randomness

 wow ooops like two months have passed already. i have been trying to read and learn things but it's been a bit difficult to juggle everything going on in my life T_T so the nobel prize winners are being announced recently which is very cool! for physics  John Clarke, Michel Devoret, and John Martinis won for their experiments in quantum computing (which were apparently conducted in 1984 and 1985 which is a while back~). they showed that the phenomenon of quantum tunneling (passing through an energy barrier that wouldn't have been possible by classical mechanics, has applications in nuclear fusion and radioactive decay) can be observed on a macroscopic scale by building a circuit with superconductors which have electrons joined together in pairs called Cooper pairs. in physiology and medicine,  Mary E. Brunkow, Fred Ramsdell and Shimon Sakaguchi won the prize for their research about peripheral immune tolerance that prevents the immune system from harming the body (?), di...

 soo school has started and i also have to work on college applications :| i guess this post will just be mainly some things i've read in school i really like this picture so i'll put it in first source: quanta magazine ten martini problem ! Hofstadter butterfly is a real life phenomenon. scientists wanted to determine the energy levels of an electron in a crystal grid placed near a magnet, so they need to solve a particular formulation of the Schrödinger equation. hofstaeder did a bunch of numericals with the old calculators to produce this butterfly pattern that showed the solutions following the cantor set when the alpha values were irrational, yet no one could prove it, until people "patched" a proof piece by piece, and then finally they got a more elegant proof :D. a week ago i watched Soul by Pixar because it was recommended by my existentialism class' teacher, and it was a really good movie. i love pixar movies!! (well my favorite movie has been inside out ...

first, i finished my kusudama, and my phone thinks they're plants :skull:, well i guess they are flower balls but... alignment and emergent behaviors quanta article so researchers fine-tuned ai models on an unstable dataset. despite the data being scales of magnitude smaller than the training dataset for the model and the fact that the dataset wasn't explicitly malicious, harmful behavior of the model still emerged, which is very concerning for alignment progress. as much as we try to safeguard existing models, if they can be very easily fine-tuned to produce malicious behavior, it is very concerning especially since people nowadays are so reliant on ai everywhere. but on the flip side, it seems like these models internally somehow understand that they're not ok! furthermore it seems like large models are particularly vulnerable to such attacks. some researchers think thus alignment should focus more on the fragility issue of models. bertrand paradox - more paradoxes! so t...

some paradoxes:  caroll's pillow problem  -  A bag contains a counter, known to be either white or black. A white counter is put in, the bag is shaken, and a counter is drawn out, which proves to be white. What is now the chance of drawing a white counter? the chance is actually 2/3! coz if we list out all possible scenarios, only 3 are possible with our additional information, and 2 give the condition we want. this is similar to many other paradoxes, like the boy or girl paradox  and the monty hall problem . so many names for essentially the same thing but different objects i guess. Learning distributions with Variational Autoencoders : theory, geometry, and applications - since i prsented at SWIM 2025 , i've been to some of the talks! a variational autoencoder learns a probabilistic latent space that can generate new data samples by modeling the data distribution. it is trained using the Evidence Lower Bound (ELBO) loss function, and an efficiency measure is u...

 nvm google deepmind also got gold  on the imo. they should test these models on the ioi too 🤔 tori! in diff geo we are learning about parametrized surfaces! this site says that a torus can be covered with one surface patch   and thought of like a rectangular piece of rubber stretched around... but in our exercise we parametrize it like so and we need 4 patches to make sure we're working with open sets. i saw some other websites saying you need at least 2 patches?!? so idk. btw this 3d plotting calculator is great for visualizing things -  https://c3d.libretexts.org/CalcPlot3D/index.html there are also different types of tori frenet-serre equations these just seem a normal triplet of equations that form the orthonormal basis for the curve (called the frenet-serre frame), but they're incredibly useful for solving problems to investigate properties for curves. t = tangent vector, n = normal vector, b = binormal vector rubiks cubing i've been trying to cube recent...

this past week was the international math olympiad!! it was exciting to see the performance of people i've met in real life, and they all did very well, though i'm not a fair judge especially since i'm not that good at oly math. also, what's funny is that i thought there was no way ai would win a gold, and initial reports from matharena.ai showed that it couldn't even achieve a bronze medal... and then the day after openai just had to tell everyone that they achieved a "not very open" model that could get 35/42 (coordbashing geo lol). the proofstyle is very strange... see in this github repo , almost like the ai has developed its own way of checking itself as it proceeds down the proof. people on r/singularity cheered! it will definitely be interesting to see the future of math competitions now, but it could be just like chess, after all ai solving these problems is not really an apples to apples comparison to the students who do math contests in general, ...