i'm conducting an experiment on how to study the theory effectively
there are i guess two main ways:
(1) read and take notes simultaneously
(2) read first, then take notes
so for the first one, there is the risk of going passive with the note-taking, writing down the symbols without focusing on their meaning. for the second one there is the risk of zoning out and just reading the symbols, again, losing their meaning
the problem seems to be that the processing of sheer symbols and processing their meanings might be disjoint and their natural tendency seems to be so
from my recent actions i noticed that (1) doesn't work for me as effectively as (2)
it might be that when i don't plan to write something down right away, i am more inclined to remember these things short-term as "i won't be able to check it later so remember it now in order to understand what comes next", and when i'm taking notes simultaneously it's "i have it written down anyway so i can take a peek anytime"
so now i'm testing the strategy of
read → try to understand the idea and memorize the elements → why all the elements are important → understand the construction in more detail and write it down
this is how i imagine my mind working:
it means that at first i start to remember the elements as points of its own but simultaneously my brain builds its idea on how they interact and then i notice the inner structure of how the elements are connected with each other in less obvious ways
this idea is cool to visualize how i imagine my thinking, because it shows how learning the topic reduces possible permutations and paths. i have this problem that when i start learning something new i see so many possibilities of what can happen to the elements that i can't discern between crucial and additional stuff. in order to use the knowledge i need to provide some structure
thus the main goal of optimized learning is to take the leap from "i memorized the elements" to "i understand their structure" as fast as possible
and so the strategy (2) might be more effective as it forces the memorization of the elements first and then it is easier to provide structure for them, where i would be defining order on something that's already in my mind. whereas (1) strikes at memorization and structuring simultaneously, it is too difficult for me to see at first in which direction the topic is going, i must know the next point
in a few days i will focus on how "the point" can be defined in this and how to characterize the connections
honestly tho this is some sorta pseudo graph theory and pseudo topology and i don't believe this could be as straightforward. otherwise nobody would ever post any study tips and we would have a field of study called "learning optimazation", this would be too big to go unnoticed. i wish it was so easy to just know how brain works and be able to build such an algorithm that would optimize the desired processes lmao
i wish i was a σ-field or something
side not is, i love this kind of thinking and i love to analyze how the thinking works, especially when it can me algorithmized or structured in some ways. the moment i see something is structured or algorithmic it becomes interesting to me
Shortest math paper ever.
And with so much impact! It just disproved a widely accepted theorem from the year 1769 in 5 rows!!!
I'll never publish anything even remotely badass like this! But I want it so much!!!
If you want to rizz up a mathematician, just tell them that they "proved love at first sight exists by giving an explicite example".
homotopy groups of fucking spheres
I'm still salty about this half a decade later.
What was the most upsetting result in mathematics for you?
if you don't want to learn tikz but still need them arrows, check out quiver. it's super useful for complicated and unconventional diagrams
Learning LaTex has been a way more pleasant experience than I thought it would be this stuff is way simpler than it looks and the results fuck hard
just had a reflection about perfectionism. today I had an exam for which I was prepared very well, but my stupid brain happened and I didn't get the highest grade. my boyfriend was comforting me and he asked since when I want to ace everything, this question made me think
indeed, I don't want to ace everything. I am taking 4 courses this semester, one of which I don't care about enough to strive for the best grade, one of which is way too hard to aim that far, two of which I thought were achievable. and now I didn't achieve that. it feels different to set unrealistic goals and then never achieve them than to set very realistic ones and still fail, that's what I realized today
I am not a perfectionist. I used to be, years ago, and then I learned to set realistic goals. now I'm thinking, isn't perfectionism a kind of a coping mechanism? deep down you know your goals are impossible, so it's not really surprising when you fail. you are never satisfied, sure, but maybe it does feel more safe this way than to not know if you will be satisfied or disappointed. if that's the case then setting realistic goals is absolutely not the way to heal perfectionism
Me: I should write something
me : … or I could spent 78 hours straight making a miniature library with a working LED chandelier
hey netizens! i'm not sure how many people are aware, but youtube's been slowly rolling out a new anti-adblock policy that can't be bypassed with the usual software like uBlock Origin and Pi-Hole out of the gate
BUT, if you're a uBlock Origin user (or use an adblocker with a similar cosmetics modifier), you can add these commands in the uBlock dashboard (under My Filters) to get rid of it!
youtube.com##+js(set, yt.config_.openPopupConfig.supportedPopups.adBlockMessageViewModel, false) youtube.com##+js(set, Object.prototype.adBlocksFound, 0) youtube.com##+js(set, ytplayer.config.args.raw_player_response.adPlacements, []) youtube.com##+js(set, Object.prototype.hasAllowedInstreamAd, true)
reblog to help keep the internet less annoying and to tell corporations that try shit like this to go fuck themselves <3
I have a bet going on with a friend. We need a third opinion. Can one find the square root of 2 in pi? And pi in the root of 2
Gut instinct says no. But when you work with infinities, gut instinct is NOT proof. (And such a gut feeling could have easily been the dodgy dinner I cooked myself last night.)
However I cannot even provide a proof.
I have, however tried to give some insight in another post (it should be the one immediately below this one) to perhaps help/provoke a more concrete argument from someone else :)
that's an interesting perspective
recently I've been thinking about it in an opposite way. it started during a conversation about brains, in particular how stupid and flawed they are, I realized that I enjoy math because it gives me a break from being human. there is no place for emotion and cognitive bias, only formal reasoning and proofs. it feels so safe and so distant from the day-to-day life filled with problems caused by the human nature, it feels so clean. it's a place for me to enjoy only the best qualities of my existence. it's an acceptable way to separate myself from everyone, and simultaneously stay connected
I love how different this is from what is described above, as if math offered a place for everyone to find something that they will like
Im trying to find a really long Tumblr post that talked about how sad it was that people are so happy to complain about how much they hated math and how math can be a way to connect with your fundamental humanity and...
Yeah, I've been studying a little bit of it on my own, ten years after I dropped out of college, I've been going back to seeing some basics of calculus, and I've been really feeling some of that.
There is this sense that math is this alien thing, separate from the true concerns of humanity. This external topic, strange and inhumane that only those few weirdos with a eccentric and atypical cast of mind, who are themselves separate by a few degrees from human nature, can grasp.
But it's not that, We, messy warm emotional dumb humans came up with it, we silly atavistic creatures dedicated so much time and effort to develop it and explore it, this silly, quirky, wet, ape-like species is the only living creature on this planet that concerns itself with doing math in any serious capacity. It didn't come from aliens or the gods or from dolphins, math came from humans and humans are the only ones that use them. There could be nothing more human, more fundamentally ours, more intrinsic to our nature than math.
And it's not just a tool! Is not just this thing to be celebrated because its useful in a purely base pragmatical, prosaic way. Is not this thing we have to dissapasionatly conceed credit to because I guess it does useful things like bridges and rockets and computers and taxes. Math is not just the civilizational equivalent of going to the dentist or eating your vegetables.
i hesitate to call it a philosophy or an art, it is a way of human thinking, it is a way of thinking like a human, of thinking in a way that only humans can think. its is one of our oldest and proudest traditions, it is a way to feel greater than onself, it is a way of growing. it is a song with a prosody all its own. There is such a profound sense of meaning and beauty and truth and purpose to be found in math, and the best of all is that it works, when it says something it means something, its telling you a thing that is meaningful, that represents something true, that couldnt be any other way, that has consequences and uses and can be relied upon, that it representes something which carries weight and its ours, its truly a part of our nature, of what we are.
⁕ pure math undergrad ⁕ in love with anything algebraic ⁕
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