold. CDM originated with Peebles. Why it had to be cold had nothing to do with rotation curves, or clusters.

>ONLY if you're working with an object of known distance as the lens (though you still need to make assumptions about lensed source morphology); i'm referring to dark matter mapping there, which attempts to extrapolate collections of entirely non-visible mass from lensing alone
Nope, most maps from weak lensing are 2D in projection. And it's rather strange to say "only", when most of the field of lensing is working with clusters or galaxy strong lenses where you know the distance. And in all of these things can be used to test CDM, and have. What you're describing is some sort of 3D weak lensing, which I don't think has ever even been done. It certainly isn't a standard analysis.

>>16238285
>easy example here is Brans-Dicke, which was discarded largely in response to its coupling constant being a tunable parameter, despite the fact lambda is also a tunable parameter
It wasn't discarded. People still study it as part of modified gravity. It has never taken center stage because it is a more complex model. It's an alternative to GR, not to CDM.
Also Lambda was reintroduced in the 90s. Long after interest in DB cooled off.

>>16223477
I guess Isaac Newtown just enabled creative mode and turned off friction when he discovered the first law of motion. We don't necessarily need technology to build a reasonable hypothesis but its continual advancement is necessary for testing and proving them repeatedly.

>>16238436
>t. reddit

>>16232498
>Anon goes on scale
>Reads 328 pounds
>T-The machine is broken! I am only 303 pounds!

>>16223055
Maybe the rest of physics is wrong.
>but it works otherwise!
Yeah and I can make a retarded proof that addition and multiplication are actually the same thing because 2+2=2*2.
>we can't just change all physics!
Sunken cost fallacy. If it's wrong, it's wrong.

>>16240743
And change it to what exactly?
Unless somebody can fly out there and bring back experimental proof of new physics you will literally be replacing proven models with fantasy.
Fact is people will just have to get used to the idea of not knowing. If they need to cope go watch sci-fi shows or read up on Cosmology.

>>16239834
more ad hominem, kek

>>16240743
>Maybe the rest of physics is wrong.
Oh great. That really narrows it down. Surely we can test that.