Are we living in a simulation?
>>8848221
No point in asking because there's no logical necessity for a homology between mechanics as presented to the simulated, actual mechanics governing the simulated, and the mechanics of the universe containing the simulator.
go to bed elon
>>8848221
It's highly likely
http://www.simulation-argument.com/simulation.html
It's been peer reviewed by many
Brian weathersons critique:
http://brian.weatherson.org/sims.pdf
Bostroms rebuttal to the critique:
http://www.simulation-argument.com/weathersonreply.pdf
Basically if it's possible to simulate a universe, we're most likely simulated
Post your favorites
1+1=11
>>8848133
onety-one
Z=[r,theta]
I want to self study a math major, for my own self respect. But I want to only do like the main 75% of it not all the way. I'm sure, as with all majors, there is some fluff that you can probably live without
What textbooks should I buy to self study in their entirety to get that 75% of a math major?
start by telling us what is your background and, since you don't want to learn everything, what is your interest? (analysis/algebra/geometry/foundations/statistics or whatever)
Some of the MIT Open Courseware classes are pretty decent. If you look up a topic and see that they have several semesters archived, look for one that's labeled "OCW Scholar" if you want the one that's most geared to online study; it will have assignments and exams for you to practice and test yourself, and also have videos from the recitation section.
Start with Calculus I, and then after that see what courses have that as a pre-requisite and go where you like.
A good and useful practical core to start with is:
Calculus I (single-variable)
Calculus II (multivariate)
Linear Algebra
Differential Equations
Introduction to Probability and Statistics
If you get serious about math it eventually starts leading to some high courses where you write a lot of proofs, and then it can get really interesting. A good course from the MIT selection that will get you started on that and have some practical application is their "Mathematics for Computer Science" course. I took some courses on discrete structures, algorithms, and theoretical computer science in college and they were really interesting.
Another route to higher math is "Book of Proof" by Richard Hammack.
>>8847973
I'm a CS major who wishes he was a math major but is happy that I can actually make money unlike you guys, but also wishes he was a math major
The most math I know is Calc 3 but I forgot most of it, I only know Calc 2 for sure
I would want to learn the most important math major topics regardless of whether I like them, but my personal interest would lean towards physics simulations and computational fluid dynamics in the end, also circuit simulations. This requires physics as well after I guess.
Did the nazis contribute to science or were they like the dark age in the long run?
>>8847848
>Heisenberg was a Nazi
>Von Braun was a Nazi
So yeah some contributions. But their insistence on Deutsche Physik was only ever going to end badly.
>implying we aren't in a dark age now
https://en.wikipedia.org/wiki/Oswald_Teichm%C3%BCller
I'm graduating and I've come to realize that I will lose access to IEEE Xplore library and that it costs 50$ per month for 10 downloads if I try to access it legally!
So aside from scihub, what other legal or illegal methods do you use to access papers? I don't want to go back to begging in forums. Do local libraries have access to websites like IEEE Xplore anyway?
>>8847836
This is relevant to my interests
I would like access to AIAA journals
>>8847836
One time I exchanged 10 emails with a representative from IEEE trying to get a free trial. I was bullshitting claiming to be from some made up school.
>>8847836
See if your school has a program for alumni membership, you might be able to donate and keep access privileges.
Is there any proof that modern humans are more intelligent than our prehistoric ancestors were?
our prehistoric ancestors didnt do shit
No. Modern technology has made people weak and dumb. The ancients would look at us in shame.
>>8847669
Humans from 2000 years ago probably were smarter than us but the lack of electronics made them look like morons. Humans back in the neolithic era would need to be good thinker to survive in Europe, where as the original humans were most likely dumber than black people today so yes we are more intelligent than our ancient ancestors once you go to the mesolithic era.
Has anyone ever actually been autistic enough to systematically read and work through a series of textbooks like this? Or is there a better way to go about this?
>>8847320
There are plenty of free online courses. You can use these books to supplement what they are teaching. It does really take a lot of time to go through any 1 textbook but if you do it well you only need to do it once.
[spoiler] Yes I am autistic enough to go trough a bunch of text books fit mi fgt[/spoiler]
>>8847320
Having an application helps a lot.
>>8847519
>Yes I am autistic enough to go trough a bunch of text books
But why
Redpill me on topology, /sci/. Point-set was kind of a drag, but I like the idea of studying very general and abstract spaces, manifolds, etc. and I don't want one class to turn me off it. Why do you like topology and where do you use it?
In particular, what's some cool stuff at the intersection between topology and generalized harmonic analysis? I am interested in studying L-functions by means of things like integral transforms (think Tauberian theory), and I want to know if there's a topological viewpoint in that direction.
>>8847307
I think topology is coolest from a homotopical perspective. Homotopy theory distills topology from the (ugly, in my opinion) pointset stuff to the abstract concept of connectivity and interactions between paths of different dimension. Things start behaving very, very nicely after you mod everything out by coherent homotopy.
First off, the homotopy hypothesis: infinity groupoids are models for homotopy types (spaces up to homotopy equivalence). An infinity groupoid has 0-cells (points), 1-cells connecting them (paths), 2-cells between these (homotopies), and you can compose all of these cells to get new ones (for example, you can whisker a 2-cell and a 1-cell to get a new 2-cell, which is "degenerate" along the 1-cell). The fundamental operations in homotopy are suspensions, deloopings, and the smash product (after passage to pointed homotopy types). There is a process of stabilization, producing things called spectra. Spectra can be thought of as higher algebraic things, though: they are infinity modules over the sphere spectrum, which has the integers for all of its positive homotopy groups. The sphere spectrum is thus the Eilenberg-MacLane spectrum for the integers, and the statement that spectra are modules over this thing is essentially equivalent to Brown representability: spectra and generalized cohomology theories can be weakly identified (the caveat being that cohomology cannot detect some maps, called phantom maps).
This algebraic approach gets cooler, though: there is a notion of "good" cohomology theories, called complex orientable cohomology theories. There is a universal one, called MU, which is a spectrum representing complex cobordism cohomology theory. This is called the Thom spcetrum, and its cohomology ring calssifies formal group laws. This ties chromatic homotopy theory to algebraic geometry in some nifty ways.
Then you have a ton of methods for modelling homotopy theory, many of which have combinatorial flavours. (continuing)
(>>8847377)
My personal favorite combinatorial model for homotopy theory is the theory of symmetric simplicial sets, which are like standard simplicial sets without orderings on cells. These objects relate homotopy theory to linear algebra, because a symmetric simplicial set is to the field on one element as a finite-dimensional manifold is to the real numbers. From here one can find more ties back to algebraic geometry, differential geometry, and even knot theory.
Important algebraic facts can be derived using homotopy theory, such as the link between Frobenius' theorem and the Hopf fibrations.
Differential geometry can be described in terms of homotopy theory, a la synthetic differential geometry. Things such as de Rham's theorem are quite trivial to prove in this setting, as they use more simple constructions in geometric/classical homotopy theory and show that they are facts in all homotopy theories. We use modalities to relate certain theorems and to show that they are true in any infinity topos.
Homotopy theory is used in quantum field theory. Cobordism cohomology theories can be interpreted as placing limits on particle interactions; Witten et alii have used the theory of genera on cobordism cohomology rings to derive physical laws. Physicists also use vector bundles everywhere, and homotopy theory gives the tools for classifying such bundles. This leads to higher Chern-Weil theory and its relatives.
Homotopy Type Theory, which is the abstract language of any flavour of homotopy theory, has applications in computer science and logic, as well as philosophy. Voevodsky's univalence axiom has Leibniz's identity of indiscernibles as a corollary, for example. The homotopy theory of topological spaces is universal amongst homotopy theories.
Homotopy theory is used in number theory, where we want to find nice homotopical descriptions of higher stacks, which vastly generalize Grothendieck's scheme theory.
Just peruse the nLab, friend.
>Call people brainlets on /sci/ all the time for having the wrong major or not going to a top 10 school
>actually in community college with a 2.1 GPA
>>8847155
>Whenever diversity threads appear I go in and say that I am a low IQ black with a shit GPA that was accepted into an Ivy. I finish with "lol white boise mad topkek, how is it going at Poodunk U?"
>Actually a hispanic who doesn't even study in America or Europe.
>mfw I was responsible for starting the .999.... = 1 troll threads and now everyone takes it seriously
How do I scientifically escape my crippling depression? I have no motivation to work on my research, to interact with people, to care about my """""career""""", to make any effort for something "better."
Do you guys see psychiatrists or something? Take meds? I've achieved all I thought I wanted, but now it all feels worthless
Pic unrelated
>>8846998
just man up start lifting I guess. act like trump and think you're hot shit all the time even when you mess up. you'll feel better eventually. it'll change ur brain to be more happy. also get rid of the coffee even the turks started banning it because it made people unhappy
>>8846998
I systematically destroyed every positive relationship I've ever had and abandoned all of my hobbies to devote myself to studying. It's not a happy existence, but it's a productive one. And one day I'll be dead, so I have that going for me.
>>8846998
Detachment
>tfw interested in math and science but i'm also a brainlet
>>8846452
That's why I'm going into engineering :(
>>8846452
then learn math and science
it's possible
just feel bad that you'll probably never contribute anything of value
>>8846461
> contribute anything of value
literally nobody except for real geniuses contribute useful things to mathematics
aka nobody who browsed /sci/
been on /sci/ for a few months now...
>0.999=1 memes
>existentialism shitposts
>consciousness memes
>ai faggotry
has it always been this bad?
tell me about...the old /sci/?
[math]1+2+3+4+...=\dfrac{e^{\pi i}}{11.999...}[/math]
>>8846336
/sci/ is, always has been, and always will be shit.
What are some nice, relatively unknown, unsolved problems in mathematics that interest you?
>>8846239
Homological Mirror Symmetry Conjecture.
Relatively unknown in the sense it is so niche that very little people who aren't explicitly working with it actually even understand the problem.
Generalizing the hyperoperation.
Addition, multiplication, and exponentiation are all part of the hyperoperation sequence. There's an infinite number of operations that come after them but their behaviors are almost completely unknown beyond how they act like iteration of the previous operation(when using positive integers). So all hyperoperations above 3(exponentiation) need to be defined for everything up to the complex numbers, then the hyperoperation itself needs to be defined for as many sets of numbers as possible(it might not actually be possible to extend this beyond natural numbers but if it is that would be rad).
>>8846239
Fermat's last theorem is pretty neat, because it's so easy to state:
[math] x^p-x=0 [/math] (mod p)
for any integers x and p.
And yet, after 300-some-odd years, no one knows whether this is true or not!
> electric
> flies vertically and horizontally
https://www.youtube.com/watch?v=ohig71bwRUE
Is this even possible /sci/?
Why would you focus on VTOL when we live in a world of roads everywhere
Notice how they don't show it lifting a person, because it can't
>>8846040
It's totally possible. The problem is that it's not likely to reliably run as long as they say it will, and it looks far too fragile to deal with confounding effects like wind and debris. If they were to make it robust, they'd only face further problems with aerodynamics and battery efficiency.
>>8846071
possible? Yes, but is the video cgi?
I'm aware of /sci/ and pretty much 4chan entirely's opinion on psychology. Is neurology just as bad, or is it ok? Pic unrelated, of course.
>>8846004
Neurology is more than ok, it actually treats diseases.
Neurology is psychology. Both fields are converging at a rapid pace. /sci/'s autism is about clinical psychotherapy, not research psychology (which is heavily tied in with neuroscience) per say.
>>8846004
Cognitive Science BTFO both neuroX and psychology desu.
At least they're doing lots of good research.