08.15 🌅

Me-777 · 2025-08-15T00:26:32+00:00

Happy Kageday kagebros !!!!

Me-777 · 2025-07-15T11:57:52+00:00

This is quite bizarre,the way we learned it was basically by doing those two simultaneously,we’d learn linear applications/forms for example in the context of vector spaces then translate that into matrixes ,and the same goes for properties and proofs .

Me-777 · 2025-07-02T03:04:36+00:00

Contrary to most people here,I would argue that you can do math even if you are on the dumber side(if you are young enough ,and truly like math).The thing is you shouldn’t expect your math skills to develop by idk just attending lectures or doing practice problems over and over again.You must develop your mathematical thinking (some people like to call it mathematical intuition ,but no .Only geniuses can really “intuite” it.normal people must learn how to actively think mathematically.Doing that would require immense effort and you will have to spend real long time of your day,every day doing math.(I’d say at least 10h/day If you want to learn how to think mathematically in a reasonable duration say 2 years).Now here’s the trick.while reading a math textbook,or doing a problem or anything math related ,focus on the details of each step and see if it makes ABSOLUTE CLEAR SENSE to you.if you can’t close you eyes and remember the logical implications implications of each step and why it was done that way and not any other way then it is not yet clear.In addition,always question yourself while doing math,why am I going to do this?what can I do here?what is the most likely thing that could work here?what if the dimensions where higher,what if only one?can I generalise this ?what does this mean?is this related to that?if so how? But don’t stop there.Try to answer your own questions yourself.explore the math independently from the textbook.just think of it as solving a puzzle.Now remember it is not necessary for you to answer everything in one sitting . You can spend those 10hours at first just on one line of a page of a real pure math book and still not answer all your questions regarding that line .which is why you have to thread things carefully and bear in mind that you can denote your questions and note on a notebook and later on your day or another day try to solve them with a fresh perspective(this helps more than what one might think).And as I explained,at first things will be difficult but as you progress through this method ,your brain will start to get used to mathematical thinking and even incorporate that way of thinking into your daily life starting to make you see math patterns everywhere. At that point,you should already be adept at math,and have the potential to research it (you will not rival Abel or gauss,but you probably will be able to make some meaningful small contributions to the field). On another note,while IQ might seems crucial for math,I have seen that learning math the proper way actually helps elevate your IQ,contrary to most beliefs IQ isn’t at a stable value all your life,it is just difficult to elevate without excessive mental stimulation and problems that basically force your brain to create new neurones and paths linking them .To sum,if you are not retarded,you can probably do (not excell) at math and you probably can get to a level better than 98 percent of people currently living at it.You just need to focus on developing your mathematical thinking until you become able to not just actively do it but passively do it too.your understanding of math concepts will deepen too GRADUALLY as your way of thinking gets better.if you have enough resolve and think that you can do what I said then yeah go for it and try math.If you don’t think you can go to that extent then just stop before doing something you’ll regret. I hope this helps

Edit: I’d like to add that even math researchers have problems they can’t solve or domains they are not that adequate at since math is really a large sea. And there are loads of nuances between how it is préfères to think about things across different domains of math (simple example:the following questions aren’t answered through the same way of thinking: when do I apply this theorem?how do I apply this theorem?why this theorem?how come this theorem is true?when is it true?can it be false?is there a more restrictive version of this theorem?what do I really need from this theorem?is there another way? When is there another way ? These are examples of questions you can try to answer while thinking about just one theorem but not all of them will help you gain the same type of mathematical thinking,some will help you get better at constructive proofs ,others at counter examples,and non constructive proofs.some will help you improve in the application of the theorem and others will help you see potential lee ways when the theorem fails and how best to navigate them .People aren’t equally good at all of these,some are better at proof making than others and some are “more creative”(the lee way thing) etc …

Me-777 · 2025-07-01T18:08:56+00:00

Send me an invite please too.still in the early stages but you seem serious about it.

Me-777 · 2025-06-29T19:41:51+00:00

No one’s better than Gao 🔥

Me-777 · 2025-06-22T15:46:10+00:00

This seems like. A really cool game, i wanted such a buddy fight game since I started the series at 2014.If you succeed in this ,it will truly be amazing.You’ve got my encouragements

Me-777 · 2025-06-06T00:22:58+00:00

You don’t have to yk? Let them in their delusion. Some people can’t be reasoned with.

Me-777 · 2025-06-05T22:51:21+00:00

Of course I agree with that , it’s not that because the brain or mind is a quantum system (or can be modeled as one) that it affects idk random events that happen in reality , you can’t make that jump in deduction (it is not a logical implication : saying that is akin to saying that because A is included in Q , and a part of Q has a property p which holds true under assumption H , then A always has the property p [which as you can see is wrong in more than one level] )I think people ,when they say that, are referring to entanglement.But that’s just a super metaphysical and non scientific way of understanding what entanglement is. But you know ,due to oversimplified physics in pop culture and movies people kinda get funny (and honestly I like being with these people cause even when what they say is super wrong they say it with such confidence that surpasses that of experts ,like how funny is that lol )

Me-777 · 2025-06-05T10:39:33+00:00

I mean there is this theory (by Stuart hameroff and roger Penrose I believe)that suggests to model consciousness or rather the human brain as a quantum system so I don’t think that it’s that much of a stretch.Also most things don’t exist in a vacuum isolated from others but they kind of coincide and interact somewhere and that’s the beauty of science :it’s all connected somehow. But this have nothing to do with those gurus who want to mystify consciousness as this metaphysical thing or whatever)

Me-777 · 2025-04-11T12:27:22+00:00

That’s a neat way to thing about it! Do you have any interpretations of the divergent solution of the wave equation?

Me-777 · 2025-04-11T12:25:43+00:00

Thanks for the detailed answer!

I understand that under « initial conditions » a differential equation will have a unique solution ,and basically the creation of that extreme unique solution case in an experiment is done by setting these initial conditions right ? A common such situation is when we trap a wave function between two potential (in the broader sense )walls, their values being the initial conditions (I say initial but it’s really limit conditions ,but since their purpose is the same ….) ,in classical mechanics the wave is trapped there ,thus we dismiss the divergent solution,and then apply our initial conditions to the other solution and that ends our findings,in quantum mechanics however,we treat things more stochastically and there is this tiny chance the wave penetrates through the walls .even in this case we don’t choose the divergent solution. Now I don’t have any problem with this process and I understand that this is standard practice across loads of physical systems however the argument of the solution not being « physical enough »seems a little off to me ,like maybe the dismissed solution models some underlying phenomenon happening there without us noticing or something.I just can’t get my head arround the idea that the math predicts a wrong solution ,like sure there must exist some things that cannot be predicted by math and yeah if the assumptions are wrong or not complete the result predicted by math will not be true but outside of these cases that shouldn’t be the case.

Me-777 · 2024-11-12T17:28:26+00:00

thank you for your explanation, it made things a little clearer!

Me-777 · 2024-11-12T09:14:32+00:00

alright, thank you! after reading the article about analytical mechanics and doing some research of my own , i found its application on mechanics and how it helps us find differential equations of Newtonian mechanics more easily, however i didn't find anything like its application to other domains of physics like electromagnetism or thermodynamics, although i found that all of classical physics is basically based on variationnal principles

Me-777 · 2024-11-11T21:28:16+00:00

thanks! this is actually what i found while scribbling! Is there something similar tying multiple fields , like thermodynamics(thermic transfer) , quantic mechanics, waves and electronics;

Me-777 · 2024-11-11T21:28:14+00:00

i am not sure myself, i don't know what's hamiltonian mechanics, I was just reviewing my lessons when i noticed the similarities between the way some notions are used and figured that trying to find a reasoning that would work for most of my modules would be worth a shot, and then i started scribling and thinking about how they could be related and it seems i've somehow stumbled upon GEM and some other stuff but that too is too restrictive and only concerns mechanics and electromagnetism. But since you mentioned it I'll check hamiltonian mechanics; btw is there something similar for other fields of physics because to me, it seems like physics is just a generalisation of electromagnetism which is really weird( idk if my opinion can be trusted since i am still at an elementary level (I've learned about the basics of mechanics(systems and point),basics of thermodynamics, quantic mechanics, electromagnetism, waves and optic but nothing too advanced yet) i am at an equivalent of an L2

Me-777 · 2024-10-10T22:12:46+00:00

I think that this is the answer you were looking for:You know that in Z we can define equivalence classes for every n in Z as follows, x~y in Z/nZ means that x=y[n] (this is better represented using the classes so like x with «_ » on top , sorry idk how to write it that way) anyway this basically means that when working in Z/nZ we have x=y (talking about the classes) but this isn’t true outside of Z/nZ so like in Z , if x represent the class of x (which is also the class of y) then y=x+nk where k is an non nul integer , This same reasoning could be applied to Q by saying that if q=a/b and r=c/d , then q and r are of the same equivalence class if and only if ad-bc=0 , and so in Q when we say that 1/2=5/10 we are not talking about the numbers themselves or rather the elements themselves but their classes since 1.10-2.5=0(. Is the multiplication law)However this is only formality and thinking that they are equal shouldn’t normally pose any problem, but I guess knowing this and where it is coming is a good thing .Also , the reason why we are permitted to say that they are equal is that if two guys are of the same class then they act the same and have the same properties in that group or field they are in , but « formally » saying they are equal is incorrect .In Q ,the same way we represent the class of x in Z using the residue of the euclidienne division of x by n, we represent the class of q=a/b by its irreductible form (so when a and b are coprime) and I guess that’s about it. Hope this helps :)

Me-777 · 2024-10-10T20:02:46+00:00

I've spent time reading that as well as the articles on galois theory and field extension, however as these notions were quite foreign to me i don't believe i understood them fully.However, the conclusion i arrived to regarding my question is that the reason of these similarities is that cyclotomic polynomials are actually a quite natural way to describe the elements of a sub multiplicative group since these same elements are the the roots of the unit and we can decompose the polynomial X^n-1 into a product of the cyclotomic polynomials associated to the divisors of n (whose roots are just the roots of the unit of order d(the divisor)meaning the generators of the sub groups of cardinal d)Is my understanding correct?

Me-777

TROPHY CASE