Answer to your last question: I think it looks cool, most people seem to be repulsed by hard looking math, but I think it’s pretty, and it makes me want to learn it
I get scared but I'll fight it, not run. I always want to learn more (It feels dope to know, at least for me) I remember when I saw integral signs far off in the distance and I was like: dafuq is that symbol it must be quantum string theory of dark matter
I was the same 🤣 I remember having a quick look in a textbook and seeing that symbol. I thought if I reached that level then it was the top and no one could possible go further 🤣 how wrong was I. Turns out you could probably teach basic integral techniques to kids
For me, I've definitely always had an affection for mathematical symbols (tbh. symbols in general, eg. exotic writing systems like that of the Georgian language, musical notation etc.). Though with maths it's always been the strongest. I can clearly remember looking at the chalkboard with stuff still written on it from prior calc classes when I was in middle school and feeling this urge to not only understand these symbols but also to be able to use them properly. Looking back at that, I still get a deep satisfaction from looking at mathematical formulas and understanding not only the symbols in them, but being able to imagine what they represent outside of their algebraic notation. Maths is like a language which has no words, only grammar, but once you've internalize these grammatical rules, you can imagine a story unfold without ever needing to use words.
I think what this video shows is how deep the subject is. There just loads of concepts you must grasp and grasp well. It's a reminder that you need to master each subject in turn. For those of you going to uni soon, you're going to be tempted to skimp on things at times due to time constraints... you don't dictate the pace of learning, and that can be a massive challenge. Don't fall into the trap of "getting through it" at the expense of really learning the material. It will catch up to you at some point.
It makes me excited, because I knew like 80% of those terms, however I don't know how to compute them (the highest math I know atm is Linear Algebra up to Eigenvalues and Determinants and the differential side of Multivariable Calculus). It's very cool that you can combine so many of these things
I’ve always been inclined towards math, and this year as a high school junior I took an electricity and magnetism class at a local college. But even then, as long as I can remember, I’ve always had the thought in my mind that I’m going to be in the medical field working as a doctor. Your channel is really making me reconsider this thought, and I’m now seriously considering double majoring in math+physics and head to grad school for physics; I’d like to thank you for it. Keep up the good content!
If I were you I'd double major in math/physics (and pick up as much programming as you can along the way) and then do a PhD in something like medical physics or bioinformatics or something like that where you apply math/physics in solving complex problems in biotech and medicine. Take genetic engineering, for example. Due to the complexity and sheer number of genes and how they interact to create macroscopic effects (like illnesses, desirable traits etc.) it is in many ways more of a math problem than a biology problem. Consider how many more people you'd be able to help if you came up with some genetic engineering technology that could cure cancer as opposed to being "just a regular doctor" (not dissing medical doctors in any way, you have my utmost of respect, I'm just laying out the facts). I'm about to go to grad school for applied mathematics and I'm seriously considering writing my thesis on something related to biotech/genetic engineering.
Hey, I was in the exact same position as you a few years ago. I was always better at Maths/Physics than I was at Biology but yet I always said that I wanted to be a doctor from when I was very young. I think partly that's because I just said that once when I was young and all the adults seemed to respond positively and so I just carried on saying it lol. In the end I was 18 years old and applying for med school (I'm from the UK, here you go straight into med skl for university and it's like 5/6 yrs). I ended up getting in but by then I decided that I actually wanted to do Maths/Physics. So I had to take a gap year and re-apply to do Physics. Which I did and now I'm in my 3rd year doing Maths and Physics at university. Looking back it feels crazy that I was actually headed to med skl, I can't imagine forcing myself to memorise a bunch of textbooks, it also would have been much better if I had known what I wanted to do in the first place and not be forced to take a gap year. All this is to say that, if you said you wanted to be a doctor from when you were very young, chances are your young self had no idea what they were talking about (and perhaps there's parental/societal influence/pressure there). And so now that you're older and more knowledgeable. You should actually ask yourself from as unbiased a place as possible what it is you want to do in life and if actually you enjoy the subject of medicine and the job of being a doctor.
2:00 Yeah, that's definitely a thing. I think the exciting part about spending energy to understand equations from a textbook is that in the end you'll get a meaningful interpretation/result. Also, this makes me appreciate the effort (with no guarantee of results!) required to derive a model that represents reality.
I'm finishing my sophomore year for a bachelor's in electrical engineering. I do really enjoy designing circuits and dealing with processors and low-level protocols but seeing math like that makes me want to pursue a mathematics or physics degree. I'm taking E&M right now and thoroughly enojiying it. Last semester I took linear algebra and found it to be my favorite math course yet because of its abstractness compared to the calculus trilogy (quartet if you count diff.eq). Now I'm taking "Introduction to Mathematics" so that next semester I can take some 4000 level abstract math courses just for the sake of doing more math. Anyone else in a similar situation?
Last December I got my bachelor’s in electrical engineering and in two weeks I’ll get a second bachelor’s in pure mathematics. And this fall I’m starting a top master’s program for electrical engineering. Thanks for asking
2:10 LITERALLY ME... (DON'T KNOW A THING ABOUT QFT BUT LOOK AT THE SCHROEDINGER EQUATION IN FIELD TERMINOLOGY ANYWAYS) HADRONIC TENSOR DEFINITELY COOOL...
OK. We as humans tend to see zero as nothing and infinite zeroes as something as long as there is a 1 in front of all the zeroes. what if there is not one in front of all the zeroes? Do you understand the whole Ideal of Schrodinger? Take Schrodinger's Cat and yeah it is not "Schroedinger" but Schrodinger. Just thought something to point out but... The Universe may be bigger and expand more than we know. the whole Schrodinger Cat deal is that the cat is either alive or dead outside of human observation. The coat would have died and just become meat or jerkey but "we don't know" until we observe it. What makes a human so special to decide that another life form is alive or dead? If the Cat died then the cat may know or not exist anymore. So all the physicist out there is there not one that understands Quantum Physics outside of a freakin' classroom of a College or University? I mean you really have to learn Quantum physics from a book right and a lesson or listening to someone else that gives you a grade? Science itself is not much different than their own alter egos which would be Religions. Both learn from books and and listening to others Dictate what is right on wrong. I can make up an equation for eternity and surprisingly it is not difficult but what about infinite time and space? We as humans have made it to the mood due to equations yet all people see the Universe as it is as they see it in their present perceptions. The moon reflects light which travels at a constant speed but our limitations are limited to perception and calculations though mathematics. How about all the physicists out there tell me where in space time we perceive the Universe? Wait am minute because I know. We perceive the universe in the past Tight now at this moment in time we may be doomed due to gamma rays from another galaxy that we can't even see or perceive in this moment in space/time. Physics itself is the observable and d 2+2 equals 4. 2x2= 4 too so multiplication and addition with more than one equals the same answer. So "bro" you may not know all the secrets of the Universe or even comprehend the totality of Infinity. Yeah there is a difference between Eternity and Infinity.
@@jonasdaverio9369 Yeah I messed up but meant to spell it right I have no idea why I reversed it. Probably too much Chablis. You won't believe it but I actually screwed up and reversed what I meant. But the meaning is still the same. That would be why anyone would abuse an animal for their own curiosity? "Schroedinger" should have locked himself in a box with no external sensual influences and let people observe or theorize about him. A cat can't talk or explain but a human can. So the cat is alive or dead and will live or die in the box. A human can leave a record but subjecting a human to the same conditions would be cruel right? There was not an actual cat though as far as I know. The bigger picture is without humans would the Universe exist? Every understanding of the Universe that we accept as fact exists only in our minds as a species that can observe it. Everything from science to religion to music to works of art to whatever is caused within two factions of the human mind which is dependent on the condition of the Individual brain within our own species. The problem with the human species as a whole is that we want the answers now. All we know about time is what we observe in the moment. A day which is sixty minutes in 1 hour and 24 hours in a day and 364 and 1/4 days in a year which is the time it takes for the Planet we live on to make one revolution around our parent star and why we have leap years to keep the Julian Calendar accurate. Even the whole ideal of Schroedinger's cat was the observation between life and death. But if the cat dies, what is that cat now? If the cat is dead what did the energy contained within that cat's mind and body transform into? But on a more philosophical and psychological scale the cat was aware and the cat felt the physical aspects of the experiment and where did the cat's energy transform to if the cat died. That energy contained within the brain? You do know those electrical impulses that make the heart beat, to breath even subconsciously, the basic emotions and fear and desperation of being contained within a box with no or very little external conditions and so on? Even Einstein said energy can be transformed but not destroyed. But we observe if the cat is alive or dead and we observe it. But all the energy contained within the cat, how may it have been transformed? If the cat was dead then it was already starting to decompose. So it is more than just a Theoretical question. It contains Philosophical questions, Psychological questions, Theological questions and so on. The same questions are relevant in the whole ideals of space/time the absolute speed of light and so on. We are judging the Universe as fact by our own observations in or planet. As for the Earth and the Sun, we really don't know or consider all the variables in that even. If the speed of light is an absolute constant then everything we see and observe is in the past. So just think about it. We think we believe we live in the present but we don't. We exist in the past. I just opened a Bud Light and used a bottle opener to flip the tab on the can because I just polished my nails and don't want to screw up my nail polish. I had to calculate on where to pick up the bottle opener and yeah very little will change in pertaining to the speed of light. But my eyes through evolution has evolved to perceive light that is reflected from matter that reflects light that I react with. Sound is a different subject though. When I was about 4 and riding my bike down a road and not even in school yet and observing through sight and sound how I could see my uncle hitting a steel fence post into the ground and hearing it later. My eyes picked it up faster than my ears did. yes I could hear it. Later on I would go to big construction sights and watch "Pile Drivers" witness the sound and then feel the sensation of touch due to vibrations in my body. Hell I may not even feel the touch depending on the Geology of the area until I got closer but those waves are still there. That would probably be the whole essence of "The Butterfly Effect". We may not acknowledge the effect but we are so beholden to all forces in the universe. Life and existence is nothing more than an experience. It sux but we tend to follow ideals as a species that makes us feel good and justifies our own beliefs. OK so I made a mistake. That is all and I meant to say one pertaining to the other and you caught it. I didn't even catch it when I hit reply. So thank you. Like I said too much Chablis an not paying attention.
Hey Andrew, I just finished my sophomore year today and feeling pretty good about it! I started following you about 3 months ago, and it was very interesting to stumble upon your channel because I had a similar pass-time activity idea of my own to start a youtube channel about all the beauty of physics and maths, and not in a half-ass babbling way, but not too rigorous either; your content, in my opinion, is right on top of that sweet spot for people that might be interested about all of this, and I wanted to thank you for the videos and what not! Keep the good content up (as much as you can allocate time!)
I did an astrophysics degree and applied for another in math with theoretical physics - still unsure. But after watching this, im so freaking excited and now i know I've made the right decision. Thanks!
Wow, Wow, Wow! I have so much RESPECT for anyone in Theoretical Physics who understands these equations. It is truly mind-boggling and challenging to even the best mathematicians.
I’m finishing up Calc 1 and I want to know everything going on there, I’m looking forward to getting to the point where I understand what you just showed us.
I'm only in Community college taking Alg 2 and I think that looks beautifully fascinating. Thanks for your videos brotha, I have no friends that care about anything academic so your like my imaginary smart friend who isnt imaginary you just dont know me haha.
I'm not sure if it is terrifyingly interesting or interestingly terrifying. But it's cool, and also scares the shit out of me while because it is extremely beautiful.
The way you described it is straight up what went through my mind when you showed it - "Holy sh- whats going on here. I wanna know what it is 🤩" This kind of feeling really got stronger with this sort of things the deeper I get with my undergrad, makes me realize it might just be the right path for me 😊
Like you, Andrew, I think the equations look really cool. I have no idea what they are talking about, but that is the excitement that provides the motivation to want to learn and understand what the equations are describing!🤓
as for me it's super-exciting and this pushes me towards theoretical physics even more despite I am not that far, I am doing PhD in photonics and lasers but more on the experimental side. Please keep up the good efforts!
Haha xD. I've always liked this strange mathematical symbols, they looked very artistic to me xD. Once I i intended the school, I've taken some books of my mom about finite dimensional vector spaces and looked at the symbols. It looked like science fiction to me and I always imagined that I could build a time machine from it, haha xD. Of course, I didn't know a shit about that, but I always wanted to know what these symbols represent. Now, as I am in college, I know you can't build a time machine from it xD. All in all, the complex mathematical notation does not scare me personally as I am a person who likes challanges, but I think that most of the people does get scared from it and that is probably the reason why most people ditch Mathematics and Physics in college. They think that they can't do that, but in reality they could if they just tried it.
I dont know that whether am correct or not but as far as i have concluded from my mathematical experiences in physics ,maths allow us to think the theory used in physics in our very own mind with our very own perspective and point out questions from our very own model created in our mind from the mathematical expressions
One of my goals when I started down the journey to being a mathematician, was I saw a physics equation that looked rather similar to this one, and I couldn't read it. So I set being able to even read stuff like this as an initial goal. While I ended up not going with Physics, I still take understanding things as a challenge. Curiosity and all that
Dude, thank you so much for putting your time and effort into these videos. Few people tackle the inbetween spaces of introduction and rigor; You're killing it. Mind Sorcery and Mathemagics. I love that Mathematical Notation reminds me of Arcane glyphs of profound meaning. I favor analogies of Mystical truths that have to be meditated on AND worked through to understand well. It's either Wizardry or mystical Kung fu. You always feel progress, but never feel like you've achieved ultimate mastery. Theoretical Physics all the way! Much respect to the importance of Experimentalists, but they can keep all their knobs. (No experimentalists were actually harmed in the typing of this.)
Being utterly fascinated is one of the earliest (5-6 years old) memories that has never left. Nor has the fascination itself. Luckily there is more there than anyone could learn in a dozen lifetimes. Especially if you start learning the history of math and physics, including biographies.
Man, is this Halzen & Martin? I'm struggling through this book! It'd be awesome if you make a detailed video on exactly all those symbol of leptonic and hadronic tensors are! Thank you!
I’ve been watching you for the last 2-3 years. I’m about to start my freshman year in a uni, and tbh I’m scared it’ll accelerate into very complex staff quite quickly. To answer your question, this is a very beautiful and sexy eq imo😂 I think I have the same thing that you do with symbols, like common they are pretty and they actually mean something?!
I have no idea what an integral or differential is but the big equation looked fun. I understood you when you explained what each individual part was asking for.
Its great, very exciting, would love to learn it,but i have a huge gap in my maths..but this was vividly well explained and was so inspiring! Thank you!
I have seen and worked with all these types of math, but I would have no idea how to solve this eq. mostly because I'm unsure what should be calculated first or how the diferent parts interact with each other...
It looks cool but it gives me anxiety in the sense that I will never be able to know what most of that stuff is (i am a sophomore in high school btw). Hopefully, calc bc next year will clear things up.
“Those weird multiplication “are just Lorentz invariance ,you may check d^3p/E is Lorentz invariant.Through Weinberg you might see all theory of quantum fields are based on Lorentz invariance.
Having taken many courses on the theory behind linear algebra along with numerous in advanced computational courses in linear algebra and PDEs, it is extremely interesting to see all the components of such complicated courses meshed into a branch of physics. Conclusion: theoretical physicists definitely earn the title of mathematician in some respect
I loved the breaking down of that Leptonic Tensor at 2:48 . Hence can you like discuss various Physics papers on your channel. It was my idea when I started out on TH-cam.I think I will do it later when I have more subscriber base.
My reaction to equations like the one you talked about 8-39 has always been like yours. I draw a blank but it makes me want to get to the point where I know what it is saying! It was how I got through my first hard upper division course E&M a zillion years ago. I picked up Corson and Lorraine to help me and was pretty intimidated but very driven to get to the point where it spoke to me (and I could solve problems).
Andrew, that was brilliant. But now we have to go deeper. Why the different components, what do they do? What are the problems, and how are they solved? MAWR, please!
Thank you for this. I knew somewhere there was math involved. My first exposure to weird lookimg math was in the book "The Beauty of Fractals". That led to a wild goose chase where at 13 i decided to read a trig and calculus book over the summer. Sadly (?) i ended up in a vastly different field but the love of math never really dies. Im an old (?) man now but my kids freak out when i am teaching math and i see something cool and say,"Oh yes!" They say "Oh no...." bc it invariably means im goimg to fanboy over something.
That stuff looks super fun! I’m a computer science major and I now plan on minoring in physics. I’m more of the math type than writing up lab reports haha theoretical physics looks like the field for me! 😁
I was super hopeful before I started. Poor guy haha I settled with mechanical engineering and whew, circuits and engineering dynamics really made me realize I don't understand physics like I thought! I still have a love for physics
I have a degree in TP, but it still scares me. The end is not so heavy after all - both delta and bra are just "pick up" instruments. But the product sign right after the integral and dimensions - this means I cannot just check up myself with a pencil and paper. It'll almost certain to end up programming to see real numbers. So the magic obscured.
Your definition of differential cross section is pretty different from mine. I worked in the heavy ion physics field during my undergraduate research. To my understanding, a cross section is the area a particle "presents" to another particle during a collision event. You can imagine that if the area the particle presents is BIG then the more probability a collision (or interaction) is possible to occur. Thus, a cross section can also mean the probability of a certain QM or QCD process to occur. The differential cross section is just the probability density if you will. The little probability of a process occurring with respect to a certain differential energy/solid angle.
Ok so I'm a second year AP physics student at my high school, and during first year my teacher said learning physics is essentially learning another language. Did not realize what he meant... But now... Yeah... This video opened my eyes
The link doesn't work for me. I did nuclear theory way back in the 90s. It was a blast. I still thumb through Yndurain's QCD book and Walecka's Theoretical Nuclear and Subnuclear Physics.
I think we should find simple way to describe the universe because for me math is so beautiful but for a lot of people is not (Simplicity is the final achievement)
Technically, learn high school calculus well, then add some linear algebra and go on to a textbook like Arfken & Weber's "Mathematical methods for physicists". But also doing the physics that use the maths is important, to get the practical working skills, and because some of the notation is pretty specific to a particular field of physics and not found outside of it.
Math for me is more like a language kinda. Like, I generally want to see what's actually going on in my minds eye, when looking at equations i.e. a diffusion equation or an oscillator for certain differential equations, or the movement into frequency space by spinning the waveform around a circle or spiral, and so on. Not being able to do that for say, tensors makes me want to know more, I think, because it's something I don't know, and I'm ill-content in ignorance. But that's just me.
That stuff is actually hot. I've always wanted to study astronautical engineering in cambridge or imperial, but physics is really tempting me now. Should I do engineering or physics at university?
The hadron tensor is really cool and all, but who the hell brackets off a summation like that? Can someone explain because that looks like they've neglected to tell me what is being summed.
I'm studying physics in Mainz, Germany and I had to understand exactly these equations in my Quantum Field Theory course to pass the exam, so please let me explain in words, how I felt during my learning phase: "When you have a nightmare where you experience as an observer that your whole family is robbed and even threatened by some strangers in black hoodies at midnight..", this is not as difficult to get through as to learn all this theoretical sh*t (sorry bro). My future lies in experimental particle physics and hopefully not so much in theory^^ ..but still a great video! :D
I want to ask just one thing, that how people starting to develop the hadronic tensor? I mean how do psychists create mathematics for their theories? If I have a hypothesis, then how would I make mathematics for this? Please make a video on it.
Your video just scared me!!! I am an engineering student who applied for physics graduate study and luckily got admission. Problem is I don't hvae a strong background in math or physics !!! I was really excited at first, but now I'm pretty scared!!!!
All math that I see that I know nothing about and looks exotic looks really cool to me as if it were saying, "hey boy don't you want to know what I mean". I then almost immediately start looking at the symbology and thinking what part of this looks like something I've seen before and can that past thing help me understand this?
Physics is like a fairytale, and you are the night in shining armor going out to slay the dragon. The more the dragon terrifies you, the more rewarding it is when you win the battle.
Wow!! Now this is something that is really inspiring for a Physics major student and the Hadronic Tensor is really cool. Thanks for this video and really overwhelmed!!!!
Are there any books/textbooks you’d recommend that cover a wide variety of topics in math needed for physics (tensor calc, ODE, etc) or do you sort of have to piece it together through various math classes?
You lost me at, "what's going on smart people?"
Mike Hughes lol 😂
lol
He lost me at "what's"
You lossssst me at “peoplesssss”
🏆
Those equations are the universe nude. lmao.
Jeez!!! the best comment I ever seen yet!!!
Big bang theory?
Answer to your last question: I think it looks cool, most people seem to be repulsed by hard looking math, but I think it’s pretty, and it makes me want to learn it
I get scared but I'll fight it, not run. I always want to learn more (It feels dope to know, at least for me)
I remember when I saw integral signs far off in the distance and I was like:
dafuq is that symbol it must be quantum string theory of dark matter
no its a music note!
Same
Meanwhile I thought it was my hair on the paper.
I was the same 🤣 I remember having a quick look in a textbook and seeing that symbol. I thought if I reached that level then it was the top and no one could possible go further 🤣 how wrong was I. Turns out you could probably teach basic integral techniques to kids
Fran R
I'mma save the swinging for when I'm good and ready, AKA done or at least _further_ in my "training".
For me, I've definitely always had an affection for mathematical symbols (tbh. symbols in general, eg. exotic writing systems like that of the Georgian language, musical notation etc.). Though with maths it's always been the strongest. I can clearly remember looking at the chalkboard with stuff still written on it from prior calc classes when I was in middle school and feeling this urge to not only understand these symbols but also to be able to use them properly. Looking back at that, I still get a deep satisfaction from looking at mathematical formulas and understanding not only the symbols in them, but being able to imagine what they represent outside of their algebraic notation. Maths is like a language which has no words, only grammar, but once you've internalize these grammatical rules, you can imagine a story unfold without ever needing to use words.
You should do a series on Lagrangian and Hamiltonian mechanics after the tensor stuff.
I am the 69th like
@@maxwellsequation4887 nice
I think it looks really cool AND terrifying.
That's the reality of science
I think what this video shows is how deep the subject is. There just loads of concepts you must grasp and grasp well. It's a reminder that you need to master each subject in turn. For those of you going to uni soon, you're going to be tempted to skimp on things at times due to time constraints... you don't dictate the pace of learning, and that can be a massive challenge. Don't fall into the trap of "getting through it" at the expense of really learning the material. It will catch up to you at some point.
Honestly, it looks both terrifying and wildly amazing. Maths tends to become less scary the more you understand what it means.
but the thing is you can understand 90 percent of it but still can get an F in the exam that's the scary part for me
Im only at the ending of Calculus 2 and I haven’t took Physics yet, but omg this video is just raising my curiosity!
Sherlock Banks go for it bro good luck
That’s me rn
It makes me excited, because I knew like 80% of those terms, however I don't know how to compute them (the highest math I know atm is Linear Algebra up to Eigenvalues and Determinants and the differential side of Multivariable Calculus). It's very cool that you can combine so many of these things
Update: now I know some pure math linear algebra and ALL of Calc 3
One of the best pieces of advice I learned was to write down new equations as you encounter them. You understand so much from doing that!
Andrew makes my aspirations of being a theoretical physicist seem to be in reach :) You're doing a great job man, keep the good energy flowing
Thanks a lot!
I’ve always been inclined towards math, and this year as a high school junior I took an electricity and magnetism class at a local college. But even then, as long as I can remember, I’ve always had the thought in my mind that I’m going to be in the medical field working as a doctor. Your channel is really making me reconsider this thought, and I’m now seriously considering double majoring in math+physics and head to grad school for physics; I’d like to thank you for it. Keep up the good content!
If I were you I'd double major in math/physics (and pick up as much programming as you can along the way) and then do a PhD in something like medical physics or bioinformatics or something like that where you apply math/physics in solving complex problems in biotech and medicine. Take genetic engineering, for example. Due to the complexity and sheer number of genes and how they interact to create macroscopic effects (like illnesses, desirable traits etc.) it is in many ways more of a math problem than a biology problem. Consider how many more people you'd be able to help if you came up with some genetic engineering technology that could cure cancer as opposed to being "just a regular doctor" (not dissing medical doctors in any way, you have my utmost of respect, I'm just laying out the facts). I'm about to go to grad school for applied mathematics and I'm seriously considering writing my thesis on something related to biotech/genetic engineering.
That's not far from where I was either. I initially pursued the pre med track. Good luck!
Hey, I was in the exact same position as you a few years ago. I was always better at Maths/Physics than I was at Biology but yet I always said that I wanted to be a doctor from when I was very young. I think partly that's because I just said that once when I was young and all the adults seemed to respond positively and so I just carried on saying it lol. In the end I was 18 years old and applying for med school (I'm from the UK, here you go straight into med skl for university and it's like 5/6 yrs). I ended up getting in but by then I decided that I actually wanted to do Maths/Physics. So I had to take a gap year and re-apply to do Physics. Which I did and now I'm in my 3rd year doing Maths and Physics at university. Looking back it feels crazy that I was actually headed to med skl, I can't imagine forcing myself to memorise a bunch of textbooks, it also would have been much better if I had known what I wanted to do in the first place and not be forced to take a gap year.
All this is to say that, if you said you wanted to be a doctor from when you were very young, chances are your young self had no idea what they were talking about (and perhaps there's parental/societal influence/pressure there). And so now that you're older and more knowledgeable. You should actually ask yourself from as unbiased a place as possible what it is you want to do in life and if actually you enjoy the subject of medicine and the job of being a doctor.
That equations looks super cool! thanks for uploading man you're super awesome for doing this : )
2:00 Yeah, that's definitely a thing. I think the exciting part about spending energy to understand equations from a textbook is that in the end you'll get a meaningful interpretation/result. Also, this makes me appreciate the effort (with no guarantee of results!) required to derive a model that represents reality.
I'm finishing my sophomore year for a bachelor's in electrical engineering. I do really enjoy designing circuits and dealing with processors and low-level protocols but seeing math like that makes me want to pursue a mathematics or physics degree. I'm taking E&M right now and thoroughly enojiying it. Last semester I took linear algebra and found it to be my favorite math course yet because of its abstractness compared to the calculus trilogy (quartet if you count diff.eq). Now I'm taking "Introduction to Mathematics" so that next semester I can take some 4000 level abstract math courses just for the sake of doing more math. Anyone else in a similar situation?
2 years later, what did you decide on?
Last December I got my bachelor’s in electrical engineering and in two weeks I’ll get a second bachelor’s in pure mathematics. And this fall I’m starting a top master’s program for electrical engineering. Thanks for asking
And the focus of my master’s and my master’s thesis will be in E&M, more specifically antennas.
@@thoughtyness great, glad you figured it out.
2:10 LITERALLY ME... (DON'T KNOW A THING ABOUT QFT BUT LOOK AT THE SCHROEDINGER EQUATION IN FIELD TERMINOLOGY ANYWAYS)
HADRONIC TENSOR DEFINITELY COOOL...
Or failing that, look at the SCHRODINGER EQUATION.
OK. We as humans tend to see zero as nothing and infinite zeroes as something as long as there is a 1 in front of all the zeroes. what if there is not one in front of all the zeroes?
Do you understand the whole Ideal of Schrodinger? Take Schrodinger's Cat and yeah it is not "Schroedinger" but Schrodinger. Just thought something to point out but... The Universe may be bigger and expand more than we know. the whole Schrodinger Cat deal is that the cat is either alive or dead outside of human observation. The coat would have died and just become meat or jerkey but "we don't know" until we observe it. What makes a human so special to decide that another life form is alive or dead? If the Cat died then the cat may know or not exist anymore.
So all the physicist out there is there not one that understands Quantum Physics outside of a freakin' classroom of a College or University? I mean you really have to learn Quantum physics from a book right and a lesson or listening to someone else that gives you a grade?
Science itself is not much different than their own alter egos which would be Religions. Both learn from books and and listening to others Dictate what is right on wrong. I can make up an equation for eternity and surprisingly it is not difficult but what about infinite time and space? We as humans have made it to the mood due to equations yet all people see the Universe as it is as they see it in their present perceptions. The moon reflects light which travels at a constant speed but our limitations are limited to perception and calculations though mathematics.
How about all the physicists out there tell me where in space time we perceive the Universe? Wait am minute because I know. We perceive the universe in the past Tight now at this moment in time we may be doomed due to gamma rays from another galaxy that we can't even see or perceive in this moment in space/time.
Physics itself is the observable and d 2+2 equals 4. 2x2= 4 too so multiplication and addition with more than one equals the same answer.
So "bro" you may not know all the secrets of the Universe or even comprehend the totality of Infinity. Yeah there is a difference between Eternity and Infinity.
It is indeed Schroedinger and not Schrodinger. Schroedinger is another way of writing Schrödinger, but Schrodinger definitely isn't.
@@jonasdaverio9369 Yeah I messed up but meant to spell it right I have no idea why I reversed it. Probably too much Chablis. You won't believe it but I actually screwed up and reversed what I meant. But the meaning is still the same. That would be why anyone would abuse an animal for their own curiosity? "Schroedinger" should have locked himself in a box with no external sensual influences and let people observe or theorize about him. A cat can't talk or explain but a human can. So the cat is alive or dead and will live or die in the box. A human can leave a record but subjecting a human to the same conditions would be cruel right? There was not an actual cat though as far as I know.
The bigger picture is without humans would the Universe exist? Every understanding of the Universe that we accept as fact exists only in our minds as a species that can observe it. Everything from science to religion to music to works of art to whatever is caused within two factions of the human mind which is dependent on the condition of the Individual brain within our own species.
The problem with the human species as a whole is that we want the answers now. All we know about time is what we observe in the moment. A day which is sixty minutes in 1 hour and 24 hours in a day and 364 and 1/4 days in a year which is the time it takes for the Planet we live on to make one revolution around our parent star and why we have leap years to keep the Julian Calendar accurate. Even the whole ideal of Schroedinger's cat was the observation between life and death. But if the cat dies, what is that cat now? If the cat is dead what did the energy contained within that cat's mind and body transform into? But on a more philosophical and psychological scale the cat was aware and the cat felt the physical aspects of the experiment and where did the cat's energy transform to if the cat died. That energy contained within the brain? You do know those electrical impulses that make the heart beat, to breath even subconsciously, the basic emotions and fear and desperation of being contained within a box with no or very little external conditions and so on? Even Einstein said energy can be transformed but not destroyed. But we observe if the cat is alive or dead and we observe it. But all the energy contained within the cat, how may it have been transformed? If the cat was dead then it was already starting to decompose.
So it is more than just a Theoretical question. It contains Philosophical questions, Psychological questions, Theological questions and so on. The same questions are relevant in the whole ideals of space/time the absolute speed of light and so on. We are judging the Universe as fact by our own observations in or planet. As for the Earth and the Sun, we really don't know or consider all the variables in that even. If the speed of light is an absolute constant then everything we see and observe is in the past.
So just think about it. We think we believe we live in the present but we don't. We exist in the past. I just opened a Bud Light and used a bottle opener to flip the tab on the can because I just polished my nails and don't want to screw up my nail polish. I had to calculate on where to pick up the bottle opener and yeah very little will change in pertaining to the speed of light. But my eyes through evolution has evolved to perceive light that is reflected from matter that reflects light that I react with. Sound is a different subject though. When I was about 4 and riding my bike down a road and not even in school yet and observing through sight and sound how I could see my uncle hitting a steel fence post into the ground and hearing it later. My eyes picked it up faster than my ears did. yes I could hear it. Later on I would go to big construction sights and watch "Pile Drivers" witness the sound and then feel the sensation of touch due to vibrations in my body. Hell I may not even feel the touch depending on the Geology of the area until I got closer but those waves are still there. That would probably be the whole essence of "The Butterfly Effect". We may not acknowledge the effect but we are so beholden to all forces in the universe.
Life and existence is nothing more than an experience. It sux but we tend to follow ideals as a species that makes us feel good and justifies our own beliefs.
OK so I made a mistake. That is all and I meant to say one pertaining to the other and you caught it. I didn't even catch it when I hit reply.
So thank you. Like I said too much Chablis an not paying attention.
@@jamiewead4361 nobody will probably ever have the patience to read what you meant to say...
Hey Andrew, I just finished my sophomore year today and feeling pretty good about it! I started following you about 3 months ago, and it was very interesting to stumble upon your channel because I had a similar pass-time activity idea of my own to start a youtube channel about all the beauty of physics and maths, and not in a half-ass babbling way, but not too rigorous either; your content, in my opinion, is right on top of that sweet spot for people that might be interested about all of this, and I wanted to thank you for the videos and what not! Keep the good content up (as much as you can allocate time!)
Awesome! Glad you like the channel, thanks for the nice comment
I did an astrophysics degree and applied for another in math with theoretical physics - still unsure. But after watching this, im so freaking excited and now i know I've made the right decision. Thanks!
Thank you, Andrew. As is often the case, your videos are the only bridge from what I've just learned to what I want to understand next.
Wow, Wow, Wow! I have so much RESPECT for anyone in Theoretical Physics who understands these equations. It is truly mind-boggling and challenging to even the best mathematicians.
I thought this was about physics. Why is he showing us a Greek novel?
For me it looks really cool. The fact that something as abstract as that equation has a meaning to it is just beautiful
I’m finishing up Calc 1 and I want to know everything going on there, I’m looking forward to getting to the point where I understand what you just showed us.
Did you get to that point?
That looks sexy
Cool but I didn't understand anything
😂
I think it looks really cool.. .
Makes me want to decode it, then harness its powers for both good and evil.. but mostly for good
I'm only in Community college taking Alg 2 and I think that looks beautifully fascinating. Thanks for your videos brotha, I have no friends that care about anything academic so your like my imaginary smart friend who isnt imaginary you just dont know me haha.
I'm not sure if it is terrifyingly interesting or interestingly terrifying. But it's cool, and also scares the shit out of me while because it is extremely beautiful.
The way you described it is straight up what went through my mind when you showed it - "Holy sh- whats going on here. I wanna know what it is 🤩"
This kind of feeling really got stronger with this sort of things the deeper I get with my undergrad, makes me realize it might just be the right path for me 😊
Like you, Andrew, I think the equations look really cool. I have no idea what they are talking about, but that is the excitement that provides the motivation to want to learn and understand what the equations are describing!🤓
It looks so cool!!( I know nothing more than ap calc but this video gave me confidence to get through the exams with good grades and pursue my dream )
as for me it's super-exciting and this pushes me towards theoretical physics even more despite I am not that far, I am doing PhD in photonics and lasers but more on the experimental side. Please keep up the good efforts!
Haha xD. I've always liked this strange mathematical symbols, they looked very artistic to me xD. Once I i intended the school, I've taken some books of my mom about finite dimensional vector spaces and looked at the symbols. It looked like science fiction to me and I always imagined that I could build a time machine from it, haha xD. Of course, I didn't know a shit about that, but I always wanted to know what these symbols represent. Now, as I am in college, I know you can't build a time machine from it xD. All in all, the complex mathematical notation does not scare me personally as I am a person who likes challanges, but I think that most of the people does get scared from it and that is probably the reason why most people ditch Mathematics and Physics in college. They think that they can't do that, but in reality they could if they just tried it.
xD
ecks dee
I dont know that whether am correct or not but as far as i have concluded from my mathematical experiences in physics ,maths allow us to think the theory used in physics in our very own mind with our very own perspective and point out questions from our very own model created in our mind from the mathematical expressions
For me the most awesome problems is when in their uses perturbation and asymptotic methods , like in hydrodynamic stability
That equation looks sexy and terrifying at the same time.
Wow!...Thanks Andrew! I'm sticking with Applied Physics!
One of my goals when I started down the journey to being a mathematician, was I saw a physics equation that looked rather similar to this one, and I couldn't read it. So I set being able to even read stuff like this as an initial goal. While I ended up not going with Physics, I still take understanding things as a challenge. Curiosity and all that
Dude, thank you so much for putting your time and effort into these videos. Few people tackle the inbetween spaces of introduction and rigor; You're killing it.
Mind Sorcery and Mathemagics.
I love that Mathematical Notation reminds me of Arcane glyphs of profound meaning. I favor analogies of Mystical truths that have to be meditated on AND worked through to understand well. It's either Wizardry or mystical Kung fu. You always feel progress, but never feel like you've achieved ultimate mastery.
Theoretical Physics all the way! Much respect to the importance of Experimentalists, but they can keep all their knobs. (No experimentalists were actually harmed in the typing of this.)
Lol "they can keep all their knobs"
Being utterly fascinated is one of the earliest (5-6 years old) memories that has never left. Nor has the fascination itself. Luckily there is more there than anyone could learn in a dozen lifetimes. Especially if you start learning the history of math and physics, including biographies.
Math seems so beautiful when I see it applied on physics. But I just cant get it in calculus courses
Yes, I too am enchanted by the symbols, and their particular order of progression
Man, is this Halzen & Martin? I'm struggling through this book! It'd be awesome if you make a detailed video on exactly all those symbol of leptonic and hadronic tensors are! Thank you!
Holy cow! This is pretty cool stuff. I look forward to learning about it.
I’ve been watching you for the last 2-3 years. I’m about to start my freshman year in a uni, and tbh I’m scared it’ll accelerate into very complex staff quite quickly. To answer your question, this is a very beautiful and sexy eq imo😂 I think I have the same thing that you do with symbols, like common they are pretty and they actually mean something?!
1. Multivariable calculus
2. Linear Algebra
3. Tensor analysis
I have no idea what an integral or differential is but the big equation looked fun. I understood you when you explained what each individual part was asking for.
Its great, very exciting, would love to learn it,but i have a huge gap in my maths..but this was vividly well explained and was so inspiring! Thank you!
I have seen and worked with all these types of math, but I would have no idea how to solve this eq.
mostly because I'm unsure what should be calculated first or how the diferent parts interact with each other...
It looks cool but it gives me anxiety in the sense that I will never be able to know what most of that stuff is (i am a sophomore in high school btw). Hopefully, calc bc next year will clear things up.
BRO I RELATE TO YOUR VIDEOS SOO MUCH EVEN THO IM PRE-MED IM THINKING ABOUT ENTERING THEORETICAL PHYSICS LIKE A LOT NOW
“Those weird multiplication “are just Lorentz invariance ,you may check d^3p/E is Lorentz invariant.Through Weinberg you might see all theory of quantum fields are based on Lorentz invariance.
Having taken many courses on the theory behind linear algebra along with numerous in advanced computational courses in linear algebra and PDEs, it is extremely interesting to see all the components of such complicated courses meshed into a branch of physics.
Conclusion: theoretical physicists definitely earn the title of mathematician in some respect
I loved the breaking down of that Leptonic Tensor at 2:48 . Hence can you like discuss various Physics papers on your channel. It was my idea when I started out on TH-cam.I think I will do it later when I have more subscriber base.
omg a free 400 page pdf YEEEEEEEE thanks!!
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Got any more of those 👀 to the other viewers as well!
My reaction to equations like the one you talked about 8-39 has always been like yours. I draw a blank but it makes me want to get to the point where I know what it is saying! It was how I got through my first hard upper division course E&M a zillion years ago. I picked up Corson and Lorraine to help me and was pretty intimidated but very driven to get to the point where it spoke to me (and I could solve problems).
Andrew, that was brilliant. But now we have to go deeper. Why the different components, what do they do? What are the problems, and how are they solved? MAWR, please!
yeah now I feel I need to switch from bio to physics...
Well the guy in this video did just that
2:10 exactly . It just make me want to learn physics and I feel that its so exciting
Congratulations for the channel.
Those types of equations definitely pretty and cool
Thank you for this. I knew somewhere there was math involved. My first exposure to weird lookimg math was in the book "The Beauty of Fractals". That led to a wild goose chase where at 13 i decided to read a trig and calculus book over the summer. Sadly (?) i ended up in a vastly different field but the love of math never really dies. Im an old (?) man now but my kids freak out when i am teaching math and i see something cool and say,"Oh yes!" They say "Oh no...." bc it invariably means im goimg to fanboy over something.
Its cool i get excited when i see those things that i didn't understand
That's why i love physics
I have always love quantum theoretical physics, but I have never worked with the Hydronic Tensor before though.
Oooh math pretty symbols and stuff.
That stuff looks super fun! I’m a computer science major and I now plan on minoring in physics. I’m more of the math type than writing up lab reports haha theoretical physics looks like the field for me! 😁
I was super hopeful before I started. Poor guy haha I settled with mechanical engineering and whew, circuits and engineering dynamics really made me realize I don't understand physics like I thought! I still have a love for physics
I have a degree in TP, but it still scares me. The end is not so heavy after all - both delta and bra are just "pick up" instruments. But the product sign right after the integral and dimensions - this means I cannot just check up myself with a pencil and paper. It'll almost certain to end up programming to see real numbers. So the magic obscured.
And I'm here studying multivarible calculus 😅
Your definition of differential cross section is pretty different from mine. I worked in the heavy ion physics field during my undergraduate research. To my understanding, a cross section is the area a particle "presents" to another particle during a collision event. You can imagine that if the area the particle presents is BIG then the more probability a collision (or interaction) is possible to occur. Thus, a cross section can also mean the probability of a certain QM or QCD process to occur. The differential cross section is just the probability density if you will. The little probability of a process occurring with respect to a certain differential energy/solid angle.
great vid, the math makes physics more interesting than just theorizing about how this became of that.
Ok so I'm a second year AP physics student at my high school, and during first year my teacher said learning physics is essentially learning another language. Did not realize what he meant... But now... Yeah... This video opened my eyes
Awesome language put into mathematical terms that describes reality.
The link doesn't work for me. I did nuclear theory way back in the 90s. It was a blast. I still thumb through Yndurain's QCD book and Walecka's Theoretical Nuclear and Subnuclear Physics.
I think we should find simple way to describe the universe because for me math is so beautiful but for a lot of people is not (Simplicity is the final achievement)
Where does one start to get to this mathematical lvl, serious inquiry
4 years of uni for me
But most of the individual components I had seen in my second year
Technically, learn high school calculus well, then add some linear algebra and go on to a textbook like Arfken & Weber's "Mathematical methods for physicists". But also doing the physics that use the maths is important, to get the practical working skills, and because some of the notation is pretty specific to a particular field of physics and not found outside of it.
Math for me is more like a language kinda. Like, I generally want to see what's actually going on in my minds eye, when looking at equations i.e. a diffusion equation or an oscillator for certain differential equations, or the movement into frequency space by spinning the waveform around a circle or spiral, and so on. Not being able to do that for say, tensors makes me want to know more, I think, because it's something I don't know, and I'm ill-content in ignorance. But that's just me.
the delta function with that serie inside looks cool, but man, thats alot to keep track of
That stuff is actually hot. I've always wanted to study astronautical engineering in cambridge or imperial, but physics is really tempting me now. Should I do engineering or physics at university?
I know the values of the W (+1, 2/3, 0, -1/3 and -1) How do you get these?
Yes!! Sometimes I just write cool equations on my white board and just look at it, because it's so dang pretty!!
I'm just here for the math
aren't we all?
Highly intimidated but kind of excited. Would be a ride to do this while being stoned LOL
I got a bunch of upper division books because I LOVE to look at the equations
share it?
The hadron tensor is really cool and all, but who the hell brackets off a summation like that? Can someone explain because that looks like they've neglected to tell me what is being summed.
I'm studying physics in Mainz, Germany and I had to understand exactly these equations in my Quantum Field Theory course to pass the exam, so please let me explain in words, how I felt during my learning phase: "When you have a nightmare where you experience as an observer that your whole family is robbed and even threatened by some strangers in black hoodies at midnight..", this is not as difficult to get through as to learn all this theoretical sh*t (sorry bro). My future lies in experimental particle physics and hopefully not so much in theory^^ ..but still a great video! :D
Seeing that equation makes me want to work even harder to get to that level! These videos are very helpful and fun to watch, thank you.
I want to ask just one thing, that how people starting to develop the hadronic tensor? I mean how do psychists create mathematics for their theories? If I have a hypothesis, then how would I make mathematics for this? Please make a video on it.
Your video just scared me!!! I am an engineering student who applied for physics graduate study and luckily got admission. Problem is I don't hvae a strong background in math or physics !!! I was really excited at first, but now I'm pretty scared!!!!
Just now i'm using that book to study lepton nucleus scattering in a Fermi gas model. Quite tough
All math that I see that I know nothing about and looks exotic looks really cool to me as if it were saying, "hey boy don't you want to know what I mean". I then almost immediately start looking at the symbology and thinking what part of this looks like something I've seen before and can that past thing help me understand this?
It initially scared the shit outta me, then looking at it, my mind wanted to learn more :)
Is there an updated link for the PDF? The current link is a 404 deadlink.
Physics is like a fairytale, and you are the night in shining armor going out to slay the dragon. The more the dragon terrifies you, the more rewarding it is when you win the battle.
I wish I was able to do all this, because it looks really interesting. But here I sit as a burned out developer with math as a hobby 🙄
had to work with these in my particle physics class and it was difficult but once you start playing with the equations some cool stuff pops up
Nicholas Bazan cool
do u have a solution manual for this book? i am struggling with some assignment problems.
Wow!! Now this is something that is really inspiring for a Physics major student and the Hadronic Tensor is really cool. Thanks for this video and really overwhelmed!!!!
Are there any books/textbooks you’d recommend that cover a wide variety of topics in math needed for physics (tensor calc, ODE, etc) or do you sort of have to piece it together through various math classes?