#serious-discussion

1 messages · Page 192 of 1

solid yarrow
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Yeah... the contour thingy is given.

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But I am just too stupid to figure out the two remaining complex integrals

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Like for fresnel it's supposedly some quarter-circle

latent edge
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yes :3

solid yarrow
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I tried calculcating the border of the circle. But the integral I get is...

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no

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I can't even solve it

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I was thinking of maybe showing that it's bounded by some sort

latent edge
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could be

solid yarrow
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But another thing I am wondering. When you self-study and get stuck on problem. Do you also put some problems on your "to-be-done proof list"? Or do you skip those? @latent edge (ping scary, pls don't hurt me)

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:3

hardy scarab
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Hello

neat lintel
latent edge
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I don't make lists like this

flat harbor
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everyone wanna talk abt uni entry rn... so bust

steel vessel
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I tried soba noodles

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and they're my favourite dish atm

flat harbor
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omg hi

steel vessel
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Soba noodles with soup

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hi

flat harbor
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soba cold?

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with a bit of wasabi?

steel vessel
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Warm and got cold later

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Since I was basically stuffing my mouth with meat

steel vessel
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and apple

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and berries...

flat harbor
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ooh

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thats mm fancy

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i shuld try that sometime

steel vessel
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definitely

flat harbor
steel vessel
flat harbor
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a decent amnt of work myself

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life cannot be dream

steel vessel
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no, it can't

flat harbor
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they say we still gotta try..

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but maybe to them life could be

steel vessel
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blo woke up and chose the meaning of life

flat harbor
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stay woke

gusty socket
left moth
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@empty rapids

empty rapids
sterile vessel
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yeahh

left moth
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So as a pharmacy technician, we organize and bag drugs for people (pretty straight forward)

sterile vessel
empty rapids
empty rapids
left moth
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we can also handle up to class 3 drugs, but pharmacists can handle class 2 drugs. Class 1 drugs are entirely banned in America

left moth
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I gotta be careful tho bc not everyone will take it well

empty rapids
empty rapids
left moth
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Class 2 drugs are stuff like adderall

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Which I really need as someone who has ADHD but they keep being back ordered😓

sterile vessel
empty rapids
sterile vessel
empty rapids
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💀

empty rapids
sterile vessel
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just do it

empty rapids
sterile vessel
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who's starting out in a vicious world of oppression and angst

empty rapids
empty rapids
sterile vessel
empty rapids
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you could say its almost my middle name

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and by almost my middle name i mean its my first name :>

left moth
sterile vessel
empty rapids
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i answered every question didnt I blobsweat

sterile vessel
empty rapids
empty rapids
empty rapids
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:>

sterile vessel
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with the answers

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he's too old so forgive ya broiee

left moth
sterile vessel
left moth
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@empty rapids btw how are you liking calculus 3 and differential equations so far? What are you learning in ODEs?

empty rapids
# left moth <@764342735732867072> btw how are you liking calculus 3 and differential equatio...

I think they're both pretty interesting and relatively easy, I've been learning about techniques for solving odes like first order linear odes, bernoulli odes (basically linear after a substitution), homogeneous odes just using a substitution, exact odes using the total differential, using reduction of order/variation of parameter to solve second order linear odes given one of the linearly independent solutions. Then you can tell if two (or more) functions arelinearly dependent or independent using the Wronskian, which is basically the determinant of a matrix based on these functions and their derivatives. Then there was also existence and uniqueness theorems for first order odes and second order linear odes, and we also learned how to graph slope fields better by using the first and second derivatives to find behaviors of general solutions....

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i may have went into too much detail but im trying to see what i can remember off the top of my head LOL

left moth
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Easy? Wow I think that calculus 3 is hard, maybe its the combination of classes and my work schedule

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I think it can get difficult but it’s very manageable

empty rapids
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i, for instance, don't have a job as well ☠️

left moth
broken thicket
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Hello!

left moth
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Hello

empty rapids
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i think odes is a little bit harder ig idk

left moth
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Okay the difference between a 96% and a 100% is nothing

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Literally it’s like if you made some silly algebra or arithmetic mistakes

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Are you taking any other classes?

empty rapids
empty rapids
left moth
empty rapids
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honestly the english is the most annoying one 💀

left moth
empty rapids
agile fiber
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all odes are either linear, in which case it's just linear algebra, or nonlinear, in which case it's hard

empty rapids
left moth
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I’m wondering if I’d be more consumed by calculus 3 this semester or differential equations next semester

empty rapids
left moth
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I’d be taking differential equations and physics 1 next semester and I might retake chemistry 1

empty rapids
empty rapids
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😂

left moth
empty rapids
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i mean there also a bit of overlap in odes

left moth
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Not 100% but maybe 70-80% of conepts overlap so far

empty rapids
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like total differential (for exact d.es) and partial derivatives ig

empty rapids
left moth
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Bruh ODEs and physics 1 will feel so different bc the level of math is so different

empty rapids
left moth
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Calculus 3 applies to physics 1 but only if you already understand the physics concepts which I don’t

empty rapids
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wait btw how do you think difficulty calc 2 to calc 3?

left moth
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Bc most of the math in the class is just algebra…from a formula sheet

empty rapids
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pretend this question made sense you know what i mean 💀^

empty rapids
left moth
agile fiber
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physics education is interesting because the level of math you need to get the concepts is usually a class or two ahead of the level of math you use to do calculations

left moth
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Dish, washer, and whatever methods…those haunts me. I got like a 60% on that exam

empty rapids
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like the more conceptual XD

left moth
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Those things probably traumatized me lol

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I really enjoyed Taylor series

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I got like a 85% on that exam without studying bc I didn’t have time to bc of my tutoring job

empty rapids
agile fiber
left moth
empty rapids
left moth
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Bc I was using double integrals for this one rocket problem in my physics class and that’s calculus 3 material but most of my class were just learning power rule with derivatives for the first time

left moth
empty rapids
left moth
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I don’t wanna say that calc 3 is easy just to eat my words later on

empty rapids
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like yeah i havent gotten to the vector calc stuff so i might eat my words later 💀

agile fiber
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half of vector calculus is learning an entire alphabet of derivatives and the other half is learning the fundamental theorem of calculus 3 times

empty rapids
left moth
# left moth Bc I was using double integrals for this one rocket problem in my physics class ...

My professor was like:

“dim sum, how did you solve this?” so I could say it to the class

me: you’re basically given the final position s2 which you can use to isolate a1 by adding together a double integral being s1, another double integral being a2 which is just gravity, and an integral that accounts for the change of position due to momentum.

Him: “Yeah, I can’t show that to the class.”

empty rapids
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i dont like the fact that theres "theorems" tho :l

left moth
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After class I told him that if I wrote what I did on the board, my class would’ve panicked lol

empty rapids
agile fiber
empty rapids
empty rapids
left moth
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The difference quotient

empty rapids
empty rapids
# agile fiber

you keep showing this but i never know what it means <:) 😭

left moth
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Honestly I would’ve lowkey enjoyed seeing all of those horrified faces lol

empty rapids
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imagine the professor pulls one over you and gives you the most horrendous physics problem ever seen to man 💀

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the students would be even more traumatized but... XD

agile fiber
empty rapids
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☠️

left moth
empty rapids
left moth
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I don’t think I would be able to use differential equations in physics 1 though

empty rapids
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i mean maybe like seperable but 💀

left moth
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Calculus 2 is a coreq for our physics 2 class here but apparently the class is mostly just algebra as well

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Like bruh

empty rapids
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especially when they hype up calc 2 in difficulty and then i get there and realize they were hyping it up for nothing 💀

left moth
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Me too

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Because calculus literally exists just because of physics

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How are these classes so separate?

empty rapids
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like physics should just be "here's some facts on how math applies irl, now use these facts to figure out how to solve this problem"

left moth
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🌳 🍎

empty rapids
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granted that COULD be hard but i feel like with practice and understanding....it really shouldn't be

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*as long as you have time and are not taking 2 other math classes and working a job at the same time 🗿

left moth
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lol

left moth
agile fiber
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a lot of physics teachers take the approach that the difficulty in physics should be from setting up the math rather than the math itself

empty rapids
left moth
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That’s also an interesting point

empty rapids
left moth
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The calculus is can be considered a shortcut

empty rapids
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but setting up math seems like it can be learned

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fully learned

left moth
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Unless you’re dealing with nonconstant acceleration in physics 1 which idk if you do

left moth
empty rapids
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i rate things by difficulty on how hard it is to get a deep understanding

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lol

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physics is...wel....physics

empty rapids
empty rapids
left moth
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I’d like to ask someone who’s understand better if I’d be able to use differential equations in my physics 1 class lol

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Sometimes scaring people with math is cool🙀

long ferry
left moth
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How?

long ferry
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Although the use case depends, you could always abuse measure theory and the like

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Physicists don't delve into the topic early on

left moth
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Idk measure theory lol

long ferry
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What topics are within this physics 1 class?

left moth
plain parcel
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Who do we think are the most whimsical mathematicians? Like, the areas of math with the best names for stuff

long ferry
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However, the ones with most potential might be the high general areas, such as category theory or model theory

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I do wonder whether future mathematicians may employ slang when naming constructions

plain parcel
coarse bridge
neat lintel
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any indian?

tight marsh
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I probably asked this here years ago but I still can't get it out of my head
Do you believe it is possible for hypothetical alien species to develop math numbers concept in a completely different way than humans?
Humans arithmetic began as a way to count objects, so the humans developed the concept of natural numbers first
Then it gradually evolved towards the whole continuum, e.g., real numbers

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So for example consider a gas species that has no idea of differentiating between objects. Let's say their "vision" (or whatever senses) is kinda blurry and they do not sense the borders clearly. They develop the real numbers first, as the concept of counting for them is not obvious. And then they come up with natural numbers as the subset of R

river moon
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people that have few words for colors in their language use the same word for different colors as if they were the same color, so why not

tight marsh
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I don't really see the analogy here

river moon
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what's more important at the moment and natural will be developed first

tight marsh
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Chatgpt said their sensory systems would be distributed across the whole body
They would prioritize the perception of the change in environment like temperature, vibrations and electromagnetic field
So they sense the "gradients" of the environment

north topaz
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<@&268886789983436800> if someone's username is 'bigga', what should happen to that person?

fresh comet
plain island
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so 1) pls modmail instead of here
2) i suppose they would rather not get smalla

burnt ledge
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why wld anything happen to the person

lucid raven
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my money getting bigga and bigga 💯

north topaz
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there was someone with a really offensive username, but not racist or transphobic or anything

gusty socket
north topaz
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like "f*ck your mom's p-"

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and then I ModMailed

burnt ledge
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ijust rememebered that christian rap

north topaz
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someone else pinged mods

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and roketto it was actually banned that person

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and banned them again for rejoining

plain island
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(roketto had seen the modmail and was talking about it)

north topaz
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okok

gusty socket
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we love roketto

finite wave
wanton bough
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How can electrons be fundemental particles if they emit photons when jumping to a lower orbit

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Were the photons sticked to the electron giving it energy

inner canopy
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no the photons are created when the electron loses energy

wanton bough
vivid halo
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electrons and photons are both fundamental particles, photons are how the electromagnetic force is communicated in the first place

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or rather, the electromagnetic field is what gives rise to the electromagnetic force, and photons are localized oscillations in that field

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when two electrons repel each other, you can think of this as happening because there is some (virtual) photon that communicates this repulsion in the first place

wanton bough
vivid halo
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the photon isn't made of any smaller things, neither is the electron

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both are localized oscillations in their respetive fields

wanton bough
vivid halo
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well that's not quite what is happening

knotty comet
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can u help me with functions homework

solid snow
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!help

quasi jettyBOT
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To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

vivid halo
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like mathematically speaking there are two fields, let's call them the electron field and the photon field. These two fields are coupled and influence each other

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trying to find a good picture for this

inner canopy
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just for reference here a field is a function that takes in a spacetime coordinate and spits out some scalar or vector or tensor or whatever

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different fields model different particles and their interactions are tracked by an object called the lagrangian

vivid halo
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right the electron field is more complicated, it's a little easier to say what is happening with the photon field without lying so much and then you can imagine a similar thing happens with the photon field

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I'm trying to avoid saying too many big math words here and just giving some intuition

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but like imagine the photon field as like the surface of the ocean, with a bunch of random waves and oscillations

wanton bough
vivid halo
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when you have some actual localized wave in this field, that is a photon

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photons are localized standing waves like this, which propagate in some direction at the speed of propagation in this field (the speed of light)

wave.png
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electrons are like this too, they are standing waves in their field

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(it is just more complicated for electrons because rather than the field being something simple like a number at every point of space, it's some vector or tensor, so harder to picture)

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the point is these fields are coupled

inner canopy
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the photons are vector valued but the electrons are uhhhhhhh

vivid halo
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so certain things happening in the electron field can kick off an oscillation like this in the photon field, and vice versa

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when an electron emits/absorbs a photon like this, that's what is happening

wanton bough
vivid halo
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you have some oscillation in the electron field which kicks off some oscillation in the photon field

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this is true of basically every kind of particle and force in quantum field theory

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each particle has its own field

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when two particles interact, it's because their respetive fields are coupled, and oscillations in one field induce oscillations in the other

wanton bough
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that makes sense

gritty crater
wanton bough
vivid halo
vivid halo
gritty crater
vivid halo
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I guess there is a philosophical question of like

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is this actually real, or do we just have a very nice mathematical picture that seems to describe everything accurately

mellow geyser
inner canopy
vivid halo
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it works well enough to be incredibly useful at making predictions about how the world behaves, which is useful wisdom I suppose

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but for example vortual particles aren't really "real"

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nevertheless they do help us a lot with computing things like this

inner canopy
wanton bough
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mhm, I see

vivid halo
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like suppose you want to compute some mathematical details of how two electrons repel each other

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the picture we have in terms of virtual particles which seems to work even if it's not literally real is like

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you compute the probabilities (or "scattering amplitudes") for every possible way that these two electrons can exchange a virtual photon

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the simplest way is they just exchange a virtual photon, as in this Feynman diagram

Feynman-diagram-of-two-electrons-interacting-through-the-exchange-of-a-photon.png
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from this Feynman diagram there is some recipe for writing down some complicated integral which basically tells you the probability of this exchange happening

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but there are more complicated ways you can scatter

wanton bough
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Intresting work

vivid halo
north topaz
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at a conceptual level you just need to know that charge, mass, and baryon/lepton etc numbers are conserved

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also strangeness is conserved in non-weak interactions

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and like how to read it, so time in that diagram is going up

vivid halo
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like the next most complicated thing is like, photon is emitted, it spontaneously creates a virtual electron/positron pair, those annihilate back into a photon, etc

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these possible scatterings get like, arbitrarily complicated, but more complicated scatterings become less and less likely

north topaz
vivid halo
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what seems to work in practice is that you compute the probabilities for enough different possible ways to scatter like this, and you get predictions that seem to match what happens in reality

north topaz
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and that counting all the possible ways requires you to be extra, super methodical

vivid halo
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well right and part of the reason why this "perturbative" computation works so nicely for electromagnetism is like

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the coupling constant is the fine structure constant, which is roughly 1/137, which is a small number

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when you go to higher and higher order scatterings, the probabilities are scaled by powers of this coupling constant

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so by the time you're at some 10th order thing, your probabilities are scaled by like (1/137)^10

gritty crater
vivid halo
north topaz
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The theory of QED predicts a relationship between the dimensionless magnetic moment of the electron and the fine-structure constant α (the magnetic moment of the electron is also referred to as the electron g-factor ge). One of the most precise values of α obtained experimentally (as of 2023) is based on a measurement of ge using a one-electron so-called "quantum cyclotron" apparatus,[12] together with a calculation via the theory of QED that involved 12672 tenth-order Feynman diagrams

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wow

vivid halo
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but because the probabilities decay very rapidly with the complexity of scattering, you only have to do finitely many computations to get some desired numerical accuracy

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this is why this sort of method of Feynman amplitudes works VERY POORLY for something like the strong force

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the coupling constant is 1

north topaz
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ohhhhhh

vivid halo
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so the probabilities don't quite decay like this anymore

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but in some sense this perturbative computation with Feynman diagrams like this is just a mathematical trick, it's not really "real" or "honest" to what is actually happening, it just seems to work in practice in lots of examples

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if one is being more "honest" you would compute these things more directly

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this is what people tend to do when working with the strong force, where these perturbative computations don't work so well anymore

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in those situations, people tend to do things like lattice QCD

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like virtual particles aren't really real, but the fields are real

north topaz
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damn you seem to have quite the background in physics

vivid halo
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if you want to just compute what the fields are doing directly you might try to do this by discretizing the problem, and pretending the world exists on a lattice

inner canopy
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I think some people in the physics community might also argue whether or not fields are actually physical because we can't really measure them directly

vivid halo
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and then you try to model what the actual fields are doing on some lattice with discrete length intervals

north topaz
inner canopy
north topaz
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hence the name natural philosophy

vivid halo
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if we had an INSANE amount of computing power you could take the length intervals in this lattice to be close to the Planck length and probably you would get something which is pretty much indistinguishable to modelling reality, but in practice you never need to work at such fine scales

vivid halo
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I have a casual interest in this stuff and read about it when I'm bored, but I can't do a lot of the computations that actual physicists can do easily

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also what I'm saying is almost certainly not 100% accurate, what tends to happen is I yap about this stuff and it sounds like I know what I'm talking about, but when actual physicists are watching there are quite a few minor corrections that end up being made

inner canopy
north topaz
latent edge
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@flat harbor

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can confirm?

gritty crater
jagged forge
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you should see ng's integrals

vivid halo
jagged forge
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i'd say yours have more sigils

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and therefore look more like casting magic

vivid halo
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yeah okay that's fair

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but in terms of scale

jaunty ibex
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I remember deltoid sending me a paper about NT and it had cursed sums and integrals

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I took a peek and said "nope im good"

vivid halo
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a lot of the modern computations that physicists do with Feynman amplitides are done on computing clusters and involve millions of integrals

latent edge
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cursed

vivid halo
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there is some very nice motivic stuff around Feynman amplitudes though

latent edge
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true

vivid halo
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I have studied some of this from that perspective

boreal ridge
latent edge
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feynman amplitude and their corresponding graphs

boreal ridge
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why isnt my gif gifing

inner canopy
vivid halo
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there is a nice story of how the motivic Galois group (or some quotient of it, the amusingly named Cosmic Galois group) acts on these Feynman amplitudes

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and that action very nicely explains some very spooky numerical coincidences that exist between these amplitudes

jaunty ibex
latent edge
# jaunty ibex omfg yes

I found another paper but it was more algebraic and MUCH BETTER. they got the same results

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Analysts took the L this time

vivid halo
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there is a very nice dream of like, in some sense most of these amplitudes are redundant, and computations would be much simpler if somehow you only had to compute a small handful of "master amplitudes" and then understood how the action of this motivic Galois group turns these "master amplitudes" into general ones

latent edge
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im trying to remember what was the name of the paper

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I forgor

jaunty ibex
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I understand nothing but I at least react cuz funny

vivid halo
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like there are a huge number of amplitudes involving the number \zeta(3), up to some rational number

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maybe these all come from the same "master amplitude" (say the simplest one proportional to \zeta(3)) and the particular rational multiple is what this group action determines

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there are some toy examples where you can make this sort of idea precise, like for \phi^4 theory

vast wraith
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pretty

vivid halo
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these kind of numerical constraints are pretty striking, and optimistically one could use them to massively save on computation

true zinc
#

what the shiver is this stuff

vivid halo
#

physics \cap number theory shiver

latent edge
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I love these stuff ngl

vivid halo
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yeah unironically this stuff is very fun

latent edge
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thank you nG

vivid halo
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I want to learn more about graph cohomology stuff

latent edge
#

Graph cohomology owo

vivid halo
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my advisor has been thinking more about this stuff recently

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as have Francis and other people

latent edge
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cohomology would only make sense for like

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well the first two

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unless im missing something

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At least for homology

vivid halo
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by "graph (co)homology" I mean something pretty specific

latent edge
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H_0 and H_1

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oh

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elaborate

vivid halo
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it's very easy to define but really hard to compute

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you take the Q-vector space generated by connected graphs with orientation, say with no vertices of degree \leq 2, and no tadpoles (loops on a single vertex)

latent edge
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Oh so you are taking a Directed graph?

vivid halo
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undirected

latent edge
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oh so undirected but you put in orientation cuz cohomology

latent edge
vivid halo
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I mean you can have loops, just not self-loops based at a single vertex

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like this is still fine

96E00583-2A91-4612-B656-CB463199AF99.png
latent edge
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oh gotcha

vivid halo
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an orientation here is just an ordering on the set of edges of such a graph, one way to say this is like

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$\eta\in(\wedge^{e_G}\mathbb{Z}^{E_G})^\times$

fathom swallowBOT
#

nGroupoid

375570548316438528.png
vivid halo
#

where E_G is the set of edges with cardinality e_G

latent edge
#

wtf

vivid halo
#

like if e_1,...,e_n are the edges of your graph G

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then e_1\wedge...\wedge e_n is an orientation

latent edge
#

what is wedge?

vivid halo
#

quite literally the wedge product

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the point that matters is that if you swap the order of any two edges you pick up a minus sign

latent edge
#

ok I thought it was something esoteric

vivid halo
#

so any other orientation is equal to either e_1\wedge...\wedge e_n itself, or its negative

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you take this big Q-vector space generated by pairs (G,\eta) where G is a connected graph and \eta is an orientation, with no tadpoles or vertices of degree \leq 2

latent edge
#

okay fair

vivid halo
#

you mod out by some simple equivalence relations like (G,-\eta)=-(G,\eta) and (G,\eta)=(G',\eta') whenever you have a graph isomorphism G->G'

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this vector space is naturally graded or bigraded by like, loop number and degree

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the loop number h_G is self explanatory

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the degree deg_N(G) is a little funny, it's deg_N(G)=e_G-N*h_G, where N is some integer you fix

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for N=0 this deg_N is just the number of edges

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let GC_N be this resulting Q-vector space bigraded by loop number h and degree deg_N (so it's always the same underlying vector space no matter what N is, just the bigrading changes as N changes)

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now define a differential on this guy:

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G//e is the contraction of an edge e in a graph G

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so your differential is sort of the most obvious thing you could think of: you're taking the alternating sum of contractions of edges with the induced orientation

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graph homology is ker(d)/im(d) for this differential, it's again bigraded by loop number h and degree deg_N

latent edge
#

interesting

vivid halo
#

the H_0 is pretty well understood

vivid halo
#

there is a natural structure of a Lie algebra on this H_0, and the wheel graphs give you generators for this

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so for example the generator in degree 8 (in black) is the bracket [W_3,W_5] of the 3-spoke wheel generator W_3 and the 5-spoke wheel generator W_5, etc

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but the H_n for n>0 are like, really insanely mysterious

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since you like M_{g,n} you will be VERY pleased to know that any time you have a nontrivial class in graph cohomology, it produces a nontrivial cohomology class on M_{g,n}

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for example the 3-spoke wheel class W_3 corresponds to the fact that H^6(M_3,Q)=Q(-6)

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this also gives some indication of how complicated you should expect graph homology to be, since the cohomology of M_g is also awfully complicated

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there is a tight relation between the story for H_0 and multizetas actually

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like the wheels with 2n+1 spokes which generate H_0 as a Lie algebra correspond to the odd zeta values \zeta(2n+1) in a precise sense

#

their brackets correspond to multizetas, e.g. the generator [W_3,W_5] in degree 8 corresponds to \zeta(3,5)

#

but it's not so clear what the H_n for n>0 means in terms of periods

latent edge
latent edge
vivid halo
#

YEAH

latent edge
#

Source?

#

I mean papers

#

I wanna read more

vivid halo
#

this is the paper that I am pulling from, it's a fantastic read, as all of Francis' papers are https://arxiv.org/abs/2101.04419

arXiv.org
Invariant Differential Forms on Complexes of Graphs and Feynman Int...

We study differential forms on an algebraic compactification of a moduli space of metric graphs. Canonical examples of such forms are obtained by pulling back invariant differentials along a tropical Torelli map. The invariant differential forms in question generate the stable real cohomology of the general linear group, as shown by Borel. By in...

#

if you go to Francis' arxiv his 4 most recent papers are on this too

#

he's been doing some stuff with like, the cohomology of A_g and the cohomology of locally symmetric spaces for GL_n(Z) and SL_n(Z) and their relation to graph complexes like this

#

e.g. you can use these techniques to show that dim H^{2g+k}_c(A_g) grows at least exponentially in g for k=0 and for all but finitely many integers k>0, since we know the corresponding exponential growth statements for graph homology

vivid halo
#

if you have a candidate for a nontrivial class it's very easy to check that it is in the kernel of d, but very hard to check that it it isn't in the image of d

#

but with the techniques here you can attach a Feynman amplitude to this graph, and if that amplitude is nonzero then your class is nontrivial

latent edge
#

me after this

#

no more like

vivid halo
#

there is a paper my advisor wants me to finish now which plays a similar game with moduli of K3 surfaces

#

this is kind of the original paper that develops these methods and they apply to lots of other moduli spaces not just M_g

#

the mechanism that relates M_g to the graph complex is like, you have a proper morphism of topological spaces M_g->M^trop_g to the moduli of tropical curves

#

you get a space \Delta_g which parameterizes isomorphism classes of genus g tropical curves of volume 1; it is homeomorphic on one hand to the link of the vertex in M^trop_g, and on the other hand to the dual complex of the boundary divisor in \bar{M}_g

#

the top weight cohomology of M_g is isomorphic to the reduced homology of this \Delta_g

#

but then the reduced homology of this \Delta_g is isomorphic to graph homology

flat harbor
vivid halo
#

tropical curves definitely have a much more graph theoretic flavor to them, so that's maybe why it's reasonable that this approach relates this to graph homology

latent edge
#

I love computing integrals

#

I love computing integrals
TO A NUNNERY, GO!

vivid halo
#

in the case of moduli of K3 surfaces I'm just kind of working with what I know of the boundary of the moduli directly, so I'm skipping most of this story

latent edge
#

ok guys

#

I think it's time for me to be a geometer

#

I will do the switch

vivid halo
#

you're studying motives and M_{g,n} you're already a geometer

sonic flame
ocean harbor
stray fox
#

wtf

potent cobalt
#

Can sum1 please share their physical paper notes in where you are working with rational numbers with hella equations within them, bc I'm convinced that it's impossible to write rational numbers between the line margins on paper.

granite crag
fervent flame
brittle socket
#

I agree with printer paper

#

Its nice

vivid halo
#

or use lined paper where the lines are light enough that it doesn't look horrendous if you write between them

#

if you can't stand blank paper dotted paper is a good alternative

#

doesn't have distracting lines like lined or graph paper, but still has a dot grid for when you need this

gusty socket
#

speaking of, i just got another dot notebook

vivid halo
jagged forge
#

anyway it does the trick

vivid halo
#

yes it takes some practice if you're not used to writing with training wheels

#

but it gets better and it's worth sticking with it

jagged forge
#

my handwriting is so bad i've resorted to using large spacing and writing REALLY SLOW and REALLY BIG

#

at least when submitting stuff for other people to reaad

#

i'm basically a 3rd grader

fresh comet
#

we don’t talk about my handwriting

north topaz
fresh comet
light horizon
north topaz
fresh comet
#

here’s both

IMG_2032.jpg
light horizon
fresh comet
north topaz
#

if you can read it who cares

fresh comet
#

if

#

sometimes I can’t even read it blobcry

north topaz
#

I guarantee you what I wrote for my psets was like your handwriting

#

maybe better since I had to stop and think, so neater

#

but yes I did all of them on paper

fresh comet
#

this is a better notebook than the one I used for my psets

#

the writing looks a little nicer

#

I honestly should’ve just tore the pages out of the notebook when I used to write my solutions there

#

it probably would’ve helped

jagged forge
fresh comet
#

I can read it

#

can you read mine

jagged forge
#

i've been told it's readable with some effort

fresh comet
#

I can read it with nearly no effort

jagged forge
#

let's see

jagged forge
north topaz
#

I mean it helps the words are familiar cause topology or something

jagged forge
#

Now write mx'' = -k[x - A <stuff>] and get x'' + w0^2x = w0^2 A_x cos(wt) with w0^2 = k/m. This eq. is inhomogenous, so the <stuff> is a sum of a <primitive?> sol. and a homogenous solution

#

oh particular duh

north topaz
#

which will be very helpful for sociology

#

it was very useful in high school also

#

I got professionally assessed by an OT

fresh comet
fresh comet
north topaz
#

even though I know it's about damping

fresh comet
#

yeah see that’s a bad sign

north topaz
#

so it will be in phase with the

#

and then

#

.........

jagged forge
#

here's me trying to write more legibly

image.png
#

basically writing everything really big

north topaz
jagged forge
#

but i'm happy someone called me asian

#

because i am the least asian asian person to exist

north topaz
north topaz
jagged forge
#

my korean vocabulary consists of the names of korean foods that my mom makes

north topaz
#

I mean language is another thing

north topaz
#

it's okay if you don't

#

in terms of identity, who you feel on the inside

#

that's what I mean

jagged forge
#

i don't feel super connected to it

#

though i'm told koreans love pork and i share this 👍

north topaz
#

JOKBAL

jagged forge
#

had to look that up lol

#

i think i may have tried that recently actually

north topaz
#

honestly if you watch KoreanEnglishman + Jolly you might unironically gain some Korean culture

jagged forge
#

ngl i wasn't a fan skully

#

i don't think it was braised tho

jagged forge
north topaz
#

nice

north topaz
#

I've watched this also and it hit me in the feels

#

it's designed to be relatable to AAPI people in general

#

but like since you're actually (half) Korean

jagged forge
#

hmm

latent edge
limber thunder
#

don't post unsolicited advertisements here, we also discourage paid services in general

quaint cipher
#

what's this notation

image.png
surreal sapphire
#

probably real part

burnt ledge
#

yea thats real part

forest yoke
#

@ornate copper are u from france?

crisp bison
#

I'm from Thaïlande

forest yoke
#

ther' no way

vast wraith
#

mwahahaha

static loom
#

where do i buy nonvisual geometry and topology 🧐

deep mango
#

fomenko is so based

vast wraith
#

ok i was a bit worried about this "MyCopy" thing (i really don't trust springer, for good reason), turns out they've changed the aspect ratio, stretching every page vertically by a factor of 2.4 %, which us just enough to be quite clearly visible. i guess to fit this "MyCopy" banner on the front page hmmcat

burnt dune
#

i like this

kind shell
jagged forge
kind shell
#

nothing

#

lemme show you

fickle hound
fickle hound
kind shell
#

no

#

im looking for an image on google

fickle hound
kind shell
#

cant find it

#

@jagged forge my bad 💀

fickle hound
#

all that jazzz for nada

kind shell
#

wai

#

nvm

#

never insulting somones hand writing again

fickle hound
kind shell
#

show me and i will roast it devilish

#

do u code python

fickle hound
kind shell
#

ok

#

simple challenge

#

take 2 squares and a plane that goes from 0 to infinity. at 0, there is an immovable wall. if square 1 has a mass of 1 gram and is sitting between 4 and 6 with an initial velocity of 0, and square 2 has a mass of 100 and initial velocity of -1, how many times will mass 2 collide with mass 1? remember, mass 2 will push mass 1 againtst the immovable wall. this is a perfect enviroment with 0 friction, 0 air resistance. calculate this in python.

sturdy gulch
kind shell
#

again??

sturdy gulch
#

Idk I've seen it kind of often

kind shell
#

where is the code for it in python

sturdy gulch
#

Zero clue on that front lmfao

kind shell
sturdy gulch
solar ridge
#

hello and good evening

sturdy gulch
#

I think you'd just use conservation of momentum normally and use elastic collisions

sturdy gulch
solar ridge
#

so whats going on in here

#

who needs help

sturdy gulch
#

Tyler needs help with an elastic collision program problem thing on Python

solar ridge
#

python is a thing on here too?

#

lol

sturdy gulch
#

I mean i don't think so but it's in the same general realm? Idfk

solar ridge
#

lmao

#

hmm

#

i dont know nothing about python tbh

burnt ledge
sturdy gulch
#

There's a software channel but it'd kinda dead rn

solar ridge
#

i know some c++ but thats it

kind shell
sturdy gulch
#

I know basic Python but I'm not sure how you'd implement the collisions

#

Because I have the physics skills of a toddler

burnt ledge
#

just keep track of two velocities and while not (both positive and smaller is slower than larger) collide them appropriately

gusty socket
#

oh the actual software channel

#

yeah

#

that is more active

burnt ledge
#

the appropriate collision is smaller gets reflected, if smaller is negative, and a normal elastic two-body collision otherwise (which u can solve in the general case by hand )

limber thunder
#

stuff like matlab, mathematica, julia, prob packages like numpy/pandas to some extent

burnt ledge
#

conserve momentum and energy separately

#

this gives you two equations in two unknowns which u can solve simultaneously

sturdy gulch
#

I understand like a grand total of zero of the conservation laws 😔 like the idea makes sense but the units don't

vast wraith
#

a circle uwu

sturdy gulch
#

Like I understand some vague thing should be conserved through interactions, but not why that thing is kg m^2/s^2

burnt ledge
#

u know energy is proprotional to square of velocity right

jagged forge
burnt ledge
#

and proportional to mass

sturdy gulch
#

Yep

burnt ledge
#

thats good enough

#

whats ibis i heard of the polars is meant to be overtaking pandas but i never knew there was a multi way competition

sturdy gulch
#

But why conserved

azure horizon
#

Differentiate x^lnx wrt lnx

burnt ledge
#

bcs of differential geometry or somrthing idrk its just like that

jagged forge
#

really it's kind of doing something different in the sense that it's not implementing the dataframe execution code like polars

#

but it is a dataframe library and it's much nicer to use than polars imo

#

except the fact that it's relatively new

#

so the error messages and docs need some love

limber thunder
#

i also have never heard of either polars or ibis

#

not too deep into the data rabbit hole tbh

jagged forge
#

aanyway it's a godsend for me cuz i can use ibis which is a nice dataframe library, and have the backend be my company's user analytics database
so i can avoid writing gross clickhouse SQL code bleak

azure horizon
jagged forge
#

and then you can use the same tool whether you're dealing with databases or just processing some data locally like you would with polars

#

or pandas

burnt ledge
# sturdy gulch But why conserved

one of gods rules for the world is that energy is (not quite but very very almost) always conserved, we may never know exactly why. but there are mathematical situations where u can have conserved quantities appear see Noether theorem. and the conditions for an energy symmetry to appear are very very almost satisfied in real life, and exactly satisfied in simple models of real life, so "thats why" energy is conserved.

pure cliff
#

Haha

sturdy gulch
azure horizon
sturdy gulch
#

😔

#

What's x in terms of lnx

azure horizon
#

The answer that I get is (x^lnx).lnx but it is 2(x^lnx).lnx

sturdy gulch
limber thunder
azure horizon
#

Lemme try

azure horizon
sturdy gulch
azure horizon
sturdy gulch
azure horizon
burnt ledge
azure horizon
#

Just a random question in my booklet

sturdy gulch
sturdy gulch
azure horizon
#

It is 2(x^lnx)(lnx)

sturdy gulch
#

One sec 😭

#

I messed up smwhere

burnt ledge
#

there are other quantities with the same units that are not conserved

#

and other quantities that are conserved but have different units

azure horizon
#

Y=arcsinx/arccosx what does arc mean here?

static loom
azure horizon
slim niche
#

yo just asked a question in the help chat. now i cant find it lol. is there a reason to that?

sturdy gulch
eternal crow
#

then differentiating wrt y, u get 2y e^{y^2}

#

then substitute lnx back u get 2lnx x^lnx

sturdy gulch
chrome granite
#

is that math

#

where are the numbers

eternal crow
#

ln is log with base e

#

x and y are variables

pearl eagle
#

Is the khan academy digital sat good

#

Cuz i need to get better sat scores

#

Im from indonesia

burnt dune
#

yes

harsh geyser
#

do you guys know what to study for the MMATHS

ocean harbor
harsh geyser
#

wdym

ocean harbor
#

you asked what to study for math

harsh geyser
#

no like there is a competition called MMATHS

unborn meteor
harsh geyser
#

oh thank you

ocean harbor
#

oh wow I didn't know

limber thunder
unborn meteor
#

oh lol

harsh geyser
#

thank you kind strangers

eternal crow
#

i agree this math server has the kindest strangers in any servers I've been

true zinc
#

hiii chat

neat lintel
static loom
neat lintel
jagged forge
#

this place hurts me

neat lintel
#

I bet it makes you cry

static loom
#

I'd stick around but I gotta say goodbye

neat lintel
#

I'm not gonna lie, sorry if I hurt you

unborn meteor
#

LOL

static loom
quaint cipher
#

I thought it can be discussed here cuz it's not a formal question just a random thought

#

Sorry for bringing you trouble anyway, I've deleted

finite wave
sturdy gulch
#

might be dumb but i just used dot products for animating something and i have never felt so validated for liking math holy shit IT ACTUALLY FUCKING WORKS

sage mulch
#

snot product smugsmug

surreal jacinth
#

im going to change my pro nouns to she her and ask for homework help a second time

neat lintel
surreal jacinth
neat lintel
surreal jacinth
#

ok uwu

neat lintel
#

rule of the internet number 37

pulsar pagoda
#

dont know why this place is less chaotic than discussy

coarse bridge
pulsar pagoda
#

he was banned

coarse bridge
#

yeah lmfao

pulsar pagoda
#

doing one time read scanners is a pain

#

maybe I should take the L and do this with multiple loops

#

well not really an L but more of a pride L kekw

past pecan
#

Hi guys I m sigma

north topaz
fathom swallowBOT
#

higher's secret twin brother

1151031274413228043.png
coarse bridge
#

$\Sigma$

fathom swallowBOT
queen hornet
#

-algebra

past pecan
#

Yeah I heard ant that

#

Abt*

fathom swallowBOT
unborn meteor
#

<@&268886789983436800>

gusty socket
#

please don’t do that

pure cliff
#

I have been quarantined yet again

tawdry pecan
pure cliff
#

What friends

#

:friggten:

#

Jk

tawdry pecan
#

all of your friends

neat lintel
#

hi

pure cliff
#

U have

#

I don’t like this

#

Are u the one bullying me

tawdry pecan
#

whar

#

what symbols

#

i dont bully people

pure cliff
#

Can I send FRIEND REQUEST

tawdry pecan
#

sure!

pure cliff
#

aw

tawdry pecan
#

<@&268886789983436800>

agile fiber
#

<@&268886789983436800> advertisement

gusty socket
#

don’t advertise this here please.

vast wraith
#

tfw invariance of domain

#

i guess i need to learn alg top now

burnt dune
bronze pelican
#

Rodbet is just like me

vast wraith
#

on a whole other note...

#

> continues idly looking through texts recommended by my logic prof
> finds actual fire scathing review of book recommended by prof
> review mentions invariance of domain

#

actually i've been having so much fun reading book reviews

#

this one is just amazing, it starts "That there is something wrong with the present teaching of mathematics is indisputable." and elaborates for a full page about the general state of things, before turning to the book under review, namely henle's an outline of set theory.. "Consider the actual historical development of set theory" following with another page quickly summarising this history, mentioning some key facts from analysis and topology that influenced the developments of set theory (among other things brouwer's proof of the invariance of domain) before the bombshell, quoting henle's version:

image.png
#

Other than to suggest that he be raked over the coals, or at least flogged, for the sentence about Euclid, I do not want to attack Prof. Henle for having written an unscholarly book

#

the quote from Henle is actual comedy though

icy heron
sturdy gulch
#

holy shit smay is playing peak no way ?!

icy heron
# vast wraith

also, I was curious what book is this one about manifolds?

vast wraith
vast wraith
icy heron
#

I see, thanks catthumbsup

eternal crow
#

hi @void loom

void loom
eternal crow
#

ohh my name is reversed!

eternal crow
#

i see

#

android spells my name right to left

#

while ios is left to right

#

nope

#

android is left to right ans ios is right to left

#

@eternal crow

void loom
#

Sometimes I wonder why math professors wagecuck for like $150k/yr when they could make millions doing quant trading

jagged forge
#

wagecuck is crazy

small dust
#

your average math professor doesn’t know anything about quant trading

#

nor do they want to i imagine

void loom
#

Why don’t they at least be a software engineer at FAANG making twice their professor salary?

static loom
jagged forge
small dust
#

idk i’d be very happy making $150k doing something i enjoy even slightly and wouldn’t want to do something i don’t enjoy much for more money

jagged forge
#

$150k is like, way more than enough for most people

#

unless you want to live in.... idk manhattan

void loom
#

Not in the Bay Area / NYC

agile fiber
#

why would [insert profession] not decide to do [completely different profession] 🤔

jagged forge
#

well then you can live in new jersey or something

#

and take the train

#

i doubt most math professors could get into faang anyway

#

i mean step 1 you have to like programming

#

which probably disqualifies a lot of them

small dust
#

few of my math professors know anything about programming

jagged forge
#

yea that sounds about right ig

void loom
#

Do they know discrete math at least

small dust
#

of course

jagged forge
#

and the kind of programming you do as a software engineer is pretty different from writing python programs to compute things

#

you have to get used to crawling around blindly in large codebases, sifting through layers of code to isolate bugs, writing lots of tests, designing interfaces, blah blah blah blah

#

boring stuff that math professors would probably hate

pulsar pagoda
#

indeed

small dust
#

that would just make them instantly love it

peak tide
#

did someone say money

jagged forge
#

i mean honestly i'll say that money definitely can change how you feel about something

#

i forgot who said it but

#

absolutely nobody would be passionate about tax law if they didn't get paid for it

small dust
#

it wouldn’t change much for me if i was already making enough

void loom
#

Coding is not even the worst part of working at FAANG

jagged forge
#

yeah $150k is plenty skully

small dust
void loom
#

I would say dealing with quotas is worse

jagged forge
#

quotas?

void loom
#

And being forced to cut corners because you have deadlines

peak tide
void loom
eternal crow
#

hi @thin canyon

small dust
#

bungo sir hello

jagged forge
#

oh some bs performance review stuff where they cut X% or whatever right

peak tide
#

good evening layla ma'am

jagged forge
#

companies that do that are wild

hardy iron
peak tide
eternal crow
hardy iron
#

Yeah

#

Who were they again?

void loom
eternal crow
#

and yes we're 4 now

eternal crow
peak tide
jagged forge
hardy iron
peak tide
jagged forge
#

now imagine having to sit in standups for 2 hours bleakkekw i've heard it gets bad some places

hardy iron
void loom
peak tide
#

at one point i had more meeting time than work time in my weekly calendar

eternal crow
peak tide
#

that's when i finally started declining meetings as my default response

jagged forge
#

my brother's fiancee sometimes just has meetings from the beginning of the day to the end
but she's an engineering manager so

#

that's her job ig

hardy iron
eternal crow
#

brb

hardy iron
#

The main reason for the fall of manyland is that Philipp know nothing about math and he relies on ChatGPT too much

static loom
peak tide
#

i eventually got smart and blocked out 8am-1pm every day for "real work" but this designation was not visible publicly, it just showed me as not available

jagged forge
pulsar pagoda
peak tide
pulsar pagoda
#

oh bro

#

once I have my mvp

#

and I get those green bills

#

Ill bring rat to this hell hole

#

worst part is this shit is php

peak tide
#

horror

pulsar pagoda
#

He can squeeze 10 clock cycles out of a raw pointer allocation

#

im sure he can manage that shit

jagged forge
#

like how high up were you

queen pulsar
#

when do i use NPQ or NP/Q

peak tide
jagged forge
#

oh, interesting

thin canyon
#

Rip manyland!

peak tide
#

just called "senior software engineer"

jagged forge
#

i am just a regular software engineer

#

when i gave my talk at this event a few weeks ago i was presenting next to ceo's and staff engineers skully

peak tide
#

my previous employer had all sorts of pretentious titles like "master engineer"

jagged forge
#

master engineer clopencry

hard cairn
#

thats not pretentious

peak tide
#

i was too embarrassed to put that on my resume or linkedin haha

jagged forge
#

nobody says master engineer in software engineering

#

that's crazy

hardy iron
#

and there's offlineland but cow milks everyone who's using it

peak tide
#

i just used my original title (senior principal) before they went over to that nomenclature

hard cairn
void loom
#

Is applied computation closer to math or software engineering?

hardy iron
#

and there's thingistan but it's an elitist circle

thin canyon
#

I do not want to join but thank you

jagged forge
peak tide
#

what is applied computation?

jagged forge
#

ask anyone in the industry no respectable engineer has the title "master engineer" skully

peak tide
jagged forge
#

for IC it's software engineer -> senior -> staff -> some combination of senior/staff/principal/distinguished/whatever

peak tide
#

a friend of mine literally put "rocket scientist" on his business cards (back when people had business cards)

void loom
jagged forge
void loom
jagged forge
#

preferably not at a company with 10 people

peak tide
jagged forge
jagged forge
peak tide
void loom
peak tide
#

some companies put things like technical director somewhere in between principal/distinguished/fellow

jagged forge
#

the heck is a putnam fellow

jagged forge
peak tide
#

that's only good when you can have the title technical director without having to manage anyone

peak tide
void loom
peak tide
jagged forge
#

well that sounds different from engineering fellow ig

peak tide
#

yea there are a lot more engineering fellows out there than putnam fellows haha

void loom
#

Have any of you ever met a Putnam fellow?

peak tide
void loom
#

My landlord was 1 point off

peak tide
#

median score of 0 or 1
reminds me of the kolmogorov 0-1 law

eternal crow
void loom
#

But he got honorable mention

jagged forge
#

without becoming something different altogether like an executive or smth

eternal crow
#

oh wow

peak tide
#

i had to check the list of putnam fellows, i have met at least one of them (was my grad algebra professor)

jagged forge
#

oh nice

peak tide
#

check these chads who won four times each (the maximum possible)

image.png
jagged forge
#

sheeeesh

void loom
#

Reid and Brian were on my landlord’s IMO team in high school

peak tide
jagged forge
#

i see

peak tide
#

but it varies depending on how many people they give the title to ig

#

looks like apple has had around 12 in its history, only one granted this century

jagged forge
#

jeeeez

peak tide
#

and you're competing with woz himself if you want into that club

jagged forge
#

yea idk if im aiming for that lmao

peak tide
#

it's already damn hard to get to ICT6, let alone distinguished or fellow

jagged forge
#

wait so if ICT5 was equivalent to senior principal, what is ICT6 if not distinguished

#

staff principal?

peak tide
#

ICT6 means you have to be recognized throughout whatever larger org you're in (software engineering org in my case)

pulsar pagoda
#

has woz done cool stuff since he retired from apple?

void loom
#

Is it impossible or nearly so to become fellow without a PhD?

jagged forge
#

oof no recognition

peak tide
#

i dunno what title you'd give ICT6, it's above 5 and below distinguished

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i only knew a few ICT6's

#

most people will never get above 4 or 5

pulsar pagoda
#

sorry to dissapoint

jagged forge
#

damn microprocessor engineer with no phd

#

is that even possible anymore

pulsar pagoda
#

he is THE microprocessor engineer

#

bachellors back then were built different I guess

jagged forge
#

well i guess maybe you don't need a phd just to become a rank and file microprocessor engineer.... but i imagine nowadays if you want to be near the top...

peak tide
# jagged forge damn microprocessor engineer with no phd

depends on how you define it ig
i'm sure there are many hundreds of people at intel and such who work on microprocessors, probably most don't have phd's
and if they're anything like the intel engineers i've had to deal with, they are idiots

#

we acquired their mobile semiconductor business and iirc we only kept 11% of their people

jagged forge
#

jeez

#

apple acquired intel's mobile semiconductor business?

peak tide
#

yea