#serious-discussion

1 messages Ā· Page 469 of 1

rancid meadow
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lmao

deep mango
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sorry jesse

rancid meadow
#

yeah cuz its for grinding ryc

cold needle
rancid meadow
#

the desk spaces r mad nice actually

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orange WanWan

deep mango
#

SUCCESS
IS MAKING
those who
BELIEVED IN US
LOOK
BRILLIANT

rancid meadow
#

what type of chairs are those

bronze pelican
#

Thats great hyperhonk

rancid meadow
#

do u think they are eames chairs

deep mango
rancid meadow
#

valid question.

deep mango
#

ok survivor is starting

fair wedge
#

ima study software development by myself and get a job at an environment-caring company

neat lintel
#

Genshin Impact has a magic square puzzle 😳

neat lintel
#

cool

stray kite
#

If you have a vector field V, what exactly does $V \nabla V$ denote?

fathom swallowBOT
#

CoolShot

neat lintel
#

ccccccontext?

neat lintel
neat lintel
#

Ping me if you think anything neat

inner finch
#

woffolin bruv

fathom swallowBOT
#

copinghagen

pale orchid
neat lintel
neat lintel
#

guys are composite functions , functions which use other functions?

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for example this g(x) = x + 1
and
f(x) = x * 2

f(g(x)) //is this a composite function?

deep mango
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Yes

fringe needle
#

Every day I’m amazed by how powerful simple theorems can be

bronze pelican
#

Like what

fringe needle
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Fundamental things like pigeonhole, or simple introductory theorems like the monotone convergence theorem

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The latter are only powerful when they can be applied which to be fair can be quite a limited set of problems but it’s still awesome how you can get quick conclusions from them

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Lagrange is a good example of a powerful simple theorem ig

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You’d probably have better ones

rare frigate
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Can I ask a question

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How much algebra do you need for calculus

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Like how good

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Like do you need Olympiad level algebra

neat lintel
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You need high school algebra and trigonometry

rare frigate
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Ik

neat lintel
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Competition math is fake math

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It doesn’t matter really

rare frigate
#

But like do you need to be like Olympiad level in algebra

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Like in terms of algebra skill

cold needle
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No

neat lintel
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can you solve a quadratic equation

rare frigate
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Easily

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Formula, factor or square

neat lintel
#

do you know what a logarithm is

rare frigate
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I know what it is

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Haven’t learnt it yet

neat lintel
#

Do you know trig

rare frigate
#

I’m still learning algebra 2 on my own

rare frigate
#

I know that a log is an inverse of an exponent

cold needle
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if everyone needed to be good at olympiad level algebra to do calculus then who would be doing calculus

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this is absurd

neat lintel
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Alright, learn algebra II fully and know exponentials and logarithms well

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do you know what homotopy is?

cold needle
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that someone is wrong

rare frigate
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Hell na

rare frigate
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Or do I need to make my algebra like insanely good

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Because idk

neat lintel
unborn trellis
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you should probably have a mastery of trig at least

rare frigate
#

What is meant by mastery

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@neat lintel how is competition math fake math

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Is it just too hard

neat lintel
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it’s useless for real maths and physics

unborn trellis
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like, if I explained something in calculus that used techniques from trig, you could follow along

deep mango
neat lintel
#

You can do it if you want

neat lintel
rare frigate
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The only thing I haven’t mastered

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Is algebra II

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I’m working on that

unborn trellis
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do those things not go hand in hand

rare frigate
unborn trellis
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we had trig/algebra II as one class

rare frigate
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Not the logarithms bit

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Ok so thanks

neat lintel
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Anyways time to do a ā€œsimpleā€ calculation for my PI dan

rare frigate
#

I thought you had to be competition level at algebra

unborn trellis
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okay yeah should have a good understanding of exponentials, logarithms, quadratic equations, graphing, inequalities, and radicals

rare frigate
#

For a sec I thought everyone here was an Olympiad level

unborn trellis
#

if everyone needed to be a comp math prodigy to learn calculus then few would know calculus

deep mango
rare frigate
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Wait how hard is the Olympiad even

deep mango
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is this what jealousy looks like anime boy?

rare frigate
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Because people told me about some think called the ā€˜calculus trap’ or whatever it is @unborn trellis

unborn trellis
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i have no idea what that is

deep mango
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the calculus trap...

unborn trellis
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i suck ass at competition math but i taught myself calc in like 10th grade

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it's not as difficult as you think

rare frigate
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I’m in 9th grade

rare frigate
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I’m doo doo at comps

neat lintel
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Yang Mills theory cool

cold needle
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bruh

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bacono stealin my lines!!!

unborn trellis
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I didn't even read that lol

cold needle
unborn trellis
neat lintel
unborn trellis
#

are these compatible things

neat lintel
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That is, in fact, my About Me

unborn trellis
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nothing against your beliefs, just kind of curious

cold needle
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i think they are compatible

neat lintel
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May God bless all of us

cold needle
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i assume people make the right modifications to their religious beliefs so that they become compatible (?)

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unsure how it works

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since i am not religious

neat lintel
#

same

cold needle
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i am doomed

neat lintel
#

Christianity and the modern scientific consensus are fully compatible. A website I like a lot with good information is https://biologos.org.

neat lintel
cold needle
#

right

unborn trellis
#

this is a pretty funny headline

neat lintel
#

It’s moreso selection of proper interpretations than random modification

cold needle
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i see

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ive been wondering like

neat lintel
cold needle
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at what point do the interpretations deviate enough that you end up with some kind of new religion even

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i guess this is how the sects form?

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i am not educated on these matters

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oog

neat lintel
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whycat.

rare frigate
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@neat lintel do you believe in the lord

neat lintel
cold needle
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i see

neat lintel
#

Christianity holds that there is one God who is three Persons. Each of these Persons is not any of the other Persons, but all three are one God.

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and he deleted his message

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oh well

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I am agnostic as pertaining to the existence of the muffin man

eager crescent
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It's muffin time

swift sinew
# neat lintel

I feel like I’m reading an axiomatization of Christianity

neat lintel
#

The proper name for that is ā€œsystemic theologyā€

inner finch
neat lintel
#

A quite famous historical example is Aquinas’s Summa Theologica

brazen locust
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Taking a math class and whispering to myself math is synthetic a priori and dreaming of getting a good grade while making a 30

neat lintel
neat lintel
#

the theists in this server are pretty devoted and seem to work hard to not end up with a defective theological idea of their respective God/gods

inner finch
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the greatest olympic mental athletes of our time

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best thing to come out of that place

sick burrow
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where is this from mirza

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like you said that in response to the theology discord being linked but that looks like reddit to me

neat lintel
inner finch
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lol

jovial ember
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Dude

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That’s from r/bewitchthetaliban

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Hahahaha

pale orchid
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mirza taking a page out of shin megami tensei

light needle
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should have just banned her smh

errant rock
sick burrow
#

You ever just feel like you can't focus on anything

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Like between ADD, laziness, and a small dose of crippling self hate I barely spend any time on any of my classes

static loom
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delete the internet

sick burrow
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It's not just the internet

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Sometimes I'll sit down and be literally unable to focus

static loom
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I find I feel that way for the first hour or so of trying to focus on something

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but then it goes away and I get into it

sick burrow
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But I'll admit that the internet is certainly a major

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The thing is, I rarely can spend that much time focusing on something

static loom
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it's easier to short circuit it if I go straight to doing it when I wake up

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and don't touch any electronic devices in between, minus maybe turning off an alarm

sick burrow
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Like I'll spend an hour maybe 2 hours tops working at a time

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Often much less

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Not sure to what extend that's laziness/internet and to what extend it's ADD

static loom
#

personally I just attribute it to me being a monkey

sick burrow
#

But the end result is I rarely spend more than a few hours per week on any of my classes

static loom
#

like something distinctively unnatural about sitting at a desk reading for hours

sick burrow
#

*few hours per week each not total

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And the thing is, I generally do well in my classes, like I have a 4.0 gpa, but I think that's just a combination of the classes not being demanding and just being carried by the fact that I pick up on things quickly

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I have this constant fear that I'm not actually learning any math and am just blackboxing everything

static loom
#

dunno, sounds like your expectations for yourself are too high so you are constantly disappointing yourself

sick burrow
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And relying on just intuition and theorems I don't know the proofs for

sick burrow
static loom
#

you're doing well it sounds like, but we're still mortal

sick burrow
#

In terms of time commitment

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But like the thing is

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For example

static loom
sick burrow
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I didn't really take notes until this semester

static loom
#

well, I'm not a therapist so I'll just stop it there, but good luck working it out

sick burrow
#

I feel like I don't retain things

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At least not as much as I could

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And that I'm always doing just the bare minimum

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In like reading courses and research projects

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And in terms of my expectations

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Is it really unreasonable to think I should be spending closer to 6-7 hours per week on an upper level algebraic topology reading course rather than 3-4

neat lintel
limber thunder
limpid niche
#

Is sacred geometry pseudo-math? Is it actually considered math? when I see something like the flower of life, I think of Set Theory, but it doesn’t seem like that’s the use and just seems like it’s not actually any real math.

inner finch
#

lololol

leaden torrent
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"pseudo-math" is too high a compliment

limpid niche
#

Lol

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So false math is a compliment lol

limber thunder
#

from wiki

Sacred geometry ascribes symbolic and sacred meanings to certain geometric shapes
math doesn't care the slightest about the "symbolic" or moral meaning of numbers or shapes

limpid niche
#

Numbers are symbols though

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Moral meaning no

limber thunder
#

I don't mean symbolic in that way

limpid niche
#

Oh okay

limber thunder
#

it's as in, symbols that represent human values and virtues

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and things like sacred geometry and numerology are just that, finding patterns and giving them interpretations in terms of the (subjective) human experience

deep mango
leaden torrent
#

its not really mathematics at all

crystal stone
#

1 respresents wholeness and health

limpid niche
#

Could certain values be quantified somehow though?

leaden torrent
#

you can take whatever theological conclusions you want

crystal stone
#

4 is a really unlucky number for me

leaden torrent
#

but a mathematician would not study anything like "sacred geometry"

crystal stone
#

I don't mesh well with Libras

deep mango
leaden torrent
#

that said, mathematicians HAVE proved that the existence of God implies the consistency of zfc

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take this as you may

crystal stone
#

I've heard that God is a Libra, is there a chance for me?

limpid niche
#

Thanks for the answer guys, I appreciate it.

limpid niche
#

It just made absolutely no sense to me

inner finch
#

damn he had it on his clipboard ready to go

limber thunder
leaden torrent
#

"existence of god" means in the sense of godels ontological proof

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so im stating it in a misleading way

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for comedic effect

limpid niche
#

I thought people were just seeing something within it that I couldn’t figure out or notice

inner finch
#

im not going to read this but this is realshit

leaden torrent
#

but its a valid paper

inner finch
#

damn

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i heard ultra say this before but i couldn't find a paper for it last time

deep mango
#

I lost my water bottle cap on the train sully pandaScreams

inner finch
#

use ur mouth

deep mango
#

It came off somehow and water sloshed all over my backpack

deep mango
#

And then the train left

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And now its gone forever

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My favorite water bottle

limpid niche
#

I wrote a metaphysical proof before, but the thing is that I got a physics assumption wrong.

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I thought matter couldn’t be created or destroyed at all, but I didn’t realize it could be transferred. In other words E = MC^2

limber perch
deep mango
#

I have the bottle, the cap just came off

limber perch
#

the bottle is nothing without the cap

bronze pelican
#

the cap is basically a bottle with out a cap

velvet dagger
#

That's cap

mint patio
#

what's a p-adic number?

hollow vale
#

Hey, does anybody know if there's anything neat that comes with representing graph colorings as matrices. I'm thinking of the following: a matrix where the rows are vertices, columns are colors, and the entry i, j is 1 when vertex i has been assigned color j. Or, we could do a matrix where the rows are colors, columns are vertices, the entry i, j is 1 when color i has been assigned to vertex j. It seems like you could view a graph coloring as a linear transformation this way (taking "color vectors" to "vertex vectors" or vice-versa) but I'm not sure if that's interesting at all. Someone elsewhere said you can't get much info about the graph from this matrix so it might not be useful. Although I think if it's a complete multipartite graph, you should still be able to recover the adjacency matrix from the first matrix representation idea I listed.

bronze pelican
fathom swallowBOT
#

nYaminoid

bronze pelican
#

With the coefficients $a_n$ being in the range $0\leq a_n < p$

fathom swallowBOT
#

nYaminoid

mint patio
#

What’s their significance?

blazing pawn
#

the short answer is that you can "do calculus" on the field of p-adic numbers in a way you cant on Q

mint patio
#

Pog

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So it’s analysis related?

blazing pawn
#

Yes but it also has a lot of algebra connections

mint patio
#

Just from the name I thought it was NT

bronze pelican
#

Doing arithmetic with p-adic numbers is like doing arithmetic mod $p^n$ for all $n>0$

fathom swallowBOT
#

nYaminoid

leaden torrent
#

to be a bit more explicit

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theyre an alternate way to complete the rationals

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we can complete them by naively filling in the holes with sequences

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that gives us the reals

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but its often useful (especially number theoretically) to consider alternate completions

blazing pawn
#

is completion going to mean anything to feather

mint patio
#

Does the series always converge? Or can we only make a p-adic with certain ps only

It looks geometric but iirc geometric requires n < 1 to converge doesn’t it? I haven’t done series in a while…

Interesting. So can every real number be represented as a p-adic?

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Yes I know what you mean by completion

leaden torrent
#

no, reals and p-adics are fundamentally different objects

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theyre incomparable

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(except the rationals)

mint patio
#

thonk
Do they not have a computable value/something we can approximate?

bronze pelican
#

Just like you have the decimal expansion for real numbers you have the p-adic expansion for p-adic number, which is the formal sum i wrote above

mint patio
#

Ahhh okay okay

static loom
#

there are divergent p-adic sums

mint patio
#

What the

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That was gonna be my next comment LOL

static loom
#

it's relative to that absolute value

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like 1+1/p+1/p^2+... diverges because 1/p^n has a large p-adic absolute value

mint patio
#

Smth like ā€œso is there something like cauchy criterion that guarantees every series convergesā€

static loom
#

there is exactly cauchy criteria

mint patio
static loom
#

and for p-adics it's even stronger

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you just need |a_{n+1}-a_n| -> 0 for a sequence to be cauchy

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also if a_n->0 then sum_n a_n converges

mint patio
#

Right

static loom
#

lot of this stems from the ultrametric inequality

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a stronger version of the triangle inequality

mint patio
#

never heard of that :o cool

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I gotta drive real quick but I’ll be back in a min

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What subject/field would I look into to learn more about this?

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hi again

bronze pelican
#

I think a good place to start is the construction of the p-adic rationals and Hensel's lemma

mint patio
#

Okay

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Thank you

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what the

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This is crazy

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LOL

leaden torrent
#

they are just power series of a prime (or whatever p is) basically

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formal power series that is

bronze pelican
mint patio
#

I'm going through the Wikipedia article rn because it's more easy language but I'll keep looking into it

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So it's a different number system is all

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But it has nicer properties for some stuff

leaden torrent
#

formal power series means we consider the power series itself rather than evaluating it

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like

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you can view it as a sequence rather than as a sum

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and we just happen to separate the elements of the sequence with + symbols

bronze pelican
#

$\mathbb{R}$ is like the sun, while the $\mathbb{Q}_p$ are the infinitely many stars

leaden torrent
#

basically like infinite polynomials

fathom swallowBOT
#

nYaminoid

mint patio
#

stareFlushed ing your own Tex sully

mint patio
#

Like for this

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The power series would look like 1 + 3 + 1 + 3 + 1 + 3 + 2?

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But not 14

bronze pelican
#

You need to include the powers of 5

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Those digits are the coefficients

mint patio
#

So 1^5 + 3^5 + ...?

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or no

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gah I remember this it's similar to expansion of real numbers

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just don't remember the specifics

bronze pelican
#

No, its $2\cdot 1 + 3\cdot 5 + 1\cdot 5^2 + 3\cdot 5^3 + ...$

fathom swallowBOT
#

nYaminoid

mint patio
#

Ah

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That's the expanded power series right

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And then to form the actual number we just take the coefficients in front of 5^n

bronze pelican
#

Notice that in $\mathbb{Z}/5\mathbb{Z}$ that the multiplicative inverse of 3 is 2.

Also in $\mathbb{Z}/5^2 \mathbb{Z}$ the multiplicative inverse of 3 is $2 + 3\cdot 5$

And in $\mathbb{Z}/5^3\mathbb{Z}$ the multiplicative inverse of 3 is $2 + 3\cdot 5 + 1 \cdot 5^2$

In this way, the inverse of 3 in $\mathbb{Q}_5$ encodes the information of the inverse of $3$ in $\mathbb{Z}/5^n\mathbb{Z}$ for all $n>0$

fathom swallowBOT
#

nYaminoid

surreal sapphire
#

if a fool persists in his folly, he can become wise...

mint patio
#

Oh man

So Z/5Z looks like 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2? So multiplying 3 by 2 then taking mod 5 gives 1...is that right? I think that's it

This is cool though, thanks for the example

#

What do you mean by the inverse of 3 in Q_5?

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What is the inverse of a p-adic number?

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Ohhh okay

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So the inverse of 3 is 1/3 so it's 1/3 in Q_5

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Encodes information about the multiplicative inverse of 3 in Z/5Z

bronze pelican
#

$\mathbb{Q}_p$ is a field. The inverse of an element is some other element which when you multiply them together, you get 1

fathom swallowBOT
#

nYaminoid

mint patio
#

Q has negative numbers too right? That's why I was confused about inverse, can't you have additive inverses too? But I guess it should've been obvious because we don't care about addition here

bronze pelican
#

Yeah you have additive inverses too

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What is $-1$ in $\mathbb{Q}_5$?

fathom swallowBOT
#

nYaminoid

bronze pelican
mint patio
#

One sec

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fuck okay problem is I don';t actually understand the math behind how to find the terms of the power series LMFAO I didn't understand it over text (on wikipedia) so I just skipped that part

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I will do this after I'm gonna be busy for like an hour or 2 rn

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But I'll respond once I figure it out

bronze pelican
#

Yeha its okay, the construction of the p adics is hard to wrap your head around the first time

mint patio
#

I understood everything you said

rare pond
#

How do I do a math PhD so I can make money in industry afterwards

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@crystal stone

leaden torrent
#

doing a cs phd

deep mango
little vine
#

I'm focusing on stat and analysis

crystal stone
#

Mr. Berg

rare pond
#

@crystal stone mr bear

crystal stone
#

Mr. Berg

mint patio
mint patio
bronze pelican
#

Whats -1 in Z/5^2Z?

mint patio
#

24 yes?

bronze pelican
#

Yeah and 24 = 4 + what*5?

mint patio
#

Ohhhh there was my problem

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I was doing -1 + x*5 (mod 5) = 24

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okay so the secnod digit is gonna be 4 too

bronze pelican
#

Mhm

mint patio
#

Let me do the third

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So we have 124 = 4 + 4*5 + x*5^2 => 100 = x*5^2, so the third is also 4?

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sorry that took so long šŸ’€

bronze pelican
#

Yes

mint patio
#

Ah okay that's not hard

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Thank you PTY :D

bronze pelican
#

It turns out $-1 =\sum_{n=0}^\infty 4\cdot 5^n$ in $\mathbb{Q}_5$

fathom swallowBOT
#

nYaminoid

mint patio
#

Is -n always sum (-n mod p) * p^n in Q_p?

bronze pelican
#

So the 5-igit representation of -1 is -1 = ...44444444

bronze pelican
mint patio
#

Night night 😁 Thanks for your time

leaden torrent
uncut totem
#

hey when do we learn linear algebra

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anyone?????

surreal sapphire
#

what kind of answer are you looking for?

uncut totem
#

i mean what math subjects do you need to learn in order to learn linear algebra

surreal sapphire
#

know how to add and multiply i guess

uncut totem
#

i meant advanced linear algebra

surreal sapphire
#

like what?

uncut totem
#

wait let me send a screenshot

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i meant this

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@surreal sapphire

surreal sapphire
#

the prerequisites is knowing how to add and multiply

uncut totem
#

really thats it????

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but look

surreal sapphire
#

yes, that's it

uncut totem
#

at the screenshot

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oh ok

surreal sapphire
#

yes, this is a standard introduction to linear algebra

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its very self contained

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it could be a bit abstract, but there is no concrete prerequisite to prepare you for that

uncut totem
#

ok tq

surreal sapphire
#

maybe some intro proofs and logic kinda thing

uncut totem
#

but see

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bro see

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@surreal sapphire

untold sapphire
#

this is such a weird conversation

surreal sapphire
#

what am i supposed to be seeing

uncut totem
#

nvm

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leave it

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bye

surreal sapphire
#

i mean i know what is or isn't required to take linear algebra classes

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and calculus certainly is not

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i have successfully taken linear algebra classes without calculus

static loom
#

can't hurt you to take calculus first, derivatives and integrals are nice examples of linear operators

odd narwhal
#

they actually left lmao

surreal sapphire
#

am i toxic? sad

timid spindle
odd narwhal
#

they got frustrated because they can't read

odd narwhal
distant vortex
#

Lmao @ "bro see"

thorn brook
#

Hatcher has a book about k theory catThink

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Just noticed that lmao

devout nacelle
#

Apologise and bring back the user devilish

bronze pelican
neat lintel
#

i'm currently doing math as a hobby in my spare time after high school before I go to college. I already know some calculus and differential equations. I started at reading a book on discrete math by Susanne Epp, afterwards I read a book on precalc, now i'm going into calculus 1, 2 and 3 again. Should I read a book on proof writing before I go into differential equations and linear algebra, or should I do that before calculus?

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I know a bit of proof writing from discrete math, but not a lot

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then your good, just use a proof book as reference.

devout nacelle
#

You'll probably gain little from a "proofs" book if you've already done discrete math

bronze pelican
#

Hatcher has a book of Topology of Numbers

neat lintel
#

I struggled a bit with proofs in discrete math and skipped most of the problems, and just did set theory, graph theory etc. instead

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so i'm not really great at it

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I just heard it's good to get good at proof writing before you go further in mathematics

devout nacelle
#

Proofs can be (are usually) learnt in the context of a particular topic

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Typical choices for a first proof-based class are discrete math, linear algebra, real analysis

neat lintel
#

alright thanks

neat lintel
#

maybe this would help, it very quick

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thanks, i'll look into it

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but I thought of getting the book Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand, Polimeni, and Zhang or An Introduction to Abstract Mathematics by Bond and Keane

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just to get good at proof writing

#

for reference use book of proof, you can find a free pdf from author website.

#

but I can see that the pdf you gave me covers alot of good stuff, so that's great

swift sinew
#

How do yall typically remember material you've learned on a topic after you're done focusing on it. Like I feel like all of my classes are so disconnected, and "self-contained" that I rarely get to use what I've learned in other classes and then forget a lot of what I've learned. For example, I've forgotten so much abstract algebra, even the basics, because my other classes almost avoid utilizing or referencing it

static loom
#

do more math in your free time that does utilize it

eager crescent
#

Reread past courses regularly

swift sinew
eager crescent
#

Idk about others but I have terrible long term memory so I have to reread my notes every now and then if I don't do things that utilize past knowledge

#

By regularly I don't mean every other week

#

But something like every two-three months

static loom
#

I just work on stuff, and as I go I naturally realize things I may have to review and just review in the moment

#

I don't think it's wise to just constantly be going back and reviewing without trying to make progress towards something, you'll just constantly be stuck in the past imo

swift sinew
#

could you possibly expand a bit more on what you work on in your free time? I think I just have a hard time thinking of stuff to occupy my free time with since i've only ever really done math in a class setting

eager crescent
#

Don't you study outside of class time ?

static loom
#

I guess it depends, are you a math major or not

#

if you're a math major, you sound like you're in the wrong degree

swift sinew
#

Gator, When i say class setting, I just mean learning math for a class. And yes that does involve studying outside of class.
M, and I am a math major and in my senior year so I don't think that's quite the conversation to be had

deep mango
hollow grotto
#

LOL

eager crescent
#

You can pick up books that aren't directly related to what you study to delve into the topic. Researchers usually work on interesting questions that arise in research (either ones they found while doing their own research or reading other papers, or questions that were brought up in the community) if that's your question

swift sinew
#

Ah ok. Also I'm a bit confused by the reactions to my message. Is it kinda frowned upon to not have experience delving into other topics in your free time at this stage?

eager crescent
#

Eh I think it's fine. The priority is always to understand as best you can what you are seeing in class imo. Delving into one topic or another is if you have more time and want to.

#

Depends on what your goals are after undergrad too

steep mountain
#

depends on what you want from math

swift sinew
#

That's kinda the thing, I've put an absolute ton of time trying to decide what I want to do after undergrad and just cannot decide. Even now, I'm afraid of doing something that I think I'll enjoy and later realize that I don't actually enjoy it and end up wasting valuable time. That is precisely the reason why it's taking me five years to graduate tbh.

#

I enjoy being around math a lot but rarely have the mental energy and attention span to dive into something deeply that isnt required for a class. And that has definitely limited how much I've been able to get out of math

eager crescent
#

Do you at least have a list of things you want to do ?

steep mountain
#

there is a lot of methods to realize the things you might be passionate about
i think math itself is a great tool to anything you might do later tbh its not a waste of time

eager crescent
#

Or do you not know at all

#

Yeah you can continue for a masters in almost any other field with a maths degree

#

Including maths, of course catThin4K

#

If it's your senior year you should really try to figure out what you want soon since depending on which country you're in, applications to grad school might be soon

swift sinew
#

Regarding timing of applying, I'm going to take a gap year to settle into the country that I'm moving into. But I have a semi-good idea of what I want out of a career, but not necessarily what specific field I'd want it to be in. And whether its a good idea or not, I'm not sure this is actually the conversation that I'm interested in having. I think I'm moreso interested rn in finding a way to get myself to spend more free time on math since I have yet to successfully do that

#

I'm also getting the vibe that this conversation might be getting a bit too personal and out of the scope of what this channel/server are meant for

eager crescent
#

Do you have enough free time to do more maths besides studying?

#

If yes then you just have to pick up any book in a topic you like and work at your own rythm

swift sinew
#

Oh yes absolutely, I just don't know what to bite my teeth into. I notice that when I've decided to delve into something, I often am more attracted to another shiny topic and have trouble keeping myself on the first topic

eager crescent
#

If you don't have a good idea you can just choose one of your classes, look at the recommended books and pick one

swift sinew
#

To just try to get a deeper understanding for what's going on?

eager crescent
#

Yep

#

Also to see if you like the topic

deep mango
#

I dont "delve into topics" in my free time...

eager crescent
#

You have free time ?

hollow grotto
deep mango
#

I play video games, hang out with people, enjoy my day, find interesting places to go...

eager crescent
#

I mean you also use some of that time to do maths surely

deep mango
#

I do what I need to to satisfy the math I want to learn, and I don't do much more than that

#

And I don't consider that free time, that's part of work

pale orchid
#

i'm with ryc on this one

deep mango
#

I will never review my notes from an algebra class because I do not care to remember anything from that class

pale orchid
#

poor work-life balance will get you nowhere fast

deep mango
#

And if I ever need to remember anything from it, I will go look in a textbook and see what it was I needed to know

#

And it will take a few minutes to relearn cause the connections were already built in my head a while ago

#

This mindset works for me because I'm very productive when I need/want to be, and yet I keep up a very healthy work-life balance imo

cold needle
#

someone said that math is just a job

#

i am trying to internalize this bleak tough because everyone so competitive oog

#

or it feels like it

deep mango
#

I try as much as possible to separate non work things from math (besides being on this server).

#

Not like "try"

swift sinew
#

So is the reason you have a vast understanding of topics because you use them a lot? becuase that's what Im having trouble with, my classes rarely require me to know anything from other classes, even fundamental ones like algebra

deep mango
#

I just... Do what I want in my free time, and it's not math 90% of the time

deep mango
#

I have a familiarity with a lot of topics and a deep understanding of the ones that are relevant to me

#

Which I use all the time

#

I.e. most kinds of analysis

#

And that deep understanding is probably aided by me having a pretty good memory + study routine (time management wise) so I can see where you're coming from there

hollow grotto
#

Analysus

deep mango
#

Like for me just having time to really think through a problem or an idea fully is what lets me internalize it

static loom
#

@swift sinew suppose you knew of someone who went to art school but only did the art that was assigned by teachers and didn't work on any art outside of class, would you think that was normal

deep mango
#

I should say even if I don't do math in my free time as much, I do spend A LOT of time thinking about problems and what I actually am supposed to be doing

deep mango
pale orchid
#

imagine a doctor that doesn't go to the hospital in their free time

static loom
#

what kind of grass? šŸ˜

pale orchid
#

smh

deep mango
#

Obviously there is a happy medium

latent forge
#

I think the point of the arguement is that mathematics is a different activity than doctoring and arting that you need to have extra practice outside the classroom

deep mango
#

But also if you talk to most professional mathematicians about what they do in their free time, you'll get something like "uh... I hang out with my family" 9 times out of 10

eager crescent
latent forge
#

Maybe its similar to arting because you need to do it recreationally to get good

#

Like you are asking mathematicians what they do outside of math?

deep mango
hollow grotto
#

Imagine you are good in math, that is only when you are me but you are not so obviously math is not for you noob go code

latent forge
#

Im talking in terms of solving problems

deep mango
#

Maybe that's cause I have been in really rough programs in terms of difficulty

steep mountain
#

i don't think its necessary for everyone to be THAT passionate and invested on there studies
having free time to do other stuff is for 95% of people needed
if you chose to spend more free time studying i mean hey good for you man but dont force yourself to do so just do what you enjoy imo

ashen river
#

Ryc you should see Subhashs Khots interview

eager crescent
#

Eh you don't need to enjoy maths

ashen river
#

"what do u do with your family" "i teach my son math"

eager crescent
#

Physicists don't necessarily enjoy maths even though they may do a bit of it

deep mango
ashen river
#

Khots son is probably better at math than me

#

Also outside of literal job, hanging with family + friends sounds ideal

#

What a wonderful life that would be. Haha

inner finch
#

jujjy jaja

eager crescent
#

Obviously you still need "real" free time

deep mango
#

Idk I used to beat myself up over how my best friend could and did literally think about math every waking hour, and talked to me about it all the time, and that I couldn't do that

hollow grotto
#

Lol friends and family what

inner finch
#

yeah that's kinda unhealthy sotrue

deep mango
#

And then I got used to it and realized I was learning just as quickly just doing what was healthy for me

inner finch
#

imagine wanting to do math

deep mango
#

It's healthy for him and that's fine

#

We're just not the same person

ashen river
#

I can't do that either and I'm worried about that too 😭 good to hear that you got over it

latent forge
#

Yea I think I was putting myself down for not being as obsessed with certain math topics as I thought others were, but I realize Im just as obsessed but with different parts of math

ashen river
#

I need human relationships lol

deep mango
#

I'm kind of glad I was forced into this realization

wicked plank
latent forge
inner finch
#

bu tao rune

swift sinew
#

just an aside/closure: ryc I think you've actually helped me find the heart of my problem because I agree that I only really need to think through ideas fully to internalize them long term and I would be surprised if in my first couple years of undergrad, I failed to put in that effort and that's why I dont remmeber much of the material

inner finch
#

fireeeeeee

#

dun dun dun dun dun dun duun

deep mango
#

But I also understand the perception that, if you don't go to a super intense program, you might need to supplement with your own stuff in order to be competitive in a very hypercompetitive application-driven space

#

This is more a practical thing than a philosophical thing

#

But imo it is more important lol

#

So

inner finch
eager crescent
#

If you don't do anything that uses the material you'll end up forgetting it after a certain time no matter how well you understood it at the time

ashen river
#

I beat myself up because my dad can work like almost every waking hour

inner finch
#

when you're more healthy mental wise you'll put out better math

ashen river
#

And i cant

deep mango
eager crescent
#

I bet if you just look at some notes you'll start remembering things

inner finch
#

ppl have different tolerences

#

like my dad has been

wicked plank
inner finch
#

for the past 3-4 years going out to work at 6 and returning approx 12 at night

deep mango
#

it is fine sotrue

swift sinew
#

I really really appreciate all that insight, advice, and help

inner finch
latent forge
#

wtf

#

why cant mental health be fake

#

its real and it sucks

inner finch
#

its just how it is ukwim

#

some ppl are more used to it than others

deep mango
eager crescent
#

Mental health? What's that

inner finch
#

Dont discount the other stuff you were hearing though! Trying out other styles of working that you dont expect to help can be surprisingly productive and fun

eager crescent
#

Robots don't need mental health

inner finch
#

new copypasta just dropped sotrue

deep mango
#

Like sometimes for me I get into slumps with my usual working style and I need to change to something more recreational and exploration based to motivate myself

#

Usually it's just for a little bit and then I get inundated with coursework again and need to just stick to that lol

latent forge
#

lol

#

ryc

crystal dagger
steep mountain
latent forge
#

this is main reason why i contemplate going into industry and living a slow life

#

i dislike that i have to focus on coursework even though i like the coursework

#

it just feels like I lose freedom

ashen river
#

Yeah lol doing coursework does feel like saying "yes sir šŸ™‹ā€ā™‚ļø. Whatever you say" even moreso than working a real job

#

Still

#

I've been trying to see how far ahead of coursework i can get

#

Like studying all summer

#

Bc that way I'm free to do extra work if i want to right

#

šŸ˜‚

#

Freedom regained

latent forge
#

lol i thought it would work out

#

i tried this summer

#

but i dodnt have good enough consistency

#

so i didnt accomplished much

ashen river
#

Yeah. It helps that i had a super structured life back at home

#

Now that I'm in NYC

#

No such thing as structure here lol

latent forge
#

where in

#

im from

crystal dagger
#

as a researcher i feel you may get good freedom

latent forge
ashen river
#

NYU :-) I'm not from here but my dad's family is. Im actually hanging with them right now

pale orchid
#

in germany, many positions handle work hours on "trust basis"

#

you don't even need to go to the office

ashen river
#

Huge fan

pale orchid
#

just produce results

steep mountain
latent forge
#

i would move to germany

#

but idk german and history

pale orchid
#

neither do many phd students lol

ashen river
#

My dream is being reincarnated as a brilliant french mathematician

latent forge
#

im a lil spooked about europe ngl

crystal dagger
ashen river
#

German mathmeticians are intense lol

crystal dagger
#

Germans are intense.

crystal stone
#

I like the American higher education system a lot, I think there's just so much flexibility in how you can be a student

ashen river
#

I'm CS not math. Italian CS grad students are intense too

crystal dagger
#

cs kekw

latent forge
#

i like american higher education besides forcing gen eds

#

id also not like to be in america tbh

ashen river
#

I promise it's the Mathier side of CS

#

Hence why I'm always here

latent forge
#

actually thats false

crystal stone
#

But it is a pain

latent forge
#

i just wish my location was less political snd we had less political conversations

crystal stone
#

The US in general is very political

latent forge
#

yea

#

i really hate it ngl

crystal stone
#

Everywhere I've been politics has been front and center

pale orchid
#

avoid all of europe then haha

latent forge
#

yea

ashen river
#

I wish I was in a magical place that was the research triangle in North Carolina except theoretically focused instead of focused on application and no political tomfoolery

latent forge
#

i have a particular aversion towards europe especially as someone who never went there but has only met european international students

#

they are nice for most part

crystal stone
#

You're getting a very narrow viewpoint

#

If it's just international students

#

I mean, I only spent like 6 weeks in Paris

ashen river
#

North Carolina is such a good place to live... So much nature and people are so friendly

ashen river
#

Schools are aweful tho

crystal stone
#

NCSU is good

ashen river
#

Oh yeah i mean

crystal stone
#

UNC Chapel Hill?

ashen river
#

Highschools are awful

latent forge
#

yea narrow viewpoint rip

ashen river
#

Like pre college

crystal stone
#

oh, schools are bad everywhere

#

Even when they're good, they're really not that good

#

It's just like, less degrees of bad

latent forge
#

i just need to get pro math research experience and then i can think about where to live around the world

crystal stone
#

I think schools for k-12, even some university courses, are too fixated on micro assignments, and micro tasks

#

Like if you have to write an essay

deep mango
#

I like microtasks

crystal stone
#

You have 2 rough drafts, you have to idetify your topic sentences, thesis statement, supporting evidence

#

Then you just piece it together, and if you don't do any of the parts by itself, but instead opt to do the whole essay

ashen river
#

My hs was super focused on essays lol. It was mostly kids wanting to go into law and medicine

crystal stone
#

You get marked down

ashen river
#

Now that I'm in CS it's like

#

What a waste of my time

#

šŸ˜‚

deep mango
#

In real life you do big projects by breaking them up into micro tasks, and someone should definitely teach you how to do the breaky down bit

#

I only learned this in my data structures class

#

Never anywhere else

crystal stone
deep mango
#

(academics wise)

crystal stone
#

Did you state you used the subtraction principle?

deep mango
#

No of course not

latent forge
#

thats becsuse ive seen that problem before

crystal stone
#

Exactly, that's what micro-tasks amount to in the k-12 system

steep mountain
latent forge
#

if i ask x+146=37

deep mango
#

Well the point is

latent forge
#

ofc ur gonna microtask jt

ashen river
#

I agree with moonbears, American education is super dumbed down

#

HS education

crystal stone
#

I agree that breaking up large projects into smaller manageable chunks is a very useful skill

#

Especially in Higher Ed for complicated stuff

ashen river
#

Even when it's a hard topic like AP euro or smth

deep mango
#

I can write an essay now and not think at all about topic sentences, and the essay will be good

ashen river
#

Gets spoonfed to u

crystal stone
#

But they apply it to the most rudimentary things

#

That 95% of students don't need assistance with

deep mango
#

But when I tried to do that in middle school I wrote a messy piece of shit

latent forge
#

do they qq

#

i wish my classes had more examples

#

too much theory not enuf examples

#

imo

crystal stone
#

See if it works

latent forge
#

oh good point

crystal stone
#

If they say no, ask them where you can find more examples to read up on

#

šŸ¤·ā€ā™‚ļø

deep mango
#

Similarly you'll talk to people who have no idea what x is if 5x + 2 = 12, and you and I can just look at it and go "it's 2. Just look at it!" because we just look at it and 2 pops into our head

eager crescent
steep mountain
deep mango
#

But i dont see how you can teach 2 popping into someones head

ashen river
#

Me when i talk to students who came from IIT to NYU

crystal stone
ashen river
#

Their arguments skip so many basic operations

#

It makes my head hurt

deep mango
#

I was taught "subtract 2, and then divide by 5" and then at some point that morphed into "2 pops into my head"

crystal stone
#

It's fine to teach that, but I'm specifically talking about micro-tasks where they specifically make you do that for like 40-50 problems

steep mountain
#

interesting way to explain building intuition

crystal stone
#

Like 5x + 2 = 12

deep mango
#

Ok, sure, I see what you mean

crystal stone
#

By the subtraction principle 5x = 10

#

By the division principle x = 2

deep mango
#

As opposed to like, teaching why the thing is working

crystal stone
#

It's good for a few examples, to give students some sort of structure or scaffolding

#

Especially if students need it

deep mango
#

Which is what some kids figure out of course

#

But

#

Always on their own

crystal stone
#

I almost always do problems without the scaffolding first, and ask students to think of the processes that led to the answer

#

And have them discover what the rules are

#

Overall, for the students that participate in this, do better (in my experience)

#

But if students just don't do anything, then of course this is worse

latent forge
#

btw

#

random question

crystal stone
#

Because I'm not feeding a recipe to solve everything

ashen river
#

My best calc class that i ever had (😌 still gives me chills it was so good) she'd teach us all the principles and then have us do huge amounts of problemsets on our own

latent forge
#

but as someone looking for math career, when should you worry about drug testing

#

do they do it for grad school

crystal stone
steep mountain
#

drug testing for what?

latent forge
#

ive been discouraged from doing so

pale orchid
#

i've never heard of them doing that at all

crystal stone
#

Ok, so then you don't need to worry

ashen river
#

R u thinking of trying to adderal your way into grad school? Lol

crystal stone
#

Grad schools can't drug tust

#

test*

#

The faculty would fail

#

C'mon

latent forge
#

lol

latent forge
#

also reus might?

crystal stone
#

No

#

They don't drug test

pale orchid
#

eating too many poppy seeds?

crystal stone
#

That being said

#

You shouldn't be doing drugs without a prescription

#

That's my two cents

latent forge
#

im just going to stay away from all drugs to stay safe

#

i trust you moonbears

crystal stone
#

I mean that's the wise choice

#

I've seen drugs destroy so many lives

#

Albeit by their own choosing, and I think people have a fundamental right to choose what goes in their body

#

But

eager crescent
#

I don't want maths to go anywhere my body

pale orchid
#

that is very much a different usage of "go fuck yourself"

eager crescent
#

My body, my choice

latent forge
#

yea

steep mountain
#

there is always that "i wont get addicted to it im just trying it" guy
best not to imo
there is better pleasures out there

latent forge
#

i dont want to destroy my brain

#

its a bit scary

eager crescent
#

Some drugs are very addictive

#

And they get addictive after the first taste

#

Others are less so

#

I don't know much about which is which, I just don't do drugs KEK

steep mountain
#

its not like alcohol where you can just say "ahhh whats the harm in doing it a couple times"
its made to build addiction

#

but its your choice after all

eager crescent
#

Your brain, your choice

pale orchid
#

until it isn't because you've developed a dependence on the substance

latent forge
#

yea its bad bad

latent forge
#

in that they build perspective

steep mountain
#

sadist

crystal stone
#

Not details, just friends and family

#

Doing drugs they shouldn't do. No one OD'd, but they definitely ruined their lives for at least 2 or 3 years

#

Luckily they got it together, but it came close to the point of no return

#

For my family, we were almost homeless when I was 9

pale orchid
#

i've seen doctors have to move out of the states cuz they had their license revoked

crystal stone
#

Due to my dads drug addiction

pale orchid
#

can't get a job anymore

ashen river
#

The best drug is trying to be a good person

pale orchid
#

for too many DUIs

#

(influence of prescription narcotics)

eager crescent
latent forge
#

damn

ashen river
#

Why try weed when u could try working i a soup kitchen

latent forge
#

actually

eager crescent
#

Oh is this weed that make you dumb?

latent forge
#

good points

eager crescent
latent forge
#

i was thinking alcohol and weed were fine

#

but not mixed

#

thats nono

vivid halo
eager crescent
#

Also people have different reactions to drugs, you never know if you're gonna have an uncommon reaction

ashen river
#

Binge drinking ages your brain

#

Don't do that either

steep mountain
#

its fine from time to time

eager crescent
#

Does binge drinking water also do that

steep mountain
#

as long as you know what you're doing

pale orchid
#

it kills you very quickly, yes

#

water intoxication is a thing

latent forge
#

yea

vivid halo
#

like if you're going to drink it's healthier to do a little bit more often than a lot a bit less often

eager crescent
#

Shit. My brain must be at least 23 years old now

vivid halo
#

yea all amounts being equal

latent forge
#

its healthier to not touch it ngl

vivid halo
#

oh sure

ashen river
#

Yeah. Drinking some beer or wine with friends

latent forge
#

same with psychedelics

pale orchid
#

a lot of people also forget that each bottle of beer is 200~500 cals

latent forge
#

how do people manage after a bad trip

pale orchid
#

you can lose weight very easily by cutting out drinks

ashen river
#

Every week is a lot better than pulling up to a frat party every month

steep mountain
#

since im skinny i guess i should drink more

#

gotcha

ashen river
#

Beer will fatten u up

latent forge
#

wtf is that reaction

vivid halo
#

idk it's pretty easy to avoid bad trips

steep mountain
#

busting out 6 cans of beer rn

ashen river
#

You can drink small beer

vivid halo
#

and even if you do get one it's like

ashen river
#

Not very alcoholic

vivid halo
#

usually not the end of the world

ashen river
#

Don't have to get drunk

surreal sapphire
#

there are no bad trips, only difficult ones

#

and thats kinda what you signed up for

latent forge
#

bad trips feel like end of the world wtf

vivid halo
#

I mean there are definitely bad trips lol

ashen river
#

Small beer (also known as small ale or table beer) is a lager or ale that contains a lower amount of alcohol by volume than most others, usually between 0.5% and 2.8%. Sometimes unfiltered and porridge-like, it was a favoured drink in Medieval Europe and colonial North America compared with more expensive beer containing higher levels of alcohol...

#

I'm actually 100% serious

#

Small beer can fatten u up

latent forge
#

im just confused how its not discouraging

ashen river
#

If u need

eager crescent
#

Porridge like

vivid halo
#

I mean yea it's discouraging for sure

surreal sapphire
#

i dunno, my best trips were "difficult" at least in part

vivid halo
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but like

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idk

eager crescent
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Just don't drink sully

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How is it discouraging

surreal sapphire
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also you can kinda hard cancel the hallucinations part at least of psychedelics

vivid halo
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I had a particularly difficult trip once and I'd still do psychs again if I had access to them

surreal sapphire
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i mean what

vivid halo
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just have to be like

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not stupid with them

latent forge
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stupid like dosages?

vivid halo
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no it's more like

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don't be stupid and take a bunch of psychs with a large group of people you don't know that well

surreal sapphire
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set and setting

latent forge
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yea man

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friends are super fucking nice

eager crescent
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Not taking any also works

vivid halo
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I mean I prefer to take them alone tbh

latent forge
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i mean for bad trips?

steep mountain
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ye i'd like to be the boring guy who doesnt trip and make sure everyone stays alive tbh

latent forge
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i want someone there incase i fucking die lol

vivid halo
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you won't lol

latent forge
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it feels like it

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its all psychological afterall

surreal sapphire
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its all temporary

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and as i said, you can hardcancel the hallucinations

latent forge
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yeah but it can feel like forever

vivid halo
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worst that happens is you get like really incredibly anxious and freak out for a bit

latent forge
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you cant hardcancel delusions

surreal sapphire
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ofc this requires access to more drugs lmao

vivid halo
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so you just like

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lie down and let it happen

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helps to have some xanax to abort the trip

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if anything just knowing that you can do that if need be makes most of the anxiety go away

latent forge
#

wait wut

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xanax is antipsychotic?

vivid halo
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I mean if you take a xanax while you're on psychs

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it like

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hard cancels the effects

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and more or less aborts the trip

surreal sapphire
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benzodiazepines shut down the part of the brain that is responsible for most of the trip

latent forge
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i wish i knew

surreal sapphire
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benzos are kinda super dangerous though

latent forge
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yea

surreal sapphire
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not sure about xanax specifically but in general

vivid halo
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yea definitely

pale orchid
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you can die from an od with them, yeah. they're also addictive themselves.

latent forge
#

ng whats worst trip u had like?

vivid halo
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they're definitely really bad to fuck around with

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for very particular applications like this they can be worth it

surreal sapphire
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the od is not the main danger

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i know lots of people who (accidentally) mix them with alcohol

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and its super easy to die from that

vivid halo
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yea that's really bad

latent forge
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wait wtf

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nvm then

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i wish i didnt. know this

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good thing you brought up warning lol

vivid halo
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I mean I had some trip involving a lot of acid with people I didn't know very well and got really panicked and disoriented and had to call my dad and get picked up because I was freaking out lol

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was fine after that

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just very chaotic at the time

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could not talk coherently

surreal sapphire
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"dad i did acid again, pls come pick me up"

vivid halo
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got stuck in a bit of a time loop lol

latent forge
#

yea

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time loops suck

vivid halo
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yea it was somewhat frightening

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but it was just like

latent forge
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5 minutes feel like 3 hours

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so sad when it happens

vivid halo
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afterwards it was like "oh I know why that happened lmfao"

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and it was fine

latent forge
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just never ask for the. time

vivid halo
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mostly what set it off was like

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other people around me were freaking the fuck out

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which caused me to freak the fuck out

latent forge
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yes that adds to it

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bruh how is that not discouraging

vivid halo
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I mean I probably wouldn't do that kind of set and setting again lmfao

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maybe if that were my first and only experience with psychs I'd probably stay away from them

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I had enough really good experiences before that to know why that went wrong

latent forge
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so learning from mistakes in a way

vivid halo
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I mean yea it was kinda obvious why that trip went south lol

latent forge
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when anxeity and delusions are at their peak thats the scariest imo

vivid halo
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yea definitely very jarring

latent forge
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i wouldnt have balls to call parents like u anyways

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cus they arent in position to help

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also cant reliably focus to call anyone or look at phone tbh

vivid halo
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I mean I just needed to get out of there and my parents were always really clear about the whole "if you get into some shitty situation and need to be picked up we won't judge you"

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oh yea it took like

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a few fucking attempts

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for that call to make sense

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I think the first two were like

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total jibberish

latent forge
#

lol

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also someone said its all temporary

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i agree sorta to an extent

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i feel like somethings can be permanent

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but maybe we dont know

surreal sapphire
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there is more research into that now

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as psychedelics are used more and more in research

latent forge
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im convinced there are permanent effects

surreal sapphire
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i.e. some scientists think that microdosing will permanently alter brain structure

latent forge
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tbh idk what this is supposed to mean

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brains are really complicated and im sure lots of menial tasks have effects on our brains

vivid halo
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I mean lots of things have permanent effect on the brain lol

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I don't think there's any evidence for like permanently fucking up your brain from psychs, bad trips in particular

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other than cases of like schizophrenia where the evidence seems to point towards just triggering this earlier than it might have otherwise

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you can probably fuck yourself up more or less permanently if you're like

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taking heroic doses literally every week

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but that's silly

latent forge
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what would you consider heroic doses lol

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lol

vivid halo
#

I mean I've known people that took like 500ug+ doses every week for a while

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they got kinda fried for a while lmfao

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but ended up fine after they cleaned up their act for a while

latent forge
#

yes cleaning up act is important ig

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idk probably should stay away from drugs entirely if I wanna minimize developing mental illness

vivid halo
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yea the brain is surprisingly resilient, you can definitely go back to near normal even after insanely heavy drug abuse in a lot of cases

latent forge
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thats my top fear

surreal sapphire
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eh, there are some things to consider i.e. i would not suggest psychedelics to anyone under the age of ~25 as their brains are not yet fully developed

vivid halo
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yea

latent forge
#

bruh

vivid halo
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or at least a good deal of caution

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and awareness of mental health history in the family

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like you should stay away from them entirely if your family has a history of certain mental health issues

latent forge
#

i dont truly understand what that claim means even though ive heard it often, but I can blindly take advice

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yea