#serious-discussion

1 messages · Page 213 of 1

surreal sapphire
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"make it your life"?

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this also sounds very wrong lol

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there is lots of different kinds of math in cryptography, most of it elementary

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but if you want to see more advanced math, you can do that too

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i mean just to define a standard notion of security, you need to know what a turing machine is, probability theory and (depending on how you want to look at it) game theory

true zinc
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meow

pure hollow
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no.

delicate tendon
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definitely, im still getting exposed to the basics of it all so I can definitely see that I have a bias perspective

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I became a math major and wanting to pursue academia in it because of cryptography

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Outside of reading application papers before, im happy to being able to read more theory and mathy stuff now

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Oh shoot i forgot i already said that, practically repeated myself soz

surreal sapphire
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in that case my recommendation would be to take classes in algebra, number theory and elliptic curves and then take as many CS (and possibly even EE) classes as possible nozoomi

delicate tendon
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I also finished my ug math major, and added cs to get that side too as im only a 3rd year

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but in generality it also makes me start thinking about other potential grad school programs since i can either go to the application/discrete side of it all, or do the more pure mathy side of it all since there are two ways to tackle the problem

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A couple of options im considering is an Algo,Comb,Graph (discrete) phd, math phd, cs with crypto focus, and of the sort

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Thank you for the recs tho!

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I also took an AG course and also taking AT this semester

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I planned on also sitting in a Hodge theory course but it was honestly too much for me haha

jaunty ibex
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Hodge theory is great I love it

delicate tendon
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It seems soo cool, I wish I had a better understanding of the prereqs honestly

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We are also approaching hodge theory from a complex geometry perspective rather than algebraic

jaunty ibex
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I'm planning to read more about these after my course in representation theory

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Just realizing very lately representation theory is not my thing lol

delicate tendon
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Maybe im missing something, but can you explain how rep theory is used in hodge theory?

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im also not too familiar with it other than the general idea lol

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Atleast from the approach I tried to study about hodge theory, it mainly needed a complex analysis, lin alg, and manifolds background

jaunty ibex
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Idk the connections but I know they exist. I was just saying atm I'm focused on representation theory

delicate tendon
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Ohhhh gotcha my bad

river yew
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@surreal sapphire what I meant by that is that going deeper than a couple of courses in the average uni

delicate tendon
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Oh also, Loch, are you interested in cryptology too?

jaunty ibex
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He works in crypto

delicate tendon
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Thats cool af

jaunty ibex
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Not as in NFT of course

delicate tendon
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Yes ofc lol

jaunty ibex
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An actual cryptographist

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If that's even a word

vast wraith
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cryptographer is more common

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cryptanalyst is also a thing but i dunno the difference

topaz trout
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which one is better for a beginner C or python

solid snow
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either

dapper smelt
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Awaa did bad on my calc 3 exam

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Chat how do we feel about mint ice cream

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I hate it

topaz trout
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I'm trying to learn both and so far I like C a little better but python has a simple syntax but because I'm a beginner I don't know the power of coding

topaz trout
delicate tendon
# vast wraith cryptographer is more common

cryptographer works on encryption creation via implementation, cryptanalyst analyzes/breaks down the encryption, cryptologist does a bit of both iirc but i think more mathy

vast wraith
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lovely

delicate tendon
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my brain exploded with bliss after talking to a grad student resulting in my realization that Data Science is just topology but with coding theory and different terminology (over generalization ofc)

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this makes me feel less out of place

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@versed drum

snow pumice
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I got a question,

what should I study in math for the ACT or SAT exams?

verbal quest
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the prep guides

agile fiber
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there are also official practice exams available which gives you an idea of the kinds of questions that may be asked

dapper smelt
long matrix
burnt ledge
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otherwise it can get especially easy to mix things up or get confused about differences

vivid quest
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First of all toothpaste is delicious

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So is mint ice cream

dapper smelt
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really? :O+

vivid quest
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And there is no second point

dapper smelt
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i cannot agree

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but i respect it

vivid quest
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🐷

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Ok

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Coffee icecream stays the best

long matrix
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i did swallow toothpaste as a kid cus i didnt know

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apple flavor

vivid quest
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Is it supposed to be bad?

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I always swallow toothpaste

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Like

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To lazy to get water

long matrix
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yes.

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fluoride

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split it out

topaz trout
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i like drinking cold water with mint gum

vivid quest
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You think it's ok?

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Must be

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Just toothpaste lol

dapper smelt
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its not gonna kill you, but it might make you stomach upset

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with time

flat harbor
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so we got Big Pharma telling us to not swallow toothpaste now

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flips calendar to see 1984 January

vivid quest
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Radioactive toothpaste used to be a thing

candid compass
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How's Schoolhouse (the tutoring service by Sal Khan)? What is it like to be a tutor on there?

proven raft
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integrals are the base of a lot of things tho like area and stuff

proven raft
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area under a curve

foggy path
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The way you are expected to get the solution in a traditional way

proven raft
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antiderivative then

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subsitute the x values

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minus

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done

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except like the hard ones

foggy path
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Like an integral possibly has infinite number of solutions

proven raft
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ye

foggy path
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Like the same solution can be manifested into different functions

proven raft
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derivatives and or differentiation is still the goat

foggy path
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It can be logarithmic trigonometric or any hypothetical function f(x)

proven raft
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limits are second

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cuz rationalize

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but l'hopital is an alt

foggy path
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I have made few algorithms to rigorously deduce integrals

proven raft
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how

foggy path
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Like the same thing can be understood intuitively without that trig substitution or anything

proven raft
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the only way i know is trig sub

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is it possible to use u sub

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cuz it's like easier

foggy path
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Cuz it's 1/(1+x²)

proven raft
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it's a common integral

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but like solving it

foggy path
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You can look it geometrically

proven raft
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like on a graph?

foggy path
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1 be the base x be the perpendicular and √1+x² be the hypotenuse

proven raft
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base as in adjacent

foggy path
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Wait I can't send images in this channel?

proven raft
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ye

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i also realized

foggy path
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That's pathetic

proven raft
foggy path
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Check dm

proven raft
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so like

north topaz
foggy path
neat lintel
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hello guys

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can you guys teach me math

surreal sapphire
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but uh, very few people work in actually implementing (new) methods of encryption

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my work is more making small improvements to known methods

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and somewhat focusing on "small" implementations, think embedded systems and the like

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post quantum cryptography is quite ressource hungry (compared to classical methods anyway), so im trying to find improvements here

green talon
surreal sapphire
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quantum computers break all classical encryption due to shors algorithm

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so we need new ways to do public key cryptography

neon garnet
oblique inlet
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Yo people , quick question ❓
What's
ln(0)

fresh oriole
oblique inlet
fresh oriole
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something bad

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where Li_2 is a 'polylogarithm'

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actually Li_2 is a known enough polylogarithm to get its own name: https://en.wikipedia.org/wiki/Dilogarithm

In mathematics, the dilogarithm (or Spence's function), denoted as Li2(z), is a particular case of the polylogarithm. Two related special functions are referred to as Spence's function, the dilogarithm itself:

      Li
      
        2
      
    
    ⁡
    (
    z
    )
    =
...
vivid quest
fresh oriole
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roughly because the big encryption/decryption scheme is based on knowing the prime factors of some specially chosen very very large integers

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you can think of the prime factors as like a password

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(extremely rough analogy)

surreal sapphire
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all encryption is based on one-way/trapdoor functions, which are easy to compute in 1 direction but hard to compute in the other direction

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it is very easy to compute the product of two large integers

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it is very hard to factor a large integer though

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this is the one-way function underlying RSA

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it becomes easy to factor a large integer (that has two prime factors) once you know one of the prime factors

vivid halo
surreal sapphire
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this fact makes it a trapdoor function

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shors algorithm breaks the hardness assumption, so this is no bueno anymore

fresh oriole
vivid halo
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well the first really nice property of this function is that it computes volumes of hyperbolic 3-simplices

fresh oriole
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I did see something about hyperbolic stuff and simplices on that wiki page. Sounds cool

vivid halo
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the second really nice property of this function is that it computes algebraic K-theory groups K_2 and K_3 of fields

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these two facts are related

fresh oriole
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whaaat

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I barely know what K-theory is but I definitely did not see that coming

vivid halo
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this is kind of a miracle because K-theory is like, insanely hard to compute in general

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there is some general story about how polylogarithms are related to algebraic K-theory it just gets very hard to write down after the dilogarithm

fresh oriole
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didn't somebody get a Fields medal just for giving a good definition for K_2 or something?

vivid halo
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but the dilogarithm case is very clean

fresh oriole
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hm, maybe it was only a PhD.. there's some story about this I recall

vivid halo
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maybe Quillen for defining algebraic K-theory in general

fresh oriole
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that could be it

vivid halo
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but yeah specifically you can write down a length 2 complex defined in terms of the 5-term functional relation satisfied by the single-valued dilogarithm

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the cokernel of the differential computes K_2, the kernel computes K_3 up to mild torsion issues which can be fixed

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this should be true for other polylogarithms it's just that the functional relations they satisfy get very complicated very quickly

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we know this up to K_7 and up to the tetralogarithm

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but yeah polylogarithms show up everywhere and they have very simple integral representations

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oh yeah the other fun thing from this story is like

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if you've seen the analytic class number formula before, it is a formula for the residue at s=1 of the Dedekind zeta function \zeta_F(s) for any number field F

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one of the main terms involved in that formula is the regulator which is a determinant of logarithms of units of F

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the polylogarithms appear similarly in formulas for \zeta_F(n) at integers n>1

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so for example you can write the special value \zeta_F(2) for any number field in terms of (a determinant of a matrix of) special values of the dilogarithm

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when F is imaginary quadratic you can prove this by computing the volume of an arithmetic hyperbolic manifold in two ways: first way involves a volume formula involving \zeta_F(2), second way involves decompsing this into ideal hyperbolic geodesic simplices and computing their volumes with the dilogarithm

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Special values of zeta functions are arithmetically deep things and this gives you a nice way to study them: rather than considering infinitely many functions with the number field F varying, you can consider a single function but now with its evaluation points varying

vast wraith
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is there anything algebraic going on here

vivid halo
delicate tendon
vast wraith
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1.5 million views

languid lagoon
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i truly despise multiple choice questions in maths

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now that i am able to take my studies seriously it's the fucking death of me

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written questions are great because you can do a little positing and get some feedback on your suppositions but if you get a multiple choice question wrong they just give you the correct answer and tell you to kill yourself

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completely unrelated to the above, is the product of periodic functions always periodic

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it seems everyone on stack exchange only wishes to discuss the inverse

leaden torrent
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have you thought about it?

languid lagoon
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i have

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even put it in desmos

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wait

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do you mean killing myself or the product of periodic functions

leaden torrent
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the latter.

languid lagoon
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right right

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at the very least i know that one of my functions is either cos or sin (im trying to answer a question about fourier series) but im just thinking about how those behave when multiplied with some periodic function

leaden torrent
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the answer is "in general no, but when encountered in practice, it often is"

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in particular, if you know the ratio of the two periods is rational, that implies the product is periodic as well

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(why?)

languid lagoon
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so im thinking that i have to see what the period of the innerproducts would be - that way i know what terms will be vanishing by way of looking at the coefficients

vivid quest
true zinc
vivid halo
true zinc
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Ahhhh

vivid halo
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but like most methods for computing algebraic K-theory blow up combinatorially and are hard to get a handle on

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it's a similar problem to computing homotopy groups of spheres, even stably

true zinc
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oh also, fun thing related to that integral that kinda started this whole convo, about two years ago we walked into the math department and were like "ah what if I try to integrate...say....ln(tan(x))"

That was our first intro to polylogs and it still shows up in my nightmares sometimes

vivid halo
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like you can do it by hand in low degree, or we can break up the problem into a sequence of easier problems and maybe understand the first couple of steps

true zinc
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I see

vivid halo
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but I think these things are not meant to be simple in general

true zinc
vivid halo
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lmao yeah

true zinc
vivid halo
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rip

true zinc
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yeah

vivid halo
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but yeah the dilogarithm is very beautiful and shows up everywhere, the trilogarithm is still quite beautiful but starts to get hard to understand

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beyond that it's kind of a nightmare

true zinc
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wait I still have the pictures on my phone one sec

true zinc
vivid halo
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one spooky thing is that there is a weird complex-valued variant of the real single-valued dilogarithm

vivid halo
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this is spooky because among other things it lets you define a "complex volume" for arithmetic hyperbolic 3-manifolds among other things

true zinc
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what's an "arithmetic" manifold?

vivid halo
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they are defined from arithmetic subgroups of PGL_2(C) acting on hyperbolic 3-space

true zinc
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OHHHHHH

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okay

vivid halo
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specifically ones obtained from quaternion algebras over certain number fields

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when such a hyperbolic 3-manifold is arithmetic and defined over such a number field F like this, then the volume will be related to \zeta_F(2)

true zinc
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I feel troubled that I still have these mental walls that split "arithmetic" "algebra" "geometry", etc... even when the actual borders and topics starts to blur like crazy at some point

vivid halo
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most knot complements are like this

true zinc
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is "discriminant" here at all related to discriminants of polynomials? AFAIK algebraic number fields are related to algebraic numbers and those are roots of nonzero polynomials

vivid halo
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yeah they are related

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at least when the ring of integers have a power integral basis (so it's of the form Z[a]) then the discriminant is equal to the discriminant of the minimal polynoimal of a

true zinc
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I see

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I need some food, brb

vivid halo
true zinc
inner canopy
vivid halo
inner canopy
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is it some polylogarithm calculation shiver

vivid halo
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no

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I mean one might want to compute the same volume in terms of dilogarithms later to prove this neat result about \zeta_F(2) but that's after you have this volume formula

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the volume formula involving \zeta_F(2) is a volume computation for the Tamagawa measure

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you can prove these sorts of formulas for any arithmetic locally symmetric space without any more work

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it's really easy if you only care about the volume up to some nonzero rational factor, if you want the actual volume you just have to be a bit more careful about how things are normalized but this can be done very generally without so much issue

inner canopy
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ah

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is there some specific reason why we would want to know the volume of such spaces?

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ik there's a similar kind of calculation when deriving the class number formula

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as in it's the volume of some lattice

sonic sentinel
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https://www.bbc.com/news/articles/clyz6e9edy3o
TL;DR A scientist worked years on a biology problem (not niche and had important real world impacts afaiu), asked a research-based AI to work on the same problem as him, and the AI made five plausible sounding hypotheses which the scientist thinks would have taken years for a Normal Human Person to make from the research the AI had access to.

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so uh

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does anyone have a plan for what to do with the inevitable silicon-based lifeforms which are smarter than us in almost every way

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maybe we can tack "dont have any sort of negative effect on humans please" somewhere in the system prompt

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that should work right

sonic sentinel
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🥱

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you could also sleep your way through the whole ai thing and wake up at the end

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in which case, hope for soft landings, friend

limber thunder
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at least we got decent local models and cheapish cloud infrastructure

sonic sentinel
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???

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doesn't matter whether openai is malicious, they're reckless

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also open source models make most forms of ai misuse more prominent

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if open sourcing ai is a net positive its because its being used to do productive stuff

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you'd run into basically the same problem here if you made everyone on earth more intelligent while keeping them at the same level of compassion: people would be more productive and have to rely less on external authority, but they would also be better able to cause harm to others

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(this issue is less important in humans since most forms of increasing intelligence also increase compassion as a byproduct)

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kid named probabilities:

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oh yeah whats up with higher math and ai

limber thunder
sonic sentinel
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but i havent seen much of an attempt at explanation

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aside from like "theres less of it in the training data" or "math uses higher level abstraction", but from what i understand about llms this doesnt seem to explain it too well

limber thunder
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I don't understand the technicalities either but I'm sure the key is in the fact that they're language models, they're great at tasks that involve generating coherent text, but the claim that they can reason logically is either outright false or they just can't do it at an advanced enough level yet with the constraints on inference and context window sizes

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like I have a hunch this is why but I haven't read anything supporting this

half kayak
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Can you learn logic by just listening to people speak a language?

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Can u learn reasoning?

limber thunder
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a language is organized and hence has some inherent logic doesn't it

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hence why things like reinforcement learning seem to be working fine I guess -- let the model explore the training data by themselves and with enough compute time they'll perform decently at other tasks

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I guess the question is whether there's a more efficient way, whether this is actually reflective of how we humans learn, etc.

sonic sentinel
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oh logic mb

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i read it as language

sonic sentinel
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black magic?

sonic sentinel
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also almost all human reasoning is learned/taught through language

sonic sentinel
limber thunder
limber thunder
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I don't wanna yap much bc I'm supposed to be busy bleakkekw and ofc this is not my specialty and I prob should read more

sonic sentinel
sonic sentinel
sonic sentinel
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i would guess, just intuitively, not a lot of support for this idea, that you see people (both in present time and historically) sort of having a u-shape curve of how intelligent they think animals actually are as they get more experience with them

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like: first you're prone to anthropomorphizing the animal, then as you see the mistakes the animal makes you think its dumb, then as you learn more about how the animal experiences the world you become more forgiving of the animals mistakes

sonic sentinel
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from Claude:

However, [...] humans don't learn reasoning purely through language - we have embodied experiences, sensorimotor learning, and causal learning from interacting with the physical world from birth. Language helps us formalize and communicate reasoning, but isn't its sole source.

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thinking about the topic more i think a big determining factor in whether an LLM ends up being able to do a certain type of reasoning is how often that reasoning is expressed in terms of language (or at least text that exists in the models training data)

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spatial reasoning and object manipulation are good examples, we understand that stuff intuitively, from direct experience, and when we want to communicate that sort of reasoning to someone else you would normally use diagrams with language only playing a small role

vivid quest
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I'm sure there is data about the impact of modern maths reforms at school on reasoning later

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It's a similar problem llm's have to deal with

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Ig

sonic sentinel
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also ive heard math people complain that math papers are good for proof verification but tend to be bad for understanding the process used to make that proof

solid snow
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yes because failed attempts are usually not included

vivid quest
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I think "intuition" might be just reasoning in another language than formal maths

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One that we're more familiar with

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Bu i still think language is the major component to reasoning

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Idk if it makes much sense (even to me)

sonic sentinel
#

theres also stuff like idk what motivated you to think in this way

vivid quest
# sonic sentinel wdym

The trend in certain countries to reform mathematical education from very early on in the 60's/70's

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Which happened to be a very bad idea

sonic sentinel
vivid quest
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But we also as humans aren't always taught our intuition, it just appears with experience, why not the same with llm's?

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Like textbooks, they don't teach intuition

sonic sentinel
solid snow
sonic sentinel
#

chad ramanujan

solid snow
#

there's also that one guy who was trying to prove his dead friend wrong

vivid quest
vivid quest
sonic sentinel
# sonic sentinel chad ramanujan

this makes me wonder: would ramanujan have been remembered more or less greatly if he could actually describe what the fuck he was thinking?

solid snow
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i will say that a lot of mathematical eureka moments come up in unexpected times when doing other stuff

vivid quest
solid snow
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theres times where im not consciously thinking of steps or things but just abstractly pushing against a problem in my head

vivid quest
solid snow
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i dont know how this could be translated to llms or if it even needs to be

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not necessarily llms either tbf

sonic sentinel
vivid quest
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Some companies try to feed LLM's things that look as much as textbooks as possible to simulate education

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And i think it works pretty well

sonic sentinel
vivid quest
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I don't think it works like that

sonic sentinel
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fuck its weird to think that far more likely than not some of my classmates have had dreams including me

vivid quest
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That's normal

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I've had dreams with some classmates inside

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Well...

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Not exactly what you said but...

sonic sentinel
#

bro said well

solid snow
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lol something that i actually did in a level maths was pretend i was the british examiner reviewing my work and this would unironically give me some ideas on what to do on the problem

vivid quest
sonic sentinel
solid snow
#

stand power

sonic sentinel
#

sand powder

sonic sentinel
#

o.o

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where

vivid quest
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But it can't be used to much times in a row before it becomes shit

sonic sentinel
#

oh

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like users doing that

vivid quest
sonic sentinel
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no i meant like something integrated into the actual system

vivid quest
#

Nono real devs do that

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To train the model

sonic sentinel
vivid quest
#

I need to review the 30min video to find the source smh

sonic sentinel
#

you could just send the video link

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does it include a transcript

vivid quest
#

The video is in french

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Which is a problem most likely

sonic sentinel
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i was unfortunately born with a condition that made me unable to understand french

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and i never really recovered from it

vivid quest
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And it gives good results up to a certain point of at which it becomes dumb

sonic sentinel
#

yeah thats cool

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i heard that was mainly what was happening with all the CoT models you see these days

vivid quest
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Wait

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She said deep mind and gpt4 did that

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But "model collapse" happens if the chain is too long

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That happens for humans too lol

ember laurel
#

hi i have a question, someone once told me a lot of advanced math is reducing questions in various fields to equivalent questions in linear algebra, which makes them easier to solve

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for example the entire field of representation theory is based around this

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how true is this statement in general

sharp mulch
#

Pretty true

unique slate
stark silo
#

so much of the maths I'm doing right now feel like cheating, precisely because we're encouraged to reduce the problems

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this exponent too big? throw it out, make it run towards zero and say byeeee

unique slate
#

M.@sharp mulch m mm mm m mm m...,mmmmkm mm mmmmmm mm mmmm.mmm mm mm mm m.m mm mmm..mmmmkmmmmmm,m.mmmv h. Vvvvvvvvv.vvvv vv gvvvvbvb v hvvvvv.vvv v.vv .vv vbvvvh vcvvvg v gv gv v vvvvg cc vvvgvg g vc vvv.g glvvvvvgv g vvvvvv, m mm

sharp mulch
#

<@&268886789983436800>

jovial ember
proven knoll
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I agree

wide patrol
#

Hey, I have some problem.

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I took part in the programming contest in codechef site.

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There was a difficult problem for me.

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But interesting

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Here is the url.

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Who can explain about this.?

verbal granite
#

How to find Null Space of ?
Step 1: Row reduce the matrix
Step 2: Find independent columns (which do not have pivot elements) and dependent (pivot elements are there)
columns.
Step 3: Number of independent columns = Nullity of the matrix
Number of dependent columns = Dimension of the matrix

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is this correct?

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independent columns are pivot columns rght

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very confused

agile fiber
#

pivot columns: columns with a pivot
free columns: columns without a pivot
rank of matrix: number of pivot columns
nullity if matrix: number of free columns
i would not use the phrases "dependent columns" and "independent columns", or "dimension of matrix", they are too ambiguous

normal pawn
#

Do you find a woman's softness, sweet submission, and vulnerability appealing—something that evokes your instinct to protect and care for her?

neat lintel
#

Isn't this what the female nature is about?

fresh comet
#

<@&268886789983436800> two bad posts back to back hmmcat

neat lintel
#

I don't think there is need to ping mods. I mean, the questions are weird ❓ but there's nothing wrong

#

Btw where is the math discussion channel? Cuz I thought these were math discussion, but they are not

upbeat heart
half kayak
gusty socket
limber thunder
#

yeah if unsure it's probably best to ping (or DM @polar panther with a message link) and we'll determine whether it's worth moderating or not

foggy path
#

Gender roles are made just to make women look inferior and submissive to men

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There's no point of having gender roles in an ideal society

crystal arch
#

Is chess a game or something that makes your more intelegent

north topaz
languid lagoon
#

lord there's this question i encountered when i was teaching last week it's been haunting me

#

dang ion rmb how to use latex lmaooo

main elbow
languid lagoon
#

it's question 4d

#

it irritated me severely that they just equated the root to 3 instead of expanding the brackets but i cant think of any reason why not besides "i wouldnt do it that way"

#

cause in my mind the rationalisation is that you "lose" a solution but none of the solutions you get by expanding are the ones they got

north topaz
#

now recall your laws of indices

#

ah okay you still get to that step with the 9

north topaz
#

$(x + 1)^2 - (3(2x - 3))^2 = 0$

fathom swallowBOT
north topaz
#

or $(x + 1 + 6x - 9)(x + 1 - (6x - 9)) = 0$

fathom swallowBOT
north topaz
#

yeah then the left bracket gives 7x - 8 = 0 so they've missed a solution

#

,w 2log9 (x + 1) = 2 log9 (2x - 3) + 1

north topaz
#

yeah turns out it doesn't work

#

,calc (8/7 + 1)/(2 * 8/7 - 3)

fathom swallowBOT
#

Result:

-3
north topaz
#

this is negative sorry so you can't take the log of a negative number

languid lagoon
#

ive gotten 8/5 and 10/7 tho, if it was a missing solutions thing wouldnt at least one answer be the same?

north topaz
#

so it must equal 3

#

normally you get two solutions yes

#

to a^2 = b^2

languid lagoon
#

right

#

like just taking a=b is a little rogue is it not

north topaz
#

but you need to remember the domain of any logarithm

languid lagoon
#

is x>0 ouioui

foggy path
languid lagoon
#

but that doesnt necessarily mean that i cant solve it by expanding cause i could very well not get a negative value (as you see by my solutions)

north topaz
#

I'd say you become a better thinker about strategy

north topaz
foggy path
#

Intelligence is just a small factory in it

north topaz
foggy path
#

It's mostly about super fast working memory

north topaz
#

you need to check every solution you get by subbing back into the original

foggy path
#

You need to have exceptional working memory inorder to be a chess prodigy

languid lagoon
#

right right

north topaz
#

like a^2 = b^2 is the non reversible step

#

cause it can come from a = b or from a = -b

#

everything else can be reversed

languid lagoon
foggy path
#

Creating chess strategies require intelligence

languid lagoon
foggy path
#

But being a good chess player

#

Not necessarily

north topaz
languid lagoon
#

sec

sharp mulch
languid lagoon
#

sksksksk that's a typo in the textbook it's written z sqrt y

sharp mulch
#

real maffs moment

languid lagoon
#

this textbook series has so many mistakes lmao when i was a student it was never a surprise for us to ask a teacher to clarify something and he was like no shit ur right the book is wrong

#

now i am the teacher who must do this

brazen mulch
#

honestly, why wouldn't they write log_a(sqrt(y)z) instead 💀

#

ass notation

languid lagoon
# languid lagoon sec

ok i accept that 2 is the only solution having substituted back but i have no clue why doing it the way i did it only yielded incorrect solutions

languid lagoon
brazen mulch
#

ye 😭

#

(yoo same pronouns)

languid lagoon
neat lintel
neat lintel
teal lynx
#

We first show that $\Phi$ is linear. Let $v, w \in \mathcal{D}_pM, k \in \R$, and let $f \in C_p^\infty(M)$. Then
\begin{align}
\Phi(v + kw)(f) = (v + kw)([f]_p) = v([f]_p) + kw([f]_p) = \Phi(v) + k \Phi(w)
\end{align}
so $\Phi$ is linear.
\medskip\newline
Now define $\Phi^{-1}: T_pM \to \mathcal{D}_pM$ by $\Phi^{-1}(v)([f]_p) = v(f)$. We need to show that $\Phi^{-1}(v)$ is well defined, that it really does send elements of $T_pM$ to elements of $\mathcal{D}_pM$, and that it really is the inverse of $\Phi$.
\medskip\newline
To show that $\Phi^{-1}(v)$ is well defined, suppose that $f$ and $g$ are smooth real functions such that $[f]_p = [g]_p$. Then by definition, $f \equiv g$ on some open neighbourhood $U$ of $p$. This implies that $v(f) = v(g)$, which in turn means that $\Phi^{-1}(v)([f]_p) = \Phi^{-1}(v)([g]_p)$. This proves that $\Phi^{-1}(v)$ is well defined.
\medskip\newline
To show that $\Phi^{-1}(v)$ is really an element of $\mathcal{D}_pM$, we need to show that it is linear and satisfies the product rule. Thus, let $[f]_p, [g]_p \in C_p^\infty(M)$ be arbitrary, let $k \in \R$, and suppose $v \in T_pM$. Then
\begin{align}
\Phi^{-1}(v)([f]_p + k[g]_p) & = \Phi^{-1}(v)([f + kg]_p)
& = v(f + kg)
& = v(f) + kv(g)
& = \Phi^{-1}(v)([f]_p) + k \Phi^{-1}(v)([g]_p)
\end{align}
and
\begin{align}
\Phi^{-1}(v)([fg]_p) & = v(fg)
& = f(p)v(g) + g(p)v(f)
& = f(p)\Phi^{-1}(v)([g]_p) + g(p)\Phi^{-1}(v)([f]_p)
\end{align}
which proves that $\Phi^{-1}(v)$ is indeed linear and satisfies the product rule. Thus, $\Phi^{-1}$ does in fact send elements of $T_pM$ to elements of $\mathcal{D}_pM$.
\medskip\newline
To prove that $\Phi^{-1}$ is the inverse of $\Phi$, let $v \in T_pM, w \in \mathcal{D}_pM$ and compute for any $f \in C^\infty(M)$ and $[g]_p \in C_p^\infty(M)$:
\begin{align}
\Phi(\Phi^{-1}(v))(f) & = \Phi^{-1}(v)([f]_p) = v(f)
\Phi^{-1}(\Phi(w))([g]_p) & = \Phi(w)(g) = w([g]_p)
\end{align}

#

That is why

fathom swallowBOT
#

ASda

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l.49 ...ar. Let $v, w \in \mathcal{D}_pM, k \in \R
                                                  $, and let $f \in C_p^\inf...
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of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.```
teal lynx
#

<@&268886789983436800> Free gift for all your moderating work

#

Someone is gonna get vanished

languid lagoon
neat lintel
wild lantern
neat lintel
wild lantern
inner canopy
#

what do we live in

#

1950 lmao

#

"instinct to protect her"

#

lmao

#

you can't make this shit up

wild lantern
#

Thanks 🫡

terse fiber
foggy path
#

Well your perspective of what a women should be will only work in a society of fools

#

An ideal human should attain his own individuality

#

Being enforced a gender identity is pathetic

#

The difference must only be biological

#

Not sociological

foggy path
#

And even majority of women have nothing against it they just blindly follow the same

#

Women should be just like men ( excluding biological differences )

keen monolith
foggy path
neat lintel
#

men were caretakers of women and women were caretakers of men

#

with different rights

#

you still havent explaained why its paathetic though

neat lintel
#

from what ive seen the more power women get the more destructive and degenerate society is

#

simple observation; and thats a objective fact

foggy path
#

@neat lintel what do you want a woman to be like?

neat lintel
fresh comet
#

this is not an obvious fact, if true at all

#

and I highly doubt it’s true

foggy path
#

So you mean women are dumb?

#

You really want your partner to be a housewife?

foggy path
neat lintel
foggy path
#

I mean society is already so dumb where majority is religious

fresh comet
foggy path
#

The concept of God should be separated from these pre-existing religions

royal condor
#

I'm new here

fresh comet
royal condor
#

Thx

foggy path
neat lintel
# foggy path Well these roles only work in a society with low intelligence

I'm saying they should fulfill their duties, which include managing the household and family at a minimum. In summary, I don't believe women should have political power or be able to become leaders, aka patriarchy. I could give you examples of amazing women who were submissive housewives and at the same time scholars, and also their negative influences at a point where they had political power.

foggy path
#

Give examples

#

I am not talking about the political power

neat lintel
foggy path
#

I am talking about individuality

neat lintel
#

These were teachers and submissive wives at the same time

neat lintel
#

they were influential women in the islamic golden ages (and early islam)

foggy path
royal condor
#

Wtf, are people still discussing femininsm in 2025?

neat lintel
#

Governed by the sharia divine law

#

Ottoman and abbasid for example

foggy path
#

Nuh i ain't calling them educated by that mean

neat lintel
#

alaot of historians complimented how they structured societies and gender roels

neat lintel
foggy path
neat lintel
foggy path
neat lintel
foggy path
#

What if your future wife denies to be a housewife

neat lintel
foggy path
#

Don't marry bro @neat lintel

supple flame
#

A married woman can be a house wife if she wishes but by no mean should she be locked down into that role only

neat lintel
foggy path
#

@neat lintel what if you were a woman?

#

Would you have done the same?

#

Be a housewife?

neat lintel
#

like I sid

#

we need women for more things

#

teachers and etc

foggy path
#

Why can't a man do the households?

neat lintel
foggy path
foggy path
karmic spear
#

yo

#

what are we discussing

foggy path
#

We are not in stoneage anymore

neat lintel
foggy path
neat lintel
#

thats just the coin toss nature we are born in

foggy path
clever quail
#

Guys I study in class 11 and I have discovered some theorems in mathematics so where can I publish them

neat lintel
foggy path
#

Most probably they have already been discovered by somebody else

#

Happened with me too

karmic spear
foggy path
#

I have discovered tons of theorems and what I got to know they were already discovered by somebody else 100's of years back

karmic spear
#

Its all about presenting yourself

neat lintel
clever quail
karmic spear
#

if you talk about women filling these roles yes

foggy path
clever quail
karmic spear
#

statistically there are men born w/ fked up hormones that cant lift a log and there women who are born to lift strong stuff, but yes like in MOST MOST cases men are stronger and they are more suited for the military

neat lintel
foggy path
#

That women and men shouldn't have different requirements for military just to give women extra rights

karmic spear
#

strength matters in the military

foggy path
clever quail
foggy path
#

We are talking about an ideal man or an ideal woman

#

They both should focus on their individuality and carry an intellectual pursuit

#

That's it

neat lintel
karmic spear
neat lintel
karmic spear
#

if ur a woman and u want to be in these positions u must be born with extraordinary nature

neat lintel
#

dude it can be easily multi-tasked

karmic spear
#

like strength, physicality etc

neat lintel
#

not even steroids could help you

karmic spear
#

how

foggy path
#

@neat lintel there are exceptions

karmic spear
#

there are like, 0.3% of women who are stronger than the average men

#

idk the percentage actually but y get my point

neat lintel
#

im saying we also need women for feminine jobs aswell

foggy path
karmic spear
#

career is a career bro why do you make distinctions

neat lintel
neat lintel
#

the youth wouldnt developed

karmic spear
#

political career, business career, they are all neutral

neat lintel
#

if both maan and women were aalways too busy the kid would have mental issues and that is proven

foggy path
karmic spear
#

yes thats what im saying

neat lintel
foggy path
karmic spear
foggy path
#

For a typical kid

karmic spear
#

but thats like

foggy path
#

Maybe yes

karmic spear
#

its an issue parents will have to manage

foggy path
#

But yes being controlled by gender roles you are just making yourself dumb

neat lintel
#

if the kid doesnt get educated by his parents and doesnt spend time with his parents aswell

karmic spear
#

on how they want to nurture their kid

foggy path
#

Bro

#

It's about perspective what's more important to you

neat lintel
foggy path
#

The society or the individual

foggy path
#

And we are not considering that superficial status

neat lintel
#

maybe greeks

#

im not a historian

#

but gender roles and rights were established perfectly during the islamic golden age

foggy path
#

@neat lintel what's important for the society isn't necessary a supirior way of life

clever quail
#

Guys does anyone know how to publish a math theorem

foggy path
#

@neat lintel let me give you an example

vivid halo
karmic spear
foggy path
#

There's a restricted area where any individual steps in it gets detonated. There's a danger sign board in the border. There are 100 individuals each individual has assigned its own task and then there comes an animal who couldn't read that sign board and enters the area which gets detonated. Hence the rest of the people now can safely pass that area

#

And that was only possible cuz the animal was dumb enough to not be able to read and understand that signboard

#

So according to you being that dumb is an ideal trait?

neat lintel
clever quail
foggy path
raven plaza
clever quail
neat lintel
clever quail
vivid halo
#

dm me you draft

#

I have a phd I can give you a quick opinion

upbeat heart
clever quail
vivid halo
#

yes

karmic spear
#

outside of the housewife thing

neat lintel
#

but as far as I studied I dont think thats the case for the caliphates

foggy path
#

That's it

#

Nothing too complicated

karmic spear
#

Science fe

#

If a woman pursued science

#

she would be heavily criticized

#

Science does impact politics as far as I am concerned

neat lintel
karmic spear
#

If you dont allow women to become scientists thats dumb asf bro

#

even if they decide to get married and all

foggy path
foggy path
karmic spear
#

no

neat lintel
#

education helps express potential genetic intelligence

foggy path
neat lintel
# foggy path No

learning algorithms and techniques for things doesnt help you think more efficiently ?

neat lintel
#

a man is also responsible

#

but the housewife is also more responsible because shes not the one working all day to finincially protect them

foggy path
#

Ideal couples shouldn't have kids tho

neat lintel
foggy path
#

It will just be a distraction from their intellectual journey

neat lintel
#

ideal couples would give birth to ideal and intelligent kids

foggy path
#

An ideal person is not a slave of the society

karmic spear
#

Then the ideal child would need to be facilitated in order to maximize its intelligence 😭

neat lintel
karmic spear
#

w/ super professors and inhuman teaching

neat lintel
#

wait no

#

i agree with myself

foggy path
#

If you are talking about general masses

#

Sure they are fine to follow their surface level way of life

neat lintel
karmic spear
#

Yes and I want to say that

#

Clarify what y mean by ideal

#

as the other guy said

foggy path
#

It's just like how animals are useful for human beings in various ways

#

They are useful only because they are inferior to us

#

Same for the humans

#

And the society

#

"Muslim woman"

#

Lol

neat lintel
foggy path
#

Ok

foggy path
foggy path
#

Is not about an ideal woman

#

It's about ideal human

#

Ideal for the society maybe

neat lintel
#

actually heres a lecture by one of the greatest modern islamic scholars

foggy path
#

That's what you mean

#

Not objectively ideal

neat lintel
#

cant make up a opinion/stance if you dont know the roles and qualities of a muslim women

foggy path
neat lintel
foggy path
neat lintel
#

again not true

#

islam teaches tht men and women are equal

#

but born with differen nature, different rights, and different qualities

foggy path
#

Well I have explained everything

#

Now you if you still can't understand this

#

I have nothing to say

karmic spear
#

Ideal Muslim Woman fills her role perfectly according to the needs that an "Islamic" world needs

#

now I dont believe an Islamic world is an ideal world

#

If y do ok

foggy path
#

@karmic spear wasn't my example sufficient?

neat lintel
karmic spear
#

Ideal woman is not the ideal islamic woman based on all peoples' perspectives

#

only for the Islamic World

neat lintel
karmic spear
#

By the way that example covers a lot on the world of politics and how the elites manage us

#

but not related to the topic we are discussing

foggy path
neat lintel
karmic spear
#

Because the ideal Islamic state does not optimize liberalism

foggy path
#

@neat lintel what about couples without any child ? According to u?

karmic spear
#

And I believe individualism, political equality etc are way more important in our society than anything else

#

Freedom is everything

#

If you take humans as work machines and you optimize them on a massive scale then life becomes dull

#

If you want to make an empire sure

neat lintel
karmic spear
#

But if you are talking about life in general, living must be however y want to engineer it based on the potential y carry since the moment y were born

karmic spear
#

no

#

how are the things I said associated by communism?

#

They are literally the opposite idea of communism

neat lintel
#

never came across a scenario like that

karmic spear
foggy path
neat lintel
#

but a wife who isnt a mother has less responsibility with managing household

neat lintel
foggy path
#

Wth?

neat lintel
#

with cooking and etc

foggy path
#

Cooking is a basic thing both men and women should do it

neat lintel
karmic spear
#

huh

neat lintel
#

like i said a man should be working and providing for his wife financially

#

men are caretakers of women and women are caretakers of men

foggy path
#

You are again discussing about the average humans with surface level perspective of life

supple flame
#

How are you guys still at this debate when I shouted the conclusion from start

#

smh

neat lintel
karmic spear
#

how?

#

Every thought of the human mind has flaws

neat lintel
karmic spear
#

Political ideas have flaws

neat lintel
#

because its the human mind

karmic spear
#

Systems have flaws

neat lintel
#

I dont believe thats applied to the islamic law though

#

not even terriosts like hitler thought so aswell

karmic spear
#

Yes because you believe that a flawless being created these laws

#

I believe opposed to you, that a human mind made these laws

#

and that Islam is nothing more than an Idea

#

Every political idea is a religion if you view it objectively

neat lintel
karmic spear
#

Communism is a religion, Capitalism is a religion, every religion is a religion

neat lintel
#

life is too much to discuss every aspect

karmic spear
#

Or you could say that they are all ideas

#

idk

#

History

lunar ruin
neat lintel
#

not the definition of a religion

neat lintel
#

at some point youre gonna need to be married

karmic spear
lunar ruin
neat lintel
neat lintel
karmic spear
lunar ruin
karmic spear
#

If you want to believe that Islamic laws are flawless because some perfect existence made them, ok go along w/ it

neat lintel
karmic spear
#

But in the end of the day if you analyze the system of Islam, politically you will come to see that its an ideology

#

Atelast on how it applies to politics

#

Its only just a system

neat lintel
karmic spear
#

With flaws that are ignored because you believe that these flaws are exceeded by obeying a higher god

#

who claims that your system doesnt have any flaws at all

#

you believe that this being exists, I believe that this is mythology

#

Its all about perspective

#

And thats when you start to shape your different opinions about men and women

neat lintel
karmic spear
#

Not being ignorant of a religion doesnt mean I am accepting the claims of that religion

#

Not being ignorant means I know what this religion says and how this religion has evolved through out history

#

And therefore, I decide on what stance I want to hold against that

neat lintel
supple flame
#

Waiting for someone to bring up islam's approval of slaves

karmic spear
#

man

neat lintel
#

slaves werent approved

karmic spear
#

I told you before

#

wtf

neat lintel
#

islam waas the first religion to free slaves

supple flame
neat lintel
#

Allah told slave owners to free slaves if they could because if the caliphates freed slaves all at once it would create disastors

karmic spear
#

Look

neat lintel
#

concubinage is a valid thing

supple flame
#

lol

neat lintel
#

how they established feudalism

#

and man made laws

#

abused their people

supple flame
#

...maybe because the topic is about islam and how its laws can be problematic.......

coarse bridge
neat lintel
#

and islam came and liberated these lower class people by giving them rights to education and health-care for free at a low tax rate of 2%?

supple flame
#

yeah true

#

Islam did actually massively improve things for a lot of people

#

women were little more than cattle before islam, that much is true

#

It was fairly forward thinking in its age, but it is no longer that in this day and age

karmic spear
#

Evolution

neat lintel
#

dont take extremeists as examples

neat lintel
# karmic spear .

If I explained why liberalism is problematic would you alter your beliefs?

karmic spear
#

No because like you, I have a perspective that I have justified on why I think it's the most "suited" for society and the individual

neat lintel
supple flame
# neat lintel in what aspect?

Lots of things in islam state that a woman needs a man's premission, sometimes for things a lot of people take for granted, take a look: https://islamqa.info/en/answers/69937/can-the-wife-go-out-without-husbands-permission-in-islam

karmic spear
#

what are ur thoughts

#

Subjectivity explains everything by the way you said it yourself

neat lintel
karmic spear
#

you are heavily opposed to individualism

#

right?

neat lintel
karmic spear
#

I just can't see a better way of living

#

You are born

#

Then raised

#

whats a better idea than being able to do whatever the fk with every resource you have available to you , while operating like a human , inside of laws and rules

neat lintel
karmic spear
#

well

#

There will be divisions

#

And thats a flaw of liberalism

neat lintel
karmic spear
#

sorry but

neat lintel
#

prophet muhammad for example

karmic spear
#

I think Islam does not have a good reputation for being peaceful

neat lintel
#

told us that it is obligatory to support a poor man or donate to charity or it would result in major sin if one refuses & capable of it

karmic spear
#

but you could say to me that if all people could turn to the idea of the islamic state then there would be no wars ok and no conflicts sure

neat lintel
#

prophet muhammaad also used to feed orphans and play with them, and authentic stories like the blind old man and prophet muhammad

karmic spear
#

but

#

thats unrealistic

#

and only just a theory

neat lintel
#

they violated quranic rulings

karmic spear
#

alright

neat lintel
#

thats just something we can minimize but not eliminate

#

human-maade laws are the worst when it comes to reducing these types of issues

neat lintel
#

even democracy is childish compared to islamic law if you truly understood both philosophically

karmic spear
#

As I said, I believe your laws and human made

#

Ok?

#

So

neat lintel
foggy path
#

God made Sharia?

karmic spear
#

I cant see your point from that perspective

#

Im irreligious

neat lintel
#

if you can show one flaw in the sharia I would leave islam because mistakes occur by humans

neat lintel
foggy path
#

Are you being sarcastic?

#

I guess no

#

You are serious

neat lintel
karmic spear
neat lintel
karmic spear
#

We could just agree that we disagree

foggy path
#

How was god created?

neat lintel
#

and willing to hear arguments

foggy path
#

Yk what

karmic spear
foggy path
karmic spear
#

Alr

foggy path
#

@karmic spear you?

karmic spear
#

me neither

#

im agnostic

foggy path
#

I am agnostic atheist

neat lintel
karmic spear
#

yes agnostic atheist

neat lintel
#

anywaays ima go now I had a nice time discussing with you guys

foggy path
#

But yes the idea of god what religions claim is definitely wrong

karmic spear
neat lintel
tight copper
#

Hmm

vivid halo
#

most religious texts are often laughably false if you're judging them at the level of literal factual truths, but that's also kind of not the point and value of those texts

#

"earth is 6000 years old" or whatever lol

karmic spear
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Simplified I just believe that:, Humans had insecurities and tried to explain stuff. Humans then tried to explain stuff through out gods and religions. Then they made the idea of religion more sophisticated and "reasonable". Then they used these ideas in order to create political systems and justify both how they will operate and things they cannot discover through their perception (metaphysics.). Which as a thought is very flawed because it comes from a human. But the world is so random and absurd that you cant reject metaphysics, so I take my stance as being agnostic. Most religious texts (bible, quran) are very "human" if you read them and you could also say that its pure mythology. Thats why I dont reject the idea of something higher we cannot even imagine, but I completely reject the idea of religions. Because they are super flawed

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and they defy truths yes as y said

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I can only see how religion has benefited the political world even tho I believe political systems without any base on religion are better and I am not a communist

vivid halo
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they are very human and there is a very big range of how you can pick and choose from the texts, like even if you are agnostic you can derive lots of profound lessons and meaning from a lot of these texts, and even if you are religious you can find plenty of ways to extract excuses to excuse one's own awful bigoted behavior monkey

karmic spear
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yea

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they are ok as philosophies

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but there are things y must filter out tbh

vivid halo
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I prefer that religion would have less of an influence on society but this is still a lot better overall than mass nihilism

supple flame
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I personally prefer myths as stories but I can see why people prefer them as religions

karmic spear
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yeah

vivid halo
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yeah I enjoy mythology a lot even as an atheist and I've got a lot of meaning from reading various religious texts from time to time in this way

karmic spear
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thinking about metaphysics and forming religious helped a lot w/ evolution I think

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and there is more to come

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in the future

foggy path
# karmic spear wdym

It's just there lack of understanding related to consciousness and human narure

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Humans tend to relate everything to the other humans

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Humans can have emotional attachment to a thing which isn't even alive

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They can have emotional attachment to a stuffed toy

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The reason?

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Cuz the stuff toy tends to have a cuter features similar as a human child which triggers their instict to nurture it

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That's why humans can somewhat get attached to these things

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Same goes for the concept of god

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The thing with humans is that

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Most of the things that humans find obvious and evident is just a result of their natural instinct and unconscious influences

karmic spear
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I agree

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consciousness is one of the most interest topics to discuss

foggy path
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Your every action is determined

karmic spear
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And who do you think is the one who determines?

foggy path
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Like just take an example of basic physics

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Two objects are comming together at a certain velocity with certain path